Answers
By the angle-angle-side theorem, triangles ∠ACE and ∠ECA are congruent, and we can conclude that:
AC = EC.
What is the congruent angle?
When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.
Since AB || DE and BC = DC, we can use the alternate interior angles theorem to conclude that angle BCA is congruent to angle DCE:
∠BCA = ∠DCE
We also know that angles ∠BAC and ∠ACD are supplementary:
∠BAC + ∠ACD = 180 degrees
Since AB || DE, we can use the corresponding angles theorem to conclude that ∠BAC is congruent to ∠ECD:
∠BAC = ∠ECD
Substituting this into the equation above, we get:
∠ECD + ∠ACD = 180 degrees
Simplifying this equation, we get:
∠ECA = 180 degrees - ∠ACD
Also, ∠DCE is supplementary to ∠ACD, so:
∠DCE + ∠ACD = 180 degrees
Substituting this into the equation above, we get:
∠ECA = ∠DCE
Since angles ∠ECA and ∠DCE are congruent, we can use the vertical angles theorem to conclude that angles ∠ACE and ∠AEC are congruent:
∠ACE = ∠AEC
Therefore, by the angle-angle-side theorem, triangles ∠ACE and ∠ECA are congruent, and we can conclude that:
AC = EC.
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Related Questions
Solve for x. Round your answer to the nearest tenth
Answers
Hence, value of variable y in the triangle is 7.5
Define triangle proportionalityTriangle proportionality is a relationship that exists between the sides of a triangle when a line is drawn parallel to one side of the triangle, intersecting the other two sides. Specifically, the line divides the two sides in proportion to the length of the third side.
We know that, if a line is drawn parallel to one side of a triangle, then the line divides the other two sides in proportion.
AB/AC=2y+5/2y+25
We know that
AB=BC=1/2AC
½=2y+5/2y+25
2y+25=4y+10
2y=15
y=7.5
value of variable y in the triangle is 7.5.
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Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 5, 10, 15, 20, ... an =
Answers
Answer:
[tex]a_{n}[/tex] = 5n
Step-by-step explanation:
there is a common difference between consecutive terms, that is
10 - 5 = 15 - 10 = 20 - 15 = 5
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 5 and d = 5 , then
[tex]a_{n}[/tex] = 5 + 5(n - 1) = 5 + 5n - 5 = 5n
an = 5n
Step-by-step Explanation:
The sequence goes up by 5 each time, so we can represent it using the formula:
an = 5n
Where n represents the position of the term in the sequence. To find a specific term, we substitute the value of n into the formula. For example, to find the 6th term:
a6 = 5(6)
a6 = 30
So the 6th term in the sequence is 30.
35 divided by two plus thirteen
Answers
Answer:
30.5
Step-by-step explanation:
35/2 is 17.5 add 13 is 30.5
Answer:
[tex]35 \div 2 + 13 \\ = 17.5 + 13 \\ = 30.5[/tex]
1. 3 6 12 24 2. 2 9 16 23 3. 53 46 39 32 4. 5 12 26 54 5. 5 20 50 110
FIND 3 NEXT TERMS
Answers
Answer:
Step-by-step explanation:
1. 48 96 192 (multiplying by 2)
2. 30 37 44 ( adding 7)
3. 25 18 11 ( subtracting 7)
4. 110 232 456 ( adding 7, 14, 28, 56 and so on)
5. 230 470 950 (adding 15, 30, 60 120 and so on)
Graph the following equation on the coordinate plane.
y = -3x + 8
Answers
Answer:
See the picture below
Step-by-step explanation:
To graph this linear function, you need two things: slope and y-intercept.
y-intercept:
This is where the line crosses the x axis. It will cross when x = 0. (0,b). The b is the y-intercept. You see this in the equation at the end. In this case the y-intercept it 8.
Slope:
This is the change in y over the change in x. On the graph I highlighted two points (0,8) and (1,5). If you start at (0,8) and go to (1,5), you go straight down 3 units and 1 unit right. This is your slope. Going down is a negative direction and going right is a positive direction. The slope would be the change in y over the change in x. [tex]\frac{-3}{1}[/tex] which simplified would be -3. The slope is -3.
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a bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and astandard deviation of 50. if 36 different applicants are randomly selected, find the probability that their mean isabove 215.a) 0.0359 b) 0.1179 c) 0.0287 d) 0.3821find the indicated probability. (4 points)27) the weekly salaries of teachers in one state are normally distributed with a mean of $480 and a standarddeviation of $55. what is the probability that a randomly selected teacher earns more than $530 a week?a) 0.7823 b) 0.1814 c) 0.2177 d) 0.2823use the given data to construct a frequency distribution. (4 points)28) on a math test, the scores of 24 students were91 71 75 66 75 75 91 87 75 66 82 7171 82 75 71 82 75 71 87 71 82 87 66construct a frequency distribution. use 4 classes beginning with a lower class limit of 60. use a class width of10.score frequency10
Answers
The probability that their mean is above 215 is 0.0359.
Therefore the answer is (a) 0.0359.
To find the probability that the mean rating of 36 applicants is above 215, we can use the central limit theorem, which states that the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. So, the mean of the distribution of sample means is 200, and the standard deviation is 50/sqrt(36)=8.33.
We can then standardize the sample mean using the z-score formula:
z = (x* - μ) / (σ / sqrt(n))
where x* is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values, we get:
z = (215 - 200) / (8.33) = 1.8.
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score greater than 1.8 is 0.0359. Therefore, the answer is (a) 0.0359.
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What does y equal?
5(2y-1)<-15
Answers
Answer:
To solve for y in the inequality 5(2y - 1) < -15, we can simplify the expression on the left-hand side as follows:
5(2y - 1) < -15
10y - 5 < -15 // Distribute the 5 on the left side
10y < -10 // Add 5 to both sides
y < -1 // Divide both sides by 10 and flip the inequality
Therefore, the solution is y < -1.
An number, n more than 18 is seven times the difference of n and three
Answers
In the equation , value of n is 13/3.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given statement is n more than 18 then,
=> n+18
It is equal to seven times the difference of n and three then,
=> n+18 = 7(n-3)
Now simplifying the given equation then
=> n+18= 7n-21
=> 18+21=7n-n
=> 6n=39
=> n = 39/6 = 13/3
Hence the value of n is 13/3.
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If someone work 48.5 hours in a week, they would get how many amount of overtime hours?
Answers
If someone works 48.5 hours in a week and their regular work week is 40 hours, then they would have worked 8.5 hours of overtime.
What is meant by a week?
A week is a unit of time equal to seven days, usually beginning on Monday and ending on Sunday. It is commonly used to measure and organize time.
What is meant by hours?
Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.
According to the given information
In most cases, overtime pay is calculated as 1.5 times the employee’s regular hourly rate.
If someone works 48.5 hours in a week and their regular workweek is 40 hours, then they would have worked 8.5 hours of overtime.
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What is the equation of the line that passes through the point
(
5
,
0
)
(5,0) and has a slope of
6
5
5
6
Answers
The equation of the line that passes through the point (5, 0) and has a slope of 6/5 is:
y = (6/5)x - 6To find the equation of the line that passes through the point (5, 0) and has a slope of 6/5,
we will use the point-slope form of the equation of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Step 1: Plug in the given point (5, 0) as (x1, y1) and the slope (6/5) as m.
y - 0 = (6/5)(x - 5)
Step 2: Simplify the equation.
y = (6/5)(x - 5)
Step 3: Distribute the slope (6/5) on the right side.
y = (6/5)x - 6
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
Answer part a, b, and c for brainliest!!
Answers
The sample space when 2 lollipops are randomly selected with replacement is S_with_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}
The sample space when lollipops are selected without replacement is S_without_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}.
The experiment with replacement (Part A) shows independent events because the probability of each lollipop being chosen is the same for both selections.
How to find the sample space ?When selecting 2 lollipops with replacement, we put the first lollipop back into the bag before choosing the second one. When selecting 2 lollipops without replacement, we do not put the first lollipop back into the bag before choosing the second one.
The outcome of the first event does not affect the probability of the second event.
The experiment without replacement (Part B) shows dependent events because the probability of the second lollipop being chosen is affected by the outcome of the first event. When one lollipop is removed from the bag, there are fewer options available for the second selection, and the probabilities of the remaining lollipops change.
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if f(x) = 2x^2 + 3x - 1 and g(x)= 4x+ 10 then (f . g) (x) is whar rype of function?
Linear
Cubic
Quartic
Quadratic
PLSS HELPPP
Answers
Answer:
quadratic
Step-by-step explanation:
see image above for explanation.
1. Kourtney invests $10,000 in an account that earns 4% interest compounded continuously.
What is the total amount of her investment after 12 years? Round to the nearest cent.
Answers
Answer: $14,983.50
Step-by-step explanation:
if you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
Answers
Answer:
6050 square meters
Step-by-step explanation:
You want to know the largest rectangular area that can be enclosed using 220 meters of fencing for 3 sides.
DimensionsFor enclosure length x, the width of the enclosure is half the remaining fence: (220 -x)/2. The area is the product of length and width.
A = (x)(220 -x)/2
This is the equation of a parabola that opens downward. Its vertex (maximum) is halfway between the zeros, which are x=0 and x=220. This means the area is maximized when x=110 and the width is (220-110)/2 = 55.
The maximum area is (110 m)(55 m) = 6050 m².
__
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The answer is 2025 sq. meter.
If you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, the largest area you can enclose is 4840 square meters. Explanation: To determine the largest possible area, we have to find out how to divide the 220 meters of fencing so that we can maximize the space enclosed by it. If one side of the rectangle is x meters long, the other side is (110 - x) meters long (because we have one straight wall to use as a side).The perimeter of the rectangle can be calculated by adding up all four sides of the rectangle. Hence:2x + (110 - x) + (110 - x) = 220We simplify the equation to solve for x:2x + 220 - 2x = 220-x = 55Therefore, one side of the rectangle is 55 meters long, and the other side is (110 - 55) = 55 meters long as well. The area of a rectangle is given by its length multiplied by its width. In this case, the area is:55 x 55 = 3025.
Therefore, the largest area that can be enclosed is 3025 square meters.
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I need help!!!!!!!!!!!!!!1
Answers
Answer:
∠2 = 125°
Step-by-step explanation:
∠1 and ∠2 form a straight angle of 180° (∠3 and ∠4 aswell)
∠1 = ∠3, because they are cross angles (∠3 and ∠4 aswell)
We can write an equation according to this and find y:
(8y - 9)° = (6y + 7)°
8y - 6y = 7 + 9
2y = 16 / : 2
y = 8
∠1 = 8 × 8 - 9 = 55°
∠2 = 180° - 55° = 125°
∠3 =∠1 = 6 × 8 + 7 = 55°
∠4 = 180° - 55° = 125°
you are testing a new medication to see if it lowers high blood pressure. subjects with high blood pressure volunteered to take part in the experiment. 290 subjects were randomly chosen to receive the medicine (population 1: treatment) and 170 received a placebo (population 2: control). blood pressure was lowered to healthy levels in in 157 of the treatment group and 90 of the controls. test the claim that the new beta-blocker medicine is effective at a significance level of
Answers
The new beta-blocker medicine is effective in lowering high blood pressure.
A hypothesis test can be used to test the claim that a new beta-blocker is effective at the significance level α (significance level).
Let us define the null and alternative hypotheses as follows:
Null Hypothesis (H0):
This drug does not affect high blood pressure.
Alternative hypothesis (Ha):
The drug is effective in lowering high blood pressure.
To test this hypothesis, we can use a two-sample proportional z-test comparing rates of success (lowering blood pressure) in two independent populations (treatment and control groups).
First, we need to calculate the sample proportions and the standard errors of their differences. Let p1 = treatment group success rate,
p2 = control group success rate,
and p = pooled rate.
p1 = 157/290 = 0.541
p2 = 90/170 = 0.529
p = (157 + 90) / (290 + 170) = 0.536
The standard error of the difference in proportions can be calculated as:
SE = sqrt[p*(1-p)(1/n1 + 1/n2)]
= square[0.536(1-0.536)*(1/290 + 1/170)]
= 0.056
Then you can compute the test statistic z.
z = (p1 - p2) / SE
= (0.541 - 0.529) / 0.056
= 2.143
Finally, we can compute the p-value associated with the test statistic z, assuming a standard normal distribution.
p-value = P(Z > 2.143) = 0.0169
The p-value (0.0169) is less than the significance level α, so we neglect the null hypothesis and can say that this drug is effective in lowering high blood pressure.
The chosen importance is not specified in the question, so it is not sure if it's important at that level. If α is given, you can compare the p-value to α and make a decision based on that.
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Use the discriminant to describe the roots of each equation. Then select the best description. 3x2 - 10 = 0
real and rational roots
non-real roots
double root
real and irrational roots
Answers
Equation [tex]3x^{2}[/tex] - 10 = 0 has two real and irrational roots, which are [tex]±\sqrt{10}[/tex]. Therefore, the best description of the roots is "real and irrational."
To use the discriminant to describe the roots of the equation [tex]3x^{2}[/tex] - 10 = 0, we can first recall that the discriminant is the expression under the square root sign in the quadratic formula, which is [tex]b^{2}[/tex] - 4ac for the general quadratic equation [tex]ax^{2}[/tex] + bx + c = 0. In this case, we have a = 3, b = 0, and c = -10, so the discriminant is:
[tex]b^{2}[/tex] - 4ac = [tex]0^{2}[/tex] - 4(3)(-10) = 120
Since the discriminant is positive, the roots of the equation are real. Furthermore, since the discriminant is not a perfect square, the roots are irrational. Specifically, the roots can be found using the quadratic formula:
[tex]x = (-b +- \sqrt{(b² - 4ac)} ) / (2a)[/tex]
= [tex](0 +- \sqrt{120} ) / (2(3))[/tex]
= [tex]+-\sqrt{10}[/tex]
Thus, the equation [tex]3x^{2}[/tex] - 10 = 0 has two real and irrational roots, which are [tex]+- \sqrt{10}[/tex]. Therefore, the best description of the roots is "real and irrational."
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What is the radius of a cone with diameter d? An ice cream cone is filled exactly level with the top of the cone. The cone has a -cm diameter and -cm depth. Approximate how much ice cream (in ) is in the cone? Use 3.14 for .
Answers
Answer: radius is 2.5 and volume of ice cream is 58.9 cm cubed
Step-by-step explanation:
Find the length x to the nearest whole number.
Answers
As a result, 390 cm equals the length x to the nearest whole number as a right triangle is equal to the sum of the squares of the other two sides .
what is Pythagoras theorem ?The relation between the opposite sides of a right triangle is a central idea in mathematics known as Pythagoras' theorem. According to this rule, the square of the hypotenuse's length—the side that faces the right angle—in a right triangle is the same as the total of the squares of both the lengths of the other two sides. The following is a mathematical formulation of the theorem where a and b are really the lengths of the right triangle's two shorter sides (called its legs), and c is the height of the hypotenuse.
given
The Pythagorean theorem, which asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the other two sides, can be used to determine the length x.
cos 34°= b/h
that is 0.829 = 450 cm/ h
h = 450/0.829
h = 542cm
sin 34° = p/h
that is, sin34° = x/542
0.559=x/542
so, x= 542×0.559
x= 390 cm
As a result, 390 cm equals the length x to the nearest whole number as a right triangle is equal to the sum of the squares of the other two sides .
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PLS HELP ASAP
MAKE A NUMBER LINE AND MARK ALL THE POINTS THAT REPRESENT THE FOLLOWING VALUES OF X
Answers
Answer: 1. Since the inequality can never be true, there is no solution.
Step-by-step explanation:
Justine just ran her first race. Her distance from the finish line decreased as she ran.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation?
Answers
The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero.
What is linear equation?
A linear equation is a mathematical equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.
What is y-intercept?
In a linear equation of the form y = mx + b, the y-intercept (b) is the point where the line intersects the y-axis.
According to given information:The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero. In the context of Justine's race, the y-intercept would represent her starting distance from the finish line.
It would be the distance from the finish line when she began the race, or the distance she would have to run to reach the finish line if she started at the beginning. The slope of the line would tell you how much the distance decreases as she runs.
Together, the y-intercept and slope of the line can provide useful information for understanding and analyzing Justine's race.
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The answer of the given question based on the linear relationship is , the y-intercept gives information about Justine's initial position or starting point before she started running the race.
What is Linear relationship?A linear relationship is a type of relationship between two variables where their relationship can be described by a straight line. In other words, the change in one variable is directly proportional to the change in the other variable. This means that as one variable increases or decreases, the other variable also changes in a consistent and predictable way. Linear relationships are commonly studied in mathematics, statistics, and other fields as they provide a useful framework for understanding the relationship between two variables and making predictions based on that relationship.
In the context of this linear relationship, the y-intercept represents the starting point of Justine's race. It is the point where her distance from the finish line is zero, which is the beginning of the race. Therefore, the y-intercept gives information about Justine's initial position or starting point before she started running the race.
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I need help with this problem please
5+3{4-3+2)×9^2+100
Answers
Answer:
834
Step-by-step explanation:
5 + 3(4 - 3 + 2) x [tex]9^{2}[/tex] + 100
5 + 3(3) x 81 + 100
5 + 9 x 81 + 100
5 + 729 + 100
834
Helping in the name of Jesus.
Finding equations of exponential function
Answers
The exponential function are y = 10(2)^x, y = 1.270(1.389)^x, y = 5.656(0.957)^x and y = 6.567(0.870)^x.
What is the equation of the exponential function1. (a) To find the equation of the exponential function that passes through the points (0,10) and (3,80), we can use the formula:
y = a(b)^x
where a and b are constants that we need to find.
First, we can use the point (0,10) to solve for a:
10 = a(b)^0
10 = a
Next, we can use the point (3,80) to solve for b:
80 = 10(b)^3
8 = b^3
b = 2
Therefore, the equation of the exponential function is:
y = 10(2)^x
(b) To find the equation of the exponential function that passes through the points (0.18, 2.8) and (2, 8), we can use the same formula:
y = a(b)^x
First, we can use the point (0.18, 2.8) to solve for a:
2.8 = a(b)^0.18
Next, we can use the point (2, 8) to solve for b:
8 = a(b)^2
Dividing the second equation by the first, we get:
2.857 = (b)^1.82
b = 1.389
Substituting this value of b back into one of the equations to solve for a, we get:
2.8 = a(1.389)^0.18
a = 1.270
Therefore, the equation of the exponential function is:
y = 1.270(1.389)^x
2. (a) To find the equation of the exponential function that passes through the points (2, 5.12288) and (1.92, 2.192), we can again use the formula:
y = a(b)^x
First, we can use the point (2,5.12288) to solve for a:
5.12288 = a(b)^2
Next, we can use the point (1.92,2.192) to solve for b:
2.192 = a(b)^1.92
Dividing the second equation by the first, we get:
0.427 = (b)^(0.08)
b = 0.957
Substituting this value of b back into one of the equations to solve for a, we get:
5.12288 = a(0.957)^2
a = 5.656
Therefore, the equation of the exponential function is:
y = 5.656(0.957)^x
(b) To find the equation of the exponential function that passes through the points (1.192,5) and (5,0.75), we can use the same formula:
y = a(b)^x
First, we can use the point (1.192,5) to solve for a:
5 = a(b)^1.192
Next, we can use the point (5,0.75) to solve for b:
0.75 = a(b)^5
Dividing the second equation by the first, we get:
0.149 = (b)^3.808
b = 0.870
Substituting this value of b back into one of the equations to solve for a, we get:
5 = a(0.870)^1.192
a = 6.567
Therefore, the equation of the exponential function is:
y = 6.567(0.870)^x
3. To find the equation of the exponential function that passes through the points (2.14,7) and (7,205), we can use the same formula as before:
y = a(b)^x
First, we can use the point (2.14,7) to solve for a:
7 = a(b)^2.14
Next, we can use the point (7,205) to solve for b:
205 = a(b)^7
Dividing the second equation by the first, we get:
29.285 = (b)^(4.86)
b = 5.474
Substituting this value of b back into one of the equations to solve for a, we get:
7 = a(5.474)^2.14
a = 0.00061
Therefore, the equation of the exponential function is:
y = 0.00061(5.474)^x
Rounding a and b to the nearest hundred, we get:
a = 0.0006
b = 5.47
So, the final equation of the exponential function is:
y = 0.0006(5.47)^x
We can check if the points (2.14,7) and (7,205) fall on the curve by plugging them into the equation:
y = 0.0006(5.47)^x
When x = 2.14:
y = 0.0006(5.47)^2.14 ≈ 7
When x = 7:
y = 0.0006(5.47)^7 ≈ 205
So, the points do fall on the curve, which means that the equation we found is correct.
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Gabriel goes out to lunch. The bill, before tax and tip, was $9.50. A sales tax of 7.5% was added on. Gabriel tipped 15% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answers
Answer:
Gabriel left $1.53 in tips.
Step-by-step explanation:
Sales tax: 9.50*0.075=0.7125
9.50+0.71=10.21
Total with Sales Tax: $10.21
Tip: 10.21*0.15=1.5315
20
Your friend won't get many stars like this! What changes
would you make to the equation to help your friend
collect all the stars? Why are those changes going to
work?
-16
.
-12
✓
Share With Class
-8
12
16
y= $x+4{x<2}
-4
Answers
Answer:
Step-by-step explanation:
10-16=to 4
the area of this parallelogram is 51.5 cm2. work out the value of x
Answers
Answer:
The formula for area of a parallelogram is A=bh
x=10.3
Step-by-step explanation:
We don't have the base but we have the height.
the base is x and the height is 5
if the area is 51.5
we should divide the height to find the base.
51.5÷5=10.3
so the base is 10.3
Check if answer is correct:
b=10.3
h=5
a= 51.5
10.3(5)=51.5
a= 51.5cm²
I hope this helps as long as you know the formula it's easy :D
a test of writing ability is given to a random sample of students before and after they completed a formal writing course. the results below provide a before and after score for each student. construct a 99% confidence interval for the mean difference between the writing scores before and after the writing course.
Answers
The 99% confidence interval for the mean difference between the before and after scores is (-0.5 ,4.5).
A writing-test is taken for sample of students which are randomly selected, before and after they completed formal writing-course.
The results of the test scores before and after the test are :
Before ⇒ 80, 70, 92, 99, 97, 93, 76, 63, 68, 71, 74
After ⇒ 79, 69, 90, 96, 95, 91, 75, 64, 62, 64, 76
So,
Diff(d) ⇒ 1, 1, 2, 3, 2, 2, 1, -1, 4, 7, -2,
⇒ d² ⇒ 1, 1, 4, 9, 4, 4, 1, 1, 16, 49, 4,
Sum of difference = Σd = 22, and
Sum of d² = 114;
Mean difference is = 2,
The degree of freedom (df) = 11 - 1 = 10,
So, the standard deviation (S.D.) =√(Σd²-(Σd)²/n)/(n-1) = 2.645751 , and
the standard error (Se) = (S.D.)/√n = 2.6457/√11 = 0.7977,
For 99% confidence interval , 10 degree of freedom , t-value is = 3.169,
We know that, confidence interval = {(sample mean) ± t × standard error};
So, Margin of error = t × standard error = 2.527987 ≈ 2.5,
The lower confidence limit is = 2 - 2.5 = -0.5,
The upper confidence limit is = 2 + 2.5 = 4.5,
Therefore, the required 90% confidence interval is (-0.5 ,4.5).
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The given question is incomplete, the complete question is
A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores. Round the limits to the nearest tenth.
Before 70 80 92 99 93 97 76 63 68 71 74
After 69 79 90 96 91 95 75 64 62 64 76
confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. what degrees of freedom should you use?
Answers
The expected counts are large enough to use a chi-square distribution to calculate the p-value because the predicted-counts are at least 5, the degree-of-freedom that should be used is 2.
The "degree-of-freedom" is defined as the number of independent parameters or variables that must be specified to completely describe a system or equation.
We see that the projected counts(expected-counts) are large enough to use a chi-square distribution if all predicted counts are at least 5,
So, This condition is satisfied and it satisfies that the expected counts are large enough to use a chi-square distribution to calculate the p-value.
In the table we see that the number of categories are three : {Red, Black, Green},
So, degree of freedom is = (number of categories) - 1 = 3 - 1 = 2.
Therefore, the degree of freedom is 2.
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The given question is incomplete, the complete question is
Confirm that the expected counts are large enough to use a chi-square distribution to calculate the p-value. The information table is given below.
What degrees of freedom should you use?
A scatter plot is shown on the coordinate plane.
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8
Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 5 comma 7 and 10 comma 9
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 2 comma 7 and 6 comma 7
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 1 comma 4 and 5 comma 6
scatter plot with points at 1 comma 4, 2 comma 6, 3 comma 4, 3 comma 8, 4 comma 10, 5 comma 6, 6 comma 8, and 9 comma 8, with a line passing through the coordinates 1 comma 4 and 3 comma 8
Answers
The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates [tex](1,4)[/tex] and [tex](5,6)[/tex] .
What is a graph?The best way to determine which graph shows a line that fits the data is to plot the line on the scatter plot and see how well it fits with the points.
Let's start with option A, which shows a line passing through the coordinates 5 comma 7 and 10 comma 9. When we plot this line on the scatter plot, we can see that it doesn't fit the data very well.
The line doesn't pass through many of the points and seems to be a poor representation of the relationship between the x and y values.
Option B shows a line passing through the coordinates 2 comma 7 and 6 comma 7. Again, when we plot this line on the scatter plot, we can see that it doesn't fit the data very well.
The line passes through some points, but not all of them, and it doesn't seem to represent the relationship between the x and y values very well.
Option C shows a line passing through the coordinates 1 comma 4 and 5 comma 6. When we plot this line on the scatter plot, we can see that it fits the data fairly well. The line passes through several of the points and seems to capture the overall trend of the data.
Option D shows a line passing through the coordinates 1 comma 4 and 3 comma 8. When we plot this line on the scatter plot, we can see that it fits the data fairly well. The line passes through several of the points and seems to capture the overall trend of the data.
Therefore, The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates [tex](1,4)[/tex] and [tex](5,6)[/tex] .
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The graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates (1,4) and (5,6).
What is the best-fit line?A line of best fit is a straight line that minimizes the distance between it and some data. It is used to express a relationship in a scatter plot of different data points.
Option A Some points are too far from the line when we draw a line through the points (5, 7, and 10). It is not the minimum distance between the line and the scattered data. So, it's not a line on the scatter plot that fits the data.
Option B When we draw a line through (2,7) and (6,7) then the distance between the line and the scattered is still much. So, it's not a line on the scatter plot that fits the data.
Option C When we draw a line through (1,4) and (5,6) then most of the points are nearer to the line and it defines a relation between the points and the line more efficiently. So, this line is the best-fit line for this scattered graph.
Option D When we draw a line through (1,4) and (3,8) then some points are too far from this line. It is not the minimum distance between the line and the scattered data. So, it's not a line on the scatter plot that fits the data.
Therefore, the graph that shows a line on the scatter plot that fits the data is the one with a line passing through the coordinates (1,4) and (5,6).
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PLEASE HELP!! 50 POINTS!!
Christopher borrows 7,500$ to build a garage. He agrees to pay 475$ a month for 24 months but pays off the loan after 18 months.
Part A: Determine the amount of unearned interest.
Part B: Determine the amount needed to repay the loan using the Rule of 78.
Part C: Show your work to support your answers to Part A and Part B.
Answers
Christopher paid more interest than he would have if he had made all 24 monthly payments, the unearned interest is negative. The total amount needed to repay the loan using the Rule of 78 is $7,500.75
How to calculate the amount of unearned interest and the amount needed to repay the loan using the Rule of 78.Part A:
To determine the amount of unearned interest, we need to first calculate the total interest that Christopher would have paid if he had made all 24 monthly payments.
Total interest = Monthly payment x Number of payments - Principal
Total interest = $475 x 24 - $7,500
Total interest = $11,400 - $7,500
Total interest = $3,900
However, Christopher only made 18 monthly payments. To determine the amount of unearned interest, we need to subtract the interest he actually paid from the total interest calculated above.
Interest paid = Monthly payment x Number of payments made
Interest paid = $475 x 18
Interest paid = $8,550
Unearned interest = Total interest - Interest paid
Unearned interest = $3,900 - $8,550
Unearned interest = -$4,650
Since Christopher paid more interest than he would have if he had made all 24 monthly payments, the unearned interest is negative.
Part B:
To determine the amount needed to repay the loan using the Rule of 78, we first need to calculate the total amount of interest that would have been paid if Christopher had made all 24 monthly payments.
Total interest = Principal x Rate x Rule of 78 factor
where Rate = Annual interest rate / 12
and Rule of 78 factor = Number of remaining payments / Sum of digits of all payments
The annual interest rate is not provided, so let's assume it is 6%.
Rate = 6% / 12
Rate = 0.005
The sum of digits of all payments is 1 + 2 + ... + 24 = 300.
Rule of 78 factor = (24 - 18) / 300
Rule of 78 factor = 0.02
Total interest = $7,500 x 0.005 x 0.02
Total interest = $0.75
The total amount needed to repay the loan using the Rule of 78 is the principal plus the total interest calculated above.
Total amount = Principal + Total interest
Total amount = $7,500 + $0.75
Total amount = $7,500.75
Part C:
To support our answers to Part A and Part B, we can compare the total interest paid using the actual method of repayment (18 monthly payments) and the Rule of 78 method of repayment.
Using the actual method, Christopher paid $8,550 in interest.
Using the Rule of 78 method, the total interest would have been $0.75.
As we can see, the Rule of 78 method results in a much lower amount of interest. This is because the Rule of 78 assigns more of the interest to the earlier payments, so paying off the loan early results in less total interest paid.
Regarding the unearned interest, we calculated a negative amount of $4,650 using the actual method of repayment. This is because Christopher paid more interest than he would have if he had made all 24 monthly payments.
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