Answer:
i think the answer is 96
Step-by-step explanation:
Prove that triangle FGH is right-angled at F
Triangle FGH is a right triangle because (HG)²= (FG)²+ (FH)²
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The ratio of corresponding sides of similar triangles are equal.
Therefore;
6/5 = 3.6/FH
represent FH by x
6/5 = 3.6/x
6x = 5 × 3.6
6x = 18
divide both sides by 6
x = 18/6 = 3
Since FH is 3, this means that the sides of triangle FGH are Pythagorean triple, hence FGH is a right triangle.
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For thousands of years, gold has been considered one of the Earth's most precious metals. One hundred percent pure gold is 24-karat gold, which is too soft to be made into jewelry. Most gold jewelry is 14-karat gold, approximately 58% gold. If 18 karat-gold is 75% gold and 12-karat gold, how much of each should be used to make a 14-karat gold bracelet weighing 500 grams
The solution is: 14 karat gold is 58.3333...% gold
We have given that;
75% gold and 50% gold and we need to make 200 grams of 58.3333...% gold.
Since, A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
A) x + y = 200
B) .75x + .50y = ( (14/24) * 200)
We multiply equation B) by -1.3333... and get
B) -x -.6666...y = -155.5555... then adding A)
A) x + y = 200 we get
.3333...y = 44.4444...
y = 133.3333... grams 12 karat gold
x = 66.6666... grams 18 karat gold
Double-Checking the answer
133.3333... * .5 = 66.6666...
66.6666 * .75 = 50.0000...
Hence, Concentration of final solution = (66.6666... + 50) / 200 = 58.3333...% which is 14 karat gold
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Issac wants to save up some money to buy a new smartphone, so he babysits on the weekends. There is a proportional relationship between the time Oscar spends babysitting(in hours) , z, and the amount of money he earns babysitting(in dollars) , y. What is the constant of proportionality? Write your answer as a whole number or decimal
The constant of proportionality represents the rate at which Issac earns money while babysitting and can be found by dividing the amount of money he earns by the time spent babysitting.
Let's say that Issac earns $10 per hour of babysitting. Then, the constant of proportionality would be:
$10 per hour = $10/1 hour = 10
Therefore, the constant of proportionality is 10, which means that Issac earns $10 for every hour of babysitting. This relationship is an example of proportionality because the amount of money earned is directly proportional to the time spent babysitting. As Issac spends more time babysitting, he will earn more money in a proportional relationship.
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Research on the major types of businesses in your province. Based from the data you have gathered, create 1 revenue problem involving quadratic functions.
The top industries are agriculture, mining, tourism, and manufacturing.
The quadratic equations are as given.A manufacturing company in my fiefdom produces and sells ceramic pots.
The company has fixed costs of$ 10,000 per month and variable costs of$ 5 per pot. The company's profit is given by the quadratic function R( x) = -0.2 x2 50x, where x is the number of pots produced and vended in a month.
What's the maximum profit that the company can induce in a month: To break this problem, we can use the formula for chancing the maximum value of a quadratic function, which is given by x = - b/ 2a. In this case, the measure of the x2 term is-0.2, and the measure of the x term is 50. Plugging these values into the formula, we get x = -50/( 2 *(-0.2)) = 125 Hence we obtain the quadratic equation.
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If P = (1,1), Find:
Rx=5 (P)
([?], []
The coordinate of the image point is (9,1).
There are eight types of rules for the transformation of a point. When the takes place across a line, then the point (x,y) is changed to the point (y,x).
Given that the rule for the transformation of a point P(1,1) is [tex]R_{x=5} (P)[/tex], which defines the reflection of a point about a line, that is parallel to the y-axis. The line [tex]x=5[/tex] is like a mirror. So, the distance between the line and the image point is equal to the distance between the line and the original point.
Using the point-line distance formula, the distance between the line [tex]x=5[/tex] and a point (1,1) is given by [tex]|5-1|=4[/tex].
Similarly, by the above statement, the distance between the line [tex]x=5[/tex] and the image point will also be 4.
Therefore, the coordinate of the image point is (9,1).
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If P = (1,1), then find the reflection [tex]R_{x=5} (P)[/tex].
Hunter needs 10 ounces of a snack mix that is made up of seeds and dried fruit. the
seeds cost $1.50 per ounce and dried fruit costs $2.50 per ounce. hunter has $22
to spend and plans to spend it all.
let x = the amount of seeds
let y = the amount of dried fruit
part 1: create a system of equations to represent the scenario. (2 points)
part 2: solve your system using any method. write your answer as an ordered pair. (2
points)
Hunter needs 3 ounces of seeds and 7 ounces of dried fruit, which will cost him $22 in total. The system of equations is 1.5x + 2.5y = 22 and x + y = 10. The solution is (x,y) = (3,7).
The total amount of snack mix required is 10 ounces. So, the sum of the amount of seeds and dried fruit should be 10.
x + y = 10 ---(Equation 1)
The cost of seeds is $1.50 per ounce and the cost of dried fruit is $2.50 per ounce. The total cost of snack mix should be $22.
1.50x + 2.50y = 22 ---(Equation 2)
To solve the system, we can use substitution method. Solving Equation 1 for y, we get
y = 10 - x
Substituting this value of y in Equation 2, we get
1.5x + 2.5(10 - x) = 22
Simplifying and solving for x, we get
1.5x + 25 - 2.5x = 22
-x = -3
x = 3
So, Hunter needs 3 ounces of seeds and 7 ounces of dried fruit to make 10 ounces of snack mix with a total cost of $22.
The ordered pair is (3, 7).
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6 Moses makes a school spirit flag. He has as many yards of red fabric as blue
fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and
blue fabric. Use x to represent the amount of blue fabric. Which equations could
you use to find the amount of red fabric Moses has? Select all that apply.
A X =
B x= x + 2?
x = 2
1/x + 273
x= 1/3x - 223
E x + 2 2 2 = 1/3 x + 2 2 3
C X=
D x- 27 28 = 1/3 x
F * = }}x+ 2
2 2 3
The equations to find the amount of red fabric Moses has are X = x + 2 and X + 222 = 1/3x + 223. These equations are obtained by using x as the amount of blue fabric and setting up equations based on the given information. So, the correct answer is A) and E).
There are two equations that can be used to find the amount of red fabric Moses has
X = x + 2, This equation represents the fact that Moses bought 2 more yards of red fabric than he originally had of blue fabric. So, the amount of red fabric (X) is equal to the amount of blue fabric (x) plus 2.
X + 222 = 1/3x + 223, This equation represents the fact that after buying 2 more yards of red fabric, Moses has equal amounts of red and blue fabric.
So, the amount of red fabric (X) plus 222 (the additional 2 yards he bought) is equal to one-third of the amount of blue fabric (1/3x) plus 223 (the original 2 yards of red fabric he had).
Therefore, the equations that could be used to find the amount of red fabric Moses has are A) and E).
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--The given question is incomplete, the complete question is given
" 6 Moses makes a school spirit flag. He has as many yards of red fabric as blue fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and blue fabric. Use x to represent the amount of blue fabric. Which equations could you use to find the amount of red fabric Moses has? Select all that apply.
A X = x + 2
B x = 2
C 1/x + 273
D x= 1/3x - 223
E x + 2 2 2 = 1/3 x + 2 2 3
F x- 27 28 = 1/3 x
G = x+ {{22}*2}^3 "--
a machine in a manufacturing plant has on the average two breakdowns per month. find the probability that during the next three months it has (a) at least five breakdowns, (b) at most eight breakdowns, (c) more than five breakdowns.
The probability that during the next three months it has;
(a) at least five breakdowns is 0.036.(b) at most eight breakdowns is 0.00085.(c) more than five breakdowns is 0.012.Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events.
The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
The plant has on the average two breakdowns per month,
so the Poisson distribution is,
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
where,
X is the random variable representing the number of events
λ is the average rate at which the events occur
k is the number of events that occur
a) at least five breakdowns
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
P(X =5) = [tex]\frac{e^{-2} 2^5}{5!}[/tex]
= 0.036
Thus, probability that at least five breakdowns in three months is 0.036.
b) at most eight breakdowns
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
[tex]P(X=8) = \frac{e^{-2} 2^8}{8!}[/tex]
= 0.00085.
Therefore, probability of at most eight breakdowns is 0.00085.
c) more than five breakdowns.
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
P(X = 6) = [tex]\frac{e^{-2} 2^6}{6!}[/tex]
=0.012
Therefore, probability of more than five breakdowns is 0.012.
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The number of coyotes found in certain state counties is decreasing at a rate of 4. 5% per year. A wildlife biologist recently counted 100 coyotes in one tri-county area. The biologist uses a function to model the population over time and then uses this model to predict the coyote population. Which function model did the biologist correctly use to predict when the population would be fewer than 50 in this tri-county area?
The biologist predicts that the population would be fewer than 50 in approximately 30 years from the initial count.
The biologist likely used the exponential decay function to model the coyote population over time. This function takes the form:
P(t) = P0 * (1 - r)^t
Where:
P(t) is the population at time t,
P0 is the initial population (100 coyotes),
r is the rate of decrease (0.045 or 4.5%),
t is the time in years.
To predict when the population would be fewer than 50, the biologist would solve the equation:
50 = 100 * (1 - 0.045)^t
t = 30
This equation can be used to find the value of t, which represents the number of years it takes for the population to decrease to fewer than 50 coyotes in the tri-county area, which is 30 years.
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Find the measure of angle D.
The measure of angle D is 25°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the opposite interior angles.
Angle D and angle C are the two opposite angles.
Therefore;
40+9x-2 = 20x +5
38+9x = 20x +5
38-5 = 20-9x
11x = 33
divide both sides by 11
x = 33/11
x = 3
Therefore since angle D = 9x-2
substitute 3 for x
D = 9(3) - 2
D = 27 -2
D = 25°
Therefore the measure of angle D is 25°
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y=1.5 In(et.t+5) for t=1; round your answer to the whole number (exponent "t.t" read (means) t square)
when t=1, y is approximately equal to 5.
To solve for y when t=1 in the equation y=1.5 In(et.t+5), we first need to plug in t=1:
y=1.5 In(e(1)(1)+5)
We simplify the exponent e(1)(1) to just e:
y=1.5 In(e+5)
Using the properties of natural logarithms, we can simplify this further:
y=1.5(1+ln(5+e))
We can use a calculator to evaluate ln(5+e) to be approximately 2.063, so we can plug that in and simplify:
y=1.5(1+2.063)
y=1.5(3.063)
y=4.5945
Rounding this answer to the nearest whole number, we get:
y=5
Therefore, when t=1, y is approximately equal to 5.
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It is kinda hard but just try it
Answer:
we 1st can get the weight of rat by
1 rat and 1 cat + 1 dog and rat = 30
2 rat + 1 cat + 1 dog = 30
Then 1 rat and cat measure 24 so
2 rat + 24 =30
2 rat + 24 =30 1 rat = 3 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg 1 dog = 17kg
so we get the weight of each now we r going to sum them 1 rat + 1 cat + 1 dog = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x 27 kg = x ..... is the mass of 3 of them
Estimate the radius of the object. Round to the nearest hundredth if necessary.
C = 8. 9 mm
radius: about
mm
The estimated radius of the object is about 1.42 mm.
The given information is that the circumference( C) of the object is8.9 mm.
We know that the formula for the circumference of a circle is given by
C = 2πr
where r is the compass of the circle.
To estimate the compass, we can rearrange the formula as
r = C/ 2π
Substituting the given value of C, we get
r = 8.9/ 2π
we can estimate this expression to get
r ≈1.42 mm( rounded to two decimal places)
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Nicole has 28 nickels and dimes that amount to $1. 85 how many of each coin does she have
Answer:
Nicole has 9 dimes and 19 nickels.
Find the indicated probability using the two/way table: p(drive to school | senior)
The probability that a senior drives to school is 0.3 or 30%.
To find the indicated probability using the two-way table, we need to locate the row for "senior" and the column for "drive to school" and then find the corresponding cell.
Let's assume that the two-way table shows the number of students who either drive or take the bus to school based on their grade level. We are interested in finding the probability that a student drives to school given that they are a senior.
So, we locate the row for "senior" and the column for "drive to school". Let's say that the cell in the intersection of these two is labeled "30". This means that there are 30 seniors who drive to school.
Next, we need to find the total number of seniors in the sample. Let's say that the total number of seniors in the sample is 100.
To find the probability that a senior drives to school, we divide the number of seniors who drive to school by the total number of seniors in the sample:
P(drive to school | senior) = 30/100 = 0.3 or 30%
Therefore, the probability that a senior drives to school is 0.3 or 30%.
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HELP PLEASE BRAINLIEST + POINTS
Answer:
CD = 34 units--------------------------
Since CD is diameter, therefore the angle CAD opposite to it is a right angle.
We are given the lengths of two legs, AD = 16 and AC = 30.
Use Pythagorean theorem to find the length of the hypotenuse CD:
CD² = AD² + AC²CD² = 16² + 30²CD² = 1156CD = √1156CD = 34what is the value of sin 45 but as a fraction?
The exact value of sin 45° is [tex]\dfrac{\sqrt{2} }{2}[/tex]
Since we have given that
[tex]\text{sin} \ 45^\circ[/tex]
We need to find the exact value of sin 45°.
From the trigonometric table,
[tex]\text{sin} \ 45^\circ=\dfrac{1}{\sqrt{2}}[/tex]
We need to write it as a simplified fraction,
So, for this, we will rationalize the denominator:
[tex]\dfrac{1}{\sqrt{2}}\times\dfrac{\sqrt{2} }{\sqrt{2}}[/tex]
[tex]=\dfrac{\sqrt{2} }{2}[/tex]
Hence, the exact value of sin 45° is [tex]\dfrac{\sqrt{2} }{2}[/tex]
Answer: 1 divided by the square root of 2
Step-by-step explanation:
Let's set up an example, if the angle is forty five degrees, and the opposite length is 1, we can solve this as sin to get to the hypotenuse,
1. sin(45) = 1/hyp
2. sin(45) times hyp = 1
3. hyp = sin(45)/1
If we take any answer and put it over the hypotenuse as sin, we can see that it is going to end up as 1/√2, or 0.707
I did 1 because you are just asking for sin(45).
how much money do winners go home with from the television quiz show jeopardy? to determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. estimate with 98% confidence the mean winning's for all the show's players. 256592886121164159762297615479276802828316105181371690216879240102008815149
The mean winnings for all of the show's contestants can be estimated with 92% certainty. 35014.48385 is the lower bound, while 40669.38281 is the upper bound.
Lower Bound = [tex]X - t(\alpha/2) * s / \sqrt{(n)[/tex]
Upper Bound = [tex]X + t(\alpha/2) * s / \sqrt{(n)[/tex]
where
[tex]\alpha/2 = (1 - confidence\: level)/2 = 0.04 \\ X = sample\: mean = 37841.93333 \\ t(\alpha/2) = critical\: t \:for \:the\: confidence\: interval = 1.887496145 \\ s = sample\: standard\: deviation = 5801.688541 n = sample\: size = 15 \\ df = n - 1 = 14[/tex]
Thus,
Lower bound = 35014.48385
Upper bound = 40669.38281
A lower bound refers to the smallest possible value or limit that a given quantity or parameter can take. In various fields of mathematics and computer science, lower bounds are used to establish limits on the performance of algorithms, the complexity of computational problems, and the amount of resources required to solve a problem. This information can be useful in developing more efficient algorithms or determining the practicality of a given approach.
Lower bounds are useful for understanding the fundamental limits of a system or process. By establishing a lower bound, researchers and practitioners can better understand the potential of a given technology or approach, and can work to optimize it within the constraints imposed by the lower bound.
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Complete Question:-
How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 92% confidence the mean winning's for all the show's players.
30692 43231 48269 28592 28453
36309 45318 36362 42871 39592
35456 40775 36466 36287 38956
Lower confidence level (LCL) = ?
Upper confidence level (UCL) = ?
Find the divergence of vector fields at all points where they are defined.
div ( (2x^2 - sin(x2)) i + 5] - (sin(X2)) k)
The divergence of the given vector field at all points where it's defined is div [tex]F = 4x - 2x × cos(x^2).[/tex]
To find the divergence of the given vector field at all points where it's defined, we will use the following terms:
divergence, vector field, and partial derivatives.
The given vector field is[tex]F = (2x^2 - sin(x^2)) i + 5j - sin(x^2) k.[/tex]
To find the divergence of F (div F), we need to take the partial derivatives of each component with respect to their
respective variables and then sum them up. So, div [tex]F = (∂(2x^2 - sin(x^2))/∂x) + (∂5/∂y) + (∂(-sin(x^2))/∂z)[/tex].
Find the partial derivative of the first component with respect to x:
[tex]∂(2x^2 - sin(x^2))/∂x = 4x - 2x × cos(x^2)[/tex] (applying chain rule).
Find the partial derivative of the second component with respect to y:
∂5/∂y = 0 (since 5 is a constant).
Find the partial derivative of the third component with respect to z:
[tex]∂(-sin(x^2))/∂z = 0[/tex] (since there is no z variable in the component).
Sum up the partial derivatives:
[tex]div F = (4x - 2x × cos(x^2)) + 0 + 0 = 4x - 2x × cos(x^2).[/tex]
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solve by completing the square x^2-14x+49=16
ANSWER:
(x+7)^2=16
Step-by-step explanation:
x^2-14x+49=16
x^2-14x+49-16=0
x^2-14x+33=0
subtract -33 on both sides
x^2-14x+33-33=-33
x^2-14x=-33
Add 49 on both sides
x^2-14x+49=-33+49
x^2-14x+49=16
x^2-7x-7x+49=16
x(x-7)-7(x-7)=16
(x-7)(x-7)=16
(x-7)^2=16
4
Consider the inequalities -1/4a > 3 a and b – 12> -3. What values, if any, make
both inequalities true? Show your work.
To solve the inequality -1/4a > 3a, we need to first multiply both sides by -4 to get rid of the fraction:
-1a > 12a
Next, we can subtract 12a from both sides to get:
-13a > 0
Dividing both sides by -13 gives us:
a < 0
To solve the inequality b – 12 > -3, we can add 12 to both sides:
b > 9
Now we need to find values of a and b that satisfy both inequalities. Since a < 0, we can try any negative value of a. Let's try a = -1:
-1/4(-1) > 3(-1)
1/4 > -3
This inequality is true, so we can move on to the next inequality. Let's plug in a = -1 and see if it satisfies b > 9:
b – 12 > -3
b > 9
Since -1 satisfies both inequalities, the values that make both inequalities true are: a = -1 and any value of b greater than 9.
Create trig ratios for sin, cos, and tan
Sin(z) = 4/5, Cos(z) = 3/5, tan(z) = 4/3
We know that
sin(z) = perpendicular/hypotenuse
cos(z) = base/hypotenuse
tan(z) = perpendicular/base
Now putting we get,
Sin(z) = 4/5
Cos(z) = 3/5
tan(z) = 4/3
3. (3 points) For ordinary differential equation
X =1- ƛx³6
with ƛ > 0, compute the update Ax= x(t+h) - x(t) using
⚫ Euler's method
⚫ the implicit Euler method
⚫ the midpoint method.
The following are the updates for the given ordinary differential equation using Euler's method, the implicit Euler method, and the midpoint method.
To compute the update Ax for the given ordinary differential equation using Euler's method, we first need to discretize the time domain. Let t0 be the initial time and tn = t0 + nh be the time after n steps of size h. Then, using Euler's method, we have:
xn+1 = xn + hf(xn, tn)
where f(xn, tn) = 1 - ƛxn³/6. Therefore,
Ax = xn+1 - xn = h(1 - ƛxn³/6)
Using the implicit Euler method, we have:
xn+1 = xn + hf(xn+1, tn+1)
where f(xn+1, tn+1) = 1 - ƛxn+1³/6. Solving for xn+1, we get:
xn+1 = (xn + h)/[1 + ƛh/6(xn+1)²]
which is a nonlinear equation that needs to be solved iteratively at each step. Therefore, the update Ax becomes:
Ax = xn+1 - xn
Using the midpoint method, we have:
xn+1 = xn + hf(xn+½h, tn+½h)
where f(xn+½h, tn+½h) = 1 - ƛ(xn+½h)³/6. Therefore,
xn+1 = xn + h(1 - ƛxn³/6 + 3ƛx²n h/4)
and the update Ax becomes:
Ax = xn+1 - xn = h(1 - ƛxn³/6 + 3ƛx²n h/4)
These are the updates for the given ordinary differential equation using Euler's method, the implicit Euler method, and the midpoint method.
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The mean number of sit-ups
done by a group of students is
46 with a standard deviation
of 7. If Rylee's Z-score was
1. 8, how many sit ups did she
do?
Rylee did approximately 58.6 sit-ups.
We are given that the mean number of sit-ups is 46 and the standard deviation is 7. We are also given that Rylee's Z-score was 1.8, we can use the formula for Z-score to find how many sit-ups she did.
The formula for Z-score is [tex]Z = \frac{X-\mu}{\sigma}[/tex]
Z = Z-score
μ = mean
σ = standard deviation
X = ?
Substituting these values into the formula
1.8 = (X - 46)/7
1.8 × 7 = X - 46
X - 46 = 12.6
X = 12.6 + 46
X = 58.6
Therefore, Rylee did approximately 58.6 sit-ups.
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Which correctly compares the numbers? 158,364 > 158,379 > 158,397 158,364 > 158,379 > 158,397 518,317 > 518,246 > 518,197 518,317 > 518,246 > 518,197 290,061 > 289,937 > 290,324 290,061 > 289,937 > 290,324 678,200 > 678,194 > 678,227
The correct comparison of the numbers is:
678,200 > 678,194 > 678,227
Therefore, the answer is the last option, "678,200 > 678,194 > 678,227".
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Find the radius of an eyebrow window with width 62.8 inches and height 18.5 inches
The radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches is approximately 36.7 inches.
To find the radius of an eyebrow window, we first need to understand its shape. An eyebrow window is a type of arched window that has a curved shape similar to that of an eyebrow. The shape of an eyebrow window is created by a combination of a circular arc and a straight line.
To find the radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches, we need to use some geometry formulas. The height of the eyebrow window represents the height of the circular arc, and the width represents the diameter of the circle.
The formula for the radius of a circle is r = d/2, where r is the radius and d is the diameter. To find the diameter, we divide the width by pi (3.14). So, the diameter is 62.8/3.14 = 20 inches.
The height of the circular arc is half of the width, which is 18.5/2 = 9.25 inches. To find the radius, we use the formula for the height of a circular arc, h = r(1-cos(a/2)), where h is the height, r is the radius, and a is the angle of the arc.
The angle of the arc can be found using trigonometry. The sine of half the angle is equal to the height divided by the radius. So, sin(a/2) = h/r. Solving for a, we get a = 2arcsin(h/r).
Plugging in the values, we get a = 2arcsin(9.25/r). To find the radius, we solve for r using a calculator or algebra. The radius is approximately 36.7 inches.
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If f(x) = 3(5") + x and g(x) = 3cos(x), what is (f9)'()? O (3(5*) In(5) + 1)(3cos(x)) + (3(5") + x)(sin(x)) O (3(5") In(5) + 1)(3sin(x)) O (3(5") In(5) + 1)(-3sin(x)) O (3(5) In(5) + 1)(3cos(x)) + (3(5") + x)(-3sin(x))
The derivative of (f∘g)(x) can be found using the chain rule, which states that the derivative of (f∘g)(x) is (f'(g(x)))(g'(x)).
In this case, (f∘g)(x) = f(g(x)) = 3(5^x) + 3cos(x), so we need to find f'(g(x)) and g'(x) and then multiply them together. The derivative of f(x) is f'(x) = 15^x * ln(5) + 1, so the derivative of f(g(x)) with respect to g(x) is f'(g(x)) = 15^(g(x)) * ln(5) + 1. The derivative of g(x) is g'(x) = -3sin(x). Therefore, using the chain rule, we have:(f∘g)'(x) = f'(g(x)) * g'(x) = (15^(g(x)) * ln(5) + 1) * (-3sin(x))Substituting g(x) = 3cos(x), we get:(f∘g)'(x) = (15^(3cos(x)) * ln(5) + 1) * (-3sin(x))So the correct answer is: (3(5^3cos(x)) ln(5) + 1) * (-3sin(x))
For more similar questions on topic a) The intervals for which f(x) = -5.5sin(x) + 5.5cos(x) is concave up and concave down on [0,2π] can be found by analyzing the second derivative of the function. Taking the second derivative of f(x), we get:
f''(x) = -5.5cos(x) - 5.5sin(x)
To find the intervals of concavity, we need to determine where f''(x) is positive and negative.
When f''(x) > 0, the function is concave up. When f''(x) < 0, the function is concave down.
Setting f''(x) = 0, we get:
-5.5cos(x) - 5.5sin(x) = 0
Simplifying, we get:
cos(x) + sin(x) = 0
Solving for x, we get:
x = 3π/4, 7π/4
These are the possible points of inflection for the function.
Using test intervals, we can determine the intervals of concavity:
When 0 ≤ x < 3π/4 or 7π/4 < x ≤ 2π, f''(x) < 0, so f(x) is concave down.
When 3π/4 < x < 7π/4, f''(x) > 0, so f(x) is concave up.
b) The possible points of inflection for f(x) on [0,2π] are x = 3π/4 and x = 7π/4. To find the coordinates of these points, we can substitute each value of x into the original function f(x):
f(3π/4) = -5.5sin(3π/4) + 5.5cos(3π/4) = 5.5√2 - 5.5√2/2 = 5.5√2/2
So the coordinates of the point of inflection at x = 3π/4 are (3π/4, 5.5√2/2).
Similarly, we can find the coordinates of the point of inflection at x = 7π/4:
f(7π/4) = -5.5sin(7π/4) + 5.5cos(7π/4) = -5.5√2 - 5.5√2/2 = -5.5(3/2)√2
So the coordinates of the point of inflection at x = 7π/4 are (7π/4, -5.5(3/2)√2).
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Your parents decide that they will help you out the first two months you are at college
by helping you buy groceries for your meals, but they won't cover the cost of you going
out to eat at restaurants or fast food.
for the first month you submit your receipts, 13 are for fast food and four for kroger, and
totaled $487. the second month you submit receipts for six fast food meals and two for
kroger, and totaled $232. the receipts do not list the per-item price.
a. write the two equations for the cost of buying groceries and meals. (4 points)
• 13f + 4k = 487
• 65+2k = 232
i
b. what were the average costs of one fast food meal and of one trip to kroger?
show your work and justify your thinking. (6 points)
a. The two equations for the cost of buying groceries and meals are 13f + 4k = 487 and 65+2k = 232
b. The average costs of one fast food meal and of one trip to kroger is $77.33
To calculate the average cost, we divide the total cost by the number of meals or trips. For example, in the first month, the total cost of fast food meals and grocery trips was $487, and there were 13 fast food meals and 4 grocery trips. Therefore, the average cost of a fast food meal can be calculated by dividing the total cost of fast food meals ($487) by the number of fast food meals (13):
Average cost of a fast food meal = $487 / 13 = $37.46
Similarly, we can calculate the average cost of a grocery trip in the first month by dividing the total cost of grocery trips ($487 - total cost of fast food meals) by the number of grocery trips (4):
Average cost of a grocery trip = ($487 - $37.46 x 13) / 4 = $89.38
Using the same method, we can calculate the average cost of a fast food meal and a grocery trip in the second month. In the second month, the total cost of fast food meals and grocery trips was $232, and there were 6 fast food meals and 2 grocery trips. Therefore, the average cost of a fast food meal is:
Average cost of a fast food meal = $232 / 6 = $38.67
And the average cost of a grocery trip is:
Average cost of a grocery trip = ($232 - $38.67 x 6) / 2 = $77.33
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LA and LB are vertical angles. If mLA=(x+21)° and mLB=(4x-30)°, the find then measure of LB
Answer:
38 degrees
Step-by-step explanation:
Vertical angles are congruent(equal measures), so mLA = mLB
STEP 1:
Let's use some simple substitution.
mLA = mLB
mLA = x+21, mLB = 4x-30
You plug these two in and get:
x+21 = 4x-30
This is your equation.
STEP 2:
Let's solve our equation!
x+21 = 4x-30
(add 30 to both sides)
x+51 = 4x
(subtract x from both sides)
51 = 3x
(switch order for comprehension)
3x = 51
(divide both sides by 3)
x = 17
Ta-da! You get the measure of x = 17 degrees.
STEP 3:
Let's plug in our value of x to get the value of LB.
mLB = 4x - 30
mLB = 4(17) - 30
mLB = 68 - 30
mLB = 38
This is your answer.
(My question has a part A and part B)
The salesperson earns a 5%
commission on the first $5000
she has in sales. • The salesperson earns a 7. 5%
commission on the amount of her sales that are greater than.
Part A
This month the salesperson had $1,375
in sales. What amount of commission, in dollars, did she earn?
A) The total commission she earned is $475
B) Total sales for commission of $1375 is $20000
How to calculate the amount of commission?A) Total Commission = Commission 1+ Commission 2
Where:
Commission 1 = 5% of first $5000
Commission 2 = 7.5% of the amount left after $5000 is subtracted
thus
Commission 1 = $5000 * 0.05 = $250
Commission 2= $3000 * 0.075 = $225
Commission total = $250 + $225 = $475
The total commission she earned is $475
B) Total sales = Sales with 5% commission + Sales with 7.5% commission
Sales with 5% commission = $5000
Commission At 7.5% = Total commission -Commission with 5% = $1375 - $250
Sales * 0.075 = $1125
Sales with 7.5% commission = $15000
Total sales = $5000+$15000
Total sales = $20000
Total sales for commission of $1375 is $20000
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Complete question is:
A salesperson earns commission on the sales that she makes each month. The salesperson earns a 5% commission on the first $5,000 she has in sales.
The salesperson earns a 7.5% commission on the amount on her sales that are greater than $5,000.
Part A:
This month the salesperson had $8,000 in sales. What amount of commission, in dollars, did she earn?
Part B:
The salesperson earned $1,375 in commission, last month. How much money, in dollars, did she have in sales last month?