The distance a car travels varies directly with the amount of gasoline it uses. If a car uses 28 gallons of gasoline to travel 924 miles, the car can travel 627 miles with 19 gallons of gasoline.
We can set up a proportion to solve the problem:
distance / gasoline = constant
Let's use x to represent the distance the car can travel with 19 gallons of gasoline:
924 / 28 = x / 19
Simplifying and solving for x:
x = (924 / 28) * 19 = 627 miles
Therefore, the car can travel 627 miles with 19 gallons of gasoline.
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A study was performed on a type of bearing to find the relationship of amount of wear y to x1 = oil viscosity and x2 = load. The following data were obtained. Estimate the unknown parameter for x1 of the multiple linear regression equation. Use 4 decimal places.
y x1 x2 y x1 x2
193 1.6 851 230 15.5 816
172 22.0 1058 91 43.0 1201
113 33.0 1357 125 40.0 1115
The estimated coefficient for x1 in the multiple linear regression equation is 2.3529.
How we find the multiple linear regression equation coefficient for x1?To estimate the coefficient for x1 in the multiple linear regression equation, we can use the following formula:
b1 = [(nΣxy) - (Σx)(Σy)] / [(nΣx^2) - (Σx)^2]where n is the number of data points, x and y are the respective variables, and Σ denotes the sum of the values.
Using the provided data, we can calculate the coefficient for x1 as follows:
n = 6Σx1 = 115.1Σy = 772Σx1y = 18822.1Σx1^2 = 1952.86b1 = [(6 x 18822.1) - (115.1 x 772)] / [(6 x 1952.86) - (115.1)^2]= 2.3529 (rounded to 4 decimal places)
In this problem, we are given data on the amount of wear of a type of bearing, as well as the oil viscosity and load that the bearing was subject to. We want to estimate the coefficient for oil viscosity (x1) in the multiple linear regression equation for this data.
To do this, we can use the formula for calculating the coefficient for x1 in the multiple linear regression equation. This formula takes into account the number of data points, the sums of the values for x1 and y, and the sum of the products of x1 and y, as well as the sum of the squares of x1.
Using the provided data and this formula, we find that the estimated coefficient for x1 is 2.3529. This means that, for this data, the amount of wear of the bearing is estimated to increase by 2.3529 units for every one unit increase in oil viscosity, while holding the load constant.
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After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function f(x) = 120 (0.86)x. Find and interpret the given function values and determine an appropriate domain for the function
Answer:
The appropriate domain for the function is [0, ∞).
Step-by-step explanation:
Given function: f(x) = 120 (0.86)x
To find the function values, we can substitute the given value of x into the function:
f(0) = 120 (0.86)^0 = 120 (1) = 120
Interpretation: When the medication is first taken, there are 120 milligrams of medicine in the person's bloodstream.
f(2) = 120 (0.86)^2 ≈ 84.24
Interpretation: After 2 hours, there are approximately 84.24 milligrams of medicine remaining in the person's bloodstream.
f(6) = 120 (0.86)^6 ≈ 34.17
Interpretation: After 6 hours, there are approximately 34.17 milligrams of medicine remaining in the person's bloodstream.
The domain of the function is all non-negative real numbers, since the amount of medicine in the bloodstream can't be negative and time is measured in non-negative hours. So the appropriate domain for the function is [0, ∞).
You can model the arch of a building entrance using the equation y = − 1/3(x + 6)(x − 6), where x and y are measured in feet. The x-axis represents the ground. Find the width of the arch at ground level.
The arch has a width of 6 - (-6) = 12 feet at ground level.
To find the width of the arch at ground level, we need to find the x-values where y = 0, since the width of the arch is the distance between these two x-values.
So, we set y = 0 and solve for x:
0 = − 1/3(x + 6)(x − 6)
Either x + 6 = 0 or x - 6 = 0
If x + 6 = 0, then x = -6.
If x - 6 = 0, then x = 6.
To find the width of the arch at ground level, we need to find the x-values where y=0.
y = − 1/3(x + 6)(x − 6)
Setting y=0:
0 = − 1/3(x + 6)(x − 6)
We can solve for x using the zero product property:
0 = x + 6 or 0 = x - 6
x = -6 or x = 6
The arch intersects the ground at x = -6 and x = 6.
Therefore, the arch has a width of 6 - (-6) = 12 feet at ground level.
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Violet goes to a store an buys an item that costs � x dollars. She has a coupon for 35% off, and then a 8% tax is added to the discounted price. Write an expression in terms of � x that represents the total amount that Violet paid at the register.
Answer:
The amount of discount is 35% of � x, which is (35/100)� x = 0.35� x. So, the discounted price is � x minus the discount, which is � x - 0.35� x = 0.65� x.
Then, the tax is added to the discounted price, which is 8% of the discounted price, or (8/100)(0.65� x) = 0.052� x.
Therefore, the expression for the total amount that Violet paid at the register is:
0.65� x + 0.052� x = 0.702� x
PLEASE HELP!!!
I don’t know how to solve this.
The length a of the right angle triangle is 13.74 cm.
How to find the length of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the opposite side of the right triangle a cm. The side a cm can be found using Pythagoras's theorem or trigonometric ratios.
Let's use Pythagoras's theorem,
a² + b² = c²
where
a and b are the legsc is the hypotenuse side15² - 6² = a²
225 - 36 = a²
1809 = a²
square root both sides of the equation
a = √189
a = 13.7477270849
a = 13.74 cm
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Suppose that P(x) represents the percentage of income spent on health care in year x and I(x) represents income in year x. Determine a function H that represents total health care expenditures in year x.
The function H that represents total health care expenditures in year x is _______
The total health care expenditures in year x would be equal to the product of the percentage of income spent on health care (P(x)) and the income (I(x)) in year x. Therefore, the function H can be expressed as:
H(x) = P(x) * I(x)
This function takes into account both the amount spent on health care as well as the income level, providing a comprehensive representation of health care expenditures.
Step-by-step explanation:
that depends on the result dimension of P(x).
if P(x) delivers the percentage in the form xx.xx%, then
H(x) = I(x) × P(x) / 100
if P(x) delivers the percentage in the form 0.xxxx, then
H(x) = I(x) × P(x)
very basically, the absolute amount of a percentage of a whole is the product between both (and divided by 100).
e.g.
let's say, the whole amount is $64,000.
and we need to know 10% of that.
10% of 64,000 is then
64,000 × 10 / 100 = 6,400
or
64,000 × 0.10 = 6,400
can you see the connection, and why both versions do the same ?
A summary of two stocks is shown.
52W high 52W low Name of Stock Symbol High Low Close
37.18 29.39 Zycodec ZYO 39.06 32.73 34.95
11.76 7.89 Unix Co UNX 16.12 12.11 15.78
Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss?
Answer:
The gain is 139.
Step-by-step explanation:
34.95x25= 873.75
29.39x25= 734.75
873.75- 734.75= 139
You have $10,000 to invest, and three different funds from which to choose. The municipal bond
fund has a 7% return, the local bank's CDs have an 8% return, and the high‐risk account has an
expected (hoped‐for) 12% return. To minimize risk, you decide not to invest any more than $2,000
in the high‐risk account. For tax reasons, you need to invest at least three times as much in the
municipal bonds as in the bank CDs. Assuming the year‐end yields are as expected, what are the
optimal investment amounts?
Best investment amounts are $2,000 in high-risk account, $1,000 in bank certificates of deposit, and $7,000 in municipal bonds and remaining $4,000 placed in municipal bonds to optimize return while lowering risk.
We must adhere to two criteria in order to find the best investment amounts: reducing risk and satisfying tax obligations.
Let's think about the high-risk account first. We will only put $2,000 in this account because that is the most we are ready to risk because we want to keep the risk to a minimum.
Let's go on to the tax regulations. We must invest at least $3,000 in municipal bonds to reach the three times minimum investment requirement in municipal bonds compared to bank CDs. We will therefore put $1,000 into bank CDs and $3,000 into municipal bonds.
We currently have $2,000 set aside for the high-risk account, $1,000 for bank CDs, and $3,000 set aside for municipal bonds. We are now left with $4,000 to invest.
This $4,000 can be invested in a way that strikes a compromise between the need to reduce risk and the desire for great returns. We have the choice of investing the final $4,000 in either municipal bonds or CDs from a nearby bank, depending on our investment alternatives.
Our total investment would be $5,000 in bank CDs, $3,000 in municipal bonds, and $2,000 in the high-risk account if we choose to invest the additional $4,000 in the local bank CDs. The expected return from this is:
($5,000 x 8%) + ($3,000 x 7%) + ($2,000 x 12%) = $400 + $210 + $240 = $850.
If we choose to invest the $4,000 in municipal bonds, our overall investment will consist of $2,000 in the high-risk account, $1,000 in bank CDs, and $7,000 in municipal bonds. The expected return from this is:
($1,000 x 8%) + ($7,000 x 7%) + ($2,000 x 12%) = $80 + $490 + $240 = $810.
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I need Helpppp my teacher sucks at teaching
Answer: 10
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary (add up to 180), so we know that the unknown angle equals 100°, since the adjacent angle equals 80°.
So, we can set up an equation:
[tex]11x-10=100\\11x=110\\x=10[/tex]
Need help with the first 4 problems
Answer:
1) ABE is NOT SIMILAR to DBC
2) FPG is SIMILAR to FGH (AAA)
3) CAN is SIMILAR to HLV (SAS)
4) QRP is SIMILAR to XYP (SSS)
Step-by-step explanation:
1) ABE is NOT SIMILAR to DBC
Since DC and AE are not parallel
2) FPG is SIMILAR to FGH (AAA)
QPF = 180 - 93
QPF = 87
PQF = 180 - 63 - 87
PQF = 30
PQF = GHF
FGH = 180 - 63 - 30
FGH = 87
FGH = QPF
GFH = PFQ
3) CAN is SIMILAR to HLV (SAS)
63 = [tex]x[/tex] x 42
[tex]x[/tex] = 1.5
51 = [tex]x[/tex] x 34
51 = 1.5 x 34
51 = 51
Hypotenuse of CAN = 1.5 x Hypotenuse of HLV
4) QRP is SIMILAR to XYP (SSS)
10 = [tex]x[/tex] x 8
[tex]x[/tex] = 1.25
(20 + 5) = 1.25 x XY
XY = 20
(24 + 6) = 1.25 x XP
XP = 24
2. The length of a rectangular floor is 4 feet longer than its width w. The area of the floor is 165 ft2.
(a) Write a quadratic equation in terms of w that represents the situation. Show how you created it.
(b) Solve the quadratic equation using one of the methods covered in Unit 4 and then clearly state the dimensions of the floor in a sentence.
Show your work.
Answer:
(a)
[tex]W^2+4W-165=0[/tex]
(b)
Width: 11 feet
Length: 15 feet
Step-by-step explanation:
Given:
Width (W) = W ft
Length (L) = (4 + W) ft
Area (A) = 165 ft^2
(a)
The area of a rectangle is equal to the product of its length and width, therefore:
[tex]A=L\times W[/tex]
[tex]\text{We replacing}[/tex]
[tex]165=(4+W)\times(W)[/tex]
[tex]4W+W^2=165[/tex]
[tex]W^2+4W-165=0[/tex]
(b)
We solve the equation by factoring:
[tex]W^2+4W-165=0[/tex]
[tex]4W=-11W+15W[/tex]
[tex]W^2-11W+15W-165=0[/tex]
[tex]W(W-11)+15(W-11)=0[/tex]
[tex](W-11)(W-15)=0[/tex]
[tex]W-11=0\rightarrow W=11[/tex]
[tex]W+15=0\rightarrow W=-15[/tex]
The width of the rectangle is equal to 11 feet and the length of the rectangle is equal to 15 feet.
graph the inequality on a number line.
Answer:
you would put a solid circle on the 3 and go to the left, for example:
Step-by-step explanation:
You would want the variable to be on the left, so you would need to see that the 3 is bigger or equal to a.
3 √5 + 3 √5
I need help adding this please
The answer is 6√5
In 3√5 and 3√5, √5 is multiplied with 3 in both terms,
∴ 3 is the common factor
∴ 3√5+3√5= 3(√5+√5)
= 3×2√5
= 6√5
Hence the answer is 6√5
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HELP PLEASE!!!
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
A- 14 and 1 over 7 in2
B -23 and 4 over 7 in2
C -47 and 1 over 7 in2
D - 84 and 6 over 7 in2
A,B,C,D which one
Hence, it takes 23 and 4 over 7 in² of paper's surface area to wrap six cylindrical mini muffins.
Describe the cylinder's shape:A cylinder is only a three-dimensional shape in geometry. A cylinder has a cylinder-like form and a top and bottom that are shaped like circles. Both the top and bottom are flat and of the same size. I think the simplest way to visualise a cylinder's shape is to think of a soup can.
Given data:
Height of mini muffins 1 ¹/₄ = 5/4 in = 1.25 inDiameter d = 2 inRadius r = 2/2 = 1 in.surface area of total 6 number of cylindrical mini muffins:
S = 6*(π*r²*h)
S = 6* (22/7 * 1² * 1.25)
S = 23.55 in²
S = 23 ⁴/₇ in²
Hence, it takes 23 and 4 over 7 in² of paper's surface area to wrap six cylindrical mini muffins.
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Can someone HELPPPP ME PLEASEEEE
Answer:find the root of 6
Step-by-step explanation:
Fifteen students purchase lunch at the restaurant for $1.75 each. Another 15 purchase the same snack at the restaurant, but the cost is unknown. Together, the cost of all the food is $35.55.
Write an equation that can be used to find the price of each snack, x. Solve for x.
After answering the presented question, we can conclude that equation Therefore, the price of each snack is $0.62.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
price of each snack x.
15 × $1.75 = $26.25
cost of snacks for the other fifteen students
$26.25 + 15x = $35.55
15x = $35.55 - $26.25
15x = $9.30
x = $0.62
Therefore, the price of each snack is $0.62.
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5. a random sample of 484 consumers is surveyed about their online shopping habits, and 121 of these consumers admit to shopping online at least once a week. from this information, we know the sample proportion must be equal to a. 0.48. b. 0.12. c. 0.25. d. 0.37. e. 0.09. 6. return to question 5. a sample proportion is a a. statistic. b. parameter. c. standard deviation. d. level of confidence. e. margin of error. 7. what proportion of osu undergraduates have full-time jobs? you survey a random sample consisting of 920 osu undergraduates and find that 368 of them have full-time jobs. use this information to construct a 95% confidence interval in order to estimate the proportion of all osu undergraduates who have full-time jobs. as you construct the interval, try not to do a lot of rounding until you reach the end of your calculations, and then choose the answer below that is closest to what you calculate. a. 0.200 to 0.600 b. 0.384 to 0.416 c. 0.368 to 0.432 d. 0.350 to 0.450 e. 0.374 to 0.426
Now, we can construct the confidence interval: [tex]0.4 ± 1.96 * 0.0157 ≈ 0.4 ± 0.0308. [/tex]The resulting interval is 0.3692 to 0.4308, which is closest to option e. 0.374 to 0.426
5. To calculate the sample proportion, divide the number of consumers who shop online at least once a week (121) by the total number of consumers surveyed (484). So, the sample proportion is[tex] 121/484 = 0.25.[/tex] The correct answer is c. 0.25.
6. A sample proportion is a statistic because it is a measure derived from a sample of the population. The correct answer is a. statistic.
7. To construct a 95% confidence interval for the proportion of OSU undergraduates with full-time jobs, we first find the sample proportion:[tex] 368/920 = 0.4[/tex].
Next, we find the standard error (SE) for the sample proportion: SE = sqrt(0.4 * (1 - 0.4) / 920) ≈ 0.0157. For a 95% confidence interval, the critical value (z-score) is approximately 1.96.
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Which is the BEST system to measure the likelihood of an event occurring? A between 0 and 12 B between 0 and 1 C between 0 and 10
D between 0 and 100
D) Between 0 and 100.
The best system to measure the likelihood of an event occurring would be option D between 0 and 100. This system allows for a greater level of granularity and precision in the measurement of probability, as it provides a wider range of possible values to represent different levels of likelihood. The other options may not provide enough resolution to accurately capture and distinguish between different probabilities.
For a class project, a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches. how much paper is wasted? (60 â€" 15Ï€) square inches 15Ï€ square inches 45 square inches (60 â€" Ï€) square inches
If a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches, then (60 - 1.5 π) square inches paper is wasted.
The area of each circle is given by the formula [tex]A = \pi r^2[/tex], where r is the radius of the circle. Since all 15 circles are congruent, they all have the same radius.
Let's first find the radius of each circle. Since the circles are cut from a 6 by 10 inch sheet of paper, we know that the diameter of each circle cannot be greater than 6 inches or 10 inches. Let's take the smaller dimension (6 inches) and divide it by 15 to find the maximum possible diameter of each circle:
6 inches ÷ 15 = 0.4 inches
Therefore, the maximum possible radius of each circle is 0.2 inches.
Now we can calculate the total area of all 15 circles:
Total area of circles = [tex]15 * \pi * (0.2)^2[/tex]
[tex]= 1.5 \pi[/tex] square inches
The area of the original sheet of paper is 6 inches * 10 inches = 60 square inches. Therefore, the amount of paper wasted is:
Amount of paper wasted = Area of sheet - Total area of circles
= 60 square inches - 1.5 π square inches
= 60 square inches - 4.71 square inches (using π ≈ 3.14)
= 55.29 square inches (rounded to two decimal places)
Therefore, the answer is (60 - 1.5π) square inches.
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There are 12 boys and 14 girls in Mr. Rowe's class. Each week, Mr. Rowe puts pieces
of paper with each student's name in a box and randomly pulls one out. The chosen
student spins the arrow on the spinner shown.
10 free
points
Free
assignment
5 free
points
Which expression can be used to find the probability that this week a boy will be
chosen and the arrow will land on "Free assignment"?
Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.
Which expression can be used to find the probability that this week a boy will be?
chosen and the arrow will land on "Free assignment"?
The probability of a boy being chosen is the ratio of the number of boys to the total number of students, which is:
[tex]P(boy) = 12 / (12 + 14) = 12/26 = 6/13[/tex]
The probability of the arrow landing on "Free assignment" is 1/3, since there are 3 equal sectors on the spinner.
To find the probability that both events occur (i.e., a boy is chosen and the arrow lands on "Free assignment"), we multiply the probabilities:
[tex]P(boy and "Free assignment") = P(boy) x P("Free assignment")[/tex]
[tex]P(boy and "Free assignment") = (6/13) x (1/3) = 2/13[/tex]
Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.
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Write an inequality for the graph below.
In Mathematics, the relationship between two values which are not equal is expressed by inequalities. The equation of inequality for the given graph is y ≥ -1/2x + 2.
Define inequalities.In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size. There are different notations used to represent different types of inequalities.
The notation a < b means that b is greater than a.The notation a > b means that a is greater than b.In both the cases a is not equal to b and such relationships are known as strict inequalities. This means that a is either strictly less than or greater than b. Equivalents are excluded whereas in inexact inequalities.
The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or equivalently at most b or less than or equal to b).The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or equivalently at least greater than or equal to b or b).For the given graph:
take run = 1 and rise = -1/2
Thus, the slope will be,
Slope = (⁻¹/₂)/1
Slope = -1/2
Since, the y intercept is 2. Then the equation is y = -1/2x + 2
Take point (1,2) on the graph and apply in the equation:
y = -1/2x + 2
2 = -1/2 (1) + 2
2 = -1/2 + 2
2 = 3/2
As, 2 > 3/2. We can replace the = sign into ≥.
So, the eq inequality equation is y ≥ -1/2x + 2.
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Can someone please help me ASAP it’s due today!! I will give brainliest if it’s correct.
Answer:
C
Step-by-step explanation:
About 16 days because 0.58 x 28 is 16.24
a report on high school graduation stated that 85 percent of high school students graduate. suppose 3 high school students are randomly selected from different schools. what is the probability that exactly one of the three graduates? question 4 options: 0.019 0.003 0.614 0.057 0.850
The probability that exactly one of three randomly selected high school students graduate, given an 85% graduation rate, is 0.057. This calculation was based on the combination formula and the binomial probability distribution.
This problem involves calculating the probability of a specific outcome (exactly one of the three students graduating) in a binomial distribution. We know that the probability of any one student graduating is 0.85, so the probability of one student not graduating is 0.15. Using the binomial probability formula, we can calculate the probability of exactly one student graduating out of three as:
P(X = 1) = (3 choose 1) * (0.85)^1 * (0.15)^2 = 3 * 0.85 * 0.0225 = 0.057
Therefore, the answer is 0.057, or approximately 5.7%. This means that if we randomly select three high school students from different schools, there is a 5.7% chance that exactly one of them will graduate.
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PLS HELP!!
Will give brainliest!!
The length of the side AC or the height of the smaller equilateral triangle is 3√2 inches.
What is the length AC?The length of the side AC is equal to the height of the smaller equilateral triangle.
We know that in an equilateral triangle, all sides are equal, and all angles are 60 degrees.
Let's call the height of the smaller equilateral triangle h, and the length of one side of the smaller triangle x.
We can use the Pythagorean theorem to find the value of h:
(1/2)x^2 + h^2 = x^2
h^2 = x^2 - (1/2)x^2
h^2 = (1/2)x^2
h = sqrt((1/2)x^2)
Now, we also know that the side of the large equilateral triangle is 6 inches, so x = 6 inches.
Substituting this value into the equation for h, we get:
h = √((1/2)(6^2))
h = √(18)
h = 3√2 inches.
Therefore, the height of the smaller equilateral triangle is 3√2 inches.
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f the null hypothesis is correct, the probability of getting a sample mean greater than $189,500 is .0668 [mean valuation of homes]. a. true b. false
Given statement "f the null hypothesis is correct, the probability of getting a sample mean greater than $189,500 is .0668" is true. Because, It's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.
The null hypothesis is a general statement that there is no significant effect or difference between the considered groups or variables.
In this case, the null hypothesis would be that the true mean valuation of homes is equal to or less than $189,500.
The probability of 0.0668, mentioned in the question, represents the likelihood of getting a sample mean greater than $189,500 if the null hypothesis is true.
In other words, it's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.
This probability (0.0668) is also known as the p-value.
The p-value helps to determine the significance of the results.
If the p-value is less than a predetermined significance level (usually 0.05), the null hypothesis is rejected in favor of the alternative hypothesis.
In this case, the p-value of 0.0668 is higher than the common significance level of 0.05.
We cannot reject the null hypothesis, meaning the probability of getting a sample mean greater than $189,500 is indeed 0.0668 if the null hypothesis is correct
Hence, the statement is true.
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data was collected for 300 fish from the north atlantic. the length of the fish (in mm) is summarized in the gfdt below. what is the lower class boundary for the first class? class boundary of a frequency table
The lower class boundary for the first class is 122.5.
Data was collected for 300 fish from the North Atlantic.
The length of the fish (in mm) is summarized in the GFDT below.
| Length (mm) | Frequency | 123 - 145 | 34 | 146 - 168 | 89 | 169 - 191 | 107 | 192 - 214 | 44 |
The class boundaries for a frequency table are calculated by taking the lower limit of one class and subtracting 0.5
from it to find the lower class boundary, and taking the upper limit of the previous class and adding 0.5 to it to find the
upper class boundary.
For the first class, the lower limit is 123 and the upper limit is 145. So the lower class boundary is:123 - 0.5 = 122.5
Therefore, the lower class boundary for the first class is 122.5.
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MANY POINTS, PLEASE HELP ME
Given: ABCD is a trapezoid
Segments BA & CO are congruent
Prove: segment BD is congruent CA
Assemble the proof by dragging tiles to
the Statements and Reasons
Please send full proof chart, or picture of completed proof chart. The assignment is found on edguinty or other school platforms and is a multiple step answer. Will mark brianlist and give points
Angles:
Triangles:
BAD
CDA
Statements:
ABCD is a trapezoid
ABCD is an isosceles trapezoid
Reasons:
Given
Base angles theorem
Reflective property
def. if isosceles trapezoid
Therefore, segment BD is congruent to segment CA, as required.
What is trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, we are given that AB is parallel to CD. The base angles theorem states that the base angles of an isosceles trapezoid are congruent. Since AB and CD are congruent (as given by the reflective property of congruence), the opposite angles formed by the intersecting lines BA and CD (i.e., ∠BAD and ∠CDA) are congruent as well. This establishes that ABCD is an isosceles trapezoid. An isosceles trapezoid has two pairs of congruent sides: AB = CD and AC = BD. Since BA and CO are congruent (as given), we can conclude that AC and BD are congruent as well (by the isosceles trapezoid definition). Finally, the symmetric property of congruence allows us to state that BD is congruent to CA.
Here,
given that ABCD is a trapezoid and segments BA and CO are congruent:
Statements | Reasons
ABCD is a trapezoid | Given
AB || CD | Definition of a trapezoid
∠BAD ≅ ∠CDA | Base angles theorem
AB ≅ CD | Reflective property of congruence
BA ≅ CO | Given
AC ≅ BD | Isosceles trapezoid definition
BD ≅ CA | Symmetric property of congruence
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GEOMETRY PLS HELP ASAP
Answer:
C) 56
Step-by-step explanation:
2(AE) = BD
AC = BD
2(2x + 6) = 6x - 10
4x + 12 = 6x - 10
-2x = -22
x = -22/-2 = 11
AC = 6(11) - 10 = 56
In a scale drawing, an airplane has a length of 35 centime-
ters. The length of the actual plane is 87.5 feet.
What is the scale of the drawing?
Be sure to write the scale in simplest form.
So how do I solve this?
Answer:
x = y = 2√7 = 5.292
Step-by-step explanation:
We have a right isosceles triangle, so the length of the hypotenuse is √2 times the length of each leg. Since the hypotenuse is 2√14, each leg measures 2√7.
The length of the sides of the right isosceles triangle is 5.292units.
What is right isosceles triangle?A right isosceles triangle is a special type of triangle that has two equal-length legs and a right angle between them. Because it has two equal legs, it is also an isosceles triangle. The name "right isosceles" comes from the fact that it has a right angle and two equal legs.
In the given question,
In a right isosceles triangle, the two legs are congruent, and the length of the hypotenuse can be found using the Pythagorean theorem:
a² + b² = c²
Since this is an isosceles triangle, we know that a = b, so we can simplify the equation to:
2a² = c²
Taking the square root of both sides, we get:
a√2 = c
In this case, we are given that the hypotenuse has a length of 2√14, so we can set c equal to that value and solve for a:
a√2 = 2√14
a = (2√14)/√2
Simplifying the expression by canceling the square root of 2 in the denominator, we get:
a = 2√7
Therefore, each leg of the isosceles triangle has a length of 2√7, which agrees with your answer.
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