A square-based prism made of clay had dimensions of 6 by 6 by 10. A pyramid was removed from the prism so the prism has no top. what is the total surface area of the remaining clay solid if the slant height of the pyramid is 10.5​

Answer:

i believe the answer is 1/27

Step-by-step explanation:

you take the fractions and multiply them all together.

1x1x1 equals 1

and 3x3x3 equals 27

meaning the answer is 1/27 :)

To calculate 1/3 x 1/3 x 1/3, you're effectively cubing 1/3, which results in (1/3)^3 or 1^3/3^3, simplifying to 1/27.

The student is asking about the multiplication of fractions and exponentiation rules in algebra. To solve 1/3 x 1/3 x 1/3, you multiply the fractions normally. When multiplying identical fractions, we simply raise the fraction to the power of the number of times it is being multiplied by itself. So 1/3 x 1/3 x 1/3 is equivalent to (1/3)^3. When you raise a fraction to an exponent, you raise both the numerator and the denominator to that power. Therefore, (1/3)^3 equals 1^3/3^3, which simplifies to 1/27.

The example given with 3².35 relates to the rules of exponents, which state that when multiplying exponential terms with the same base, you can add the exponents (x^p x x^q = x^(p+q)). For the concept of cubing of exponentials, you would cube the base and multiply the existing exponent by 3 to execute the operation effectively.

Answer:

7

Step-by-step explanation:

The surface area is the lateral area plus the base area. The base area is 9*5=45. Since there are two bases, its 90. Subtract that from 286 to get the lateral surface area, which is 196. The lateral surface area is the base perimeter*height. The base perimeter is 9+9+5+5= 28. 196/28=height. The height is 7

Answer:

Height= 7in

Step-by-step explanation:

Use the surface area formula and pulg in.

2(wl)(hl)(hw)=286

divide by 2 to get it to the other side.

143=45+9h+5h

subtract 45 and divide by 14 (9+5)

the height is 7

Answer:

(y-12)/4

Step-by-step explanation:

If g(x) is the inverse of f(x)

and f(x) = 4x + 12

f⁻¹(x) = g(x)

let f(x) be represented as y

f(x) = y

y = 4x + 12

subtract 12 from both sides

y-12= 4x

divide both sides by 4

(y-12)/4 = x

so f  ⁻¹ (y)=  (y-12)/4 so g(x) =  (x-12)/4

Answer:

-4

Step-by-step explanation:

Each term is 4 less than the term before it, so the common difference is -4.

Answer:

B. -4 on edge !!

Step-by-step explanation:

Got it right :)

Answer:

The answer to the nearest foot is = 15 feet

Step-by-step explanation:

Solution

The first set taken is to  Compute L for a 55-mph speed limit

Given that

L =(θ2 -θ1)/200 (h +S Tan ∝) =

= ( u + 5) 336²/200 (1.9 +336 tan 0.7°)

= 9° (336)²/200 (1.9 +336 tan 0.7°) = 14.7652094

= 15 feet  { 9° = 9*π/180 = π/20}

Note: Kindly find an attached image for the complete question given and answered

Answer:

1. There are 648 total combinations that can be chosen.

2. After she choses two possiblilities the total number changes to 108 total posibilities to chose from

Step-by-step explanation:

possibility: 1/2 x 1/3 x 1/2 x 1/6 x 1/9 = 648

then you remove the first two because she chose those ones

1/2 x 1/6 x 1/9 = 108 possibilities left

Answer:

Step-by-step explanation:

1.       C

2.        C

3.         B

Answer:

(-0.5,-2.5)

Step-by-step explanation:

(x1 + x2) / 2 = x midpoint

(y1 + y2) / 2 = y midpoint

x)

2 + -3 = 5

5 / 2 = -0.5

y)

4 + -9 = -5

-5 / 2 = -2.5

= (-0.5, -2.5)

The midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

We have to find the midpoint of A and B where A has coordinates (2, 4)

and B has coordinates (-3, -9).

Midpoint = (2-3/2, 4-9/2)

=(-1/2, -5/2)

Hence, the midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)

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Answer:

the answer is container c

b=11.14in2

12in

Step-by-step explanation:

Answer:

Answer is C

Step-by-step explanation:

This mathematics question from middle school algebra asks to solve a system of equations to find the price of pool passes and gym memberships at a recreation center. The problem is partially incomplete due to a cutoff in the additional information needed to set up the second equation. Consequently, we cannot provide a final answer without this information.

The question involves a linear system of equations, which is a topic in algebra within the field of mathematics. The problem presents a scenario where a family purchases a combination of pool passes and gym memberships for a total cost, and another individual purchases a different combination of the same items for a different total cost. To solve, we set up two equations based on the given information.

Step-by-step solution:

Without the full information, this question is incomplete, and thus we cannot provide a final answer.

Step-by-step explanation:

a) $1,000 or more?

As the data is usually distributed, using the 3-step approach to solve the problem: draw the image (I'm not going to do it here), locate the z-point, and identify the region on the graph.

(1000-951)/96 = .5104 = 0.51 = Z, so area = 1 -0.6950 = 0.3050

b) Between $900 and $1,100?

(900-951)/96 = -0.53 = Z, and (1100-951)/96 = 1.55 = Z So area = 0.9394 - 0.2981 = 0.6413

c) Between $825 and $925?

(825-951)/96 = -1.31 = Z, and (925-951)/96 = -0.27 = Z So area = 0.3936 - 0.0951 = 0.2985

d) Less than $700?

(700-951)/96 = -2.61 = Z, so area = 0.0045

The percentage increase in apartment supply is 30%, and the price sensitivity or price elasticity of supply is 3.90, indicating a relatively elastic supply to price changes.

The question deals with the concept of price elasticity of supply, which measures the responsiveness of the quantity supplied to a change in price. To determine the percentage increase in apartment supply, we calculate the change in quantity supplied, divide it by the original quantity supplied, and then multiply by 100 to convert to a percentage:

The original quantity supplied was 10,000 units, and the new quantity supplied is 13,000 units. So the change in quantity supplied is 13,000 - 10,000 = 3,000 units.

The percentage increase in supply is (3,000 units / 10,000 units) × 100% = 30%

Next, we calculate the price sensitivity, also known as price elasticity of supply, using the formula:

Price Elasticity of Supply (Es) = (% Change in Quantity Supplied) / (% Change in Price)

The price increased from $650 to $700, which is an increase of $700 - $650 = $50. The percentage change in price is ($50 / $650) × 100% = 7.69%

Then the price elasticity of supply is 30% / 7.69% = 3.90, indicating that the supply is relatively elastic.

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Answer:

(a)[tex]\frac{7}{25}[/tex]

(b)[tex]\frac{19}{116}[/tex]

(c)[tex]\frac{28}{125}[/tex]

Step-by-step explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

(a) P (a junior who did not attend prom)

[tex]P(J')=\frac{56}{200}= \frac{7}{25}[/tex]

(b)

[tex]P(Senior)=\frac{116}{200}[/tex]

[tex]P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}[/tex]

(c)P (junior | attended prom)

[tex]P(Senior)=\frac{84}{200}[/tex]

[tex]P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}[/tex]

Answer:

A. P = 7/25

B. P = 19/116

C. P = 28/125

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly this way:

      Juniors  Seniors   Totals

Yes       28         97          125

No       56         19           75

Totals   84        116          200

2. Find the probability of each of the events.

Let's recall that the formula of probability is:

P = Number of favorable outcomes/Total number of possible outcomes

A. P (a junior who did not attend prom)

P = Juniors who did not attend prom/Total number of students surveyed

P = 56/200

P = 7/25 (Diving by 8 numerator and denominator)

B. P (did not attend prom | senior)

P = Seniors who did not attend prom/Total number of seniors surveyed

P = 19/116

C. P (junior | attended prom)

P = Juniors who attend prom/Total number of students attended prom

P = 28/125

The restaurant pay $24,192 for 9 pounds of truffles.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A restaurant buys 9 pounds of truffles.

as, 1 pound = 16 ounce

So, the restaurant buys

= 16 x 9

= 144 ounce of truffles.

If truffles cost $168 per ounce.

So, the cost for 9 pounds ruffles is

=  144 x 168

= $ 24,192

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Answer:

15/56

Step-by-step explanation:

Total = 8

3/8 × 5/7

15/56

Answer:

Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.

Step-by-step explanation:

Given that,

The diameter of cylindrical bucket = 12 in.

Depth is increasing at the rate of = 4.0 in per minutes.

i.e [tex]\frac{dh_1}{dt}=4[/tex]

[tex]h_1[/tex] is depth of the bucket.

The volume of the bucket is V = [tex]\pi r^2 h[/tex]

                                                 [tex]=\pi \times 6^2\itimes h_1[/tex]

[tex]\therefore V=36\pi h_1[/tex]

Differentiating with respect yo t,

[tex]\frac{dV}{dt}=36\pi \frac{dh_1}{dt}[/tex]

Putting  [tex]\frac{dh_1}{dt}=4[/tex]

[tex]\therefore\frac{dV}{dt}=36\pi\times 4[/tex]

The rate of volume change of the bucket = The rate of volume change of the aquarium .

Given that,The aquarium measures 24 in × 36 in × 18 in.

When the water pumped out from the aquarium, the depth of the aquarium only changed.

Consider h be height of the aquarium.

The volume of the aquarium is V= ( 24× 36 ×h)

V= 24× 36 ×h

Differentiating with respect to t

[tex]\frac{dV}{dt}=24\times 36 \times \frac{dh}{dt}[/tex]

Putting [tex]\frac{dV}{dt}=36\pi\times 4[/tex]

[tex]36\pi\times 4= 24\times 36\times \frac{dh}{dt}[/tex]

[tex]\Rightarrow \frac{dh}{dt}=\frac{36\pi \times 4}{24\times 36}[/tex]

[tex]\Rightarrow \frac{dh}{dt}=\frac{11}{21}[/tex]

Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.

To find the rate at which the aquarium water level is dropping, calculate the volume of water being pumped into the bucket per minute and the volume of the aquarium. Then, divide the volume of water by the volume of the aquarium to find the rate.

To find the rate at which the aquarium water level is dropping, we first need to determine the flow rate of water being pumped into the cylindrical bucket.

Now, let's find the rate at which the aquarium water level is dropping:

By calculating the above expression, you can find the rate at which the aquarium water level is dropping.

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The water level in the aquarium is dropping at an average rate of π/6 inches per minute. This is obtained by relating the volumes and their rates of change in both the bucket and the aquarium.

The subject of this question is calculus, specifically, related rates. The situation describes two rates: one at which the depth of water in the bucket is increasing, and one at which the water level in the aquarium is dropping - a classic related rates problem.

To comprehend this, let us calculate the volume rates of each one: the bucket and the aquarium. The bucket is referred as cylindrical with a radius of 6 inches (half of 12 inches). The volume of a cylinder is V = πr²h. The depth or height, h, is increasing at the rate of 4 inches per minute, so dh/dt = 4 in/min. The rate at which the volume has been changing, dV/dt = πr²dh/dt = π * (6 in)² * 4 in/min = 144π in³/min.

The aquarium is a rectangular prism, thus its volume can be calculated by V = l*w*h. Therefore, the rate at which the water level is dropping is dV/dt / (l*w) which equals 144π in³/min divided by the area of the aquarium (24in*36in = 864 in²), which gives dh/dt = 144π / 864, which reduces to dh/dt = π/6 in/min downwards. Hence, the water level in the aquarium is dropping at π/6 in/min on an average.

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Answer: gang in la

Step-by-step explanation:

Answer:

[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]    

[tex]df=n-1=80-1=79[/tex]  

[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=18.7[/tex] represent the sample mean for the content of active ingredient

[tex]s=5[/tex] represent the sample standard deviation for the sample  

[tex]n=80[/tex] sample size  

[tex]\mu_o =20[/tex] represent the value that we want to test

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean for the active agent is at least 20 mg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 20[/tex]  

Alternative hypothesis:[tex]\mu < 20[/tex]  

The statistic would be:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Now we can calculate the statistic:

[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]    

P value

The degrees of freedom are calculated like this:

[tex]df=n-1=80-1=79[/tex]  

Since is a one left tailed test the p value would be:  

[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]  

Option (e) 0.0113 is correct. The approximate p-value for the lab's one-sample t-test on fluoxetine is 0.0113.

To determine the approximate p-value for the lab's test on fluoxetine, we can use a one-sample t-test. Here's a step-by-step explanation:

(bar{x} - μ) / (s/√n)

where bar{x} is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

bar{x} = 18.7, μ = 20, s = 5, n = 80

t = (18.7 - 20) / (5/√80)

t = -1.3 / (5/8.944)

t = -1.3 / 0.559

t = -2.325

Therefore, the correct answer is e. 0.0113.

Complete question:

Fluoxetine, a generic anti-depressant, claims to have, on average, at least 20 milligrams of active ingredient. An independent lab tests a random sample of 80 tablets and finds the mean content of active ingredient in this sample is 18.7 milligrams with a standard deviation of 5 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test?

a. 0.0226

b. 0.4885

c. 0.5115

d. 0.15

e. 0.0113

Answer:

$220262

Step-by-step explanation:

We are given that an exponential function

[tex]g(x)=190000\cdot(1.03)^x[/tex]

Where x=Number of years

We have to find the value of Evie's house after 5 years .

Substitute the values in the given function

[tex]g(5)=190000\cdot(1.03)^5[/tex]

[tex]g(5)=220262.07[/tex]

[tex]g(5)\approx 220262[/tex]

Hence, the value of Evie's house after 5 years=$220262

Answer:

90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

Step-by-step explanation:

We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.

Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;

                            P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average speed of cars = 70.7 miles per hour

             s = sample standard deviation = 6.3 miles per hour

             n = sample of cars = 37

             [tex]\mu[/tex] = true mean speed

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the true mean, [tex]\mu[/tex] is ;

P(-1.688 < [tex]t_3_6[/tex] < 1.688) = 0.90  {As the critical value of t at 36 degree of

                                 freedom are -1.688 & 1.688 with P = 5%}  

P(-1.688 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.688) = 0.90

P( [tex]-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

P( [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                    = [ [tex]70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] , [tex]70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] ]

                    = [68.9517 miles per hour , 72.4483 miles per hour]

Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.

Answer:

Barney 145 3 Days 310 Miles

Mary   250 5 Days 600 Miles

A)  3 D + 310 M = 145

B) 5 D + 600 M = 250

Multiplying A) by -5/3

A) -5 D - 516.6666M = -241.66666666

B) 5D + 600M = 250

Adding A) and B)

83.3333 M = 8.3333333333

M = .10 per mile

3 D = 114

Daily Rate = 38 dollars per day

Step-by-step explanation:

Answer:

a. (4, 650), (8, 400)

b. -62.5

Step-by-step explanation:

a......................

Data points are (4, 650) and (8, 400) since price is independent variable and weight of coffee is dependent

b......................

Slope = (y2-y1)/(x2-x1)

Slope = (400 - 650)/(8-4) = -250/4 = - 62.5

The data points representing the price and quantity of coffee sold are ($4, 650) and ($8, 400). The slope of the line connecting these points, which shows the relationship between price and quantity, is -62.5.

This question is about mathematical calculations used in economics, specifically related to pricing and demand. Let's turn these scenarios into data points, with price ($4 and $8) as the independent variable and quantity (650 lbs and 400 lbs) as the dependent variable. So, your data points are ($4, 650) and ($8, 400).

To find the slope of the line connecting these points, use the slope formula. The slope(m) is equal to the difference in the y-values divided by the difference in the x-values. So, m = (400-650) / (8-4) = -250/4 = -62.5.

Thus, the slope of the line connecting these two points, representing the relationship between the price and quantity of coffee sold, is -62.5.

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Answer:

We conclude that the college students spend less time on extra-curricular activities than they did ten years ago.

Step-by-step explanation:

We are given that Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities.

A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours.

Let [tex]\mu[/tex] = average time spent on extra-curricular activities.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 120 hours     {means that the college students spend more or equal time on extra-curricular activities than they did ten years ago}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 120 hours     {means that the college students spend less time on extra-curricular activities than they did ten years ago}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                       T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average number of hours spent per semester = 107 hrs

             s = sample standard deviation = 45 hours

             n = sample of college students = 100

So, test statistics  =  [tex]\frac{107-120}{\frac{45}{\sqrt{100} } }[/tex]  ~  [tex]t_9_9[/tex]

                               =  -2.889

The value of t test statistics is -2.889.

Now, the P-value of the test statistics is given by following formula;

               P-value = P( [tex]t_9_9[/tex] < -2.889) = 0.00314

Since, the P-value is less than the level of significance as 0.05 > 0.00314, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the college students spend less time on extra-curricular activities than they did ten years ago.

Answer:

For the maximize the total area, the all wire i.e. 26 m should be used for the square.

Step-by-step explanation:

Length of the wire = 26 m

Let Amount of wire cut for square = x

Amount of wire cut for triangle  = 26 - x

Side of the square = [tex]\frac{x}{4}[/tex]

Area of the square = [tex]\frac{x^{2} }{16}[/tex]  ------ (1)

Side of the triangle is given by

[tex]a = \frac{26 - x}{3}[/tex]

Side of the triangle is [tex]a = \frac{26 - x}{3}[/tex]

Area of the triangle is given by

[tex]A = \frac{\sqrt{3} }{4} a^{2}[/tex]

Area of the triangle is

[tex]A =\frac{\sqrt{3} }{36} (26 - x)^{2}[/tex]  ------- (2)

Now the total area = Area of square + Area of triangle

The total area = [tex]\frac{x^{2} }{16} + \frac{\sqrt{3} }{36} (26 - x)^{2}[/tex]  ------- (3)

Differentiate above equation with respect to x we get

[tex]A' = \frac{x}{8} - \frac{\sqrt{3} }{18} (26 - x)[/tex]

Take [tex]A' = 0[/tex]

[tex]\frac{x}{8} - \frac{\sqrt{3} }{18} (26 - x) = 0[/tex] ------- (4)

By solving the above equation we get

x = 11.31 m

Again take [tex]A''[/tex] by differentiating equation  (4)

[tex]\frac{x}{8} + \frac{\sqrt{3} }{18} (26)[/tex]

Which is greater than zero. so the value x = 11.31 m gives the area minimum.

Thus for the maximize the total area, the all wire i.e. 26 m should be used for the square.

Answer:

z-test

Step-by-step explanation:

-A z-test is a test used to determine the difference in two population means of known variances.

-The sample size has to be large enough, [tex]n\geq 30[/tex](n=71).

-And, the population must follow a normal distribution.

-Since our sample meets all the above conditions, the hypothesis test used is a z-test

Answer:

  y = -2

Step-by-step explanation:

The equation of a horizontal line is ...

  y = constant

In order to make it go through a point with a y-coordinate of -2, the value of the constant must be -2.

Your line is y = -2.

Answer:

The model car is 10 inches long

Step-by-step explanation:

To solve this question, we use conversion of units

Feet to inches.

Each feet has 12 inches.

The car is 15ft long.

So the car has 15*12 = 180 inches.

.5 inches = 9 in.

Rule of three

.5 inches - 9 inches

x inches - 180 inches

[tex]9x = 180*0.5[/tex]

[tex]9x = 90[/tex]

[tex]x = \frac{90}{9}[/tex]

[tex]x = 10[/tex]

The model car is 10 inches long

To find the length of Uni's model car, we convert the actual car's length to inches, set up a proportion with the given scale, and cross-multiply to solve for the model car's length, resulting in a model that is 10 inches long.

The subject matter of the question is related to scale models, which falls under the field of Mathematics. To solve this problem, we need to find the length of the model car based on the given scale and the actual length of the car.

The scale given is 0.5 inches = 9 inches. Firstly, we need to convert the actual length of the car from feet to inches, so we can work in the same units. There are 12 inches in a foot, so a 15 feet long car is 15 x 12 inches long, which is 180 inches. Now, we need to set up a proportion to find the length of the model car:

Actual car length (inch) : Model car length (inch) = Actual scale (inch) : Model scale (inch) 180 inches (actual car length) : x inches (model car length) = 9 inches (actual scale) : 0.5 inches (model scale)

By cross-multiplying, we get:

(180 inches x 0.5 inches) = (x inches x 9 inches)

Dividing both sides by 9 inches, we get:

x inches = (180 inches x 0.5 inches) / 9 inches

So, the length of the model car is:

x inches = 10 inches.

Therefore, Uni's model car is 10 inches long.

Answer:

A rectangle and a triangle

Step-by-step explanation:

Answer:

0.3876<p<0.4389

Step-by-step explanation:

-Given [tex]n=2472, \ x=1022 , \ CI=0.99[/tex]

-We calculate the proportion of surveys returned:

[tex]\hat p=\frac{1022}{2472}\\\\=0.4134[/tex]

For a 99% confidence interval:

[tex]z_{\alpha/2}=2.576[/tex]

#The margin of error is calculated as;

[tex]ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255[/tex]

The confidence interval are then:

[tex]CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389][/tex]

Hence, the confidence interval is 0.3876<p<0.4389

Answer:

Weight of mixing water=224.541 lb

Step-by-step explanation:

Taking 1 cubic yard of concrete

Mass of gravel = 2314 lb

Moisture content = 3.5% Absorption 4.2%

Extra water needed = (4.2-3.5)*2314/100= 16.198 lb

Mass of sand= 899 lb

Moisture content = 5.7% Absorption =1.4%

Water released = (5.7-1.4)*899/100= 38.657 lb

Free water = 244 lb

Weight of mixing water = free water + extra water needed-water released = 244+16.198-38.657=224.541 lb

Weight of mixing water=224.541 lb

Answer:

25 Inches

Step-by-step explanation:

Given the table:

[tex]\left|\begin{array}{c|c|c|c|c}\text{Number of Inches}&2&10&&40\\\text{Number of Centimeters}&5.08&25.04&63.5&101.6\end{array}\right|[/tex]

We want to determine the missing value on the table.

Let the missing value be x.

1 inch = 2.54 cm

x inch = 63.5

Expressing the above as a ratio

[tex]\dfrac{1}{x}=\dfrac{2.54}{63.5} \\$Cross Multiply$\\2.54x=63.5\\$Divide both sides by 2.54$\\x=25 \:Inches[/tex]

Therefore, the missing value is 25.

Answer:

25 Inches

Step-by-step explanation:

hope this helps :))

Answer:

The calculated value z = 1.3145 < 2.326 at  0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

Step-by-step explanation:

Step(i):-

An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

The mean of the Population 'μ' = 28.0miles/gallon

Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.

The sample size 'n' = 270

Mean of the sample 'x⁻' = 27.8

Given Population variance 'σ² = 6.25

The standard deviation of Population 'σ' = √6.25 = 2.5

Step(ii):-

Null hypothesis :H₀: 'μ' = 28.

Alternative hypothesis :H₁: 'μ' ≠28.

The test statistic

[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}[/tex]

Z = -1.3145

|Z| = |-1.3145|= 1.3145

Step(iii):-

The tabulated value  of z-score at 0.02 level of significance = 2.326

The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.