1. According to a recipe for cooking roast beef, it takes 3/4 hour for each pound of beef in an oven heated
to 325 Fahrenheit. How long should it take to cook a roast that weighs 12 pounds?

i might have read this problem wrong since i didnt get a clear understanding because of the wording of this problem but i will do the best i can!

step-by-step explanation:

first step is to make a table! and ill just make one on here so you can get a better understanding on this problem :)

----------------------------------

| boxes sold (b) | money collected (m) |

----------------------------------

|    1    |          1.50           |

----------------------------------

|    2    |          3           |

----------------------------------

|    3    |          4.50            |

----------------------------------

|    4    |          6           |

----------------------------------

|   5    |          7.50           |

----------------------------------

|   6    |          9           |

----------------------------------

|   7    |          10.50           |

----------------------------------

|   8    |          12           |

----------------------------------

(b * 1.50) = m

the independent variable = boxes sold (b)

the dependent variable = money collected (m)

hope this helps you and please tell me if i did something wrong or if you need extra help understanding this problem! :)

The volume of each shape (A right triangular prism and the trapezoidal prism are):

A right triangular prism is a three-dimensional shape that has a triangular base and three rectangular faces. It is a prism because its two bases are identical and parallel. The formula for finding the volume of a right triangular prism is V = (1/2) * base * height * length.

A trapezoidal prism is a three-dimensional shape with trapezoidal bases and four rectangular faces. It is also a prism because its two bases are identical and parallel. The formula for finding the volume of a trapezoidal prism is V = ((b1 + b2) / 2) * height * length, where b1 and b2 are the lengths of the two parallel sides of the trapezoidal base.

Recall that the formula for the volume of a trapezoidal prism is:

V = (1/2)h(b1+b2)L

where:

Hence, substituting the given values, we have:

V = (1/2)(20 + 19)(7) 4

V = (1/2)(39)(7) 4

V = (273/2) 4

V = 546ft³

Therefore, the volume of the trapezoidal prism is 546ft³

2) Recall that the formula for the volume of a right triangular prism is:

V = (1/2) * b * h * L

Where:

b is the length of the base of the triangle

h is the height of the triangle

L is the length of the prism (the distance between the triangular faces)

The factor of (1/2) is included since the base of the prism is a triangle.

Given the forumla above:

b = 9ft

h = 7ft

L = 4ft


Plugging in the values given:

V = (1/2) * 9ft * 7ft * 4ft

V = 126ft³

Therefore, the volume of the right triangular prism is 126ft³

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Answer:

The 95% confidence interval   \( 81.852  <  \mu <  280.098 \)

Step-by-step explanation:

From the question we are told that

   The  sample mean is  \(\= x  =  180.975\)

   The standard deviation is  \(\sigma  =  143.042\)

   The sample size is n = 8

Given that the confidence level is  95%  then the level of significance is  

    \(\alpha =( 100- 95) \%\)

=>  \(\alpha =0.05\)    

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>  \(E = 1.96 *  \frac{ 143.042 }{\sqrt{8} }\)

=>  \(E = 99.123 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=>    \(180.975 -99.123 <  p <  180.975 +99.123\)

=>    \( 81.852  <  \mu <  280.098 \)

Using the t-distribution, it is found that the 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

The information given is:

We have the standard deviation for the sample, hence, the t-distribution is used.

The interval is given by:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The critical value for a two-tailed 95% confidence interval with 8 - 1 = 7 df is t = 2.3646.

Then:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 180.975 - 2.3646\frac{143.042}{\sqrt{8}} = 61.39\)

\(\overline{x} + t\frac{s}{\sqrt{n}} = 180.975 + 2.3646\frac{143.042}{\sqrt{8}} = 300.56\)

The 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

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Answer:

42.

Step-by-step explanation:

14% of 300 is 42.

hope this helped

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

79.3, 75.1, 78.2, 74.1, 73.9, 75.0, 77.6, 77.3, 73.8, 74.6, 75.5, 74.0, 74.7, 75.9, 72.9, 73.8, 74.2, 78.1, 75.4, 76.3, 75.3, 76.2, 74.9, 78.0, 75.1, 76.8

a) Calculate a point estimate of the mean pull-off force of all connectors in the population. State which estimator you used and why.

The mean can be used as a point estimate for the pull of force.

Using a calculator :

The mean(m) :

Σx /n = 1966/26

= 75.62 pounds

(b) Calculate a point estimate of the pull-off force value that separates the weakest 50% of the connectors in the population from the strongest 50%.

To obtain this, we calculate the median:

Median = 0.5(n + 1)th term

Median = 0.5(27)th term = 13.5

Take the 13th and 14th term:

(75.1 + 75.3) / 2 = 75.2 pounds

(c) Calculate point estimates of the population variance and the population standard deviation.

Using calculator ; the variance (s²) = 2.73815

The standard deviation (s) = √variance

s = √2.73815 = 1.655

(d) Calculate the standard error of the point estimate found in part (a). Interpret the standard error.

Standard Error = standard deviation / √n

Standard Error = 1.655 / √26

= 0.3245

(e) Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds

Number of Proportions less than 73 pounds / number of samples

= 1 / 26

= 0.0385

When a distribution has three or more peaks then it is said to be a multimodal distribution .

In histograms, there are often three types of distributions which are classified according to the number of peaks that they have . A unimodal distribution would be a histogram that has a single peak in its distribution .

Then there are binomial distributions which boast of having two peaks , Then finally, there is the multimodal distribution which is for all distributions with either three peaks, or more than that .

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Answer:

Since this is a proportional relationship,

We know that the number which are proportional are a multiple of each other

the number which we can multiply one of the numbers to get the other number is the constant of proportionality

we could check for proportionality by using the following formula:

p1 / s1 = p2/s2 = p3/s3 = p4/s4  if they were equal, we can say that the relation is proportional

The value of any of the above values, p1/s1 , p2/s2 , p3/s3 , p4/s4 is the constant of proportionality

Therefore, the constant of proportionality = 20 / 5 = 4

Answer:

Since this is a proportional relationship,

We know that the number which are proportional are a multiple of each other

the number which we can multiply one of the numbers to get the other number is the constant of proportionality

we could check for proportionality by using the following formula:

p1 / s1 = p2/s2 = p3/s3 = p4/s4  if they were equal, we can say that the relation is proportional

The value of any of the above values, p1/s1 , p2/s2 , p3/s3 , p4/s4 is the constant of proportionality

Therefore, the constant of proportionality = 20 / 5 = 4

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

\(\displaystyle \text{Displacement}=\int_a^bv(t)\, dt\)

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

\(\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt\)

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

\(\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt\)

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

\(\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}\)

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

\(\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}\)

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

\(\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}\)

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

\(\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}\)

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

\(\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt\)

In other words, all of our values are now positive. We will utilize the same strategy:

\(\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt\)

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

\(\displaystyle \text{Distance} =5.6+1.5+2.4=9.5\)

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

Answer:

4192.4 cm³

Step-by-step explanation:

x = length of one side

x² = area of one side

There are 5 sides because it's an open top.

5(x²) = 1300

x² = 1300/5 = 260

x = √260 = 16.12

Volume = x³ = 16.12³ = 4192.4 cm³

The transformation in the picture is option c Reflection.

Given,

Reflection transformation:

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.

According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.

Here,

In the picture the transformation is reflection.

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Answer

TN=22

Step-by-step explanation:

You know that MT+TP+TN using the Orthocenter thereom.

Answer:

Step-by-step explanation:

You don't ask any question that can be answered from the info,  but the study does clearly show that adults sleep less than teenagers.  what was the question that you want an answer to?

As of the given data, teenagers slip more than adults as a mean of the teenager is greater than adults.

As given,
A sample of 16 teenagers has a mean of 8.9 hours slept and a standard deviation of 1.2. A sample of 12 adults has a mean of 6.9 hours slept and a standard deviation of 0.6.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
The mean of the adults = 6.9
The mean of teenagers = 8.9
Where teenagers have a greater mean,

The standard deviation of the adults = 0.6
The standard deviation of teenagers = 1.2
Where teenagers have a greater  standard deviation,

Thus, as of the given data, teenagers slip more than adults as a mean of the teenager is greater than adults.

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The range of the expression is: 4.2  < √5 + 2 < 4.3.

For the stated question;

2.2 < √5  <2.3  .....eq 1

To find the range of √5 +2.

2.2 + 2 < √5 + 2 <2.3 +2

4.2  < √5 + 2 < 4.3

Thus, the range of the expression is: 4.2  < √5 + 2 < 4.3.

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Answer:

4 Blue chips

6 Yellow chips

10 Red chips

Imagine 20% as 2 of 10. We have 20 chips, and that's double of that. So if we have 2/10... we will have 4/20

Same with the yellow chips. Imagine 30% as 3 of 10, again double that... 6/20.

It doesn't directly say the percent of design a computer representation but we can infer that if we have 20% and 30%... that makes 50%, there is only 100 in a percent, so that means there is 50% left! We repeat the process where we envision 50% as 5 of 10, double that. Now we have 10 of 20, 50%!

Answer:

Yes it is reasonable

Step-by-step explanation:

0.78 is greater than 0.7

Please mark me as brainliest.

Answer:

its B.

Step-by-step explanation:

all you have to do is y divided by x to find the constant of proportionality

so it would be two  y=2x

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The Correct choices are :

Answer:

x=24

Step-by-step explanation:

Answer:

cyclist will travel 64 kilometres in 4 hours

Step-by-step explanation:

speed of cyclist = 10 miles per hour

given 1 mile is equal to 1.6 kilometres.

1*10 miles will be equal to 1.6*10 kilometres

thus , 10 mile is equal to 16 kilometres

using 16 km in place of 10 miles in 10 miles per hour

we have

speed of cyclist = 16 kilometres per hour

we know that distance = speed * time

speed is 16 kilometres per hour

time 4 hours

thus , distance = 16*4 kilometres= 64 kilometres.

cyclist will travel 64 kilometres in 4 hours.

(Hope this helps can I pls have brainlist (crown)☺️)

The domain of the function f(x)= -long(5-x)+b is all real numbers except for x = 5.

Function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.

The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.

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The complete question is: Will changing two or more objective function coefficients simultaneously affect the optimal solution?

We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).

For the 100 m race with Mark Chase and Beatrice, the sample space of all the possible ways in which the three runners can win first, second, and third place is:

{M-C-B, M-B-C, C-M-B, C-B-M, B-M-C, B-C-M}

where M stands for Mark, C stands for Chase, and B stands for Beatrice. We have six possible permutations because there are three choices for the first place, two choices for the second place (as one person has already won first place), and one choice left for the third place.

If there were four runners and three positions to be won, the sample space would be:

{A-B-C-D, A-B-D-C, A-C-B-D, A-C-D-B, A-D-B-C, A-D-C-B, B-A-C-D, B-A-D-C, B-C-A-D, B-C-D-A, B-D-A-C, B-D-C-A, C-A-B-D, C-A-D-B, C-B-A-D, C-B-D-A, C-D-A-B, C-D-B-A, D-A-B-C, D-A-C-B, D-B-A-C, D-B-C-A, D-C-A-B, D-C-B-A}

where A, B, C, and D represent the four runners. We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).

Note that in both cases, we assume that all runners are equally skilled and have an equal chance of winning each position. In reality, there may be differences in skill levels, which would affect the probabilities of each possible outcome.

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2.2

Question:

Brody bought 17 chicken wings for $37.40. What's the unit cost of one wing?

Solution given:

17 chicken wings = $37.40

1chicken wings =$37.40/17*1=$2.2

2.2

Answer: 2√5 - 3

Step-by-step explanation:

\($$Simplify the following:$\sqrt{29-12 \sqrt{5}}$$$\begin{aligned}&29-12 \sqrt{5}=9-12 \sqrt{5}+20=9-12 \sqrt{5}+4(\sqrt{5})^{2}=(2 \sqrt{5}-3)^{2}: \\&\sqrt{\left((2 \sqrt{5}-3)^{2}\right)}\end{aligned}$$Cancel exponents. $\sqrt{(2 \sqrt{5}-3)^{2}}=2 \sqrt{5}-3$ :\\Answer:$$2 \sqrt{5}-3$$\)