A carpenter makes bookcases in 2 sizes, large and small. It takes 4 hours to make a
large bookcase and 2 hours to make a small one. The profit on a large bookcase is
$35 and on a small bookcase is $20. The carpenter can spend only 32 hours per
week making bookcases and must make at least 2 of the large and at least 4 of the
small each week. How many small and large bookcases should the carpenter make
to maximize his profit? What is his profit?

Step-by-step explanation:

All of the angles in a triangle add up to 180. Since we know that the box in the left corner is 90° because it is a right angle then we just need to find x

2x+90=180

subtract 90

2x=90

divide by 2

x=45

Hope that helps :)

Answer:

Step-by-step explanation:

The two xs are contained in the same triangle.

Every triangle has 180 degrees.

2*x + 90 = 180                  Subtract 90 from each side

2x +90 - 90 = 180 - 90

2x = 90                             Divide by 2

2x/2 = 90/2

x = 45

(1) Price (P) is an increasing function of income (Y) based on the assumption that S'(P) > 0, 37¹ D(Z,Y) < 0, and By Dr. = D(Z,Y) > 0. (2) Price (P) is an indeterminate function of tax (T) based on the given information.

(1) To determine the relationship between price (P) and income (Y), we need to analyze the sign of dP/dY, the derivative of price with respect to income. From the assumptions given, S'(P) > 0 implies that the supply function is strictly increasing with respect to price. Additionally, 37¹ D(Z,Y) < 0 implies that the demand function is strictly decreasing with respect to price. By Dr. = D(Z,Y) > 0 indicates that the demand function is strictly increasing with respect to Y. Therefore, when we differentiate equation (1) with respect to Y, we get S'(P) - D'(Z,Y) * (dZ/dY) = 0. Since S'(P) > 0 and D'(Z,Y) < 0, the sign of (dP/dY) depends on the sign of (dZ/dY). However, the information given does not specify the relationship between Z and Y, so we cannot determine the exact relationship between P and Y.

(2) Similarly, to determine the relationship between price (P) and tax (T), we need to analyze the sign of dP/dT, the derivative of price with respect to tax. Unfortunately, the information provided does not include any direct assumptions or relationships regarding the derivatives of the supply and demand functions with respect to tax. Therefore, based on the given information, we cannot determine the relationship between price (P) and tax (T).

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Answer:

5

Step-by-step explanation:

Answer:  5

Step-by-step explanation:

We rerange the number in 1,2,3,4,9,12,13

The median is 4, and a number x between 4 and 9.

We have 4.5 for median, which is the average of 4 and x.

(4 + x) /2 = 4.5

4 + x = 9

x = 5

A. P(62 or over and has a loan)= 4.05%

B. P(has a loan)=48.6%

C.  P(62 or over and has a loan)=0.486

15% of the population are 62 or over

27% of those 62 or over have loans

54% of those under 62 have loans

To find the probabilities that a person fits into the following categories:

a) 62 or over and has a loan:

P(62 or over) = 15% = 0.15

P(62 or over and has a loan) = P(62 or over) * P(have a loan|62 or over)

= 0.15 * 0.27

= 0.0405 or 4.05%

b) Has a loan:

P(has a loan) = P(62 or over) * P(have a loan|62 or over) + P(under 62) * P(have a loan|under 62)

= 0.15 * 0.27 + 0.85 * 0.54

= 0.486 or 48.6%

c) P(62 or over and has a loan) = P(62 or over) * P(have a loan|62 or over)

= 0.15 * 0.27

= 0.0405 or 4.05%

P(62 or over) = 0.15 and P(have a loan) = 0.486

So, P(62 or over and has a loan) ≠ P(62 or over) * P(have a loan)

Hence, the events that a person is 62 or over and that the person has a loan are not independent.

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Answer:

first is x second is y third is -2-3

Step-by-step explanation:

make me brainliest or yo gay

Answer:

Molecules

Step-by-step explanation:

I hope this helps!

Answer:

3/8

Step-by-step explanation:

Total = 8

Probability of blue: 1/8

Probabiity of white: 2/8

Probbility of blue AND white:

1/8 + 2/8

3/8

Answer:

3/8

Step-by-step explanation:

because there are 3 possbile places the spinner can go, and that there are 8 sections, the answer is 3/8

Answer:

I think C or D

Step-by-step explanation:

(A) The confidence level for the results of the poll is 90%

(B) The confidence interval is (58.411, 69.589).

(C) The range of the mean number of classmates who could expect better dental checkups is approximately 1867 to 2229.

(A) The confidence level for the results of the poll is 90%. This means that there is a 90% probability that the true percentage of users reporting better dental checkups falls within the stated range.

(B) To determine the confidence interval, we need to consider the margin of error. The margin of error is calculated by multiplying the critical value (obtained from a standard normal distribution table) by the standard deviation of the sample proportion. In this case, the standard deviation is determined by the given accuracy of 3.4 percent points.

Using a critical value of 1.645 (corresponding to a 90% confidence level), we can calculate the margin of error as 1.645 times 3.4, which equals 5.589.

To find the confidence interval, we subtract and add the margin of error from the reported percentage of users who reported better dental checkups. Subtracting 5.589 from 64 gives us a lower bound of 58.411, and adding 5.589 gives us an upper bound of 69.589. Therefore, the confidence interval is (58.411, 69.589).

(C) If all 32 students in a mathematics class used this toothpaste, the range of the mean number of classmates who could expect better dental checkups can be calculated by applying the confidence interval to the sample size. Taking the lower bound of the confidence interval (58.411) and multiplying it by 32, we get 1867.552. Rounding down, we have a minimum estimate of 1867 classmates who could expect better dental checkups.

Similarly, multiplying the upper bound of the confidence interval (69.589) by 32 gives us 2228.448. Rounding up, we have a maximum estimate of 2229 classmates who could expect better dental checkups.

Therefore, the range of the mean number of classmates who could expect better dental checkups is approximately 1867 to 2229.

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The dimensions of the provided rectangle's sides ST and PT are 4 and 4√3 units, respectively.

Given: PFST is a rectangle with a radius of four and angle SOT of 60 degrees.

We must locate ST and PT.

We will thus apply the idea of cosine of an angle to find the same.

The law of cosine is expressed as follows for a triangle with sides α, β, and γ with angles, and:

[tex]\mathrm {b^2=a^2+c^2-2ac\cdot \cos \left(\beta \right)}[/tex]

Since the radius of the circle O is made up of the points OS, OP, OF, and OT, their measurements are all equal.

Now, considering the Δ SOT for ST.

We have,

β = 60° and a and c = 4.

Applying the law:

[tex]\mathrm b=\sqrt{4^2+4^2-2\cdot \:4\cdot \:4\cos \left(60^{\circ \:}\right)}[/tex]

Solving we get,

b = 4

Therefore, ST = 4 units.

Similarly, considering the Δ POT for PT.

Here, ∠POT = 180° - 60° [linear pair]

∠POT = 120°

So, we have,

β = 120° and a and c = 4.

Applying the law:

[tex]\mathrm b=\sqrt{4^2+4^2-2\cdot \:4\cdot \:4\cos \left(120^{\circ \:}\right)}[/tex]

Solving we get,

b = 4√3 units

Therefore, PT = 4√3 units.

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The figure is given below:

Answer:

Origin

Step-by-step explanation:

Origin is the starting points (0,0)

Hope this helped :)

Answer:

I got 9.03

Step-by-step explanation:

the formula is V=pir2h

(pi, radius squared, and height)

Answer:

choice 2) 4/3πr³

Step-by-step explanation:

The volume of the sphere is 678.24 u³  

V = ⁴⁄₃ * π * (6u)³

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius  = 6 units

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * (6u)³

V = 4.187 * 216 u³

V = 678.24 u³

The volume of the sphere is 678.24 u³

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In order to interpolate between the two points (3,0) and (4,-3), the linear polynomial p(x) is equal to -3x + 3, and this equation is employed. The value of the constant term is 3, but the value of the coefficient x is -3.

A linear polynomial is a type of polynomial that has only one degree of complexity. This suggests that it can be stated using the formula p(x) = axe + b, where a and b are values that continue to be the same. a and b are values that remain unchanged. These two sentences inform us that the value of p(3) is zero, and that the value of p(4) is negative three. When we enter these values into the equation p(x) = axe + b, we obtain the two equations that are presented further down in this section:

0 = 3a + b -3 = 4a + b

Following the resolution of the equations for a and b, we find that the respective solutions are a = -3 and b = 3. Since this is the case, the linear polynomial p(x) that interpolates the two points (3,0) and (4,-3) is -3x + 3, as was demonstrated in the preceding sentence.

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Answer: 97/100

Step-by-step explanation:

Answer:

The answer is 0.97 or 97/100

Step-by-step explanation:

9/10 = 0.9

7/100 = 0.07

0.9 + 0.07 = 0.97

Hope this helps!

Please mark as brainliest!

Answer:

[tex] A = \dfrac{8x}{3x + 1} [/tex]

Step-by-step explanation:

[tex]A = \dfrac{bh}{2}[/tex]

[tex] A = \dfrac{16x^2}{9x^2 - 1} \times \dfrac{6x^2 - 5x + 1}{2x^2 - x} \times \dfrac{1}{2} [/tex]

[tex] A = \dfrac{(16x^2)(6x^2 - 5x + 1)}{2(9x^2 - 1)(2x^2 - x)} [/tex]

[tex] A = \dfrac{(16x^2)(2x - 1)(3x - 1)}{2(3x - 1)(3x + 1)(x)(2x - 1)} [/tex]

[tex] A = \dfrac{8x}{3x + 1} [/tex]

Answer:

your answer to this question is 35

Answer: 11

Explanation: You did everything right in terms of the steps you took. It looks like you accidentally wrote "1" instead of "-4" as the answer to "2(-2)".

Based on the given information, the correct answer is: c) 105 observations

To calculate the required sample size, we can use the formula:

n = (Z * σ / E)^2

Where:

n = sample size

Z = Z-score corresponding to the desired level of confidence (for a 99% confidence level, Z = 2.576)

σ = standard deviation or variability

E = desired margin of error

Given:

Variability (standard deviation) = 2

Margin of error (E) = 0.5

Z = 2.576 (corresponding to a 99% confidence level)

Plugging in the values into the formula:

n = (2.576 * 2 / 0.5)^2

n = 10.304^2

n ≈ 106.01

Rounding up to the nearest whole number, the researchers would need at least 106 observations to obtain a margin of error no larger than 0.5 for a 99% confidence interval. Therefore, the correct answer is c) 105 observations.

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Answer:

I would need to see the variables to answer this questions.

Answer:

4 6/10+ 6 8/10= 11 4/10

Step-by-step explanation:

The 4+6=10, and 6/10+8/10=14/10 which converts to 1 4/10. 10+1 4/10= 11 4/10

Answer:

11 and 4/10

Step-by-step explanation:

Hope this helps!

Answer/Step-by-step explanation:

a. Given that 32° is the reference angle, thus:

Hypotenuse is the side opposite to the right angle

Opposite side is opposite to the defence angle = x

Adjacent side is adjacent to defence angle = 15 m

b. Recall SOHCAHTOA.

We know the length of the adjacent side. We are asked to find x, which is the opposite side. So, we are dealing with Opposite side and Adjacent side.

The trigonometric function we will use to find x would be TOA:

That is,

Tan θ = Opp/Adj

c. Applying TOA:

Tan θ = Opp/Adj

θ = 32°

Opp = x

Adj = 15 m

Plug in the values

Tan 32 = x/15

15 × Tan 32 = x

9.37304028 = x

x = 9.4 (nearest tenth)

Answer:

the answer is -3.375 hope this helped

Formula for a cone's volume: V=1/3hπr²

So...

1) V = 1/3*10*π*5^2

(We got the 5 from the diameter and divided it by 2 to get the radius).

Answer: I got 261.799 m^3.

After simplifying the inequality we get 6 < 28 which is true. Hence the given statement is true.

An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.

It signifies that the expression on the left should be more or smaller than the expression on the right, or vice versa. Literal inequalities occur when the relationship between two algebraic expressions is defined using inequality symbols.

The given inequality is:

3(2 - b) < 10 - 3(b-6)

Distribute the number inside the bracket,

6 - 3b < 10 - 3b + 18

Add 3n on both sides,

6 < 10 + 18

Simplifying it,

6<28

Hence,

The given statement is true.

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The complete question is:

Check whether the statement is true or false:

3(2 - b) < 10 - 3(b-6)

a. To determine if the two populations of crawfish from Devon and Cornwall have the same mean carapace length, we can use the two-sample t-test.

This test compares the means of two independent samples to assess whether they are significantly different.

We can calculate the sample means and sample standard deviations for both groups:

Next, we calculate the t-value using the formula:

To determine if this t-value is statistically significant, we need to compare it to the critical value from the t-distribution for the given degrees of freedom

If the calculated t-value falls outside the critical region, we can reject the null hypothesis and conclude that the two populations have different mean carapace lengths. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the mean carapace length between the two populations.

b. To answer the question using the Wilcoxon rank sum test, we need to combine the observations from both samples, assign ranks based on their relative positions, and calculate the sum of ranks for one of the samples (either Devon or Cornwall). The null hypothesis for this test is that the two distributions are the same.

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Answer:

B

Step-by-step explanation:

It is what it is

Answer:

D?

Step-by-step explanation:

Im not exactly sure

Answer:

i believe the answer you're looking for is A/ 15

Step-by-step explanation:

hi there!

so its been a quick minutes since i have done a stem and left plot but the question is asking how many quarters had less then 20 points scored

here is a stem and leaf plot that i had made to make it easier for me to explain this problem it you!

_stem__|__leaf_____________________________________

         0   |  0, 2, 3, 7, 7, 8, 9

         1    |  0, 1, 4, 4, 4, 7, 7, 7

         2   |  0, 1, 7, 8, 9

         3   |

         4   | 2, 3, 6, 8

as you can see, i bolded each number that was less then the number 20, if we counted how many of the numbers that were bold in that stem and leaf plot the number would be 15!

sorry this was such a short answer! but i do hope i helped you with this :)

Answer:

i dont know this is to hard

Step-by-step explanation:

pay back for saying that on my question