A plumbing bill was $200. This included $50 for parts and $25 per hour for labor. Find the number of hours of labor.

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

\( - \frac{1}{6} \)

Step-by-step explanation:

\( - \frac{1}{2} + \frac{1}{3} = - \frac{1}{6} \)

(a) To find the exact cost of producing the 71st food processor, we plug in x=71 into the cost function C(x) = 1900 + 90x - 0.4x^2.

C(71) = 1900 + 90(71) - 0.4(71)^2

C(71) = 1900 + 6390 - 1783.6

C(71) = 6506.4

Therefore, the exact cost of producing the 71st food processor is $6,506.40.

(b) The marginal cost is the derivative of the cost function with respect to x.

C'(x) = 90 - 0.8x

To approximate the cost of producing the 71st food processor using the marginal cost, we first calculate the marginal cost at x=70:

C'(70) = 90 - 0.8(70)

C'(70) = 90 - 56

C'(70) = 34

This means that the cost of producing the 71st food processor will increase by approximately $34 if one more unit is produced.

So, to approximate the cost of producing the 71st food processor using the marginal cost, we add the marginal cost at x=70 to the cost of producing the 70th food processor:

C(70) = 1900 + 90(70) - 0.4(70)^2

C(70) = 1900 + 6300 - 1960

C(70) = 6240

Approximate cost of producing the 71st food processor = $6,240 + $34

Approximate cost of producing the 71st food processor = $6,274

Therefore, using the marginal cost, we can approximate the cost of producing the 71st food processor to be $6,274.

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The correct option is C. Green image of triangle ABC.

How to find the rotated shape or coordinates of image about origin?

As we know that triangle ABC, is rotated 270° counterclockwise about the origin. So, the algebraic rule for a figure is,

90° Clockwise or 270° counter clockwise, (x,y) = (y,-x)

As, C(-3,3) which is equal to (3,3) from the algebraic rule.

And (3,3) belongs to 1st quadrant i.e. green image is the correct answer.

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Triangle below represents is  option  C. Green image of triangle ABC.

A triangle is a geometric shape with three sides and three angles. It is one of the most fundamental shapes in geometry and is used extensively in mathematics, physics, engineering, and many other fields. Triangles are often classified based on their angles and sides.

As we know that triangle ABC, is rotated 270° counterclockwise about the origin. So, the algebraic rule for a figure is,

90° Clockwise or 270° counter clockwise, (x,y) = (y,-x)

As, C(-3,3) which is equal to (3,3) from the algebraic rule.

And (3,3) belongs to 1st quadrant i.e. green image is the correct answer.

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

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Answer:

2

Step-by-step explanation:

Answer:

the answer to the question is 2

Check the picture below.

Step-by-step explanation:

the domain of a function is always the interval or set of all valid input values (usually x, but here t).

the range is the interval or set of all valid result values (usually y or f(x), here h(t)).

as the graph shows, the function works only for values of t starting at 0 (at 0 seconds the object has 0 ft height, it is still on the ground and about to launch).

and it ends at t = 7.

obviously the object hits the ground after 7 seconds again after coming back down. so, the height function does not make any sense for values of t after that.

so, again, the domain is

0 <= t <= 7

Answer:

Step-by-step explanation:

The difference in the values of the two cars when they are each 7 years old is equal to $6,000.

In order to determine the difference in the values of the two cars, we would have to write an equation that models the price of the cars after a length of time, by using the data points shown in the graph above.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For Car A, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (9 - 12)/(4 - 2)

Slope, m = -3/2

Slope, m = -1.5

At point (4, 9), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 9 = -1.5(x - 4)

y = -1.5x + 15

In 7 seven years, the value of Car A is given by:

y = -1.5x + 15

y = -1.5(7) + 15

y = $4,500

Note: The negative sign indicates that the value of the car is depreciating.

For Car B, we have:

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (10 - 18)/(5 - 1)

Slope, m = -8/4

Slope, m = -2

At point (5, 1), a linear equation for car's value can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - 1 = -2(x - 5)

y = -2x + 11

In 7 seven years, the value of Car B is given by:

y = -2x + 11

y = -2(7) + 3.5

y = $10,500

Now, we can determine the difference as follows:

Difference = $10,500 - $4,500

Difference = $6,000.

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The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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Answer:

M=(2,-2)

Step-by-step explanation:

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

M=(4/2,-4/2)

M=(2,-2)

Answer:

\(\frac{1}{72}\)

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) ⇔ \(\frac{1}{a^{m} }\) thus

\(2^{-3}\) = \(\frac{1}{2^{3} }\) = \(\frac{1}{8}\)

\(3^{-2}\) = \(\frac{1}{3^{2} }\) = \(\frac{1}{9}\)

Then

\(\frac{1}{8}\) × \(\frac{1}{9}\) = \(\frac{1}{72}\)

Answer:

1/72.

Step-by-step explanation:

2^-3 = 1 / 2^3 = 1/8.

3^-2 = 1/3^2 = 1/9

So the answer is 1/8 * 1/9

= 1/72.

Answer:

BRO IS GERMAN LOL

Step-by-step explanation:

The solution to one half cubed − 2 ÷ square root of 64 is negative one eighth

The expression is given as:

one half cubed − 2 ÷ square root of 64

Rewrite the expression properly as follows:

(1/2)^3 − 2/√64

Take the square root of 64

(1/2)^3 − 2/8

Evaluate the quotient of 2 and 8

(1/2)^3 − 1/4

Take the cube of 1/2

1/8 - 1/4

Evaluate the difference

-1/8

Hence, the solution to one half cubed − 2 ÷ square root of 64 is negative one eighth

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Answer:

100 cubic in

Explanation

step 1: divide the figure into two

step 2 : find area then multiply by height of the cuboid

step 3 : add both

Answer:

The answer is 100.

Step-by-step explanation:

Volume = weight times height times length = 5 times 1 times 8 = 40

Volume = weight times height times length = 5 times 2 times 6 = 60

So now that we have the volume of each rectangular prism, we must add them together to get the full volume.

60 + 40 = 100

The word phrase for h + 6 is Six more h or the sum of six and h.

Converting algebraic expression to word phrase:

An algebraic expression is a mathematical phrase that uses variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Converting an algebraic expression to a word phrase means expressing the mathematical expression in words.

This can be useful in situations where mathematical symbols may not be understood or when communicating mathematical concepts to someone who may not be familiar with them.

Here we have the expression h + 6

Where 6 is added to h

Hence,

The word phrase for h + 6 is Six more h or the sum of six and h.

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Answer:

she will start making it at 10 am

When the diagonal of a rectangle splits the rectangle into two producing angles 30 - 60 - 90 the sides of the rectangle is

Area of a rectangle is solved to get 191 square in

The problem is solved using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The shape describes a right triangle of

opposite = width

adjacent = length

hypotenuse = diagonal

The dimensions are calculated using SOH and CAH

sin 30 = opposite / hypotenuse

sin 30 = width / 21

width = 21 * sin 30

width = 10.5

For the length

cos 30 = adjacent / hypotenuse

cos 30 = length / 21

length = 21 * sin 30

length = 18.19

Area of a rectangle = length * width

Area of a rectangle = 18.19 * 10.5

Area of a rectangle = 190. 995

Area of a rectangle = 191 square in

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Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

<BAC ≅ BCA by rule Base angle theorem

Step-by-step explanation:

What we know:

BAC = DAC

BC = BA

ΔBCA is an isosceles so ∠BCA  =  ∠DCA and ∠BAC

and we found that out by base angle theorem since

Base angle Theorem  = Two base angles of a icosceles triangle are equal.

And since ΔBCA is an isoceles then ∠A and ∠C will be equal. And so we can prove BC is a parallel to AD

The proof that BC ∥ AD from the given statements is that;

BC ∥ AD because of the definition of alternate angles

We are given;

AB = BC  

 AC is ∠ bisector of ∠BAD

Since AC is the angle bisector of ∠BAD, it means that;

∠BAC  = ∠DAC (definition of a bisected angle)

Now, since AB = BC, it means that ΔBCA is an isosceles triangle.

Thus; ∠BCA = ∠BAC  (base angle theorem)

Now, since ∠BCA = ∠BAC, and ∠BAC  = ∠DAC, we can say that;

∠BCA = ∠DAC

This means  ∠BCA and ∠DAC are alternate angles. Thus, we can say that AC is the transversal line carrying the two equal angles.

Thus, we can say that BC is parallel to AD as they are the parallel lines cut by the transversal line AC.

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The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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Answer: 85

Step-by-step explanation:

Answer:

2248+2224.91= 4472.91

Step-by-step explanation:

A = $2,248.00

I = A - P = $248.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3.1%/100 = 0.031 per year.

Solving our equation:

A = 2000(1 + (0.031 × 4)) = 2248

A = $2,248.00

The total amount accrued, principal plus interest, from simple interest on a principal of $2,000.00 at a rate of 3.1% per year for 4 years is $2,248.00.

A = $2,224.91

A = P + I where

P (principal) = $2,000.00

I (interest) = $224.91

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.7/100

r = 0.027 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,000.00(1 + 0.027/1)(1)(4)

A = 2,000.00(1 + 0.027)(4)

A = $2,224.91

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,000.00 at a rate of 2.7% per year compounded 1 times per year over 4 years is $2,224.91.

If repeats are forbidden, the provided letters u, v, w, x, y, and z can be used to create 8 lists of length 3, each of which has a w or u in the second entry.

We can apply the inclusion-exclusion concept to resolve this issue.

First, let's determine how many total lists of length three can be created using the provided letters without any limitations. There are six options for the first submission, five for the second (since it must be either w or u), and four for the third (since no characters can be repeated). Thus, there are a total of the following lists:

6 × 5 × 4 = 120

Next, let's count the number of lists of length 3 that do not have a w or u in the second entry. We have 6 choices for the first entry, 4 choices for the second entry (since we can't choose w or u), and 4 choices for the third entry (since we can't repeat any letters). Thus, the total number of such lists is:

6 × 4 × 4 = 96

Similarly, we can tally the number of lists of length 3 lacking a w or u in the first entry as well as the number of lists of length 3 lacking a w or u in either the first or second entry. Which are:

4 × 5 × 4 = 80 (no w or u in first entry)

4 × 4 × 4 = 64 (no w or u in first or second entry)

Finally, we can use the principle of inclusion-exclusion to count the number of lists that have a w or u in the second entry. This is:

120 - 96 - 80 + 64 = 8

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The calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

An engine additive is being tested to see whether it can effectively increase gas mileage for a number of vehicles. Twenty assorted vehicles had their gas mileage, in miles per gallon, measured. Then, the engine additive was placed into each of the engines, and the gas mileage was measured again. Let µd be the true mean difference in the gas mileage before and after the engine additive is placed into the engines. We want to test the hypothesis that the engine additive has no effect. The null hypothesis is: H0: µd = 0The alternative hypothesis is: Ha: µd > 0 (one-tailed test)Assuming that the difference in gas mileage before and after the engine additive is approximately normally distributed, we can use a one-sample t-test. The test statistic is given by: $$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$$Where, $\bar{x}$ is the sample mean difference in gas mileage, μ is the hypothesized population mean difference, s is the sample standard deviation of the differences, and n is the sample size. We can use a significance level of α = 0.05.To determine the critical value of the t-distribution, we need to find the degrees of freedom (df). Since we have a sample size of n = 20, we have n - 1 = 19 degrees of freedom. Using a t-distribution table with 19 degrees of freedom and a significance level of 0.05 for a one-tailed test, we get a critical value of t = 1.734. If the calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

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300-275 = 25

25/300 × 100%

= 25/3 %

= 8.3 % (approx.)

brainliest plz

The major assumption in factor analysis (but not PCA) is that the observed variables are caused by a smaller number of underlying, unobserved (latent) variables, which are called factors.

Factor analysis and principal component analysis (PCA) are both techniques used for data reduction and dimensionality reduction. However, they differ in their assumptions and goals.

In factor analysis, the focus is on identifying the underlying latent variables (called factors) that explain the observed correlations among a set of variables. The major assumption in factor analysis is that the observed variables are caused by a smaller number of underlying factors. These factors cannot be directly measured, but are inferred from patterns of correlations among the observed variables. The goal of factor analysis is to extract these factors and to estimate how much each factor contributes to each observed variable.

In contrast, PCA is a technique that focuses on finding a linear combination of the original variables that explain the maximum amount of variance in the data. The major assumption in PCA is that the observed variables are not caused by any underlying factors, but are simply linearly related to each other. The goal of PCA is to find a set of orthogonal (uncorrelated) principal components that capture the maximum amount of variance in the data.

Therefore, the major assumption in factor analysis (but not PCA) is that there are underlying latent variables (factors) that cause the observed correlations among the variables.

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