Find the value of f(–2) for the function f(x) = 4x + 10.

A. –3
B. –2
C. 2
D. 18

The present age of the Father is 35 and the age of the Son is 15 years after solving the given problem.

By examining the given problem we can solve it in the following way:

Present age:

Let x = Son's present age

x + 20 = Father's present age

5 years ago:

x - 5 = Son's age 5 years ago

x + 20 -5 = father's age 5 years ago

Father's age 5 years ago = 3( Son's age 5 years ago )

x + 20 - 5 = 3 (x - 5)

x + 15 = 3x - 15

2x = 30

x = 15

x = 15, Son's present age

x + 20 = 35 = father's present age.

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Answer:

y - 2 = 3 (x - 4) - Point-Slope form.

y = 3x - 10 - Slope-intercept form.

Step-by-step explanation:

I will solve by using the formula:

y - y1 = m (x - x1)

Substitute:

y - 2 = 3 (x - 4)

This is the answer written in point-slope form.

I will put it into slope-intercept form.

Distribute:

y - 2 = 3x - 12

add 2 to both sides:

y = 3x - 10

Point (4 , 2) with a slope of 3 as an equation written in slope-intercept form looks like:

y = 3x - 10

The equation in point-slope form is y = 3x - 10 for the line that passes through the point at (4,2) with the given slope m=3.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

Given that line that passes through the point at (4,2)

Let the equation in point-slope form would be

⇒ y - y₁ = m(x -x₁ )

Here, slope m = 3, x₁ = 4 and  y₁ = 2

Substitute the values in the equation, and we get

⇒ y - 2 = 3 (x - 4)

⇒ y - 2 = 3x - 12

Add 2 to both sides of the equation

⇒ y = 3x - 10

Hence, the equation in point-slope form is y = 3x - 10 for the line that passes through the point at (4,2) with the given slope m = 3.

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In the given figure, where triangle QPS = triangle SRQ, the value of

a. x = 47°

b. ∠PQS = 32°

c. ∠PSR = 74°

A triangle is a 3-sided polygon that is occasionally (though not very frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which might be the same.

In a right triangle, the two sides opposite the right angle are referred to as the hypotenuse, and the other two sides are referred to as the legs. All triangles are bicentric and convex. The triangle's interior is that part of the plane it encloses; the exterior is the rest.

Given that  ∆QPS ≈ ∆SRQ

a) ∠QPS = ∠QRS

106° = 2x + 12

106° - 12 = 2x

2x = 94°

x = 47°

b) ∠RSQ = ∠PQS

∠SQR + ∠SRQ + ∠RSQ = 180°

42° + 2(47°) + 12 + ∠RSQ = 180°

148 + ∠RSQ = 180°

∠RSQ = 180° - 148°

∠RSQ = 32°

∠PQS = 32°

c) ∠PSR = ∠PSQ + ∠RSQ

[ ∠PSQ = 42° = ∠SQR ; ∠RSQ = 32°]

∠PSR = 42° + 32°

∠PSR = 74°

Thus, In the given figure, where triangle QPS = triangle SRQ, the value of x = 47°, ∠PQS = 32°, ∠PSR = 74°.

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Answer:

y=-2x+10

Step-by-step explanation:

i graphed it i graphed all of them

Answer:

y-2x-2

Step-by-step explanation:

The way I would do this is by first using the information given and making an equation in point-slope form, before bringing it to y=mx+b.

We know that the slope is -2, and we have a point, (2,-6). The formula for equations in point slope form is \(y-y_{1} =m(x-x_{1} )\). So, we can insert the given information into this formula to get \(y+6=-2(x-2)\).

Next, we distribute the slope to the the parenthesis to get \(y+6=-2x+4\)

Then, we subtract 6 from both sides to get \(y=-2x-2\)

Since this equation is now in the form \(y=mx+b\), the answer is \(y-2x-2\)

Hope this helps! :)

The OLS estimate of the slope (β₁) in the population regression model is given by:

\(\[\beta_{1} = \frac{\sum_{i=1}^{n} (STR_{i} - \text{mean(STR)})(TestScore_{i} - \text{mean(TestScore)})}{\sum_{i=1}^{n} (STR_{i} - \text{mean(STR)})^2}\]\)

where \(\( STR_{i} \)\) represents the value of the STR variable for observation i, \(\( TestScore_{i} \)\) represents the corresponding \(TestScore\) for that observation, and \(\( \text{mean(STR)} \)\) and \(\( \text{mean(TestScore)} \)\) represent the sample means of the respective variables.

To estimate the OLS (Ordinary Least Squares) estimate of the slope (β₁) in the population regression model:

\(\[ \text{TestScore}_{i} = \beta_{0} + \beta_{1} \text{STR}_{i} + u_{i} \]\)

where \(\( E[u_{i} \mid \text{STR}_{i}] = 0 \)\), we need to perform several calculations.

1. Calculate the sample means of the independent variable (STR) and the dependent variable (TestScore):

  Let's assume we have n observations. Calculate the mean of STR (mean(STR)) and the mean of TestScore (mean(TestScore)).

2. Calculate the sum of the cross-deviations and the sum of squared deviations:

  Compute two sums:

  - Sum of the cross-deviations:

\(\(\sum_{i=1}^{n} (STR_{i} -\)\(\text{mean(STR)})(TestScore_{i} - \text{mean(TestScore)})\)\)

  - Sum of squared deviations of STR:

\(\(\sum_{i=1}^{n} (STR_{i} - \text{mean(STR)})^2\)\)

3. Calculate the OLS estimate of the slope (β₁):

  Using the sums calculated in step 2, the OLS estimate of the slope is given by:

 \(\(\beta_{1} = \frac{\sum_{i=1}^{n} (STR_{i} - \text{mean(STR)})(TestScore_{i} - \text{mean(TestScore)})}{\sum_{i=1}^{n} (STR_{i} - \text{mean(STR)})^2}\)\)

This estimate represents the average change in TestScore associated with a one-unit change in STR, assuming other variables are held constant.

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Answer:

I think A

Step-by-step explanation:

I am not quite sure what this is asking, but based off of what I can tell it should be A.

Hope this helps :)

Answer:

1 - x-axis, 2 - y-axis, 3 - y-axis, 4 - x-axis

Step-by-step explanation:

The function for the rate of increase in total cost in material cost is dC/dx = 2 + 44y, and the function for the rate of increase in total cost for each $1 per hour increase in labor costs is dC/dy = 8 + 44x.

(a) To find the function that describes the rate at which the total cost increases for each increase of $1 per pound in material cost, we need to differentiate the total cost function with respect to x, while holding y constant.

Given the total cost function C(x, y) = 38 + 2x + 8y + 44xy, we differentiate with respect to x:

dC/dx = d(38 + 2x + 8y + 44xy)/dx = 2 + 44y

Therefore, the function that describes the rate at which the total cost increases for each increase of $1 per pound in material cost, with labor costs held constant, is dC/dx = 2 + 44y.

(b) Similarly, to find the function that describes the rate at which the total cost increases for each $1 per hour increase in labor costs, we differentiate the total cost function with respect to y, while holding x constant.

Differentiating C(x, y) = 38 + 2x + 8y + 44xy with respect to y, we get:

dC/dy = d(38 + 2x + 8y + 44xy)/dy = 8 + 44x

Therefore, the function that describes the rate at which the total cost increases for each $1 per hour increase in labor costs, with material costs held constant, is dC/dy = 8 + 44x.

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Answer:

(c-1)(3c-1)

Step-by-step explanation:

3c² - 4c +1

get rid of square and write like this : (3c ... )(3c....   )

you need to din what multiplies to (3 x 1) = 3 but also adds to -4

-3 + -1 = -4

-1 x -1 = 3

put into the brackets

(3c -3 )(3c-1 )

simplify

(c-1)(3c-1)

The time taken for the particle to travel more than 8 meters from the point of projection is 0.59 s.

The time taken for the particle to travel more than 8 meters from the point of projection is calculated as follows;

s = v₀t + ¹/₂at²

8 = 12t + (0.5 x 5)t²

8 = 12t + 2.5t²

2.5t² + 12t  - 8 = 0

solve the equation using formula method

t = 0.59 s

Thus, the time taken for the particle to travel more than 8 meters from the point of projection is 0.59 s.

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\(\\ \tt\hookrightarrow 15x-10y=-10--(3)\)

\(\\ \tt\hookrightarrow 15x-9y=-12--(4)\)

Subtracting

\(\\ \tt\hookrightarrow -y=+2\)

\(\\ \tt\hookrightarrow y=-2\)

Put in eq(1)

\(\\ \tt\hookrightarrow 3x+4=-2\)

\(\\ \tt\hookrightarrow x=-2\)

Answer:

x = -2 and y = -2

Explanation:

Given equations:

3x - 2y = -2

5x - 3y = -4

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

Make the value before y equal:

( 3x - 2y = -2 ) * 3

9x - 6y = -6 .........equation 1

( 5x - 3y = -4 ) * 2

10x - 6y = -8 ...........equation 2

solve them by elimination:

10x - 6y = -8

-9x + 6y = +6

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

x = -2

If x is -2

Then y:

10x - 6y = -8 .................from equation 2

-6y = -8-10x

y = [-8 - 10(-2)]/-6

y = -2

The Mode of the Price of Gas in the 50 states and Washington D.C. is $5.076. This is the value that appears most frequently in the dataset.

To calculate the Variance of the Price of Gas in the 50 states and Washington D.C., you can use the formula:

Variance = (Sum(X^2) / n) - (mean^2)

From the given data, Sum(X^2) is 1272.484440, and n (sample size) is 51. The mean can be calculated by finding the average of the quartiles Q1, Q2, and Q3, which is (4.724 + 5.076) / 2 = 4.900. Plugging these values into the formula, you can calculate the variance.

The Coefficient of Variation (CV) of the Price of Gas can be calculated as the ratio of the standard deviation to the mean, multiplied by 100 to express it as a percentage:

CV = (standard deviation / mean) * 100

To determine if the value of 6.434 for California is an outlier, you need to compare it to the mean and consider its distance in terms of standard deviations. If the value is more than 3 standard deviations away from the mean, it can be considered an outlier. However, without knowing the standard deviation of the dataset, it's not possible to determine if the given value is an outlier or not.

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Answer:

2.2%

Step-by-step explanation:

Use the percent error formula:

% error = | (approx - exact) ÷ approx | x 100

Plug in the approx. and exact values:

| (8.9 - 8.7) ÷ 8.9 | x 100

| (0.2) ÷ 8.9 | x 100

= 2.2

So, the percent error is 2.2%

Answer:1.2%

Step-by-step explanation:

∣experimental−actual∣

​

×100

The formula

∣

8.7

−

8.6

∣

8.6

×

100

8.6

∣8.7−8.6∣

​

×100

Plug in values

∣

0.1

∣

8.6

×

100

8.6

∣0.1∣

​

×100

Subtract

0.1

8.6

×

100

8.6

0.1

​

×100

Take the absolute value

0.0116279

×

100

0.0116279×100

Divide

1.16279

1.16279

Multiply by 100

1.2

%

1.2%

Answer:

y = (-3/2x) + (35/4)

Step-by-step explanation:

So the perpendicular line will have a slope that is the opposite reciprocal of the other line's slope. Solve for the original line's slope first:

2x - 3y = 7 --> -3y = -2x + 7 --> y = (2x/3) - (7/3)

So, the slope of the perpendicular line will be (-3/2x)

Solve for the y-intercept of the perpendicular like by using the linear equation and substituting in (2,8):

8 = (-3/(2*2)) + b --> (32/4) = -(3/4) + b --> b = (35/4)

So, y = (-3/2x) + (35/4)

Hope that helps! :D

Answer:

3x+1 is the correct answer

Answer:

3x + 1

Step-by-step explanation:

                       3x + 1          

x - 5     I 3x² - 14x - 5                   3x²÷x = 3x; (x-5)*3x = 3x² - 15x

              3x² - 15x                          Subtract

             -       +      

               0  +  x   - 5                       x ÷x = 1 ;  (x -5)*1 = x - 5

                       x   - 5                      Subtract

                     -     +    

                          0    

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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a. A 25-year mortgage at a rate of 10 %.

(i) Monthly payment: $970.41

(ii) Total amount of interest paid: $161,122.85

b) 15-year mortgage:

(i) Monthly payment: $1,133.42

(ii) Total amount of interest paid: $72,195.84

a) 25-year mortgage at a rate of 10%:

Let's calculate the monthly payment and the total amount of interest paid for this mortgage.

(i) Monthly Payment:

To calculate the monthly payment, we can use the formula for the monthly payment of a mortgage:

M = P * r * (1 + r)^n / ((1 + r)^n - 1),

where:

M is the monthly payment,

P is the principal amount (the price of the house minus the down payment),

r is the monthly interest rate (10% divided by 12 months),

n is the total number of monthly payments (25 years multiplied by 12 months).

P = $140,000 - 20% * $140,000

= $140,000 - $28,000

= $112,000

r = 10% / 12

= 0.10 / 12

= 0.00833333

n = 25 years * 12 months

= 300

Plugging these values into the formula, we get:

M = $112,000 * 0.00833333 * (1 + 0.00833333)^300 / ((1 + 0.00833333)^300 - 1)

Using a calculator, we find that the monthly payment is approximately $970.41.

(ii) Total Amount of Interest Paid:

To calculate the total amount of interest paid, we can subtract the principal amount from the total amount paid over the loan term.

Total amount paid = M * n

Total amount of interest paid = Total amount paid - P

Total amount of interest paid = ($970.41 * 300) - $112,000

Using a calculator, we find that the total amount of interest paid is approximately $161,122.85.

b) 15-year mortgage at a rate of 10%:

Let's calculate the monthly payment and the total amount of interest paid for this mortgage.

(i) Monthly Payment:

Using the same formula as above with adjusted values for n:

P = $112,000 (same as before)

r = 10% / 12

= 0.10 / 12

= 0.00833333

n = 15 years * 12 months

= 180

Plugging these values into the formula, we get:

M = $112,000 * 0.00833333 * (1 + 0.00833333)^180 / ((1 + 0.00833333)^180 - 1)

Using a calculator, we find that the monthly payment is approximately $1,133.42.

(ii) Total Amount of Interest Paid:

Using the same approach as before:

Total amount paid = M * n

Total amount of interest paid = Total amount paid - P

Total amount of interest paid = ($1,133.42 * 180) - $112,000

Using a calculator, we find that the total amount of interest paid is approximately $72,195.84.

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Answer:

3,2 i think but I could be wrong

Step-by-step explanation:

Step-by-step explanation:

Standard polynomial is:

\( - 20 {x}^{3} - 3 {x}^{2} + 4x\)

Leading co effecient is:

-20

This indicates that approximately 47.7% of the sampled subjects responded definitely or probably not beneficial to family planning.

From the given data, we can analyze the proportions of respondents who considered family planning beneficial and those who did not.

The proportion of respondents who responded definitely or probably beneficial is 651 out of 1245 sampled subjects. Therefore, the proportion can be calculated as:

Proportion = 651/1245 ≈ 0.523

This indicates that approximately 52.3% of the sampled subjects responded definitely or probably beneficial to family planning.

On the other hand, the proportion of respondents who responded definitely or probably not beneficial is 594 out of 1245 sampled subjects. The proportion can be calculated as:

Proportion = 594/1245 ≈ 0.477

This means that roughly 47.7% of the sampled participants indicated that family planning was either definitely advantageous or probably not beneficial.

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The support of X is [0,1].Hence, option (B) is the correct answer.

Given: There is an interval, B which is [0, 2]. Uniformly pick a point dividing interval B into 2 segments. Denote the shorter segment's length as X and taller segment's length as Y. We have to find X's support to find its distribution.Solution:The length of interval B is [0,2]. Now we have to uniformly pick a point dividing interval B into two segments. Denote the shorter segment's length as X and taller segment's length as Y.Now we will find the probability density function of X.

Since the points are uniformly chosen on interval B, the probability density function of X will be f(x)=1/B, where B is the length of interval B. Here, B=2.Now the length of interval X can be any number from 0 to 1 since X is the shorter segment. So, the support of X is [0,1]. Hence the probability density function of X is:f(x) = 1/2, 0 ≤ x ≤ 1, 0 elsewhereTherefore, the support of X is [0,1].Hence, option (B) is the correct answer.

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Data integration combines data collected from various platforms to increase its value for your company. It enables your staff to collaborate more effectively and provide more for your clients.So IT is important to integrate information.

The combining of data from diverse sources with various conceptual, contextual, and typographic representations is known as information integration. It is utilised for data aggregation and mining from unstructured or partially organised sources. You may connect all of your data, people, and processes in a single solution by using an integrated solution. Today's top HSEQ management teams regard this strategy as best practise. The justification for this is straightforward: it improves reporting, efficiency, uniformity, speed, and ease of use. An integrated report's main goal is to describe to financial capital providers how a company builds, protects, or loses value over time. As a result, it includes pertinent information, both financial and otherwise.

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assuming you mean question 35?

35. A or 4

Answer: A, 75.4 cm^3

Step-by-step explanation:

The formula for the volume of a cone is \(V = \pi r^{2} \frac{h}{3}\), but in this case \(\pi\) will be substituted for 3.14, as this is what the question requests.

If you look at the diagram, you can see that height (h) is 8cm and the radius (r) is 3cm (it shows the diameter is 6cm. Divided by 2 is 3cm).

We can substitue these values into the equation and we get:

\(V = 3.14(3)^{2}(\frac{8}{3} )\)

According to BEDMAS, we do exponents first.

\(V = 3.14 (9) (\frac{8}{3})\)

Then, with a scientific calculator (you can use DESMOS scientific calculator online) we can multiply these three values together.

We get:

\(V = 75.36 cm^{2}\)

Since we need to round to the nearest tenth, we end up with 75.4cm³, which is answer A

Answer:

Line A has a slope of -4

Line A and line B have the same slope

Step-by-step explanation:

Line A is in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.  As we can see, -4 is m in line A so -4 is the slope of line A.

If we have two points on a line, we can find the slope using the slope formula

\(m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }\), where x1 and y1 are one of the points and x2 and y2 come from the other point.

Thus, if we allow (-2, 1) to be x1 and y1 and (1, -11) to be x2 and y2,

\(m=\frac{-11-1}{1-(-2)}\\ m=-4\)

Since the slope of Line B is -4, it has the same slope as line A

Answer:

She will need to fill her spoon twice, once adding in the full amount, and the second adding half the amount.

3/4  ÷ 4/8

=3/4 * 2/1

=6/4

=1.5

So, that much amount would be needed o be added to the recipe during the two times

The value of the test statistic is **2.73**.

The test statistic is calculated using the following formula:

z = (sample proportion - population proportion) / standard error of the proportion

In this case, the sample proportion is 0.35, the population proportion is 0.32, and the standard error of the proportion is 0.014. Plugging these values into the formula, we get a test statistic of 2.73.

A z-score of 2.73 is significant at the 0.01 level, which means that there is a 1% chance that we would get a sample proportion of 0.35 or higher if the population proportion is actually 0.32. Therefore, we can reject the null hypothesis and conclude that there is enough evidence to support the claim that the percentage of residents who favor construction is over 32%.

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Answer:

when I find out the two others ill edit this,sorry i'm kinda slow lol

Step-by-step explanation:

Team     Wins    Losses

Tigers     20        

Vikings    25        10

Cougars   30       12

Pirates      35

There is still an negative you have to change the subtraction sign to an addition sign ALONG with the negative number

Answer:

The mistake was converting the expresssion

Step-by-step explanation: