If f() = 3 -3 and g(x) = 3x2 + x - 6, find (f+ g)(x).
O A. 3x?- 1x-3
B. 3x2 + x - 3
C. 4x2 - 9
D. 3x2 + x - 9

The length of JK is 10.4 units and length of J'H' is 3.1 units as the two triangles are similar

The triangles HJK and triangle H'J'K' are similar

We know that the sides of a similar triangle are proportional

Let us write a proportional equation to find JK and J'H'

JH/J'H' = HK/H'K' = JK/J'K'

12.4/J'H' = 9.6/2.4 = JK/2.6

12.4/J'H' = 4 = JK/2.6

Now equate each of the equations

12.4/J'H' = 4

12.4/4 =J'H'

J'H' = 3.1

Now 4 = JK/2.6

JK=4×2.6

JK=10.4

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The standard error of the mean for 100 samples having a mean of 44 and a standard deviation of 14 is 1.4

No. of samples = 100

The mean of those samples = 44

The standard deviation of those samples = 14

The standard error of the mean can be found using the formula

                                 \(\displaystyle \sigma_{\bar x} = \frac{\sigma}{\sqrt n}\)

where \(\displaystyle \sigma_{\bar x}\) is the standard error of the mean

          σ is the standard devaition

          n is the number of samples.

Let us substitute the known values in the above, we get

                              \(\displaystyle \sigma_{\bar x}\) = 14 / √100

                                   = 14 / 10

                                   = 1.4

Therefore, the standard error of the mean is 1.4

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Answer:

The equation x = -3y + 4 6y + 2x = 8 has infinite number of solutions.

Answer:

Exact Form:

2√7/7

Decimal Form:

0.75592894…

I believ this is right sry if it's not

The simplest radical form of the number \(\sqrt{\dfrac{4}{7}}\) is, \(\dfrac{2\sqrt{7} }{7}\)

Used the concept of the square root of a number that states that,

The square root of a number is the number that, when multiplied by itself, gives the original number.

Given that the number is,

\(\sqrt{\dfrac{4}{7}}\)

Simplify the expression by taking the square root of numbers as

Since, \(\sqrt{4} = \sqrt{2^2}\)

= \(2\)

Hence, the simplest radical form is,

\(\sqrt{\dfrac{4}{7}} = \sqrt{\dfrac{2^2}{7}}\)

\(= \dfrac{2}{\sqrt{7}}\)

Multiply and divide by \(\sqrt{7}\);

\(= \dfrac{2\times \sqrt{7} }{\sqrt{7}\times \sqrt{7}}\)

\(= \dfrac{2\sqrt{7} }{7}\)

Therefore, the simplest form is, \(\dfrac{2\sqrt{7} }{7}\)

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Step-by-step explanation:

The answer is -9

Answer:

-9

Step-by-step explanation:

Answer:

$6.5 dollars

Step-by-step explanation:

We can make an equation to find out the original total.

2y+4=17

(subtract 4 from both sides)

2y=13

(divide by 2)

y=6.5

Hope this helped :D

Answer:

\(3\sqrt7\)

Step-by-step explanation:

This is because you can split 63 into two numbers, \(\sqrt{9}\) and \(\sqrt{7}\). When you simplify \(\sqrt{9}\) turns into 3 but \(\sqrt{7}\) will not simplify further so it will be \(3\sqrt{7}\).

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

Answer:

triangle pjl is congruent to it's by side side side theorem

A type of article that provides a quantitative summary of the evidence is a systematic review and meta-analysis.

A systematic review is a comprehensive and rigorous approach to synthesizing existing research literature on a specific topic. It involves a systematic search for relevant studies, an assessment of their quality and relevance, and a synthesis of the findings.

A meta-analysis, on the other hand, is a statistical method that combines the results of multiple studies to generate a quantitative summary of the evidence.

Systematic reviews and meta-analyses are considered the highest level of evidence in evidence-based medicine and other fields. They provide an objective and rigorous assessment of the available evidence, helping to guide clinical practice, policy decisions, and further research.

By pooling data from multiple studies, meta-analyses can provide more precise estimates of treatment effects or other outcomes of interest.

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Answer:

1÷36=(1/36)

Step-by-step explanation:

ez

The equation of the line in slope-intercept form that passes through the points (-3,6) and (0,0) is y = -2x.

What is equation of slope?

The differentiation of the tangent equation is slope. Here, dy/dx = 1. This slope results from our initial differentiation. This indicates that the first derivative is slope.

To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept of the line.

The slope of a line passing through two points (x1,y1) and (x2,y2) is given by the formula:

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

Using the points (-3,6) and (0,0), we can find the slope of the line as follows:

slope = (0 - 6) / (0 - (-3))

slope = -6 / 3

slope = -2

Now, we can use the point-slope form of the equation of a line to write the equation:

y - y1 = m(x - x1)

where m is the slope and (x1,y1) is one of the points on the line. Let's use the point (-3,6) as (x1,y1):

y - 6 = -2(x - (-3))

Simplifying the equation:

y - 6 = -2x - 6

y = -2x

Therefore, the equation of the line in slope-intercept form that passes through the points (-3,6) and (0,0) is y = -2x.

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Answer:

Option A is your answer ☺️

Answer:

x = 5

Step-by-step explanation:

Laws of indices states that if the base is same the power can be added or subtracted. Since this is division, the powers are subtracted.

So, 2x - 3 = 7

or, 2x = 7 + 3

or, 2x = 10

or, x = 10/2

or, x = 5

Answer:

-4 yards

Step-by-step explanation:

3X6=18

2x11=22

18-22=-4

You do know that there is no 11 yard penalty, right?

The residual for this observation is 31.05.

As per given data in question ,

Starting price of a used game with one wheel = 0.99

Total observed price = 37.04

We have to calculate the residual, we need to first calculate the predicted value using the linear regression equation, then subtract the predicted value from the observed value.

Linear regression equation: `

y = mx + b`

Here, `y` is the dependent variable, which is the total price of the sale. `x` is the independent variable, which is the starting price of the used game. `m` is the slope of the regression line, which can be calculated as:

`m = (y2 - y1) / (x2 - x1)

`Where `(x1, y1)` and `(x2, y2)` are any two points on the line.

Let's use the following two points:

`(0.99, 5.99)` and `(40.00, 44.00)`.

Therefore, `m = (44.00 - 5.99) / (40.00 - 0.99) = 0.9303`

Now, to find `b`, we need to substitute the slope and one of the points in the equation `y = mx + b`.

Let's use the point `(0.99, 5.99)`.

Therefore, `5.99 = 0.9303(0.99) + b`,

which gives `b = 5.10`.

Thus, the linear regression equation is `y = 0.9303x + 5.10`.

Now, to calculate the predicted value, we need to substitute the starting price in the equation.

Here, the starting price is 0.99. Therefore, `y = 0.9303(0.99) + 5.10 = 5.99`.

Hence, the predicted value is $5.99.

To calculate the residual, we need to subtract the predicted value from the observed value.

Therefore,

`residual = observed value - predicted value = 37.04 - 5.99 = 31.05`.

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Answer:

No

Step-by-step explanation:

Because first you have to distribute so you will do

\(3 \times 4 = 12\)

\(3 \times x = 3x\)

Than You will combine 5x and 3x

\(5x + 3x = 8x\)

Last you will get

\(8x - 12\)

Answer:

b) f(x) = x² - 256

Step-by-step explanation:

Since we have been given the zeros of a function, -16 and 16. We are asked to find which function truly has those zeros.

To find this, we can substitute the zeros for x in the functions to find the one that is true/correct.

A) f(x) = x² - 16

 ⇒  0 = 16² - 16          and          ⇒  0 = (-16)² - 16

 ⇒  0 = 256 - 16        and          ⇒  0 = 256 - 16

 ⇒  0 = 240 ✘          and          ⇒  0 = 240 ✘

B) f(x) = x² - 256

 ⇒  0 = 16² - 256          and          ⇒  0 = (-16)² - 256

 ⇒  0 = 256 - 256        and          ⇒  0 = 256 - 256

 ⇒  0 = 0 ✔                  and          ⇒  0 = 0 ✔

C) f(x) = x² - 32x + 256

 ⇒  0 = 16² - 32(16) + 256         and        ⇒  0 = (-16)² - 32(-16) + 256

 ⇒  0 = 256 - 512 + 256           and        ⇒  0 = 256 + 512 + 256

 ⇒  0 = 512 - 512                       and        ⇒  0 = 512 + 512

 ⇒  0 = 0 ✔                               and        ⇒  0 = 1,024 ✘

D) f(x) = x² + 32x + 256

  ⇒  0 = 16² + 32(16) + 256         and        ⇒  0 = (-16)² + 32(-16) + 256

  ⇒  0 = 256 + 512 + 256           and         ⇒  0 = 256 - 512 + 256

  ⇒  0 = 512 + 512                       and         ⇒  0 = 512 - 512

  ⇒  0 = 1,024 ✘                          and        ⇒  0 = 0 ✔

Therefore, Function B has the zeros of x = -16 and x = 16.

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if the data is skewed or otherwise biased, the least squares line may not accurately represent the true relationship between the number of stories and building height.

The estimated height of a building with six stories would depend on the average height of each story, which can vary depending on the building's design and construction materials. However, a general rule of thumb is that each story in a building is typically between 10 and 14 feet in height, which would put a six-story building between 60 and 84 feet tall.

As for whether the least squares line gives an accurate estimate of height, that would depend on the data being used to generate the line. The least squares method is a statistical technique used to find the line of best fit for a set of data points, with the goal of minimizing the sum of the squared distances between each data point and the line.

If the data used to generate the line is representative of the population of buildings with six stories, then the least squares line should provide a reasonably accurate estimate of height. However, if the data is skewed or otherwise biased, the least squares line may not accurately represent the true relationship between the number of stories and building height. Therefore, it is important to carefully examine the data and consider potential biases before using the least squares method to make predictions.

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Critical value with 35 degrees of freedom at 0.05 Los = 2.030

Given information,

Departmental liabilities have a mean and standard deviation that are unknown for the population. What t-score should be used to establish a 95% confidence interval estimate for the population mean if a random sample of 36 departments is utilized to estimate the mean liabilities?

Here,

By assuming a 95% confidence interval and by considering the t-value we have,

Therefore;

Critical value at 0.05 Los with 35 degrees of freedom =2.030

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The expression that is equivalent to the (10a⁵b³) (5a⁶b²) is

(10 × 5) (a⁵⁺⁶)(b³⁺²).  

Equivalent expressions are two or more mathematical expressions that have the same value for all possible values of the variables in the expressions.

If we substitute the same values for the variables in two different expressions, and the values we get for each expression are always the same, then the two expressions are said to be equivalent.

Here we have

=> (10a⁵b³) (5a⁶b²)  

Which can be solved as follows

=> (10a⁵b³) (5a⁶b²)    

Multiply the coefficients of two terms

=>  (10 × 5) (a⁵b³) (a⁶b²)            

As we know aˣ × aᵇ = a⁽ˣ⁺ᵇ⁾  

=> (10 × 5) (a⁵ × a⁶) (b³ × b²)          

=> (10 × 5) (a⁵⁺⁶) (b³⁺²)        

Therefore,

The expression that is equivalent to the (10a⁵b³) (5a⁶b²) is

(10 × 5) (a⁵⁺⁶)(b³⁺²).        

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Complete Question in picture

Answer:

Step-by-step explanation:

ok so this is pretty simple,

Imagine a was the number 1

45% of 1, which would obviously be

45/100 * 1

Same thing here but for the variable a.

45/100 * a!

That would be the algebraic expression for 45% of a!

Cheers! I hope you can understand the problem better now.

9514 1404 393

Answer:

  50°

Step-by-step explanation:

Angle DEG is also angle DEC. It subtends arc DC as does inscribed angle DFC. Inscribed angles that subtend the same arc have the same measure.

  ∠DFC = ∠DEG = 50°

Answer: 50

Step-by-step explanation: Khan Academy

Answer:

the third one

Step-by-step explanation:

-5 is the least out of all of them and 6 is the greatest so then you can put the numbers in between

Answer:

The answer is m = x + 2kn

Step-by-step explanation:

Rewrite the equation as  − 2 k n  +  m  =  x . Add  2 k n  to both sides of the equation.

a) There are 27,405 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25 with no restrictions.

b) There are 1,001 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, with xi ≥ 3 for i = 1, 2, 3, 4, 5.

c) There are 5,561 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10.

d) There are 780 solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10 and 2 ≤ x₂ ≤ 7.

a) No Restrictions:

In this arrangement, the first urn contains 5 balls, the second urn contains 3 balls, the third urn contains 9 balls, and the fourth urn contains 8 balls.

By applying this method, we need to find the number of ways we can arrange the 25 balls and 4 separators. The total number of positions in this arrangement is 29 (25 balls + 4 separators). We choose 4 positions for the separators from the 29 available positions, which can be done in "29 choose 4" ways. Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25 with no restrictions is:

C(29, 4) = 29! / (4! * (29 - 4)!) = 27,405.

b) xi ≥ 3 for i = 1, 2, 3, 4, 5:

In this case, each xi should be greater than or equal to 3. We can use a similar approach to the previous case but with a few modifications. To ensure that each variable is at least 3, we subtract 3 from each variable before distributing the balls. This effectively reduces the equation to x₁' + x₂' + x₃' + x₄' + x₅' = 10, where x₁' = x₁ - 3, x₂' = x₂ - 3, and so on.

Now, we have 10 balls (representing the value of 10) and 4 urns (representing the variables x₁', x₂', x₃', and x₄'). Using the stars and bars method, we can determine the number of ways to arrange these balls and separators. The total number of positions is 14 (10 balls + 4 separators), and we need to choose 4 positions for the separators from the 14 available positions.

Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where each xi is greater than or equal to 3, is:

C(14, 4) = 14! / (4! * (14 - 4)!) = 1001.

c) 3 ≤ x₁ ≤ 10:

Now, we have a specific restriction on the value of x₁, where 3 ≤ x₁ ≤ 10. This means x₁ can take any value from 3 to 10, inclusive. For each value of x₁, we can determine the number of solutions to the reduced equation x₂ + x₃ + x₄ + x₅ = 25 - x₁.

Using the stars and bars method as before, we have 25 - x₁ balls and 4 urns representing the variables x₂, x₃, x₄, and x₅. The total number of positions is 25 - x₁ + 4, and we need to choose 4 positions for the separators from the available positions.

By considering each value of x₁ from 3 to 10, we can calculate the number of solutions to the equation for each case and sum them up.

Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10, is:

∑(C(25 - x₁ + 4, 4)) for x₁ = 3 to 10.

By evaluating this sum, we find that there are 5,561 solutions.

d) 3 ≤ x₁ ≤ 10 and 2 ≤ x₂ ≤ 7:

In this case, we have restrictions on both x₁ and x₂. To count the number of solutions, we follow a similar approach as in the previous case. For each combination of x₁ and x₂ that satisfies their respective restrictions, we calculate the number of solutions to the reduced equation x₃ + x₄ + x₅ = 25 - x₁ - x₂.

By using the stars and bars method again, we have 25 - x₁ - x₂ balls and 3 urns representing the variables x₃, x₄, and x₅. The total number of positions is 25 - x₁ - x₂ + 3, and we choose 3 positions for the separators from the available positions.

We need to iterate over all valid combinations of x₁ and x₂, i.e., for each value of x₁ from 3 to 10, we choose x₂ from 2 to 7. For each combination, we calculate the number of solutions to the equation and sum them up.

Therefore, the number of solutions to the equation x₁ + x₂ + x₃ + x₄ + x₅ = 25, where 3 ≤ x₁ ≤ 10 and 2 ≤ x₂ ≤ 7, is:

∑(∑(C(25 - x₁ - x₂ + 3, 3))) for x₁ = 3 to 10 and x₂ = 2 to 7.

By evaluating this double sum, we find that there are 780 solutions.

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To calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

What is rate ?

In mathematics, a rate is a ratio that compares two quantities with different units. It is typically expressed as the amount of change of one quantity with respect to another quantity. Rates are often used in the context of describing how quickly or slowly something changes over time or space.

To calculate a rate, we need to divide two quantities that have different units. For example, if we want to find the rate of a car's speed, we divide the distance traveled (in miles) by the time taken to travel that distance (in hours).

The formula for rate is:

rate = quantity / time

To calculate a unit rate, we need to divide a rate by the quantity being measured. For example, if the rate is the number of miles traveled per hour, the unit rate would be the number of miles traveled in one hour. To find the unit rate, we divide the rate by 1 hour.

The formula for unit rate is:

unit rate = rate / 1

When calculating rates or unit rates, it is important to make sure that the units of the quantities being divided are consistent. If the units are not the same, we need to convert them to the same unit before performing the division.

Therefore, to calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

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