Given f(x) = x2 + 5x − 6 and g(x) = 2x2 − 8, find each value.

f(−2) =

g(3) =

we can use the proportion: (Number of votes received by the candidate) / (Total number of votes) = 43% / 100%. the candidate received approximately 37.41 votes.

In the given local election, the candidate received 43% of the votes. To determine the number of votes they obtained, we need to use a proportion. A proportion is an equation that states that two ratios are equal.

Let's represent the number of votes received by the candidate as "x." The total number of votes cast in the election is stated as 87.

We can set up the proportion:

x / 87 = 43% / 100.

To solve for "x," we can cross-multiply:

100 * x = 43% × 87.

Simplifying further, we have:

x = (43/100) × 87.

By multiplying the fraction (43/100) by 87, we can determine the number of votes received by the candidate. Evaluating this expression, the candidate received approximately 37.41 votes.

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Answer:

64

Step-by-step explanation:

16 times 4

Based on the amount of paper that Pedro was able to recycle over 5 weeks, the kilograms of paper that Pedro's office would have recycled after 6 weeks is 18 kilograms

The relationship is assumed to be directly proportional. The first thing is do therefore is to find the kilograms of paper recycled per week.

The papers recycled per week in Pedro's office is:

= Kilograms of paper / Number of weeks

= 15 / 5

= 3 kilograms per week

In 6 weeks therefore, the amount of paper that would be recycled is:

= Number of weeks x Kilograms recycled per week

= 6 weeks x 3 kilograms per week

= 18 kilograms

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Answer:

B) 6<x<90

Step-by-step explanation:

48+42=90

48-42=6

There will be a number greater than and a number less than x.

90>6

6<x<90

Hope this helps :)

Answer:

2

Step-by-step explanation:

Answer:

d:113 sq in

Step-by-step explanation:

Answer:

\( 40 \: {cm}^{2} \)

Step-by-step explanation:

Area of the figure = Area of rectangle with dimensions 6 cm by 5 cm + Area of triangle with base 5 cm and height 4 cm

\( = 6 \times 5 + \frac{1}{2} \times 5 \times 4 \\ \\ = 30 + 10 \\ \\ = 40 \: {cm}^{2} \)

(s - t)(-1) evaluates to 0.

To find the expressions for (s + t)(x) and (s * t)(x), we can simply add and multiply the given functions s(x) and t(x) accordingly.

(s + t)(x) = s(x) + t(x)

           = (2x - 4) + (6x)

           = 2x - 4 + 6x

           = 8x - 4

(s * t)(x) = s(x) * t(x)

           = (2x - 4) * (6x)

           = 12x^2 - 24x

To evaluate (s - t)(-1), we substitute x = -1 into the expression (s - t)(x) and simplify:

(s - t)(x) = s(x) - t(x)

           = (2x - 4) - (6x)

           = 2x - 4 - 6x

           = -4x - 4

Now, substitute x = -1:

(s - t)(-1) = -4(-1) - 4

           = 4 - 4

           = 0

Therefore, (s - t)(-1) evaluates to 0.

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Suppose that the functions s and t are defined for all real numbers x as follows. s(x) = 2x - 4 t(x) = 6x Write the expressions for (s + t)(x) and (s t)(x)and evaluate(s - t)(-1)

Answer:

M²-14m+13 = 0

m²-13m-m+13 = 0

m(m-13)-1(m-13) = 0

(m-1)(m-13) = 0

m = 1 & 13

Step-by-step explanation:

M²-14m+13=0

=> m²-13m-m+13=0

=> m(m-13)-1(m-13) = 0

=> (m-1)(m-13)=0

=> m= 1 and 13

Hope it is helpful....

The sector of the circle is bounded by 2 radii, and the measure of the central angle that forms the sector is 120 degrees

The given parameters are:

The area is calculated using

Area = α/360 * πr^2

So, we have:

α/360 * π * 15^2 = 75π

Evaluate the exponent

α/360 * π * 225 = 75π

Divide both sides by 75π

α/360 * 3 = 1

Multiply

α/120  = 1

Multiply both sides by 120

α = 120

Hence, the measure of the central angle that forms the sector is 120 degrees

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Answer:

12 and 8

Step-by-step explanation:

→ Set up two equations

x - y = 4

\(\frac{x+y}{2} =10 \\ \\x + y = 20\)

→ Add the 2 equations together

2x = 24

→ Solve for x

x = 12

→ Substitute into original equation

12 - y = 4

→ Solve

y = 8

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

the answer you are looking for is C

Answer:

Use the degree and the leading coefficient to determine the behavior.

Falls to the left and falls to the right

Step-by-step explanation:

The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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Answer:

11/30

Step-by-step explanation:

Stephen suggests using at least 20 questions in a baseline survey.

Stephen suggests using at least 20 questions in a baseline survey. Baseline survey refers to the gathering of data from a sample or population to obtain a set of measures that can be used to assess the current status of the population or sample of interest. The goal of a baseline survey is to generate an understanding of the status of a particular variable(s) at the outset of an intervention.Stephen recommends using at least 20 questions in a baseline survey as a general rule of thumb. In addition to using at least 20 questions in a baseline survey, it is important to pay close attention to the type of questions asked, the format of the questions, and the phrasing of the questions to ensure that the responses obtained are reliable and valid

Stephen suggests using at least 20 questions in a baseline survey. The goal of a baseline survey is to generate an understanding of the status of a particular variable(s) at the outset of an intervention. In addition to using at least 20 questions in a baseline survey, it is important to pay close attention to the type of questions asked, the format of the questions, and the phrasing of the questions to ensure that the responses obtained are reliable and valid.

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The Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

Define Domain and Range

Given expression is,

f(x) = -1/4x³ + 4x - 3

In this x ∈ R, so

Domain = (-∞,∞) , { x|x  ∈ R }

Range =   (-∞,∞) ,{ y|y ∈ R }

Hence, the Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

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The probability that the duration of rainfall at least 2 hours is 0.473,  at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.

1. Find the rate parameter (λ):
λ = 1/2.725 ≈ 0.367
2. To find P(X ≥ 2):

P(X ≥ 2) = 1 - P(X < 2).

The (pdf) is:
P(X < x) = 1 - e^(-λx)
P(X < 2) = 1 - e^(-0.367 * 2) ≈ 0.527
P(X ≥ 2) = 1 - 0.527 ≈ 0.473
3. To find P(X ≤ 3):
P(X ≤ 3) = 1 - e^(-0.367 * 3) ≈ 0.683
4. To find P(2 ≤ X ≤ 3):
P(2 ≤ X ≤ 3) = P(X ≤ 3) - P(X ≤ 2) = 0.683 - 0.527 ≈ 0.156
The probability that  duration  at least 2 hours is 0.473,  at most 3 hours is 0.683, and between 2 and 3 hours is 0.156.

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The probability that  on a randomly selected​ day, he wrote at least one check is 0.3843

A year is made up of 365 days

The number of checks written = 177

λ = 177 / 365

= 0.4849

P(x ≥ 1) = 1 - p(x < 1)

p(x < 1) is going to be 0

so we would have 1 - p(x = 0)

the Poisson distribution is given as

P = e^-λ (λκ) / κ!

This is written as

1 - e^-0.485 x 0.485⁰ / 0!

1 - 0.6157

= 0.3843

The probability that  on a randomly selected​ day, he wrote at least one check is 0.3843

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Answer:

Below in bold.

Step-by-step explanation:

The smallest angle for which -0.25 is the tangent is in the  second quadrant and is 165.96 degrees. The other angle in the fourth quadrant is 345.96 degrees.

So for the range 0 to 720, x = 165.96, 345.96 and  360 + 165.96 = 525.96 and 345.96+360 = 705.96 degrees.

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

15 nickels and 11 quarters

Answer:

So, Y (the up and down part of the graph) equals K (The constant of proportionality, you get it by dividing Y by X), times X (the side by side part of the graph.)

Answer:

1, 2, 3, 4, 6, 9, 12, 18, 36

Step-by-step explanation:

From smallest to biggest, the necessary variables are 1, 2, 3, 4, 6, 9, 12, 18, and 36. By expressing 36 as the product of the components, we may get the factors.

By assuming that the zero conditional mean assumption holds, the regression model is less likely to be affected by omitted variable bias.

When interpreting OLS estimates of a simple linear regression model, assuming that the zero conditional mean assumption holds is important for statistical inference.

What is OLS?

OLS stands for Ordinary Least Squares. This method is the most widely used method for the estimation of linear regression models. It is used to find the line of best fit that goes through the points in a scatter plot. OLS Estimates in Simple Linear Regression OLS estimates in simple linear regression are used to calculate the slope and the intercept of the regression line. The slope is the change in Y per unit change in X, and the intercept is the point at which the regression line crosses the Y-axis.

Assuming that the zero conditional mean assumption holds is important for statistical inference because it is a requirement for unbiasedness of the OLS estimates. This assumption states that the error term in the regression model has a mean of zero given any value of the independent variable. If this assumption is violated, the OLS estimates will be biased and will not accurately represent the relationship between the independent and dependent variables.

The zero conditional mean assumption is also important for causal inference because it ensures that the regression model is not affected by omitted variable bias. Omitted variable bias occurs when a variable that affects the dependent variable is left out of the regression model. If this variable is correlated with the independent variable, it can cause bias in the OLS estimates.

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The measure of angle MQS is 18°.

In mathematics, angles are typically measured in degrees or radians.

An angle is formed by two rays that have a common endpoint called the vertex. The rays are the sides of an angle, and the endpoint is called the vertex.

There are different types of angles:

Acute angle: an angle measuring between 0 and 90 degrees.

Right angle: an angle measuring exactly 90 degrees.

Obtuse angle: an angle measuring between 90 and 180 degrees.

Straight angle: an angle measuring exactly 180 degrees.

Reflex angle: an angle measuring between 180 and 360 degrees.

Draw QT  and QS

Angles TQP, SQT, and  SQR  will trisect the interior angle PQR

And PQR  = 108

So  ...angle  SQT  = 108 / 3   = 36

But...by symmetry....angle XQS  =  (1/2)angle SQT  = (1/2)36  = 18°

Therefore, The measure of angle MQS is 18°.

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The rate at which air is being pumped in when the radius of the sphere is 10 cm and increasing at a rate of 2 cm/s is 400π/3 cm³/s.

The volume V of a sphere with radius r is given by V = (4/3)πr³. Taking the derivative of this expression with respect to time t, we get dV/dt = 4πr²(dr/dt). This equation relates the rate of change of volume to the rate of change of the radius. We are given that the radius is increasing at a rate of 2 cm/s, so dr/dt = 2 cm/s.

At the instant when the radius is 10 cm, we can find the rate at which air is being pumped in by substituting r = 10 cm and dr/dt = 2 cm/s into the equation for dV/dt. Thus, we have dV/dt = 4π(10)²(2) = 800π cm³/s.

Therefore, when the radius of the spherical balloon is 10 cm and is increasing at a rate of 2 cm/s, the rate at which air is being pumped in is 400π/3 cubic centimeters per second.

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We can solve the equation:

(a - 3)/√a = -√a

To get the value of a = 1.5

Here we want to solve the following equation.

(a - 3)/√a = -√a

First, notice that the square root of a is on the denominator, then we can't have a = 0.

Now we can multiply both sides by √a to get:

(a - 3) = -√a*√a

(a - 3) = -a

Now we can write:

a - 3 = -a

a + a = 3

2a = 3

a = 3/2

a = 1.5

The value of a is 1.5

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