Here is a box plot that summarizes data for the time, in minutes, that a fire department took to respond to 100 emergency calls. Select all the statements that are true, according to the box plot. Most of the response times were under 13 minutes. Fewer than 30 of the response times were over 13 minutes. More than half of the response times were 11 minutes or greater. There were more response times that were greater than 13 minutes than those that were less than 9 minutes. About 75% of the response times were 13 minutes or less.

The option that represents the first step is x² + 4x = -3

The equation is given as:

x² + 4x + 3 = 0

The first step is to isolate the constant.

So, we have:

x² + 4x = -3

Hence, the option that represents the first step is x² + 4x = -3

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Answer:

First, we can use the information given to find out how many people can be seated at one table:

Next, we can use the information given to find out how many people can be seated in a row of tables:

Using this information, we can find out how many people can be seated in a row of any number of tables:

So, if 3 tables are placed together in a row, 15 people can be seated. If 4 tables are placed together in a row, 20 people can be seated. If 5 tables are placed together in a row, 25 people can be seated.

The pattern we notice is that the number of people seated in a row of tables increases by 5 for each additional table added.

To summarize, the equation that would help find the number of people seated for any number of tables is:

Number of people seated = 5x, where x is the number of tables placed together in a row.

Answer:

we are given that

6 people can sit together at 1 rectangular table.

2 tables are placed together, 10 people can sit together.

14 people can sit if three tables are put together.

It mean we get a sequence

6,10,14..........

So its making an arithmetic progression, where

First term=a=6

Common difference

Number of terms=number of table

As we know the nth term is given by the formula

Hence 402 people can sit

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The equation that represents the graph is g(x) = |x – 1| + 3. Then the correct option is C.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The graph is shown.

In the graph, the mode function is given.

If the subtracts 1 from the variable then the function gets shifted toward the right and if 3 is added to the function then it gets shifted upwards.

Then the correct equation that represents the graph is g(x) = |x – 1| + 3.

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Answer:

Step-by-step explanation:

The equation that represents the graph is g(x) = |x – 1| + 3. Then the correct option is C.

What is a function?

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The graph is shown.

In the graph, the mode function is given.

If the subtract 1 from the variable then the function gets shifted toward the right and if 3 is added to the function then it gets shifted upwards.

Then the correct equation that represents the graph is g(x) = |x – 1| + 3.

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Answer:

x = 4.7

Step-by-step explanation:

You will need to subtract 3.9 from 5.78, then divide by 0.4. The answer is 4.7 because you are left with x = 4.7.

Hope this helps you!

The value of f^−1(4)f is the result of applying the inverse of the function f to 4.

To calculate f^−1(4)f, the inverse of the function f must be applied to 4.

Firstly, the inverse function of f, denoted as f^−1, is obtained by exchanging the x and y coordinates of all points on the graph of f. This means that the equation of f^−1 is obtained by solving the equation of f for y.

Next, 4 is substituted into the equation of f^−1 and the resulting equation is solved for x. This gives the value of f^−1(4).

Finally, the value of f^−1(4) is then substituted into the equation of f and the resulting equation is solved for y. This gives the value of f^−1(4)f.

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Answer:

0.85(x - 350)

Step-by-step explanation:

x - This is the employees salary before tax exempts

$350 - This is the amount of tax exempted from the employers salary

Income left after tax exempt expenses have been deducted = (x - 350)

If 15% of taxed income is collected, the remaining income would be - 100% - 15% = 85%

85% / 100 = 0.85

Therefore, the remaining salary that the employees take home is 0.85(x - 350)

Answer:

im failing this too!

Step-by-step explanation:

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Answer:

The percentage change is a 40% increase.

Step-by-step explanation:

Given

To determine

The percent change from the first value to the second

Using the formula

Percentage change = [New value - Old value] / | Old value | × 100

                                 = [42 - 30] / |30| × 100

                                 = 12 / 30 × 100

                                 = 0.4 × 100

                                 = 40% change

                                  = 40% increase

Therefore, the percentage change is a 40% increase.

Answer:

irrational,  it can't be written as a fraction

Step-by-step explanation:

Answer:

26.6°

Step-by-step explanation:

The measure of the angle the ramp makes with the ground is approximately 30 degrees.

We have,

To find the measure of the angle the ramp makes with the ground, use trigonometry.

In this case, a right triangle is formed by the ramp, the ground, and the vertical height of 1 meter.

Denote the angle the ramp makes with the ground as θ (theta).

Using the trigonometric function "sine" (sin), we can set up the following equation:

sin(θ) = opposite/hypotenuse

The opposite side is the height of the ramp, which is 1 meter, and the hypotenuse is the length of the ramp, which is 2 meters.

So,

sin(θ) = 1/2

θ = arcsin(1/2)

Using a calculator or a trigonometric table.

θ = arcsin(1/2) = 30 degrees.

Therefore,

The measure of the angle the ramp makes with the ground is approximately 30 degrees.

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Step-by-step explanation:

The values of x for which f(x) and g(x) are equal are given by

f(x)=g(x)

⟹2x

2

−1=1−3x

2x

2

+3x−2=0

(x+2)(2x−1)=0

x=−2,1/2.

Thus, f(x) and g(x) are equal on the set {-2, 1/2}.

Answer:

Your answer would be -2, 1/2

Step-by-step explanation:

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Answer:

(3x−27)o

Step-by-step explanation:

we know that

m\angle BEC=m\angle AEDm∠BEC=m∠AED ----> by vertical angles

we have

m\angle BEC=(2x+3)^om∠BEC=(2x+3)o

The value of x is given

x=30

so

m\angle BEC=(2(30)+3)=63^om∠BEC=(2(30)+3)=63o

That means that the measure of angle AED is also 63 degrees

so

The expression that could represent the measure of Angle A E D is

(3x-27)^o(3x−27)o

because

For x=30

(3(30)-27)=63^o(3(30)−27)=63o

Answer:

(3x−27)o

Step-by-step explanation:

Answer:

y=2x+2

Step-by-step explanation:

Use the method rise overrun from 0,2 to 2,6 it rises 4 and runs 2(moves positively on the x-axis). divide 4 by 2 and get 2.

then check the y-intercept( when x is 0 on y-axis) the y intercept is 2

then plug in y=slope(x)+b(intercept)

to get y=2x+2.

It cannot determine causation as there may be other variables or factors that could be influencing the relationship between the two variables being analyzed.

Which one of the following cannot be determined from a scatterplot is a cause and effect relationship.

A scatterplot can show the strength and direction of a relationship between two variables, whether it is a positive or negative relationship, and whether it is curvilinear.

However, it cannot determine causation as there may be other variables or factors that could be influencing the relationship between the two variables being analyzed.

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The radius of convergence,R, of the series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\) is (1, ∞)

We know that for a power series ∑an (x - p)^n

if |x - p| < R then the series converges,

and if |x - p| > R then the series diverges.

Here, the number R is called the radius of convergence.

We have been given a series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\)

We need find the radius of convergence.

We use ratio test.

We know for \($\lim_{x\to\infty}~ | \frac{a_{n+1}}{a_n}|=L\)

if L < 1, then the series converges

and If \($\lim_{x\to\infty}~a_n \neq 0\) then \(\sum a_n\) diverges.

Using ratio test for given series,

\($\lim_{x\to\infty}~ | \frac{9(-1)^{n+1}~ (n+1)x^{n+1}}{9(-1)^n~ nx^n}|\\\\\\\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x^{n+1}}{nx^n}|\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x}{n}|\)

\(=|x| $\lim_{x\to\infty}~ | \frac{n+1}{n}|\)

= |x|

This means, the series is convergent for |x| < 1.

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Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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Answer:

C

Step-by-step explanation:

I’m pretty sure

The line whose slope will be same as that of the graph given, will be the line parallel to the given line.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a graph of a line.

For a given line to be parallel to the given line, its slope should be same as that of the line plotted. Since the graph is not given, we can make an estimate for the equation of the line parallel to the given line. The four equations given will have their slopes as mentioned -

[A] -   4x + 5y = - 10       [m] = -4/5

[B] -   4x - 5y = 0           [m] = 4/5

[C] -   5x + 4y = 24        [m] = -5/4

[D] -   5x - 4y = -8          [m] = 5/4

Now, the line whose slope will be same as that of the graph given, will be the line parallel to the given line.

Therefore, the line whose slope will be same as that of the graph given, will be the line parallel to the given line.

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Step-by-step explanation:

this simply means that Dell can do 1/3 of the work in 1 hour, and Max can do 1/4 of the work in 1 hour.

so, working together, they can complete 1/3 + 1/4 of the work in 1 hour.

to really add these fractions, we need to bring them to the same denominator by finding the smallest (or lowest) common multiple of the existing denominators, which is in this very simple case just 3×4 = 12

1/3 + 1/4 = 4/12 + 3/12 = 7/12

therefore, together they can complete 7/12 of a flower bed in 1 hour.

so, by defining the variable fb as the number of completed flower beds :

fb = 7/12 × t

Step-by-step explanation:

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Two unit vectors that make an angle of 60 degrees with v = (3, 4) are approximately (2.5000, 4.3301) and (-2.5000, -4.3301).

To find two unit vectors that make an angle of 60 degrees with vector v = (3, 4), we can use trigonometry and vector operations.

Step 1: Calculate the magnitude of vector v:

|v| = sqrt(3^2 + 4^2) = 5

Step 2: Convert the given angle of 60 degrees to radians:

θ = 60 degrees * (π/180) = π/3 radians

Step 3: Calculate the components of the unit vector in the same direction as v:

u1 = cos(θ) = cos(π/3) ≈ 0.5000

u2 = sin(θ) = sin(π/3) ≈ 0.8660

Step 4: Multiply the components by the magnitude of v to obtain the unit vectors:

u1 = u1 * |v| ≈ 0.5000 * 5 ≈ 2.5000

u2 = u2 * |v| ≈ 0.8660 * 5 ≈ 4.3301

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Answer:

1. -4

2. 10

3. -19

4. 5

Step-by-step explanation:

1. 5 + -9= -4

2. -3 + 13 = 10

3. -8 + 11 = -19

4. 6 + -1 = 5

Answer:

Step-by-step explanation:

you just add it

The solution to the equation is z = 15.

To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.

On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:

2(2z) - 2(3) = 4z - 6

On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:

3(z) + 3(3) = 3z + 9

Now we can rewrite the equation as:

4z - 6 = 3z + 9

Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:

4z - 3z = 9 + 6

Simplifying gives us:

z = 15

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Answer:

Yes it can!

Step-by-step explanation:

In the given triangles,
∠B = ∠F
Also, ratio of sides given are
2.3/13.8 ≈ 1.67 -> (i)
And 1.9/11.4 ≈ 1.67 -> (ii)
Thus, (i) = (ii)
∴ AB/BF = BC/DF

So we can prove both triangles are similar as the two sides are proportional and the angle between the corresponding sides are equal, so we can use the SAS similarity postulate as the two sets of corresponding sides are proportional and the included angles are congruent .

Let G be some point on the diagonal line away from point E.

Angle DEG represents angle 1.

We're given that angle DEF is a right angle which means it's 90 degrees. Angle DEG is some angle smaller than 90 degrees. By definition, that must mean angle 1 is acute. Any acute angle is smaller than 90 degrees. There's not much else to say other than this is just a definition problem.

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

Extra side notes:

If angle 1 was a right angle, then that would mean angle GEF would have to be 0 degrees; however the diagram shows this isn't the case.

If angle 1 was obtuse, then there's no way we'd be able to fit it into angle DEF. In other words, there's no way to have an angle larger than 90 fit in a 90 degree angle.

Answer:

8

Step-by-step explanation:

So 4(1)+4: 4+4=8

Answer:

The answer is c

Step-by-step explanation:

if you add the first 2 numbers squared out of the 3 on i and ii and divide the by the 3rd number on i and ii you get the last number which means you did it correctly. Demonstration

3,4,5 3×3=9 4×4=16 9+16=25 25÷5=5 that is the correct formula to answers thrs types of questions :)

Answer:

x = 17/4, or 4.25

The x-intercept is (4.25, 0)

Step-by-step explanation:

We can get the intercepts by isolating x and y.

4x - 3y = 17

Subtract 4x from both sides.

-3y = -4x + 17

Divide both sides by -3.

y = 4/3x - 17/3

Input 0 for x.

y = -17/3

The y-intercept is (0, -17/3)

4x - 3y = 17

Add 3y to both sides.

4x = 3y + 17

Divide both sides by 4.

x = 3/4y + 17/4

Input 0 for y.

Answer:

a=7 b=2 c=0.2 d=9 e=0.064 f=8 g=16 h=0.03 i=0.714

Step-by-step explanation: