The table below represents the function, and the following graph represents the function g.
4 -3 -2 -1 0 1
X-6 -5
f(x) 8-2
-8 -10 -8 -2 8 22
Complete the following statements.
The functions f and g have
The y-intercept of fis
the y-intercept of g.
Over the interval [-6, -31, the average rate of change of fis
m. All rights reserved.
9
-6 -4
-2
6
4
2
4-
N
6
2
4 6
the average rate of change of g

Answer:

y = 5

Step-by-step explanation:

[tex]14y-7y=35\\7y=35\\y=5[/tex]

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Answer:

6.24 x [tex]10^{-7}[/tex]

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x [tex]10^{-7}[/tex]

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

Rounding the given value to the nearest tenth would be 1020.5

The tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .

Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.

Learn more on rounding numbers : https://brainly.com/question/28128444

#SPJ1

Answer:

123°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , then

third angle + 22° + 35° = 180°

third angle + 57° = 180° ( subtract 57° from both sides )

third angle = 123°

Answer:

(Look at the picture)

The end of 6 months, Ram should pay Rs. 276250 compounded half-yearly.

Ram borrowed Rs. 250000 from Sit at an interest rate of 21% per annum. To calculate the compound interest, we need to know the compounding period. In this case, the interest is compounded half-yearly, which means it is calculated twice a year.

To find out how much Ram should pay at the end of 6 months, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the amount to be paid at the end of the time period
P = the principal amount (the initial amount borrowed) = Rs. 250000
r = the interest rate per period (in decimal form) = 21% = 0.21
n = the number of compounding periods per year = 2 (since it's compounded half-yearly)
t = the number of years = 6 months = 6/12 = 0.5 years

Plugging in these values into the formula, we get:

A = 250000(1 + 0.21/2)^(2*0.5)

Simplifying the equation:

A = 250000(1 + 0.105)^(1)

A = 250000(1.105)

A = Rs. 276250

For more question compounded

https://brainly.com/question/17544895

#SPJ8

Answer:

y=15

Step-by-step explanation:

y varies directly as x so:

y=k(x)

y = kx

if y is 6 and x is 2;

input the values

y=kx

6=k(2)

[tex] \frac{6}{2} = \frac{2k}{2} [/tex]

k = 3

then find y if x=5

use the previous formula

y=kx so:

y=3(5)

therefore y=15

The Math Club raised $400.

To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.

Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.

According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.

To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:

Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%

Now we can set up a proportion to determine the amount raised by the Math Club:

(x / $2000) = 20% / 100%

Cross-multiplying:

x = ($2000 * 20%) / 100%

Simplifying:

x = $400

For more such questions on Math Club

https://brainly.com/question/31896144

#SPJ8

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

Learn more about percentage below.

https://brainly.com/question/24304697

#SPJ4

The expression that What formula(s) below represents the frequency of

that E are Option A, C and E.

A stored expression that can be invoked from other expressions is known as an expression rule. You can use rule inputs in your expression rules to allow you to dynamically alter the data your expression returns.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is called an expression or a mathematical expression.

From the option A, we have [tex]440. 2^{\frac{7}{12} } \\\\[/tex]

Then  this can be written as ; [tex]440 ^{\sqrt[12]{2} }[/tex]

which can be written as [tex]440 .10597^7}[/tex]

Read more about expression

https://brainly.com/question/1859113

#SPJ1

25 quarter cups in 6 1/4 cups

answer: 61

The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

The length of an arc with a central angle Ф with circle radius (r) is given by:

Length of arc = (Ф/360) * 2πr

Given the length of arc as 115π/6 in and angle of 138°, hence:

Length of arc = (Ф/360) * 2πr

Substituting:

115π/6 = (138/360) * 2πr

r = 25 inches

The radius of the circle is 25 inches.

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

The study described is an experimental study in nature. It follows a randomized double-blind placebo-controlled trial design, where participants were randomly assigned to either a verum (onabotulinumtoxinA) or placebo (saline) group.

The researchers administered the treatment (botulinum toxin injection to the glabellar region) to the verum group while the placebo group received a saline injection. The primary end point was the change in depressive symptoms measured using the Hamilton Depression Rating Scale.

The statistical hypothesis in this study does involve a cause/effect relationship between the explanatory variable (botulinum toxin injection) and the response variable (alleviation of depression symptoms).

Potential confounding variables in this study could include factors such as participants' previous medication history, severity of depression, and other ongoing treatments or therapies for depression.

Learn more about experiments on

https://brainly.com/question/25303029

#SPJ1

A ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

The steps for constructing a copy of an angle:

Step 1: Draw the angle.

Step 2: Place the center of the protractor on the vertex of the angle.

Step 3: Line up the baseline of the protractor with one of the angle's rays.

Step 4: Read the degree measure where the other ray crosses the protractor.

Step 5: Draw a ray from the vertex of the angle to the right.

Step 6: Use a ruler to mark the same distance on the ray that was just drawn.

Step 7: Draw a ray from the vertex through the point just marked on the ray.

This is the copy of the angle's second ray.

Step 8: Use a compass to draw an arc centered at the vertex of the original angle that passes through one of the angle's rays.

Step 9: Without adjusting the compass, draw another arc that intersects the previous arc at a point.

Step 10: Draw a ray from the vertex through the point where the two arcs intersect.

This is the copy of the original angle.

Using a compass, draw an arc centered on the vertex of the original angle passing through one of the angle rays. Place the tip of the

compass on the vertex of the original angle and draw an arc that intersects one of the angle rays.

Draws another arc that intersects the previous arc at a point without adjusting the compass.

Draw a second arc that intersects the first arc at another point, keeping the compass latitude.

Using a ruler or ruler, draw a ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

For more related questions on original angle.:

https://brainly.com/question/27243531

#SPJ8

The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

For similar question on transmitter.

https://brainly.com/question/29221269  

#SPJ8

first of all, you need to assume that this shape is like a cone. So cone has a height and you can find it by using Thales's theorem. so it would be

[tex] \frac{x}{x + 6} = \frac{4}{8} [/tex]

x is 6. So the total height of the cone has founded.

To find the volume of this frustum we have to subtract the volume of the small cone(at the top of the frustum) which has 6 cm in height from the big cone with 12 cm in height.

big cone Volume: ⅓(8²π×12)

-

small cone Volume: ⅓(4²π × 6)

=

frustum volume : 224π

The net cost of insurance, considering the alternative investment with a 5% annual yield, is $5,000.

The net cost of insurance can be calculated by considering the opportunity cost of investing the annual premium in an alternative investment that yields a 5% annual return.

Let's break down the calculation step by step:

Calculate the future value of the annual premium after 10 years:

Using the compound interest formula, the future value (FV) of the $2,000 premium invested at a 5% annual yield for 10 years can be calculated as:

FV = PV * (1 + r)^n,

where PV is the present value (annual premium), r is the interest rate (5% or 0.05), and n is the number of periods (10 years).

FV = $2,000 * (1 + 0.05)^10

FV = $2,000 * (1.05)^10

FV ≈ $3,263.18

Calculate the net cost of insurance:

The net cost of insurance is the difference between the total premiums paid over 10 years and the cash value of the policy after 10 years.

Total premiums paid over 10 years = Annual premium * Number of years = $2,000 * 10 = $20,000

Net cost of insurance = Total premiums paid - Cash value of the policy after 10 years

Net cost of insurance = $20,000 - $15,000 = $5,000

Therefore, the net cost of insurance, considering the alternative investment with a 5% annual yield, is $5,000.

For more such questions on insurance visit:

https://brainly.com/question/7326890

#SPJ8

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The average rate of change over the interval from -3 to 1 is 2.000

To find the average rate of change over the interval from -3 to 1, we need to calculate the change in y divided by the change in x.

Δy = y₂ - y₁ = (-10) - (-18) = 8

Δx = x₂ - x₁ = 1 - (-3) = 4

Now, we can calculate the average rate of change using the formula:

Average Rate of Change = Δy / Δx

Average Rate of Change = 8 / 4 = 2

Learn more about mathematical model at

https://brainly.com/question/28592940

#SPJ1

a : 10<x<=20

b: 20<x<=30

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

The formulas for the piecewise function graphed below are:
f(x) =  x + 3  for -2 ≤ x < 0, 3 for 0 ≤ x < 2, -2x + 7 for  2 ≤ x ≤ 4.

The piecewise function graph provided consists of three distinct pieces.

To give the formulas for each piece, we can break it down as follows:
For the left piece:
The left piece of the graph starts at x = -2 and ends at x = 0. It appears to be a linear function with a positive slope. Let's call this function f₁(x).
The formula for the left piece, f₁(x), can be written as:
f₁(x) = mx + b
To find the slope (m) and y-intercept (b), we can use two points on the graph.

From the graph, we can see that when x = -2, y = 1. And when x = 0, y = 3.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 1) / (0 - (-2))
m = 2 / 2
m = 1
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
1 = 1(-2) + b
1 = -2 + b
b = 1 + 2
b = 3
Therefore, the formula for the left piece is:
f₁(x) = x + 3
For the middle piece:
The middle piece of the graph starts at x = 0 and ends at x = 2. It appears to be a horizontal line.

Let's call this function f₂(x).
The formula for the middle piece, f₂(x), can be written as:
f₂(x) = c
To find the value of c, we can observe that the y-values of this piece are all equal to 3.

Therefore, the formula for the middle piece is simply:
f₂(x) = 3

When x = 2, y = 3. And when x = 4, y = -1.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (-1 - 3) / (4 - 2)
m = -4 / 2
m = -2
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
3 = -2(2) + b
3 = -4 + b
b = 3 + 4
b = 7
Therefore, the formula for the right piece is:
f₃(x) = -2x + 7
To summarize, the formulas for the piecewise function graphed below are:
f(x) =
x + 3     for       -2 ≤ x < 0
3           for       0 ≤ x < 2
-2x + 7   for      2 ≤ x ≤ 4

For more related questions on piecewise function:

https://brainly.com/question/31806828

#SPJ8

Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

a. The probability of spending less than 10 minutes is approximately 0.6255.

b. The probability of spending longer than 5 minutes is 0.9741.

c. The probability of spending between 8 and 15 minutes is 0.7181.

(a) We'll use the z-score formula:

z = (x - μ) / σ

Plugging in the values:

z = (10 - 9.3) / 2.2 ≈ 0.3182

Now, we'll look up the cumulative probability corresponding to the z-score of 0.3182 in the standard normal distribution table or use a calculator. The cumulative probability is approximately 0.6255.

(b) To find the probability of spending longer than 5 minutes, we'll again use the z-score formula:

z = (x - μ) / σ

z = (5 - 9.3) / 2.2 ≈ -1.9545

Therefore, the probability of spending longer than 5 minutes is approximately 1 - 0.0259

= 0.9741.

(c) For 8 minutes:

z1 = (8 - 9.3) / 2.2 ≈ -0.5909

For 15 minutes:

z2 = (15 - 9.3) / 2.2 ≈ 2.5909

Next, we find the cumulative probabilities for these z-scores using a standard normal distribution table or a calculator. The cumulative probability for z1 ≈ 0.2776, and for z2 ≈ 0.9957.

Finally, we subtract the cumulative probability for 8 minutes from the cumulative probability for 15 minutes to get the probability between these two values:

0.9957 - 0.2776

≈ 0.7181

Learn more about probability on

https://brainly.com/question/24756209

#SPJ1

The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

For more such questions on equation visit:

https://brainly.com/question/17145398

#SPJ8

(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.

(3b) The cost of 3 miles taxi ride is $8.1.

(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;

C = f + nx

where

C = 2.55 + 1.85x

(3b) The cost of 3 miles taxi ride is calculated as follows;

C = 2.55 + 1.85x

where;

C = 2.55 + 1.85 (3)

C = $8.1

Learn more about equations here: https://brainly.com/question/2972832

#SPJ1

The square root of the expression -36 is DNE

From the question, we have the following parameters that can be used in our computation:

[tex](-36)^\frac 12[/tex]

By definition, the square root of negative numbers are complex numbers

using the above as a guide, we have the following:

[tex](-36)^\frac 12[/tex] is not a real number

Hence, the solution is DNE

Read more about expression at

https://brainly.com/question/31819389

#SPJ1