g(x)
12 fy
10
88
8
6
4
4-3-2-12
-8
10
-1²1
f(x)
4 5 6 x
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)



PLEASE HURRY IM TIMED!!!!

1. Daily cost of keeping the bulb lit for 5 hours is 5 cents.

2. Switching to an LED bulb could save $13.50 in a year.

Power consumed by the 100-watt bulb in 5 hours is:

= 100 watts x 5 hours

= 500 watt-hours

= 0.5 kilowatt-hours

The cost of electricity for 0.5 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:

= 0.5 kWh x 10 cents/kWh

= 5 cents

b. The power consumed by the 26-watt LED bulb over 5 hours is:

= 26 watts x 5 hours

= 130 watt-hours

= 0.13 kilowatt-hours

The cost of electricity for 0.13 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:

= 0.13 kWh x 10 cents/kWh

= 1.3 cents

Annual savings is:

= (Daily cost 100-watt bulb - Daily cost LED bulb) * 365 days

= (5 cents - 1.3 cents) x 365 days

= $13.50.

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The increase in Fahrenheit temperature  is of 12.6 degrees.

The formula to have a change of units is:

To convert Celsius to Fahrenheit, you can use the formula:

°F = (°C x 1.8) + 32

(So you are correct, the rate is 9/5 = 1.8)

The increase of 7°C wold be given by the difference:

increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32

Solving that equation we can see that

increase =  12.6°F

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Answer:

he increase in Fahrenheit temperature  is of 12.6 degrees.

What is the increases in Fahrenheit temperature?

The formula to have a change of units is:

To convert Celsius to Fahrenheit, you can use the formula:

°F = (°C x 1.8) + 32

(So you are correct, the rate is 9/5 = 1.8)

The increase of 7°C wold be given by the difference:

increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32

Solving that equation we can see that

increase =  12.6°F

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Step-by-step explanation:

The exact value of x is 24

To determine the value, we need to that the different trigonometric identities are;

From the information given, we need to determine the value of the opposite side.

The hypotenuse side = 16√3

The opposite side = x

Using the sine identity;

sin θ = opposite/hypotenuse

substitute the values

sin 60 =x/16√3

cross multiply the values

x = 16√3 × √3/2

Divide the values, then multiply the square roots of the values

x = 8×3

x = 24

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Sure, I'd be happy to help you with this problem!

Given that the ratio of boys to girls in the school is 4:3, we can say that for every 4 boys, there are 3 girls.

Let's start by finding the total number of students in the school, using the information that there are 18 girls.

If 3 girls represent a part of the whole, then we can find the total number of parts by dividing the total number of girls by 3:

18 girls ÷ 3 = 6 parts

So, there are 6 parts in the whole.

Now, since there are 4 boys for every 3 girls, we know that for every 7 parts (4 boys + 3 girls), there are 4 boys.

To find the total number of boys, we need to figure out how many groups of 7 parts there are in the whole.

6 parts ÷ 7 = 0 with a remainder of 6

This tells us that there are 0 groups of 7 parts in the whole, with 6 parts left over.

Since we know that for every 7 parts there are 4 boys, we can find the number of boys in the remaining 6 parts by multiplying 4 by the fraction of 6/7:

4 boys × 6/7 = 24/7 boys

This tells us that there are 24/7 boys in the remaining 6 parts.

To find the total number of boys in the school, we need to add the number of boys in the groups of 7 parts and the number of boys in the remaining 6 parts:

0 groups of 7 parts × 4 boys per group = 0 boys

6 parts × 4 boys per 7 parts = 24/7 boys

Total number of boys = 0 boys + 24/7 boys = 24/7 boys

So, there are 24/7 boys in the school. We can simplify this fraction by dividing both the numerator and the denominator by 3:

24/7 ÷ 3/3 = 8/7 boys

Therefore, there are 8/7 boys in the school, which is approximately 1.14 boys.

However, since we cannot have a fraction of a person, we can round this number to the nearest whole number, which is 1.

Therefore, there is 1 boy in the school for every 3 girls, making a total of:

1 boy × 18 girls = 18 boys

So, there are 18 boys in the school.

Answer:

Step-by-step explanation:

just do how tall times the diamiter divided by the

Answer:

Step-by-step explanation:

The required probability is simply the (shaded area)/(area of the whole box)

The area of the whole box would be:

6r*2r = 12 r^2

The shaded area is tough to calculate, but you can get the

white area instead.

The left hole (white area) consists of a semi-circle and a rectangle.

The center hole is a circle.

The right hole (white area) consists of a semi-circle and a rectangle.

The 2 semi-circles in the left and right hole combine to be a circle.

The 2 rectangles in the left and right hole combine to be a square.

The total area of holes are:

(area of circle)*2 + (area of square)       ### 2 circles 1 square in total

=r^2*pi*2 + (2r)^2

=r^2*pi*2 +4*r^2

then we can get the shaded area by:

(area of the whole box) - (The total area of holes)

= 12 r^2 - (r^2*pi*2 +4*r^2)

=8*r^2 - r^2*pi*2

Finally:

(shaded area)/(area of the whole box)

=(8*r^2 - r^2*pi*2)/(12 r^2)

=(8-pi*2)/(12)

=0.143067891

=14.3% (corr. to 3 sig. fig.)

The solution to all parts from a to f is shown below.

A) Matrix A:

[ 2  -3 ]

[ 4   3 ]

B) The determinant of matrix A is:

det(A) = (2*3) - (-3*4) = 6 + 12 = 18

C) Matrix X:

[ -8  -3 ]

[ -34  3 ]

D) The determinant of matrix X is:

det(X) = (-8*3) - (-3*-34) = -24 - 102 = -126

E) Matrix Y:

[ 2  -8 ]

[ 4  -34 ]

F) The determinant of matrix Y is:

det(Y) = 2(-34) - (-8) (4) = -68 + 32 = -36

G) Using Cramer's rule, we can solve for x and y as follows:

x = det(X) / det(A) = -126 / 18 = -7

y = det(Y) / det(A) = -36 / 18 = -2

Therefore, the solution to the system is (-7, -2).

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Answer:

Quick internet search:

Answer:

x = 99

Step-by-step explanation:

Since x is on a straight line the adjacent angle and x must equal 180. We will call this adjacent angle B. The angle to the right of B also is on a straight line.

So,

180 - 123 = the inside angle             Simplify

57

The addition of a triangles interior angles equals 180

180 = 42 + 57 + B                              Move variables to one side

180 - (42 + 57) = B                             Simplify

81 = B

Now we can solve for X

180 - 81 = x                                        Simplify

99

2401/16 square inches

Step-by-step explanation:

Given:

The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is  in long.

To find: the area of the whole quilt

Solution:

Side of each quilt =

Quilt is in the form of a square such that area of square is given by

Therefore, area of quilt =   square inches

Answer:

13 + 8 + 13 + (1/2)(8π) = 34 + 4π feet

= 46.57 feet

The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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At the 0.05 significance level, the degree of freedom is 1. So, correct option is B.

To test the hypothesis that the proportion of wins is the same for teams wearing suits as for teams wearing jeans, we can use the chi-square test for independence. The null hypothesis is that the proportion of wins is the same for both groups, and the alternative hypothesis is that they are different.

Using the given data, we can calculate the expected frequencies under the assumption of equal proportions of wins for both groups. The expected frequency for each cell is given by (row total x column total) / grand total.

The calculated chi-square statistic is 2.667, and the degrees of freedom are (r-1)(c-1) = (2-1)(2-1) = 1.

Using a chi-square distribution table with 1 degree of freedom and a significance level of 0.05, the critical value is 3.84. Since the calculated chi-square value is less than the critical value, we fail to reject the null hypothesis.

Therefore, we can conclude that there is not enough evidence to suggest that the proportion of wins is different for teams wearing suits versus jeans and t-shirts at the 0.05 significance level.

The answer choice that corresponds to 1 degree of freedom is B

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Answer:

1. The slope of the line is 3. The line goes up 3, over 1, and since slope is rise/run, the slope is 3.

2. The slope of the line is 4. The line goes up 4, over 1, and since slope is rise/run, the slope is 4.

3. The slope of the line is 2. The line goes up 2, over 1, and since slope is rise/run, the slope is 2.

4. The slope of the line is -4. The line goes down 4, over 1, and since slope is rise/run, the slope is -4.

The gradients of line equations are listed below:

In this question we have four cases of line equations shown on Cartesian plane, whose gradients must be found. The gradient of each line can be computed by means of secant line formula and two points:

m = Δy / Δx

Where:

Case 1: (x₁, y₁) = (- 1, - 4), (x₂, y₂) = (1, 2)

m = [2 - (- 4)] / [1 - (- 1)]

m = 3

Case 2: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (0, 3)

m = [3 - (- 1)] / [0 - (- 1)]

m = 4

Case 3: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (1, 3)

m = [3 - (- 1)] / [1 - (- 1)]

m = 2

Case 4: (x₁, y₁) = (0, 4), (x₂, y₂) = (2, - 2)

m = (- 2 - 4) / (2 - 0)

m = - 3

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Answer:

(2,1)

Step-by-step explanation:

The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.

So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:

4(1) - 2(2) = 0

So the point (2,1) is on the line.

Answer:

AB = 90° , AC = BC = 135°

Step-by-step explanation:

the arc AB is equal to the measure of the central angle it subtends, then

AB = 90°

the sum of the arcs in a circle = 360° , then since AC and BC are congruent

AB + AC + BC = 360° ( since AC = BC ), then

90° + 2AC = 360° ( subtract 90° from both sides )

subtract 90° from both sides

2AC = 270° ( divide both sides by 2 )

AC = 135°

since AC = BC , then

AC = BC = 135°

Answer: 2,001.57

Step-by-step explanation:

there ya go!

The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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The function f(x) = 12/x + 1/2 is given. To find f(3), we substitute x=3 in the function expression and simplify: f(3) = 12/3 + 1/2 = 4 + 0.5 = 4.5. Therefore, the value of the function f at x=3 is 4.5.

To find f(3) for the function f(x) = 12/x + 1/2. Start with the given function f(x) = 12/x + 1/2. Replace x with 3: f(3) = 12/3 + 1/2. Simplify the first term: 12/3 = 4

Add the two terms: f(3) = 4 + 1/2

Convert the mixed number to an improper fraction: 4 + 1/2 = 8/2 + 1/2 = 9/2

Simplify the fraction: 9/2 = 4 1/2

So, f(3) = 4 1/2 or 9/2, depending on the desired form of the answer.

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The vector v can be decomposed into v₁ = -2i - 2j and v₂ = -6i + 6j.

The decomposition of the vectors is calculated as follows;

v₁ = (v · w / |w|²) w

v₂ = v - v₁

The dot product of v and w is calculated as;

v · w = (-8)(1) + (4)(1)

v · w = -4

The magnitude of w is calculated as;

|w| = √1² + 1²)

|w|= √2

|w|² = 2

The value of v₁ is calculated as;

v₁ = (-4 / 2) (i + j)

v₁  = -2i - 2j

The value of v₂ is calculated as follows;

v₂ = v - v₁

v₂  = (-8i + 4j) - (-2i - 2j)

v₂ = -6i + 6j

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Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Using rules for logarithms we can see that the statement is false.

Here we have the equation:

logₐ(x^3 + y^3) = 3logₐ(x) + 3logₐ(y)

And we want to see if it is true.

First, remember two rules:

logₐ(x^n) = n*logₐ(x)

and:

logₐ(x) + logₐ(y) = logₐ(x*y)

Then, the right side of the statement can be rewritten as:

3logₐ(x) + 3logₐ(y)

3(logₐ(x) + logₐ(y)) = 3*logₐ(x*y) = logₐ((x*y)^3)

And that is different to what we got in the statement, so the statement is false.

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Answer:

Step-by-step explanation:

Answer:

G^-1(t)=t/7+4

Step-by-step explanation:

G(t) = 7(t - 4)

y = 7(x - 4)

x = 7(y - 4)

x/7 = y - 4

y = x/7 + 4

G^-1(t) = t/7 + 4

Answer: G^-1(t)=t/7+4

Answer:

K5.60.

Step-by-step explanation:

For the function f(x) = -2x² + 5x + 7 the slope of the secant line between x = -3 and x = 5 is -4

Consider the function f(x) = -2x² + 5x + 7

We need to find the slope of the secant line between x = -3 and x = 5

We know that the slope of secant line for the function f(x) on the interval [a, b] is given by the formula,

m = [f(b) - f(a)] / (b - a)

Let [a, b] = [-3, 5]

For x = -3 the value of the function would be,

f(-3) = -2(-3)² + 5(-3) + 7

      = -2(9) - 15 + 7

      = -18 - 15 + 7

      = -26

And the value of the function for x = 5 would be,

f(5) = -2(5)² + 5(5) + 7

      = -2(25) - 25 + 7

      = -50 - 15 + 7

      = -58

Using above formula the slope would be,

m = [f(5) - f(-3)] / (5 - (-3))

m = [-58 - (-26)] / 8

m = (-58 + 26) / 8

m = -4

Thus, the required slope is -4

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Answer:

Slope = 1

Step-by-step explanation:

A secant line is a straight line that intersects a curve at two or more points.

Given a curve represented by a function f(x), a secant line is determined by choosing two distinct points on the curve, (x₁, f(x₁)) and (x₂, f(x₂)).

The secant line passes through these two points and can be represented by a linear equation in the form y = mx + b, where m is the slope of the secant line and b is the y-intercept.

The slope of the secant line between the points (x₁, f(x₁)) and (x₂, f(x₂)) is given by the formula:

[tex]m = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

To find the slope of the secant line between x = -3 and x = 5 for the function f(x) = -2x² + 5x + 7, first find f(-3) and f(5).

[tex]\begin{aligned}f(-3)&=-2(-3)^2+5(-3)+7\\&=-2(9)-15+7\\&=-18-15+7\\&=-26\end{aligned}[/tex]

[tex]\begin{aligned}f(5)&=-2(5)^2+5(5)+7\\&=-2(25)+25+7\\&=-50+25+7\\&=-18\end{aligned}[/tex]

Input the values into the slope formula:

[tex]m = \dfrac{f(5) - f(-3)}{5 - (-3)}=\dfrac{-18-(-26)}{5+3}=\dfrac{8}{8}=1[/tex]

Therefore, the slope of the secant line between x = -3 and x = 5 is 1.

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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The best method to describe data is use median value for how number of daily downloads varies, and mean value or interquartile range for number of daily downloads. So, correct options are A, D and E.

The median value is a measure of central tendency that represents the middle value of a set of data. It is useful to describe how the number of daily downloads varies, as it gives an idea of the typical value of the dataset.

However, mean absolute deviation is a measure of dispersion that describes how far the data values are from the mean. It is not an appropriate method to describe how the number of daily downloads varies, as it does not give information about the distribution of the data.

The maximum value is a measure of the largest value in a dataset, which can provide information on the upper limit of the number of daily downloads. However, it is not an appropriate method to describe how the number of daily downloads varies, as it does not give information on the spread or distribution of the data.

The mean value is a measure of central tendency that summarizes the data with a single number, but it may not be the best choice if the data is skewed or has outliers.

The interquartile range is a measure of dispersion that summarizes the spread of the middle 50% of the data. It can be used to summarize the number of daily downloads with a single number, but it does not give information on the typical or extreme values of the dataset.

The minimum value is a measure of the smallest value in a dataset, which can provide information on the lower limit of the number of daily downloads. However, it is not an appropriate method to summarize the number of daily downloads with a single number, as it does not give information on the spread or distribution of the data.

So, correct options are A, D and E.

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