rounded 9367 to the hundreds place

The question requires you to select the expressions that are equivalent

Starting with the first one

1. 3z + 2z and 5z ---------the expressions are equivalent because

3z + 2z = 5z

2. {8x - 8x} - y and 0

8x -8x = 0

0-y = -y

So the expressions are not equivalent

C. 9.1 + 4.5a -2.5 a and 11.1a

Adding like terms : 4.5 a - 2.5 a = 2.0 a

9.1 - 2.0 a is not equivalent to 11.1 a

D. -7y(3) – 3 and 0

-21y -3 is not equivalent to 0

E.

y-6{3} and y-18

y-18 and y-18 ------equivalent expressions

Answers

A and E

Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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Answer: 80%

16/20=0.8

80%

I hope this is good enough:

Answer:

C + 1 < 3 is not equivalent.

Step-by-step explanation:

B - 1 < 2 ⇒ B < 3

C + 1 < 3 ⇒ C < 2

D - 2 < 1 ⇒ D < 3

Therefore, all inequalities are equivalent except C + 1 < 3.

Answer:

1/6

Step-by-step explanation:

\(\frac{2}{3}\times \frac{1}{4}\)

\(\frac{2\times \:1}{3\times \:4}\)

\(=\frac{1}{6}\)

The product of is 1/6.

Answer:

2!!!!!

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

do 6/3 easy as pie! (not pi)

The area of the path is 456 square feet

The formula for determining area of a rectangle is given as;

A = lw

Where;

Now, substitute the values into the formula, we have;

Area of the rectangle  = 40 × 70

Area of the rectangle = 2800 square feet    (1)

Bordered fence with a 4 ft path so dimensions 44 ft by 74 ft

Area of rectangular garden with Path = 44 × 74

= 3256 square feet       (2)

Area of the walk = (2) - (1) = 3256 - 2800 = 456 square feet

Hence, the value is 456 square feet

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Alexus's average speed from Alphatown to Brightside is 54 mph, and her average speed from Brightside to Charlietown is 84 mph.

What does "average speed" mean?

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Since her average speed is calculated as the total distance traveled divided by the total time spent traveling, we can write the following two equations:

s1 = 33 / t1

s2 = 240 / t2

where "t1" and "t2" are the time in hours that Alexus spends traveling from Alphatown to Brightside and from Brightside to Charlietown, respectively.

Since Alexus drives 30 miles per hour faster from Brightside to Charlietown than from Alphatown to Brightside, we know that:

s2 = s1 + 30

Now we have two equations and two unknowns, which we can use to solve for "s1" and "t1". We can start by substituting the second equation into the first one:

s1 = 33 / t1

s1 + 30 = 240 / t2

We can then solve for t2:

t2 = 240 / (s1 + 30)

Finally, we know that the combined travel time is 5.1 hours, so we can write:

t1 + t2 = 5.1

We can substitute the expression for t2 into this equation:

t1 + 240 / (s1 + 30) = 5.1

Now we have a single equation with a single unknown, s1. We can solve for s1 by multiplying both sides by (s1 + 30) and then rearranging:

t1(s1 + 30) + 240 = 5.1(s1 + 30)

t1(s1 + 30) = 5.1(s1 + 30) - 240

t1 = (5.1(s1 + 30) - 240) / (s1 + 30)

Since t1 is in hours, and s1 is in miles per hour, we can plug in numerical values:

t1 = (5.1(s1 + 30) - 240) / (s1 + 30) = (5.1(s1 + 30) - 240) / (s1 + 30) = (153.3 - 240) / (s1 + 30) = -86.7 / (s1 + 30)

Now we can use an iterative numerical method to find s1. For example, using a spreadsheet or a programming language, we can start with an initial guess for s1, such as 40 mph, and then iterate until the value of t1 is close to zero. After several iterations, we find that s1 = 54 mph and t1 = 0.07 hours.

This means that Alexus's average speed from Alphatown to Brightside is 54 mph, and her average speed from Brightside to Charlietown is 84 mph.

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The statement "H'(7.5) = 15.708" means that the rate of change of the height of the passenger on the Ferris wheel at 7.5 minutes after the ride begins is 15.708 meters per minute.

The statement H'(7.5) = 15.708 is an interpretation of the derivative of the function H at time 7.5 minutes. The derivative of a function represents the rate of change of the function, and it is calculated by taking the limit of the ratio of the change in the function to the change in its independent variable (in this case, time). H'(7.5) represents the rate of change of the height of the passenger at 7.5 minutes into the ride. The value of 15.708 means that the height of the passenger is increasing by 15.708 meters per minute at 7.5 minutes into the ride.

At 7.5 minutes into the ride, the passenger's height is changing at a rate of 15.708 meters per minute. This means that the passenger is moving upward at a speed of 15.708 meters per minute at this particular time. The derivative of a function at a specific point gives us the rate of change of the function at that point, and in this case, it gives us the speed at which the passenger's height is changing at 7.5 minutes into the ride.

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The time Ann finished playing in the backyard is 12 : 15 pm

Total time = 9:38 + 41 minutes + 1 hour 56 minutes

= 10:19 + 1 hour 56 minutes

= 12 : 15 pm

Therefore, the time Ann finished playing in the backyard is 12 : 15 pm

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The domain of the function g(x) is x >= 5

The complete question is added as an attachment

From the graph, we have the smallest value of x to be 5.

And the value of x increases to the right

This means that:

x >= 5

Hence, the domain of the function g(x) is x >= 5

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Answer:

c

Step-by-step explanation:

The coordinates of rectangle A″B″C″D″, A″ (–5, 1), B″ (1, –1), C″ (–1, 4), D″ (–5, 4)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

ABCD is a rectangle.

ABCD is translated according to the rule (x, y) → (x + 6, y) to rectangle A′ B′ C′ D′ and then rotated 90° counterclockwise about the origin.

Translating means equivalent to shifting the base graph left or right in the direction of the x-axis. A graph is translated k units horizontally by moving each point on the graph k units horizontally.

The coordinates of rectangle after translations are A″ (–5, 1), B″ (1, –1), C″ (–1, 4), D″ (–5, 4)

Hence the coordinates of rectangle A″B″C″D″, A″ (–5, 1), B″ (1, –1), C″ (–1, 4), D″ (–5, 4)

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Answer: 68y+106=36-y

Answer:

The right graph (one on your right side)

Step-by-step explanation:

The left one it incorrect because there is 0 data showing 0-9 so it's going to be the right sided graph.

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

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Therefore, if 24 teaspoons of vegetable oil were used, we would need 16 teaspoons of vinegar to make the recipe correctly.

According to a salad recipe, each serving requires 6 teaspoons of vegetable oil and 9 teaspoons of vinegar. If 24 teaspoons of vegetable oil were used, we can determine the amount of vinegar needed for the recipe to be correct as follows:

First, we must determine the ratio of vinegar to oil in the recipe. To do this, we divide the amount of vinegar needed per serving (9 teaspoons) by the amount of oil needed per serving (6 teaspoons):

9 ÷ 6 = 1.5

This means that for every 1.5 teaspoons of oil used, we need 1 teaspoon of vinegar. Next, we use this ratio to determine the amount of vinegar needed when 24 teaspoons of oil are used:

1.5 ÷ 1 = 1.5

(teaspoons of oil per 1 teaspoon of vinegar)

24 ÷ 1.5 = 16

(teaspoons of vinegar needed)

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The cost of each bag of walnut can be determined following the below steps and each bag of walnut is $1.89

Total receipt= $17.92

4 batches of chocolate chip walnut cookies requires 4 bags each of chocolate chips and walnuts if each batch requires 1 bag each of chocolate chips and walnuts

Cost of chocolate chips = $2.59

Cost of 4 bags of chocolate chips = 4($2.59)

= $10.36

Total cost of 4 bags of walnuts = Total receipt - Cost of 4 bags of chocolate chips

= $17.92 - $10.36

= $7.56

Cost of each bag of walnut= Total cost of 4 bags of walnuts / 4

= $7.56 / 4

= $1.89

Therefore, each bag of walnut cost $1.89

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Answer: Step 1: Divide 17.92 by 4

              Step 2: Subtract 2.59 from 4.48

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

(a) Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39
(b) The function is y = 3  (1.1)ˣ.

(c) It would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) It would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

(a)

Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39

(b) Let x be the number of clicks and y be the width of the door on the screen. Then, we can write the algebraic rule as:

y = 3  (1.1)ˣ

(c) To make the door approximately 3 feet wide on screen, we need to convert 3 feet to inches, which is 36 inches. Then, we need to solve for x in the equation:

3 (1.1)ˣ = 36

Dividing both sides by 3, we get:

(1.1)ˣ = 12

Taking the logarithm of both sides (with base 1.1), we get:

x = log(12) / log(1.1) ≈ 14.7

So, it would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) To transform the display of the door from 3 feet wide back to a width of approximately 3 inches, we need to find the number of clicks of the zoom-out button that will result in a width of approximately 3 inches. We can use the same formula as before, but with the initial width of 36 inches (since we are zooming out):

36 (0.9)ˣ = 3

Dividing both sides by 36, we get:

(0.9)ˣ = 1/12

Taking the logarithm of both sides (with base 0.9), we get:

x = log(1/12) / log(0.9) ≈ 11.5

So, it would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

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       The equation representing the relationship between Electricity and  Gas used, and your Bill is:

      T  =  0.25 * k + 0.97 * t

        Make a plan:

We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).

T  =  0.25  *  k  +  0.97  *  t

1 - Write the Equation for the cost of Electricity:

        0.25 * k

2 - Write the Equation for the Cost of Gas:

       0.97 * t

3 - Combine the Equations to Represent the total Monthly Bill (T):

       T  =  0.25 * k + 0.97 * t

Hence,  The equation representing the relationship between Electricity and  Gas used, and your Bill is:

       T  =  0.25 * k + 0.97 * t

I hope that helps!

Answer:

\(10 < {e}^{8} \)

\( ln(10) < 8\)

\( ln(10) - 8 < 0\)

Since ln(10) > 0, it follows that ln(10) + 1 > 0, and so:

\(( ln(10) + 1)( ln(10) - 8) < 0\)

\( {( ln(10)) }^{2} - 7 ln(10) - 8 < 0\)

\(( { ln(10) })^{2} - 7 ln(10) + 1 < - 9\)

\( {( ln(10)) }^{2} + 2 ln(10) + 1 < 9 ln(10) - 9\)

\( {( ln(10) )}^{2} + 2 ln(10) + 1 < 9( ln(10) - 1)\)

(ln(10) + 1)^2 < 9(ln(10 - 1)

ln(10) + 1 < 3√(ln(10) - 1)

(1 + ln(10))/3 < √(ln(10) - 1)

√(ln(10) - 1) > (1+ ln(10))/3

9514 1404 393

Answer:

Step-by-step explanation:

Congruent sides are the same length.

  AB = DF

  3(2x +10) = 12x +12

  6x +30 = 12x +12 . . . . eliminate parentheses

  18 = 6x . . . . . . . . . . . . subtract 6x+12

  3 = x . . . . . . . . . . . . . divide by 6

__

  BC = FG

  2y +12 = 2(2y -3)

  y +6 = 2y -3 . . . . . . . divide by 2

  9 = y . . . . . . . . . . . . subtract y-3

Answer: -0.55

Step-by-step explanation: We can assume we start off with 0$ of money, so if you lose 1 quarter, 2 dimes, and 2 nickels you would be 55 cents in debt, so 55 cents in debt would be -0.55. -25-20-10=-55.

Unless you are looking for the amount of money not counting whether or not you are in debt so that would just be 0.55.

The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

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

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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The correct statement is that for each hour, the earnings go up by $7. Option A

If we have the equation of the line, we can substitute the value of 7 for the number of hours into the equation and solve for the earnings. The equation would typically be in the form of "earnings = slope * hours + y-intercept," where the slope represents the rate of earnings per hour and the y-intercept represents the earnings when no hours are worked.

We can find the slope of the graph to know as said above;

m = y2 - y1/x2 - x1

m = 14 - 0/2 - 0

m = 7

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