Which of the following expressions is equivalent to 2 to the power of 3x − 4?

the quantity 1 to the power of x end quantity over 8
the quantity 3 to the power of x end quantity over 4
the quantity 6 to the power of x end quantity over 8
the quantity 8 to the power of x end quantity over 16

Answer:[tex]m[/tex] = [tex]d[/tex]/[tex]25[/tex]

Step-by-step explanation:I don't know if this is correct but i think it is:

Solve D=25m

Evaluate powers D = 25m

Subtract D from both sides D= 25m[tex]1[/tex] - D

Add D to both sides D=25m1

Evaluate powers D=25m

Divide both sides by 25 D/25 =m

Solution m = D/25

The slope of a line parallel to the line whose equation is 5x - 3y = 18 is equal to 5/3.

In Mathematics, the slope-intercept form of an equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Making y the subject of formula, we have the following:

5x - 3y = 18

3y = 5x - 18

y = 5x/3 - 6

In Geometry and Mathematics, two (2) lines are said to be parallel under the following conditions:

m₁ = m₂ ⇒ 5/3 = 5/3

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Answer:

x = -4/3

Step-by-step explanation:

hope this helps^^

The value of y, given that Triangle FEG is similar to Triangle IHJ is 10.

Seeing as Triangle FEG is similar to Triangle IHJ, we can assume that angle EGF is the same as angle HJ1.

This means that 5 y + 8 is equal to 58 degrees.

The value of y is therefore :

5 y + 8 = 58

5 y = 50 - 8

y = ( 50 - 8 ) / 5

y = 50 / 5

y = 10

In conclusion, given the two similar triangles and the angles EGF and HJI, the value of y can be found to be 10.

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Answer:

500 words per minute.

Step-by-step explanation:

It should be noted that AP'Q'R' a 180° rotation about the origin of APQR.

It should be noted that to perform a 180° rotation about the origin, one has to draw the original figure and label its coordinates and draw the origin and label it O.

One can also use the following formula to find the coordinates of the image of a point (x,y) after a 180° rotation about the origin:

(x', y') = (-x, -y)

Here, P'Q'R' represents the coordinates of the image of the point PQR. We simply take the negative of the original x and y coordinates to find the new coordinates after the rotation.

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PLEASE GIVE BRAINLIEST <3

Answer:

I'm pretty sure it's bumper cars ( B ).

Hope this helped! <3

1) The volume of the first rectangular prism is 175 ft³

2) The volume of the second rectangular prism is 60ft³

3) The volume of the third rectangular prism 140ft³

4) The volume of the Fourth rectangular prism 216ft³

Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.

Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:

a)

Length = 7ft

Height = 2ft

widht = 2ft

Volume = Volume = 7ft x 2ft x 2ft
Volume = 28  ft³

b)

Length = 7ft

Height = 3ft

width = 7ft
Volume = 147 ft³

Total Volume = 28  ft³ + 147 ft³

Volume for Shape 1 = 175 ft³

Shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 3ft

Height = 2ft

width = 1ft

Volume = 6 ft³

b) Length = 6ft

Height = 3ft

width = 3ft

Volume = 54 ft³

Thus, total volume for shape 2 is:

Volume = 6 + 54

Volume = 40 ft³

Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 7ft

Height = 1ft

width = 2ft
Volume = 14ft³

b)
Length = 7ft

Height = 3ft

width = 6ft
Volume = 126ft³

Thus, the total volume fior shape 3, =

Volume = 14ft³ + 126ft³

Volume = 140ft³


Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 4ft

Height = 3ft

width = 2ft
Volume = 24 ft³


b) Length = 4ft

Height = 12ft

width = 4ft
Volume = 192 ft³

Thus, the total volume for Shape 4:

Volume =  24 ft³+ 192 ft³
Volume = 216ft³

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Answer:

x^2 - 9 = 0

Step-by-step explanation:

its right one.......

geometric series:

[tex]\dfrac{4}{-8} = - \dfrac{1}{2}[/tex]

[tex]\dfrac{-2}{4} = - \dfrac{1}{2}[/tex]

[tex]\implies r = - \dfrac{1}{2} \ \ and \ \ a_{1} = -8[/tex]

[tex]\boxed{S_{n} = \dfrac{a_{1}\cdot (1 - {r}^{n}) }{1 - r}}[/tex]

a. n = 3

[tex]S_{3} = - 8 + 4 - 2 = 4 - 10 = \bf -6\\[/tex]

b. n = 6

[tex]S_{6} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{6}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 - \dfrac{1}{2^{6}}\Big)}{1 + \dfrac{1}{2}} = \dfrac{-8 + \dfrac{1}{2^{3}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= \dfrac{-64+1}{2^{3}} \cdot \dfrac{2}{3} = -\dfrac{63}{2^{2}(3)} = \bf -\dfrac{21}{4}[/tex]

c, n = 25

[tex]S_{25} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{25}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 + \dfrac{1}{2^{25}}\Big)}{1 + \dfrac{1}{2}} = - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} = - \dfrac{1 + 2^{25}}{2^{22}} \cdot \dfrac{2}{3} = \bf - \dfrac{1 + 2^{25}}{(3)2^{21}}\\[/tex]

According to the probability, the answer is option D: 1/98,000.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The chance of Steve being selected is 1. This means that out of 1 individual, Steve is selected. The probability of Steve being selected is 1/1 or 1. Since the sample is a simple random sample, each individual in the population has an equal chance of being selected. If there are a total of 98,000 individuals in the population, then the probability of Silva being selected is 1 out of 98,000, or 1/98,000.

Therefore, the answer is option D: 1/98,000.

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The value of cot A is √55/3

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cot A = 1/tanA

AC = √ 8²-3²

AC = √64-9

AC = √ 55

tanA = 3/√55

cot A = 1/tanA

cot(A )= 1/(3/√55)

cot( A) = √55/3

therefore the value of cot(A) = √55/3

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The dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).

An area is just a surface that is empty. The length and breadth of a form are used to compute its area. The units used to measure length are unidimensional and include feet (ft), yards (yd), inches (in), etc. Nevertheless, a shape's area can only be measured in two dimensions. As a result, it is expressed in square units such as square inches (in2), square feet (ft 2), square yards (yd2), etc. Most forms and things have edges and corners. When determining an object's area, the length and breadth of these edges are taken into account.

Let us suppose the width of the rectangle = x.

The length of the rectangle = y

Thus,

Perimeter = 2 (x + y) + πx

34 = 2x + 2y + πx

2y = 34 - 2x + πx

The area of the window is:

A = (1/2)πx²+ xy

Substitute y = 34 - 2x + πx / 2

To maximize the area we differentiate the area and equate it to 0:

A = (1/2)πx²+ x(34 - 2x + πx / 2)

A =  (1/2)πx²+ 17x - x² + π/2x²

dA/dx = πx + 17 - 2x + πx

2πx + 17 - 2x = 0

2x(π - 1) = - 17

x = 17/(π - 1)(2)

Substitute the value of x in equation:

2y = 34 - 2x + πx

2y = 34 - 2(17/(π - 1)(2)) + π( 17/(π - 1)(2))

y = 17 - (17/(π - 1)(2)) (1 + π )

Hence, the dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).

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The price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne maths οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn. There are twο sοrts οf expressiοns in mathematics: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables. Expressiοns can be categοrised as arithmetic/numerical expressiοns, fractiοnal expressiοns, οr algebraic expressiοns depending οn the terms they cοntain.

Given the expressiοn as:

1.35 + 0.40(s)

This is used tο calculate the price οf a ticket οn the lοcal cοmmuter train.

s = number οf stοps

Nοw the cοmplete questiοn is tο calculate the price οf the ticket fοr 13 stοps.

Sο s = 13

Substitute in the expressiοn,

1.35 + 0.40(s) = 1.35 + 0.40 * 13 = 1.35 + 5.2 = $6.55

Therefοre the price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.

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Answer:

20cm³

Step-by-step explanation:

Volume = Base x Height

1/2 x 5 x 2 x 4

=20cm³

The set using Roster method is, D = {76, 90, 92, 94, 96}

The roster technique is defined as a method for displaying the elements of a set by listing the elements within brackets.

A roster method example is to write the set of numbers from 1 to 10 as

{1, 2, 3, 4, 5, 6, 7, 8, 9, and 10}.

Given:

Set D is the set of positive two-digit even numbers greater than 74

that do not contain the digit 8

First, Even numbers greater than 74 are

76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98.

Now, Even Number doe not contain 8 are 76, 90, 92, 94, 96.

Using Roster method the set is

D= {76, 90, 92, 94, 96}

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Answer:

25

Step-by-step explanation:

let the no of days food avl for eat be X .

according to question...

100/80=X/20

=X × 80 = 100×20

=80x =2000

= x =2000/80

x=25 days

Answer:

16yd

Step-by-step explanation:

I am from Michigan thank me this is really easy you nerd

This is funny helping you big people as a kid.

Answer:

x=6

Step-by-step explanation:

The value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.

What is piece wise function ?

A piecewise function is a function that is defined by different mathematical expressions or formulas for different intervals or "pieces" of the domain. In other words, a piecewise function is a function that is defined by multiple sub-functions, each corresponding to a different part of the domain.

While considering piece wise function:

[tex]F(6) = 4[/tex]                                                                 [tex](x \geq 3)[/tex]

[tex]F(-5) = x + 3 = (-5) + 3 = -2[/tex]                            [tex](x\leq -3)[/tex]

[tex]F(-1) =[/tex] [tex]-x^2 + 1 = -(-1)^2 + 1 = -1 + 1 = 0[/tex]       [tex](-3 < x < 3)[/tex]

Now put the value of F(6), F(-5) and F(-1) in the expression :

[tex]2F(6) + F(-5) - 3F(-1)[/tex]

we get :

[tex]= 2F(6) + F(-5) - 3F(-1) \\= 2(4) + (-2) -3(0)\\= 8 -2\\= 6[/tex]

Therefore, the value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.

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Answer:

x = 9/4 y = 15/4

Step-by-step explanation:

The ordered pair representing the point where both companies would charge the same amount is (25, 136.25).

From the given table, we can form the following equation for monthly cost of each company.

Company 1, the function for the monthly cost is;

(5, $55.25 ) and (10, $75.5). Let the monthly cost = y₁

(y₁ - 55.25 )/(x - 5) = ( 75.5 - 55.25 )/ (10 - 5)

y₁ = 4.05x + 35

Company 2, the function for the monthly cost is;

(5, $31.25 ) and (10, $57.5). Let the monthly cost = y₂

(y₂- 31.25 )/(x - 5) = ( 57.5 - 31.25 )/ (10 - 5)

y₂ = 5.25x + 5

To find the point where both companies charge the same amount, we need to set their costs equal to each other and solve for the number of garments, x:

y₁ = y₂

4.05x + 35 = 5.25x + 5

Subtracting 4.05x and 5 from both sides:

30 = 1.2x

Dividing both sides by 1.2:

x = 25

So both companies would charge the same amount when 25 garments are laundered. T

To find the cost, we can plug x = 25 into either equation:

y₁ = 4.05(25) + 35 = 136.25

y₂ = 5.25(25) + 5 = 136.25

Ordered pair = (25, 136.25)

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The complete question is below:

Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.

Number of Garments      Company 1       Company 2

5                                         $55.25              $31.25

10                                        $75.50             $57.50

15                                        $95.75              $83.75

Determine when both companies would charge the same amount and what that cost would be. Write your answer as an ordered with x representing the number of garments and y representing the cost.

Answer:

Equal to.

Step-by-step explanation:

multiply both numbers by 2

it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.

what is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

To determine the number of loads of trash from the garbage truck that will fill a 40-foot by 9-foot by 8-foot storage container, we need to compare the volume of the container to the volume of the garbage truck's back.

The volume of the garbage truck's back is:

V_garbage_truck = length x width x height

V_garbage_truck = 23 ft x 8 ft x 12 ft

V_garbage_truck = 2,208 cubic feet

The volume of the storage container is:

V_container = length x width x height

V_container = 40 ft x 9 ft x 8 ft

V_container = 2,880 cubic feet

To find out how many loads of trash from the garbage truck will fill the storage container, we need to divide the volume of the container by the volume of the garbage truck's back:

Number of loads = V_container / V_garbage_truck

Number of loads = 2,880 cubic feet / 2,208 cubic feet

Number of loads ≈ 1.30 loads

Therefore, it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.

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The best represent graph of the function is option a.

What is a function?

It is an expression which contains one independent variable and another is dependent variable.

The given function is

   f(x)= [tex]4^{x[/tex] - 4

As it is an exponential function so it must have a horizontal asymptote. Here the horizontal asymptote is f(x)= -4

For x intercept we need to take f(x)=0 and for y intercept substitute 0 for x and solve for y. [Here y can be treated as f(x).]

Here x intercept(s)= None

y intercept(s) = (0,-3)[ putting x=0 in   f(x) so 1-4= -3]

Hence the graph is given below.

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Answer:

See below.

Step-by-step explanation:

Hello!

The topic we should review for this problem is Order of Operations.

Order of Operations is a rule that identifies which part of an equation should be simplified first.

You might've heard of PEMDAS, where;

P for Parentheses, always first unless there's an exponent inside.

E for Exponent, simplified after the Parentheses.

M or D - Multiplication or Division after the Exponent(s).

A or S - Addition or Subtraction after Multiplication or Division.

[tex](5+3^2)+18[/tex]

First we know that there's an Exponent inside the Parentheses, so we must evaluate that number first.

[tex](5+9)+18[/tex]

Next, evaluate what's in the Parentheses.

[tex]14+18\\32[/tex]

Our correct answer is 32.

We are asked what mistake did Raquel make, and what's the correct simplified version of the expression.

1a.) Raquel's mistake is combining unlike terms. It's impossible to combine together a natural number (5) and an exponential number. (3²)

1b.) The correct simplified version of the expression is represented here;

[tex](5+9)+18\\(First \ Step)[/tex]

By answering the above question, we may state that As a result, there is standard deviation a roughly 0.9999 or 99.99% chance that the sample mean will be within 8 of the population mean.

A statistic known as standard deviation may be used to indicate the variation or variability of a set of statistics. A low standard deviation means that the values tend to be closer to the established mean whereas a large standard deviation shows that the values are widely spread. The standard deviation serves as a gauge for how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is low, and are more scattered when the standard deviation is high. Standard deviation is a measurement of the data set's average variability. It displays the standard deviation of each score with respect to the mean.

population + standard deviation departure from the mean / sqrt (sample size)

Standard deviation is 90/sqrt(100) and equals 9.

z is equal to (x - ) / ( / sqrt(n)).

where:

The sample mean is x. We are looking for the probability given the following conditions: where is the sample size, which is 100; is the population mean, which is 400; is the standard deviation of the distribution of sample means, which is 9;

When we change the values, we obtain:

[tex]Z = (9 / sqrt(100) / (x - 400)\\z = (x - 400) / 0.9\\P(392 < = x < = 408)\s= P[(392 - 400) / 0.9 < = z < = (408 - 400) / 0.9] .9]\\= P[-8.89 < = z < = 8.89] .89]\\[/tex]

To determine this probability, we can use a calculator or a conventional normal distribution table.

[tex]P[-8.89 < = z < = 8.89] = 0.9999[/tex]

As a result, there is a roughly 0.9999 or 99.99% chance that the sample mean will be within 8 of the population mean.

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Answer:

a. 480       Then 384

b. 845       Then 591.5
c. 1,189      Then 653.95
d. 153.75   Then 149.90625
e. 315        Then 299.25

f. 430.5     Then 419.7375

The line of reflection that produces X'(2, 4) is,

⇒ y - axis

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Triangle XYZ is drawn with vertices X(-2, 4), Y(-9, 3), Z(-10, 7).

Now, We know that;

The rule for a reflection over the y -axis is (x, y) → (- x, y)

Here, The line of reflection is produces X'(2, 4).

Hence, We get;

The rule for line of reflection that produces X'(2, 4) is,

⇒ y - axis

Thus, The line of reflection that produces X'(2, 4) is,

⇒ y - axis

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