(SAT prep) Find the value of x in each case of the following exercises:

The calculated value of x at g(x) = 2 is x = 2.5

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

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

\($\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$\)

Here, \($t_{\alpha/2,n-1} = t_{0.05/2,10-1}$\)

                       = 2.145

Substitute the values

\($24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$\)

(26.17, 21.83)

When the \(\text{sampling of the same size}\) is repeated from the \(\text{population}\) \(n\) infinite number of \(\text{times}\), and the \(\text{confidence intervals}\) are constructed, then \(95\%\) of them contains the \(\text{true value of the population mean}\), μ in between \((26.17, 21.83)\)

b). The formula to calculate 95% prediction interval is given by :

    \($\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$\)

   \($24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$\)

   (31.13, 16.87)

Answer:

3/24 and 35/63

Step-by-step explanation:

3 / 6 of 1 / 4 = 3 x 1 / 6 x 4 = 3 / 24

7 / 9 of 5 / 7 = 7 x 5 / 9 x 7 = 35/63

Answer:

3            1               1

_     X    _      =       _  

6            4              8

7            5              5

_     X     _   =        _

9            7              9

Hope this helped :)

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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Answer:

The North American Free Trade Agreement (NAFTA) among the United States, Canada and Mexico went into effect on January 1, 1994. It is the first trade agreement the United States has entered into with a geographically-close developing country and has raised concerns about its economic effect, particularly on U.S. communities and workers. Since the mid-1980s, when Mexico began reducing trade restrictions, the U.S. and Mexican economies have become more highly integrated. This is evidenced by the rapid growth in U.S. merchandise trade with Mexico, which is now 12% of all U.S. trade

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

Answer:

4 5/8

Step-by-step explanation:

7 7/8= 63/8

3 1/4= 13/4= 26/8

63/8 - 26/8= 37/8

37/8= 4 5/8

Given:

Two cards are drawn from a standard deck of cards without replacement.

To find:

The probability of drawing a heart and a club in that order.

Solution:

We have,

Total number of cards = 52

Number of cards of each suit (Spade, club, diamond, heart) = 13

The probability of drawing a heart card is:

\(P(Heart)=\dfrac{\text{Number of heart cards}}{\text{Total number of cards}}\)

\(P(Heart)=\dfrac{13}{52}\)

\(P(Heart)=\dfrac{1}{4}\)

Now, the number of remaining card is 51. So, the probability of drawing a club card is:

\(P(club)=\dfrac{\text{Number of club cards}}{\text{Total number of remaining cards}}\)

\(P(club)=\dfrac{13}{51}\)

Using these probabilities, the probability of drawing a heart and a club in that order is:

\(P(\text{Heart and club})=P(\text{Heart})\times P(\text{Club})\)

\(P(\text{Heart and club})=\dfrac{1}{4}\times \dfrac{13}{51}\)

\(P(\text{Heart and club})=\dfrac{13}{204}\)

Therefore, the required probability is \(\dfrac{13}{204}\).

a) The terminal point is 0.896 radius length.

b) The value returned is -0.896.

We have,

The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)

a. Since the circle's radius is 3 units long, we divide the x-coordinate by 3:

x-coordinate of terminal point: -2.69

Number of radius lengths to the right: -2.69 / 3 ≈ -0.896

However, since the angle is measured from the 3-o'clock direction, we consider it to be in the clockwise direction.

Thus, the number of radius lengths to the right is

Number of radius lengths to the right: -(-0.896) = 0.896

Therefore, the terminal point is 0.896 radius length.

b. Using Trigonometry

cos(h) = x-coordinate of terminal point / radius length

cos(h) = -2.69 / 3 ≈ -0.896

c. As, θ = h. From the given information, we have:

θ ≈ -0.896 radians

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Answer:

it is not likey bc inless the class have over 2 mil ppl in it itis doouptfull

Step-by-step explanation:

Option 4 is the correct choice.

We have a graph that represents a inequality.

We have to determine which of the following given inequalities is plotted in the graph

An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.

According to the question, we have -

The straight line is not uniform but dashed. Hence, the type of inequality will be strict (either < or > ).

The y - intercept of the line is at : + 3.

The slope of the line will be = \(\frac{3 -0}{0-1.5} = -2\)

Now, it is clear from the above discussion that the we are left with two possible options - option C and D. Consider a point (0, 0) and check both the inequalities mentioned in option C and D.

For y > -2x + 3 at (0,0)

0 > 0 + 3

0 > 3

which is false.

For  y < -2x + 3 at (0,0)

0 < 0 + 3

0 < 3

Which is true.

Hence, the inequality represented by the graph is :  y < - 2x + 3

Therefore, Option 4 is the correct choice.

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Step-by-step explanation:

use the above picture as a reference and solve

Answer:

36°

Step-by-step explanation:

So, the angle measure of x+15 is 36 because x = 21

The angle measure of 3x-9 is 54, but this is bigger than the one before.

So, the smallest angle is 36

Please give the other person brainliest cause they deserve it more than me.

Answer:

C. 15

Step-by-step explanation:

You just need to add the number of dots, hoped this helped and was fast enough

The property used in step 2 is the addition property of inequality.

The Addition Property of Inequality states that if the same number is added to both sides of an inequality, then the sense (inequality symbol) of the inequality remains unchanged.

Given is an inequality, 7x + 4 < 46, we need to solve for x,

The given inequality, 7x + 4 < 46,

Solving x,

7x + 4 < 46 [given]

Add -4 both sides

7x < 42 [addition property]

Divide by 7 both sides,

x < 6 [division property]

Hence, the property used in step 2 is addition property.

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Answer: To calculate the average cost per widget, we need to consider both the fixed costs and the variable costs.

Fixed costs: $34,000

Variable costs per widget: $5.00

Total costs = Fixed costs + (Variable costs per widget × Number of widgets)

Total costs = $34,000 + ($5.00 × 7,000)

Total costs = $34,000 + $35,000

Total costs = $69,000

Average cost per widget = Total costs / Number of widgets

Average cost per widget = $69,000 / 7,000

Average cost per widget ≈ $9.86

Therefore, the average cost per widget of producing 7,000 Wild Widgets is approximately $9.86.

Step-by-step explanation: :)

Answer:

(1,0)

Step-by-step explanation:

A.K.A the y and x intercepts you might need to do a little more math you get the y intercept tho

Answer:

9 pcs of fruit

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5x5 = 25

Answer:

25

Step-by-step explanation:

Let's go through our times tables really quick!

5x1 = 5 (5 + 0)

5x2 = 10 (5 + 5)

5x3 = 15 (5 + 5 + 5 [10 + 5])

5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)

As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5

So, 5x5 is 25

Hope this helped!

Answer:

The answer is 5.

Step-by-step explanation:

-3-(-8) = -3+8 = 5.

Answer:

The answer is 5.

Step-by-step explanation:

For the polynomial function,

The leading terms of the polynomial is 4

The degree of f(x) is 23

And the leading coefficient is 4x²³

Polynomial function:

Polynomial function means a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given,

Here we have the polynomial function

f(x) = -4(x-2)¹²(6-x)¹¹

Now, we need to find the leading term, degree and the leading coefficient of the polynomial function.

The degree of a polynomial is the highest of the degrees of the polynomial's individual terms. In our case, the degree is 23.

The leading term is the term with the highest degree. In our case, the leading term is 4x²³

The leading coefficient is the coefficient of the leading term. In our case, the leading coefficient is 4.

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Answer:

Step-by-step explanation:

Piecewise function 'f' has been given as,

f(x) = 4x + 3 when x < 0

        (x + 7) when x ≥ 0

By using the piecewise function,

a). f(-2) = 4(-2) + 3  (Use f(x) = 4x + 3, since x = -2 is less than 0)

           = -8 + 3

           = -5

b). f(0) = 0 + 7 (Use f(x) = x + 7, since x = 0 is equal to 0)

           = 7

c). f(1) = 1 + 7 (Use f(x) = x + 7, since x = 1 is greater than 1)

         = 8

Answer:

2,4 3,5

Step-by-step explanation:

Answer:

The dimensions that will maximize the enclosed area of the pen is 250 ft by 250 ft

Step-by-step explanation:

we have the perimeter as 1000

So the sum of the lengths will be

1000/2 = 500

The dimensions that will maximize these pens will be such that they will have equal values

Mathematically, that will be 500/2 = 250 by 250

Answer:

Step-by-step explanation:

First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03

That means that there was a gain of $7.03 per share for Archie.

That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:

(7.03x100)= 703

The answer then is:

Archie gained $703 from selling all of his shares.

Answer:

52 and 26

Step-by-step explanation:

2x=y

x+y=78

3x=78

x=26

2(26)=y

y=52

To check:

52+26=78

Answer:

5(x+4) (x-2)

Step-by-step explanation:

5x^2 + 10x - 40

Factor out a 5

5(x^2 +2x - 8)

Looking at the inside of the parentheses

What 2 numbers multiply to -8 and add to 2

4 *-2 = -8

4+-2 = 2

5(x+4) (x-2)

Given.

\(5x^2+10x-40\)

Factor out the GCF.

\(5(x^2+2x-8)\)

Use AC method.

\(x^2+bx+c\)

\(x^2+2x-8\)

Find product of b (-8) and sum of c (2x).

(-2,4)

When you solve.

\(5((x-2)(x+4))\)

Answer:

$159.24 is the balance after 9 months is the answer that you seek

Step-by-step explanation:

Answer:

the savings plan balance after 9 months with an APR of 8% and monthly payments of $250 is approximately $2,366.98.

Step-by-step explanation:

To find the savings plan balance after 9 months with an APR of 8% and monthly payments of $250, we can use the formula for the future value of an annuity:

FV = Pmt x ((1 + r/n)^(n x t) - 1) / (r/n)

where:

FV = future value

Pmt = monthly payment

r = annual interest rate

n = number of compounding periods per year

t = time in years

In this case, we have:

Pmt = $250

r = 8%

n = 12 (since payments are made monthly)

t = 9/12 = 0.75 (since 9 months is three-quarters of a year)

Substituting these values into the formula, we get:

FV = $250 x ((1 + 0.08/12)^(12 x 0.75) - 1) / (0.08/12)

FV ≈ $2,366.98

Therefore, the savings plan balance after 9 months with an APR of 8% and monthly payments of $250 is approximately $2,366.98.

Answer:

\( z= \frac{2.1-1.98}{0.08}= 1.5\)

And we can use the normal standard table and the complement rule and we got:

\(P(z>1.5)= 1-P(Z<1.5) =1- 0.933= 0.067 \approx 0.07\)

And the best answer would be:

C 0.07

Step-by-step explanation:

Let X the random variable who represent the amount of soda filled in large bottles and we know this:

\(\mu = 1.98, \sigma =\sqrt{0.0064}= 0.08\)

And we want to find this probability:

\( P(X> \mu +1.5 \sigma = 1.98 +1.5*0.08 =2.1)\)

And for this case we can use the z score formula given by:

\( z=\frac{X -\mu}{\sigma}\)

And replacing we got:

\( z= \frac{2.1-1.98}{0.08}= 1.5\)

And we can use the normal standard table and the complement rule and we got:

\(P(z>1.5)= 1-P(Z<1.5) =1- 0.933= 0.067 \approx 0.07\)

And the best answer would be:

C 0.07