I think I got part 1 correct but i have no idea which graph I should pick

Sue must earn an annual interest rate of 6.9% on the $20,000 in order to reach her goal of saving $50,000 in 10 years.

Amount If you wish to make an additional deposit to this account, you must first provide the amount you wish to deposit. Once the amount has been provided, you will be able to make the deposit. Please note that all deposits must be made in accordance with applicable laws and regulations.

In order to reach her goal of saving $50,000 in 10 years, Sue must earn an annual interest rate of 6.9%. This rate is calculated by using the formula A = P (1 + r)ⁿ, where A is the future amount, P is the present amount, r is the rate of interest, and n is the number of years.

In this case, Sue has a present amount of $20,000 and a future amount of $50,000. Therefore, the formula becomes $50,000 = $20,000 (1 + r)^10. Solving for r, the rate of interest is 6.9%. This means that Sue must earn an annual interest rate of 6.9% on the $20,000 in order to reach her goal of saving $50,000 in 10 years.

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Answer: 10.46 m

Step-by-step explanation:

C=[tex]\pi d[/tex]

=[tex]\pi (3.33)[/tex]

=10.46 m

Answer:

Step-by-step explanation:

C = π × 3.33

C = 3.14 × 3.33

C = 10.45 m  (round 10.5 m)

The correct justification for the similarity between ∆MNO and ∆PQR is:

∆MNO was dilated by a scale factor of 3 from the origin, then rotated 90° clockwise about the origin to form ∆PQR.

To see why this is the case, we can apply the transformations to the vertices of ∆MNO and see if they match the vertices of ∆PQR.

First, we dilate ∆MNO by a scale factor of 3 from the origin:

M' = 3M = (3(3), 3(9)) = (9, 27)

N' = 3N = (3(9), 3(9)) = (27, 27)

O' = 3O = (3(12), 3(3)) = (36, 9)

Next, we rotate the dilated triangle 90° clockwise about the origin:

P' = (cos(90°)P - sin(90°)Q, sin(90°)P + cos(90°)Q)

= (0P - (-1)Q, 1P + 0Q) = (Qx + 1, Py)

Q' = (cos(90°)Q - sin(90°)P, sin(90°)Q + cos(90°)P)

= (0Q - (-3)P, 1Q + 0P) = (Px + 3, Qy)

R' = (cos(90°)R - sin(90°)S, sin(90°)R + cos(90°)S)

= (4R - 4S, -4R - 4S) = (4(R - S), -4(R + S))

Substituting the coordinates of the original vertices, we get:

P' = (-1 + 1, -3) = (0, -3)

Q' = (-3 + 1, -1) = (-2, -1)

R' = 4(-4 + 1, -1 + 3) = (-12, 8)

Comparing the coordinates of ∆PQR with those of the transformed ∆MNO, we can see that they match. Therefore, the similarity between ∆MNO and ∆PQR can be justified by dilating ∆MNO by a scale factor of 3 from the origin, then rotating it 90° clockwise about the origin to form ∆PQR.

The distance between the points (-3, -3) and (-6, 1) is 5 units

We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

We need to find the distance between the points (-3, -3) and (-6, 1)

Let us assume that (x₁, y₁) = (-3, -3)

and (x₂, y₂) = (-6, 1)

Using above distance formula, the distance between the points (-6,7) and (-1,1) would be,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(1 - (-3))² + ((-6) - (-3))²]

d = √[(1 + 3)² + (-6 + 3)²]

d = √[(4)² + (-3)²]

d = √[16 + 9]

d = √(25)

d = 5 units

This is the required distance.

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The value of [tex]x _{238} = 111.1875 _{238}[/tex] for the given equation in congruence.

Congruence is an equivalence relation that is applied to compare numbers in discrete or modular arithmetic. If the difference between two numbers, a and b, is divisible by n, then the two numbers are said to be congruent modulo n (abbreviated as a b mod n). In other words, when a and b are divided by n, the remainders are equal. A key idea in number theory, congruence has a wide range of uses in domains like computer science and encryption.

For the given expression we have:

[tex]2142 . x _{238} = 442 _{238}\\x _{238} = 442 _{238} / 2142 _{238}\\x _{238} = 111.1875 _{238}[/tex]

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The associative property of 9 + (6 + 3) is 6+ (9 + 3) and it's simplified as 6+12 = 18.

The associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result.

For example, a+(b+c) is the same as b+(a+c). If a,b,c are real numbers.

This means that 9 + (6 + 3) can also be written as

6+ (9 + 3). The two expression must give thesame result.

6+ (9 + 3) = 6+ 12 = 18

Therefore the associative property of 9 + (6 + 3) is 6+ (9 + 3) and it's simplified as 6+12 = 18

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It is given that cos(θ)=4/5 and 0 <0< 90, the value of sin(θ) would be 24/25. So, the correct answer is option b.  

To find sin(2θ) in terms of cos(θ), we will use double angle formula for sin which states that:

sin(2θ) = 2 sin(θ) cos(θ)

It is given that cos(θ) = 4/5,

Using the Pythagorean identity to find sin(θ):

[tex]sin^2[/tex](θ) + [tex]cos^{2}[/tex](θ) = 1

[tex]sin^2[/tex](θ) = 1 - [tex]cos^{2}[/tex](θ)

sin(θ) = [tex]\sqrt{(1 - (4/5)^2)}[/tex]

sin(θ) = 3/5

Substituting these values into double angle formula for sin:

sin(2θ) = 2 sin(θ) cos(θ)

sin(2θ) = 2 (3/5) (4/5)

sin(2θ) = 24/25

Therefore, the answer is (b) 24/25.

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Scott will pay $10.26 for 4 lbs of chicken.

What is unitary method?

Simply put, the unitary method is used to find the value of one unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. This method is mainly used for the concept of ratio and proportion.

Given,the chicken costs $2.29 and it's being marked up by 12%.

Then the new price of the chicken will be

[tex]2.29 + (2.29 \times 0.12) = 2.29 + 0.275 = 2.565[/tex]

So, the price of the chicken per pound will be $2.565 / 1 lb = $2.565.

By the concept of unitary method ,If Scott buys 4 lbs of chicken, then the total cost will be 4 lbs x $2.565/lb = $10.26

Therefore, Scott will pay $10.26 for 4 lbs of chicken.

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In the given problem, solving using the given formula, after ten years, the value of the annuity in which you put $10,000 at a 4% annual interest rate is roughly $14,802.42.

The given formula to solve the problem is fv=P(1+r)n.

Where:

P = $10,000 (the principal)

r = 0.04 (the annual interest rate)

n = 10 (the number of years)

Furthermore, plugging in the values into the formula, we have:

fv = P(1+r)^n

= $10,000(1+0.04)^10

= $14,802.42 (rounded to two decimal places)

In conclusion, the ten-year value of a annuity of $10,000 with a 4% annual interest rate will approximately be $14,802.42.

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Answer:

0.29    

Step-by-step explanation:

Knowing that the shaded angle is 106 degrees, and a circle's angle total is 360 degrees, we will know what fraction of the circle is shaded by dividing the shaded region's angle by the angle of an entire circle:

106/360 = 0.29              

The fraction of the circle that is shaded is also the probability that a randomly selected point within the circle falls in the shaded region since we just divided the desired outcome by all of the possible outcomes.

4g to 3.5g written as a fraction in simplest form is equal to 8/7.

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this exercise, you are required to determine the ratio as a fraction in simplest form. Therefore, we would multiply both the numerator and denominator by 2 as follows;

Ratio = 4g/3.5g × 2/2

Ratio = 8g/7g

Ratio = 8/7

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Answer:

x=5

Step-by-step explanation:

Add 4 to both sides to eliminate the constant term on the left side.

53x​−4+4=−6+x+4

53x​=−2+x

Multiply both sides by 5 to clear the fraction on the left side.

5×53x​=5×(−2+x)

3x=−10+5x

Subtract 3x from both sides to collect the variable terms on the right side.

3x−3x=−10+5x−3x

0=−10+2x

Add 10 to both sides to eliminate the constant term on the right side.

0+10=−10+2x+10

10=2x

Divide both sides by 2 to get the value of x.

210​=22x​

5=x

Step-by-step explanation:

3/5  x  -4 = -6 + x       add 6 to both sides of the equation

3/5 x + 2 = x               subtract 3/5 x from both sides

2 =  2/5 x                   multiply both sides by  5/2

5/2 * 2  = x = 5

According to Daniel's theory, 18 customers would buy a toaster that costs $750.

If the popularity of a toaster is inversely proportional to its cost, we can set up a proportion as:

popularity of toaster 1 / cost of toaster 1 = popularity of toaster 2 / cost of toaster 2

Let's let x be the number of customers who would buy a toaster that costs $750.

We can write:

12 / 500 = x / 750

Simplifying:

12(750) = 500x

9000 = 500x

x = 18

Therefore, according to Daniel's theory, 18 customers would buy a toaster that costs $750.

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Answer:

D. -1/3

The slopes of perpendicular lines are negative reciprocals of each other. In other words, the product of the slopes of perpendicular lines is -1. So the slope of a line perpendicular to a line with a slope of 3 will have a slope of -1/3. D is correct.

The domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

Function is a process or a set of rules that take input values and produces an output. It is a mathematical expression that takes the inputs, performs an operation and produces an output. Functions are used to model real-world scenarios and to solve problems. It helps to simplify the code and makes it easier to understand and debug. Functions are also used to create reusable code that can be used in different applications.

A: Domain: (Negative infinity, infinity), Range: (Negative infinity, infinity)

B: Domain: (Negative infinity, 4), Range: (Negative infinity, 4)

C: Domain: (Negative infinity, 4], Range: (Negative infinity, 4]

D: Domain: [-3, 4], Range: [-7, 4]

Answer: D: Domain: [-3, 4], Range: [-7, 4]

The domain of f(x) is the set of all x-values for which the function is defined, which in this case is [-3, 4]. The range of f(x) is the set of all y-values for which the function is defined, which in this case is [-7, 4]. The value of f(-3) is -7, according to the graph.

To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤ -3, f(x) = x + 7. For -3 < x ≤ 0, f(x) = -x. For 0 < x < 4, f(x) =√x.

In conclusion, the domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

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The domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

What is function in math?

Function is a process or a set of rules that take input values and produces an output. It is a mathematical expression that takes the inputs, performs an operation and produces an output. Functions are used to model real-world scenarios and to solve problems. It helps to simplify the code and makes it easier to understand and debug. Functions are also used to create reusable code that can be used in different applications.

A: Domain: (Negative infinity, infinity), Range: (Negative infinity, infinity)

B: Domain: (Negative infinity, 4), Range: (Negative

infinity, 4)

C: Domain: (Negative infinity, 4], Range: (Negative infinity, 4]

D: Domain: [-3, 4], Range: [-7, 4]

Answer: D: Domain: [-3, 4], Range: [-7, 4]

The domain of f(x) is the set of all x-values for which the function is defined, which in this case is [-3, 4]. The range of f(x) is the set of all y-values for which the function is defined, which in this case is [-7, 4]. The value of f(-3) is -7, according to the graph.

To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤-3, f(x) = x+7. For -3 <x≤0, f(x)=-x. For O <x<4, f(x)=√x.

To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤-3, f(x) = x + 7. For -3 <x ≤ 0, f(x) = -x. For O <x<4, f(x)=√x.

In conclusion, the domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.

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Answer:

Step-by-step explanation:

You want the x-coordinates of the absolute extrema of the function f(x) = 5x² -8x +7 on the interval [0, 8].

The absolute extrema of a function on an interval will lie at the ends of the interval or at a turning point within the interval.

For a quadratic ax²+bx+c, the turning point is at x=-b/(2a). For the given function, the turning point is at ...

  x = -(-8)/(2·5) = 0.8

This lies within the interval, and represents the location of the absolute minimum of this function whose graph opens upward.

The graph of the function is symmetrical about the vertical line through the turning point. The function increases as x-values are farther from the turning point, so the end of the interval farthest from x = 0.8 will be the location of the absolute maximum. That is at x = 8.

The absolute minimum at x = 0.8; the absolute maximum is at x = 8.

The area of the blacktop in square meters is: 272m²

The formula for the area of a rectangle is:

A = l * w

where:

l is length

w is width

Thus:

A = 10m * 8m

A = 80m²

That’s the area of the first rectangle.

A = l x w

A = 24m x 8m

A = 192m²

That’s the area of the second rectangle.

Total area of composite shape = 192m² + 80m² = 272m²

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The margin of error, using a 95% confidence level is 0.026. The Option C.

The margin of error can be calculated using the formula which is "Margin of Error = Critical Value * Standard Deviation"

Given:

Sample proportion is 26%

Sample size is 1100

We can then calculate the Standard Deviation as follows:

= sqrt((p * (1 - p)) / n)

Plugging in the values, we get:

= sqrt((0.26 * (1 - 0.26)) / 1100)

= sqrt (0.00017490909)

= 0.01322497637

≈ 0.013

We must find Critical Value for a 95% confidence level. For a normal distribution, the Critical Value is approximately 1.96. Now, we can calculate the Margin of Error which is

= Critical Value * Standard Deviation

= 1.96 * 0.013

≈ 0.026

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Answer:

The measure of both of the smaller angles is 43°.

The measure of the larger angle is 94°.

Step-by-step explanation:

We can model the larger angle in relation to the smaller angle by representing each of the smaller angles (which are equal in measure) as a variable x and the larger angle as a variable y.

[tex]y = 2x + 8[/tex]

This shows that the larger angle is eight degrees more than twice (2 times) the smaller angles' measures.

We can now model the sum of all the triangle's angle measures because we know that a triangle's interior angle measures add to 180°.

[tex]2(\text{small}) + \text{large} = 180[/tex]

[tex]2x + y = 180[/tex]

What we have now is a system of equations which we can solve for using substitution. The first equation ([tex]y = 2x + 8[/tex]) is a definition of y in terms of x, so we can substitute that definition into the second equation and solve for x.

[tex]\begin{cases} y = 2x + 8 \\ 2x + y = 180\end{cases}[/tex]

[tex]2x + (2x + 8) = 180[/tex]

[tex]4x + 8 = 180[/tex]

[tex]4x = 172[/tex]

[tex]\boxed{x = 43\textdegree}[/tex]

So, the measure of each of the smaller angles is 43°.

Now, we can plug that x-value back into the first equation and solve for y.

[tex]y = 2(43) + 8[/tex]

[tex]y = 86 + 8[/tex]

[tex]\boxed{y = 94\°}[/tex]

So, the measure of the larger angle is 94°.

Answer:

-11<-1

-5>-8

11>-6

Step-by-step explanation:

In this case I'm assuming we're looking for the greater number. When it comes to negative number the number thats closest to zero would be greater than the one not. Positive numbers are always greater than negative numbers.

Answer: -11<-1, -5>-8, 11>-6.

Step-by-step explanation:

-1> -11 because -1 is closer to positive than -11

-5>-8 because -5 is closer to positive than -8

11>-6 because 11 is a positive number

Answer:   -3 x y + x + 4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To calculate the total number of different outfits possible, we can use the multiplication principle of counting. We multiply the number of choices for each item together to get the total number of outfits.

Number of choices for jeans: 2 (pair of jeans AB)

Number of choices for shirts: 4 (shirts CDEF)

Number of choices for shoes: 2 (pair of shoes GH)

Total number of outfits: 2 x 4 x 2 = 16

Here's a tree diagram showing the possibilities:

modify it

    Jeans                   Shirt               Shoes

      /\                         /\                      /\        

     /  \                       /  \                    /  \

    A    B                  C    D              G    H

   /          \              /           \         /             \

  CDEF   CDEF  CDEF    CDEF  CDEF   CDEF

  / \             / \         / \         / \         / \       / \

 GHGH   GHGH  GHGH  GHGH GHGH GHGH

The tree diagram shows that there are 2 choices for jeans (A or B), 4 choices for shirts (C, D, E, or F), and 2 choices for shoes (G or H). We can follow the branches of the tree to see all the possible outfit combinations, which total to 16.

Answer:4/3

Step-by-step explanation:48/36

A. The percentage of students who passed the exam and completed the exam review is given as 55%.

B. The percentage of students who did not complete the exam review and passed the exam is given as 20%.

C. There is most probably an association between completing the exam review and passing the exam.

Part A:

The percentage of students who passed the exam and completed the exam review is given as 55%.

Part B:

The percentage of students who did not complete the exam review and passed the exam is given as 20%.

Part C:

The percentage of students who passed the exam and completed the exam review is 55%, while the percentage of students who passed the exam and did not complete the exam review is 20%.

These percentages are significantly different from each other, indicating that there is likely an association between completing the exam review and passing the exam.

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Answer:

3.5 litres.

Step-by-step explanation:

We can use the unit rate method to find how much tea Ben drinks per hour.

First, we can convert 2/3 of an hour to an hour by multiplying it by 3/2:

2/3 hour * 3/2 = 1 hour

This tells us that the rate of drinking tea is constant, and Ben drinks 3 and 1/2 liters of tea per hour.

Therefore, Ben drinks 3.5 liters of tea per hour.

The surface area of solid B is calculated as:

13. 144π ft²       14. 85.3 ft²

Recall that the ratio of the surface areas of similar solids is equal to the square of the ratio of their linear measures.

Thus, we have the following:

13. Let the surface area of solid B be represented as x, therefore:

36π / x = 4² / 8²

x * 4² = 36π * 8²

16x = 2,304π

16x/16 = 2,304π/16 [division property of equality]

x = 144π ft²

14. Let the surface area of solid B be represented as x, therefore:

48 / x = 27² / 36²

Cross multiply:

x * 27² = 48 * 36²

729x = 62,208

729x/729 = 62,208/729 [division property of equality]

x = 85.3 ft²

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The value k of the exponential growth rate will be 0.045.

Given that:

$228 in 1975

$472 in 1986

Let 'x' be the number of years and 'y' be the selling price. Then the equations are given as,

[tex]\rm 288 = P_o \times e^{k *1975} \ \ \ \ \ \ ...(1)\\\\\rm 472 = P_o \times e^{k *1986} \ \ \ \ \ \ ...(2)[/tex]

From equations (1) and (2), then

[tex]e^{k(1986 - 1975)} = \dfrac{472}{288}\\\\e^{k(1986 - 1975)} = 1.63889[/tex]

Take log on both sides, then

k x (11) = ln 1.63889

k = 0.494/11

k = 0.045

The value k of the exponential growth rate will be 0.045.

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Answer:

Let's represent the width of the flag with 'w'. Then, according to the problem, the length would be 'w + 90'.

We know that the perimeter of a rectangle is given by:

P = 2(length + width)

Substituting the values from the problem, we get:

500 = 2(w + w + 90)

Simplifying, we get:

250 = 2w + 90

2w = 160

w = 80

So, the width of the flag is 80 feet.

And the length of the flag would be:

w + 90 = 80 + 90 = 170 feet.

Step-by-step explanation:

(212900 + 213500) ÷ 2

426400/2 = 213200

The number exactly halfway between 212,900 and 213,500 is 213,200.

Finding the number that is halfway between two given values is a fundamental concept in mathematics, and it involves a simple calculation using basic arithmetic.

To find the number that is exactly halfway between two values, you need to add the two values together and then divide the sum by 2.

In this case, 212,900 + 213,500 = 426,400.

Dividing 426,400 by 2 gives us 213,200, which is the number exactly halfway between the two given values.

Therefore, 213,200 is the answer to the question.

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