Sarah needs to earn a C in her Algebra class. Her current test scores are 69, 75, 65, and 83. Her final exam is worth 4 test scores. In
order to earn a C Sarah's average must lie between 70 and 79 inclusive. What range of scores can Sarah receive on the final exam to
earn a C in the course?
s final exam scores[
(Type an integer or a simplified fraction.)

Answer:

[tex]x = - \frac{2}{9} [/tex]

Answer:   [tex]\text{x} = \boldsymbol{-\frac{2}{9}}[/tex]

2 goes in the green box up top

9 goes in the gray box down below.

=========================================

Work Shown:

[tex]-2(4+3\text{x}) = 3(\text{x}-2)\\\\-8-6\text{x} = 3\text{x}-6\\\\-6\text{x}-3\text{x} = -6+8\\\\-9\text{x} = 2\\\\\text{x} = \boldsymbol{-\frac{2}{9}}\\\\[/tex]

Answer:

y = -x - 1

Step-by-step explanation:

y = mx +c

y = -x + c [ m = slope]

As the line passes through (4,-5)

-5 = -4 + c [Substituting value of x and y]

c = -1 [Solving the above equation]

The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

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The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the prism is given as,

Volume = (Base area) x (Height)

The rectangular prism has a volume of 9 cubic inches. The area of the base is 4 square inches.

Then the height of the rectangular prism is given as,

9 = 4 h

h = 9 / 4

h = 2.25 inches

The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.

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We can see that the triangle is given as one of the angles is 90 degrees . The triangle is a right-angle triangle, and scalene also.

A right-angled triangle is a triangle having one of its angles with measure of 90°

The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

We can see that the triangle is given as one of the angles is 90 degrees and the other two angles are 36 and 54 degrees.

If one of the angles is 90°  then the triangle is a right-angled triangle.

Also, the length of the two sides is given as 8.66 units and 5.1.

We have already concluded that the triangle is a right-angle triangle, so all the three sides of the triangle must be different.

This implies that the triangle is scalene also.

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we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell.

What is mean ?

Mean can be defined as the ratio of sum of the given observations and total number of observations.

a) Since the life spans of the hot water heaters are normally distributed with a mean of 13 years and a standard deviation of 1.5 years, we can use the empirical rule to estimate the range of years we would expect the hot water heater to last. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

Using this information, we can estimate that the range of years we would expect the hot water heater to last is approximately 10.5 to 15.5 years. This is because one standard deviation below the mean is 13 - 1.5 = 11.5 years, and one standard deviation above the mean is 13 + 1.5 = 14.5 years. Therefore, we can reasonably expect the hot water heater to last between 10.5 and 15.5 years with about 95% confidence.

b) To set the warranty on the product so that we have to replace at most 5% of the hot water heaters that we sell, we need to find the number of years that corresponds to the 5th percentile of the distribution. This is the value below which 5% of the data falls.

We can use a standard normal distribution table or a calculator to find the z-score corresponding to the 5th percentile, which is -1.645. We can then use the formula z = (x - mu) / sigma to find the number of years, x, that corresponds to this z-score.

-1.645 = (x - 13) / 1.5

Solving for x, we get x = 10.83 years.

Therefore, we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell

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The second option is the correct representation of the given context.

A number line is a one-dimensional horizontal line where we can represent any real number.

The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

Look at the model, it starts at 125 and drops to 90.

If she has $125 and spends $35 on gas, the remaining balance is reduced by that amount.

125 - 35 = 90.

Q. Holly has $125 she spends $35 on gas for her car which model represents how much money holly has left?

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{(11, 16), (12, 14), (14, 14), (11, 13), (21, 12)}

This is because the the number 11, an x-value, is used twice and if an x-value is used more than once then it is not a function. A function is a relation between sets where there is only one output for each input

Answer:

42x + 24

Step-by-step explanation:

6(7x + 4)

42x + 24

Answer:

QR = 15

Step-by-step explanation:

Opposite sides of parallelograms are congruent. This means that their lengths are the same.

Hence,

PS = 15 = QR.

Answer:

16, 64, 256

Step-by-step explanation:

Answer: No.

Step-by-step explanation: Unless I read and calculated wrongly, it should be equal to 2b^4/(a^3b^2c^2-2)a^4c^2   -1/256

All three options involve conducting a survey using random sampling, which is the most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school. The correct answer would be A, B, or C, depending on the availability of resources.

The most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school would likely be a survey using random sampling.

Random sampling is a statistical method in which a representative sample of a larger population is selected, in order to make inferences about the population as a whole. When conducting a survey, random sampling helps to ensure that the sample is representative of the population, reducing the potential for bias.

There are several different types of surveys that could be used to estimate the level of support for a new middle school, including telephone surveys, online surveys, and in-person surveys.

Complete question:

The superintendent of a large school district wants to estimate the percentage of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents. What is the most appropriate method for the superintendent to estimate the percentage of district residents who support the building of a new middle school?

A. Telephone survey using random sampling

B. Online survey using random sampling

C. In-person survey using random sampling

D. Observing the behavior of district residents

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Answer:

10[tex]\sqrt{50}[/tex]

Step-by-step explanation:

Since it's a isosceles right triangle, so

x^2+x^2=100^2

2x^2=10000

x^2=5000

x=[tex]\sqrt{5000}[/tex]=10[tex]\sqrt{50}[/tex]

Answer:

18

Step-by-step explanation:

The median of a set of data is the value that separates the lower and upper halves of the data. To find the median, the data must be arranged in numerical order.

The data, arranged in numerical order, is:

5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20

Since the number of data points is an odd number (17), the median is simply the middle value, which is:

18

So the correct answer is A) 18.

Answer: C

Step-by-step explanation:

To find the median, arrange the numbers in sequential order.

5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20

When there are an odd number of data in the set, choose the middle number in the set. For example, see the following data set.

2, 4, 6, 8, 9

The middle number in the data set is 6, so it is the median.

When there is an even number of data in the set, choose the middle two numbers, add them together, and then divide them by 2.

There are 16 numbers in this data set. We need to find the two middle numbers in the set.

5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20

10 and 12 are the two middle numbers in the set.

10 + 12 = 22

22/2 = 11

Median = 11

Total cards = 4 (6,7,8,9), If the card is not 9, the required card will be (6,7,8), Number of cards that are not 9 is 3, Probability = expected/total P( 5) = 3/4 and the probability of picking 5 is 16.67%.

What is Probability?

There are a total of 6 numbers in the grid, and only one of them is 5. Therefore, the probability of selecting 5 is:

P(5) = 1/6

To write this as a percentage, we multiply by 100:

P(5) = 1/6 * 100% = 16.67%

Therefore, the probability of picking 5 is 16.67%.

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Ryan has the faster time when compared to each of their teams,

"Information available from the question"

The time taken by Nick is 10.8 seconds.

The mean time taken by Nick is 11.4 seconds.

The standard deviation of Nick is 0.4 seconds.

The time taken by Ryan is 11.2 seconds.

The mean time taken by Ryan is 11.5 seconds.

The standard deviation of Ryan is 0.1 seconds.

The z-score of Nick is:

[tex]z_1=\frac{10.8-11.4}{0.4}[/tex]

[tex]z_1=-1.5[/tex]

The z-score of Ryan is:

[tex]z_2=\frac{11.2-11.5}{0.1}[/tex]

[tex]z_2=-3[/tex]

Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams.

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Answer:

A) [tex](3,5)[/tex] and [tex](-4,12)[/tex]

Step-by-step explanation:

[tex]x+y=8\\x+(x^2-4)=8\\x^2+x-4=8\\x^2+x-12=0\\(x-3)(x+4)=0\\x_1=3,\,x_2=-4\\\\x_1+y=8\\3+y=8\\y_1=5\\\\x_2+y=8\\-4+y=8\\y_2=12[/tex]

The total number of possibilities for four digit pin with the condition of no digit is repeated is equal to 5040.

Total number of digit used to form pin = 4

Condition is : No digit is repeated.

Number of digits are :

( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 )

Total digits are = 10

Number of possibilities to form four digit pin with no digit repeated

=  ¹⁰P₄

= ( 10! ) / ( 10 - 4 )!

= ( 10 × 9 × 8 × 7 × 6! ) / 6!

= 10 × 9 × 8 × 7

= 5040

Therefore, the total number of possibilities to form four digit pin with the given condition is equal to 5040.

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the value of "t" will be 28 degrees for the given circle.

The following four properties and their proofs were introduced:

1: The angles at the center and at the circumference of a circle are subtended by the same arc.

2: Angles at the circumference are subtended by a diameter.

3: Angles at the circumference of a circle subtended by the same arc.

Given, a circle with an angle between two secants of 28 degrees.

From the intersecting Secant theorem of a circle:

The angle between secant = bigger arc -smaller arc)/2

In our case,

28 = (3t -t)/2

2t/2 = 28

t = 28

therefore, the value of "t" will be 28 degrees for the given data.

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The missing values in table should be completed as follows;

X(input)         Y(output)

10                     19

12                     23

Rule: y = 2x - 1.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (3, 5), a linear equation of this line in slope-intercept form can be calculated by using the point-slope form as follows:

y - 5 = (11 - 5)/(6 - 3)(x - 3)

y - 5 = 6/3(x - 3)

y = 2(x - 3) + 5

y = 2x - 1

When x(input) = 10, the y(output) is given by:

y = 2x - 1

y = 2(10) - 1

y = 20 - 1

y = 19.

When y(output) = 23, the x(input) is given by:

y = 2x - 1

23 = 2x - 1

2x = 24

x = 12.

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The function that represent the balance A in the account after t years is f(t) = 13000( 1.013 )^( 2t ).

This question is incomplete, the complete question is:

Rawan deposits $13,000 into an account that pays 2.6% annual interest compounded every 6 months.

Write a function to represent the balance A in the account after t years.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that;

First, convert R as a percent to r as a decimal

r = R/100

r = 2.6/100

r = 0.026

Given that time = t.

A = P( 1 + r/n )^( n × t )

f(t) = 13000( 1 + 0.026/2 )^( 2 × t )

f(t) = 13000( 1 + 0.026/2 )^( 2t )

f(t) = 13000( 1 + 0.013 )^( 2t )

f(t) = 13000( 1.013 )^( 2t )

Therefore, the accrued amount after t years is f(t) = 13000( 1.013 )^( 2t ).

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It  takes for the account to reach $200 is 4 years.

Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only quantity.

Given that aldonia deposits $150 into an account that pays 7.3% annual interest compounded quarterly.

[tex]A = P(1 +\frac{r}{n})^n^t[/tex]

where:

A = the total account balance after t years

P = the initial deposit $150

r = the annual interest rate =0.073

n = the number of compounding periods per year, which is 4 (quarterly) in this case

t = the number of years the money is in the account

Now let us substitute the values

[tex]A = 150(1 + \frac{0.073}{4} )^4^t[/tex] is the equation to represent Caldonia's account balance after t years.

Now let us determine the number of  years it will take for the account to reach $200.

[tex]200 = 150(1 + \frac{0.073}{4} )^4^t[/tex]

200=150(1+0.01825)^4t

[tex]1.333=1.018^4^t[/tex]

Take log on both sides

log1.333=4tlog(1.018)

0.1248=4t 0.0077

0.1248=0.0309t

Divide both sides by 0.0309

t=4.038

Hence, it takes 4 years to reach account balance of $200

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The missing reasons for the proof are given as follows:

1) AB/DB = CB/EB - Given

2) ∠ABC ≅ DBE - Opposite Angles

3) ΔABC ~ ΔDBE - Angle - Side - Side Postulate.

The Angle-Side-Side (ASA) Postulate states that if two angles and a side of one triangle are congruent to two angles and the corresponding side of another triangle, then the two triangles are congruent.

In other words, if two triangles have the same orientation and their corresponding angles and sides match in size, the two triangles are identical. The ASA Postulate can be used to determine the congruence of triangles and to prove theorems and solve problems in geometry and related fields.

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Answer:

5 mx plus b which you have to do 5 plus m to get 5m which is ur answer

The angle of elevation is 66.50 degrees

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

Rise = 46 ft

Length = 20 ft

The angle of elevation, x is calculated as

tan(x) = 46/20

Evaluate

tan(x) = 2.3

Take the arc tan of bth sides and evaluate

x = 66.50

Hence, the angle is 66.50 degrees

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Answer:

Step-by-step explanation:

C is chosen 12 times (7 + 5)

You have 50 total picks.

So the experimental probability is 12/50.

By answering the given question, we may state that Hence, the interest appropriate response is X = 40 and 8x + 10y = 600

Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to calculate interest. The most typical technique to figure out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a friend and agrees to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.

Selling x calendars will cost 8x, while selling y mugs will cost 10y. The scenario is therefore represented by the following system of inequalities in order for her to reach her objective of selling at least $600 worth of stuff, including at least 40 calendars:

(Total cost of goods sold must be at least $600; 8x + 10y)

x ≥ 40 (must sell at least 40 calendars) (must sell at least 40 calendars)

In the first inequality, you'll see that we used the symbol "" rather than ">" since Dominique needs to sell at least $600 worth of goods, not just more than $600.

Hence, the appropriate response is

X = 40 and 8x + 10y = 600

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