14. Ronny is taking a jar with 50 dimes and
quarters to CoinMaster to redeem for dollar
bills. The total value of his jar is $8.
a. Write a system of equations to represent the
number of quarters, q, and the number of
dimes, d, in the jar.
b. Solve the system to determine the number of
quarters and dimes in the jar.

After finding the value of the angle CAE will be equal to 22°.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the information provided in the question,

 The perpendicular bisector of side AB of ABC intersects side AB at point D and BC at point E in the ABC equation. Also, m∠CAB = 82° and m∠C = 68°.

Join A and E.

In Δ ABC

∠A+∠B+∠C = 180° (Angle sum property of triangle.)

82°+∠B+68° = 180°

∠B = 180°-150°

∠B =30°

In Δ ADE and Δ BDE

AD=B D(DE shown is a perpendicular bisector.)

∠ADE =∠BDE = 90°

DE is common.

Δ ADE ≅ Δ EDB (By using the property SAS)

∠DEB=∠D A E [By using the property CPCT]     (1)

In Δ DBE

∠EDB + ∠DBE+∠BED = 180°

90° +30°+∠BED = 180°

∠BED = 180°-120°

∠BED = 60°

So, ∠BAE=∠BED=60° (By using equation 1)

∠CAE=∠CAB - ∠BAE

∠CAE = 82°-60°

∠CAE = 22°.

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The dimensions of the garden would be length = 28 meters and width = 9.5 meters

A database of research funds called Dimensions connects funding to articles, clinical trials, and patents as well as other outcomes. Dimensions is a division of the technology firm Digital Science, which has its global headquarters in London, United Kingdom.

Let the width be = w

Let the length be = L

enclose three side ( 2w+L) = 47 meter

L = 47-2w

Area of field = w*L

Area = w(47 - 2w)

266  = 47w - 2w²

2w² - 47w + 266 = 0

Solving this, we get

w = 14 or w = 9.5

The width should be less than the length so w = 9.5

Length = 47 - 2(9.5)

           = 47 - 19

           = 28 meters.

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1. The average gas price for 2010 is of: $2.22.

2. The linear regression equation is given as follows: y = 0.176x + 0.5.

3. The domain is: [0,∞).

4. The range is: [0.5,∞).

5. Gas is expected to cost $4.55 in 2025.

The linear regression is obtained inserting the points of the table into a linear regression calculator.

The variables of the problem are given as follows:

Hence the points are given as follows:

(0, 0.7), (1,1.04), (2, 1.15), (3, 1.38), (4, 1.86), (5, 1.70), (6, 2.55), (7, 1.29), (8, 2.22), (9, 2.56).

Inserting these points into a calculator, the equation is given as follows:

y = 0.176x + 0.5.

The estimate for 2025 is the numeric value when x = 23, as 2025 is 23 years after 2002, hence:

y = 0.176(23) + 0.5 = $4.55.

The domain and the range are given as follows:

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Answer: 27.3 %

Step-by-step explanation:

There are 8 blue and 3 red marbles in the bad so total is 11 marbles

We just need to take 3 divided by 11, then timed 100 and will get the percent of 27.27, or I round up to 27.3%

Answer:  34.00 and 2.10

Step-by-step explanation:

The required regression equation is y = -2.78x + 48.5 for the line of best fit where x represents the month and y represents the time.

The table is given in the question.

As per the given table, the required solution would be as:

Let x represents the month and y represents the time

[tex]\bar{x}[/tex] = (1+2+3+4+5+6)/6 = 21/6 = 3.5

[tex]\bar{y}[/tex] = (47+43+39+36+35+33)/6 = 233/6 = 38.83

Sum of x = 21

Sum of y = 233

Mean x = 3.5

Mean y = 38.8333

Sum of squares (SSX) = 17.5

Sum of products (SP) = -48.5

Regression Equation = y = bx + a

b = SP/SSX = -48.5/17.5 = -2.77143

a = MY - bMX = 38.83 - (-2.77×3.5) = 48.53333

y = -2.78x + 48.5

Thus, the required regression equation is y = -2.78x + 48.5 for the line of best fit.

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Answer:

y = -2.78x + 48.5

Step-by-step explanation:

I just took the test like 2 seconds ago...

Answer:

48 movies

Step-by-step explanation:

8/16=1/2

24/48=1/2

The correct answer is Independent groups design.

Given that,

Participants in a study are randomly allocated to one of two groups; one group is run at night, while the other is run during the day. Then, each member of each group is measured twice under the red and blue conditions, respectively.

Independent groups design.

Independent measures style, conjointly called between groups is an experimental style wherever completely different participants are employed in every condition of the experimental variable. This suggests that every condition of the experiment includes a distinct cluster of participants.

Therefore, the correct answer is Independent groups design.

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(i) The percentage of dogs of this breed that weigh less than 53 pounds P(X<53) = 50.0%

(ii) The percentage of dogs of this breed that weigh less than 46 pounds P(X<46) = 15.2%

(iii) The percentage of dogs of this breed that weigh more than 46 pounds P(X>46) = 84.8%

What is Standard Deviation?

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values of the set tend to be near to the mean (also known as the expected value), whereas a high standard deviation shows that the values are spread out over a larger range.

Solution:

Mean weight (μ) = 53 pounds

Standard deviation (σ) = 6.2 pounds

The z-score for any given weight, 'X', is given by the following expression;

z = (X - μ)/σ

(i) P(X<53)

Since 53 pounds is exactly the mean weight, 50% of the dogs weight more than 53 pounds while 50% weight less than 53 pounds.

P(X<53) = 50.0%

(ii) P(X<46)

z = (46-53)/6.2

z = -1.12

this is equivalent to 15.2 percentile

P(X<46) = 15.2%

(iii) P(X>46)

P(X>46) = 100% - P(X<46) = 100% - 15.2%

P(X>46) = 84.8%

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Answer: Nonlinear.

Step-by-step explanation:

Answer: x = 3

Step-by-step explanation: both expressions are equal to each other because the angles are opposite of each other, so you would set the expressions equal to each other and solve from there.

set equations = to each other: 6x - 7 = 4x - 1

add 7 to the other side: 6x = 4x + 6
subtract 4x to the other side: 2x = 6

divide both sides by 2: x = 3

I think it might be all them but the third one, if I'm wrong sorry.

Answer:

(a-1)^2-9

Step-by-step explanation:

First you divide the coefficient of a by 2, which is 1. Now, do this: [tex](a-1)^2-8[/tex] where the -1 is half the coefficient of a. What this does is get the first two terms: a^2 and 2a, but we have an extra + 1(expanding this out gives [tex]a^2 -2a + 1[/tex]. So we have to subtract 1 to cancel it out. This gives [tex](a-1)^2-9[/tex], because -8-1=9. We can check this by expanding it out, and seeing if it equals our previous equation. Expanding this out gives [tex]a^2-2a+1-9[/tex], which is equal to our originial equation.

The claim to be indicated is that there is enough evidence to reject the null hypothesis and the test statistic would be 21.75

A type of statistical inference called hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution. The parameter or distribution is initially assumed in a preliminary manner. The null hypothesis is also known as H0, because it is the default assumption. Then, the opposite of what the null hypothesis claims is characterized as an alternative hypothesis (designated Ha). Using sample data, the hypothesis-testing technique determines whether or not H0 may be rejected. If H0 is rejected, the statistical inference is that the alternative hypothesis Ha is correct.

How to solve?

If the die is fair, the probability of getting any of the six numbers is equal (1/6).

The test statistic (TS) is given as:

TS=∑(Oi−Ei)2Ei∼χ2n−1

TS=(4−8)^2/8+(13−8)^2/8+…(2−8)^2/8

TS=21.75

In conclusion, the die is unfair.

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Answer:ralph got an 90 on his math test and a 80 on his history test

Step-by-step explanation:

so i divided 170 and that = to 85 so i took the two 5 from the two 80 and added it to the 80 for math

3206 students are randomly chosen since there is no knowledge of the sample fraction.

The following can be used to represent the formula for calculating the margin of error for a single proportion:

ME = z√p(1 - p)/n

In order to be 91% certain that the sampling percentage seems to have an error margin of 1.5 percentage points, the number of randomly chosen students that must be surveyed is equal to;

0.015 = 1.6954×√0.5(1 - 0.5)/n

0.015/1.6954 = √0.5(0.5)/n

On further solving,

n = 3205.128

n ≈ 3206

As a result, 3206 students are randomly chosen since there is no knowledge of the sample fraction.

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The correct question is-

College officials want to estimate the percentage of students who carry a gun, knife, or other such weapons. How many randomly selected students must be surveyed in order to be 91% confident that the sample percentage has a margin of error of 1.5 percentage points?

a) Assume that there is no available information that could be used as an estimate of p.

Answer:

1/c2

Step-by-step explanation:

Answer:

x=-12

Step-by-step explanation:

it would be -2=-x-14 then solve as normal algebraic equation

add 14 to each side 12=-x

then divide by -1 on each side so you get x=-12 for the final answer hope this helps

For the octagon whose measure of angle is (9w + 8)°, the value of w is 14.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Angle of regular octagon = 9w + 8

Since, angle of an octagon is 135°

Equate 9w + 8 to 135,

9w + 8 = 135

9w = 127

w = 14.11

w = 14

The required value of w is 14.

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Answer:

he octagon whose measure of angle is (9w + 8)°, the value of w is 14.

Step-by-step explanation:

What is angle?

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Angle of regular octagon = 9w + 8

Since, angle of an octagon is 135°

Equate 9w + 8 to 135,

9w + 8 = 135

9w = 127

w = 14.11

w = 14

The required value of w is 14.

i hope this helps !!!!!

By using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

So, draw a figure of the 2 buildings as follows:

(Refer to the  image attached below)

Now, we know that we can get the distance between the rooftops using the Pythagorean theorem.

Pythagorean theorem: c² = a² + b²

Now, insert the values and calculate as follows:

c² = a² + b²

c² = 12² + 16²

c² = 144 + 256

c² = 400

c = √400

c = 20ft

Therefore, by using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.

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The correct statement regarding the rate of change of the functions is given as follows:

The amount of wood required has a constant rate of change, but the amount of glass does not.

The rate of change of a function is obtained as the change in the output of the function divided by the change in the input of the function.

For the wood function, we have that when x is increased by one, the output of the function W(x) is increased by 10, hence the rate of change is constant.

For the glass function, we have that:

Hence the rate of change is not constant, and then the second statement is the correct statement.

The table is given by the image shown at the end of the answer.

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Option B. Because when you have quantitative data, but assumptions of normality are not met. This is because, unlike parametric tests, non-parametric tests do not make assumptions about the data's underlying distribution.

Non-parametric tests are often used when dealing with data that is not normally distributed, as they allow for a more accurate analysis of such data. They can also be used when a linearity of the data cannot be assumed and when dealing with ordinal data. Non-parametric tests are more powerful than parametric tests, which makes them a good choice when a more precise analysis is needed.

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Based on the slope (-8) of the linear equation, the amount Austin pays each week, which is $8.

A linear equation can be defined as y = mx + b, which shows the relationship between variable x and variable y, where we have the following:

Slope value = m = change in y / change in x [this is also the unit rate]

Y-intercept of initial value = b.

Given that the table represents a linear equation, find the slope or unit rate of the linear equation, which represents the amount Austin pays every week.

Slope (m) = change in L / change in t

Using two pairs of values from the table, (2, 24) and (4, 8):

Slope (m) = change in L / change in t = (24 - 8) / (2 - 4) = 16/-2

Slope (m) = -8

This implies that, Austin pays $8 every week.

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Answer:

Okapi weighs 290, and llama weighs 160.

Answer: x≥3

Step-by-step explanation:

The derivative dy/dt when the x coordinate's rate of change 18 feet is 13.5 feet.

Given,

The radius of the circular track in which the jogger runs = 70 feet

The coordinates of the jogger = (42, 56)

The rate of change in x coordinate = 18 feet/sec

Let (x,y) be the coordinates

We have to find dy/dt;

Then we know x,y satisfies the equation of the circle as

x² + y² = 70²

Let us differentiate this implicit function with respect to t

2x dx/dt + 2y dy/dt = 0

At this point, dx/dt 18 and x = 42. y = 56

Substitute to have

2 × 42 × 18 + 2 × 56 dy/dt = 0

1512 + 112 dy/dt = 0

dy/dt = 1512/112

dy/dt = 13.5 feet

Therefore,

The derivative dy/dt here is 13.5 feet

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Answer:  The correct answer is C. y + 3 = 5(x − 1)

Step-by-step explanation:

Change the equation into slope-intercept form

y + 3 = 5(x − 1)

y = 5x - 8

Using the slope-intercept form of y = mx + b, m = slope, and b = the y-intercept.

Therefore, y = 5x - 8 has a slope of 5 and a y-intercept of -8

When we graph the slope from y = -8, it passes through (1, -3)

The additive inverse of (-4x - 8)  is  4x+8.

What is Additive Inverse?

Additive inverse refers to any number that when added to the original number gives the result as zero. For instance, the additive inverse of 8 is -8 as 8 + (-8) = 0. It is possible to get the additive inverse of negative numbers too. For example, the additive inverse of -10 will be 10 as -10 + 10 = 0.

The additive inverse of any given number can be found by changing the sign of it. The additive inverse of a positive number will be a negative, whereas the additive inverse of a negative number will be positive. However, there will be no change in the numerical value except the sign. For example, the additive inverse of 8 is -8, whereas the additive inverse of -6 is 6.

The addition of a number and its additive inverse is equal to the additive identity.

we know that (-4x - 8)  +  (4x+8) = 0 .

Hence, The additive inverse of (-4x - 8)  is  4x+8.

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Answer:

z = − 5 + 7i

Step-by-step explanation:

z + 14 - 5i = 9 + 2i
Subtract 14 from both sides.

z - 5i = 9 + 2i -14
Subtract 14 from 9 to get -5.

z - 5i = -5 +2i
Add 5i to both sides.

z = -5 + 2i + 5i
Combine real and imaginary parts.

z = -5 + (2+5)i
Add 2 to 5.

z = -5 + 7i

Hope this helps!

Answer:

7i - 5

Step-by-step explanation:

z + (14 - 5i) = 9 + 2i

=> z + 14 - 5i = 9 + 2i

=> z = 9 + 2i + 5i - 14

=> z = 7i - 5

On solving the provided question, significant difference between the four testing conditions is α = 0.10

An alternative hypothesis is one in which the researchers predict a difference (or an effect) between two or more variables, indicating that the observed pattern of the data is not the result of chance.

Null hypothesis:  : μ1 ≥ μ2, There is no significant difference in history test scores between students with different academic major

Alternative Hypothesis: Ha : μ1 < μ2. Exam outcomes in history are substantially more varied among students with different academic specialties.

Determine the significance level. α = 0.10

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