11
David made a class banner out of a large rectangular piece of paper. He cut a
triangular piece out of one side, as pictured below.
14 in.
5 in.
3 in.
-11 in.-
14 in.
What is the area, in square inches, of the banner?

C.

Step-by-step explanation:

To calculate the total distance Tyson traveled, we need to use the formula: distance = speed x time. First, we calculate the distance traveled during the first segment at 60 mph for 1.5 hours: distance = 60 x 1.5 = 90 miles. Then, we calculate the distance traveled during the second segment at 70 mph for 2.5 hours: distance = 70 x 2.5 = 175 miles. Adding these two distances together, we get: 90 + 175 = 265 miles. Therefore, the answer is C, 265 miles.

The probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion is  98.6%.

We are given that the population proportion, p, is 0.6, and we want to find the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of p. Let's first find the standard error of the sample proportion:

SE = √(p*(1-p) / n)

where p is the population proportion, 1-p is the proportion of voters who do not support the candidate, and n is the sample size.

Substituting the given values, we get:

SE = √(0.6 * 0.4 / 1000) = 0.01549193338

To find the probability that the sample proportion is within 0.04 of p, we can use the normal distribution and the z-score formula:

z = (sample proportion - p) / SE

where the sample proportion follows a normal distribution with mean p and standard deviation SE.

Substituting the values, we get:

z = (0.64 - 0.6) / 0.01549193338 = 2.590020246

z = (0.56 - 0.6) / 0.01549193338 = -2.590020246

Using a standard normal distribution table or calculator, we can find the area under the curve between z = -2.590020246 and z = 2.590020246 to be approximately 0.986.

Therefore, the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of the actual proportion is approximately 0.986 or 98.6%.

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The number 320.5492492492... is rational and can be expressed as the fraction 1829/333.

To show that the number 320.5492492492... is rational, we can follow the same approach as before and express it as a sum of rational numbers.

Let x = 320.5492492492...

We can separate the integer part of x and the repeating decimal part:

x = 320 + 0.5492492492...

To express the repeating decimal part as a fraction, we can subtract a portion of it from the original number, like this:

1000x - 320000 = 549.2492492...

100000x - 32000000 = 549249.2492492...

Now we can subtract the first equation from the second equation:

99900x = 549249.2492492... - 549.2492492...

This simplifies to:

99900x = 548700

x = 548700/99900

Simplifying the fraction by dividing both numerator and denominator by their greatest common factor, we get:

x = 1829/333

Therefore, the number 320.5492492492... is rational and can be expressed as the fraction 1829/333.

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0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).
Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.
Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.
So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.
To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.
We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.
Using these estimates, we can calculate the z-scores as follows:
z1 = (35 - 48)/17 = -0.76
z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.
To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:
0.3514 * 380 ≈ 133.7
So, the answer is not one of the choices given.

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The answer is not one of the choices given.0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).

Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.

Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.

So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.

To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.

We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.

Using these estimates, we can calculate the z-scores as follows:

z1 = (35 - 48)/17 = -0.76

z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.

To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:

0.3514 * 380 ≈ 133.7

So, the answer is not one of the choices given.

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The solving of equation 3²x=4 in both the given cases gives the answer

x = 0.631.

We have,

A mathematical statement composed of two representations joined by an equal sign is known as an equation.

3x - 5 = 16 is an example of an equation.

We obtain the value for the variable x as x = 7 after solving this equation.

So,

(1) Common logarithm:

2x log 3 = log 4, or 2x(0.47712) = 0.60206

When we solve for x, we get 0.95424x = 0.60206, and x = 0.60206/0.95424.

x = 0.631

(2) Logarithm with base 3:

2x (log to the base 3 of 3) = (log to the base 3 of 4)

This can be reduced to 2x(1) = 2x = (log 4)/log 3 = 1.262.

Divide the result by 2 to get x = 0.631

Therefore, the solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

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complete question:

Show that solving the equation 3 ²x=4 by taking the common logarithm of each side is equivalent to solving it by taking the logarithm with base 3 of each side.

The answer to AC of the circle geometry with tangent is 26.

Since CD is the diameter of the circle,  then triangle ADC is a right-angle triangle with right angle at D.

Using Pythagorean theorem to find AC:

AC² = AD² + DC²

AC² = 10² + 26²

AC² = 676

AC = √676

AC = 26

Therefore, AC = 26.

Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the three sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words:

a² + b² = c²

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Since Callie cannot make a fraction of a necklace, she can make a maximum of 5 necklaces from the given length of leather cord.

To determine the number of necklaces Callie can make from the given length of leather cord, we need to convert the measurements to a consistent unit.

Given:

Length of leather cord = 4 yards

Length of each necklace = 28 inches

First, let's convert the length of the leather cord from yards to inches:

1 yard = 36 inches (since there are 3 feet in a yard and 1 foot = 12 inches)

4 yards = 4 * 36 = 144 inches

Now we can calculate the number of necklaces:

Number of necklaces = Length of leather cord / Length of each necklace

Number of necklaces = 144 inches / 28 inches ≈ 5.143

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The solution to each of the arithmetic sequence are:

1) a₁₀ = 56

2) a₁₀ = 87

3) missing term is 13

4) missing term is 14

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is nth term

d is common difference

1) a = 2

d = 6

a₁₀ = 2 + (10 - 1)6

a₁₀ = 2 + 54

a₁₀ = 56

2) a = 15

d = 8

a₁₀ = 15 + (10 - 1)8

a₁₀ = 87

3) The missing term will be gotten by finding the common difference.

d = (22 - 4)/2

d = 18/2

d = 9

missing term = 4 + 9 = 13

4) The missing term will be gotten by finding the common difference.

d = (53 - 25)/2

d = 28/2

d = 14

missing term = 4 + 9 = 14

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The solution of the equation is c= 2/5 and d= 3/2.

We have Equation.

5c + 4d = 8

-5c + 2d = 1

Solving above equation we get

5c + 4d = 8

-5c + 2d = 1

___________

         6d = 9

          d = 3/2

and, 5c + 4(3/2)= 8

5c = 8 - 6

5c = 2

c= 2/5

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Answer:

-----------------------

Simplify the expression in below steps:

[tex]\cfrac{\left(-6x^{2}y^{3}\right)^{4}}{8x^{9}y^{7}\cdot3xy^{5}}=[/tex]                      Power of power and product of exponents rules

[tex]\cfrac{\left6^4x^{2\cdot4}y^{3\cdot4}\right}{(8\cdot3)x^{9+1}y^{5+7}}=[/tex]                 Multiply or add up powers

[tex]\cfrac{\left2^43^4x^8y^{12}\right}{(2^3\cdot3)x^{10}y^{12}}=[/tex]                    Subtract powers or cancel same terms

[tex]\cfrac{\left2\cdot3^3\right}{x^2}}=[/tex]                               Simplify

[tex]54/x^2[/tex]                                   Answer

Answer:

2 1/2 ft

Step-by-step explanation:

Is this what you meant?

Length = 1/2 ft

Width = 3/4 ft

If so, then:

Perimeter = length + length + width + width

P = 1/2 ft + 1/2 ft + 3/4 ft + 3/4 ft

P = 2/4 ft + 2/4 ft + 3/4 ft + 3/4 ft

P = 10/4 ft

P = 5/2 ft

P = 2 1/2 ft

The population mean is greater than 30.To determine the sample mean that would result in a p-value of 0.05, we need to work backwards from the given significance level.

First, we need to find the test statistic. Since the alternative hypothesis is one-sided (μ>30), we will use a one-sample z-test. The test statistic is calculated as:

z = (xbar - μ) / (s / sqrt(n))

where xbar is the sample mean, μ is the hypothesized population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

Since we want the p-value to be equal to 0.05, we need to find the z-score that corresponds to a one-tailed area of 0.05. Using a standard normal distribution table or calculator, we find that this z-score is 1.645.

Substituting this value into the formula for the test statistic, we get:

1.645 = (xbar - 30) / (10 / sqrt(70))

Solving for xbar, we get:

xbar = 30 + 1.645 * (10 / sqrt(70))

xbar = 31.77

Therefore, the sample mean that would result in a p-value of 0.05 is 31.77. This means that if we were to obtain a sample mean of 31.77 or higher, we would reject the null hypothesis at a significance level of 0.05 in favor of the alternative hypothesis that the population mean is greater than 30.

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Anissa's statement suggests that the variable "distance," denoted as "d," can be considered both an independent variable and a dependent variable, depending on the context or the specific relationship being examined.

Independent Variable: In certain situations or experiments, the distance can be treated as an independent variable. This means that the distance is manipulated or controlled by the researcher or experimenter, and it is used to determine or study the effect it has on other variables. In this case, the distance would be considered the cause or predictor variable, and its value is intentionally set or changed to observe how it influences the dependent variable(s).

Example: In a study on the impact of distance on running performance, researchers may vary the distance of a race (e.g., 5 km, 10 km, or 15 km) and measure the effect it has on the runners' performance times. Here, distance would be the independent variable, as it is being deliberately altered to observe its influence on the dependent variable (performance time).

Dependent Variable: Conversely, in other scenarios, the distance can be considered a dependent variable. This means that the distance is the outcome or result of other factors or variables that are being studied or manipulated. In this case, the distance is observed or measured as the response to changes in other variables.

Example: Suppose researchers are investigating the relationship between the time spent studying and the distance walked to school for a group of students. The researchers measure the students' study time and observe the corresponding distance they walk to school. In this context, the distance would be the dependent variable, as it is influenced by the independent variable (study time) and is used to assess the relationship between the two.

In summary, Anissa's statement indicates that the variable "distance" can be considered either an independent variable or a dependent variable, depending on the specific context and the relationship being examined in a given study or experiment.

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The phrase that completes the sentence is "determined by."

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Answer: B. y = 3x - 5

Step-by-step explanation:

    First ,we know Option C will not be an option because of the y-intercept (the point at which the line intersects the y-axis) is -5. This is shown by the point (0, -5). Option C shows it as 1.

    We will substitute a point into the given equations and see if the simplified version remains true.

✗ A ➜ y = -3x - 5

  ➜ -2 = -3(1) - 5

  ➜ -2 ≠ -8

✓ B ➜ y = 3x - 5

  ➜ -2 = 3(1) - 5

  ➜ -2 = -2

✗ D ➜ y = -x - 5

  ➜ -2 = -1 - 5

  ➜ -2 ≠ -6

    Using this method of substitution, we can see the answer is B.

Answer:

88

Step-by-step explanation:

The formula for a parallelogram to find the area is:

B x h

So, the numbers we are given is the:

base: 11

height: 8

slant height: 9

We do not need the slant height for finding the area, so we can just substitute the base and height values into the equation:

8 x 11

=88

So, the area of this parallelogram is 88 square units

Hope this helps :)

lim sin(pi/3+h) - sin(pi/3)/ h as h approaches 0 is  Non existent. The correct answer is option e.

To evaluate the limit, we can use the formula for the derivative of sin(x), which is:

lim f(x+h) - f(x) / h as h approaches 0 = f'(x)

where f(x) = sin(x).

So, in this case, we have:

lim sin(pi/3+h) - sin(pi/3) / h as h approaches 0

which can be rewritten as:

lim [sin(pi/3+h) - sin(pi/3)] / h as h approaches 0

Using the identity for the difference of two sines, we can simplify this expression to:

lim [2cos(2pi/6+h/2)sin(h/2)] / h as h approaches 0

Now, we can cancel out the factor of sin(h/2) in the numerator and denominator, and we are left with:

lim 2cos(2pi/6+h/2) / h as h approaches 0

We can evaluate the limit using direct substitution, and we get:

2cos(pi/3) / 0

Since the denominator is 0, the limit does not exist. Therefore, the answer is option E: Nonexistent.

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The requried to calculate an F ratio, we need to perform an analysis of variance (ANOVA) test.

To calculate an F ratio, we need to perform an analysis of variance (ANOVA) test. The F ratio is the ratio of two variances, and it is calculated by dividing the mean square of the between-group variability by the mean square of the within-group variability.

The formula for the F ratio is:

F = MSB / MSW

Where MSB is the mean square of the between-group variability and MSW is the mean square of the within-group variability.

The F ratio is used to test the null hypothesis that the means of the groups are equal. If the F ratio is greater than the critical value for a given level of significance (based on the degrees of freedom), we reject the null hypothesis and conclude that at least one group's mean is different from the others.

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The fruit stand owner can make 23 complete orange baskets.

Division is a mathematical operation which involves the sharing of an amount into equal-sized groups. For example, “12 divided by 4” means “12 shared into 4 equal groups”, which would be 3.

To determine the number of complete orange baskets that can be made, divide the total number of oranges by the number of oranges per basket.

Total oranges: 185

Oranges per basket: 8

Divide 185 by 8 to find the number of complete baskets:

185 ÷ 8 = 23

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We can conclude that the socioeconomic class of the offender is related to the likelihood of arrests.

Based on the information provided, we can conclude that there is a significant relationship between arrests and the socioeconomic class of the offender.
Identify the chi-square critical score: 9.488

Identify the chi-square test statistic: 12.2
Compare the test statistic to the critical score:

If the test statistic (12.2) is greater than the critical score (9.488), then there is a significant relationship between the variables.
In this case, 12.2 > 9.488, so there is a significant relationship between arrests and the socioeconomic class of the offender.
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a. the smallest value is approximately 5 inches. b. the median is approximately 12 inches. c. the data is more spread out in those ranges.

(a) To find the least amount of snowfall, we look at the smallest value on the box and whisker plot. From the plot, we can see that the smallest value is approximately 5 inches.

(b) To find the median amount of snowfall, we look for the line that divides the box in half. From the plot, we can see that the median is approximately 12 inches.

(c) The data is most concentrated in the second quarter. We can see this because the box is the largest in the second quarter, indicating that the data is most tightly clustered in that range. The first and fourth quarters have smaller boxes, indicating that the data is more spread out in those ranges.

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Answer:

$1.88

Step-by-step explanation:

We Know

7 packs of $13.18

What is the cost, in dollars, per pack?

We Take

13.18 ÷ 7 = $1.88

So, the cost per pack is $1.88

The IQ score that is higher than 90% of the population is 112.8.

We know that the IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 10.

Let X be the random variable representing the IQ scores. We want to find the value x such that 90% of the observations lie above x.

Using the standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile as 1.28.

The z-score formula is z = (x - μ) / σ, where μ is the mean, σ is the standard deviation and x is the value we want to find.

Plugging in the values, we get 1.28 = (x - 100) / 10. Solving for x, we get x = 100 + 12.8 = 112.8.

Therefore, the IQ score that is higher than 90% of the population is 112.8.

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The equation of circle D is (x + 2)2 + y² = 32 then the points (-6,-4) and (-4,6) lie on circle D

The equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r².

This is called the standard form of the equation of a circle.

In the given equation, (x + 2)² + y² = 32, we can see that the center of the circle is (-2, 0) and the radius is √32 = 4√2.

To determine which points lie on the circle, we substitute the x and y coordinates of each point into the equation and check if the equation is true.

If it is true, then the point lies on the circle.

Let us check if (-6, -4) lies on the circle, we substitute x = -6 and y = -4 into the equation:

(-6 + 2)² + (-4)² = 32

(-4)² + (-4)² = 32

16 + 16 = 32

32 = 32

Since the equation is true, (-6, -4) lies on the circle.

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In the given diagram, the surface area of the given sphere is approximately 5026.55 ft²

From the question, we are to calculate the surface area of the sphere

The surface area of a sphere is given by the formula

Surface area = 4πr²

Where r is the radius of the sphere

From the given information,

Diameter of the sphere = 40 ft

Thus,

Radius of the sphere = 40 ft / 2

Radius of the sphere = 20 ft

Therefore,

Surface area of the sphere = 4 × π × 20²

Surface area of the sphere = 4 × π × 400

Surface area of the sphere = 1600π ft²

Surface area of the sphere = 5026.5482 ft²

Surface area of the sphere ≈ 5026.55 ft²

Hence, the surface area of the sphere is 5026.55 ft²

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Pat played a total of 11 + 7 = 18 games in the tournament.

Let's denote the number of games Pat lost as L and the number of games Pat won as W.

We are given the following information:
Pat started with 100 points.
In each game, Pat either loses 3 points (L games) or gains 2 points (W games).
We can set up the following equations based on this information:
Total points = Initial points + Gained points - Lost points
Total points = 100 + 2W - 3L
We need to find the total number of games Pat played, which is the sum of games won and lost (W + L).

To solve for W + L, we need to find a relationship between W and L.
We can rearrange the Total points equation to find such a relationship:
2W - 3L = Total points - 100
2W = 3L + (Total points - 100)
Now, we know that both W and L must be integers since Pat can't win or lose a fraction of a game.

As 2W and 3L are both integers, their sum (3L + (Total points - 100)) must be even.

Thus, the total points must be an even number.
We can try different even values for the total points and check if the corresponding W and L values are integers. After trying different values, we find that:
Total points = 122
W = 11
L = 7.

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Answer:

RT is perpendicular to WS because when parallel lines are cut by a transversal, the corresponding angles are equal.

Step-by-step explanation:

The area of circle D is 10.56 times greater than the area of the circle A.

Given that, the radius of circles A, B, C and D,

Radius of A = 4 in

Radius of B = 9 in

Radius of C = 14 in

Radius of D = 13 in

Area of the circles = A = πr²

A = 3.14×4²

A = 50.24 in²

B = 3.14×9²

B = 254.34 in²

C = 3.14×14²

C = 615.44 in²

D = 3.14×13

D = 530.66 in²

The area of circle D is 530.66/50.24 = 10.56 times greater than the area of the circle A.

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The correct expression to create a random number in the range of [-3,3) would be option A: r.nextDouble() * 6.0 - 3.0.

Explanation: The nextDouble() method of Random class returns a double in the range of [0,1), which means it can generate any random value between 0 (inclusive) and 1 (exclusive). To create a random number in the range of [-3,3), we need to scale and shift the output of the nextDouble() method.

Option A is the correct expression as it first scales the output by multiplying it by 3.0 (which will give a range of [0,3)) and then shifts it down by subtracting 3.0 (which will give a range of [-3,0)). Therefore, we need to modify the expression to r.nextDouble() * 6.0 - 3.0 to generate a random number in the range of [-3,3).

Option B multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then subtracts 0.5, which shifts the range to [-0.5,5.5). This is not the correct expression to generate a random number in the range of [-3,3).

Option C multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then adds 3.0, which shifts the range to [3,9). This is not the correct expression to generate a random number in the range of [-3,3).

Option D multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then adds 0.5, which shifts the range to [0.5,6.5). This is not the correct expression to generate a random number in the range of [-3,3).

Option E subtracts 3.0 from the output of nextDouble() and then multiplies it by 6.0, which gives a range of [-3,3). However, this expression is not the correct way to scale and shift the output of the nextDouble() method.

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