Question 25 of 27
Which of the following matches a quadrilateral with the listed characteristics
below?
1. Figure has 4 right angles
2. Figure has 4 congruent sides
3. Both pairs of opposite sides parallel
OA. Rectangle
B. Trapezoid
OC. Square
D. Parallelogram
E

The experimental design described is using a sample survey to gather results, providing a cost-effective and efficient way to estimate the likelihood of winning for different candidates in the student council election. B Sample survey Option B

The experimental design described in the scenario, where 100 students from the school are randomly asked who they intend to vote for in the student council election, is using a Sample Survey to gather its results.

A sample survey involves selecting a subset, or sample, of individuals from a larger population and collecting data from that sample to make inferences about the entire population. In this case, the 100 students randomly chosen from the school represent the sample, while the larger population would be all the students in the school.

The use of a sample survey is a common and practical approach when the population size is large, as it would be impractical or time-consuming to survey every individual in the population (which would be a census). By randomly selecting a sample, the goal is to obtain a representative subset that reflects the characteristics and opinions of the larger population.

The purpose of this sample survey is to gauge the voting intentions of the students and make predictions about the likely winner of the student council election based on the responses obtained from the sample. The results from the 100 students surveyed would be analyzed to estimate the proportion of the larger population that supports each candidate, and the candidate with the highest estimated proportion of support would be considered the most likely to win the election.

Therefore, the experimental design in question is using a Sample Survey to gather its results and make predictions about the likely winner of the student council election.

Option b

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The two numbers are 20 and 32.

Let's assume the two numbers in the ratio 10:16 are 10x and 16x, where x is a common factor.

According to the given information, when 4 is added to each number, the ratio becomes 4:6. This means that the new numbers are (10x + 4) and (16x + 4).

To find the numbers, we can set up an equation based on the given ratios:

(10x + 4) / (16x + 4) = 4/6

To simplify the equation, we can cross-multiply:

6(10x + 4) = 4(16x + 4)

Expanding both sides:

60x + 24 = 64x + 16

Bringing like terms together:

60x - 64x = 16 - 24

-4x = -8

Dividing both sides by -4:

x = 2

Now that we have the value of x, we can substitute it back into the original ratios to find the numbers:

The first number = 10x = 10 * 2 = 20

The second number = 16x = 16 * 2 = 32

Therefore, the two numbers are 20 and 32.

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Answer:

Let the two numbers be 10x and 16x.

When 4 is added to each, the resulting numbers are (10x + 4) and (16x + 4).

According to the problem, the ratio of (10x + 4) to (16x + 4) is 4:6.

We can write this as:

(10x + 4)/(16x + 4) = 4/6

Cross-multiplying, we get:

6(10x + 4) = 4(16x + 4)

Simplifying the equation, we get:

60x + 24 = 64x + 16

48 = 4x

x = 12

Therefore, the two numbers are:

10x = 120

16x = 192

So the two numbers are 120 and 192.

The 8th term of the given Sequence is 26.

A sequence is a list of numbers arranged in a particular order. It can be finite or infinite. The nth term of a sequence is represented by Tn.

It can be found using the formula: Tn = a + (n-1)d, where a is the first term, d is the common difference and n is the number of terms being considered.

If we know any three of the terms, we can use the formula to find the fourth term. Let's consider an example to understand this concept better. Example: Find the 8th term of the sequence 5, 8, 11, 14,...Solution:

We can see that the first term of the sequence is 5. Also, the common difference between the terms is 3. Using the formula Tn = a + (n-1)d, we get:T8 = 5 + (8-1)3T8 = 5 + 21T8 = 26

Therefore, the 8th term of the given sequence is 26.

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Answer:  (x² - 5)(x - 7)

Step-by-step explanation:

Grouping the terms, we have:

(x^3 - 7x^2) + (-5x + 35)

Now, let's factor out the common factors from each pair:

x^2(x - 7) - 5(x - 7)

Notice that we have a common factor of (x - 7) in both terms. We can factor it out:

(x^2 - 5)(x - 7)

Therefore, the resulting expression after factoring by grouping is (x^2 - 5)(x - 7).

Answer:

Rental cost for each movie = $3.25

Rental cost for each video game = $5.25

Step-by-step explanation:

We can find the rental cost for each movie and each video game using a system of equations where:

First equation:

Since Jina rented 6 movies and 2 video games for a total of $30, our first equation is given by:

6M + 2V = 30

Second equation:

Since Jina also rented 3 movies and 5 video games for a total of $36, our second equation is given by:

3M + 5V = 36

Method to solve:  Elimination:

We can solve this with eliminate.  First, we need to multiply the second equation by -2.  Then, we must add the two equations to eliminate the Ms and solve for V:

Multiplying the entire second equation by -2:

-2(3M + 5V = 36)

-6M - 10V = -72

Adding the two equations:

    6M + 2V = 30

+

   -6M - 10V = -72

(6M - 6M) + (2V - 10V) = (30 - 72)

-8V = -42

Solving for V:

(-8V = -42) / -8

V = 5.25

Thus, the rental cost for each video game is $5.25.

Solving for M:

We can now find M by plugging in 5.25 for V in any of the two equations in our system.  

Let's use the first equation:

Plugging in 5.25 for V in 6M + 2V = 30 to solve for M:

6M + 2(5.25) = 30

(6M + 10.50 = 30) - 10.50

(6M = 19.50) / 6

M = 3.25

Thus, the rental cost for each movie is $3.25.

The calculated value of k on the line is 9

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

XZ is the perpendicular bisector of segment WY

This means that

WX = XY

substitute the known values in the above equation, so, we have the following representation

3k - 4 = 2k + 5

So, we have

3k - 2k = 4 + 5

Evaluate

k = 9

Hence, the value of k is 9

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a). Probability (3 balls are all white) = 220/1771 = 0.124

b). Probability of drawing one ball of each color = 336/1771 = 0.19

c). Probability of drawing 3 balls of the same color = 259/1771 = 0.146

(a) Probability of drawing 3 white balls:

Total number of balls = 7 red + 12 white + 4 green = 23 balls

Number of favorable outcomes = selecting 3 white balls = 12C3 = (12!)/(3!(12-3)!) = 220

Total number of possible outcomes = selecting 3 balls from 23 = 23C3 = (23!)/(3!(23-3)!) = 1771

So, Probability of drawing 3 white balls = Number of favorable outcomes / Total number of possible outcomes

P(3 white balls) = 220/1771 = 0.124

b). Probability of drawing one ball of each color:

Number of favorable outcomes = selecting 1 ball of each color = 7C1 × 12C1 × 4C1 = 7 × 12 × 4 = 336

Total number of possible outcomes (as calculated above) = 1771

Probability of drawing one ball of each color = Number of favorable outcomes / Total number of possible outcomes

P(1 ball of each color) = 336/1771 ≈ 0.19

C. Total number of favorable outcomes = 35 + 220 + 4 = 259

Total number of possible outcomes (as calculated above) = 1771

Probability of drawing 3 balls of the same color = Number of favorable outcomes / Total number of possible outcomes

P(3 balls of the same color) = 259/1771 = 0.146

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Answer:

x=7

Step-by-step explanation:

Assuming the angles to be congruent, then 7 and x are both congruent sides, which makes the figure an isosceles triangle. Therefore, x=7 as well.

In approximately the year 2001 (or the 1.373rd year since 2000), the approximate number of oil barrels imported from Country B per day will be 1.93 million.

To solve the equation y = 0.069x + 1.24 for x, we need to isolate x on one side of the equation. Let's rearrange the equation:

y = 0.069x + 1.24

Subtract 1.24 from both sides:

y - 1.24 = 0.069x

Divide both sides by 0.069:

(y - 1.24) / 0.069 = x

Now we have x isolated on one side of the equation. We can use this equation to determine the year in which the approximate number of oil barrels imported from Country B per day will be 1.93 million.

Let's substitute y = 1.93 into the equation:

(x - 1.24) / 0.069 = 1.93

Multiply both sides by 0.069:

x - 1.24 = 0.069 * 1.93

x - 1.24 = 0.13317

Add 1.24 to both sides:

x = 0.13317 + 1.24

x = 1.37317

Now we have the value of x, which represents the number of years since 2000. To determine the year, we add the value of x to 2000:

Year = 2000 + 1.37317

Year ≈ 2001.373

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Answer:

a) For an unsubsidized loan of $15,000 at 6.8% interest for 4 years, the simple interest accumulated while you are still in school is **$4,080**.

b) If you capitalized the loan, the balance when you graduate would be **$20,322.68**.

c) After you graduate, you will begin making payments on your loan at 6.8% compounded monthly for 10 years. The monthly payment for this loan is **$174.30**.

d) The total amount of interest paid for this loan is **$10,118.00**.

e) If the loan is not capitalized, it means that the interest accrued during the in-school period is not added to the principal balance of the loan. Instead, it is paid off separately after graduation.

f) For a subsidized loan of $15,000 at 6.8% compounded monthly for 10 years, the monthly payment for this loan is **$163.19**.

g) The total amount of interest paid for this subsidized loan is **$9,782.80**.

h) The difference in savings for the subsidized loan is **$335.20**.

In sampling distributions, the mean is consistently identical to the population mean. (Option C)

This concept is a fundamental property of sampling distributions and is rooted in the principles of probability and statistical theory. A sampling distribution is a theoretical distribution that represents the possible values of a statistic (such as the mean or proportion) calculated from different samples drawn from the same population. The mean of a sampling distribution is an average of the sample means, and it provides an estimate of the population mean.

When random samples are drawn from a population, the mean of each sample will vary due to random sampling variability. However, as the sample size increases, the distribution of sample means tends to converge around the population mean. This phenomenon is known as the Central Limit Theorem.

According to the Central Limit Theorem, as sample sizes become large (typically n > 30), the sampling distribution of the mean becomes approximately normal, with a mean that is identical to the population mean. In other words, on average, the sample means will be equal to the population mean. This property holds true regardless of the shape, spread, or other characteristics of the population distribution.

Therefore, the correct answer is C. Identical to.

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The value of ninth term (a₉) is equal to: B. 8/729.

In Mathematics and Geometry, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):

aₙ = a₁rⁿ⁻¹

Where:

From the second term of this geometric sequence, we have:

-24 = a₁r

a₁ = -24/r

From the fifth term of this geometric sequence, we have:

8/9 = a₁r⁴

8/9 = a₂ × r³

8/9 = -24 × r³

r³ = -8/216

r = -∛1/27

r = -1/3

Now, we can determine ninth term as follows;

a₁ = -24/(-1/3)

a₁ = 72

a₉ = a₁r⁸

a₉ = 72(-1/3)⁸

a₉ = 72/6,561

a₉ = 8/729

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Answer:

Step-by-step explanation:

d

Answer:

D. The theoretical probability that the toast lands buttered side up is 9/26.

Forgive me if im wrong....

Step-by-step explanation:

the transaction results in a net gain.Net gain percentage = Net gain / Total cost price × 100%=(2SP - 52000) / 52000 × 100%Now, we can use the above expressions to calculate the total gain or loss percentage in the transaction.

Let's assume that the cost price of the first television set is CP1 and that of the second is CP2. As per the given information, the total cost price of both television sets is 52000 rupees.

Therefore, CP1 + CP2 = 52000Assuming the selling price of both television sets is the same, let's assume it to be SP for convenience. Selling price is defined as the price at which a product is sold to the customer. Therefore, the selling price of both television sets will be SP.

Now, we have to calculate the net gain or loss percentage in the transaction.Gain or loss is calculated as the difference between the selling price and cost price.

Gain or loss on the first television set is 10% of CP1, and the gain or loss on the second television set is 10% of CP2. Therefore,Gain or loss on the first television = 10/100 × CP1 = 0.1CP1Loss or gain on the second television = 10/100 × CP2 = 0.1CP2The selling price of both television sets is the same.

Therefore,Selling price of the first television = SPSelling price of the second television = SPThe selling price of both television sets combined is:Selling price of both television sets = SP + SP = 2SPNow, let's calculate the net gain or loss percentage in the transaction.

Net gain or loss = Selling price - Cost price= (SP + SP) - (CP1 + CP2)= 2SP - 52000Now, we need to determine whether the transaction resulted in a gain or a loss. We know that the gain or loss on the first television is 0.1CP1, and the gain or loss on the second television is 0.1CP2.

Let's consider two

cases:Case 1: When CP1 < CP2 (the cost price of the first television is less than that of the second television)In this case, the gain on the first television is less than the loss on the second television, as 0.1CP1 < 0.1CP2. Therefore, the transaction results in a net loss.

Net loss percentage = Net loss / Total cost price × 100%=(2SP - 52000) / 52000 × 100%

Case 2: When CP1 > CP2 (the cost price of the first television is greater than that of the second television)In this case, the gain on the first television is greater than the loss on the second television, as 0.1CP1 > 0.1CP2.

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The probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.

q = 1 - p

q = 1 - 0.019

q = 0.981

X: The number of successful outcomes.

In this scenario, we can model the situation using a binomial distribution. Let's determine the values of n, p, q, and X:

n: The number of trials or attempts.

In this case, the number of trials is the number of Frigid Elements defeated, which is given as 20.

n = 20

p: The probability of success on a single trial.

The probability of a frozen rain item dropping after defeating a Frigid Element is given as 1.9%, which can be expressed as 0.019.

p = 0.019

q: The probability of failure on a single trial.

The probability of failure is the complement of the probability of success. Therefore:

q = 1 - p

q = 1 - 0.019

q = 0.981

X: The number of successful outcomes.

We want to find the probability of 2 frozen rains dropping, so X is 2.

X = 2

Now that we have determined the values, we can calculate the probability using the binomial distribution formula. The formula for the probability mass function of the binomial distribution is:

P(X = x) = [tex](nCx) * (p^x) * (q^(n-x))[/tex]

where nCx represents the binomial coefficient, which is the number of ways to choose x successes out of n trials.

Using this formula, we can substitute the values into the equation:

P(X = 2) = [tex](20C2) * (0.019^2) * (0.981^(20-2))[/tex]

Calculating the binomial coefficient:

(20C2) = (20!)/(2!(20-2)!)

= (20 * 19 * 18!)/(2 * 18!)

= (20 * 19)/(2 * 1)

= 190

Now substituting the values:

P(X = 2) = [tex]190 * (0.019^2) * (0.981^18)[/tex]

Now we can calculate the probability:

P(X = 2) ≈ 0.2713 or 27.13% (rounded to two decimal places)

Therefore, the probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.

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The point has an x-coordinate of -4 and a y-coorindate of -1, and it is on the third quadrant.

First, remember that for a point (x, y):

For the point that is 4 units to the lefft and 1 unit down (of the origin) it is written as:

(-4, -1)

Then we can see that this point is on the quadrant III.

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Answer: 135°

Step-by-step explanation:

1 and 1/2 right angle.

1 right angle is 90°

1/2 of a right angle = 45°

so 1 and 1/2= 90+45=135°

Answer:

157908.83

Step-by-step explanation:

RD formula is :

[tex]P(1+\frac{r}{m} ) [(1+\frac{r}{m} )^{N} -1 }]{\frac{m}{r}[/tex]

where P: Principal / rd amount = $2000

r : interest = 8% = 0.08

m : no. of times compounded in a year = 1 (compounded annually)

N : time = 25 years

Amt =

[tex]2000(1+\frac{0.08}{1} ) [(1+\frac{0.08}{1} )^{25} -1 }]{\frac{1}{0.08}[/tex]

[tex]= 2000(1.08) [1.08^{25} -1 }]{\frac{1}{0.08}[/tex]

= 157908.83

Answer:

45.

Step-by-step explanation:

so every 1/9 lightbulbs are defective, so make that L/400, (L for amount of defective bulbs).

Take the total, 400, and divide it by 9, which equals 44.4444444444. Evaluate 44.4444444444/400 and you get 0.11111111111. Evaluate 1/9, and you get 0.11111111111. So they are equivalent. But you cant have 44.4444444444 lightbulbs defective, because you can't have a lightbulb 40% defective, it either works, or doesn't work. So, round your answer up, and you get 45 total defective lightbulbs if they make 400.

The length of the fabric Sarah cut for the quilt is 97.875 inches.

To determine the length of the fabric Sarah cut for the quilt, we need to add up the lengths of the individual pieces she cut.

Number of pieces cut: 5

Length of each piece: 19 1/8 inches

Length of the remaining piece: 2 1/4 inches

To find the total length, we can multiply the length of each piece by the number of pieces and add the length of the remaining piece.

Length of each piece = 19 1/8 inches = 19 + 1/8 inches = 19.125 inches

Length of the remaining piece = 2 1/4 inches = 2 + 1/4 inches = 2.25 inches

Total length = (Length of each piece) [tex]\times[/tex] (Number of pieces) + Length of the remaining piece

Total length = 19.125 inches [tex]\times[/tex] 5 + 2.25 inches

Total length = 95.625 inches + 2.25 inches

Total length = 97.875 inches

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The derivative of f(x) = 6x + 1 at x = 2 is 6, obtained through the limit definition of the derivative.

To find the derivative of f(x) = 6x + 1 at x = 2, we can use the formula for the derivative of a function: f'(x) = lim(h → 0) [f(x + h) - f(x)]/h

We substitute x = 2 into the formula to get: f'(2) = lim(h → 0) [f(2 + h) - f(2)]/h

We plug in f(x) = 6x + 1: f'(2) = lim(h → 0) [(6(2 + h) + 1) - (6(2) + 1)]/h

Simplifying the expression:

f'(2) = lim(h → 0) [(12 + 6h + 1) - (12 + 1)]/h

      = lim(h → 0) (6h)/h = lim(h → 0) 6

The limit of 6 as h approaches 0 is simply 6. Therefore, the derivative of f(x) = 6x + 1 at x = 2 is f'(2) = 6.

The derivative of f(x) = 6x + 1 at x = 2 is 6.

In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.

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Answer:

19m75

Step-by-step explanation:

Solution:

To evaluate the expression 7×2+(7+3×(5-2)÷4×2), we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Step 1: First, we need to simplify the expression inside the parentheses.

5-2 = 3

3÷4 = 0.75

3×0.75 = 2.25

7+2.25 = 9.25

Step 2: Next, we need to simplify the multiplication and division from left to right.

3×2 = 6

0.75×2 = 1.5

Step 3: Finally, we need to simplify the addition and subtraction from left to right.

7×2+9.25+6-1.5 = 19.75

Therefore, the value of the expression 7×2+(7+3×(5-2)÷4×2) is 19.75.

The expression log 3x⁹y⁴ can be written as a sum of logarithms:

log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y)

To express log(3x⁹y⁴) as a sum and/or difference of logarithms, we use the logarithmic properties.

Using the power rule of logarithms, we can write the expression as:

log(3x⁹y⁴) = log(3) + log(x⁹) + log(y⁴)

we can further simplify so that the variables will be to the first degree as follows;

log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y).

Therefore, the expression log(3x⁹y⁴) can be written as a sum of logarithms:

log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y)

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The size of angle DAB in the quadrilateral is 48°.

The sum of the interior angles of a quadrilateral is 360°. We can say:

[tex]\angle \text{A} +\angle\text{B} + \angle\text{C} + \angle\text{D} = 360^\circ[/tex]

[tex]\angle \text{A} +38^\circ + \angle\text{C} + 226^\circ = 360^\circ[/tex]

[tex]\angle \text{A} + \angle\text{C} + 264^\circ = 360^\circ[/tex]

[tex]\angle \text{A} + \angle\text{C} = 360^\circ- 264^\circ[/tex]

[tex]\angle \text{A} + \angle\text{C} = 96[/tex]

Since angles DAB and BCD are the same size. This implies ∠A  = ∠C. Thus:

[tex]\angle\text{A} + \angle\text{A} = 96[/tex]

[tex]2\angle\text{A} = 96[/tex]

[tex]\angle\text{A} = \dfrac{96}{2}[/tex]

[tex]\angle\text{A} = 48^\circ[/tex]

Therefore, the size of angle DAB is 48°.

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Answer:

x=4

Step-by-step explanation:

angles on a straight line always add up to 180°

so...

25x+20+15x=180°

simplify the left side of the equation

40x+20=180°

take away 20

40x=160°

divide by 40

x=4

[tex]\begin{array}{ccll} inches&hours\\ \cline{1-2} 5&10\\[1em] 3\frac{1}{4}&x \end{array}\implies \cfrac{5}{ ~~ 3\frac{1}{4} ~~ }=\cfrac{10}{x}\implies \cfrac{5}{~~ \frac{ 13 }{ 4 } ~~}=\cfrac{10}{x}\implies \cfrac{20}{13}=\cfrac{10}{x} \\\\\\ 20x=130\implies x=\cfrac{130}{20}\implies x=\cfrac{13}{2}\implies x=6\frac{1}{2}[/tex]

Multiplying two signed numbers results in a product, and the sign of the product depends on the signs of the multiplied numbers.

Multiplying and dividing two signed numbers differ in terms of the rules and properties that apply to each operation. Here are the key differences:

1. Product vs. Quotient:

When multiplying two signed numbers, the result is called the product. It represents the total of repeated addition or combining equal groups. For example, multiplying -3 by -4 gives a product of 12.

When dividing two signed numbers, the result is called the quotient. It represents the ratio or partitioning of one quantity into equal parts. For example, dividing 12 by -4 gives a quotient of -3.

2. Signs of the Result:

In multiplication, the sign of the product depends on the signs of the multiplied numbers. If the signs are the same (both positive or both negative), the product is positive. If the signs are different (one positive and one negative), the product is negative. For example, (-3) * (-4) = 12, and (-3) * 4 = -12.

In division, the sign of the quotient depends on the signs of the dividend and divisor. If both numbers have the same sign, the quotient is positive. If the numbers have different signs, the quotient is negative. For example, 12 / (-4) = -3, and (-12) / (-4) = 3.

3. Properties:

Multiplication has properties like the commutative property (changing the order of the factors doesn't change the product) and the associative property (changing the grouping of factors doesn't change the product). For example, (-3) * (-4) = (-4) * (-3) = 12.

Division, on the other hand, has specific properties like the division property of zero (dividing any number by zero is undefined) and the division property of one (dividing a number by one leaves the number unchanged). For example, 12 / 1 = 12.

In summary, multiplying two signed numbers results in a product, and the sign of the product depends on the signs of the multiplied numbers. Dividing two signed numbers results in a quotient, and the sign of the quotient depends on the signs of the dividend and divisor. Additionally, multiplication has properties like commutativity and associativity, while division has properties specific to the division operation.

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