The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

A percentage is a way to describe a part of a whole. The amount of your profit is $29.86. The percent of profit, based on your investment is 58.12%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The cost of buying 72 shares is $(411/8) = $51.375

The cost of selling 72 shares is $(491/4) = $122.75

The total brokerage fees = $(1/8 × 72) = $9

All other charges amounted = $32.52

The profit is,

Profit = $122.75 - $51.375 - $9 - $32.52

          = $29.855 ≈ $29.86

Hence, the amount of your profit is $29.86.

B.) The percent of profit, is based on your investment.

Since the investment is the cost of purchasing the share, therefore, the percent of profit, based on your investment can be written as,

Profit % = $29.86 /$51.375 × 100% = 58.12%

hence, The percent of profit, based on your investment is 58.12%.

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\(0.685\)

the expanded notation form.

\(0\)

\( + 0.6\)

\( + 0.08\)

\( + 0.005\)

it can be written as a sentence also,

0 + 0.6 + 0.08 + 0.005

Answer:

are you sure

Step-by-step explanation:

bro i am trying to answer your question

The alternative hypothesis is a two-tailed hypothesis because it examines whether there is a difference in effectiveness, which can be positive or negative.

A null hypothesis is a type of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Sample data is used to assess the viability of theories. H0 represents what is referred to as "zero" on occasion. The researchers make the assumption that there may be a relationship between the factors. The null hypothesis, on the other hand, claims that no such relationship exists. Although it may not appear to be significant, the null hypothesis is an important part of research.

The following hypotheses would be appropriate for testing the difference in effectiveness between brand-name and generic ibuprofen:

The null hypothesis (H0) states that there is no difference in the mean effectiveness of brand-name and generic ibuprofen.

Alternative hypothesis (Ha): The mean effectiveness of brand-name ibuprofen and generic ibuprofen differs.

These hypotheses can be expressed symbolically as follows:

H0: _generic = _brand-name\\

Ha: _trademark _generic

Where _brand-name denotes the population mean efficacy of brand-name ibuprofen and _generic denotes the population mean efficacy of generic ibuprofen. The alternative hypothesis is a two-tailed hypothesis because it examines whether there is a difference in effectiveness, which can be positive or negative.

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Answer:
H0: μ1 – μ2 = 0

Ha: μ1 – μ2 ≠ 0

Step-by-step explanation:

took the quiz :)

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

solve

Step-by-step explanation:

do 840 divided by 60

Answer:

14 in

Step-by-step explanation:

cubic means three

take the 2 you do have:

6 and 10

multiply them:

60

divide 840 by 60 to get the third:

14

The given number 3/4 which subsets belong to a rational number. The answer is option (A) rational numbers.

As per the question,

The given number is 3/4.

As we know that a rational number is one that can be written as a ratio of two integers, where the denominator is greater than zero.

The result is rational because 3/4, can be expressed as a ratio of two integers can be 3/4 of two integers, a numerator 3, and a denominator 4 (which is a non-zero).

So, the given number 3/4 which subsets belong to a rational number.

Therefore, the correct answer is option (A) rational numbers.

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The complete question is as follows:

To which subset of real numbers does the number 3/4 belong?

A. rational numbers

B. irrational numbers

C. whole numbers, integers, rational numbers

D. whole numbers, natural numbers, integers

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Using the normal distribution, we have that:

a) There is a 0.6915 = 69.15% chance of a pride of lions having a territory less than 74-square miles.

b) There is a 0.7888 = 78.88% chance of a pride of lions having a territory between 60 and 80 square miles.

c) X = 54.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 70, \sigma = 8\)

The chance of a pride of lions having a territory less than 74-square miles is the p-value of Z when X = 74, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (74 - 70)/8

Z = 0.5.

Z = 0.5 has a p-value of 0.6915.

Hence:

There is a 0.6915 = 69.15% chance of a pride of lions having a territory less than 74-square miles.

The change of the territory being between 60 and 80 square miles is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 60, hence:

X = 80:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (80 - 70)/8

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

X = 60:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (60 - 70)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1056.

0.8944 - 0.1056 = 0.7888.

Hence:

There is a 0.7888 = 78.88% chance of a pride of lions having a territory between 60 and 80 square miles.

For item c, we have that X is found when Z = -2, hence:

\(Z = \frac{X - \mu}{\sigma}\)

-2 = (X - 70)/8

X - 70 = -2(8)

X = 54.

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Answer:

\((25,-71)\)

Step-by-step explanation:

Given

\((x,y) = (19,5)\) --- midpoint

\((x_1,y_1) = (13,81)\) --- end 1

Required

The other endpoint

Using midpoint formula, we have:

\((x,y) = 0.5 * [x_1 + x_2, y_1 + y_2]\)

So, we have:

\((19,5) = 0.5 * [13 + x_2, 81 + y_2]\)

Multiply both sides by 2

\(2 * (19,5) = 2 * 0.5 * [13 + x_2, 81 + y_2]\)

\((38,10) = [13 + x_2, 81 + y_2]\)

By comparison:

\(x_2 + 13 = 38\) and \(y_2 + 81 = 10\)

So:

\(x_2 = 38 - 13\)

\(x_2 = 25\)

and

\(y_2 = 10 - 81\)

\(y_2 = - 71\)

Henc, the other endpoint is:

\((25,-71)\)

Step-by-step explanation:

scalar multiplication is simply done by multiplying every term of the matrix by the factor.

-1/5 A =

-5×-1/5 -15×-1/5 10×-1/5

-30×-1/5 20×-1/5 -25×-1/5

=

1 3 -2

6 -4 5

for the addition of 2 matrices imagine that each one is on a transparent slide, and you simply move both slides on top of each other, and you add all numbers for a position, that overlap each other for that position.

so,

-1/5 × A + B =

1+4 3+5 -2+ -7

6+7 -4+0 5+ -5

=

5 8 -9

13 -4 0

is △ABC equilateral?  well, we dunno, however let's check for all sides' length.

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}\)

\(B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}\)

well, not quite.

Answer:

x=10

Step-by-step explanation:

you know that 12x+5+6x-5=180 you can simplify the equation to 18x=180 and then you can divide both sides by 18 to get that x=10

The observation of the pattern is discussed below.

When we calculate the squares of the numbers from 1 to 10 and observe the digits at the one's place of each square, we notice a pattern:

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

If we focus on the digits at the one's place, we can see that they form a repeating pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. This pattern repeats itself as we calculate the squares of higher numbers.

This observation is known as the "digit at one's place pattern" or the "units digit pattern." It occurs because the square of any number depends only on the digit at the one's place of that number. Hence, when we square numbers that have the same digit at the one's place, we get the same digit at the one's place in the result.

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\(\huge\bold\red{₳₦₴₩ɆⱤ:-}\)

The root of unity is a number which is complex in nature and gives 1 if raised to the power of a positive integer n. These roots are used in different branches and topics of maths like number theory. It is also called as de Moivre system.

What are Cube Roots of Unity?

There are a total of three cube roots of unity which are as follows:

Cube Root of Unity Value Nature of Cube Root

1 Real

−½ + i √(3/ 2) Complex

−½ – i √(3/ 2) Complex

Here, a = 1 is the real cube root of unity while a = – ½ + i √(3/ 2) and a = – ½ – i √(3/ 2) are the imaginary or complex cube roots of unity.

Answer:

No

Step-by-step explanation:

y = -2x + 1

(-11) = -2(5) +1  \  Plug-in the values from the point given

-11 = -10 + 1  \  Reduce

-11 = -9 \ Simplify

-11 ≠ -9  \ Determine the valididity

Answer:

3 : 10

Step-by-step explanation:

2 kg = 2000g

600g peanuts : 2000 cashew nuts

600 : 2000

divide both sides by a common divisor ( 200)

600/200 : 2000/200

3 : 10

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

Similar triangles are triangles with corresponding sides that have the same ratio.

Thus:

AD is parallel to BC (bases of a trapezoid are parallel)

Therefore:

∠ACB = ∠CAD (alternate interior angles)

This implies that, ΔABC ~ ΔACD by AA similarity theorem.

Thus:

AC/DA = CB/AC

Substitute

AC² = 12 × 27

AC = √324

AC = 18 m

Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

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The 3rd graph (bottom left)

2.58

Let's see how the while loop functions for n = 2345. Inside the loop, the reversed number is calculated using the formula reverse = reverse * 10 + remainder. n. n != 0.

Given,

arr: [7, 234, 58100]

Expected Output:

7 + 432+ 18500 = 18939

Input:

arr: [0, 100, 220]

Expected Output:

0 + 100 + 220 = 320

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The median margin for victory will be 1.89.

The median of the data is the value of the middle observation discovered after the data are organized in ascending order. The median is useful in situations where it is difficult to express anything while taking into account all of the data.

One of the easy to calculate statistical summary metrics is the median. Since it bases its value on the data that is in the middle of a sequence, the median is often referred to as the place average.

Given Data:-

1.89,2.32,0.08,4.74,0.30

Mean margin of victory= 1.866

Median margin of victory= 1.89

So the median margin for victory will be 1.89.

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Complete question -

The Solution

The given percentage is

Hence, the correct answer is 31/250

Answer: 24

Step-by-step explanation

8-8-16-24-32-40

6-6-12-18-24-30-36

Answer:

311.3 feet

Step-by-step explanation:

1 yard = 3 feet

Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)

Rounding to the nearest tenth gives us 311.3 feet.

Step-by-step explanation:

See picture above for solution.

Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )