The student body of 125 students wants to elect a president, vice president, and secretary. How many possible results are there?

Answer:

The scale factor of triangle:

The scale factor of trapezoid:

See the picture for the dilated triangle

The swimming pool can hold a volume of 3.456 cubic meters of water.

The volume of water that the swimming pool can hold can be calculated by multiplying the base area of the pool by its depth. In this case, the base area is given as 192 m² and the depth is 1.8 cm.

However, it is important to note that the depth should be converted to meters before performing the calculation.

To convert 1.8 cm to meters, we divide it by 100 (since there are 100 centimeters in a meter):

Depth = 1.8 cm ÷ 100 = 0.018 m

Now we can calculate the volume of water using the formula:

Volume = Base Area × Depth

Substituting the given values, we get:

Volume = 192 m² × 0.018 m = 3.456 m³

Therefore, the swimming pool can hold a volume of 3.456 cubic meters of water.

In the explanation, we use the formula for calculating the volume of a rectangular prism, which is given by multiplying the base area by the depth. We convert the depth from centimeters to meters and then substitute the given values into the formula to find the volume of water that the swimming pool can hold, which is 3.456 cubic meters.

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Answer:

Step-by-step explanation:

Solve for x

7/8 of x is 14

7/8x = 14

x = 14 : 7/8

x = 14 * 8/7

x =16

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

check

7/8 * 16 = 14

14 = 14

the answer is good

Answer:

A is the correct answer because all sides are congurent

A parallelogram has two pairs of parallel sides.

opposite sides and opposite angles are congruent.

Option D is the correct answer.

We have,

Parallelograms have several notable properties:

Opposite sides are parallel:

In a parallelogram, opposite sides are parallel, meaning they never intersect and have the same slope.

Opposite sides are congruent:

The opposite sides of a parallelogram have equal lengths. This property applies to both pairs of opposite sides.

Opposite angles are congruent:

The opposite angles of a parallelogram have equal measures. This property applies to both pairs of opposite angles.

- Consecutive angles are supplementary.

- Diagonals bisect each other.

- Diagonals create congruent opposite triangles.

- Diagonals create equal opposite angles.

Thus,

A parallelogram has two pairs of parallel sides.

opposite sides and opposite angles are congruent.

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True, Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.

What does a response variable in an experiment mean?

Response Continuum In an experimental investigation, this is the result that is assessed after manipulating the explanatory variable; it is also referred to as the dependent or outcome variable.

                                Its value is expected or its variation is explained by the explanatory variable.

What other name would you give the answer variable?

The term "dependent variable" is one more typical moniker for the response variable. The response variable is frequently referred to as just "the response" for short.

                        There are several more terms for the predictor variables, including "explanatory variables," "independent variables," "predictors," and "regressors."

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Answer:

11

Step-by-step explanation:

5m - 9 = 4m + 2

Subtract 4m and add 9 to both sides:

m = 11

By definition of proportion, the value of x is,

⇒ x = 80

We have to given that;

In a triangle,

Perpendicular = 60

Now, By Pythagoras theorem we get;

60² = 36² + y²

3600 = 1296 + y²

y² = 3600 - 1296

y² = 2304

y = 48

Hence, By definition of proportion;

⇒ x / 48 = 60 / 36

⇒ x = 80

Thus, By definition of proportion, the value of x is,

⇒ x = 80

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Answer:

C) Increase the amplitude to 2xo and stand 2 meters from the source.

Step-by-step explanation:

Correct on Edge

The percent of the bags of chips weigh less than 176 grams is b 16%

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

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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The histogram will show the distribution of the athletes' mile running times. It will provide a visual representation of the frequency or count of athletes falling within different time intervals.

1. Determine the time intervals or "bins" for the histogram. For example, you might have bins of 5-second intervals, such as 0-5 seconds, 5-10 seconds, and so on.

2. Count the number of athletes who fall within each bin. For instance, if three athletes completed the mile in the 0-5 second bin, and five athletes completed it in the 5-10 second bin, record those counts.

3. Plot the bins on the x-axis of the histogram and the corresponding frequency or count on the y-axis.

4. Draw rectangles (or bars) on the histogram, with the height of each bar representing the frequency or count of athletes within each bin.

5. Label the axes and add a title to the histogram for clarity.

The resulting histogram will provide a visual representation of how the athletes' mile running times are distributed, allowing you to observe any patterns or trends.

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Answer:

y=3/2x-1/2

Step-by-step explanation:

Use slope formula to get the slope (3/2). Then use y=mx+b to get the y-intercept by plugging in 2 (from first coordinate) for ¨x¨ and 2.5 for y and 3/2 for m (2.5=3/2(2)+b) which when solved gives you (-1/2=b).

Hope this helped!

Answer:

\(\displaystyle \oint_C {3y \, dx + 2x \, dy} = \boxed{\bold{2}}\)

General Formulas and Concepts:
Calculus

Differentiation

Derivative Property [Multiplied Constant]:
\(\displaystyle (cu)' = cu'\)
Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Fundamental Theorem of Calculus 1]:
\(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:
\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Multivariable Calculus

Partial Derivatives

Vector Calculus

Circulation Density:
\(\displaystyle F = M \hat{\i} + N \hat{\j} \rightarrow \text{curl} \ \bold{F} \cdot \bold{k} = \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}\)

Green's Theorem [Circulation Curl/Tangential Form]:
\(\displaystyle \oint_C {F \cdot T} \, ds = \oint_C {M \, dx + N \, dy} = \iint_R {\bigg( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \bigg)} \, dx \, dy\)

Step-by-step explanation:

Step 1: Define

Identify given.

\(\displaystyle \oint_C {3y \, dx + 2x \, dy}\)

\(\displaystyle \text{Region:} \ \left \{ {{0 \leq x \leq \pi} \atop {0 \leq y \leq \sin x}} \right.\)

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

We can evaluate the Green's Theorem double integral we found using basic integration techniques listed above:
\(\displaystyle \begin{aligned}\oint_C {3y \, dx + 2x \, dy} & = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx \\& = - \int\limits^{\pi}_0 {y \bigg| \limits^{y = \sin x}_{y = 0}} \, dx \\& = - \int\limits^{\pi}_0 {\sin x} \, dx \\& = \cos x \bigg| \limits^{x = \pi}_{x = 0} \\& = \boxed{\bold{2}}\end{aligned}\)

∴ we have evaluated the line integral using Green's Theorem.

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Topic: Multivariable Calculus

Unit: Green's Theorem and Surfaces

Explanations:

The given equation is 2x + 4 = -7x

The first step is to collect like terms, which means 2x will go and meet -7x on the right.

The equation becomes:

4 = -7x - 2x

4 = -9x

Divide both sides by -9, the equation becomes:

Answer:

3 A'(-1,2) B'(4,3) C'(-2,5)

Step-by-step explanation:

The rule for a 270-degree rotation: When rotating a point 270-degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means, we switch x and y and make x negative.

 3 A'(-1,2) B'(4,3) C'(-2,5)

Answer:

103000

Step-by-step explanation:

3.5 × \(10^{4}\) + 6.8 × \(10^{4}\)

Calculate 10 to the power of 4 and get 10000.

3.5 × 10000 + 6.8 × \(10^{4}\)

Multiply 3.5 and 10000 to get 35000.

35000 + 6.8 × \(10^{4}\)

Calculate 10 to the power of 4 and get 10000.

35000 + 68000

Add 35000 and 68000 to get 103000.

103000

Answer:

Couple of choice:

A. If those x's are the multiplication symbol then your answer is 103,000

B. If those x's are variables then you don't have a definite answer.

Step-by-step explanation:

Explanation for A:

We use PEMDAS and start inside the parentheses

We do exponents before multiplication and get 10,000 for 10^4

10,000*3.5= 35,000

10,000*6.8=68,000

35,000+68,000=103,000

Explanation for B:

If the x's are variables then your question is just and expression. Without it being equal to anything, I can't solve for x. Also if the question was asked as, "What is (3.5x10^4)+(6.8x10^4), when x = 5 (or any random number)" I could solve it because I know the value of x being asked. Maybe try posting the question again if this is what you meant

Using a confidence level of 95%, the margin of error for the estimate of the mean number of television hours watched will be 1.129

The approximate margin of error can be calculated using the relation :

Margin of Error = \( 1.96 \frac{2.88}{\sqrt{25}} \)

Margin of Error = \( 1.96 \frac{2.88}{5} \)

Margin of Error = \( 1.96 \times 0.576 \)

Margin of Error = \( 1.129 \)

Therefore, the margin of error for the estimate of the mean number of television hours watched is 1.129.

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Answer:

Raphael will take 7.5 pages of notes during 3 hours of math class.

Step-by-step explanation:

Given;

35 pages were taken during 14 hours maths class

how many pages of math would Raphael take during 3 hours maths class ?

14 hours --------------35 pages

3 hours --------------- ?

= (3 x 35) / 14

= 7.5 pages

Therefore, Raphael will take 7.5 pages of notes during 3 hours of math class.

Answer:

28%. mark got 28% WRONG

Step-by-step explanation:

another way to write 18/25 is 18 divided by 25. 18/25=0.72. 0.72 as a percentage is 72%. You are asking what percent he got wrong. 100%-72%=28%. Mark got 28% wrong/

Answer:

False

Step-by-step explanation:

The total amount of books is 42 not 30 so it would be 12 : 42

The statement " when account groups are created, they will determine the valid number interval for each of the groups of general ledger accounts " is  false because it incorrectly states that account groups determine the valid number intervals for each group of general ledger accounts

Account groups in themselves do not determine the valid number intervals for each group of general ledger accounts.

Rather, the number intervals for each group of general ledger accounts are defined by the chart of accounts, which is a structured list of all the accounts used by an organization to define its financial reporting.

Account groups, on the other hand, are used to group together accounts with similar characteristics or usage, and to assign authorizations for access and maintenance of the accounts.

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Answer:

there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Step-by-step explanation:

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:

Select the first battery. There are 6 choices for the first battery.

Select the second battery. There are 5 choices left for the second battery, since we've already selected one.

Select the third battery. There are 4 choices left for the third battery.

Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:

6 x 5 x 4 = 120

Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

The exponential function that models the population of tiger gar in the lake is given as follows:

\(y = 322.63(1.25)^x\)

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

Considering x as the number of years since 2016, the points are given as follows:

(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).

Inserting these points into an exponential regression calculator, the equation is given as follows:

\(y = 322.63(1.25)^x\)

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The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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The cost of the carpet will be $2,335.5.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The dimensions of the carpet are;

⇒ 15 feet by 18 feet

Now,

The area of the carpet = 15 x 18

                                   = 279 feet²

                                   = 270 / 3 yards²

                                   = 90 yards²

Since, The carpet costs = $25.95 per square yard.

Hence, The carpet cost for 90 yards² = 90 x $25.95

                                                          = $2,335.5

Thus, The cost of the carpet will be $2,335.5.

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Answer:

Each wipe costs .12¢

Step-by-step explanation:

I think you would have to divide $12 by 100 because the are 100 wipes and that equals 0.12

Answer:

$0.12

Step-by-step explanation:

One box of wipes contains 100, which costs 12 dollars.

The price for one wipe would be the total price, $12, divided by the 100 wipes. Therefore,

12 / 100 = $0.12 each

Answer:

15

Step-by-step explanatio

The probabilities will be :

P(none) = 0.018

P(at least one) =  0.982

P(at most one) = 0.187

Pretty Betty share  is 15%, the probability that any one household is tuned to the show will be:  0.15.

To find the probability that none of the households are tuned to Pretty Betty will be:

P(none) = 0.85¹¹

            ≈ 0.018

So, to find the probability that at least one household is tuned to Pretty Betty,  i use the complement rule as well as subtract the probability of none of the households being tuned to the show from 1:

P(at least one)

= 1 - P(none)

≈ 1 - 0.018

≈ 0.982

So, to find the probability that at most one household is tuned to Pretty Betty:

P(at most one) = P(none) + P(one)

= 0.85^11 + 11(0.15)(0.85^10)

≈ 0.187

Hence, the probabilities will be :

P(none) = 0.018

P(at least one) =  0.982

P(at most one) = 0.187

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