ABCD is a rhombus. Find m

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Answer: x = 120 and y = 150

(x / y) = (4 / 5)    

1) 5x = 4y  

( (x + 20 ) / (y - 20) ) = (14 / 13)  

cross multiply fractions  

13(x + 20) = 14(y - 20)

13x + 260 = 14y - 280

2) 13x - 14y = -540  

solve equation 1) for x  

x = 4y/5  

now substitute for x in equation 2)  

13(4y/5) - 14y = -540  

multiply both sides of = by 5  

52y - 70y = -2700  

-18y = -2700  

y = 150  

x = 4(150) / 5 = 120    

x = 120 and y = 150  

check answers  (proof):  

120 / 150 = 12 / 15 = 4 / 5  

(120+20) / (150-20) = 140 / 130 = 14 / 13

We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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Answer: i do it by Dividing the whole number by 100 and multiplying by precent so i would get 15680 Divided by 100 times 35 = 5488

Step-by-step explanation:

The number of products sold each day is given by the equation A = 5,488

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of products sold be A

The total number of products = 15,680

The percentage of products sold = 35 %

So , total number of products sold A = total number of products x percentage of products sold

Substituting the values in the equation , we get

Total number of products sold A = 15,680 x ( 35/100 )

Total number of products sold A = 15,680 x 0.35

Total number of products sold A = 5,488 products

Hence , the number of products is 5,488 products

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Answer:

Length of the rectangle is 18 ft when its width is 4ft

Step-by-step explanation:

Let us assume that the length is represented by l.

Let us assume that the width is represented by w.

As given

The length of the rectangle varies inversely with its width.

Thus

L x 1/w

l=k/w

Where k is the constant of proportionality .

As given

If the

length of the rectangle is 6 feet when the width is 12 feet,

l=6, w=12

putting the values in l = k/w

6 = k/12

k = 12 x 6

k=72

As given

width is 4ft

k= 72, w = 4

Putting the values in, L = k/w

                                   L= 72/4

                                    L=18 ft

Therefore the  length of the rectangle is 18 ft when its width is 4ft

Hope this helps You

The number of ways of selecting the four students out of nine students for attending the conference is equals to the 126 from using the combination formula.

The number of combinations of n things taken r at a time is determined by the combination formula. It is the factorial of n, divided by the product of the factorial of r and the factorial of the difference of n and r respectively. Mathematically, it can be written as \(ⁿCᵣ= \frac{ n!}{r! ( n - r)!}\)

Now, we have number of students majoring in Mathematics = 4

Number of students majoring in chemistry = 5

So, total number of students majoring = 9

Four students are selected to attend conference. Here, n = 9, r = 4 so,

Number of ways to any four can attend =

\( 9C_4 = \frac{ 9!}{4! ( 9 - 4)!}\)

\(= \frac{ 9×8×7×6×5!}{4! 5!}\)

\(=\frac{ 9×8×7×6}{4×3×2}\)

= 18× 7 = 126

Hence, required value is 126.

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A function assigns values. The phase shift of a periodic function is the horizontal translation of the function.

A function assigns the value of each element of one set to the other specific element of another set.

The Phase Shift of a periodic function is the horizontal shift of the function from its normal position. The shift is either left or right.

For example, if the value of c in the function of sine is negative then the function will move towards the right side by the value of c, while if the value of c is positive then the function will towards the left.

Thus, the phase shift of a periodic function is the horizontal translation of the function.

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The height of the pole is approximately 64 feet when rounded to the nearest tenth.

To determine the height of the pole, we can use the concept of a right triangle formed by the pole and the two cables. Let's denote the height of the pole as 'h'.

In the given scenario, one cable is 48 feet long and the other is 63 feet long. The ground distance between them is 80 feet. We can visualize this as follows:

      A

     /|

    / |

 h /  | 63

  /   |

 /    |

/     |

/______C

  48    B

Here, A represents the top of the pole, B represents the point where the 48-foot cable touches the ground, and C represents the point where the 63-foot cable touches the ground.

Using the Pythagorean theorem, we can establish the following relationship:

\(AB^2 + BC^2 = AC^2\)

Substituting the given values, we get:

\(h^2 + 48^2 = 80^2\\h^2 + 2304 = 6400\\h^2 = 6400 - 2304\\h^2 = 4096\)

Taking the square root of both sides, we find:

h =\(\sqrt{4096}\)

h ≈ 64

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15 minutes ----> 1 pound

x minutes -----> 22.5 pounds

answer: Turkey should it be in the oven per 337.5 minutes

Answer:

320 teenagers

Step-by-step explanation:

10% = 0.1

Take 3200 times 0.1 = 320

So, there are 320 teenagers attended the football game.

Answer:

102 degrees

Step-by-step explanation:

Supplement means when both angles are added together they would equal 180. So,

78 + Angle 6 = 180

Angle 6 = 102

Answer:

30/8

Step-by-step explanation:

Oh im sorry feel better :( Im here if you need someone to talk to

Answer:

Sorry to hear that. I hope you feel better!

Step-by-step explanation:

Answer:

5 packages of bagels and 3 packages of muffins

Step-by-step explanation:

3 packages of muffins would be 30 muffins and 5 packages of bagels would be 30 bagels because 6x5=30

Answer: 5 packages of bagels and 3 packages of muffins

Step-by-step explanation: to esy

On multiplying 55 × 35, the answer is  1925.

The simplest way to start teaching multiplication is to establish the relationship between the concept and addition, which your pupils should already be familiar with. Make sure your students understand the first principle of multiplication—that it is just repeated addition—before continuing on.

Your youngster can learn that multiplication is actually just a means to repeatedly add multiple groups of the same number by using objects like blocks and small toys. For instance, ask your youngster to arrange the blocks into six groups of three by writing the issue 6 x 3 on a sheet of paper.

        5 5

    ×  3 5

 ------------

     2 7 5

 + 1 6 5 ×

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

    1925

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The total differential of the function \(\(f(x, y) = x^2 e^{2y} + y \ln(x)\)\) is:

\(\[df = (2x e^{2y} + \frac{y}{x})dx + (2x^2 e^{2y} + \ln(x))dy\]\)

To obtain the total differential of the function \(\(f(x, y) = x^2 e^{2y} + y \ln(x)\)\), we can compute the partial derivatives with respect to each variable and then express the total differential \(\(df\)\) as the sum of the differentials of each variable multiplied by their respective partial derivatives.

Let's calculate it step by step:

1. Calculate the partial derivative with respect to x, denoted as \(\(\frac{\partial f}{\partial x}\)\):

\(\[\frac{\partial f}{\partial x} = 2x e^{2y} + \frac{y}{x}\]\)

2. Calculate the partial derivative with respect to y, denoted as \(\(\frac{\partial f}{\partial y}\)\):  \(\[\frac{\partial f}{\partial y} = 2x^2 e^{2y} + \ln(x)\]\)

3. Express the total differential \(\(df\)\) using the calculated partial derivatives:

 \(\[df = \frac{\partial f}{\partial x}dx + \frac{\partial f}{\partial y}dy\]\)

Substituting the values of the partial derivatives we obtain the total  total differential of the function \(\(f(x, y) = x^2 e^{2y} + y \ln(x)\)\) as:

\(\[df = (2x e^{2y} + \frac{y}{x})dx + (2x^2 e^{2y} + \ln(x))dy\]\)

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The experimental probability that a coin toss results in two heads showing is 3/14

The sample space of two coins is:

S = {HH, HT, TH, TT}

In the above sample space, we have:

The theoretical probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 1/4

Hence, the theoretical probability of two heads is 1/4

To do this, we make use of the table in the question

The table is given as:

Result                                  Frequency

Two heads (HH)                     30

Two tails  (TT)                        40

One head, one tail (HT)        70

Total                                     140

The experimental probability of two heads is calculated as:

P = n(HH)/Total

This gives

P = 30/140

Simplify

P = 3/14

Hence, the experimental probability of two heads is 3/14

Using the sample space in (a), we have:

The theoretical probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 1/4

Hence, the theoretical probability of two tails is 1/4

From the table in the question, we have:

Two tails  (TT)  =40

Total = 140

The experimental probability of two tails is calculated as:

P = n(TT)/Total

This gives

P = 40/140

Simplify

P = 2/7

Hence, the experimental probability of two tails is 2/7

Using the sample space in (a), we have:

The theoretical probability of one head and one tail is calculated as:

P = n(HT)/Total

This gives

P = 2/4

Simplify

P = 1/2

Hence, the theoretical probability of one head and one tail is 1/2

From the table in the question, we have:

One head one tail  (HT)  = 70

Total = 140

The experimental probability of one head one tail is calculated as:

P = n(HT)/Total

This gives

P = 70/140

Simplify

P = 1/2

Hence, the experimental probability of one head one tail is 1/2

The reason for the difference between the probability types is because one is as a result of an actual experiment, while the other is an estimate of the experiment.

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The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

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The value of the double integral is 128/27 - 32/9 + 8ln2/3. From triangular region with vertices (0, 1), (1, 2), (4, 1) d.

To evaluate the double integral, we first need to set up the limits of integration. Since the region D is a triangle, we can use the following limits:

0 ≤ x ≤ 1

1 + x ≤ y ≤ 4 - x

The integral then becomes:

∫0^1 ∫1+x^4-x 8y^2 dy dx

Evaluating the integral with respect to y first, we get:

∫0^1 ∫1+x^4-x 8y^2 dy dx = ∫0^1 [(8/3)(y^3)]1+x^4-x dx

= ∫0^1 [(8/3)(1+x^3)^3 - (8/3)(1+x^2)^3] dx

= 128/27 - 32/9 + 8ln2/3

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Answer:

x = 15

Step-by-step explanation:

We are given the following equation:
\(\frac{9}{x^2-9} = \frac{3}{6x-18}\)

We want to find the value of x of it.

We can start by cross multiplying to get:

9(6x-18) = 3(x²-9)

Distribute the 9 and 3.

54x - 162 = 3x² - 27

Subtract 54x from both sides

-162 = 3x² - 54x - 27

Add 162 to both sides.

3x² - 54x + 135 = 0

We can divide each term by 3. We'll end up with:

x² - 18x + 45 = 0

This can be factored to become:

(x -15)(x-3) = 0

Applying zero product property,

x - 15 = 0

x = 15

And:

x-3 = 0

x = 3

We aren't done yet though; we need to find the domain of this equation, because we have variables in the denominator.

x² - 9 and 6x - 18 both cannot be zero. Because of that:

x² - 9 ≠ 0

x² ≠ 9

x ≠ ±3  

and:

6x - 18 ≠ 0

6x ≠ 18

x ≠ 3
The value of x cannot be 3 or -3. This means that our only answer is x = 15.

Answer:

a

  \(P(X = 2) =  0.2547\)  

b

  \(P(X > 2) =  0.5623 \)  

c

   \(P(2 \le X  \le 5 ) = 0.7817 \)

Step-by-step explanation:

From the question we are told that

   The  proportion of US adults who say that they are likely to make purchase during a sale tax holiday is  

         \(p = 0.28\)

  The  sample size is  n  =  10  

Generally the distribution of US adults who say that they are likely to make purchase during a sale tax holiday, follows a binomial distribution  

i.e  

         \(X  \~ \ \ \  B(n , p)\)

and the probability distribution function for binomial  distribution is  

      \(P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}\)

Here C stands for combination hence we are going to be making use of the combination function in our calculators  

Generally the probability number of adult is exactly 2 is mathematically represented as

     \(P(X = 2) =  ^{10}C_2 *  (0.28)^2 *  (1- 0.28)^{10-2}\)  

=>  \(P(X = 2) =  45 *  0.0784 * 0.0722\)  

=>  \(P(X = 2) =  0.2547\)  

Generally the probability number of adult is more than 2 is mathematically represented as

    \(P(X > 2) =  1- [P(X \le  2) ]\)  

    \(P(X > 2) =  1- [[P(X = 0)] +[P(X = 1) ] + [P(X = 2)] ]\)  

=>  \(P(X > 2) =  1- [^{10}C_0 *  (0.28)^0 *  (1- 0.28)^{10-0}] +[^{10}C_1 *  (0.28)^1 *  (1- 0.28)^{10-1}] + [^{10}C_2 *  0.28^2 *  (1- 0.28)^{10-2}] ]\)  

=>  \(P(X > 2) =  1- [0.0374 + 0.1456 + 0.2547 \)  

=>  \(P(X > 2) =  0.5623 \)  

Generally the probability number of adult is between two and​ five, inclusive is mathematically represented as

    \(P(2 \le X  \le 5 ) =  [P(X = 2 ) + P(X = 3 ) +P(X = 4) + P(X= 5 )] \)

=>  \(P(2 \le X  \le 5 ) =  [[^{10}C_32 *  0.28^2 *  (1- 0.28)^{10-2}] + [^{10}C_3*  0.28^3 *  (1- 0.28)^{10-3}] +[^{10}C_4 *  0.28^4 *  (1- 0.82)^{10-4}] + [^{10}C_5 *  0.28^5 *  (1- 0.28)^{10-5}]] \)

=>  \(P(2 \le X  \le 5 ) =  [[0.2547] + [120*  0.02195 *  0.1003] +[210 *  0.00615 *  0.1393] + [252 *  0.0017 *  0.1935]] \)

=>  \(P(2 \le X  \le 5 ) =  [[0.2547] + [0.2642] +[0.1799] + [0.0829] \)

=>  \(P(2 \le X  \le 5 ) = 0.7817 \)

The expected value of the die roll is 2.47.  Finding the value of kProbability is the measure of the likelihood of an event taking place. The sum of the probability of all events occurring must equal one, otherwise, the set of events would be incomplete, which is not possible.

Therefore, we have 0.28 + k + 0.15 + 0.3 = 1 where k is the probability of getting 2 on the die.Solving for k:k = 1 - 0.28 - 0.15 - 0.3k = 0.27Therefore, the value of k is 0.27. b. Calculating the expected valueThe expected value of the die roll is the sum of each score multiplied by its probability of occurrence. This is also called the mean of the probability distribution, given by: E(X) = ΣxP(x)where X is the random variable and P(x) is the probability of X being equal to x.Using the given table of probabilities:E(X) = 1(0.28) + 2(0.27) + 3(0.15) + 4(0.3)E(X) = 0.28 + 0.54 + 0.45 + 1.2E(X) = 2.47Therefore, the expected value of the die roll is 2.47.

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And since \(7^3\) equals 343, the correct answer is \(B.73=343\).

A logarithmic equation is an equation in which a logarithmic expression, involving one or more variables, is equated to a constant or another logarithmic expression. Logarithmic equations are commonly used in various fields of mathematics, physics, engineering, and sciences.

The general form of a logarithmic equation is:

\(log(base a)(x) = b\)

where "a" is the base of the logarithm, "x" is the argument of the logarithm, and "b" is a constant. \(The correct answer is B. 73 = 343.\)

In exponential form, the logarithmic equation log7 343 = 3 can be rewritten as:

\(7^3\) = 343

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Answer:

hlo bro what's up where r u from

Answer:

a) AAS

b) ASA

c) SAS

d) SSS

Answer: 1 5/12 cups of flour leftover

Step-by-step explanation: First, add 4 2/3 + 5 1/4. This gives you 9 11/12. 9 11/12 - 8 1/2 = 1 5/12.

The baker has \(1\frac{5}{12}\) cups of flour left after making the sheet cake.

A fraction represents a part of a whole.

Given that  baker needs \(8\frac{1}{2}\) cups of flour for a sheet cake recipe.

Baker has  \(4\frac{2}{3}\) cups of flour in a canister and buys \(5\frac{1}{4}\) cups more.

The flour he has in total =  \(4\frac{2}{3}\) +  \(5\frac{1}{4}\)

=14/3 +21/4

=56+63/12

=119/12

To find how much flour the baker has left after making the sheet cake, we can subtract the amount needed from the total amount:

119/12 - 17/2 = (119 - 102) / 12 = 17/12

Therefore, the baker has \(1\frac{5}{12}\) cups of flour left after making the sheet cake.

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Answer:

\( \frac{2}{5} \)

Step-by-step explanation:

\( \frac{40}{100} \)

divide the numerator and denominator by 20

\( \frac{40 \div 20}{100 \div 20} \)

\( \frac{2}{5} \)

Answer:

B

Step-by-step explanation:

In a function the x value cannot repeat

As long as no x value repeats it is considered a function

In answer choice A the x value "1" repeats therefore table a is not a function

In answer choice B no x value repeats twice. This one might be the answer however lets check the other tables just to be safe.

In answer choice C the x value "-4" repeats multiple times therefore table C is not a function

In answer choice D the x value "1" and "2" repeat therefore table D is not a function.

Thus, the answer is B

6 less than "something" can be written as "something" - 6.

In this case, "something" is "the sum of y and x", which can be written as x + y

So, putting them togethre, we have: