The following quadrilateral is a rhombus. The measure of angle E is 115
degrees. What is the measure of angle G?"

Answer:

70√2  units²

Step-by-step explanation:

(see attached for reference notes on parallelograms)

we are given ABCD is a parallelogram where

Short Length, AB = 10 units

Long Length, BC = 14 units

Angle A = 45°

The area of the parallelogram is hence,  

= AB x BC sin 45°

= 10 x 14 x sin 45

= 140 sin 45°    (recall from special angles, that sin 45° = 1/√2)

= 140/√2   (remove radical from denominator by multiplying by √2/√2)

= (140/√2) x (√2/√2)

=70√2  units²

The down payment is $43,200 on the house.

The 20% down payment on a $216,000 house is:

20% x $216,000

Let us convert the 20% to decimal value

To do this we have to divide 20 by 100

20/100=0.2

To find down payment multiply 0.2 with  $216,000

0.2×216,000

= $43,200

Therefore, the down payment is $43,200 on the house.

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Answer:

The cost of one foot of grass sod is $9 and the cost of one shrub is $18.

Step-by-step explanation:

Since Pranv and Paul both bought their supplies from the same store, we can assume that they paid the same price per foot of grass sod and per shrub. From the information given, we know that Pranv spent $90 on 10 feet of grass sod and 5 shrubs, which means that he paid 90/10 = $9 per foot of grass sod and 90/5 = $18 per shrub. We also know that Paul spent $50 on 5 feet of grass sod and 3 shrubs, which means that he paid 50/5 = $10 per foot of grass sod and 50/3 = $16.67 per shrub. Since both Pranv and Paul paid the same price per foot of grass sod and per shrub, the cost of one foot of grass sod is $9 and the cost of one shrub is $18.

A. The probability of rolling two numbers with a sum of 7 is given as follows: p = 1/6.

B. The expected number of rolls with a sum of 7 is given as follows: 25 rolls.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes when two dice are rolled is given as follows:

6² = 36.

There are six outcomes with a sum of 7, as follows:

(1,6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1).

Hence the probability is given as follows:

p = 6/36 = 1/6.

Hence, out of 150 rolls, the expected number of sums of seven is given as follows:

E(X) = 1/6 x 150

E(X) = 25 rolls.

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The value of x , y and z in the parallel line is 50 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

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So, the z-scores are approximately 1.34 and 2.08.

Therefore, the probability that the sample mean will be between 66.6 and 68.4 is approximately 0.4115, or 41.15% (rounded to two decimal places).

To calculate the probability that the sample mean falls between 66.6 and 68.4, we need to find the z-scores corresponding to these values and then use the z-table or a statistical calculator.

a) Calculate the z-scores:

The formula for calculating the z-score is:

z = (x - μ) / (σ / √n)

For the lower value, x = 66.6, μ = 63.3, σ = 16.0, and n = 35:

z1 = (66.6 - 63.3) / (16.0 / √35) ≈ 1.34

For the upper value, x = 68.4, μ = 63.3, σ = 16.0, and n = 35:

z2 = (68.4 - 63.3) / (16.0 / √35) ≈ 2.08

b) Find the probability:

To find the probability between these two z-scores, we need to find the area under the standard normal distribution curve.

Using a z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:

P(1.34 ≤ z ≤ 2.08) ≈ 0.4115

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The Selling Price of the Stereo will be $75

Cost Price is defined as the amount that is paid to purchase an article or the price at which an article is made is known as its cost price. The cost price can be abbreviated as C.P.

Selling Price is defined as the price at which an article is sold to the customer. The selling price is abbreviated as S.P.

Profit and Loss can be estimated through Selling Price and Cost Price.

Profit =Selling Price-Cost Price ,only when the selling price is greater than the Cost price.

Loss= Cost Price- Selling price , only when the cost price is greater than the Selling price.

Step by step explanation

As we know that the Cost Price=$150

and Selling Price is 50% of Cost Price

∴Sale Price will be $75

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Given that Steve handed him a black king, the probability of Scott's second card being a red card is 13/25, or around 0.52.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

A conventional deck of playing cards has 52 cards, including two black kings. When Steve deals a black king to Scott, the deck has 51 cards, 26 of which are red.

We only need to analyse the likelihood of obtaining a red card on the second draw because we know Scott's initial card is a black king. There are 50 cards remaining in the deck, 26 of which are red. As a result, the likelihood that Scott's second card will be a red card is:

P(red card drawn on second draw) = 26/50 = 13/25

Given that Steve handed him a black king, the likelihood of Scott's second card being a red card is 13/25, or around 0.52.

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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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The expected value of the discrete distribution, if you have to pay $.50 to pick one package at random, is of -$0.08.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For this problem, considering the cost of $0.5, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 0.2 x 0.24 - 0.3 x 0.1 - 0.2 x 0.46 = -$0.08.

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Kindly note that the spinner diagram. Wasn't given and the spinner used was just hypothetical.

Answer:

1 /18

Step-by-step explanation:

Sample space for spinner = (a, b, c, d, e, F, G, h, I) = 9

Total possible outcomes = sampme space

Vowels in spinner = (a, e, I)

Number of vowels = required outcome = 3

P(spinning a vowel) = required outcome / Total possible outcomes

P(spinning a vowel) = 3 / 9 = 1/3

For a six sided dice ;

Required outcome = (6) = 1

Total possible outcomes = (1,2,3,4,5,6) = 6

P(rolling a six) = 1/6

P(rolling a 6 and spinning a vowel) = 1/3 * 1/6 = 1/18

Answer: y = -5

Here you go

The shape of the distribution of the number of siblings can vary depending on the specific data set.

However, if we are considering the general case, the most common shape of the distribution is likely to be unimodal and skewed to the right.

This means that the majority of individuals are likely to have fewer siblings,

and as the number of siblings increases,

the frequency of individuals with that number decreases.

The distribution may also have a long tail on the right side,

indicating a few individuals with a significantly larger number of siblings.

However, it is important to note that this is just a general observation, and in specific cases,

the distribution may be different.

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The probability that a randomly selected customer had at least one order in the previous month or uses express shipping is 0.9242.

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).

The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.

P( at least one order in the previous month or uses express shipping)

=P(at least one order in the previous month) + P(uses express shipping) - P(at least one order in the previous month and uses express shipping)

\(\frac{107+63}{211} +\frac{131}{211} -\frac{65+41}{211}\)

= 0.9242

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After 24 days, there will be approximately 25 atoms of I13153 remaining. The nuclear process that occurs during the decay is the transformation of I13153 into Xe13154.

The half-life of I13153 is nearly 8 days, which means that after each 8-day period, half of the atoms will decay into Xe13154. Starting with a sample of 200 atoms of I13153, we can calculate the number of remaining atoms after 24 days. Since the half-life is 8 days, the number of remaining atoms after each 8-day period is halved. After the first 8 days, there will be 100 atoms of I13153 remaining.

After the second 8 days, there will be 50 atoms remaining. And after the third 8 days, there will be 25 atoms of I13153 remaining. The nuclear process that occurs during the decay of I13153 is radioactive decay. Specifically, it undergoes beta decay, where a neutron in the nucleus of I13153 is converted into a proton, resulting in the formation of Xe13154. This process releases radiation and transforms the original isotope into a different element.

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Answer:

0.571

Step-by-step explanation:

Answer:

0.571

Step-by-step explanation:

divide 4 and 7

Answer: x = 2√3.

Step-by-step explanation:

\(x^{2} +6^{2} =(2x)^{2}\\\\x^{2} +36=4x^{2} \\\\4x^{2}-x^{2} -36=0\\\\3x^{2} -36=0\\\\3(x^{2} -12)=0\\\\x^{2} -12=0\\\\x^{2} =12\\\\x=\sqrt{12} =2\sqrt{3}\)

There is sufficient evidence to conclude that the population standard deviation is different from 0.1.

What is test statistic?

A test statistic is a figure obtained from a statistical analysis. It explains how far your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

Given,

            \(H_0:\sigma =0.1\\H_a:\sigma \neq 0.1\)

Test statistic:

Chi square=(20-1)*0.25^2/0.1^2=118.75

df=20-1=19

p-value=CHIDIST(118.75,19)=0.0000

Reject the null hypothesis.

Hence, there is sufficient evidence to conclude that the population standard deviation is different from 0.1.

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Given:

Diameter of the hole = 30 cm

To find:

The area of the hole.

Solution:

The radius of a circle is always half of the diameter. It is given that the diameter of the hole is 30 cm. So, the radius of the hole is:

\(r=\dfrac{30}{2}\)

\(r=15\)

Area of a circle is:

\(A=\pi r^2\)

Putting \(\pi = 3.14\) and \(r=15\) in the above formula, we get

\(A=(3.14)(15)^2\)

\(A=(3.14)(225)\)

\(A=706.5\)

Therefore, the area of the hold is 706.5 square cm.

If α + β > 1, then depending on the precise values of and, (-1) and (-1) can either be positive or negative. Without additional knowledge about the signs of (-1) and (-1) the concavity of the Cobb-Douglas function cannot be calculated in this situation.

To determine whether the Cobb-Douglas function is concave, we need to examine the second-order partial derivatives of the function with respect to its variables, x₁ and x₂.

Let's start by finding the first-order partial derivatives of the Cobb-Douglas function:

∂y/∂x₁ = α(x₁)^(α-1)(x₂)^β

∂y/∂x₂ = β(x₁)^α(x₂)^(β-1)

Now, let's find the second-order partial derivatives:

∂²y/∂x₁² = α(α-1)(x₁)^(α-2)(x₂)^β

∂²y/∂x₂² = β(β-1)(x₁)^α(x₂)^(β-2)

∂²y/∂x₁∂x₂ = αβ(x₁)^(α-1)(x₂)^(β-1)

The Hessian matrix is formed using these second-order partial derivatives:

H = | ∂²y/∂x₁² ∂²y/∂x₁∂x₂ |

| ∂²y/∂x₁∂x₂ ∂²y/∂x₂² |

For concavity, the determinant of the Hessian matrix must be negative (since α and β are positive constants):

det(H) = (∂²y/∂x₁²) * (∂²y/∂x₂²) - (∂²y/∂x₁∂x₂)²

det(H) = [α(α-1)(x₁)^(α-2)(x₂)^β] * [β(β-1)(x₁)^α(x₂)^(β-2)] - [αβ(x₁)^(α-1)(x₂)^(β-1)]²

det(H) = αβ(x₁)^(α+β-2)(x₂)^(α+β-2)[α(α-1)(x₂)^β - β(β-1)(x₁)^α]

Since α + β < 1, we know that α + β - 2 < -1. This means that (x₁)^(α+β-2) and (x₂)^(α+β-2) are positive and decreasing functions of x₁ and x₂, respectively.

Now, let's consider the expression inside the square brackets: α(α-1)(x₂)^β - β(β-1)(x₁)^α.

If α + β < 1, we can observe that both α(α-1) and β(β-1) are positive, and since α and β are less than 1, the expression is also positive.

Therefore, the determinant of the Hessian matrix is negative, det(H) < 0, implying that the Cobb-Douglas function is concave when α + β < 1.

If α + β > 1, then α(α-1) and β(β-1) can be either positive or negative, depending on the specific values of α and β. In this case, the concavity of the Cobb-Douglas function cannot be determined without additional information about the signs of α(α-1) and β(β-1).

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Answer:

76

Step-by-step explanation:

decagon = 10 sides

3 heptagons = 3 × 7 = 21 sides

3 nonagons = 3 * 9 = 27 sides

3 hexagons = 3 * 6 = 18 sides

10 + 21 + 27 + 18 = 76 sides in total

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The formula for the function P(x) representing the population of the town x years after 2003 is P(x) = 50,800 + 3,500x. Using this formula, the population of the town in 2015 will be 59,800 people.

To find the formula for the function P(x) representing the population of the town x years after 2003, we start with the initial population in 2003, which is 50,800 people. Since the population has been growing linearly by approximately 3,500 people each year, we can express this growth rate as 3,500x, where x represents the number of years after 2003.

Thus, the formula for the function P(x) is given by:

P(x) = 50,800 + 3,500x.

To determine the population of the town in the year 2015, we substitute x = 12 into the formula:

P(12) = 50,800 + 3,500(12) = 50,800 + 42,000 = 92,800.

Therefore, in 2015, the population of the town will be 92,800 people.

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Answer:

Let's solve your equation step-by-step.

|−x−15|=|5x−23|

Solve Absolute Value.

|−x−15|=|5x−23|

We know either−x−15=5x−23or−x−15=−(5x−23)

−x−15=5x−23(Possibility 1)

−x−15−5x=5x−23−5x(Subtract 5x from both sides)

−6x−15=−23

−6x−15+15=−23+15(Add 15 to both sides)

−6x=−8

−6x

−6

=

−8

−6

(Divide both sides by -6)

x=

4

3

−x−15=−(5x−23)(Possibility 2)

−x−15=−5x+23(Simplify both sides of the equation)

−x−15+5x=−5x+23+5x(Add 5x to both sides)

4x−15=23

4x−15+15=23+15(Add 15 to both sides)

4x=38

4x

4

=

38

4

(Divide both sides by 4)

x=

19

2

Check answers. (Plug them in to make sure they work.)

x=

4

3

(Works in original equation)

x=

19

2

(Works in original equation)

Answer:

x=

4

3

or x=

19

2

Step-by-step explanation:

Answer:

x = 4/3

Step-by-step explanation:

|-x-15 | = | 5x - 23 |

take square root

√-x-15 = √ 5x - 23

than take square

(√-x-15 )² = (√ 5x - 23)²

than,

-x -15 = 5x - 23

-15 = x + 5x - 23  ( add x on both sides )

-15 + 23 = 6x  ( add 23 on both sides )

8 = 6x

8/6 = x   (divide 6 on both sides )

x = 4/3

Answer:

8 tablespoons of shortening

Step-by-step explanation:

mathhhh

F = (between-groups variance) / (within-groups variance) = 1.54, F = (between-groups variance) / (within-groups variance) = 5.78 , F = (between-groups variance) / (within-groups variance) = 1.16

To calculate the F statistic, we need both the between-groups variance and within-groups variance. Let's calculate the F statistic for each case:

a. Between-groups variance = 29.4, within-groups variance = 19.1.

The F statistic is the ratio of the between-groups variance to the within-groups variance: F = (between-groups variance) / (within-groups variance) = 29.4 / 19.1.

b. Within-groups variance = 0.27, between-groups variance = 1.56.

Similarly, the F statistic is the ratio of the between-groups variance to the within-groups variance: F = (between-groups variance) / (within-groups variance) = 1.56 / 0.27.

c. Between-groups variance = 4595, within-groups variance = 3972.

Again, the F statistic is the ratio of the between-groups variance to the within-groups variance: F = (between-groups variance) / (within-groups variance) = 4595 / 3972.


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The elements in the table are in proportional.

Since for every 3unit increase in x, there is a 7 unit increase in y element. Thus, the elements in the table are in proportional.

When x=0 the value of y=0, when x=3 the value of y=7, and finally when x=6 the value of y=14.

The elements is in proportional because the next element is then defined as the multiple of two of the previous element.

Answer:

44.272

Step-by-step explanation:

Answer:

Number of moles = 41.67 (Approx)

Number of carbon atom = 250.97 x 10²³ (Approx)

Step-by-step explanation:

Given:

Amount of carbon = 500 g

Find:

Number of moles

Number of carbon atom

Computation:

Number of moles = 500 / Atomic number of weight

Number of moles = 500 / 12

Number of moles = 41.67 (Approx)

Number of carbon atom = Number of moles x Avogadro number

Number of carbon atom = 41.67 x 6.023 x 10²³

Number of carbon atom = 250.97 x 10²³ (Approx)