alvin is 11 years older than ella. the sun of their ages is 59. what is elgas age

Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

Answer:

Step-by-step explanation:

-3x+y=2 --> y=3x+2

Since the two lines parallel, the line passing through (k,7) and (1,1) should be determined as y=3x+c

Then bring (1,1) into y=3x+c

3+c=1, then c=-2

So y=3x-2

Since (k,7) is also on that line, then 7=3k-2

9=3k

k=3

Filled box will be:

Box 1: Sum of angles on starlight line is 180°.

Box 2: m ∠LQR + m ∠MQR = 180°

Box 3: m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR

Box 4: m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR

Box 5: If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel.

From the given figure we have to prove that LM ∥ NP.

m ∠LQR + m ∠QRN = 180° [Given]

m ∠LQR + m ∠MQR = 180° [Sum of angles on starlight line is 180°]

m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR [Transitive property of Equality]

m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR [Subtraction property of Equality]

m ∠QRN = m ∠MQR [Definition of Congruence]

LM ∥ NP [If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel]

Hence it is proved that, LM ∥ NP.

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Answer:

17

Step-by-step explanation:

The answer is 17 because the operation PEMDAS

Answer:

17

Step-by-step explanation:

20/ 4+6x2 can be simplified. First, you can divide 20 by 4 because of the order PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction) 20 divided by 4 is 5. You can then multiply 6 and 2 which gives you 12. Therefore, your equation is down to 5+12. You can add those two and you get 17 :) Hope this helps!! :D ~Happy Halloween~

The solution is 42 : 98 : 105

The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the ratio of number of songs downloaded by Gerald and Harold be =

3 : 7

Let the ratio of number of songs downloaded by Harold and James be =

14 : 15

So , the number of songs downloaded by Gerald = 3x

The number of songs downloaded by Harold = 7x

And ,

The number of songs downloaded by Harold = 14y

The number of songs downloaded by James = 15y

So , substituting the values in the equation , we get

7x = 14y

x = 2y

And ,

The number of songs downloaded by Gerald = 3 x 14 z

The number of songs downloaded by Gerald = 42z

The number of songs downloaded by Harold = 7 x 14z

The number of songs downloaded by Harold = 98z

The number of songs downloaded by James = 7 x 15z

The number of songs downloaded by James = 105z

So , the ratio of the number of songs Gerald , Harold and James downloaded = 42z : 98z : 105z

On simplifying the proportion , we get

The ratio will be = 42 : 98 : 105

Hence , The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105

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Answer:

Perpendicular

Step-by-step explanation:

If X=3, then it looks like ‘|’

If Y=4, then it looks like ‘—’

Together they form a 90 degree angle, when two lines form a 90 degree angle it is perpendicular

Answer:

560

Step-by-step explanation:

8000x.07

Answer:

the answer is

y=3/2+4

Step-by-step explanation:

4 is found on the y-axis and 3/2 is 1,5 and it looks like its going 1,5 steps up

The tower, the flagpole and Jeff's position form similar triangles

The tower is 54 feet's tall

Using the attached figure as an illustration, we have the following highlights

So, we have the following equivalent ratios

\(AB:BE = CD:CE\)

Where:

BE = BC + CE

So, we have:

\(AB:BC + CE = CD:CE\)

This gives

\(h:40 + 20 = 18:20\)

\(h:60 = 18:20\)

Express as fraction

\(\frac{h}{60} = \frac{18}{20}\)

\(\frac{h}{60} = 0.9\)

Multiply through by 60

\(h= 54\)

Hence, the tower is 54 feet's tall

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The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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The statement that the one with a higher coefficient of variation exhibits higher variability is true.

The coefficient of variation expresses the proportionate level of variability present in a random variable and can be determined by dividing the mean by the standard deviation.

If the coefficient of variation is higher, it means that the random variable shows more variation in relation to its mean.

To illustrate, suppose that the average height of a set of males is 6 feet with a standard deviation of 2 inches.

The variance ratio would result in a coefficient of variation of 0. 033 Suppose that a group of females has an average height of 5 feet with a standard deviation of 1 inch.

The women's coefficient of variation is calculated to be 0. 02 The variance of men's height in relation to their average height is indicated by their higher coefficient of variation.

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a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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Answer:

x=48°

Step-by-step explanation:

We two lines cross over each other, making four angles, the angles opposite each other are equal. They're called vertically opposite angles.

Answer:

Base area=5*12=60

Height is 4

Perimeter or the base is 2*(12+5)=34

Surface area is 2B+Ph=120+136=256

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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Answer:

According to the Central Limit Theorem, the sampling distribution of sample means would have a mean of 5.4 years.

Step-by-step explanation:

For a normally distributed random variable X, with mean and standard deviation, the sampling distribution of sample means with size n can be approximated to a normal distribution with mean and standard deviation.

As long as n is at least 30, the Central Limit Theorem can also be applied to skewed variables.

We have the following problem:

Answer:

Step-by-step explanation:

The mean of the sampling distribution of sample means can be calculated using the formula:

μM = μ

where μ is the population mean and M is the sample mean.

Thus, μM = μ = 5.4 years.

Therefore, the mean of the sampling distribution of sample means would also be 5.4 years.

Answer:

113.1 square inches.

Answer:

415 miles

Step-by-step explanation:

Start with the speed equation:

speed = distance/time

Now solve the speed equation for distance:

distance = speed × time

Apply the speed equation solved for distance to the two parts of the trip.

4 hours at 55 mph:

distance = 55 mph × 4 hours = 220 miles

3 hours at 65 mph:

distance = 65 mph × 3 hours = 195 miles

Add the two distances to find the total distance:

total distance = 220 miles + 195 miles = 415 miles

Answer: 415 miles

Answer:

415 miles

Step-by-step explanation:

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.

How far did he drive?

d=rt

For the first part of the trip:

d = 55 * 4 = 220 miles

For the second part of the trip:

d = 65*3 =195 miles

Add the miles together

220+195 = 415 miles

Answer:

18 cm

Step-by-step explanation:

To find the distance, take the larger number and subtract the smaller number

26 cm - 8 cm

18 cm

Answer:

The test statistic value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

Step-by-step explanation:

Step(i):-

Given mean of the population (μ) =  $183,000

Given mean of the sample (x⁻)  = $198,000

Given standard deviation of the sample (S) =  $65,000.

Mean of the sample size 'n' = 51

level of significance  α = 0.05

Step(ii):-

Null hypothesis : H₀ : There is no significance difference between the means

Alternative Hypothesis :H₁: There is  significance difference between the means

Test statistic

             \(t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

           \(t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }\)

          t =  1.64

Step(iii)

Degrees of freedom  ν = n-1 = 51-1 =50

t₀.₀₅ =  2.0086

The calculated value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

Final answer:-

There is no significance difference between the means

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

The function that could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost, using proportions, is of:

C(x) = 0.8(x - 15).

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially division and multiplication, to find the desired amounts in whichever context of the problem.

The value of shoe is given as follows:

x.

The discounts are given as follows:

Hence the function that gives the total cost paid is presented as follows:

C(x) = 0.8(x - 15).

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Answer:

47 inches

Step-by-step explanation:

45 + 48 + 49 + 40 + 53 = 235

235/5 = 47

Answer: in 5 days they would eat 3 3/4 cans of cat food which costs 1.875 USD. in 21 days they would eat 15.75 cans of cat food which costs 7.875 USD. In 60 days they would eat 45 cans of cat food which costs $22.50.

The amount obtained after 1 year from the whole property is obtained as $27866.82.

The compound interest is can be considered as a case when the interest is added for every interval of time.

The amount for the previous interval becomes the principal for the current one.

The total rent for 9 condos = 9 × 1300 = $11700.

The rate of interest is 7.5% monthly.

Total time = 1 year = 12 months.
The given problem is the case of compound interest for which the expression is given as follows,

A = P(1 + r/100)ⁿ

Substitute the corresponding values to obtain,

A  = 11700(1 + 7.5/100)¹²

    = 27866.82

Hence, the total annual amount received is given as $27866.82.

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Answer:

false_(a) 3 € {2,4,6,8} false_(b) 0 € false (c) {1} € {1, 2, 3} true_(d) {2} S {1, 2, 3} true (e) {1, 3, 5, 7, 9) = {1, 5, 9, 3, 7) false_(f) {1,3,5, 9) = {1,3,5,9} true_ () Ø Ç {1,3

Step-by-step explanation:

i don't know about this is this it ?

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

The calculated value of x in the figure is 12

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

The figure

The scale is given as

A : B = 8 : 9

So, we have

48 : 2x + 30 = 8 : 9

Next, we have

(2x + 30)/48 = 9/8

This gives

2x + 30 = 48 * 9/8

2x + 30 = 54

This gives

2x = 24

So, we have

x = 12

Hence, the value of x in the figure is 12

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Answer: The radius of the circle is 5 3/8 inches.

Step-by-step explanation:

The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:

10 3/4 = (10 × 4 + 3)/4 = 43/4

So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:

r = (43/4) ÷ 2 = 43/8

To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:

r = 43/8 = 5 3/8

Therefore, the radius of the circle is 5 3/8 inches.

Answer:5 3/4

Step-by-step explanation:

10 3/4 * 1/2

1/2 * 43/4 = 43/8

8/43=5 3/4

Answer:

b= -49

Step-by-step explanation:

Well first isolate the number with the variable by performing inverse operations

1/7b= -7

now multiply by 7 on each side to isolate the variable.

b= -49

B is negative 49