The pairs of numbers below represent the price of different
quantities of books at 4 stores.
Which pair of numbers represents a proportional relationship?
o 4 books for $24,8 books for $40
o 5 books for $25, 6 books for $36
o 2 books for $14, 5 books for $35
o 3 books for $15, 7 books for $28

The number of weeks in all Elaine practiced her piano is given by the equation A = 4 2/7 weeks

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

Let the number of weeks Elaine practiced her piano be A

Substituting the values in the equation , we get

Let the total number of days Elaine practiced in a week = 5 days

So , the number of weeks Elaine practices = ( 5/7 ) weeks

Now , the total number of weeks = 6 weeks

So , the total number of weeks Elaine practices piano is A = 6 ( 5/7 )

On simplifying the equation , we get

The total number of weeks Elaine practices piano is A = ( 30/7 ) weeks

The total number of weeks Elaine practices piano is A = 4 2/7 weeks

Hence , the number of weeks is A = 4 2/7 weeks

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The complete question is attached in the picture below :

Elaine practices violin 5 days each week. The model shows the number of days Elaine practices in 6 weeks.

How many weeks in all did Elaine practice the piano during the 6 weeks?

A 4 4/7 weeks

B 4 3/7 weeks

C 4 2/7 weeks

D 4 1/7 weeks

Answer:

Rs 36 600

Step-by-step explanation:

PRT/100

P is the principle

R is the rate of interest

T is the time taken

30 000 * 2 * 11

=660 000/100

= 6600 is the amount of interest charged after the 2 years

now to find the total amount received after the 2 years

= 6600 + 30 000 =36600

The distance traveled after t seconds is given by:

\(d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|\)

Here we know that the particle moves along a straight line with the velocity:

\(v(t) = t^2*e^{-2t}\)

Remember that the velocity is the rate of change of the position, so if we want to find the distance traveled after t seconds, we need to integrate this between 0 and t, we will get:

\(\int\limits^t_0 {t'^2*e^{-2t'}} \, dt' = -\frac{(2t^2 + 2t + 1)e^{-2t}}{4}\)

That is the expression that gives the distance traveled after t seconds, if we want to get it more exactly, we should take the absolute value, then we get:

\(d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|\)

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we have

C = pw + p

solve for w

so

isolate the variable w

step 1

Factor p

C=p(w+1)

step 2

Divide by p both sides

C/p=w+1

step 3

subtract 1 both sides

The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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Answer:

$4,218.75

Step-by-step explanation:

The formula for computing simple interest I on a principal amount P for t years at an interest rate of R% is given by

I = Prt

The ending balance amount is found by adding the principal to the interest computed

Ending balance = P + I

Here r is the interest rate in % converted to a decimal. This is done by dividing by 100

r = R/100 = 2.75%/100 = 0.0275 per year

I = 2500 x 0.0275 x 25 = 1718.75

So interest I = $1718.75

Ending balance = $2,500 + $1718.75 = $4,218.75

The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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Answer:

here

Step-by-step explanation:

Answer:

Step-by-step explanation:

The quadratic function graphed is defined as follows:

y = x² - 10x + 9.

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

From the graph, the roots are given as follows:

x = 1 and x = 9.

Hence the function as a product of it's linear factors is defined as follows:

y = a(x - 1)(x - 9)

y = a(x² - 10x + 9).

When x = 5, y = -16, hence the leading coefficient a is obtained as follows:

-16 = a(5² - 10(5) + 9)

-16a = -16

a = 1.

Thus the function is:

y = x² - 10x + 9.

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Answer:

Hey bro you're welcome.

Step-by-step explanation:

Answer:

the diameter is 24 so the ray is 12

circonference = 2*pi*R = 2*3.14*12= 75.36

Answer:

Option B

Step-by-step explanation:

Don't trust answers teachers don't bother to spell correctly. Plus, finding the 100th term is very easy.

However, the explicit formula will take a long time to use, because it's explicit.

Option C is just wrong. You're supposed to multiply in the recursive formula.

Option D might be correct, but never trust those answers. Teachers do that to trip you up

The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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Answer:

The objectives of the AU are the following: To achieve greater unity, cohesion and solidarity between the African countries and African nations. To defend the sovereignty, territorial integrity and independence of its Member States. To accelerate the political and social-economic integration of the continent.

Step-by-step explanation:

Answer:

because they help people "achieve greater unity"

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:

 The exact answer is 30%

Step-by-step explanation:

Answer:

ī=80; s = 10

Step-by-step explanation:

When the standard deviation is from a finite group it is denoted by s. The number of transactions from an atm are countable in a day. So the standard deviation will be represented by s.

and ī represents the mean.

The other choices are incorrect because mean is usually represented by a bar over the alphabet such as x.

a simple alphabet does not denote the mean of the sample or population.

Parameters are the characteristics used to define a dataset.

The representation of the parameters are: \(\bar x = 80\) and  \(s = 10\)

From the question, we have:

\(Mean = 80\)

\(Standard\ Deviation = 10\)

Mean is represented as: \(\bar x\)

So, we have:

\(\bar x = 80\)

Standard deviation is represented as \(\sigma\) of s.

So, we have:

\(s = 10\)

Hence, the representation of the parameters are:

\(\bar x = 80\) and  \(s = 10\)

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The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

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

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

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Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

Sam drove approximately 246 miles.

Let's start by subtracting the base fee from the total amount Sam paid to find the additional fee he incurred for the miles driven:

213.33 - 18.99 = 194.34

We know that the additional fee is 79 cents per mile, so we can set up an equation to find the number of miles Sam drove:

194.34 = 0.79x

where x is the number of miles driven.

To solve for x, we can divide both sides of the equation by 0.79:

x = 194.34 / 0.79 ≈ 246

Therefore, Sam drove approximately 246 miles.

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Answer:

100x + 13000y = 865000

Step-by-step explanation:

x = Series A price

y = Series B price

Step-by-step explanation:

\( - 12u + 13 = 8w - 3 \\ - 12u + 13 + 3 = 8w \\ - 12u + 16 = 8w \\ w = \frac{ - 12u + 16}{8} \\ w = \frac{ - 3}{2} u + 2\)

I hope that is useful for you :)

Answer:

The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.

Step-by-step explanation:

The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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Answer: Axioms and Postulates

Step-by-step explanation:

Even if we draw more points on a line, It is an accepted statement of a fact that cannot be disproved - which which these are called Axioms or Postulates; and they are interchangeable.

I hope my explanation helped. Your welcome.

Answer:

210 miles

Step-by-step explanation:

because i said so

Loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

When energy moves through a medium (such as air, water, or any other liquid or solid matter), it creates a pattern of disturbance known as a sound wave that propagates away from the sound source.

When an object vibrates, sound waves are produced that are similar to pressure waves, like when a phone rings.

Pitch, intensity, and timbre are three key components of the field of sound psychology or psychoacoustics. People can distinguish the harmonics of a complex periodic sound wave under certain conditions thanks to the way that humans perceive sound and music.

Thus, loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

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Answer:

x° = 68°

Step-by-step explanation:

angle EGB = x° = angle AGF = complementary angle of 22°

The complementary angle of 22° is :

\(x^{o} =(90-22)^{o} =68^{o}\)

Hope this helps