The ratio of apples to pears at a farm stand is 5:3. What is the percentage of the fruit to apples?

Answer:

(a) Bako is 10 years old

(b) His mother was 30 years old when Bako was 5

(c) Bako will be 25 years old when his mother is 50

(d) Bako's mother was 25 years old when he was born

(e) The difference between Bako's age & his mother's is 25 years

Step-by-step explanation:

Let Bako's age five years ago be x years

Presently, Bako is 2x years old (according to the 1st statement)

Normal, Bako's present age should have been (x + 5) years; since he was x years old 5 years ago.

This simply means that Bako's present age is BOTH 2x years & (x + 5) years.

We have to equate them since they mean the same thing (Bako's present age)

x + 5 = 2x

2x - x = 5

Therefore x = 5 years

Remember that x signified Bako's age five years ago... This simply means that Bako's age five years ago was 5 years.

This simply means that Bako's age now is 10 years old.

His mother was then six times 5 years = 30 years old (from the 2nd statement).

If Bako was 5 years old five years ago and his mother was 30 years old... It simply means that Bako was born ten years ago when his mother was 25 years old.

This simply means that Bako's mother is older than him with 25 years.

Therefore, Bako will be 25 years old when his mother is 50 years old

Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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ANSWER

Yes, because it has a constant rate of change.

EXPLANATION

We want to check if the function represented in the table is a linear function.

A linear function is one in which there are two variables that are related in such a way that a change (increase or decrease) in one variable (independent variable) leads to a proportional change (increase or decrease) in the second variable (dependent variable).

If we look at the two variables given in the table, we see that as the x variable increases, there is a proportional increase in the y variable.

So we can say that there is a constant rate of change.

So, we can conclude that it is a Linear Function.

Answer:

60

\(2^{2} * 3 * 5\)

Step-by-step explanation:

Given the triangle:

To find the length of the missing side, considering that you know the measure of the opposite angle to the side and the length of the other two sides, you can apply the cosine law, which is:

Consider

a= 245yd

b=270yd

c= x yd

∠C=70º

Replace the values in the formula:

The length of the lake is 296yards

The various answers to the question are:

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)

Generally, the equation for is  mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

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Answer:

DB,AB,AD,CD,AC

Answer:

Surface Area is equal to 160 cm²

here is your answer

Answer:

5/7

Step-by-step explanation:

You are multiplying 56 by some number to get to 40

56x = 40

x = 40/56

x = 20/28

x = 10/14

x = 5/7

The scale factor is 5/7

-Chetan K

The diagram in the Unit 1 Lesson 11, the description of the rotation of the image ∆P'O'G' is as follows;

1. C. Rotate 60° counterclockwise around O

The diagram of the triangle ∆POG consists of a triangle placed in a grid consisting of equilateral triangles.

The location of point O in both the pre-image and the image are (approximately) the same.

Therefore;

The point about which ∆POG is rotated is the point O.

The side OG in the pre-image is vertical, while O'G' in the image 1 is rotated to the right, through to the next adjacent leg of one of the triangles in the grid with vertex at O.

Given that the triangles in the grid are equilateral triangles, that have an 60° interior angles, we have;

The rotation transformation is a 60° counterclockwise rotation about the point O.

The correct option is therefore;

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Answer: d.12

Step-by-step explanation:

Answer:

30.6

Step-by-step explanation:

if the decimal previous is 5 or above, round it up

if the decimal previous is 4 or below, leave it as it is

Answer:

31

Step-by-step explanation:

Because since .9 is a big number it would round up 5 into a 6 so the 6 would round up 30 into 31

1/6 odds of rolling a 6

1/2 odds of flipping tails

1/6 x 1/2 = 1/12

The probability that she gets a 4 and a tail is 1/12.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

Helen rolls a die and flips a coin.

The probability of getting 4 on the die,

= 1/6

The probability of getting tail on the coin,

= 1/2

The probability that she gets a 4 and a tail,

= 1/2 x 1/6

= 1/12

Therefore, the probability is 1/12.

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The coordinates of the new point  is (-6, -2)

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

Point = (6, 2)

Rule: 180 degrees rotation

The rule of 180 degrees rotation is

(x, y) = (-x -y)

Substitute the known values in the above equation, so, we have the following representation

image = (-6, -2)

Hence, the image is (-6, -2)

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Answer: HIs income was  $6744.04

Step-by-step explanation: 8798.04 + 3650 - 5700 = 6744.04 Hope this helps!

The taxable income last year is $552.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It from simdiffers ple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

We have,

Last year, a part-time housekeeper earned $8798.

He claimed he was exempt, costing $365.

$570.00 is the standard deduction.

Gross income less the standard deduction and all exemptions equals taxable income.

= 8798 - 3650 - 5700

= $-552

The negative sign indicates that he owes no taxes.

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Answer:

117 - 86 = 31°

The answe is 31

Answer:

2p-30

Step-by-step explanation:

10p-40-8p+10

=2p-30

Answer:

Answer is last option, -3.

Step-by-step explanation:

We know it's going to be a negative slope because the line is going down to the right, so it can't be eighther option 1 or 3.

Next it appears the line is going 3 units down and 1 unit to the right. So it will be written as -3/1 because of rise/run.

Hope this helps/makes sense :)

Answer:

D

Step-by-step explanation:

We can visually see the line going down so the slope is negative. (-30)

The y-intercept must be 120, because it does not intersect 90.

As the population of a state grows, it generally leads to an increase in the number of seats it holds in the House of Representatives.

The relationship between the population of a state and the number of seats in the House of Representatives can be described as a positive relationship.

As the population of a state increases, the number of seats allocated to that state in the House of Representatives also increases.

This is due to the principle of apportionment, which aims to distribute the seats in a manner that is proportional to the population of each state.

The Constitution of the United States mandates that each state is entitled to at least one seat in the House of Representatives.

The remaining seats are then allocated based on population size.

This is achieved through various apportionment methods, with the current method being the method of equal proportions.

Under the method of equal proportions, the population of each state is divided by a divisor to determine its initial seat allocation.

As the population of a state increases, its divisor decreases, resulting in a higher number of allocated seats.

Conversely, if the population decreases, the state may lose seats in the House of Representatives.

This positive relationship ensures a representation that is proportional to the population of each state.

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Answer:

G(1)=0

Step-by-step explanation:

G(1)=6(1)-6

=6-6

=0

Answer:

=3x+{4}{x}+10

Step-by-step explanation:

The sum of the rational expression is =3x+{4}{x}+10

Answer:

83/85

Step-by-step explanation:

85 is being multiplied by something to get to 83

85x = 83

x = 83/85

You cannot simplify this any further because it has no common factors.

-Chetan K

Answer: w(10) = -12

Step-by-step explanation:

w(n) = -n - 2; Find w(10)

w(10) = -(10) - 2

w(10) = -10 - 2

w(10) = -12

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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The second difference of the given number table is: Option A: -2

The second difference method can be used to determine a quadratic model.  In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.

Thus, Applying the second difference concept to our problem, we have:

First difference:

-4 - (-9) = 5

-1 - (-4) = 3

Thus, second difference is:

3 - 5 = -2

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