A father is three times as old as his son, and his daughter is 3 years younger than the son,if the sum of their ages three years ago is 63 years. find the present age of the father

Answer:

If you are asking for the X then the answer would be 7.

Answer:

X/4

Step-by-step explanation:

The number of students (X) would have to be divided by 4 (the number of groups), meaning the number of students in each group must be:

the total number of students (X)÷ the number of groups (4)

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Work Shown:

Let x be the location of E on the number line.

Since C is the midpoint of E and F, this means we can find C's location by adding E and F together and dividing that sum by 2

midpoint = (endpoint1 + endpoint2)/2

C = (E+F)/2

Plug in E = x, C = -8 and F = 4. Then solve for x

C = (E+F)/2

-8 = (x+4)/2

(x+4)/2 = -8

x+4 = 2(-8) .... multiplying both sides by 2

x+4 = -16

x = -16-4 .... subtract 4 from both sides

x = -20

The location of point E on the number line is -20

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

As a check, lets add E and F to get E+F = -20+4 = -16

Then cut this in half to get -16/2 = -8, which is the proper location of point C

This confirms our answer.

a function is a rule that assigns each value of the variable to exactly one value of the dependent variable

So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.

A mathematical method called the unitary method is used to address proportionality-related issues. It is a technique that entails determining the value of a single unit prior to applying that value to determine the value of any quantity of units. Problems involving ratios et proportions are frequently solved using the unitary technique. The unitary approach can be used to determine the price of any quantity of apples, for instance, if 5 vegetables cost $2. We can build up a proportion to determine how much 10 apples would cost: 5 apples x $2 Equals 10 apples x. where 10 apples cost x dollars.

given

We can start by applying the conversion rule that states that 6 teaspoons (tsp) of liquid equal 1 fluid ounce (FL oz). The following is how we can convert 11 FL oz to teaspoons:

6 teaspoons per FL oz times 11 FL oz equals 66 teaspoons.

Thus, an 11 FL oz can of orange juice has 66 teaspoons of orange juice.

We can also figure out how many cans of orange juice are required for the recipe as it calls for 3 tablespoons of orange juice.

\(0.5 FL oz = 3 tsp * 6 tsp/FL oz\)

So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.

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Step-by-step explanation:

1.25x=1.25x

1.25x *100=1.25x *100

125x=125x

125x-125x=125x-125x

0=0

Answer:

12.74

Step-by-step explanation:

To find the diameter of a circle with a given circumference, you can use the formula:

Circumference = π x diameter

where π (pi) is a mathematical constant approximately equal to 3.14159.

In this case, the circumference is given as 40. So we can rearrange the formula to solve for the diameter:

diameter = Circumference / π

Substituting the given values, we get:

diameter = 40 / π

To get the answer to the nearest hundredth, we can use a calculator or estimate π to a few decimal places. Let's use π ≈ 3.14.

diameter = 40 / 3.14

diameter ≈ 12.74

Therefore, the diameter of the circle to the nearest hundredth is approximately 12.74.

Step-by-step explanation:

Circumference = pi  * d

circumference / pi = d  =  40 / pi = 12.73 units

Answer:

He will read 92 pages in an hour going by the current rate at which he reads

Step-by-step explanation:

The complete question is as follows;

Jamil found that he reads 1/5 of his 115 - page book in 1/4 of an hour. At this rate how many pages does he read in an hour

We proceed as follows;

If he reads 1/5 of 115 in 1/4 hour

1/5 of 115 pages refer to 1/5 * 115 = 23 pages

This means that he reads 23 pages in quarter of an hour

So in an hours the number of pages he will read will be 23 * 4 = 92 pages

A five-number summary is a useful tool for summarizing a data set. It provides a quick and easy way to see the range of the data, the middle 50% of the data, and the median.

We have to find the five-number summary and draw a box-and-whisker plot of the given data. To find the five-number summary, we need to find the minimum, maximum, median, and first and third quartiles of the data. After that, we can create a box-and-whisker plot using these values.

The given data is not provided. Without the data, we cannot find the five-number summary and draw a box-and-whisker plot. However, we can discuss the steps involved in finding the five-number summary and drawing a box-and-whisker plot.

Let's consider a set of data:

12, 23, 34, 35, 46, 57, 58, 69, 70, 81, 92

To find the five-number summary of the above data, we follow the steps below:

Step 1: Arrange the data in ascending order

12, 23, 34, 35, 46, 57, 58, 69, 70, 81, 92

Step 2: Find the minimum and maximum values

Minimum value (min) = 12

Maximum value (max) = 92

Step 3: Find the median

The median is the middle value in the data. It is the value that separates the lower 50% of the data from the upper 50%. To find the median, we use the following formula:

Median = (n + 1)/2 where n is the number of observations in the data set.

Median = (11 + 1)/2

= 6

The 6th value in the data set is 57, which is the median.

Step 4: Find the first and third quartiles

The first quartile (Q1) is the value that separates the lower 25% of the data from the upper 75%.

To find Q1, we use the following formula:

Q1 = (n + 1)/4

Q1 = (11 + 1)/4

= 3

The 3rd value in the data set is 34, which is Q1.

The third quartile (Q3) is the value that separates the lower 75% of the data from the upper 25%.

To find Q3, we use the following formula:

Q3 = 3(n + 1)/4

Q3 = 3(11 + 1)/4

= 9

The 9th value in the data set is 70, which is Q3.

Now, we can use these values to draw a box-and-whisker plot. The box-and-whisker plot is a graphical representation of the five-number summary of the data. It consists of a box and two whiskers. The box represents the interquartile range (IQR), which is the range between Q1 and Q3. The whiskers represent the range of the data excluding outliers. The median is represented by a line inside the box.

In conclusion, the five-number summary is a useful tool for summarizing a data set. It provides a quick and easy way to see the range of the data, the middle 50% of the data, and the median. The box-and-whisker plot is a visual representation of the five-number summary. It is a useful tool for comparing data sets and identifying outliers.

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Answer:

Inequality Form:b≥6

Interval Notation:[6,∞)

Answer:

b≥6

Step-by-step explanation:

Subtract 4 from both sides

b + 4 - 4 ≥ 10 - 4

The minimum surface area of a rectangular prism with a volume of 300 units must lie somewhere between 0 and ∞.

Let's say that the rectangular prism has a length of "l" units, width of "w" units, and height of "h" units. The volume of the rectangular prism is given by the formula V = l × w × h, and we know that V = 300 units.

To find the smallest surface area possible, we need to minimize the sum of the areas of all six faces. The surface area (SA) of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh.

Using the formula for volume, we can solve for one of the variables in terms of the other two. For example, we can solve for "h" as follows:

V = l × w × h

300 = l × w × h

h = 300 / (l × w)

Substituting this expression for "h" into the formula for surface area, we get:

SA = 2lw + 2l(300 / lw) + 2w(300 / lw)

SA = 2lw + 600 / w + 600 / l

Now we need to find the minimum value of SA. To do this, we can take the derivative of SA with respect to either "l" or "w", set it equal to zero, and solve for the corresponding variable. Since the derivative is the same regardless of which variable we choose, we can take the derivative with respect to "l":

dSA/dl = 2w - 600 / l² = 0

l² = 300 / w

Substituting this expression for "l²" back into the formula for surface area, we get:

SA = 2lw + 600 / w + 600w / 300 / w

SA = 2lw + 600 / w + 2w²

Now we can take the derivative of SA with respect to "w" and set it equal to zero:

dSA/dw = 2l - 600 / w² + 4w = 0

w³ - 150lw + 150 = 0

Taking the limit as "w" approaches infinity, we get:

lim SA as w → ∞ = 2lw + 600 / ∞ + 2∞²

lim SA as w → ∞ = 2lw + 0 + ∞

This limit is also undefined, which means that there is no rectangular prism with a volume of 300 units and infinite surface area.

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Answer:

Im kind of confused if I rewrite or find the y and x intercept to this equation but I hope this helps.

if you can please give me brainliest.

Answer:

Option 4

Step-by-step explanation:

The yearly rate of change in the amount of money in the account is 1.04.

Given that:

M(t) = 4900. (1.5)

To find: Monthly rate of change in the amount of money in account.

Every year, the amount of money in the account increases by a factor.

M(t) = 4900 (1.5),          where t is in decades.

When t is 0 M(t) is 4900.

when t is 1, then M(t) is 4900 times, that is, 1.5

When t is 2, then M(t) is 4900 times 4.09 squared, then,

4900 × (1.5)²

For, One year is 0.1 decades, so M increases by a factor of:

M(t) = 4900- (1.5)°¹

      = 1.04

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Answer: 100 miles

Step-by-step explanation:

plug in 2 for h and multiply

50 by 2=100

Answer:

this looks hard i just need pints so that i can ask my question

Step-by-step explanation:

Answer:

k=-2

Step-by-step explanation:

2(6k+8)-6k=4

12k+16-6k=4

6k+16=4

6k=-12

k=-2

Answer:

14.49 inches......I think this help you.....I am not dam sure this is right or not....

Answer:

50% of blue

33.3333...% for not choosing red

The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t

Give, a lump sum of $2000 is invested at 4.2% compounded continuously.

Hence we have:

P = $2000

rate of interest = 4.2%

years = t

we know that A = Pe^rt

Substitute the above values in the formula.

Amount = f(t)

f(t) = 2000.e⁰·°⁴²t

hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t

Therefore we get the required function.

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The cost of the fence used to make the rectangular sheep pen is £57.6. The result is obtained by multiplying the perimeter by the fencing price.

The cost for fencing a building can be calculated by multiplying the price of a certain size of fence by the perimeter or the length side to be fenced.

Bill builds a rectangular sheep pen.

Find the total cost of the fence!

The total cost of the fence will be

= P × fencing cost

= 24 m × £1.20 / ½ m

= 24 × £2.40

= £57.6

Hence, the fence to make the sheep pen will cost £57.6.

Your question is incomplete. But most probably your full question was

Bill needs to build a rectangular sheep pen. The pen must have a perimeter of 24 m. Every half meter of fencing costs him £1.20. Work out the cost of the fence used to make the sheep pen!

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Answer:

i think it is 90

Step-by-step explanation:

The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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The reasoning provided, "If you build it, they will come. You build it. Therefore, they will come," is an example of deductive reasoning.

Deductive reasoning is a logical process that involves drawing specific conclusions based on general principles, premises, or known facts. In this example, the premise is "If you build it, they will come," which establishes a cause-and-effect relationship. The subsequent statement, "You build it," serves as a confirmation of the premise. From these premises, the conclusion is drawn: "Therefore, they will come." The conclusion logically follows from the premises, making it an example of deductive reasoning.

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The p-value of the test claim is calculated as; p < 0.00001.

The z-score between two samples is expressed as;

z =  (x₁ – x₂)/√(σ₁²/n₁) + (σ₂²/n₂)

The parameters given are;

Sample mean 1: x₁ = 23.38

Sample mean 2: x₂ = 18.69

Sample standard deviation 1: σ₁ = ?

Sample standard deviation 2: σ₂ = ?

Sample size 1: n₁ = 40

Sample size 2: n₂ = 35

standard error = sample standard deviation /√(sample size)

σ₁ = 23.38/√40

σ₁ = 3.697

σ₂ = 18.69/√35

σ₂ =  3.159

Thus;

z = (23.38 – 18.69)/√(3.697²/40) + (3.159²/35)

z = (23.38 – 18.69)/0.792

z = 5.92

From online p-value from z-score calculator, p < 0.00001.

Thus, the p-value is less than the significance value and the results are significant and alternate hypothesis is accepted.

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Answer:

twice

Step-by-step explanation:

y = - 1 is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of - 1

Drawing this line on the graph, from (0, - 1 ) we can see that it will intersect the graph at 2 places between (0, 0 ) and (2, - 2 ) and between (2, - 2 ) and (4, 0 )

The simplest form of the expression as we have it is; (-4x^4z^2)(2xy^3z^2)

When we are asked to simplify, what we are asked to do is to write the expression that we have in a form that is simplest. That is, we should put the expression in a form that there would not be any simpler presentation of the expression.

We have;

(-2x^2z)^2(2xy^3z^2)

Then we now have to deal with the exponent outside the bracket;

(-4x^4z^2)(2xy^3z^2)

Thus, we now have the expression in the simplest form that it can take and it can not be further broken down.

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Answer:

A

Step-by-step explanation:

because the point number are segment

To evaluate the integral ∫tan^4(x) cos^5(x) dx, we can use trigonometric identities to simplify the integrand.

We'll use the power-reducing formula for tan^4(x) and the power-reducing formula for cos^5(x) to simplify the integrand:

∫tan^4(x) * cos^5(x) dx

= ∫(tan^2(x))^2 * (cos^2(x))^2 * cos(x) * cos^2(x) dx

= ∫[(sec^2(x) - 1)^2] * [(1 - sin^2(x))^2] * cos(x) * cos^2(x) dx

Expanding the square terms, we get:

= ∫[(sec^4(x) - 2sec^2(x) + 1)] * [(1 - 2sin^2(x) + sin^4(x))] * cos(x) * cos^2(x) dx

Multiplying the terms together, we have:

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

Now, let's integrate each term separately:

∫sec^4(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 + u^2)^2 * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(1 + 2u^2 + u^4 - u^4 - u^6) du

= u + 2/3 u^3 + 1/5 u^5 - 1/7 u^7 + C

Substituting back u = sin(x), we have:

= sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x) + C

∫-2sec^2(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫-2(1 + u^2) * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(-2 + 2u^2 - 2u^2 + 2u^4) du

= -2u + 2/3 u^3 - 2/5 u^5 + 2/7 u^7 + C

Substituting back u = sin(x), we have:

= -2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x) + C

∫cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 - u^2) du

Integrating, we get:

= u - 1/3 u^3 + C

Substituting back u = sin(x), we have:

= sin(x) - 1/3 sin^3(x) + C

Putting it all together, the complete result of the integral is:

∫tan^4(x) * cos^5(x) dx

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

= ∫sec^4(x) *

cos^3(x) dx - 2∫sec^2(x) * cos^3(x) dx + ∫cos^3(x) dx

= (sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x)) - 2(-2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x)) + (sin(x) - 1/3 sin^3(x)) + C

= sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

Therefore, the final result is:

∫tan^4(x) * cos^5(x) dx = sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

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The sentence "It is below freezing or not raining" can be represented as "$p \vee \sim q$" using the provided logical connectives.

The given sentence "It is below freezing or not raining" can be expressed using logical connectives as **$p \vee \sim q$**.

In this representation, the symbol $\vee$ represents the logical OR operator, which signifies that either one or both of the statements can be true for the entire sentence to be true. The statement $p$ corresponds to "It is below freezing," and $\sim q$ represents "not raining" (the negation of the statement "It is raining").

By combining $p$ and $\sim q$ using the logical OR operator $\vee$, we create the sentence "$p \vee \sim q$" which translates to "It is below freezing or not raining."

The logical connective $\sim$ represents the negation or the logical NOT operator. In this case, $\sim q$ signifies the opposite of the statement $q$, that is, "not raining."

Therefore, the sentence "It is below freezing or not raining" can be represented as "$p \vee \sim q$" using the provided logical connectives.

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