b) The average of 9 numbers is 23. If the average of first five numbers is 20 and
that of last five numbers is 25, what is the fifth number?

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c) The average age of a husband and wife was 23 years at the time of their
marriage. After 10 years, they have now a daughter of 6 years, what is he
average age of the family at present?
​

Answer:

Step-by-step explanation:

10

Answer:

Step-by-step explanation:

[tex] {4}^{2} + (10 \times 2) \\ 16 + (10 \times 2) \\ 16 + 20 \: \: \: \: \: \: \: \: \: \: \: \\ 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]4^2+(10\times2)[/tex]

[tex]4^2+20[/tex]

[tex]16+20[/tex]

[tex]=\boxed{36}[/tex]

Answer:

x=0

Step-by-step explanation:

xx(x^2+121)=0

x=0

x^2+121=0

x=0

Answer:

scenario: GCF =15

15(30x+45 15+15)

15(2x+3) answers

The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

We have,

If a car averages 38 km/gal when driven at 95 km/h, we can calculate the fuel consumption in gallons per kilometer (gal/km).

Fuel consumption (gal/km) = 1 / (average fuel efficiency in km/gal)

Fuel consumption (gal/km) = 1 / 38

Now, to determine the energy requirement in kcal per kilometer (kcal/km), we multiply the fuel consumption by the energy released per gallon of gasoline:

Energy requirement (kcal/km) = Fuel consumption (gal/km) * Energy released per gallon (kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Now,

Fuel consumption (gal/km) = 1 / 38

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

≈ 789.47 kcal/km

Therefore,

The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

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The complete question:

"Burning gasoline in a car releases approximately 3 x 10^4 kcal/gal. If a car averages 38 km/gal when driven at 95 km/h, what is the energy requirement in kcal per kilometer (kcal/km) for the car?"

Step-by-step explanation:

So here we need to make two equations, as follows:

[tex]r + a = 37 \\ a = 2r - 5[/tex]

R being Robert and A being Aiden

Since we have A alone in the second equation, we can plug that into the first equation

R + (2R - 5) = 37

Let's add 5 to each side

R + 2R = 42

3R = 42

And lastly we will divide by 3 to get R alone

R = 14

Now that we know Robert scored 14 points, we can plug that into the first equation.

R + A = 37

14 + A = 37

Subtracting 14 from both sides

A = 23

The coordinates of C’ if the trapezoid is reflected across the y-axis is

(- 5, 3).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

A reflection through the axis and is given by the following transformation rule:

(x, y) -------> (-x, y)

We have the following point:

C = (5, 3)

Now, Applying the transformation rule we have:

(5, 3) -------> (-5, 3)

So, C' is given by:

C '= (- 5, 3)

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Step-by-step explanation:

The covariance of two variables X and Y is a measure of the relationship between their changes. It is calculated as:

cov(X, Y) = (1/n) * sum((x_i - mean(X)) * (y_i - mean(Y)))

where n is the number of observations, x_i and y_i are the values of X and Y respectively for the i-th observation, mean(X) and mean(Y) are the means of X and Y respectively.

In Python, you can use the numpy library to calculate the covariance as follows:

import numpy as np

X = [x_1, x_2, ..., x_n]

Y = [y_1, y_2, ..., y_n]

cov = np.cov(X, Y)[0][1]

A measurement of the intensity and direction of the linear relationship between two random variables, X and Y, is called covariance. A definition of covariance is:

Cov(X, Y) is equal to E[(X - E(X))(Y - E(Y))].

where E[...] is the anticipated value operator and E(X) and E(Y) is the expected values of X and Y, respectively.

If Cov(X, Y) is positive, X and Y have the propensity to rise or fall together. Cov(X, Y) is a measure of the tendency for two variables to move in opposite directions. When Cov(X, Y) equals 0, X and Y are said to be uncorrelated.

You must be aware of the expected values as well as the joint probability distribution of X and Y in order to compute the covariance of X and Y.

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Answer:

The symbol W denotes the whole number. The symbol Z denotes integers. The symbol N denotes all natural numbers or all positive integers. The symbol R denotes real numbers or any numbers that are not imaginary

i think you mean this , i hope is help

Answer: 3:2

Step-by-step explanation:

AB / BC = AB:BC

therefore,  6:4  

6:4 simplified -> 3:2

12.5ml of a 60% solution is required to create 50ml of a 15% amount solution. You can compute this using a proportion.

50% x 15% = 7.5 ml, and 7.5 ml x 60% = 12.5 ml

12.5ml of a 60% solution is required to create 50ml of a 15% solution. You can compute this using a proportion. To begin with, we must ascertain how much of the 15% solution is required to make 50ml. To accomplish this, multiply 50 ml by 15%, which yields the answer of 7.5 ml. This means that to make 50ml, 7.5ml of the 15% solution is required. The next step is to calculate how much of the 60% solution is needed to create 7.5ml. To do this, divide 7.5 ml by 60%, which yields the result 12.5 ml. This indicates that in order to create 50ml of the 60% solution, 12.5ml of the 60% solution

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Answer:

Area of the composite figure is 516

Step-by-step explanation:

picture above

If ln(x) = 3.23 , the value of x is 25.28.

Therefore the answer is 25.28.

If ln(x) = 3.23, then x can be found by using the exponential function.

The natural logarithm function, represented by ln(x), gives the power to which e (approximately equal to 2.71828) must be raised to equal x. So, if ln(x) = 3.23, it means that e^3.23 = x.

The exponential function is the inverse of the natural logarithm, so if ln(x) = 3.23, then

x = e^(ln(x))

= e^(3.23).

Using a calculator, we can find that e^(3.23) ≈ 25.28.

So, the value of x is approximately 25.28.

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Answer:

50/11

Step-by-step explanation:

because 50/11=4.54

               [tex]\sqrt[3]{100} =4.64[/tex]

              so 4.54<4.64

Answer:

hyy can you my friend,,,,

120  multiplied by 56% equals 67.2 students.

The number 67 becomes the result of rounding to the nearest whole number, which is 67.2.

A collection of positive integers and zero, whole numbers are numbers without fractions. The set of integers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,... and it is denoted by the sign "W". Whole Numbers: W = 0 through 10 (inclusive).

Absolute numbers those figures that contain zero and natural integers. neither a fraction nor a decimal. {0, 2, 3, 4, 5 6, 7, 8, 9,10, 11 …} Integer. A counting number, zero, or the negative.

The number of students who failed can be calculated by multiplying the total number of students by the percentage that failed:

120 students * 56% = 67.2 students

Rounding to the nearest whole number, 67.2 students becomes 67 students.

So, 67 students failed in the 6th grade.

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Answer:

They are supplementary angles

Answer:

Step-by-step explanation:

I dont understand the question?

Answer:

8 multiplied by 5 equals 40.

8 is a factor of 40.

40 can be divided by 8 with no remainder.

Step-by-step explanation:

The percentage decrease from first to third year is; 47.725%

To find the percentage decrease, work out the difference (decrease) between the two numbers you are comparing. Thereafter, divide the decrease by the original number and then multiply the answer by 100.

Amount of car in 2010 = £18500

It depreciated by 15% in the first year. Thus;

Amount after first year = (100% - 15%) * 18500

= £15725

It depreciated by 18% in the second year. Thus;

Amount after second year = (100% - 18%) * 15725

= £12,894.5

It depreciated by 25% in the third year. Thus;

Amount after third year = (100% - 25%) * 12,894.5

= £9,670.875

Thus;

Decrease from first to third year = (18500 - 9670.875)/18500 * 100%

= 47.725%

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Answer:

≈84,13%

Step-by-step explanation:

To find the probability of a student liking between 5.5 and 8.5 songs from Eminem, we need to find the standard normal deviate (z-score) for each of these values and then use a standard normal table to find the area between these z-scores.

For 5.5 songs:

z = (5.5 - 7.0) / 1.5 = -1.0

For 8.5 songs:

z = (8.5 - 7.0) / 1.5 = 1.0

The area between -1.0 and 1.0 on a standard normal distribution table is approximately 0.8413. This means that the probability of an individual student liking between 5.5 and 8.5 songs from Eminem is approximately 84.13%.

The actual height of the rocket is 576 inches.

Cross multiply is to multiply the numerator of each side of a proportion by the denominator of the other side.

A ratio box is a visual tool that can be used to solve proportion problems. To use a ratio box to solve this problem, we can set up the following ratio:

1/12 : 48 inches : : x : actual height

where x is the unknown value that we want to find.

To solve for x, we can cross-multiply and simplify the equation:

1/12 * actual height = 48 inches

actual height = 48 inches * 12/1

actual height = 576 inches

So the actual height of the rocket is 576 inches.

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Overhead Rate * Labor Hours , additional overhead should she expect to incur.

What is additional overhead ?

Overhead refers to the ongoing costs to operate a business but excludes the direct costs associated with creating a product or service. Overhead costs can be fixed, variable, or a hybrid of both.

To determine the additional overhead that Angie should expect to incur if she books one more catering job requiring 350 labor hours, The overhead rate is the amount of overhead costs per labor hour.

If we have the overhead rate, we can calculate the additional overhead as follows:

Additional Overhead = Overhead Rate * Labor Hours

Overhead Rate * Labor Hours , additional overhead should she expect to incur.

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Alicia will have £2,238.93 in her account after 10 years if she invests £2130 in a 0.5% account.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

principal=£2,130.00

rate=0.5%
time=10 years

Compound interest earned=£108.93

Total amount=£2,238.93

Alicia will have £2,238.93 in the account after 10 years when she invests £2130 into an account that pays 0.5%.

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Complete question:

Alicia invests £2815 into an account that pays 1% compound interest per year. Work out how much Alicia will have in the account after 10 years.

The minimum value of 3^{x²-4x+8} is 81. The solution has been obtained by using maxima-minima.

What is maxima-minima?

The extrema of a function are known as its maximum and minimum. The maximum and smallest values of a function within the predetermined set of ranges are known as maxima and minima. The function's maximum value and minimum value are referred to as the absolute maxima and absolute minima, respectively, for the function across the whole range.

We are given f(x) = 3^{x²-4x+8}

The function is minimum when {x²-4x+8} is minimum.

When the form of the equation is ax^2 + bx + c, then minimum is at -b/2a

Here, a = 1 and b = -4

So,

x = 4/2 = 2

So, {x²-4x+8} at x = 2 is

⇒(2)^2 - 4(2) + 8

⇒4 - 8 + 8

⇒4

So, the minimum value of f(x) is

3^4 = 81

Hence, the minimum value of 3^{x²-4x+8} is 81.

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The first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.

For the stated question:

f(n) :

f(1) = 6

f(n) = f(n - 1) + 7, if n > 1.

Thus,

First term, n = 1: f(1) = 6

Second term, n = 2:  

f(2) = f(2 - 1) + 7

f(2) = f(1) + 7

f(2) = 6 + 7

f(2) = 13

Third term: n = 3.

f(3) = f(3 - 1) + 7

f(3) = f(2) + 7

f(3) = 13 + 7

f(3) = 20

Fourth term: n = 4.

f(4) = f(4 - 1) + 7

f(4) = f(3) + 7

f(4) = 20 + 7

f(4) = 27

Thus, the first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.

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The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

Given that:

∫3−5f(x)dx=6

∫3−5g(x)dx=3

We need to find: ∫3−5[2f(x) 6g(x)]dx

To solve this problem, we will use the properties of integration:

Property 1:

If c is a constant, then

∫cf(x)dx=c∫f(x)dx

Property 2:

If f(x) and g(x) are two functions, then

∫[f(x) + g(x)]dx = ∫f(x)dx + ∫g(x)dx

Using Property 1, we can rewrite the given equation as:

∫3−5[2f(x) 6g(x)]dx = ∫3−5[12f(x)g(x)]dx

Using Property 2, we can further simplify the equation as:

∫3−5[12f(x)g(x)]dx = ∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx

Now we can substitute the given values:

∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx = 12∫3−5f(x)dx + 12∫3−5g(x)dx

Substituting the given values for the integrals of f(x) and g(x), we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3)

Simplifying, we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3) = 12(9) = 108

Therefore, the answer is

∫3−5[2f(x) 6g(x)]dx = 108

The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

the complete question is :

if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx will be equal to  ?

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Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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The coordinates of the midpoint of line CD is (17, 21).

A midpoint is a point that is equidistant from the endpoints of a line segment. It is the point that is exactly halfway between the two endpoints of the line segment.

The midpoint of a line segment is found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the line segment. The coordinates of the midpoint can be determined using the formula below.

midpoint (x, y) = (x₁ + x₂/2, y₁ + y₂/2)

If point C has coordinates (24, 16) and point D has coordinates (10, 26), then the midpoint is:

midpoint (x, y) = (24 + 10/2, 16 + 26/2)

midpoint (x, y) = (34/2, 42/2)

midpoint (x, y) = (17, 21)

Therefore, the midpoint of line CD has the coordinates (17, 21).

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The equation of the line in point-slope form and in​ slope-intercept form are both y = 1/2x.

1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.

3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.

If a line has a slope of 1/2 and passing through the origin, then:

m = 1/2

(x1, y1) = (0,0)

Plug in the values in the point-slope form and in​ slope-intercept form.

point-slope form

y - y1 = m(x - x1)

y - 0 = 1/2(x - 0)

y = 1/2x

slope-intercept form

y = mx + b

y = 1/2x + b

Substitute the values of x and y and solve for the y-intercept, b.

0 = 1/2(0) + b

b = 0

y = 1/2x + 0

y = 1/2x

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