The average age of family of six is 25 years.the average age of four children is 15 years.if the father is 2 years older than the mother,calculate the age of the mother?​

Answer:

50

Step-by-step explanation:

Perfect square: made by squaring a whole number (mulitplying a whole number by itself).

To find the nth perfect square, multiply n by itself, so n x n = n²

Therefore, the product of the first perfect square number & 7th perfect square:

1² + 7² = 1 x 1 + 7 x 7 = 1 + 49 = 50

Perfect squares are those numbers whose square roots are not irrational or rational rather than positive natural numbers.

So the formula is n^2

Sum=49+1=50

Answer:

llllllllllsgduehidhejeiwhu

Answer:

\(\boxed{-\frac{7}{12} }\)

Step-by-step explanation:

\(-1\frac{1}{3} +\frac{3}{4}\)

→ Make both denominators the same

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}\)

→ Convert mixed number into improper fraction

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}=-\frac{16}{12} +\frac{9}{12}\)

→ Do the -16 + 9 and leave 12 as the denominator

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}=-\frac{16}{12} +\frac{9}{12}=-\frac{7}{12}\)

The required simplification o f\(-1\frac{1}{3} +\frac{3}{4}\) into fraction form  is -1 / 12

To simplify -1 1 / 3 plus 3 / 4 into fraction form.

The process in mathematics to operate and interpret the function to make the function simple or more understandable called simplifying and the process is called simplification.

Fraction is defined as the number of compositions constituting the Whole. And it is represented as a / b, where a = numerator and b = denominator.

Since the given problem is
\(-1\frac{1}{3} +\frac{3}{4}\)

We need to simplified it into fraction form like a / b.

\(=-1\frac{1}{3}+\frac{3}{4} \\= -2/3 + 3/4\)
=  ( -8 + 9 ) / 12
= -1 / 12

Thus, The required simplification of  \(-1\frac{1}{3} +\frac{3}{4}\)  into fraction form is -1 / 12.

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Explanation:

C = circumference of a circle of radius r

C = 2*pi*r

40 = 2*3.14*r

40 = 6.28r

r = 40/6.28

r = 6.37

A = area of the circle of radius r

A = pi*r^2

A = 3.14*(6.37)^2

A = 127.41

A = 127

The area of the circular pizza is roughly 127 square inches.

The other pizza has an area of 10*10 = 100 square inches. The circular pizza is slightly larger in area, which means you should go for the circular pizza.

Neptune is 33 times farther from sun than the earth is to sun .

Given,

Distance between Earth and the sun(D) = \(9 * 10^7\) miles

Distance between Neptune and sun(d) = \(3* 10^9\) miles

Now,

Neptune is farther from sun than earth to sun is ,

Calculate d/D

So,

d/D =  \(3* 10^9/ 9 * 10^7\)

d/D = 33.33

d/D ≈ 33

Thus,

Neptune is approximately 33 times farther from the sun than earth .

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For the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given that, P equals atmospheric pressure (atm), V equals liters of volume (L), n equals the number of moles, R is the gas constant (0.0821 Latm/(molK)), and T equals Kelvins of temperature (K).

Take into account the following circumstances: a 3,500 mL tank containing 27 moles of argon gas was pressurized to 12 atm.

The ideal gas equation is,

PV=nRT

There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Thus, for the given case the variable we are solving for is temperature and the variable volume needs to be converted to L, liters.

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The formula connecting E and F is E = k/F3, where k is a constant. This formula states that the value of E is inversely proportional to the cube of F.

That is, as F increases, the value of E decreases. For example, if F increases from 3 to 4, then the value of E decreases by a factor of 8.

This inverse proportionality between E and F3 is due to the fact that, as F increases, the cube of F increases at a faster rate. In other words, when F doubles, the cube of F increases by a factor of 8. This causes the value of E to decrease by the same factor of 8.

The formula is useful in many applications, such as in physics and engineering. For example, in physics, the formula can be used to calculate the force of an object in a gravitational field. The force is inversely proportional to the cube of the distance between the object and the center of gravity, where the constant k is equal to the gravitational constant. In engineering, the formula can be used to calculate the power of a motor, where the power is inversely proportional to the cube of the speed of the motor.

Overall, the formula E = k/F3 expresses the inverse proportionality between E and F3, and is used in various applications to calculate the value of E given the value of F.

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Volume =  

1  πr2h

3

=  

1 ×π×42×7

3

=  117.28612573402 centimeters^3

The overall inequality is z ≥ -6 or z < 9. The solution set can be expressed in interval notation as:(-∞, 9)U[-6, ∞)

Given: −2(z−2)≤16 or 13+z<22

We can use the following steps to solve the above-mentioned inequality problem:

Simplify each inequality

−2(z−2)≤16 or 13+z<22−2z + 4 ≤ 16 or z < 9

Solve for z in each inequality−2z ≤ 12 or z < 9z ≥ -6 or z < 9

Using your answers from the previous steps,

solve the overall inequality problem and express your answer in interval notation

Use decimal form for numerical values.

The overall inequality is z ≥ -6 or z < 9.

The solution set can be expressed in interval notation as:(-∞, 9)U[-6, ∞)

Thus, the solution to the given inequality is z ≥ -6 or z < 9 and it can be represented in interval notation as (-∞, 9)U[-6, ∞).

Thus, we can conclude that the solution to the given inequality is z ≥ -6 or z < 9. It can be represented in interval notation as (-∞, 9)U[-6, ∞).

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Answer:

(5,3)

Step-by-step explanation:

If you graph the equation \(y=x-2\) and plot all the points given as options, you can see that (5,3) lies on the line, while all others don't. This means that option D (5,3) would get generated by the equation.

Another way to do this is to substitute 'x' and 'y' for the points given. If they satisfy the equation, then it would be correct.

\(7=5-2\\\boxed{7\neq3}\)

Option A is incorrect.

\(14=7-2\\\boxed{14\neq5}\)

Option B is incorrect.

\(9=7-2\\\boxed{9\neq5}\)

Option C is incorrect.

\(3=5-2\\\boxed{3=3}\)

Option D is correct.

Option D should the the correct answer.

Answer:

joe mama tee hee

Step-by-step explanation:

Answer:

Look DB

Step-by-step explanation:

Since m1+m2=180 and m1=76, then m2=104

m2=m4, so m4 is also 104

m3=m1, so it is 76

Hope I helped!

Answer: $48.

Step-by-step explanation:

Since each slice of pizza is $2 and Wyatt bought 14 slices of pizza, you would multiply 14 by 2 then add it onto the cost of the membership.

14 * 2 = 28

20 + 28 = 48

The monthly cost for 14 slices of pizza is $48.

Answer:

Step-by-step explanation:

54×54

The quadrilateral FGHI is a parallelogram

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

F = (0, -6), G = (7, -4), H = (8, 4), I = (1, 2)

The lengths can be calculated as

Lengths = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the above as a guide, we have the following:

FG = √[(0 - 7)² + (-6 + 4)²] = √53

GH = √[(8 - 7)² + (4 + 4)²] = √65

HI = √[(8 - 1)² + (4 - 2)²] = √53

IF = √[(1 - 0)² + (2 + 6)²] = √65

For the slopes, we have

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

FG = (-6 + 4)/(0 - 7) = 2/7

GH = (4 + 4)/(8 - 7) = 8

HI = (4 - 2)/(8 - 1) = 2/7

IF = (2 + 6)/(1 - 0) = 8

Based on the above computations, we have

Hence, the shape is a parallelogram

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Answer:

Multiply 17 by 100 / 12.5 to get the answer

Answer:

dwmkwddddncdnnknnsdlnldkldskcnds

Step-by-step explanation:

klkkl

Answer:

I know for a fact that it is Devide by nagative 5

Step-by-step explanation:

The farming conglomerate will use approximately 36,912.51 megaliters of water 5 years from now.

To calculate the amount of water the farming conglomerate will use 5 years from now, we can use the given information that its water usage increases at a rate of 7% every year.

Let's denote the current water usage as W₀ and the water usage after 5 years as W₅.

We know that W₅ = W₀ * (1 + r)^n, where r is the growth rate (in decimal form) and n is the number of years.

In this case, W₀ = 28,390 megaliters, r = 7% = 0.07, and n = 5.

Substituting these values into the formula, we have:

W₅ = 28,390 * (1 + 0.07)^5

Calculating this expression, we get:

W₅ ≈ 28,390 * (1.07)^5 ≈ 36,912.51 megaliters

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1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Answer:

m=-12

Step-by-step explanation:

Not sure where the 8 comes from, but you would subtract 9 from the left side. The result is -12.

The area of the parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet is,

⇒ four hundred thirty-three and one-eighth ft²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.

Now, We know that;

Area of a parallelogram = Base × Height

Substitute the given values, we get;

⇒ Area of a parallelogram = Base × Height

⇒ Area of a parallelogram = 22 1/2 × 19 1/4

⇒ Area of a parallelogram = 45/2 × 77/4

⇒ Area of a parallelogram = 3465/8

⇒ Area of a parallelogram = 433 1/8 ft²

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The centroid and circumcenter of triangles are both geometric notions.

The distinction between a circumcenter and a centroid

Centroid:is a place where the triangle's medians coincide is known as the centroid. A triangle's median is a line segment that runs from one of the triangle's vertices to the middle of the other side. The centroid, which is sometimes designated as "G," is situated at the junction of all three medians. It is regarded as the triangle's center of mass or equilibrium point. Each median is split into two segments by the centroid, with the larger segment being closer to the vertex and the ratio of the segments' lengths being 2:1.

The centroid's characteristics

The centroid is situated two-thirds of the way between each vertex and the opposing side's middle.

It is located within the triangle.

The centroid is a triangle's uniformly thick and dense center of gravity.

The triangle is divided into three equal-sized triangles by the centroid.

A circumcenter's  is perpendicular to a triangle's side and runs through that side's midpoint is called a perpendicular bisector. The unique circle that traverses all three of the triangle's vertices is called the circumcircle, and its center is known as the circumcenter. It is frequently indicated as "O"

The circumcenter's characteristics are:

Depending on the type of triangle, the circumcenter may be within, outside, or on the triangle.

The circumcenter is located inside the triangle if the triangle is sharp.

The circumcenter is outside the triangle if the triangle is acute.

The midpoint of the hypotenuse is where the circumcenter is found in a triangle with a right angle.

The triangle's three vertices are all equally far from the circumcenter.

The circumcenter is the point where the perpendicular bisectors, which are equally spaced from the triangle's respective sides, intersect.

Both the centroid and circumcenter are significant triangle locations with unique geometric characteristics.

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The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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Answer:

- 1/2

Step-by-step explanation:

In order to find a slope intercept we need to use,

Equation : y= mx + b to find the slope (m)

If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,

Rs 30 = 45 book

Rs 30 = 45

Rs 1 = 45 / 30

Rs 24 = 3/2 × 24

Rs 24 = 34 books

Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

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Every prime number except 2 and 5 can be expressed in the form of 10k+1, 10k+3, 10k+7, or 10k+9, where k is an integer.

To show that every prime number except 2 and 5 can be expressed in the form of 10k+1, 10k+3, 10k+7, or 10k+9, where k is an integer, we can use the following approach:

First, note that any integer can be written in one of the following forms:

10k

10k+1

10k+2

10k+3

10k+4

10k+5

10k+6

10k+7

10k+8

10k+9

Now, consider the prime numbers greater than 5. These primes must end in a digit other than 0, 2, 4, 5, 6, or 8, since otherwise they would be divisible by 2 or 5.

Thus, they can only end in 1, 3, 7, or 9. This means that every prime number greater than 5 must be of the form 10k+1, 10k+3, 10k+7, or 10k+9.

To see why, suppose a prime number greater than 5 ends in a digit x that is not 1, 3, 7, or 9. Then, we can write this number in the form 10k+x.

But this number is divisible by 2, since x is even, and therefore not prime. So every prime number greater than 5 must be of the form 10k+1, 10k+3, 10k+7, or 10k+9.

Therefore, we have shown that every prime number except 2 and 5 can be expressed in the form of 10k+1, 10k+3, 10k+7, or 10k+9, where k is an integer.

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Answer:

Question 1

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, or a right triangle)

Given:

⇒ BC² + 8² = 10²

⇒ BC² = 36

⇒ BC = 6 cm

Question 2

Given:

⇒ MB = AB - AM = 8 - x

As ΔABC ~ ΔMBN

⇒ AB : AC = MB : MN

⇒ 8 : 10 = (8 - x) : MN

\(\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}\)

\(\sf \implies \dfrac45=\dfrac{(8-x)}{MN}\)

\(\sf \implies MN=\dfrac54(8-x)\)

Question 3

D = (6, 8)

As ΔBAD ~ ΔMAP

⇒ AB : AD : BD = AM : AP : MP

⇒ 8 : 6 : 10 = x : AP : MP

\(\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}\)

\(\sf \implies AP=\dfrac34x\)

\(\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}\)

\(\sf \implies MP=\dfrac54x\)

Question 4

Perimeter of MNCDP = MN + NC + CD + PD + MP

As ΔABC ~ ΔMBN

⇒ AB : BC : AC = MB : BN : MN

⇒ 8 : 6 = (8 - x) : BN

\(\sf \implies \dfrac86=\dfrac{(8-x)}{BN}\)

\(\sf \implies BN=\dfrac34(8-x)\)

NC = BC - BN

\(\sf \implies NC=6-\dfrac34(8-x)\)

PD = 6 - AP

\(\sf \implies PD=6-\dfrac34x\)

Perimeter of MNCDP = MN + NC + CD + PD + MP

\(\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x\)

\(\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x\)

\(\sf \implies perimeter=10+8+6=24\)