A soccer ball is made of 32 pieces of leather: white hexagons and black pentagons. Each black piece borders only with white pieces, each white piece borders with three black pieces and three white pieces. How many black pieces are needed to manufacture the ball?

Answers

Answer 1

Answer:

24

Step-by-step explanation:

1+3=4

4 divided by 32 is 8

8 white ones

then 8-32 is 24

24 black ones


Related Questions

Find the 14th term in the sequence 1, 1/3, 1/9, … Find the sum of the first 10 terms of the sequence above.

Answers

Answer:

This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term

   Let Pn represent the nth term in the sequence

 

   Then Pn = (1/3)^n-1

 

   From this P14 = (1/3)^13 = 1/1594323

 

5. The sum of the first n terms of a GP beginning a with ratio r is given by

   Sn = a* (r^n+1 - 1)/(r - 1)

 

   With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500

Working together, it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 50 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? don't round

Answers

Answer:

12.5 minutes

Step-by-step explanation:

When working together,It takes two computers 10 minutes to send out an email

It takes the slower computer 50 minutes to send out an email

Let x represent the time taken by the faster computer to do the job in its own

Therefore, the time required by the faster computer can be calculated as follows

1/x + 1/50= 1/10

Collect the like terms

1/x= 1/10-1/50

1/x= 4/50

Cross multiply both sides

4 × x = 50×1

4x=50

Divide both sides by the coefficient of x which is 4

4x/4=50/4

x= 12.5

Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes

A laboratory tested n = 98 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 86 milligrams with σ = 7 milligrams. Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.

Answers

Answer:

1.3859

Step-by-step explanation:

The formula for Margin of Error is given as:

Margin of Error = Critical value × Standard Error

Critical value = z score

In the question, we are given a confidence interval of 95%.

Z score for a 95% confidence level is given as: 1.96

Hence, critical value = 1.96

Standard Error = σ / √n

Where n = number of samples = 98 chicken eggs

σ = Standard deviation = 7 milligrams

Standard Error = 7/√98

Standard Error = 0.7071067812

Hence, Margin of Error = Critical value × Standard Error

Margin of Error = 1.96 × 0.7071067812

Margin of Error = 1.3859292911

Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859

Decide whether the normal sampling distribution can be used. If it can be​ used, test the claim about the population proportion p at the given level of significance using the given sample statistics.

Claim: p>0.12; α=0.05; Sample statistics: Modifying above p with caret equals 0.08, n is equal to 250

Answers

Answer:

There is no sufficient evidence to support the claim

Step-by-step explanation:

From the question we are told that

     The level of significance is  [tex]\alpha = 0.05[/tex]

     The  sample proportion is  [tex]\r p = 0.08[/tex]

     The  sample size is  [tex]n = 250[/tex]

     

Generally for normal sampling distribution can  be used

     [tex]n * p > 5[/tex]

So  

     [tex]n* p = 250 * 0.12 = 30[/tex]

Since  

     [tex]n * p > 5[/tex] then  normal sampling distribution can  be used

The null hypothesis is  [tex]H_o : p = 0.12[/tex]

  The alternative hypothesis is  [tex]H_a : p > 0.12[/tex]

The  test statistic is evaluated as

            [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p)}{n} } }[/tex]

substituting values

            [tex]t = \frac{0.08 - 0.12 }{ \sqrt{ \frac{0.12 (1- 0.12)}{250 } } }[/tex]

            [tex]t = -1.946[/tex]

The  p-value is obtained from the z  table and the value is

        [tex]p-value = P(t > -1.9462) =0.97512[/tex]

Since the [tex]p-value > \alpha[/tex]

    Then we fail to reject the null hypothesis

Hence it means there is no sufficient evidence to support the claim

 

     

PLEASE ANSWER ASAP!!!

Equation in the picture


Solve for r in the equation in the picture. You must use the LCD (Least Common Denominator) to simplify. You can also use cross products to solve.

Must show work

A. r = 19

B. r = 21

C. r = 25

D. r = 30



any unrelated answer will be reported​

Answers

Answer:

r = 19

Step-by-step explanation:

( r-5) /2 = ( r+2) /3

The least common denominator is 6

3/3 *( r-5) /2 = ( r+2) /3 * 2/2

3( r-5) /6 = 2( r+2) /6

Since the denominators are the same, the numerators are the same

3( r-5) = 2(r+2)

Distribute

3r -15 = 2r+4

Subtract 2r from each side

3r-2r -15 = 2r+4-2r

r-15 =4

Add 15 to each side

r-15+15 = 4+15

r = 19

Find the surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder x225+y29=1

Answers

Correct question is;

Find the surface area of that part of the plane 10x + 7y + z = 4 that lies inside the elliptic cylinder x²/25 + y²/9 = 1

Answer:

A(S) = 15π√150

Step-by-step explanation:

We are given;

10x + 7y + z = 4

Making z the subject, we have;

z = 4 - 10x - 7y

Now, area of the surface as part of z = f(x, y) is;

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA

From z = 4 - 10x - 7y,

∂f/∂x = -10

∂f/∂y = -7

Thus;

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

x²/a² + y²/b² = 1 and comparing with

x²/25 + y²/9 = 1, we have;

a = 5 and b = 3

So, area of elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder [tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex] is [tex]15\pi\sqrt{150}[/tex] and this can be determined by using the given data.

Given :

10x + 7y + z = 4  ---- (1)[tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex]    --- (2)

Equation (1) can also be written as:

z = 4 - 10x - 7y      ---- (3)

The surface area is given by the equation:

[tex]\rm A(s) = \int \int \sqrt{(\dfrac{\delta f}{\delta x})^2+(\dfrac{\delta f}{\delta y})^2+1}\;dA[/tex]     --- (4)

[tex]\dfrac{\delta f}{\delta x} = -10[/tex]

[tex]\dfrac{\delta f}{\delta y} = -7[/tex]

Now, substitute the known values in the equation (4).

[tex]\rm A(s) = \int \int \sqrt{(10)^2+(7)^2+1}\;dA[/tex]  

[tex]\rm A(s) = \sqrt{150} \int \int\;dA[/tex]  

Now the area enclosed by an ellipse is given by:

[tex]\dfrac{x^2}{25}+\dfrac{y^2}{9}=1[/tex]

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

By comparing the above equation:

a = 5

b = 3

The area is given by:

[tex]\rm A(s)=\sqrt{150}\times \pi(5\times 3)[/tex]

[tex]\rm A(s) = 15\pi \sqrt{150}[/tex]

For more information, refer to the link given below:

https://brainly.com/question/11952845

Please Help! The point (8, -2) satisfies the equation of which line? (1) y+2=2(x+8) (2) y-2=2(x-8) (3) y+2=2(x-8) (4) y-2=2(x+8)

Answers

Answer:

(3) y+2=2(x-8)

Step-by-step explanation:

Substitute the point into the equation and see if it is true

(8,-2)

(1) y+2=2(x+8)

    -2+2 = 2(8+8)

    0 = 2(16)

False

(2) y-2=2(x-8)

  -2-2 = 2(8-8)

  -4 =2 (0)

  False

(3) y+2=2(x-8)

  -2+2 = 2( 8-8)

  0 = 2(0)

 True

(4) y-2=2(x+8)

  -2-2 = 2(8+8)

  -4 = 2(16)

False

Answer:

[tex]\boxed{y+2=2(x-8) }[/tex]

Step-by-step explanation:

[tex]x=8[/tex]

[tex]y=-2[/tex]

[tex]\sf Check \ the \ third \ option.[/tex]

[tex]-2+2=2(8-8)[/tex]

[tex]\sf Both \ sides \ must \ be \ equal.[/tex]

[tex]0=2(0)[/tex]

[tex]0=0[/tex]

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:

Children = 150

Students = 98

Adults = 75

Step-by-step explanation:

C + S + A = 323

5C + 7S + 12A = 2336

A = 1/2C

C = 150

S = 98

A = 75

Write the expression (x4)8 in simplest form.

Answers

The Answer is = 8x^4

Hope this helps! :)

Answer:

the 4 and 8 are exponents

Step-by-step explanation:

ASAP
Which of the following factors determine a plane? A. line and a point on the line B. two lines C. a straight line D. a line and a point not on that line

Answers

Answer:

D. a line and a point not on that line

Step-by-step explanation:

That is how you determine a plane.

The factors which determine a plane are a line and a point not on that line.

What is plane ?

In geometry, a plane is a flat surface that extends into infinity.

In a three dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.

Therefore, the factors which determine a plane are a line and a point not on that line.

Hence, option D is correct.

Learn more about plane here:

https://brainly.com/question/17458011

#SPJ2

What is the critical F value when the sample size for the numerator is seven and the sample size for the denominator is six

Answers

Answer:

Critical F value  = 4.9503

Step-by-step explanation:

Given that:

The sample size of the numerator = 7

The sample size of the denominator = 6

The degree of freedom for the numerator df = n -1

The degree of freedom for the numerator df = 7 - 1

The degree of freedom for the numerator df = 6

The degree of freedom for the denominator df = n - 1

The degree of freedom for the denominator df = 6 - 1

The degree of freedom for the denominator df = 5

The assume that the test is two tailed and using a level of significance of ∝ = 0.10

The significance level for the two tailed test = 0.10/2 = 0.05

From the standard normal F table at the level of significance of 0.05

Critical F value  = 4.9503

Today only, a suit is being sold at a 26% discount. The sale price is $259.
What was the price yesterday?

Answers

Answer:

$350

Step-by-step explanation:

1. Set up the equation. The sale price of $259 is 74% of the original price.

[tex]\frac{74}{100}[/tex] = [tex]\frac{259}{x}[/tex]

2. Cross multiply

74x = 25900

3. Solve

x = 350

On a class trip with 40 students, 14 are male. What percentage of the class is female?

66%
60%
65%
58%

Answers

Answer:

65%

Step-by-step explanation:

If 14 are male, then 26 are female.

To find the percent female, divide the number of females by the total.

26/40 = 0.65

So, the percentage of the class that is female is 65%

Answer:

C. 65%

Step-by-step explanation:

We know that of the 40 total students, 14 are male, which means the remaining students are female.

To find how many are female, we subtract 14 from 40:

40 - 14 = 26 females

Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:

(26 / 40) * 100 = 65

The answer is thus C, 65%.

~ an aesthetics lover

9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In​ general, what does mu Subscript d ​represent? Temperature (degrees Upper F )at 8 AM 98.1 98.8 97.3 97.5 97.9 Temperature (degrees Upper F )at 12 AM 98.7 99.4 97.7 97.1 98.0 Let the temperature at 8 AM be the first​ sample, and the temperature at 12 AM be the second sample. Find the values of d overbar and s Subscript d.

Answers

Answer:

[tex]\frac{}{d}[/tex] = −0.26

[tex]s_{d}[/tex] = 0.4219

Step-by-step explanation:

Given:

Sample1:  98.1  98.8  97.3  97.5  97.9

Sample2: 98.7  99.4  97.7  97.1  98.0

Sample 1           Sample 2              Difference d

98.1                        98.7                       -0.6  

98.8                       99.4                       -0.6

97.3                        97.7                       -0.4

97.5                        97.1                         0.4

97.9                        98.0                       -0.1

To find:

Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]

d overbar ( [tex]\frac{}{d}[/tex])  is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5

[tex]\frac{}{d}[/tex] = ∑d/n

 = (−0.6 −0.6 −0.4 +0.4 −0.1) / 5

 = −1.3 / 5

[tex]\frac{}{d}[/tex] = −0.26

s Subscript d is the sample standard deviation of the difference which is calculated as following:

[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1

[tex]s_{d}[/tex] =

[tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]

    =  √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −  

                                                                     (−0.26))² + (−0.1 − (−0.26))² / 5−1

=  [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]

= [tex]\sqrt{\frac{0.712}{4} }[/tex]

= [tex]\sqrt{0.178}[/tex]

= 0.4219

[tex]s_{d}[/tex] = 0.4219

Subscript d ​represent

μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.

What is the slope of the line showed?

Answers

Answer:

2

Step-by-step explanation:

The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.

Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.

Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).

Slope = rise/run

Slope = 2/1

Slope = 2

Hope that helps.

Answer:

slope=2

Step-by-step explanation:

take two points from graph (0,0) and (1,2)

m=y2-y1/x2-x1

m=2-0/1-0

m=2

What is the measure of B, in degrees?

Answers

Answer:

B = 32

Step-by-step explanation:

Since this is an isosceles triangle, C is also equal to 74 degrees

 the angles of a triangle add to 180

A + B+ C = 180

74+ B + 74 = 180

148 + B = 180

B = 180-148

B =32

Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020. If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?

Answers

Answer:

The product decreases 2022.

Step-by-step explanation:

(x + 1)(y - 1) = xy + 2020

xy - x + y - 1 = xy + 2020

-x + y = 2021

(x - 1)(y + 1) = xy + x - y - 1

  + 2021   =       -x + y

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

(x - 1)(y + 1) + 2021 = xy - 1

(x - 1)(y + 1) = xy - 2022

The product decreases 2022.

What does the tape measure say Measurement # 3 is? *

Answers

Answer:

5 and 3/32 of an inch.

A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. Exactly 3 fours.

A. 0.161

B. 0.002

C. 0.116

D. 0.216

Answers

Answer:

0.0321

Step-by-step explanation:

This can be found by binomial probability distribution as the  probability of success is constant. There are a given number of trials. the successive tosses are independent.

Here n= 5

The probability of getting a four in a roll of a die = 1/6

The probability of not getting a four in a roll of a die = 5/6

The probability of getting exactly three 4s in five throws is given by

5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321

solve 2root3+7root3​

Answers

Answer:

(2+7) root 3 equals 9 root 3

How to simplify this expression??

Answers

Answer :

[tex] \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 4}{ {x}^{3} + 3 {x}^{2} + x - 1} [/tex]

Step-by-step-explanation :

I did the explanation in the picture.

Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}

Answers

Answer:

The answer is 55, -275, 1375, -6875......

Step-by-step explanation:

What is meant by the term "90% confident" when constructing a confidence interval for a mean? Group of answer choices

Answers

Answer:

The question is not complete, below is the complete question:

What is meant by the term 90% confident? when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

Answer:

The correct answer is:

If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.  (c)

Step-by-step explanation:

a 90% confidence level means that if repeated samples were taken, 9 out of 10 times, the confidence intervals of the sample chosen will be close to the mean (true value), which is a true representation of the population parameter. when using confidence intervals, there are always margins of allowable accuracy, and this is suggested by using standard diviations snd variances.

I attached a simple document to this answer that will give you more insight into confidence intervals used in statistics.

In a certain state 22% of secondary school students study a foreign language. A group of 100 students were selected in random sample and 24 of them study a foreign language. In this example: a: What is population? b: What is the value of the proportion p1? c: What is the value of the sample proportion p2?

Answers

Answer: a. population = "All Students"

b. 0.22

c. 0.24

Step-by-step explanation:

a. Population is the largest group of individuals having same characteristics by the researcher's point of view.

Here , the interest is  "Students study foreign language"

So, population = "All Students"

b. Let p be the pro[portion of secondary school students study a foreign language.

In a certain state 22% of secondary school students study a foreign language.

The value of proportion [tex]p_1[/tex] =- 0.22

c. A group of 100 students were selected in random sample and 24 of them study a foreign language.

The value of proportion [tex]p_2=\dfrac{24}{100}=0.24[/tex]

Hi Mathies, Help with this vectors excercise pls. Givan that OA (segment) = 13x+7y , OB = 5x+12y and CO = -15+12y write down each of the following vectors in its simplest form a) BA = 8x+ 5y (l got it, i ve done it) b) AC= ?? i cant find vector AC thanks in advance

Answers

Answer:

AC = 2x-19y

Step-by-step explanation:

Given vector the following vector equations OA = 13x+7y , OB = 5x+12y and CO = -15x+12y, the following expression is true about vector OA, OB and OC;

OA+OB = CO (CO is the resultant since its is moving in the opposite direction compare to OA and OB)

Also BO+OA = BA and AO+OC = AC

If OB = 5x+12y, then BO = -(5x+12y)

BO = -5x-12y (BO = -OB)

Since BO+OA = BA

BA = -5x-12y + 13x+7y

BA = -5x+13x-12y+7y

BA = 8x-5y

Similarly AO+OC = AC

Since AO = -OA and OC = -CO

-OA-CO  = AC

AC = -(13x+7y)-(-15x+12y)

AC = -13x-7y+15x-12y

AC = -13x+15x-7y-12y

AC = 2x-19y

(12x^(2)+x-35)-:(4x+17)

Answers

Answer:

(3x-5)(4x+7) / 4x + 17

Step-by-step explanation:

Rewrite the division as a fraction

12 x ^2 + x-35 / 4x+17

Factor by grouping

(3x-5)(4x+7) / 4x + 17

Hope this was the answer you were looking for

The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,θ) . Select the correct equation in polar coordinates below.

x2+y2−4x=0

a.  r=4 sinθ
b. r=4 cosθ
c. r cos2θ=4 sinθ
d. r sin2θ=4 cosθ

Answers

Answer:

B. r = 4cosθ

Step-by-step explanation:

Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).

x = rcosθ and y = rsinθ.

Substituting the value of x and y in their polar form into the given expression we have;

x²+y²−4x=0

( rcosθ)²+( rsinθ)²-4( rcosθ) = 0

Expand the expressions in parenthesis

r²cos²θ+r²sin²θ-4rcosθ = 0

r²(cos²θ+sin²θ)-4rcosθ = 0

From trigonometry identity, cos²θ+sin²θ =1

The resulting equation becomes;

r²(1)-4rcosθ = 0

r²-4rcosθ = 0

Add 4rcosθ to both sides of the equation

r²-4rcosθ+4rcosθ = 0+4rcosθ

r² = 4rcosθ

Dividing both sides by r

r²/r = 4rcosθ/r

r = 4cosθ

Hence the correct equation in polar coordinates is r = 4cosθ

A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g/kg. The amount of REM sleep in a 24hr period was recorded, in minutes: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
A) Graph the data. Why did you choose the graph that you did and what does it tell you?B) Create an ANOVA table for the data using the formulas provided in class. C) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?D) Based on the ANOVA table, make a conclusion in the context of the problem.E) Create 95% CIs for all pairwise comparisons of means using the Tukey method.

Answers

Answer: Find answer in the attachment

Step-by-step explanation:

7 1/4 x−x=9 3/8 HELLLLPPPPP PLLSSSS

Answers

-1.5

Step-by-step explanation:

So, you do 7.25 - 1 (because it is) and you get 6.25. Make it a fraction inton 25/4 and divide bu 75/8 (9 3/8 simplified) and you get -1.5 voila.

Answer:

x = 3/2

Step-by-step explanation:

7 1/4 = 7 + 1/4 = 28/4 + 1/4 = 29/4

9 3/8 = 9 + 3/8 = 72/8 + 3/8 = 75/8

then:

7 1/4 x = 29x/4

29x/4 - x = 75/8

29x/4 - 4x/4 = 75/8

25x/4 = 75/8

x = (75/8)/(25/4)

x = (75*4)/(8*25)

x = 300/200

x = 3/2

Checking:

(29/4)(3/2) = (29*3)(4*2) =  87/8

87/8 - 3/2 = 75/8

3/2 = 12/8

then:

87/( - 12/8 = 75/8

A certain family has a husband, wife, son, and daughter. All together they are 68 years old. The husband is 3 years older than the wife, and the son is 3 years older than the daughter. Four years ago, all together the family was 54 years old. How old is the husband now?

Answers

Answer:

32

Step-by-step explanation:

Everyone added together = 68

Four years ago, they were 68 -16 = 52

But the question told 54 years.

So there was a girl who was 2 years.

Girl = 2

Boy = 2 +3 = 5

Husband = 3 +w

Wife =w

3 +w +w + 5 + 2 = 68

10 + 2w = 68

2w = 58

w = 29

Wife = 29

Husband = 29 +3 =32

Husband = 32 years

Answer:

[tex]\large \boxed{\sf \bf \ \ 32 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We know that "All together they are 68 years old." and "Four years ago, all together the family was 54 years old."

If all the family was alive four years ago, it means that four years ago the sum of their ages was 68 - 4 - 4 - 4 - 4 because they are four members, so it gives 68 - 16 =52 which is different from 54, right ?

It means that we have the daughter in between, 54- 52 = 2, so the daughter's age is 2, and then the son's age is 5.

The husband is 3 years older than the wife. Let's note W the wife's age, we can write W + 3 + W + 5 + 2 = 68

2 W + 10 = 68

2 W = 68 - 10 = 58 so W = 29

and then the husband's age is 29 + 3 = 32.

And we can verify that 32 + 29 + 5 + 2 = 68, and four years ago, 28 + 25 + 1 + 0 = 54.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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