A father's age now is three times the age that his son was four years ago. In 12 years, the father will be twice as old as his son. Find their ages.

Answer:

[tex]\textsf{Option 3}: \quad -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]

Step-by-step explanation:

Given expression:

[tex]-2x^{-3}y(5yx^5+8xy-4y^2x^2)[/tex]

Distribute:

[tex]\implies -2x^{-3}y(5yx^5) -2x^{-3}y(8xy)-2x^{-3}y(-4y^2x^2)[/tex]

Multiply the constants and collect like terms:

[tex]\implies -10 x^{-3}x^5yy-16x^{-3}xyy+8x^{-3}x^2yy^2[/tex]

Remember that a = a¹.

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies -10 x^{(-3+5)}y^{(1+1)}-16x^{(-3+1)}y^{(1+1)}+8x^{(-3+2)}y^{(1+2)}[/tex]

[tex]\implies -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]

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The length of the arc of the circle is 3.67 meters

The arc of a circle is a part of the circumference that makes up the circle

From the question, we have the following parameters

Diameter, d = 14 meters

Central angle = π/6 radians

Start by calculating the radius of the circle using

Radius, r = Diameter/2

This is so because radius is half the diameter

So, we have

r = 14 meters/2

Evaluate the quotient of 14 meters and 2

r = 7 meters

The length of the arc of the circle is then calculated using

L = Radius * Central angle

Substitute known values in the above equation

L = 7 meters * π/6

Evaluate the product of 7 and π/6

L = 3.67 meters

Hence, the length of the arc of the circle is 3.67 meters

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Answer:

8.16 Kg

Step-by-step explanation:

average is calculated as

average = [tex]\frac{sum}{count}[/tex]

here average = 0.17 and count = 48 , then

0.17 = [tex]\frac{sum}{48}[/tex] ( multiply both sides by 48 )

8.16 = sum

that is total mass = 8.16 Kg

1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t

2. the distance travelled at time t = 3.5 h is 18 Km

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

From the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.

Thus, we shall determine the distance travel in time t as follow

Speed = distance / time

12 = distance / t

Cross multiply

Distance = 12 × t

Distance in time t = 12t

But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:

s = 60 - 12t

Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t

The distance at t = 3.5 hours can be obtained as illustrated below:

s = 60 - 12t

s = 60 - (12 × 3.5)

s = 60 - 42

s = 18 Km

Thus, the distance travelled at t = 3.5 hours is 18 km

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The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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See below for the values of the probabilities

The probabilities of the whole events

For event A, the probability of the whole event is calculated using

P(A) = n(A)/Total

Using the table of values, we have:

P(F) = 130/200 = 0.65

P(M) = 70/200 = 0.35

P(L) = 60/200 = 0.30

P(S) = 40/200 = 0.20

The probabilities of the intersection events

For events A and B, the probability of the intersection events is calculated using

P(A n B) = n(A n B)/Total

Using the table of values, we have:

P(F n E) = P(E n F) = 60/200 = 0.30

P(F n L) = P(L n F) = 40/200 = 0.20

P(F n S) = P(S n F) = 30/200 = 0.15

P(M n E) = P(E n M) = 40/200 = 0.20

P(M n L) = P(L n M) = 20/200 = 0.10

P(M n S) = P(S n M) = 10/200 = 0.05

The probabilities of the Union (OR) disjoint events

For events A and B, the probability of the union (OR) disjoint events is calculated using

P(A u B) = P(A) + P(B)

Using the table of values, we have:

P(E u S) = P(E) + P(S) = 100/200 + 40/200 = 0.70

P(E u L) = P(E) + P(L) = 100/200 + 60/200 = 0.80

P(E u L u S) = P(E) + P(L) + P(S) = 100/200 + 60/200 + 40/100 = 1

P(F u M) = P(F) + P(M) = 130/200 + 70/200 = 1

The probabilities of the Union (OR) joint events

For events A and B, the probability of the union (OR) joint events is calculated using

P(A u B) = P(A) + P(B) - P(A n B)

Using the table of values, we have:

P(E u F) = P(E) + P(F) - P(E n F) = 100/200 + 130/200 - 60/100 = 0.85

P(L u M) = P(L) + P(M) - P(L n M) = 60/200 + 70/200 - 20/100 = 0.55

The probabilities of the conditional probabilities

For events A and B, the conditional probability is calculated using

P(A/B) = P(A n B)/P(B)

Using the table of values, we have:

P(F/S) = P(F n S)/P(S) = 0.15/0.20 = 0.75

P(F/E) = P(F n E)/P(E) = 0.30/0.50 = 0.60

P(M/S) = P(M n S)/P(S) = 0.05/0.20 = 0.25

P(M/L) = P(M n L)/P(L) = 0.10/0.30 = 0.33

P(S/F) = P(F n S)/P(F) = 0.15/0.65 = 0.23

P(E/F) = P(F n E)/P(F) = 0.30/0.65 = 0.46

P(S/M) = P(M n S)/P(M) = 0.05/0.35 = 0.14

P(L/M) = P(M n L)/P(M) = 0.10/0.35 = 0.29

The multiplication of dependent events

For events A and B, the conditional probability is calculated using

P(A n B) = P(A) * P(B/A)

Using the table of values, we have:

P(F n L) = P(F) * P(L/F)

This gives

P(F n L) = 0.65 * (0.20/0.30)

Evaluate

P(F n L) = 0.43

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The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625

Formula for midpoints is given as;

M = ∑0^n-1f((xk + xk + 1)/2) × Δx;

From the information given, we have the following parameters

Let' s find the parameters

Δx = (3 - 0)/6 = 0.5

xk = x0 + kΔx = 0.5k

xk+1 = x0 + (k +1)Δx

Substitute the values

= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2

We then have;

= (0.5k + 0.5k + 05.)/2

= 0.5k + 0.25.

Now f(x) = 2x^2 - 7

Let's find  f((xk + xk+1)/2)

Substitute the value of (xk + xk+1)/2)

= f(0.5k+ 0.25)

= 2(0.5k + 0.25)2 - 7

Put values into formula for midpoint

M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.

To evaluate this sum, use command SUM(SEQ) from List menu.

M = - 12.0625

A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.

Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625

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Answer:

788,000 =

788 x 10^3

78.8 x 10^4

7.88 x 10^5

.788 x 10^6

and so on

Answer:

5

Step-by-step explanation:

3 x |12 - x| - 4

3 x |12 - 15| - 4

3 x 3 - 4

9 - 4

5

Answer: 10 tables in each room 14 kids at each table

The time at which the height of the object is 114 ft rounded to two decimal places is; 5.85 seconds

We are given;

Height of cliff = 95 ft

Initial velocity of throw = 95 ft/s

The height (in feet) of the object after t sec is given by;

h(t) = −19t² + 95t + 95.

Now, we want to find the time at which the height of the object is 114 ft. Thus, we will set h(t) = 114 ft to get;

114 = −19t² + 95t + 95.

Subtract 114 from both sides to get;

−19t² + 95t + 95 = 0

Using quadratic formula, we have;

t = [-95 ± √(95² - 4(-19 * 95))]/(2 * -19)

t = [-95 ± √(16245)]/-38

t = (-95 ± 127.4559)/(-38)

t = (-95 - 127.4559)/-38 or (-95 + 127.4559)/-38

t = 5.85 s or -0.85

Time cannot be negative and so t = 5.85 seconds

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There are 5,040 different ways in which she can order the books.

We know that Donna has 9 books, but 2 of these books already have fixed positions (the first one and the last one).

So we only need to order the remaining 7 books in 7 positions.

And so on for the remaining positions.

The total number of different combinations in which she can order the books is given by the product between the numbers of options above, so we will get:

C = 7*6*5*4*3*2*1 = 5,040

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Reason:

The angles x and 71 are opposite the congruent sides. We call these the base angles. The base angles are congruent for any isosceles triangle. Therefore, x = 71.

It might help to rotate the triangle so that the angles x and 71 are flat along the ground (rather than tilted).

The length of segment A.F in the circles given is: 62 units.

A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.

Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].

Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].

CD = 4

DE = x

CD + DE = CE

Plug in the values into the equation

4 + x = 9

x = 9 - 4

x = 5

DE = 5

The length of segment DE is 5 units

A.F = AB + BD + DE + EF

Plug in the values into the equation

A.F = 24 + 24 + 5 + 9

A.F = 62 units.

Therefore, the length of segment A.F in the given circle is determined as: 62 units.

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The target cost for Model J20 is $2000.

The required cost reduction is $30.

The total saving will be $30.3.

The target cost will be:

= Sales price - (100% × Target cost)

= 400 - (100% × Y)

Y + Y = 400

2Y = 400

Y = 400/2 = 200

Target cost = $200

Therefore, the target cost is $200.

The required cost reduction will be:

= $230 - $200

= $30

The required cost reduction is $30.

The three engineering improvements together will be:

Direct labor reduction = 7.5

Additional inspection = 17

Injection molding = 5.8

Total savings = 30.3

The total savings is $30.3.

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Answer: Either Rohmbus or Parallelogram...

Step-by-step explanation: Your picture is a bit small, sry

Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

Two variables are related when a change in one of them causes a change in the other.

Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.

In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.

The simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.

To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:

A → B

C → X

So: [tex]X=\frac{AxB}{C}[/tex]

The number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:

9 days → 8 workers

6 days → amount of workers

So:[tex]amount of workers=\frac{9 daysx8 workers}{6 days}[/tex]

amount of workers= 12 workers

Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

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The cost of goods sold using LIFO is $99.

Using this formula

Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]

Let plug in the formula

Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]

Cost of goods sold=$58.5+(7 units×$5.80)

Cost of goods sold=$58.5+$40.6

Cost of goods sold=$99.1

Cost of goods sold=$99 (Approximately)

Therefore the cost of goods sold using LIFO is $99.

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The graphed system of inequalities is:

So the correct option is the third one.

On the graph we can see that the two lines are solid, so we need to use the symbols ≤ and ≥. (If instead, we had dashed lines, then we would need to use the symbols > and <).

We also can see that the region above the parabola is shaded (the shaded region represents the region of solutions for each inequality), and the region below the line is shaded, then the system of inequalities is of the form:

Only with that, we conclude that the correct option is the third option:

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Answer:

60

Step-by-step explanation:

60 + y + y = 180

2y = 120

y = 60

The critical value z_α/2 that corresponds to the confidence level 84​% is; 1.41

We want to find the two tail critical values.

This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.

Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.

However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.

From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;

z = 1.41

Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84​% is; 1.41

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Answer: 44

Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.

Answer:

255 (assuming x is the variable x)

340 (assuming x is the multiplication sign)

See explanation below.

Step-by-step explanation:

I assume that x is the variable x.

25(0.3x-4)-5(1.5x-6)+100·13/4 =

= 7.5x - 100 - 7.5x + 30 + 25 × 13

= -70 + 325

= 255

If my assumption above is incorrect, and x really means the multiplication sign, then we have this:

25(0.3×-4)-5(1.5×-6)+100·13/4 =

= 25(-1.2) - 5(-9) + 100(3.25)

= -30 + 45 + 325

= 340

The solutions for the Questions are

a) Given that, the minimum requirement is 58 out of 75.

a=0.7733

b) For  16 out of a total of 75

b=0.2133

c)  For 11 out of a total of 75

c =0.1466

Generally, we need to determine the total number of students who exhibit each behavior by seeing the habits and assets contained inside a Venn diagram.

Therefore, let's assume that:

- In Set A, I watched one of the Naruto episodes.

Set B: Observed a new segment of the anime series Death Note.

Hence, 23 of them have seen an episode of Death as well as an episode of Naruto, which means that

(A intercept B) equals 23.

In addition to this, it is a given that 42 has seen one episode of Death Note.

This indicates that B is equal to 42.

This pertains to us:

[tex]B = (B-A)+(A \cap B)[/tex]

In this case, members of B through A are individuals who have only viewed Death Note. So

42=(B−A)+23

(B-A) = 11

Finally, It is a known fact that 39 of the members have seen at least one episode of Naruto.

Therefore, the value of A is 39.

A=(A−B)+(A intercept B)

39=(A−B)+23

(A−B)= 16

(A union B)= 42+ 39- 23

(A union B)=58

In conclusion, the total number of pupils is:

58 with at least one and 17 with none, for a total of 75

a) Given that, the minimum requirement is 58 out of 75.

a=58*100/75

a=0.7733

b) For  16 out of a total of 75

b= 16/75*100

b=0.2133

c)  For 11 out of a total of 75

c= 11/75*100

c =0.1466

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The length of third side of triangle is 4 or 14.

According to the statement

we have given that the two sides of the triangle which are 5 and 9 and we have to find the length of the third side of triangle.

So, For this purpose, we know that the

If we had a triangle with sides a, b and c, then we can say

b-a < c < b+a

where b is larger than 'a'. This is the triangle inequality theorem

In this case, a = 5 and b = 9 so,

b-a < c < b+a

9-5 < c < 9+5

4 < c < 14

Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set.

And

We see that the numbers 4 and 14 are in this set. The values 2 and 7 are not in the set.

So, The length of third side of triangle is 4 or 14.

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[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]

[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]

[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787

The surface area of the cylinder is 48π inches².

Surface area of a cylinder = 2πr(r + h)

where

Therefore,

Surface area of the smaller cylinder = 2 × π × 2(2 + 10)

Surface area of the smaller cylinder = 4π(12)

Surface area of the smaller cylinder = 48π

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Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

Considering the given discrete probability distribution, the range of the variable X is given by:

Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.

The range of a random variable is the set of all values that the variable can assume.

From the table, we have that X can assume the values of 0.2, 0.4, 0.5, 0.8 and 1, hence the range of the variable X is given by:

Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.

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