A father's age is 4 times as that of his son's age. in 5 years time, the father will be 3 times as old as his son. what are their present ages?​

Answer:

[tex]\huge\boxed{f^{-1}(x)=-\dfrac{1}{8}x+1}[/tex]

Step-by-step explanation:

[tex]f(x)=-8x+8\to y=-8x+8[/tex]

change x with y

[tex]x=-8y+8[/tex]

solve for y

[tex]-8y+8=x[/tex]          subtract 8 from both sides

[tex]-8y+8-8=x-8[/tex]

[tex]-8y=x-8[\tex]        divide both sides by (-8)

[tex]\dfrac{-8y}{-8}=\dfrac{x}{-8}-\dfrac{8}{-8}\\\\y=-\dfrac{1}{8}x+1[/tex]

Answer:

A

Step-by-step explanation:

To factor x² - 5x + 4, we need to find 2 numbers that have a sum of -5 and product of 4; these 2 numbers are -1 and -4 so the factored version is (x - 1)(x - 4). Since x - 4 is not an answer choice but x - 1 is, the answer is A.

Answer:

The minimum svore required to get an A is 85.3.

Step-by-step explanation:

Complete Question

Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8.

The instructor wants to give an A to the students whose scores were in the top 10% of the class. What is the minimum score needed to get an A?

Solution

Scores in the top 10% of the class will have a minimum greater than the remaining bottom 90% of the class.

If the minimum score for the top 10% of the class is x'

P(X ≤ x') = 90% = 0.90

If the z-score of this minimum score of the top 10%, x', is z'.

P(X ≤ x') = P(z ≤ z') = 0.90

using the z-distribution tables

z' = 1.282

But the z-score of any value is given as the value minus the mean divided by the standard deviation.

z = (x - μ)/σ

So,

z' = (x' - μ)/σ

Mean = 75

Standard deviation = 8

z' = 1.282

1.282 = (x' - 75)/8

x' = (1.282 × 8) + 75 = 85.256

= 85.3 to 3 s.f.

Hope this Helps!!!

Answer:

z= 2.38

P = 0.008656

Step-by-step explanation:

Here n= 500 and p~= 464/500= 0.928 and q`= 1- 0.928 = 0.072

We formulate our null and alternate hypothesis as

H0 =  0.9 ;       H0 > 0.9

The degree of confidence = 90%

z₀.₀₅ = 1.645 for  α= 0.05

We use the test statistic

z=  x- np/√npq

z= 466-500 *0.9/ √500 * 0.9(1-0.9)

z= 466- 450/ √45

z= 16/6.7082

z= 2.38

As the calculated value of z= 2.38  is greater than α =1.645 so we reject H0.

If H0 is true the P value is calculated as

P = 1- Ф( 2.38)

P = 1-0.991344=0.008656

Step-by-step explanation:

to find the sum of nth term

equation is

n/2 ( 2a + (n-1)d) where a is the 1st term and d is the common difference

5/2 ( 120 +( 4 × 31))

5/2 ( 120 + 124)

5/2 × 244

5 × 122 dividing 244 by 2

610

Answer: 610

Step-by-step explanation:

This sequence starts at 60 and increases by increments of 31.  Thus, to get the last two numbers, do 122+31=153, and 153+31=184.  Then add 60+91+122+153+184 to get 610.

Hope it helps <3

Answer:

LotsofDebt, Inc Debt Ratio is 93.75%

LotsofEquity, Inc Debt Ratio is 6.25%

equity multiplier LotsofDebt, Inc is 16

equity multiplier LotsofEquity, Inc is 1.0666666667

debt-to-equity LotsofDebt, Inc is $15 million

debt-to-equity LotsofEquity, Inc. is $0.0666666667 million

Step-by-step explanation:

In order to calculate the debt ratio of LotsofDebt, Inc and LotsofEquity, Inc.  we would have to make the following calculations:

Debt Ratio = Debt/Assets

According to the given data we have the following:

LotsofDebt, Inc Debt=$30 million

LotsofDebt, Inc Asset=Debt + Equity = $30 million + $2 million = $32 million

Therefore, LotsofDebt, Inc Debt Ratio =$30 million/$ 32 million

LotsofDebt, Inc Debt Ratio= 93.75%

LotsofEquity, Inc. Debt=$2 million

LotsofEquity, Inc Asset= Debt + Equity = $2 million + $30 million

LotsofEquity, Inc Debt Ratio = $2 million/$32 million

LotsofEquity, Inc Debt Ratio = 6.25%

In order to calculate the equity multiplier of LotsofDebt, Inc and LotsofEquity, Inc.  we would have to make the following calculations:

equity multiplier =Assets/Equity

equity multiplier LotsofDebt, Inc.=$32 million/$2 million

equity multiplier LotsofDebt, Inc= 16

equity multiplier LotsofEquity, Inc=$32 million/$30 million

equity multiplier LotsofEquity, Inc = 1.0666666667

In order to calculate the debt-to-equity of LotsofDebt, Inc and LotsofEquity, Inc.  we would have to make the following calculations:

debt-to-equity LotsofDebt, Inc=Debt/Equity

debt-to-equity LotsofDebt, Inc=$30 million/$2 million

debt-to-equity LotsofDebt, Inc= $15 million

debt-to-equity LotsofEquity, Inc.= $2 million/$30 million = 0.0666666667

debt-to-equity LotsofEquity, Inc.= $0.0666666667 million

Answer:

Hey there!

The slope of a vertical line is undefined! The run is zero, and as we know, dividing by zero is undefined!

Hope this helps :)

Answer:

Undefined

Step-by-step explanation:

A vertical line has an undefined slope or there is no slope of the line.

Answer:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

z -value = 0.33022

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

Step-by-step explanation:

From the summary of the given statistical data sets.

Let consider to [tex]p_1[/tex] represent percentage of the first group ; &

[tex]p_2[/tex] represent percentage of the second group

The null and the alternative hypothesis can be stated s follows:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

At the level of significance ∝ = 0.1; the two tailed critical value from the z-table

[tex]z_{\alpha/2} = 1.65[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

However; from the question:

There are 55 people in the first group and this group will be administered the new drug.

There are 45 people in the second group and this group will be administered a placebo.

After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.

The test statistic for the for the first group who suffered from the second episode can be denoted as :

[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]

The test statistic for the for the second group who suffered from the second episode can be denoted as :

[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]

where;

[tex]n_1[/tex] = sample size of group 1 = 55

[tex]n_2[/tex] = sample size of group 2 = 45

The total probability of both group is :

[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]

[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]

[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]

[tex]\hat p = \dfrac{10.1}{100}[/tex]

[tex]\hat p = 0.101[/tex]

The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]

Now; The test statistics is determined to be :

[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]

[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]

z = 0.33022

Hence; the value for the test statistics =  0.33022

the value for the test statistics =  0.33

From the z value; The P-value for the test statistics can be computed as:

P-value = 2P(Z ≥ |z|)

P-value = 2P(Z ≥  0.33022)

P-value = 2 × P (Z ≤ - 0.33022)

From the z table Z ≤ - 0.33022 = 0.3707

P-value = 2 × 0.3707

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

Answer:

12

Step-by-step explanation:

Well first step to finding median is order the scores from least to greatest,

0, 3, 8, 12, 14, 15, 15

Now we can start crossing the numbers off.

After we've crossed 3 numbers off from each side,

we get 12.

Thus,

12 is the median of the number set,

Hope this helps :)

Answer:

12

Step-by-step explanation:

First we need to put the numbers in order from smallest to largest

14, 15, 8, 15, 3, 0, and 12

becomes

0 , 3 , 8 , 12 , 14, 15, 15

Then the median is the middle number

There are 7 numbers

7/2 = 3.5

The middle is  the  4th number ( 3 on the left and 3 on the right)

0 , 3 , 8 ,     12 ,     14, 15, 15

The median is 12

Answer:

[tex]g(x) = |x| + 1[/tex]

Step-by-step explanation:

Given

[tex]y = |x|[/tex]

Required

Translate 1 unit up

Start by replacing y with f(x)

[tex]f(x) = |x|[/tex]

To translate an the graph of an absolute function upward, you make use of the formula;

[tex]g(x) = f(x) + k[/tex]

Where k is the number of units

In this case; [tex]k = 1[/tex]

Hence;

[tex]g(x) = f(x) + k[/tex]

Substitute [tex]k = 1[/tex]

[tex]g(x) = f(x) + 1[/tex]

Substitute  [tex]f(x) = |x|[/tex]

[tex]g(x) = |x| + 1[/tex]

Hence, the resulting equation is [tex]g(x) = |x| + 1[/tex]

Answer:

Step-by-step explanation:

Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.

Volume of a cone V = πr²h/3

If the diameter and the height are equal, then r = h

V = πh²h/3

V = πh³/3

If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min

Using chain rule to get the expression for dV/dt;

dV/dt = dV/dh * dh/dt

From the formula above, dV/dh = 3πh²/3

dV/dh =  πh²

dV/dt = πh²dh/dt

20 = πh²dh/dt

To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.

20 = π(11)²dh/dt

20 = 121πdh/dt

dh/dt = 20/121π

dh/dt = 20/380.133

dh/dt = 0.0526ft/min

This means that the height of the pile is increasing at  0.0526ft/min

Answer:

[tex]\boxed{Side \ Length \ of \ hot \ tub = 4.8\ ft.}[/tex]

Step-by-step explanation:

Scale Factor = 5

Also,

B'C' = 24 feet

Since both are squares so both have all sides equal.

Sqaure A'B'C'D' is dilated by a scale factor of 5

So,

AB = BC = CD = DA = 24/5 = 4.8 ft.

The length of one side of the hot tub is 4.8 feet and this can be determined by using the concept of dilation.

Given :

The following steps can be used in order to determine the length of one side of the hot tub:

Step 1 - According to the given data, the dilation factor is 5.

Step 2 - So, after the dilation by a factor of 'a' the length of the side be 'b' becomes 'ab'.

Step 3 - So, according to the given data, the length of B prime C prime is 24 feet. Therefore, after the dilation by a factor of 5, the length of the segment BC becomes:

[tex]\rm =\dfrac{24}{5}=4.8\;feet[/tex]

So, the length of one side of the hot tub is 4.8 feet. Therefore, the correct option is b).

For more information, refer to the link given below:

https://brainly.com/question/2856466

Answer:

SAS

Step-by-step explanation:

.. cuz, it just is c:

By ''SAS congruency'' theorem we can prove AD = CB.

We have to given that,

In a figure,

AB = CD

∠1 = ∠4

Now, In triangle ADC and triangle ABC,

AC = AC (Common side)

∠1 = ∠4  (Given)

AB = CD (Given)

Hence, By SAS Congruency theorem,

Δ ADC ≅ Δ ABC

So, We get;

AD = CB

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

Answer:

(A) 15 centimeters

Step-by-step explanation:

A midsegment of a triangle is always 2 things:

Half the size of the bottom of the triangle (in this case AC)

Parallel to the bottom of the triangle.

Since ABC is an equilateral triangle, we know that EVERY side is 30cm, including AC.

So the midsegment of ABC, LM, must be 15 cm.

Hope this helped!

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

    ii) R control chart : upper limit =  1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on  X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 *  mean range = 50.15 - 0.577(0.5632) = 49.825

Based on  R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0  

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2  = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

Answer:

[tex]\boxed{\mathrm{Option \ C}}[/tex]

Step-by-step explanation:

=> [tex]x^2+22x = 31[/tex]

=> [tex](x)^2+2(x)(11) = 31[/tex]

Since b = 11 , So [tex](11)^2[/tex] needs to be added to both sides

Adding [tex](11)^2[/tex]  to both sides

=> [tex](x)^2+2(x)(11)+(11)^2 = 31+(11)^2[/tex]

Completing the square

=> [tex](x+11)^2 = 31+121[/tex]

=> [tex](x+11)^2 = 152[/tex]

Answer:

125/6(In(x-25)) - 5/6(In(x+5))+C

Step-by-step explanation:

∫x2/x1−20x2−125dx

Should be

∫x²/(x²−20x−125)dx

First of all let's factorize the denominator.

x²−20x−125= x²+5x-25x-125

x²−20x−125= x(x+5) -25(x+5)

x²−20x−125= (x-25)(x+5)

∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx

x²/(x²−20x−125) =x²/((x-25)(x+5))

x²/((x-25)(x+5))= a/(x-25) +b/(x+5)

x²/= a(x+5) + b(x-25)

Let x=25

625 = a30

a= 625/30

a= 125/6

Let x= -5

25 = -30b

b= 25/-30

b= -5/6

x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)

∫x²/(x²−20x−125)dx

=∫125/6(x-25) -∫5/6(x+5) Dx

= 125/6(In(x-25)) - 5/6(In(x+5))+C

Answer:

width = length = 3 inches

height = 7 inches

Step-by-step explanation:

If x is the width and length of the base, and y is the height, then:

y = x + 4

The volume of the box is:

63 = x²y

The surface area of the box is:

93 = x² + 4xy

Substitute the first equation into the third.

93 = x² + 4x (x + 4)

93 = x² + 4x² + 16x

0 = 5x² + 16x − 93

0 = (x − 3) (5x + 31)

x = 3

y = 7

Use the second equation to check your answer.

63 = (3)²(7)

63 = 63

Answer:

Length=Width=3

Height=7.

Step-by-step explanation:

First, let's write some equations. So, we have an open box (with no lid) that has a square base. It has a height 4 units more of its width/length.

First, let's write the equation for the volume. The volume of a rectangular prism is:

[tex]V=lwh[/tex]

Recall that we have a square base. In other words, the length and width are exactly the same. Therefore, we can do the following substitution:

[tex]V=(w)wh=w^2(h)[/tex]

Now, recall that the height is four units more than the width/length. Therefore, we can make the following substitution:

[tex]V=w^2(w+4)\\63=w^2(w+4)[/tex]

We can't really do anything with this. Let's next find the equation for the surface area.

So, we have 5 sides (not 6 because we have no lid). The bottom side is a square, so it's area is w^2. Since we have a square base, the remaining four sides will have an area w(w+4). In other words:

[tex]93=w^2+4(w(w+4))[/tex]

The left term represents the area of the square base. The right term represents the area of one of the rectangular sides, times sides meaning four sides. Simplify:

[tex]93=w^2+4w^2+16w\\5w^2+16w-93=0[/tex]

This seems solvable. Let's try it. Trying factoring by guessing and checking.

We can see that it is indeed factor-able. -15 and 31 are the numbers:

[tex]5w^2-15w+31w-93=0\\5w(w-3)+31(w-3)=0\\(5w+3)(w-3)=0\\w=3\\h=w+4=7[/tex]

We ignore the other one because width cannot be negative.

So, the width/length is 3 and the height is 7. We can check this by plugging this into the volume formula:

[tex]63\stackrel{?}{=}(3)^2(7)\\63\stackrel{\checkmark}{=}63[/tex]

Answer:

11/36

Step-by-step explanation:

Find the probability that neither dice shows a 5 (also means the dice can show any number except 5- where there are 5 possible choices out of 6):

= 5/6 x 5/6

=25/36

If we subtract the probability that neither dice shows a 5, we can obtain the probability that at least 1 dice shows a 5- (either one of them is 5, or both of them is 5)

1- 25/36

=11/36

Answer: 308 gallons of water.

Step-by-step explanation:

First find the volume of the water been.

The volume of a rectangular prism uses the formula

V= L * W *H

V = 8 * 5 * 1

V = 40 ft^3

Now we will convert 40ft into gallons using what they gave us that 1 gallon is 0.13 ft^3  

[tex]\frac{1}{x} = \frac{0.13}{40}[/tex]    which means if 1 gallon is 0.13 cubic feet how much will 40 cubic feet be when converted to gallons.

Solve by cross product.

0.13x = 40  divide both sides by 0.13  

x= 308

Answer:

(26+92)+17 = 26 + ( 92+17)

Step-by-step explanation:

The associative property of addition is

a + (b + c) = (a + b) + c

We want to move the parentheses

(26+92)+17 = 26 + ( 92+17)

Answer:

You will never be able to reach the sum of 2

Step-by-step explanation:

Answer:

  (x, 2 -2x)

Step-by-step explanation:

Written in standard form, both equations are ...

  2x +y = 2

Since they are both the same, there are an infinite number of solutions. We can write those solutions in terms of x as ...

  y = 2 -2x

The solutions are ...

  (x, 2 -2x)

Answer:

The Azimuths are 81 degrees, 6 degrees for Grid Azimuths and 269 degrees, 194 degrees for back Azimuths

Step-by-step explanation:

Stream = 89 degrees and Pond = 14 degrees

To Convert to grid Azimuth

G-M Azimuth of 89-8=81 degrees

G-M Azimuth of 14-8=6 degrees

To obtain the back Azimuth for the stream

89+180=269 degrees

To obtain the back Azimuth for the pond

14+180=194 degrees

1. The angles form a straight angle

2. A straight angle is defined to be 180 degrees

3. The three angles of any triangle always add to 180, as the diagram shows.

4. This is false. We need to add the three different angles A,B,C to get 180. Adding angle A to itself may not lead to 180. A+A = 180 only happens when angle A is a right angle (90 degree angle).

Answer:

The answer is option C

Step-by-step explanation:

Total surface area of a cylinder is

2πr( r + h)

The curved surface area of a cylinder is

2πrh

where r and h are the radius and height respectively

h = 10cm

r = 7cm

Total surface area is

2π×7( 7 + 10)

14π ( 7 + 10)

98π + 140π

238π

Which is

748 cm²

The curved surface area is

2π (7)(10)

140π

Which is

440cm²

The difference between the total surface area and the curved surface area of the cylinder is

748 cm² - 440cm²

Hope this helps you

Answer:

The sample size is 30.

Step-by-step explanation:

The sample size of a histogram can be calculated by summing up all the frequencies of all the occurrences in the data set

From the question the frequency is given as

Frequency = 2 4 6 8 10

The sample size n =

2 + 4 + 6 + 8 + 10

= 30

Therefore the sample size n of the data set = 30

Answer:

   (-10, -3)

Step-by-step explanation:

Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).

Answer:

Step-by-step explanation:

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