Calculate the length of the unknown side of this right angled triangle

Answer:

(b) 32

Step-by-step explanation:

From the information given :

sample mean of Philadelphia μ₁ = $1240

Sample size of Philadelphia n₁ = 15

Sample Standard deviation σ₁ = $270

sample mean of Paris μ₂ = $1,060

Sample size of Paris  n₂ = 19

Sample Standard deviation of Paris  σ₂ = $240

If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris;

the degrees of freedom for this hypothesis test can be calculated as;

degree of freedom df = n - 1

degree of freedom for both hypothesis test = (n₁ - 1 + n₂ -1)

degree of freedom for both hypothesis test  = (n₁ + n₂ - 2)

degree of freedom for both hypothesis test  = ( 15 + 19 - 2)

degree of freedom for both hypothesis test are   32  

Answer:

9a^2sqrt(ab)

Step-by-step explanation:

The first noticable thing is that 81 has a perfect square of 9.

So it is now 9sqrt(a^5b)

you can split the a^5, to a^4 × a.

you can now take the sqrt of a^4, which is a^2, and pull it out from the sqrt

You are now left with 9a^2sqrt(ab)

Answer:

9a^2sqrt(ab)

Step-by-step explanation:

Answer:

x < -( 8-2b) /a  a > 0

Step-by-step explanation:

−ax + 2b > 8

Subtract 2b from each side

−ax + 2b-2b > 8-2b

-ax > 8 -2b

Divide each side by -a, remembering to flip the inequality ( assuming a>0)

-ax/-a < ( 8-2b) /-a

x < -( 8-2b) /a  a > 0

Answer: [tex]x<\frac{-8+2b}{a}[/tex]

                  [tex]a>0[/tex]

Step-by-step explanation:

[tex]-ax+2b>8[/tex]

[tex]\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}[/tex]

[tex]-ax>8-2b[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]

[tex]\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)[/tex]

[tex]ax<-8+2b[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}a[/tex]

[tex]\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0[/tex]

[tex]x<\frac{-8+2b}{a};\quad \:a>0[/tex]

You reject the Null Hypothesis when you have a small P-Value. Here is an example! Also we never accept the null hypothesis, think of it like this if we bring someone to court you wouldn't say their innocent of a crime, you only know that if they do not get convicted of the crime they are not guilty in the eyes of the law. Same thing applies here, since there could be several answers that satisfy our assumptions made, we can not be certain that 1 of those assumptions is the REAL answer it's just AN answer.

Answer:

$7200

Step-by-step explanation:

The interest rate on $5,000 accumulated by Edgar is 20%.

He does not make any payment for 2 years and the interests are compounded continuously.

The amount of money he owes after 2 years is the original $5000 and the interest that would have accumulated after 2 years.

The formula for compound amount is:

[tex]A = P(1 + R)^T[/tex]

where P = amount borrowed = $5000

R = interest rate = 20%

T = amount of time = 2 years

Therefore, the amount he will owe on his debt is:

[tex]A = 5000 (1 + 20/100)^2\\\\A = 5000(1 + 0.2)^2\\\\A = 5000(1.2)^2\\[/tex]

A = $7200

After 2 years, he will owe $7200

Answer:7,434.57

Explanation: A= 5000(1+0.2/12)^12•2

Answer:

The GCF is the largest expression that is factor of all expressions

Answer:

The GCF of two expressions is the greatest expression that is a factor of both the expressions.

Step-by-step explanation:

For example 7x² and 14x.

7x² = 1, 7, x, x

14x = 2, 7, x

The greatest common factor of the two expressions is 7x.

Answer:

Step-by-step explanation:

Assume that f(x) = 0 for x outside the interval [4,7]. We will use the following

[tex]E[X^k] = \int_{4}^{7}x^k f(x) dx[/tex]

[tex]Var(X) = E[X^2]- (E[X])^2[/tex]

Standard deviation = [tex] \sqrt[]{Var(X)}[/tex]

Mean = [tex]E[X][/tex]

Then,

[tex]E[X] = \int_{4}^{7}\frac{1}{3}dx = \frac{7^2-4^2}{2\cdot 3} = \frac{11}{2}[/tex]

[tex]E[X^2] = \int_{4}^{7}\frac{x^2}{3}dx = \frac{7^3-4^3}{3\cdot 3} = 31[/tex]

Then, [tex]Var(x) = 31-(\frac{11}{2})^2 = \frac{3}{4}[/tex]

Then the standard deviation is [tex]\frac{\sqrt[]{3}}{2}[/tex]

Answer:

Step-by-step explanation:

x+y>0, x>0, when y=0

x+y<-5 x<-5 when y=0

since the sign is only< then it is dotted line, and since one is greater and is less than they actually do not intersect

Answer:

No solution with slanted lines

Step-by-step explanation:

Answer:

1.56 seconds

Step-by-step explanation:

When the ball hits the ground, h = 0.

0 = 20 − 5t − 5t²

Divide both sides by -5.

0 = t² + t − 4

Solve with quadratic formula.

t = [ -1 ± √(1² − 4(1)(-4)) ] / 2(1)

t = (-1 ± √17) / 2

The time must be positive, so:

t = (-1 + √17) / 2

t ≈ 1.56

Answer:

  1.9 units

Step-by-step explanation:

Since we have ...

  MN : NP = 9 : 1

then ...

  NP : MN+NP = 1 : (9+1) = 1 : 10

If MP is 2 units, then NP is 1/10 × 2 units = 0.2 units. Point K will be half that distance from N or P, so will be 0.1 unit from P.

So, the distance from M to K, the midpoint of NP is ...

  2 units - 0.1 units = 1.9 units

Answer:

1.9

Step-by-step explanation:

Answer:

the dimensions of the poster with the smallest area is 36cm by 54cm

Step-by-step explanation:

✓Let us represent the WIDTH of the printed material on the poster as "x"

✓Let us represent the HEIGHT of the printed material on the poster as "y"

✓ The given AREA is given as 864 cm2

Then we have

864 cm2= xy ...................eqn(1)

We can make "y" subject of the formula.

y= 864/x .......................eqn(2)

✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is

(y+18)

✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is

(x+12)

✓Then AREA OF THE TOTAL poster

A= (y+18)(x+12) ...................eqn(3)

Substitute eqn (2) into eqn(3)

A= ( 18+ 864/x)(x+12)

We can now simplify by opening the bracket, as

A=18x +1080 +10368/x

A= 18x +10368/x +1080

Let us find the first derivative of A which is A'

A'= 18-(10368/x²)

If we set A' =0

Then

0= 18- (10368/x²)

18= (10368/x²)

x²= 10368/18

x²= 576

x=√576

x=24

The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum

The value of "y" when x=24 can now be be calculated using eqn(2)

y= 864/x

y= 864/24

y=36cm

✓The total width of the poster= (x+12)

= 24+12=36cm

✓The total height big the poster= (y+18)=36+18=54cm

the dimensions of the poster with the smallest area is 36cm by 54cm

Answer:

The total width of the paper [tex]=36 cm.[/tex]

The total height of the paper [tex]=54cm[/tex]

Step-by-step explanation:

Given information:

Top margin of the paper = 9 [tex]cm\\[/tex]

Bottom margin of the paper = 6 [tex]cm\\[/tex]

Area of the printed material = [tex]864[/tex] [tex]cm^2[/tex]

Let, the width of the printed material = [tex]x[/tex]

And the height of the printed material = [tex]y[/tex]

So, Area [tex]x \times y=864[/tex] [tex]cm^2[/tex]

After including margins;

Width of the paper [tex]= (x+12)[/tex]

Height of the paper [tex]= (y+18)[/tex]

Area [tex](A) = (y+18) (x+12)[/tex]

[tex]A=18x+(10368/x)+1080\\[/tex]

Take first derivative:

[tex]A'= 18- (10368/x^2)[/tex]

When [tex]A'=0[/tex]

Then,

[tex]18-(10368/x^2)=0\\x^2=576\\x=24[/tex]

Now ,when we take second derivative and check if it is positive or not ,

We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.

Hence ,

[tex]x \times y=864\\y=864/24\\y=36\\[/tex]

Now ,

The total width of the paper

[tex]= 24+12\\=36 cm.[/tex]

And , total height of the paper

[tex]=36+18\\=54 cm.[/tex]

For more information visit:

https://brainly.com/question/14261130

Hi

Below the formulas to convert Celsius into Fahrenheit.

9/5 C +32 = degree in fahrenheit.

Where C is the degree in celsius. So have a try and find the answer.

Work Shown:

Replace every x with 4. Use the order of operations PEMDAS to simplify

f(x) = x + 21

f(4) = 4 + 21

f(4) = 25

The input 4 leads to the output 25.

Answer:

Step-by-step explanation:

Given the expression [tex]3\left(q+\dfrac43\right) = 23[/tex], we are to find the value of q;

[tex]3\left(q+\dfrac43\right) = 23\\on\ expansion\\\\3q + 4/3(3) = 23\\\\3q+4 = 23\\\\subtract \ 4\ from \ both\ sides \ of \ the \ equation\\\\3q+4-4 = 23-4\\\\3q = 19\\\\Diviide \both\ sides \ by \ 3\\\\3q/3 = 19/3\\\\q = 19/3[/tex]

Hence the value of q is 19/3

Answer:

-2/3

Step-by-step explanation:

Don't worry about it, i got connections.

Answer:

  growth rate = 0.1733 per day, or 17.33% per day

Step-by-step explanation:

Since the doubling time is 4 days, the growth factor over a period of t days is ...

  2^(t/4)

Then the growth factor for 1 day is

  2^(1/4) ≈ 1.189207

The instantaneous growth rate is the natural log of this:

  ln(1.189207) ≈ 0.1733 . . . per day

Answer:

Design thinking skills

Step-by-step explanation:

The design thinking skills is observable in individuals who can effectively use Intuition to create prototypes of abstract objects.

Jessie thus shows that she possess design thinking skills by been able to imagine abstract concepts at the same and she applies advanced mathematical formulas which in turn provides solutions to problems.

You are absolutely right.

Answer:

  28 • 28 • 28 • 28 • 28 • 28

Step-by-step explanation:

The exponent signifies the number of times the base appears as a factor in the product. Here, the base 28 is a factor 6 times:

  28×28×28×28×28×28

Answer:

The painting is [tex]t = 10911.1 \ years \ old[/tex]

Step-by-step explanation:

From the question we are told that

    The amount of carbon present after t year is

           [tex]y(t) = y_o * e ^{-0.00012t}[/tex]    {Note ; This is the function }

Here  [tex]y(t)[/tex] is the amount of carbon-14 after time t

        [tex]y_o[/tex] the original amount of carbon-14

Now given that the paint as at now contain 27% of the original carbon-14

  Then it mean that

            [tex]y(t) = 0.27 y_o[/tex]

So the equation is represented as

       [tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]

=>    [tex]0.27 = * e ^{-0.00012t}[/tex]

=>    [tex]ln(0.27) = -0.00012t[/tex]

=>  [tex]- 1.30933 = -0.00012t[/tex]

=>  [tex]t = \frac{-1.30933}{-0.00012}[/tex]

=>   [tex]t = 10911.1 \ years[/tex]

Answer:

The meadian decreases by 1.5 when the outlier is removed.

Step-by-step explanation:

Well first we need to find the median of the following data set,

(75, 63, 58, 59, 63, 62, 56, 59)

So we order the set from least to greatest,

56, 58, 59, 59, 62, 63, 63, 75

Then we cross all the side numbers,

Which gets us 59 and 62.

59 + 62 = 121.

121 / 2 = 60.5

So 65 is the median before the outlier is removed.

Now when we remove the outlier which is 75.

Then we order it again,

56, 58, 59, 59, 62, 63, 63

Which gets us 59 as the median.

Thus,

the median height decreases by 1.5 units when the outlier is removed.

Hope this helps :)

Answer:

28

Step-by-step explanation:

Let x be the missing segment

We will use the proportionality property to find x

24/16 = 42/x

Simplify 24/16

24/16= (4×6)/(4×4)= 4/6 = 3/2

So 3/2 = 42/x

3x = 42×2

3x = 84

x = 84/3

x= 28

Problem 10

Explanation: You'll use the equation cos(28) = d/65 to solve for d to get d = 65*cos(28) = 57.39159 approximately. We use the cosine ratio because it ties together the adjacent and hypotenuse.

=====================================

Problem 11

Explanation: This time we use the sine rule. We have the height as the opposite side (which is unknown, call it x) and the hypotenuse is the ladders length (11). So we have sin(72) = x/11 which solves to x = 11*sin(72) = 10.46162

=====================================

Problem 12

Explanation: Now we use the tangent rule to connect the opposite and adjacent sides.

tan(37) = 12.1/x

x*tan(37) = 12.1

x = 12.1/tan(37)

x = 16.05724 approximately

Answer:

Option (B)

Step-by-step explanation:

To determine the length of arc of a circle we use the formula,

Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Where θ = measure of the central angle subtended by the arc

r = radius of the circle

For the circle given in the picture attached,

Length of arc NM = [tex]\frac{30}{360}(2\pi)(2)[/tex]

                             = [tex]\frac{4\pi }{12}[/tex]

                             = [tex]\frac{\pi }{3}[/tex]

Therefore, length of [tex]\widehat{NM}=\frac{\pi }{3}[/tex]

Option (B) will be the answer.

Answer: C

Step-by-step explanation:

4#/12 = #

Answer:

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius

From the question V = 1436 cm³

[tex]1436 = \frac{4}{3} \pi {r}^{3} [/tex]

Multiply through by 3

We have

[tex]4308 = 4\pi {r}^{3} [/tex]

Divide both sides by 4π

[tex] {r}^{3} = \frac{4308}{4\pi} [/tex]

[tex] {r}^{ 3} = \frac{1077}{\pi} [/tex]

Find the cube root of both sides

[tex]r = \sqrt[3]{ \frac{1077}{\pi} } [/tex]

r = 6.99

We have the final answer as

Hope this helps

Answer:

-7/5

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -3 -4)/(8-3)

   = -7/5

Answer:

-7/5

Step-by-step explanation:

Hey there!

To find the slope of a line with 2 given points we'll use the following formula,

[tex]\frac{y^2-y^1}{x^2-x^2}[/tex]

-3 - 4 = -7

8 - 3 = 5

-7/5

Hope this helps :)

Step-by-step explanation:

a. The point estimate is the mean, 47 days.

b. The margin of error is the critical value times the standard error.

At 31 degrees of freedom and 98% confidence, t = 2.453.

The margin of error is therefore:

MoE = 2.453 × 10.2 / √32

MoE = 4.42

c.  The confidence interval is:

CI = 47 ± 4.42

CI = (42.58, 51.42)

d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.

e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.

Answer:

AC = 25.5 or 1.5

Step-by-step explanation:

If they are on a line and they are in the order ABC

AB + BC = AC

12+13.5 = AC

25.5 = AC

If they are on a line and they are in the order CAB

CA + AB = BC

AC + 12 =13.5

AC = 13.5 -12

AC = 1.5

If they are on a line and they are in the order ACB

That would mean that AB is greater than BC and that is not the case

Answer:

An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.

The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.

------

length = 91 - 2*10 = 71 ft.

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

The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.

---------

2800 <= area <= 3200

2800 <= (length)(width) <= 3200

2800 <= 71w <= 3200

39.44 <= width <= 45.07

hope it helpsss

Step-by-step explanation:

Answer: An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.

The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.

------

length = 91 - 2*10 = 71 ft.

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

The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.

---------

2800 <= area <= 3200

2800 <= (length)(width) <= 3200

2800 <= 71w <= 3200

39.44 <= width <= 45.07

Complete Question

In a small private​ school, 5 students are randomly selected from 13 available students. What is the probability that they are the five youngest​ students?

Answer:

The  probability is [tex]P(x) = 0.00078[/tex]

Step-by-step explanation:

From the question we are told that

    The number of student randomly selected is  r =  5

   The  number of available students is  n  =  13

Generally the number of ways that 5 students can be selected from 13 available students is mathematically represented as

      [tex]n(k)=\left n} \atop {}} \right.C_r = \frac{n ! }{(n-r ) ! r!}[/tex]

substituting values    

      [tex]\left n} \atop {}} \right.C_r = \frac{13 ! }{(13-5 ) ! 5!}[/tex]

    [tex]\left n} \atop {}} \right.C_r = \frac{13 * 12 * 11 * 10 * 9 *8! }{8 ! * 5 * 4 * 3 * 2 *1}[/tex]

     [tex]\left n} \atop {}} \right.C_r = 1287[/tex]

The  number of method by which  5 youngest  students are selected is n(x) =  1

   So  

          Then the probability of  selecting the five youngest students is mathematically represented as

        [tex]P(x) = \frac{n(x)}{n(k)}[/tex]

substituting values

        [tex]P(x) = \frac{1}{1287}[/tex]

        [tex]P(x) = 0.00078[/tex]