To prepare for a marathon run Sue ran 16 miles before she blistered her heel, and she walked 1 additional mile. Her running speed was 16 times as fast as her walking speed. She was running and walking for 4 hours. FIND Sues running speed.

Answer:

[tex] \angle B[/tex]

Step-by-step explanation:

[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,

Answer:

66

Step-by-step explanation:

30+25+5+6 = 66.

There are 66 students in the class.

Answer:

[tex] z=\frac{x- \mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{425-500}{75}= -1[/tex]

And we can calculate this probabilit using the normal standard distribution or excel and we got:

[tex] P(z<-1)= 0.159[/tex]

Step-by-step explanation:

If we define the random variable of interest "the amount spent by a family of four of food per month" and we know the following parameter:

[tex] \mu = 500, \sigma = 75[/tex]

And we want to find the following probability:

[tex] P(X<425)[/tex]

And we can use the z score formula given by:

[tex] z=\frac{x- \mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{425-500}{75}= -1[/tex]

And we can calculate this probabilit using the normal standard distribution or excel and we got:

[tex] P(z<-1)= 0.159[/tex]

Answer:

Step-by-step explanation:

Area of triangle = 1/2 × b × h

69.3 = 8.4 × h

h = 69.3 / 8.4

h = 8.25 mm

hope this helps

plz mark as brainliest!!!!!!

Answer:

16.5mm

Step-by-step explanation:

1. 69.3 x 2

2. 138.6 divided by 8.4

3. solve which equals 16.5mm

Hope this helps you:)

Answer:

Volume of a cylinder is πr²h

Where

r is the radius

h is the height

Volume = 154cm³

radius = 3cm

height = ? cm

154 = π × 3² × h

154 = π × 9 × h

154 = 9πh

divide both sides by 9π

h = 154/9π

h = 5.4cm

Height is 5.4cm

Hope this helps

Answer:

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Step-by-step explanation:

Let the hotel charge in the first city be x and in the second city be y.

Given that the hotel charge before tax in the second city was $ 1500 higher than in the first. That can be written as:

[tex]y - x = \$1500[/tex] ...[1]

The tax in the first city was 5 %, and the tax in the second city was 8.5 %.

The total hotel tax paid for the two cities was $ 836.25

5% of x + 8.5% of y = $836.25

[tex]0.05x+0.085y=\$836.25[/tex]...[2]

Now putting value of y from [1] in to [2]:

[tex]y = \$1500+x[/tex]

[tex]0.05x+0.085\times (\$1500+x)=\$836.25[/tex]

On solving we get :

x = $5,250

Using vakue of x in [1] to find y:

[tex]y=\$1500+\$5,250=\$ 6,750[/tex]

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Answer:

Option (3)

Step-by-step explanation:

Glide reflection of a figure is defined by the translation and reflection across a line.

To understand the glide rule in the figure attached we will take a point A.

Coordinates of the points A and A' are (2, -1) and (-2, 4).

Translation of pint A by 5 units upwards,

Rule to be followed,

A(x, y) → A"[x, (y + 5)]

A(2, -1) → A"(2, 4)

Followed by the reflection across y-axis,

Rule to be followed,

A"(x, y) → A'(-x, y)

A"(2, 4) → A'(-2, 4)

Therefore, by combining these rules in this glide reflections of point A we get the coordinates of the point point A'.

Option (3) will be the answer.

Answer:Reflection along the line y= -1

Step-by-step explanation:

took test

Answer:

Step-by-step explanation:

p/100* 400=80

*100               *100

400p=8000

:400     :400

p=20

With 5% significant level I think we consider that 22% likes the drink

Answer:

Step-by-step explanation:

33.3%

19.4%

Answer:

answer D

Step-by-step explanation:

Hello

(fog)(x)=f(g(x))=|4x+9|

so g(x)=4x+9

and f(x)=|x|

hope this helps

Answer:

$14.034

Step-by-step explanation:

40/10 means that the price has a 40% discount and then, a 10% discount from what is left. To calculate the net price, first you have to calculate the price with the 40% discount:

25.99*(1-0.4)= 15.594

Then, you have to calculate the price with the 10% discount:

15.594*(1-0.1)= 14.034

According to this, the net price is $14.034.

Answer:

x + (4x-85) = 90

Step-by-step explanation:

The two angles are complementary which means they add to 90 degrees

x + (4x-85) = 90

Answer: A

Step-by-step explanation:

Both angles are makes a right angle which adds up to 90 degrees so they both have to add up to 90 degrees.

Answer:

see below

Step-by-step explanation:

Modified problem

(x)^2-3/x

Step 1: Find f(x+h)

(x+h)^2-3/(x+h)

x^2 +2hx + h^2 -3/(x+h)

Step 2: Find f(x + h) − f(x)

x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)

Distribute the minus sign

x^2 +2hx + h^2 -3/(x+h) -  x^2+3/x

Combine like terms and get a common denominator

2hx + h^2  -3x/(x(x+h)) +3(x+h)/(x(x+h)

2hx + h^2  +3h/(x(x+h))

Step 3: Find (f(x + h) − f(x))/h

(2hx + h^2+3h/(x(x+h)) )/h

2hx/h  + h^2/h+3h/(x(x+h)) /h

2x +h +3/(x(x+h))

Step 4: Find lim  h→0  (f(x + h) − f(x))/h

2x+0 +3/(x(x+0))

2x +3/x^2

Hey there! :)

Answer:

y = 7/2x - 11

Step-by-step explanation:

Use the slope formula to calculate the slope:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates:

[tex]m = \frac{10-(-4)}{6-2}[/tex]

Simplify:

[tex]m= \frac{14}{4}[/tex]

[tex]m = \frac{7}{2}[/tex]

Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:

10 = 7/2(6) + b

10 = 42/2 + b

10 = 21 + b

10 - 21 = b

b = -11.

Write the equation:

y = 7/2x - 11

Volume before the gold:

3 x 2 x 4 = 24 cubic cm.

Volume after gold:

3 x 2 x 4.25 = 25.5 cubic cm

Volume of gold is the difference:

25.5 - 24 = 1.5 cubic cm.

Answer:

0.006772

If the last dropping digit is less than 5 then it will be ignored

0.00677

if the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.0068

if  the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.007

if  the last dropping digit is greater than 5 than the the last retained digit increases by 1

0.01

if the last digit is less than 5 so it will be ignored

0.0 is significant figure because zero to the right of decimal point are significant

Step-by-step explanation:

i hope this will help you :)

Answer:

0.007

Step-by-step explanation:

Rounding off 0.006772 to 1 significant figures:

=> 0.007

There is only 1 significant figure in this , since the zeroes on the left are not counted as significant figures.

Answer:

Length = 4x+5

Breadth = 3x

Area = l × b

= (4x+5) × 3x

= 12 x² + 15 x

Answer:

7120

Step-by-step explanation:

Answer:

[tex] X \sim Binom (n=38, p=2/5)[/tex]

By properties the mean is given by:

[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]

Step-by-step explanation:

For this case we know that the random variable follows a binomial distribution given by:

[tex] X \sim Binom (n=38, p=2/5)[/tex]

By properties the mean is given by:

[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]

Answer:

Step-by-step explanation:

Slope:  

− 1

y-intercept:  

23

Answer:

[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]

Step-by-step explanation:

From the given information:

we are to find the first four nonzero terms of the Maclaurin series of the given function.

Sec x.

If we recall ; we will realize that the derivative of sec x = [tex]\dfrac{1 }{cos \ x}[/tex]

Also; for cos x ; the first four terms of its Maclaurin Series can be expressed as ;

=[tex]1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}+...[/tex]

However, using the long division method: we have;

[tex]\dfrac{1}{1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}}[/tex]

the rule of the long division method is to first use the 1 from the denominator to divide the 1 from the numerator. the multiply it with the answer we get which is (1) before subtracting it from  that answer (1).

i.e

1/1 = 1

1 × 1 = 1

1 - 1 = 0

Afterwards; we will subtract the remaining integers from this numerator.

So, we have:

[tex]\dfrac{-(1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!} )}{0+ \dfrac{x^2}{2!}-\dfrac{x^4}{4!}+ \dfrac{x^6}{6!}}[/tex]

We are going to apply the same process to the remainder [tex]\dfrac{x^2}{2!}[/tex];

which is to divide the second integer with 1

[tex]\dfrac{\dfrac{x^2}{2!}}{1}= \dfrac{x^2}{2!}[/tex]

Then we will multiply the numerator with [tex]\dfrac{x^2}{2!}[/tex] ; the result will then be subtracted from the polynomial.

[tex]= \dfrac{-( \dfrac{x^2}{2!} - \dfrac{x^4}{2! 2!} + \dfrac{x^6}{2! 4!}- \dfrac{x^8}{2! 6!}) }{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }[/tex]

Repeating the same process for remainder  [tex]\dfrac{5}{24}x^4[/tex]; we have:

[tex]\dfrac{ \dfrac{5}{24}x^4 }{1}= \dfrac{5}{24}x^4[/tex]

so; we will need to multiply 1 with [tex]\dfrac{5}{24}x^4[/tex] and subtract it from the rest of the polynomial

[tex]=\dfrac{{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }}{ 1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]

[tex]= \dfrac {- ( \dfrac{5}{24}x^4 -\dfrac{5}{2!4!}x^6 - \dfrac{5x^8}{4!4!} - \dfrac{5x^{10}}{6!4!} } {0+ \dfrac{61}{720}x^6}[/tex]

Here ; the final remainder is [tex]\dfrac{61}{720}x^6}[/tex]; repeating the usual process for long division method; we have:

[tex]\dfrac{\dfrac{61}{720}x^6}{1}= \dfrac{61}{720}x^6}[/tex]

So;

[tex]= \dfrac{0+ \dfrac{61}{720}x^6}{1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]

[tex]= \dfrac{-( \dfrac{61}{720}x^6)}{0 }[/tex]

Now the  first four nonzero terms of the Maclaurin series is the addition of all the integers used as remainders ; i.e

[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]

Answer:

Step-by-step explanation:

Hello!

(a) Which genre has the highest mean audience score? The lowest mean audience score?

1) Action [tex]\frac{}{X}_1[/tex]= 58.63

2) Comedy [tex]\frac{}{X}_2[/tex]= 59.11

3) Drama [tex]\frac{}{X} _3[/tex] = 72.10

4) Horror [tex]\frac{}{X}_4[/tex]= 48.65

The lowest mean score is  [tex]\frac{}{X}_4[/tex]= 48.65

The highest mean score is  [tex]\frac{}{X} _3[/tex] = 72.10

(b) Which genre has the highest median score? The lowest median score?

1) Action Me₁= 51.00

2) Comedy Me₂= 58.00

3) Drama Me₃= 72.00

4) Horror Me₄= 52.00

The Lowest median is Me₁= 51.00

The Highest median is Me₃= 72.00

(c) In which genre is the lowest score, and what is that score? In which genre is the highest score, and what is that score?

Lowest or minimum scores:

1) Action 32.00

2) Comedy 31.00

3) Drama 46.00

4) Horror 25.00

The genre with the lowest score is "Comedy"

Highest or maximum scores:

1) Action 93.00

2) Comedy 93.00

3) Drama 91.00

4) Horror 78.00

There are two genres with the highest score "Action" and "Comedy"

(d) Which genre has the largest number of movies in that category?

The number of movies for each category corresponds to the sample sizes:

1) Action n₁= 32

2) Comedy n₂= 27

3) Drama n₃= 21

4) Horror n₄= 17

The largest number of movies sampled was for the genre "Action"

(e) Calculate the difference in mean score between comedies and horror movies, and give notation with your answer, using i, for the mean comedy score and, for the mean horror score.

Comedy [tex]\frac{}{X}_C[/tex]= 59.11

Horror [tex]\frac{}{X}_H[/tex]= 48.65

[tex]\frac{}{X}_C[/tex] -  [tex]\frac{}{X}_H[/tex]= 59.11 - 48.65= 10.46

I hope this helps!

Answer:

1. 51°

2. 40°

3. 65°

4. 60°

Step-by-step explanation:

The sum of the angles in a triangle is 180°. We can use the angles given to find the missing angle.

1. 51°

42+87+x=180

129+x=180

x=51

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

2. 40°

110+30+x=180

140+x=180

x=40

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

3. 65°

20+95+x=180

115+x=180

x=65

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

4. 60°

60+60+x=180

120+x=180

x=60

Answer:

See below.

Step-by-step explanation:

Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]

We know that the diameter is 14, so the radius is 7.

Plug it into the equation:

[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]

Answer:

The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.

Step-by-step explanation:

The distance between the rocket and the satellite, in feet, after t seconds, is given by the following equation:

[tex]P(t) = 9t^{2} + 34[/tex]

Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.

This is P(10).

[tex]P(t) = 9t^{2} + 34[/tex]

[tex]P(10) = 9*(10)^{2} + 34 = 934[/tex]

The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.

Answer:

100

Step-by-step explanation:

The Volume of the Rectangular prism on the left is 60

The Volume of the Rectangular prism on the right is 40

Answer:

Your correct answer is 40

Step-by-step explanation:

Multiply 8 x 5.

8 x 5 = 40

MUltiply 40 x 1.

40 x 1 = 40

So, it stays the same. Anything multiplied by 1 stays the same.

Therefore, your correct answer is 40.

Answer:

$25.00 + $10x = $115.00

Step-by-step explanation:

We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.

Answer:

True

Step-by-step explanation:

The multiple of 3 is the product of 3 with at least a number. Following the law of indices which states that

aⁿ * bⁿ = (ab)ⁿ

Then the cube of 3 and any number which results in a multiple of 3  gives a result that has 3 cube which is 27 as a factor.

Hence the answer is true

Answer:

$10452958

Step-by-step explanation:

Initial profit = $11900848

Fall rate= $48263 per year

Equation:

where P(x)= profit at year of x, and 1990<x<2020

Answer:

Step-by-step explanation:

Assume that f(x) = 0 for x outside the interval [4,9]. We will use the following

[tex]E[X^k] = \int_{4}^{9}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}^{9}\frac{1}{5}dx = \frac{9^2-4^2}{2\cdot 5} = \frac{13}{2}[/tex]

[tex]E[X^2] = \int_{4}^{9}\frac{x^2}{5}dx = \frac{9^3-4^3}{3\cdot 5} = \frac{133}{3}[/tex]

Then, [tex]Var(x) = \frac{133}{3}-(\frac{13}{2})^2 = \frac{25}{12}[/tex]

Then the standard deviation is [tex]\frac{5}{2\sqrt[]{3}}[/tex]

Possibilities Density Functions are a set of data measures that can be used to anticipate that a discontinuous value will turn out as the following calculation:

Given function= [tex]\frac{1}{5}[/tex]

interval= [4,9]

Assuming that the given function that is [tex]fx) = 0[/tex] .

For this, the x outside the interval is [4,9].

Equation:

[tex]E[X^k] = \int^{9}_{4} x^k\ f(x) \ dx\\\\[/tex]

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

The values are:

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

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

Solving the equation then:

[tex]E[X] =\int^{9}_{4} \frac{1}{5}\ dx[/tex]

         [tex]= \frac{9^2-4^2}{2\cdot 5} \\\\ = \frac{81-16}{10} \\\\ = \frac{65}{10} \\\\=\frac{13}{2} \\\\[/tex]

[tex]E[X^2] =\int^{9}_{4} \frac{x^2}{5}\ dx[/tex]

          [tex]= \frac{9^3-4^3}{3\cdot 5} \\\\= \frac{729-64}{15} \\\\ = \frac{665}{15}\\ \\=\frac{133}{3} \\\\[/tex]

[tex]\to Var(x) = \frac{133}{3} - (\frac{13}{2})^2 = \frac{25}{12}\\\\[/tex]

Therefore the standard deviation value is [tex]\frac{5}{2\sqrt{3}}[/tex]

Find out more about the probability here:

brainly.com/question/11234923