Beginning at 8:30 A.M., tours of the National Capitol and
the White House begin at a tour agency. Tours for the
National Capitol leave every 15 minutes. Tours for the
White House leave every 20 minutes.

a) How often do the tours leave at the same time?


b) When is the next time the two tours will leave at
the same time?

Answer:

3/5

Step-by-step explanation:

1/10+1/20=3/5

Answer:

[tex]y=x+3[/tex]

Step-by-step explanation:

What we need to know

1) Rewrite the equation x - y = 5 into slope-intercept form and identify the slope

[tex]x - y = 5[/tex]

Subtract both sides by x

[tex]x - y -x= -x+5\\-y= -x+5[/tex]

Divide both sides by -1

[tex]y= x-5[/tex]

Now, we can tell clearly that the slope (m) of this line is 1. Therefore, a line parallel to this would also have a slope of 1.

Plugging 1 as m into [tex]y=mx+b[/tex], we get:

[tex]y=x+b[/tex]

2) Find the y-intercept (b) of the line parallel to [tex]y= x-5[/tex] and find the final equation

[tex]y=x+b[/tex]

Plug in the given point (-5,-2)

[tex]-2=-5+b[/tex]

Add 5 to both sides

[tex]-2+5=-5+b+5\\3=b[/tex]

Therefore, the y-intercept of this line is 3. Now, plugging this back into our original equation, we get:

[tex]y=x+b\\y=x+3[/tex]

I hope this helps!

Answer:

36

Step-by-step explanation:

Answer: The required z-score = 1.25

Step-by-step explanation:

Let x be a random variable that denotes the scores in the exam.

The formula for z-score = [tex]\dfrac{X-\text{mean}}{\text{standard deviation}}[/tex]

As per given, we have

X= 625, mean=500, standard deviation = 100

Z-score = [tex]\dfrac{625-500}{100}[/tex]

i.e. Z-score = [tex]\dfrac{125}{100}[/tex]

i.e. Z-score =1.25

Hence, the required z-score = 1.25

Answer:

B

Step-by-step explanation:

find slope which is -2 then plug into equation y=mx+b to find constant of 3

Answer:

Step-by-step explanation:

Answer:

line 2

Step-by-step explanation:

on line 2 the two minuses at the end turn into a + (where the -2 is there should be a +2) because - x - = +

Answer:

(-9, 14)

Step-by-step explanation:

Let the column vector be represented as a = (3, 4) and b = (5, -2)

2a = 2(3,4)

2a = (6,8)

3b = 3(5, -2)

3b = (15, -6)

Take the difference 2a - 3b

2a - 3b = (6,8) - (15, -6)

2a - 3b = (6-15, 8 -(-6))

2a - 3b = (-9, 14)

Hence the column vector is (-9, 14)

We want to find 2a - 3b as a column vector, we will get:

[tex]2a - 3b = \left[\begin{array}{ccc}-9\\14\end{array}\right][/tex]

So we want to perform a sum (difference actually) of vectors, we have that:

[tex]a = \left[\begin{array}{ccc}3\\4\end{array}\right] \\\\\\b= \left[\begin{array}{ccc}5\\-2\end{array}\right][/tex]

Remember that when we multiply a vector by a scalar, each component gets multiplied by that scalar, so we have:

[tex]2a = \left[\begin{array}{ccc}2*3\\2*4\end{array}\right] = \left[\begin{array}{ccc}6\\8\end{array}\right] \\\\\\3b= \left[\begin{array}{ccc}3*5\\3*-2\end{array}\right] = \left[\begin{array}{ccc}15\\-6\end{array}\right][/tex]

Now we just perform the direct difference:

[tex]2a - 3b = \left[\begin{array}{ccc}6\\8\end{array}\right] - \left[\begin{array}{ccc}15\\-6\end{array}\right] = \left[\begin{array}{ccc}6 - 15\\8 + 6\end{array}\right] = \left[\begin{array}{ccc}-9\\14\end{array}\right][/tex]

If you want to learn more, you can read:

https://brainly.com/question/10435343

Answer:

Step-by-step explanation:

A Venn diagram depicts the logical relationships between two or more sets of elements by using alternating circles or other shapes. They're often used to visually arrange information, showing how objects are similar and different. In the fields of mathematics and statistics, Venn diagrams, also known as "set diagrams" or "logic diagrams," are commonly used.

From the given information:

Since we are to represent the given question into a Venn diagram, the diagram is being attached in the image below.

From the image below, we represent:

P =students that played Paino

G = students that played guitar

F = students that played flute

P = 50

G = 68

F = 59

(PUG) -35

(PUF) = 59

(GUF) = 40

since the value of (PUGUF) is not given, we represent it with x.

See the attached image below for diagrammatic representation of the Venn diagram.

Answer:

3840in²

Step-by-step explanation:

Formula:

V = whl

Insert the values:

V = 20 * 16 * 12

Multiply the values:

V = 3840in²

Answer:

Vivian will have to get a loan, and pay back the money she spent with her debit card. If she cannot pay back this loan in time, the interest will grow higher and higher. Using a debit card is NOT good because if you don't have the money for something and you buy it anyway, you'll have to pay back double the money if you miss the deadline for the loan.

Answer:

(1,1) and (2,-4)

Step-by-step explanation:

i supposed each line is 1,2,3,4,5 because it is not given the graph numbers but I hope it could help

Answer:

Step-by-step explanation:

pi r^2 for area

pi 35^2

pi1225= about 3848.45

2pi r for circumference

2pi35

pi70= about 219.9

Answer:

3y+8=3y+8

Step-by-step explanation:

10+3y-2=4y-y+8

10+3y-2 combine 10 and -2 and you get 3y+8

4y-y+8 combine the 4y with the -y and you get 3y+8

3y+8=3y+8

Answer:

1/3

Step-by-step explanation:

Answer: 2/5 (1/3 + 1/2) = 1/3 ≅ 0.3333333

Step-by-step explanation:

Answer:

2%

Step-by-step explanation:

Hello, to find the percentage of 8 and 400, you simply divide 8 over 400 and you get 2%.

Answer:

2%

Step-by-step explanation:

[tex]\frac{8}{400} =\frac{y}{100}[/tex]

Cross multiply.

400y = 800

400y ÷ 400 = 800 ÷ 400

y = 2

Answer:

the answer is 1

Step-by-step explanation:

I hope this was helpful

Answer: y/3x

Step-by-step explanation: 3 times x is 3x, so y/3x

Answer:

For example number 1 is A(-3,5), so on the graph you will go over -3 spaces to the left. Then for 5 you will go up on the graph. Your going up on the graph because it is a positive number. Then the A will be 3 spaces over from positive 5.

Step-by-step explanation:

Hope this helped :)

Answer:

The height of the tank is 0.5 yards.

Step-by-step explanation:

To determine what is the height, in yards, of a cylindrical water tank that holds 1,884 cubic yards of water and has a diameter of 120 feet, knowing that the volume of a cylinder is equal to pi multiplied by the radius squared, multiplied by the height, the following calculation must be done:

1 foot = 0.3333 yards

R = Diameter / 2

R = 120/2 = 60

3.14 x 60 ^ 2 x H = 1,884

3.14 x 3,600 x H = 1,884

3.14 x 1,200 x H = 1,884

3.768 x H = 1.884

H = 1,884 / 3,768

H = 0.5

Therefore, the height of the tank is 0.5 yards.

Answer:

14

Step-by-step explanation:

because the sum of the 2 smaller side have to add up to greater than the larger side

x+4 > 17

x > 13

14 is the next biggest whole number

Answer:

its a right angle and the area of it is 24

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

the sign flips when you divide or multiply one

Answer:

B.

Step-by-step explanation:

4x-8>(with a line underneath)12

-8 -8

4x>(with a line underneath)12

/4 /4

x>(with a line underneath)3

It stays the same because you aren't dividing or multiplying by a negative. Only a negative will cause you to flip the inequality sign.

Answer:

A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers.

Step-by-step explanation:

Answer:

Answer:16

Step-by-step explanation: 2x2 is 4

4x4. Is 16w

W stand for width

Step-by-step explanation:

Answer:

12(6)/2

B: 36

Step-by-step explanation: