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3 years ago

Mark can type 44 words in 2 minutes. Which of the following is equivalent to that rate?

Mathematics

1 answer:

allochka39001 [22]3 years ago

6 0

Answer:

D. 132 words in 6 minutes

Step-by-step explanation:

First, find the amount of words Mark can type in one minute:

44/2 = 22

Mark can type 22 words in 1 minute.

Next, solve by multiply each minute with words per minute to get the total words.

For choice D):

6 x 22 = 132

D) is your answer.

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The school that Joe goes to is selling tickets to a choral performance. On血e first day of ticket

ArbitrLikvidat [17]

Answer:

The price of one senior citizen ticket is $8, and the price of one child ticket is $11.

Step-by-step explanation:

You are looking for two things: the price of a senior citizen ticket and the price of a child ticket.

We need to write two equations using two variables.

Let s = price of 1 senior citizen ticket.

Let c = price of 1 child ticket.

First day of ticket sales:

6 senior citizen tickets, 8 child tickets, total sales of $136

Since s is the price of a senior citizen ticket, 6 tickets cost 6s.

Since c is the price of a child ticket, 8 tickets cost 8c.

The total sales is 6s + 8c.

The total sales is $136, so our first equation is

6s + 8c = 136

Now we do the same for the second day of ticket sales.

6 senior citizen tickets, 9 child tickets, total sales of $147.

Since s is the price of a senior citizen ticket, 6 tickets cost 6s.

Since c is the price of a child ticket, 9 tickets cost 9c.

The total sales is 6s + 9c.

The total sales is $147, so our second equation is

6s + 9c = 147

The system of equations is

6s + 8c = 136

6s + 9c = 147

Multiply both sides of the first equation by -1. Write the second equation below it. Then add the equations.

-6s - 8c = -136

(+) 6s + 9c = 147

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

c = 11

c = 11, so the cost of a child ticket is $11.

Now substitute 11 for c in the first equation, and solve for s.

6s + 8c = 136

6s + 8(11) = 136

6s + 88 = 136

6s = 48

s = 8

The price of a senior citizen ticket is $8.

The price of a senior citizen ticket is $8, and the price of a child ticket is $11.

6 0

3 years ago

the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a fr

Naily [24]

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\begin{array}{llll}
\stackrel{frequency}{f}\textit{ of a vibrating string varies directly}\\
\qquad \qquad \textit{with the square root of the tension }\stackrel{tension}{t}
\end{array}$

$\bf f=k\sqrt{t}\quad \textit{we also know that }
\begin{cases}
f=300\\
t=8
\end{cases}\implies 300=k\sqrt{8}
\\\\\\
\cfrac{300}{\sqrt{8}}=k\implies \cfrac{300}{\sqrt{2^2\cdot 2}}=k\implies \cfrac{300}{2\sqrt{2}}=k\implies \cfrac{150}{\sqrt{2}}=k
\\\\\\
\textit{and we can \underline{rationalize} it to }\cfrac{150\sqrt{2}}{2}\implies 75\sqrt{2}=k$

$\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\
-------------------------------\\\\
\textit{now, when t = 72, what is \underline{f}?}\qquad f=75\sqrt{2(72)}$

5 0

4 years ago

Read 2 more answers

If y = kx, what is the value of k if y = 20 and x = 0.4?

True [87]

Set up an equation 20=k(0.4)....to find k divide 20 by 0.4

8 0

3 years ago

2) Dorothy types 120 words per minute. How many words does Dorothy type in

Damm [24]

Answer:

D (210)

Step-by-step explanation:

120 times 1.75 equals 210

6 0

3 years ago

Read 2 more answers

AB is tangent to circle D. Find the value of x.

Svet_ta [14]

Answer:

c 15

Step-by-step explanation:

Tangent AB is tangent to circle D at point A. The angle made by a tangent to a circle and a radius of the circle at the point of tangency is a right angle. That means that angle is a right angle, and triangle ABD is a right triangle.

We can use the Pythagoren theorem.

a^2 + b^2 = c^2

x^2 + 20^2 = (x + 10)^2

x^2 + 400 = (x + 10)(x + 10)

x^2 + 400 = x^2 + 10x + 10x + 100

400 = 20x + 100

20x = 300

x = 15

6 0

3 years ago