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3 years ago

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The manager of a store increases the price of the bathing suits by 7%. Let t be the original price of a bathing suit. The new pr

ice is t + 0.07t. A. Find an expression equivalent to t + 0.07t.

1 answer:

Dvinal [7]3 years ago

3 0

Answer:

$t+0.07t=t(1+0.07)=t(1.07)=1.07t$

Step-by-step explanation:

There are a couple of equivalent expressions to the function $t+0.07t$ . For example:

$t+0.07t$

Factor:

$t+0.07t=t(1+0.07)$

If you add the terms inside the parentheses:

$t(1+0.07)=t(1.07)$

Basically you can add the like terms from the start and get the same result.

$t+0.07t=1.07t$

Therefore:

$t+0.07t=t(1+0.07)=t(1.07)=1.07t$

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Daryl invested $2,200 for 3 years. He received interest of $264. What was the interest rate?

Klio2033 [76]

Answer:

4%

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

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2 years ago

Maya spent 40% of her savings on a bike it cost her $85 how much money does she have left

shusha [124]

Let be Z the money ;
We have ( 40 / 100 ) x Z = $85 ;
( 4 / 10 ) x Z = $85 ;
( 2 / 5 ) x Z = $85 ;
Z = $( 85 x 5 ) ÷ 3 ;
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3 years ago

64% of US adults have very little confidence in newspapers you randomly select 10 US adults find the probability that the number

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Answer:

A) 0.1636

B) 0.7292

C) 0.0305

Step-by-step explanation:

This is a binomial probability distribution question that follows;

P(X = x) = nCx × p^(x) × q^(n - x)

In this case, p = 64% = 0.64

q = 1 - p = 1 - 0.64 = 0.36

Thus;

A) P(exactly 5) = P(5) = 10C5 × 0.64^(5) × 0.36^(10 - 5) = 0.1636

B) P(at least 6) = P(x ≥ 6) = P(6) + P(7) + P(8) + P(9) + P(10)

P(6) = 10C6 × (0.64^(6)) × (0.36^(10 - 6)) = 0.2424

P(7) = 10C7 × (0.64^(7)) × (0.36^(10 - 7)) = 0.2462

P(8) = 10C8 × (0.64^(8)) × (0.36^(10 - 8)) = 0.1642

P(9) = 10C9 × (0.64^(9)) × (0.36^(10 - 9)) = 0.0649

P(10) = 10C10 × (0.64^(10)) × (0.36^(10 - 10)) = 0.0115

Thus;

P(x ≥ 6) = 0.2424 + 0.2462 + 0.1642 + 0.0649 + 0.0115

P(x ≥ 6) = 0.7292

C) P(x < 4) = P(0) + P(1) + P(2) + P(3)

From online binomial probability calculator, we have;

P(x < 4) = 0.0305

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3 years ago

A cereal company is exploring new cylinder-shaped containers. Two possible containers are shown in the diagram.x is 6 and r=4.5

KatRina [158]

Answer:

Container $\rm X$ will have less label area than container $\rm Y$ by about $9\; \rm in$ .

Step-by-step explanation:

A rectangular sheet of paper can be rolled into a cylinder. Conversely, the lateral surface of a cylinder can be unrolled into a rectangle- without changing the area of that surface.

Indeed, the width of that rectangle will be the same as the height of the cylinder. On the other hand, the length of that rectangle should be exactly equal to the circumference of the circles on the top and the bottom of the cylinder. In other words, if a cylinder has a height of $h$ and a radius of $r$ at the top and the bottom, then its lateral surface can be unrolled into a rectangle of width $h$ and length $2\,\pi\, r$ .

Apply this reasoning to both cylinder $\mathrm{X}$ and $\rm Y$ :

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The width of the rectangle will be $6\; \rm in$ , while
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That corresponds to a lateral surface area of $54\, \pi\; \rm in^2$ .

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The width of the rectangle will be $10.5\; \rm in$ , while
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That corresponds to a lateral surface area of $63\,\pi \; \rm in^2$ .

Therefore, the lateral surface area of cylinder $\rm X$ is smaller than that of cylinder $\rm Y$ by $9\,\pi\; \rm in^2$ .

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