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3 years ago

11

Dana is the campaign manager for a candidate for governor. Through a commissioned poll, she discovers that the candidate's appro

val rating has changed from 70 to 88 percentage points, a gain of 18 percentage points. What was the percent change for the candidate's approval rating?

1 answer:

aleksley [76]3 years ago

3 0

Answer:

25.71%

Step-by-step explanation:

Although the first instinct would be to say that his approval rating changed by 18%, the actual percent change for the candidate's approval rating is given by the difference between both polls (18%) divided by the candidate's approval in the first poll (70%):

$P=\frac{18}{70} =0.2571=25.71\%$

The percent change for the candidate's approval rating was 25.71%

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Steve,Jerry and Ron were paid $29.25 to remove garden gnomes. They each worked 4 hours, exempt for Ron, who was 1 hour late. How

Alenkasestr [34]

Ron should receive $7.98. Jerry and Steve each worked for 4 hours, while Ron was one hour late, so he worked for 3 hours. Together, they worked for 4*2+3=11 hours, receiving $29.25 in total. Each hour should be paid 29.25/11=2.66 dollars. Ron worked for three hours, so he should receive 3*2.66=7.98 dollars.

5 0

4 years ago

The diagram shows how cos θ, sin θ, and tan θ relate to the unit circle. Copy the diagram and show how sec θ, csc θ, and cot θ r

DIA [1.3K]

<span>Copy the diagram and show how sec θ, csc θ, and cot θ relate to the unit circle.

The representation of the diagram is shown if Figure 1. There's a relationship between </span>sec θ, csc θ, and cot θ related the unit circle. Lines green, blue and pink show the relationship.

a.1 First, find in the diagram a segment whose length is sec θ.

The segment whose length is sec θ is shown in Figure 2, this length is the segment $\overline{OF}$ , that is, the line in green.

a.2 <span>Explain why its length is sec θ.

We know these relationships:

(1) $sin \theta=\frac{\overline{BD}}{\overline{OB}}=\frac{\overline{BD}}{r}=\frac{\overline{BD}}{1}=\overline{BD}$

(2) </span> $cos \theta=\frac{\overline{OD}}{\overline{OB}}=\frac{\overline{OD}}{r}=\frac{\overline{OD}}{1}=\overline{OD}$
<span>
(3) </span> $tan \theta=\frac{\overline{FD}}{\overline{OC}}=\frac{\overline{FC}}{r}=\frac{\overline{FC}}{1}=\overline{FC}$
<span>
Triangles </span>ΔOFC and ΔOBD are similar, so it is true that:

$\frac{\overline{FC}}{\overline{OF}}= \frac{\overline{BD}}{\overline{OB}}$ <span>

</span>∴ $\overline{OF}= \frac{\overline{FC}}{\overline{BD}}= \frac{tan \theta}{sin \theta}= \frac{1}{cos \theta} \rightarrow \boxed{sec \theta= \frac{1}{cos \theta}}$ <span>

b.1 </span>Next, find cot θ

The segment whose length is cot θ is shown in Figure 3, this length is the segment $\overline{AR}$ , that is, the line in pink.

b.2 <span>Use the representation of tangent as a clue for what to show for cotangent.
</span>
It's true that:

$\frac{\overline{OS}}{\overline{OC}}= \frac{\overline{SR}}{\overline{FC}}$

But:

$\overline{SR}=\overline{OA}$
$\overline{OS}=\overline{AR}$

Then:

$\overline{AR}= \frac{1}{\overline{FC}}= \frac{1}{tan\theta} \rightarrow \boxed{cot \theta= \frac{1}{tan \theta}}$

b.3 Justify your claim for cot θ.

As shown in Figure 3, θ is an internal angle and ∠A = 90°, therefore ΔOAR is a right angle, so it is true that:

$cot \theta= \frac{\overline{AR}}{\overline{OA}}=\frac{\overline{AR}}{r}=\frac{\overline{AR}}{1} \rightarrow \boxed{cot \theta=\overline{AR}}$

c. find csc θ in your diagram.

The segment whose length is csc θ is shown in Figure 4, this length is the segment $\overline{OR}$ , that is, the line in green.

3 0

4 years ago

a cookie baker has an automatic mixer that turns out a sheet of dough in the shape of a square 12 inches wide. His cookie cutter

iragen [17]

Answer:

All the sizes that satisfy $kd^2 =144$

Step-by-step explanation:

To answer this question we first need to find the minimum wasted area of the dough.

Let us call the diameter of the cookie $d$ , and $a$ the length of the dough sheet, then the $n$ number of cookies that fit into length $a$ will be

$n = \dfrac{a}{d}$

and therefore, the number that will fit into the whole square sheet will be

$n^2 = \dfrac{a^2}{d^2}$

Since the area of each cookie is

$A = \pi \frac{d^2}{4}$

the area of n^2 cookies will be

$A_n = n^2\pi \frac{d^2}{4}$ ,

which is the area of all the cookies cut out from the dough sheet; therefore, after the cutting, the area left will be

(1). $\text{area left}= a^2-n^2\pi \frac{d^2}{4}$

putting in the value of $n^2$ we get

$a^2- \dfrac{a^2}{d^2}\pi \frac{d^2}{4}$

which simplifies to

area left = a^2( 1 - (π/4))

putting in a = 12 we get

area left = 30.902 in^2.

Going back to equation (1) we find that

a^2-n^2(πd^2/4) =30.902

12^2- n^2(πd^2/4) =30.902

and if we call k = n^2, we get

12^2- k(πd^2/4) =30.902

113.098 = k(πd^2/4)

simplifiying this gives

kd^2 = 144.

As a reminder, k here is the number of cookies cut from the dough sheet.

Hence, our cookie diameter must satisfy kd^2 = 144,<em> meaning larger the diameter of the cookies less of the should you cut out to satisfy the above equality. </em>

8 0

4 years ago

Evaluate.<br> <br> [4•4 ÷ (2 + 3 • 2)] + [4 • (36 – 5•5

Vladimir [108]

The answer your looking for is 46

5 0

4 years ago

Read 2 more answers

Factor 2x^2+5x+3<br> plz explain your answer

Leno4ka [110]

(x+1)(2x+3)
Hope this helps you

4 0

3 years ago