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matrenka [14]
3 years ago
11

As part of a school contest, Sarah and Luis are playing a math game. Sarah must pick a number between 1 and 50 and Luis clues so

he can write an equation to find her number. Sarah says, " if I subtract 5 from my number, multiply that equality by 4, and then add 7 to the result, I get 35." What equation can Luis write based on Sarah's clues and what is Sarah's number?
Mathematics
2 answers:
nadezda [96]3 years ago
4 0
If x is Sarahs number then
(x-5)×4+7=35
subtract 7 from both sides
4(x-5)=28
divide by 4 on both sides
x-5=7
add 5 to both sides
x=12
harina [27]3 years ago
3 0

Answer:

Sarah's number is 12.

Step-by-step explanation:

First you would take Sarah's solution number, which is 35 , and do the opposite of everything that adds up to it.

i.e 35-7=28

28/4=7

7+5=12

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The table shows claims and their probabilities for an insurance company.
Dafna1 [17]

Answer:

a) Expected Value of Claims = $32,000

b) Average premium per claim, in order to break-even on claim costs

= $5,333.33

c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:

= $5,393.33 per policy

Step-by-step explanation:

a) Data and Calculations:

Amount of Claim      Probability   Expected Value

$0                               0.60             $0

$50,000                     0.25             $12,500

$100,000                   0.09                 9,000

$150,000                   0.04                 6,000

$200,000                  0.01                 2,000

$250,000                 0.01                 2,500

Expected Cost of claims =          $32,000

b) Average premium per claim, in order to break-even on claim costs

= Total Claim cost divided by number of policies

= $32,000/6 = $5,333.33

c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:

Total Claim cost + Total profit / 6 or Average Premium plus Profit per policy =

= ($32,000 + $360)/6 or $5,333.33 + $60

= $32,360/6 or $5,393.33

= $5,393.33

6 0
2 years ago
The number 0.9 is a(n) __________ number.
BigorU [14]
I just did it and it was rational
5 0
3 years ago
The vertex is (-8,- 4) and the parabola opens up.<br> The domain of f is?
sveticcg [70]
Domain is the left and right values, which means any parabola opening up or down will have a domain of (-∞, ∞)
7 0
2 years ago
Triangle ΔABC has side lengths of a = 18, <img src="https://tex.z-dn.net/?f=b%3D18%5Csqrt%7B3%7D" id="TexFormula1" title="b=18\s
ozzi

The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

<h3 /><h3>What is the law of cosine?</h3>

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

Triangle ΔABC has side lengths of a = 18, b=18√3  and c = 36 inches.

  • Part A: Determine the measure of angle A

Put the value, in the cosine law, the measure of angle A.

\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\

  • Part B: Show how to use the unit circle to find tan A

Using the chart of unit circle, the value of tangent A can be found out. The tangent A is,

\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}

  • Part C: Calculate the area of ΔABC.

Use the following formula to find area of ΔABC.,

A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2

Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

Learn more about the law of cosine here;

brainly.com/question/4372174

#SPJ1

7 0
2 years ago
find the value of an investment of $3500 for 3 years at an interest rate of 5.6% if the money is compounded weekly
sergeinik [125]
\bf ~~~~~~ \textit{Compound Interest Earned Amount}&#10;\\\\&#10;A=P\left(1+\frac{r}{n}\right)^{nt}&#10;\quad &#10;\begin{cases}&#10;A=\textit{accumulated amount}\\&#10;P=\textit{original amount deposited}\to &\$3500\\&#10;r=rate\to 5.6\%\to \frac{5.6}{100}\to &0.056\\&#10;n=&#10;\begin{array}{llll}&#10;\textit{times it compounds per year}\\&#10;\textit{weekly, thus fifty two}&#10;\end{array}\to &52\\&#10;t=years\to &3&#10;\end{cases}

\bf A=3500\left(1+\frac{0.056}{52}\right)^{52\cdot 3}\implies A=3500\left( \frac{6507}{6500} \right)^{156}&#10;\\\\\\&#10;A\approx 4139.9038869337
3 0
3 years ago
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