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Inessa [10]
3 years ago
12

For every 40 phone calls that Jess made in a month, she received 70 phone calls. What is the ratio in simplest form of the numbe

r of phone calls made to the number of phone calls received by Jess that month?
Mathematics
2 answers:
Anit [1.1K]3 years ago
5 0

Answer:

simplified answer is 4:7

insens350 [35]3 years ago
4 0
The simplified answer is 4:7
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A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by th
ollegr [7]

Total capacity = sum of the individual production capacities.

Here,

Total capacity = sum of f(m) = (m + 4)^2 + 100  and g(m) = (m + 12)^2 − 50.

Then f(m) + g(m) =  (m + 4)^2 + 100 + (m + 12)^2 − 50.

We must expand the binomial squares in order to combine like terms:

 m^2 + 8 m + 16 + 100

+m^2 + 24m + 144 - 50

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

Then f(m) + g(m) = 2m^2 + 32m + 160 + 50  

      f(m) + g(m)   = 2m^2 + 32m + 210, where m is the number of

                                minutes during which the two machines operate.

6 0
3 years ago
How to find the measure of the angle is you have the incenter?
Eduardwww [97]
Construct<span> a perpendicular from the </span>incenter<span> to one side of the triangle to locate the exact radius. 3. place compass point at the </span>incenter<span> and measure from the center to the point where the perpendicular crosses the side of the triangle</span>
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3 years ago
mark is drawing a map of his favorite park. the park is 3 miles long and 1.5 miles wide. the map scale is 1 inch = .25 miles. ho
Brilliant_brown [7]

Answer: 6 inches

Step-by-step explanation:

1.5 miles wide * 1 inch / 0.25 miles = 6 inches :D

7 0
3 years ago
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Cosθ=−2√3 , where π≤θ≤3π2 .
Alex787 [66]

Answer:

sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}

Step-by-step explanation:

step 1

Find the  sin(\theta)

we know that

Applying the trigonometric identity

sin^2(\theta)+ cos^2(\theta)=1

we have

cos(\theta)=-\frac{\sqrt{2}}{3}

substitute

sin^2(\theta)+ (-\frac{\sqrt{2}}{3})^2=1

sin^2(\theta)+ \frac{2}{9}=1

sin^2(\theta)=1- \frac{2}{9}

sin^2(\theta)= \frac{7}{9}

sin(\theta)=\pm\frac{\sqrt{7}}{3}

Remember that

π≤θ≤3π/2

so

Angle θ belong to the III Quadrant

That means ----> The sin(θ) is negative

sin(\theta)=-\frac{\sqrt{7}}{3}

step 2

Find the sec(β)

Applying the trigonometric identity

tan^2(\beta)+1= sec^2(\beta)

we have

tan(\beta)=\frac{4}{3}

substitute

(\frac{4}{3})^2+1= sec^2(\beta)

\frac{16}{9}+1= sec^2(\beta)

sec^2(\beta)=\frac{25}{9}

sec(\beta)=\pm\frac{5}{3}

we know

0≤β≤π/2 ----> II Quadrant

so

sec(β), sin(β) and cos(β) are positive

sec(\beta)=\frac{5}{3}

Remember that

sec(\beta)=\frac{1}{cos(\beta)}

therefore

cos(\beta)=\frac{3}{5}

step 3

Find the sin(β)

we know that

tan(\beta)=\frac{sin(\beta)}{cos(\beta)}

we have

tan(\beta)=\frac{4}{3}

cos(\beta)=\frac{3}{5}

substitute

(4/3)=\frac{sin(\beta)}{(3/5)}

therefore

sin(\beta)=\frac{4}{5}

step 4

Find sin(θ+β)

we know that

sin(A + B) = sin A cos B + cos A sin B

so

In this problem

sin(\theta + \beta) = sin(\theta)cos(\beta)+ cos(\theta)sin (\beta)

we have

sin(\theta)=-\frac{\sqrt{7}}{3}

cos(\theta)=-\frac{\sqrt{2}}{3}

sin(\beta)=\frac{4}{5}

cos(\beta)=\frac{3}{5}

substitute the given values in the formula

sin(\theta + \beta) = (-\frac{\sqrt{7}}{3})(\frac{3}{5})+ (-\frac{\sqrt{2}}{3})(\frac{4}{5})

sin(\theta + \beta) = (-3\frac{\sqrt{7}}{15})+ (-4\frac{\sqrt{2}}{15})

sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}

8 0
3 years ago
What is the standard deviation of the data set given below?<br> 5,7,9,11,13
Leya [2.2K]

Answer:

3.16

Step-by-step explanation:

3 0
3 years ago
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