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sashaice [31]
3 years ago
12

What is the average rate of change from x = 0 to x = −2?

Mathematics
1 answer:
yarga [219]3 years ago
8 0
-1
................... ..
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Two life insurance companies determine their premiums using different formulas:
Pie

Answer:

<em>The age at which both companies charge the same premium is 44 years</em>

Step-by-step explanation:

<u>Graph Solution to System of Equations</u>

One approach to solving systems of equations of two variables is the graph method.

Both equations are plotted in the same grid and we find the intersection point(s) of both graphs. Those are the feasible solutions.

The annual premium p as a function of the client's age a for two companies are given as:

Company A: p= 2a+24

Company B: p= 2.25a+13

The graphs of both functions are shown in the image below.

The red line indicates the formula for Company A and the blue line indicates the formula for Company B.

It can be seen that both lines intersect in the point with approximate coordinates of (44,112).

The age at which both companies charge the same premium is 44 years

8 0
3 years ago
Can anyone explain dimensional analysis pleaseeee
dimaraw [331]
Is a problem solving method that uses that fact that any number or expression can be multiplied by one without changing it's value.
3 0
3 years ago
Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing i
Nina [5.8K]

Answer:

z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358    

p_v =2*P(Z>5.358) = 4.2x10^{-8}  

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.  

Step-by-step explanation:

Data given and notation  

X_{1}=253 represent the number with no defects in sample 1

X_{2}=196 represent the number with no defects in sample 1

n_{1}=300 sample 1

n_{2}=300 sample 2

p_{1}=\frac{253}{300}=0.843 represent the proportion of number with no defects in sample 1

p_{2}=\frac{196}{300}=0.653 represent the proportion of number with no defects in sample 2

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)  

\alpha=0.05 significance level given

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if is there is a difference in the the two proportions, the system of hypothesis would be:  

Null hypothesis:p_{1} - p_2}=0  

Alternative hypothesis:p_{1} - p_{2} \neq 0  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{253+196}{300+300}=0.748  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358    

Statistical decision

Since is a two sided test the p value would be:  

p_v =2*P(Z>5.358) = 4.2x10^{-8}  

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.  

5 0
3 years ago
A group of market women sell at least one of yam, plantain and maize.12 of them sell maize,10 sell yam and 14 sell plantain,5 se
mina [271]

Let the three items be M, Y and P.

n{M ∩ Y} only = 4-3 = 1

n{M ∩ P) only = 5-3 = 2

n{ Y ∩ P} only = 2

n{M} only = 12-(1+3+2) = 6

n{Y} only = 10-(1+2+3) = 4

n{P} only = 14-(2+3+2) = 7

n{M∩P∩Y} = 3

Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.

8 0
3 years ago
In 4 ​minutes, a conveyor belt moves 800 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt
kkurt [141]

Answer:

It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.

Step-by-step explanation:

Given - In 4 ​minutes, a conveyor belt moves 800 pounds of recyclable

            aluminum from the delivery truck to a storage area. A smaller belt

            moves the same quantity of cans the same distance in 6 minutes.

To find - If both belts are​ used, find how long it takes to move the cans

              to the storage area.

Proof -

Given that,

Larger belt take 4 minutes to transfer the aluminium from delivery truck to storage area.

⇒ Time taken by Larger belt = 4 min/ shifting

Also,

Smaller belt take 6 minutes to transfer the aluminium from delivery truck to storage area.

⇒ Time taken by Smaller belt = 6 min/ shifting

Now,

As we know that Time is inversely proportional to time, so

Rate of Larger Belt = \frac{1}{4} shifting/min

Rate of Smaller Belt = \frac{1}{6} shifting/min

Now,

Let us assume that , if both belts used then,

Total time taken = x min/shifting

Then, Rate = \frac{1}{x} shifting/min

Now,

\frac{1}{4}  + \frac{1}{6}  = \frac{1}{x}

⇒\frac{6 + 4}{24} = \frac{1}{x}

⇒\frac{10}{24} = \frac{1}{x}

⇒10x = 24

⇒x = \frac{24}{10} = 2.4 minutes

∴ we get

It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.

3 0
3 years ago
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