Use this table to answer questions below. Choose the correct answer.





According to the line graph, between 1950 and 1970 approximately which year had the lowest percentage of business failures?

Answer:

This situation represents [a.) exponential decay

The rate of growth or decay, r, is equal to  c.) 0.2

So the value of the computer each year is g.) 80% of the value in the previous year.

It will take [i.) 3 years for the value of the computer to reach $512.

Step-by-step explanation:

Since the value depreciates each year, it represents exponential decay.

The rate of growth or decay, r, is equal to

Depreciates 20%, so r = 0.2.

So the value of the computer each year is ... of the value in the previous year,

Depreciates 20%, so it is 100% - 20% = 80% of the value in the previous year.

It will take x years for the value of the computer to reach $512.

The value of the computer after x years is given by:

[tex]V(x) = V(0)(1-r)^x[/tex]

In which V(0) is the initial value and r is the decay rate. So

[tex]V(x) = 1000(1-0.2)^x[/tex]

[tex]V(x) = 1000(0.8)^x[/tex]

We want to find x for which V(x) = 512. So

[tex]V(x) = 1000(0.8)^x[/tex]

[tex]512 = 1000(0.8)^x[/tex]

[tex](0.8)^x = \frac{512}{1000}[/tex]

[tex](0.8)^x = (0.512)[/tex]

Applying log to both sides:

[tex]\log{(0.8)^x} = \log{(0.512)}[/tex]

[tex]x\log{0.8} = \log{(0.512)}[/tex]

[tex]x = \frac{\log{0.512}}{\log{0.8}}[/tex]

[tex]x = 3[/tex]

So it will take 3 years.

Honestly, for me, it just provides bragging rights. Also, I guess it makes you feel better about getting your rank higher. (～￣▽￣)～

____________________________________________________________

正直なところ、私にとって、それは自慢する権利を提供するだけです。また、ランクを上げることで気分が良くなると思います。(～￣▽￣)～

Answer:

Step-by-step explanation:  You can tell whether a relation is a function by plotting the numbers on a graph and applying the vertical line test. If no vertical line passing through the graph intersects it at more than one point, the relation is a function.

______________________________

Have a nice day!

Answer:

C.     y=1/4

Step-by-step explanation:

76y=19

y=19/76

7=.25 or 1/4

Answer:

Hi! The correct answer is C. y = 1/4

Step by step explanation:

Divide each term by 76 and simplify.

Answer:

62.5%

Convert fraction (ratio) 2.5 / 4 Answer: 62.5%

Step-by-step explanation:

Creating a ratio to represent the amount he was specifically off by, which inherently gives you John's percent error.

Answer:

Increased by, added, brought up (All I know of haha)

Step-by-step explanation:

Theres really no explanation to this other than learning your mathematical terms.

Answer:

41

Step-by-step explanation:

Answer:

18+516+38=18+554=572

Answer:

The length is one

Step-by-step explanation:

The formula to find the area of aa square is B*H. This means to solve, you do 1*1, since the base and height are both 1, and 1*1=1

Answer:

true

Step-by-step explanation:

the triangle inequality statement says the sum of any two sides must be greater than the third side

value 4, 5, and 8 work

4 + 5 > 8  true

4 + 8 > 5  true

5 + 8 > 4  true

Answer: Perimeter = 2(L) + 2(W) Length = 7W - 2 Perimeter = 60 60 = 14W - 4 + 2(W) 60 =16W - 4 64 = 16W Width = 4 Length = 7(4) - 2 Length = 26

I hope this helped!

Step-by-step explanation:

Answer:

Part a) The graph in the attached figure

Part b) The units rate of change is 9

Step-by-step explanation:

we know that

A relationship between two variables, t, and d, represent a proportional variation if it can be expressed in the form  or

step 1

Find the constant of proportionality k

For

substitute

the linear equation is equal to

using a graphing tool

see the attached figure

step 2

Find the unit rate

we know that

In a proportional relationship the constant of proportionality k is equal to the unit rate of change or slope m of the line, because the line passes through the origin

so

The units rate of change is 9

That means------> A change of 1 unit in t correspond to a change of 9 units in d

see the attached figure to better understand the problem

Answer:

Have a nice day! Answer is above good luck:)

Answer:

High possibility it is A, C, D. I apologize if wrong

Step-by-step explanation:

Answer:B, C, E

Step-by-step explanation:

Answer: none of them are correct

Step-by-step explanation:

BECUASE if it is then it would show it on the nuber line.

Answer:

A

Step-by-step explanation:

Add 3 to each side, there's your answer there.

Answer:

20

Step-by-step explanation:

Answer: 4 zeros

Step-by-step explanation:

If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.

P: ±1, ±2, ±3, ±6  (all prime factors of constant term)

Q: ±1, ±7              (all prime factors of the leading coefficient)

P/Q: ±1, ±2, ±3, ±6, ±1/7, ±2/7, ±3/7, ±6/7  (all possible values of P/Q)

Now, start testing your values of P/Q in your polynomial:

f(x)=7x4-9x3-41x2+13x+6

You can tell f(1) and f(-1) are not zeros since they're not = 0Now try f(2) and f(-2):

f(2)=7(16)-9(8)-41(4)+13(2)+6

       112-72-164+26+6 ≠ 0

f(-2)=7(16)-9(-8)-41(4)+13(-2)+6

       112+72-164-26+6 = 0  OK!! There is a zero at x=-2

This means (x+2) is a factor of the polynomial.

Now, do synthetic division to find the polynomial that results from

(7x4-9x3-41x2+13x+6)÷(x+2):

-2⊥ 7   -9   -41    13     6

         -14   46   -10    -6          

      7  -23   5       3     0     The remainder is 0, as expected

The quotient is a polynomial of degree 3:

7x3-23x2+5x+3

Now, continue testing the P/Q values with this new polynomial.  Try f(3):

f(3)=7(27)-23(9)+5(3)+3

      189-207+15+3 = 0  OK!!  we found another zero at x=3

Now, another synthetic division:

3⊥ 7   -23    5     3

          21   -6   -3_

    7    -2    -1    0    

The quotient is a quadratic polynomial:

7x2-2x-1  This is not factorable, you need to apply the quadratic formula to find the 3rd and 4th zeros:

x= (1±2√2)÷7  

The polynomial has 4 zeros at x=-2, 3, (1±2√2)÷7

Step-by-step explanation:

[tex]47.1 = 2\pi \times r \\ r = \frac{47.1}{2\pi} = 7.4962996 \\ diameter = 2 \times r \\ = 14.99 = 15 \: feet[/tex]

Answer:

The expression is: [tex]P(t) = 693e^{0.3662t}[/tex]

The initial number of strands is 693

Step-by-step explanation:

A bacterial culture is known to grow at a rate proportional to the amount present.

This means that the bacterial model can be modeled by the following equation:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial population, and r is the growth rate.

After one hour, there are 1000 strands of bacteria

This means that [tex]P(1) = 1000[/tex], So

[tex]P(0)e^{r} = 1000[/tex]

[tex]P(0) = \frac{1000}{e^{r}}[/tex]

After four hours, 3000 strands.

This means that P(4) = 3000. So

[tex]P(0)e^{4r} = 3000[/tex]

Since [tex]P(0) = \frac{1000}{e^{r}}[/tex], we have that:

[tex]\frac{1000}{e^{r}}e^{4r} = 3000[/tex]

[tex]\frac{e^{4r}}{e^{r}} = \frac{3000}{1000}[/tex]

[tex]e^{4r-r} = 3[/tex]

[tex]e^{3r} = 3[/tex]

[tex]\ln{e^{3r}} = \ln{3}[/tex]

[tex]3r = \ln{3}[/tex]

[tex]r = \frac{\ln{3}}{3}[/tex]

[tex]r = 0.3662[/tex]

The initial population is:

[tex]P(0) = \frac{1000}{e^{0.3662}} = 693[/tex]

The expression is:

[tex]P(t) = 693e^{0.3662t}[/tex]

The equation becomes [tex]y=694(1.44)^t[/tex]. The initial number of strands is 694.

An exponential growth is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the number of strands after t hours.

After one hour, there are 1000 strands of bacteria:

1000 = ab¹

ab = 1000    (1)

After four hour, there are 3000 strands of bacteria:

3000 = ab⁴

ab⁴ = 3000    (2)

Dividing equation 2 by 1:

b³ = 3

b = 1.44

ab = 1000

a = 1000/b = 1000/1.44 = 694

The equation becomes [tex]y=694(1.44)^t[/tex]

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Answer:

A is the answer because divide 7 divided by 3 a

Answer:

.33 cents

Step-by-step explanation:

Answer:

We can be 95% certain that the sample mean will fall within $44.87 and $46.93

Step-by-step explanation:

Empirical Rule:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Central Limit Theorem:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population:

Mean $45.90, standard deviation $10.31.

Sample:

By the Central limit theorem, mean $45.90, standard deviation [tex]s = \frac{10.31}{\sqrt{400}} = \frac{10.31}{20} = 0.5155[/tex]

Which interval can the branch manager be 95% certain that the sample mean will fall within?

By the Empirical Rule, within 2 standard deviations of the mean. So

45.90 - 2*0.5155 = $44.87

45.90 + 2*0.5155 = $46.93

We can be 95% certain that the sample mean will fall within $44.87 and $46.93

Answer:

1440 cubic yards

Step-by-step explanation:

There are 3 feet in a yard. Multiply 480 x 3 using the algorithm and you get 1440.

Answer:

P = 8.6 m

Step-by-step explanation:

Given that,

The length of a rectangle = 2.5 m

The width of a rectangle = 1.8 m

We need to find the perimeter of the rug. The perimeter of a rectangle is given by :

P=2(l+b)

= 2(2.5+1.8)

= 8.6 m

So, the perimeter of the rug is 8.6 m.

Answer:

The ratio is 7 : 13

Step-by-step explanation:

Given that:

Number of plain glazed donuts made on Saturday = 13

Number of chocolate glazed donuts made on Saturday = 7

Ratio of chocolate glazed donuts to plain glazed donuts;

Chocolate glazed donuts : Plain glazed donuts

7 : 13

Hence,

The ratio is 7 : 13

Answer:

Length = 13.5 m

Width = 4.5 m.

Step-by-step explanation:

Use an equation in x, where x = width of the table.

Length =  3x, so:

2*3x + 2x = 36

6x + 2x = 36

8x = 36

x = 36/8 =  4.5 metres.

So the length = 3*4.5 = 13.5 and width = 4.5 m.

Length = 13.5 m

Width = 4.5 m.

A closed route that covers, encircles, or outlines a one-dimensional length or a two-dimensional form is called a perimeter.

Given, The length of a rectangular table is 3 times its width. If the total perimeter of the table is 36 meters.

Use an equation in B, where B = width of the table.

Length =  3B,

2*3B + 2B = 36

6B + 2B = 36

8B = 36

B = 36/8 =  4.5 meters.

So the length = 3*4.5 = 13.5 and width = 4.5 m.

Therefore, the length and the width of the given rectangle are 4.5 and 13.5 respectively.

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