Evaluate:
(3,251)(30)

Answer:

8 2/5

Step-by-step explanation:

42/5

to find the improper fraction, divide the numerator by the denominator

and then find the remainder

42 / 5 = 8  ( 5*8)  the remainder is 42-40 = 2

Put the remainder over the denominator

8 2/5

Hey there!

Question reads….

Which mixed number is equivalent to the improper fraction 42/5?

EQUATION:

42/5

The one that is equivalent to the fraction is:
8 2/5

Reason:

8 2/5

= 8 * 5 + 2 / 5

= 40 + 2 / 5

= 42 / 5

Therefore, your answer should be:

Option C. 8 2/5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The probability that a person chosen at random have run a red light in the past year is 0.45.

Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.

Probability lies between 0 and 1. The value of probability can be find by :

Probability= Number items/total items.

Number of people who said that they have run red light=150

Number of people who said that they have not run red light=185

Total people=150+185

=335 people

Probability that a person chosen at random have run red light in the past year=

=Number of people who said that they have run red lights / total people

=150/335

=0.447

After rounding off it will be 0.45.

Hence the probability that a person chosen at random have run a red light in the past year is 0.45.

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The total number of snakes in the zoo is 10.

The number of snake can be found using ratio as follows:

The animals in the zoo are lions, tigers and snakes and he has them in the ratio of 5 : 3 : 2. The total animal is 50 animals.

Therefore,

total snakes = 2 / 10 × 50

total snakes = 100 / 10

total snakes = 10

Therefore, the total number of snakes in the zoo is 10.

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The solution of the differential equation y(3)=29/9.

Given a differential equation y'+(y/x)=x for y(1)=1.

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

We will solve this differential equation by using the integrating factor method.

Firstly, we will find the integrating factors by using the formula, we get

[tex]I.F=e^{\int Pdx}[/tex]

Here P=1/x and substitute this in the formula, we get

[tex]\begin{aligned}I.F.&=e^{\int \frac{1}{x}dx}\\ &=e^{\log x}\\ &=x\end[/tex]

Now, we will substitute the values in the formula

[tex]y\times I.F.=\int Q\times I.F.dx[/tex]

Here Q=x an substitute this in the above formula, we get

[tex]\begin{aligned}y\times x&=\int x\times xdx\\ yx&=\int x^{2} dx\\ yx&=\frac{x^3}{3}+C\end[/tex]

Further, we will divide both sides with x, we get

y=(x²/3)+(C/x)                       ......(1)

Given that y(1)=1 means when x=1 then y=1 so substitute this in equation (1) to find the value of C, we get

1=(1/3)+C

1-(1/3)=C

2/3=C

Substitute the value of C in equation (1), we get

y=(x²/3)+(2/(3x))

Now find the value of y when x=3, we get

y=(9/3)+(2/9)

y=3+(2/9)

y=29/9

Hence, in the differential equation y'+(y/x)=x for y(1)=1 then y(3) is 29/9.

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Answer:
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Step-by-step explanation:

Lets start with 2 assumptions, what if we only used the Alexander's family sprinklers, We can define X as the variable
[tex]20x=1450[/tex]
[tex]x= 72.5[/tex]
If we just used the Alexanders it would of took 72 hours and 30 minutes.

Now lets look at the Jenkins family sprinkler, lets define it as Y.
[tex]25y=1450[/tex]
[tex]y = 58[/tex]
With only the Jenkins it would of took 58 hours.

Now, if they just of shared the work equally among the two sprinklers, the Alexanders family doing 725 L and the Jenkins with the other half.
It would of took the Alexanders
[tex]20x= 725[/tex]
[tex]x=36.25[/tex]

Jenkins
[tex]25y=725[/tex]
[tex]y=29[/tex]

Making it a combined time of 65.25 hours. 15 minutes long of our 65 hour time.

Now the Jenkins sprinkler generates 5 more L than Alexanders per hour. Which means it would only take the Jenkins family 1 hours to make 25 liters but Alexanders would take [tex]\frac{5}{4}[/tex] hours. We know that 1 hour contains 60 minutes, which means [tex]\frac{1}{4}[/tex] of a hour contains 15 minutes.

So it would take Alexanders family sprinkler 15 minutes more to produce the same amount per hour that the Jenkins does.

So from this we can conclude that if the Jenkins family sprinkler was used more we can cut the extra 15 minutes off, making the answer That the

Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Answer:

undefined

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2  x_1)

slope = (-3 - 4)/(6 - 6)

slope = -7/0

Since division by zero is undefined, this line has undefined slope.

Answer: False

Step-by-step explanation:

The only number that makes this impossible to solve is x = 0

The division of the figure based on the information is 14.09.

It should be noted that the question is simply to divide 860 by 61.

The division based on the information will be illustrated thus:

= 860 ÷ 61

= 14.09

In conclusion, the correct option is 14.09.

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The true statement about the diagram is (a) IJ ≅ JG

From the question, we understand that:

KH bisects line IG at point J

This means that:

Line segment IG is divided into two equal parts, and point J is the middle

So, we have:

IJ ≅ JG

Hence, the true statement about the diagram is (a) IJ ≅ JG

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Based on the required rate of return, the real risk free rate, and the inflation premium, the default risk premium on the corporate bonds is 1.2%

The default risk premium can be found as:

=real risk free rate + Inflation premium + default risk premium + liquidity premium + maturity risk premium

Solving gives:

= 0.07 - 0.0275 - 0.0205 - (0.1 x (t - 1)%)

=  0.07 - 0.0275 - 0.0205 - (0.1 x (5 years - 1)%)

= 1.2%

The default risk premium refers to the return that the bond is offering over what a risk-free bond would offer.

This means that the corporate bond described is offering 1.2% more than what a risk-free government bond would offer.

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Answer:

A' is (-2,-1)

B' is (3,0)

C' is (2,4)

Step-by-step explanation:

Answer:

No he's not correct.

Step-by-step explanation:

If you look closely the 2 and the 3 in the decimals are in different sections so it would not equal 0.5

It would equal 0.23

Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,

In order to determine whether x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35, we will show that f(5) = 0

Substitute x = 5 into the function to have;

f(5) = 5^3 – 5(5)^2 + 7(5) – 35

f(5) = 125 - 125 + 35 - 35

f(5) = 0

Since the value of f(5) is zero, hence x – 5 a factor of the function f(x) = x^3 – 5x^2 + 7x – 35,

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Answer:

y = 2x + 6

Step-by-step explanation:

We are given the line R, which is y=2x+5, and we want to find the equation of the line that is parallel to this line, and that also passes through the point (-2, 2).

Parallel lines have the same slope, yet different y-intercepts.

So, we should first find the slope of y=2x+5.

The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.

As 2 is in the place of where m (the slope) should be, 2 is the slope of the line.

It is also the slope of the line parallel to it.

We can write the equation of the new line in slope-intercept form as well; here is the equation so far, with what we know:

y = 2x + b

We need to find b.

As the equation passes through the point (-2, 2), we can use its values to help solve for b.

Substitute -2 as x and 2 as y.

2 = 2(-2) + b

Multiply.

2 = -4 + b

Add 4 to both sides.

6 = b

Substitute 6 as b.

y = 2x + 6

The equation of the new function is:

[tex]g(x) = \frac{2^x}{5}[/tex]

Here we have the function:

[tex]f(x) = 2^x[/tex]

A vertical compression by a factor of 5 is written as:

[tex]g(x) = f(x)/5[/tex]

Replacing the function f(x) we get:

[tex]g(x) = \frac{2^x}{5}[/tex]

That is the equation of the new function.

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Step-by-step explanation:

<1 congruent to <5.

<5 congruent to <7.

<1 congruent to <7.

Answer:

don't know but i need thee points

Step-by-step explanation:

The probability that all five end up in alphabetical order is; 1/120.

To evaluate the given probability; first, the number of possible arrangements is;

17P5 = 742,560 possible arrangements.

However, the chance of an alphabetical order arrangement in each case is; 1 out of 5! possible arrangements.

Hence, we have that the number of possible alphabetical arrangement is; (1/120) × 742,560 = 6188.

Hence, the required probability is; 6188/742,560 = 1/120

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The proportion of people with IQs above 130 is 2.3%.

Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Here the mean is 100 and a standard deviation of 15.

µ = 100, σ = 15

P(X > 130) =

= P( (X-µ)/σ > (130-100)/15)

= P(z > 2)

= 1 - P(z < 2)

Using excel function:

= 1 - NORM.S.DIST(2, 1)

= 0.023 = 2.3%

The value is 2.3%.

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The solution to the Questions are

(a)

The alternate hypothesis demonstrates that there are two possible outcomes for the test.

(b)

Here we have

[tex]n_{1}=40,\\\\ \bar{x}_{1}=102,\sigma_{1}=5,n_{2}=50,\bar{x}_{2}=99,\sigma_{2}=6[/tex]

(b)

Here the test is two-tailed. So for [tex]\alpha =0.04[/tex], the critical values of the z-test are -2.05 and 2.05.

Decision rule: If z > 2.05 or z<-2.05, reject H0

(c)

Test statistics will be

[tex]z=\frac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}} \\\\\\z=\frac{(102-99)-(0)}{\sqrt{\frac{5^{2}}{40}+\frac{6^{2}}{50}}}[/tex]

z=2.59

(d)

The two-tailed nature of the test is shown by the alternative hypothesis.

(e)

The result of the test yields the following P-value: 0.0096

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The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It has a value of π = 22/7

An equation is an expression that shows the relationship between two or more variables and numbers.

The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It is given by:

π = 22/7

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The value of x = 4.71, 0.41, or 5.89 radian value

Specification:

sinxtanx + tanx -2sinx + cosx = 0

tanx = sinx / cosx

sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0

cosx to remove the fraction

sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0

sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1

sinx -2sinxcosx + 1 = 0

sinx (1-2cosx) = -1

1-2cosx = -1 / sinx

-2cosx = -1 / sinx -1

2cosx = 1 / sinx + 1

cosx = 1 / 2sinx + 1/2

sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2

Squared on both sides

1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4

4sin ^ 2 (x) Multiply

4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)

4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0

y = sinx

4y ^ 4 -3y ^ 2 + 2y + 1 = 0

sinx = y = -1 or -0.3478

x = 270, 180-22.61 or -22.61 degrees

x = 270, 157.39 or 337 .39 degrees

or

x = 3pi / 2, 0.13pi or 1.87pi radians

or

x = 4.71, 0.41 Or 5.89 radians

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The equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = 3(x + 5)^2 - 4

Express f(x) as y

So, we have

y = 3(x + 5)^2 - 4

Swap the positions of x and y

So, we have

x = 3(y + 5)^2 - 4

Add 4 to both sides of the equation

So, we have

x + 4 = 3(y + 5)^2

Divide through by 3

So, we have

1/3(x + 4) = (y + 5)^2

Take the square root of both sides

So, we have

√[1/3(x + 4)] = y + 5

Subtract 5 from both sides of the equation

So, we have

y = -5 + √[1/3(x + 4)]

Rewrite as

f-1(x) = -5 + √[1/3(x + 4)]

Hence, the equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

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Answer:

75/4

Step-by-step explanation:

Assuming BA and ED are parallel, we know thay the two triangles are similar.

So,

[tex]\frac{25-x}{x}=\frac{36}{12} \\ \\ \frac{25-x}{x}=3 \\ \\ 25-x=3x \\ \\ 4x=25 \\ \\ x=\frac{25}{4} \\ \\ BD=25-\frac{25}{4}=\frac{75}{4}[/tex]

From the options presented,  only figure number 2 or the one that looks like a cross has a rotation symmetry.

This type of symmetry implies that when a figure is rotated it matches its original shape. An example of this is the circle.

From the options presented, only the cross has this symetry because its side are equal and this means you can rotate it and it will look the same.

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Answer:

b

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

         = [tex]\frac{5+8+12+6+7+10+14+6+13}{9}[/tex]

         = [tex]\frac{81}{9}[/tex]

         = 9

Answer:

9

Step-by-step explanation:

The mean is also known as the average. To find it, we add up all of the data and divide it by how many numbers were added.

5 + 8 + 12 + 6 + 7 + 10 + 14 + 6 + 13 = 81

81/9 = 9

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Using proportions, the property tax on a house with an assessed value of $762,000 is of $8,890.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax rate, as a proportion, is:

7280/624000 = 0.011667.

Hence, the property tax on a house with an assessed value of $762,000 is of:

0.011667 x 762,000 = $8,890.

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Answer:

x = 34

Step-by-step explanation:

The angles x + 12, 100, and x add up to a straight angle, so the sum of their measures is 180°.

(x + 12) + (100) + (x) = 180

x + 12 + 100 + x = 180

2x + 112 = 180

2x = 68

x = 34

Based on the box and whisker plot shown above, we can infer and logically deduce that the number of lepilemures have a minimum at 0 but are well spread.

A box and whisker plot is also referred to as boxplot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:

By critically observing the box and whisker plot shown above, we can infer and logically deduce that the data (number of lepilemures) have a minimum at 0 but are well spread.

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