A rare manuscript increased in value 800% over the past 5 years. This was an increase of $2,000. What was the value of the manuscript 5 years ago? What is the value of the manuscript now?

Answer:

28333.33

Step-by-step explanation:

68000/240% = 28333.33333333333

= 28333.33

Answer:

well I can't really answer I'm just gonna give you an example say the the difference between the relationship and situation about cups the relationship would be the cup and the situation is the size

136000 many bacteria will there be in 17 hours at a rate of 4 percentage per hour.

What is an example of a percentage?

given ,

          rate = 4%

bacteria  starts growing = 320

                 rate = 4%

  4% = 320

  1 = [tex]\frac{320 * 100}{4} = 8000[/tex]

bacteria will there be in 17 hours =  17 ×  8000

                                                       =  136000

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The area covered by circular rug of diameter 7 is 38.5 m².

Circle is locus of points equidistant from a center point. This distance from center to the boundary of circle is radius.

If r is the radius of a circle , then its Area = π(r²)

Given that a circular rug has diameter = 7 m

Then, Let radius of circular rug be  r ,r = diameter /2

r =  7/2 m

Area =  π(7/2)² = (22/7)*(7/2)² m² =  38.5 m²

Therefore , Area of the circular rug is 38.5 m²

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The weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds the mixture will be  15 pounds

Let the weight of coffee worth $10 to be added to mixture be x pounds

The weight of coffee worth $4 to be added to mixture is 30 pounds

We want a mixture that worth $6 a pound

The weight of mixture of coffee worth $ 6 is the sum of $10 coffee and $4 coffee

    = x + 30

From the above equation we can form a linear equation

              X 10 + 30 ×4 = (x+ 30) 6

    10x + 120= 6x +180

    10x-6x= 180 -120

         4x = 60

               X= 15

Hence, the weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds

what's a linear equation ?

A linear equation only has one or  variables. No variable in a linear equation is raised to a strength greater than 1 or used because the denominator of a fraction. while you discover pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all the factors lie at the same line

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Using translation concepts, the transformed triangles are given in the graph at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.

For this problem, the coordinates of triangle PQR are given as follows:

P(-1,-1), Q(-3,-2), R(-3,-4).

The rule for a 90º clockwise rotation around the origin is given by:

(x,y) -> (y,-x).

Hence the coordinates of triangle P'Q'R' are given by:

The rule for a reflection over the y-axis is:

(x,y) -> (-x,y).

Hence the coordinates of triangle P''Q''R'' are given by:

Both triangles are given in the graph at the end of the answer.

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[tex]3y \geqslant 9 \\ y \geqslant \frac{9}{3} \\ y \geqslant 3[/tex]

Answer: y > 3

Step-by-step explanation: 3y > 9
3y/3 > 9/3

y > 3

Answer: what is question here?

Step-by-step explanation:

Where are answers?

The amount of Alfalfa hay is 385.71 lbs

The amount of Clover is 572.45 lbs.

A percentage is a number or ratio that can be expressed as a fraction of 100.

We have,

Alfalfa hay = 18 % CP

Clover = 4% CP.

The total amount of ration is 600 lbs of a 13% CP.

Let x pounds of alfalfa hay have been used.

The amount of clover will be 600 - x lbs.

The CP amount in 600 lbs mixture will be equal to the sum of CP amounts in x lbs alfalfa and (600 - x) lbs clover.

13% of 600 = 18% of x + 4% of (600 - x)

We need to find x.

13/100 x 600 = 18/100 x (x) + 4/100 x (600 -x)

78 = 18x / 100 + 24 - 4x/100

78 - 24 = 18x/100 - 4x/100

54 = 14x / 100

14x = 54 x 100

x = 5400/14

x = 385.71 lbs

Thus,

The amount of Alfalfa hay= 385.71 lbs

The amount of Clover = 600 - 385.71 = 572.45 lbs.

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The values of x and m∠R are 15 and 50 respectively.

From the information given, we have the following parameters;

Now, let's equate the angles

m ∠ R  = m ∠ S

3x + 5 = 5x - 25

collect like terms

3x - 5x = -25 - 5

subtract like terms

-2x = - 20

Make 'x' the subject

x = -30/ -2

x = 15

But m ∠ R = 3x + 5 = 3(15) + 5 = 45 + 5  = 50

Thus, the values of x and m∠R are 15 and 50 respectively.

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For the given equation 6e^4x = 14, the value of x is [tex]x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]

Getting x alone on one side of the equation and everything else on the other side will be the first step towards solving for x. The golden rule of algebra states that everything done to one side of an equation must also be done to the other.

Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.

For the given equation,

6e^4x = 14

[tex]x = ln \frac{3^{3/4} * \sqrt[4]{7} }{3}\\ \\x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]

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Correct answer is D. For the numerical equation, If m = 8 and n = 4, all of the following represent the same value except mn.

Numbers and their operations are used to represent a numerical equation. Statements can also be used to create mathematical expressions.

On calculating, the following values,

If m = 8 and n = 4;

For 1/2m, the value will be -

1/2 × 8 = 4                                                    .......(1)

For n/1 the value will be -

4/1 = 4                                                          .......(2)

For m-n the value will be -

8 - 4 = 4                                                       .......(3)

For mn, the value will be -

8 × 4 = 32                                                     ......(4)

From (1), (2), (3), (4) it can be seen that the value is same instead for mn.

Complete question -

If m = 8 and n = 4, all of the following represent the same value except _____.

1/2 m

n/1

m-n

mn

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Answer:

true for the first one and also true for the other one.

Lower limit of 95% confidence interval is  0.464 and upper limit of 95% confidence interval is 0.594

What is Z value of 95% confidence interval and how to find 95% confidence interval?

A Z value is a numerical measure of how far is an individual score is from the mean score, within a normal distribution.

The Z value for 95% confidence interval is Z=1.96.

Let p the  estimated proportion of people in favor of a proposition and n be the sample size, n = 225

Marginal error = [tex]Z\sqrt{\frac{p(1-p)}{n} }[/tex]

Lower limit of 95% confidence interval = Z - Marignal error           

Upper limit of 95% confidence interval = Z + Marginal error

Given that in a poll of 225 randomly selected U.S. adults, 119 said they favored a new proposition,

The estimated proportion of people favored a new proposition is, p =[tex]\frac{119}{225}[/tex]

Then, p = 0.529

Marginal Error = [tex]Z\sqrt{\frac{p(1-p)}{n} } = 1.960\sqrt{\frac{0.529(1-0.529)}{225} }[/tex] = 0.065

Therefore,

Lower limit of 95% confidence interval   =0.529-0.065  = 0.464    

Upper limit of 95% confidence interval = 0.529+0.065 = 0.594

And the 95% confidence interval would be given (0.464,0.594).

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Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

360° - the know angles

360 - 20 - 70 - 20 = 250°

Step-by-step explanation:

Well this is a full circle, and in a full circle, theres 360 degrees.

So if we add up 20, 70 and 20 degrees, it comes to a total of 110 degrees.

If we subtract 110 d from 360 d, we get 250 degrees. Therefore,

Hope this helped

The total number of student present in the class is 15.

One-third of the students choose to work on an essay.

Let

x = the total number of student in the class

Therefore,

student that takes essay = 1 / 3 x

One-half of the remaining students choose to read.

Therefore, the expression is as follows

student that choose to read = 1 / 2(x - 1 / 3 x)  = 1 / 2( 3x - x/ 3) = 1 / 2(2 / 3 x) = 2 / 6 x = 1 / 3x

The remaining 5 students work on vocabulary.  Therefore, the expression is as follows:

Student that works on vocabulary = x - 1 / 3 x - 1 / 3 x

5 =  x - 1 / 3 x - 1 / 3 x

5 = 3x- x - x / 3

5 = x / 3

x = 15

Therefore,

the student present in the class = 1 / 3 (15) +  1 / 3(15) + 5

the student present in the class = 5 + 5 + 5

the student present in the class = 15

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Simplifying the given value using the law of indices is 6[tex]a^{3}[/tex]

2a * 3[tex]a^{2}[/tex]

=6[tex]a^{3}[/tex]

Index laws are the rules for simplifying expressions involving powers of the same base number.

Here are  the essential  steps to follow to simplify an algebraic expression:

Remove parentheses by multiplying factors.

Use exponent rules  to get rid of  parentheses in terms with exponents.

Combine like terms by adding coefficients.

Combine the constants.

Here's  differently  to explain it: The is used to refer to a specific or particular member of a group.  for instance , "I just saw  the foremost  popular movie of the year." There are many movies, but  just one  particular movie is the most popular.

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Answer:

Step-by-step explanation:

5(9) = 45

The answers are below.

a) (fog)(x) = f(g(x)) = 2 - ( 3x² +x+5) = -3x² - x - 3

b) (gof)(x) = g(f(x)) = 3*(2 - x)² + (2 - x) +5 = 3x² - 13x + 19

a) (fog)(2) =  -3x² - x - 3 = -3*4 - 2 - 3 = -12 - 2 - 3 = -17

b) (gof)(2) = 3x² - 13x + 19 = 3*4 - 13*2 + 19 = 12 - 26 + 19 = 5

Just replace evaluate the function g(x)= 3x² +x+5 insode of the function f(x) = 2 - xfor the first one.

a) (fog)(x) = f(g(x)) = 2 - ( 3x² +x+5) = -3x² - x - 3

b) (gof)(x) = g(f(x)) = 3*(2 - x)² + (2 - x) +5 = 3x² - 13x + 19

ok, now that you have these two values, just evaluate the equations in x = 2 to get the rest.

a) (fog)(2) =  -3x² - x - 3 = -3*4 - 2 - 3 = -12 - 2 - 3 = -17

b) (gof)(2) = 3x² - 13x + 19 = 3*4 - 13*2 + 19 = 12 - 26 + 19 = 5

These are the outcomes when we evaluate the compositions in x = 2.

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The measure of angle A is 62 degrees

Supplementary angles are angles that sunset up to 180 degrees. For instance, if A+B = 180, then A and B are supplementary

The sum of supplementary angles is 180 degrees such that;

<A + <B = 180

Given the following parameters

<A = 2x-4

<B = 4x-14

Substitute

2x-4 +4x-14 = 180

6x - 18 = 180

6x = 198

x = 198/6

x = 33

<A = 2x - 4

<A = 2(330 - 4

<A = 62 degrees

Hence the measure of angle A is 62 degrees

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Answer:

Where is the question?

Answer:

Step-by-step explanation:

0.195/12 = 0.0163 = 1.63%

Hence, the monthly periodic rate is [tex]1.63[/tex]%.

What is the periodic rate?

A periodic interest rate is a rate that can be charged on a loan, or realized on an investment over a specific period of time.

Lenders typically quote interest rates on an annual basis, but the interest compounds more frequently than annually in most cases.

Here given that,

Loan with an APR of [tex]19.5[/tex]%

So, [tex]19.5[/tex]% is

[tex]\frac{19.5}{100}=0.195[/tex]

Annual periodic rate means [tex]12[/tex] months.

then,

[tex]{0.195}{12}=0.0163\\[/tex]

[tex]=1.63[/tex]%

Hence, the monthly periodic rate is [tex]1.63[/tex]%.

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Answer:

estimate 245.7+5.8

251.5

Answer:The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

Step-by-step explanation:

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

The equation of a circle usually takes the form;

(x-a)² + (y-b)² = r²

where a and b are x- and y- coordinates of the center of the circle.

In this scenario, the center is at the origin (0,0).

In essence, the points on the circle which have an x-coordinate of 1 can be evaluated as follows;

(1-0)² + (y - 0)² = 4²

1 + y² = 16.

y² = 15

y = ±√15.

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

Considering the definition of probability and its properties:

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)= number of favorable cases÷ number of total cases

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.

A complementary event, also called an opposite event, is made up of the inverse of the results of another event.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

The conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:

P(A|B) = P(A∩B)÷ P(B)

In first place, let's define the following events:

You know:

The probability that a student is a freshman or a mathematics mayor is:

P [(F∪M)']= 1- P(F∪M)

7/51= 1 - P(F∪M)

7/51 - 1= -P(F∪M)

-44/51= -P(F∪M)

44/51= P(F∪M)

So, the probability that the student is both a freshman and a mathematics major is calculated as:

P(F∪M)= P(F) + P(M) -P(F∩M)

44/51= 23/51 + 30/51 - P(F∩M)

44/51- 23/51 - 30/51= - P(F∩M)

-3/17= - P(F∩M)

3/17= P(F∩M)

Finally, the probability that the student is both a freshman and a mathematics major is 3/17.

The probability that a student is a mathematics major, knowing that he is also a freshman, is calculated as:

P(M|F) = P(M∩F)÷ P(M)

So:

P(M|F) = 3/17÷ 30/51

P(M|F) = 3/10

Finally, given that the student selected is a freshman, what is the probability that he is also a mathematics major is 3/10.

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