Please help me with this question

Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.

To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.

A = $6,250.00

I = A - P = $1,250.00

Formula: A = P(1 + rt)

First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.

Fixing our equation

A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00

Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.

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The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

Now, According to the question:

The given sphere is of radius R.

Let h be the height and r be the radius of the cylinder inscribed in the sphere.

We know that:

Volume of cylinder

V = [tex]\pi R^2h[/tex]    .....(1)

In right Triangle OBA

[tex]AB^2 + OB^2 = OA^2[/tex]

[tex]R^2 + \frac{h^2}{4} = r^2[/tex]

So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]

Putting the value of [tex]R^2[/tex] in equation (1), We get

V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]

V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex]   ....(2)

dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)

For, Stationary point, dV/dh = 0

[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0

[tex](r^2 - \frac{3h}{4} )[/tex]   => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]

Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]

[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex]   = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0

Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]

Maximum volume is :

[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]

[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

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Answer: wutttttttttt

Step-by-step explanation: i jus need points

By plotting y-intercept (0, -5) and any one of the points given in the table we can get the required line.

What is equation of the line?

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

Equation of the line has been given as,

[tex]y=\frac{3}{2} x-5$$[/tex]

By comparing this equation with the y-intercept form of the equation,

y=m x+b

Slope of the line ' m '[tex]$=\frac{3}{2}$[/tex]

and y-intercept ' b ' = -5

Table for the points to be plotted on a graph will be,

Table for the points to be plotted on a graph will be,

x              y

-4           -11

-2           -6

0            -5

2            -4

4            -3

By plotting y-intercept (0, -5) and any one of the points given in the table we can get the required line.

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The equation of the function described as;  y = 7 sin ( 4x + π/2 ) + 3

The general equation of the sine curve can be written as;

y = a sin ( nx + α ) + b

where : a is the amplitude, n = 2π/period, b = shift in the direction of y

            α°= shift in the direction of x

We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.

 Thus,

a = (maximum - minimum)/2 = (10 - -4)/2

a = 7

 n = 2π/period = 2π/(π/2)

n = 4

 b = maximum - a = 10 - 7

b= 3

To find α as y-intercept = 10

y = 10 at x = 0

Substitute in the general function;

y = a sin ( nx + α ) + b

10 = 7 sin ( 4*0 + α ) + 3

Thus, we have;

sin α = 1

α = π/2

So, the equation of the function described is;

 y = 7 sin ( 4x + π/2 ) + 3

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(a) The differential Equation that is satisfied by y is dy/dt = k × y × (1 - y)   ,

(b) Solution of the differential equation assuming y(0) = c is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .

In the question ,

Part (a)

let the fraction of people who heard the rumor is = y

So , the fraction who have not heard the rumor is = 1 - y .

the rate of rumor spread is ⇒ dy/dt = k×y(1 - y)

dy/y(1-y) = k.dt     ...where k is the constant of proportionality .

So , the differential equation is ..

dy/dt = k × y × (1 - y)

Part (b)

So , 1/y(1-y) = 1/y + 1/(1 - y)       ....equation(1)

integrating equation(1) , we get

∫dx/(1 + ax) = ㏑(1 + ax)/a     ,....where a is the constant

㏑y + ㏑(1-y)/(-1) = kt + d     ,.....where d is the constant

By using , ㏑a - ㏑b = ㏑(a/b) and taking exponential . we get ,

y/(1 - y) = c₁[tex]e^{k\times t}[/tex]

for t = 0 and y(0) = c

solving further , we get

c₁ = c/(1 - c)

So , y = (1-y)c₁[tex]e^{k\times t}[/tex]

y(1 + c₁[tex]e^{k\times t}[/tex]) = c₁[tex]e^{k\times t}[/tex]

y = c₁[tex]e^{k\times t}[/tex]/(1 + c₁[tex]e^{k\times t}[/tex])

taking c₁[tex]e^{k\times t}[/tex] common , and substituting the value of c₁ we get ,

the solution as , y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex]    .

Therefore , (a) the differential equation is dy/dt = k × y × (1 - y)   and

(b) the solution is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex]   .

The given question is incomplete , the complete question is

One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.

(a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.)

(b) Solve the differential equation. Assume y(0) = C.

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The null hypothesis set up for the hypothesis test of the population parameter is given by H₀: p ≥ 0.1 .

We would set up the hypothesis test.

For the null hypothesis,

H₀: p ≥ 0.1

For the alternative hypothesis,

Hₐ: p < 0.1

This is a two-tailed test.

Taking into account the population proportion, p = 0.1 q = likelihood of failure = 1 - p

q = 1 - 0.1 = 0.9

b) In light of the sample,

P = x/n = sample proportion

Where x = the number of successes, n = the number of samples, and p = 13/100 = 0.13

The test statistic, the z score, would be calculated as z = (P - p)/pq/n z = (0.13 - 0.1)/(0.1 0.9)/100 = 1.

The determined test statistic is 1 for the right tail and - 1 for the left tail.

Since α = 0.05, the critical value is calculated using the normal distribution table.

α₂ = 0.51/2 = 0.025 on the left

The z score for an area to the left of 0.025 is - 1.96

α₂ = 1 - 0.025 = 0.975 for the right

1.96 is the z score for an area to the right of 0.975.

The test statistic must be less than - 1.96 or larger than 1.96 in order to reject the null hypothesis.

We cannot reject the null hypothesis since - 1 > - 1.96 and 1 1.96.

As a result of the hypothesis test results, Eagle Outfitter should take the promotion national.

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It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.

As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.

The right axis indicates the global consumption rate of oil in millions of barrels per day.

To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.

The bottom axis is time in years.

The graph attached at the end of the solution.

Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.

Let the number of years of transition from using 100 million to 200 million barrels per day be b.

From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.

But it takes 50 years to go from 100 million to 200 million.

This is known as exponential growth.

Therefore, the value of a is 120 and the value of b is 50.

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1) The enrollment in 2016 will be 7500.

2) In 2026 year the enrollment reach 10,000.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function f(x) represents the number of enrollment.

Defined as;

⇒ F(x) = 250x + 6000

Where x represents year since 2010.

(1) Now for finding the enrollment in 2016;

Put x = 2016 - 2010 = 6 in the function

⇒ F(6) = 250x6 + 6000

          = 7500

Thus, The required number of enrollment = 7500

(2) Now we have to find the year in which enrollment reach 10,000;

i.e f(x) = 10,000

=> 250x + 6000 = 10000

=> 250x = 4000

=> x = 16

Thus, The required year = 2010 + 16

                                     = 2026 answer.

1) The enrollment in 2016 will be 7500.

2) In 2026 year the enrollment reach 10,000.

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Answer:

70

Step-by-step explanation:

The correct answer is A) y = 9000x + 65,000.

The correct answer is A) y = 9000x + 65,000.

The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).

The equation y = 9000x + 65,000

models the value of the house after x years, where y is the value of the house,

9000x is the slope of the equation,

and 65,000 is the y-intercept.

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The solution of the equation written as an imaginary number is y =  3i or -3i

An imaginary number is a number of the form ai, where a is a real number and i is the square root of -1. Imaginary numbers are often denoted with the letter "i".

Given: y² + 11 = 2

y² + 11 = 2

y² = 2 - 11

y² = -9

y = ±√-9                      

y = ± 3i

y = 3i or -3i

(Note: √9 = 3 and √-9 = 3i)

Thus, the solution is y =  3i or -3i

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Answer:

[tex]k = -4-\sqrt{7} \\or\\k = -4+\sqrt{7}[/tex]

Step-by-step explanation:

The Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample. Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.

We can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypotheses. However, the hypotheses can also be phrased in a general way that applies to any test.

We are given that to test the claim that marble color preference and club membership are related.

Thus, the Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".

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A sample of oxygen gas has a density of  0.0731 g/L g/L at a pressure of 1.12 atm and a temperature of 30∘C.

Let's start from the ideal gas law:

PV = nRT

Density = mass / volume.

While the ideal gas equation includes volume (V),  Well, we know that the mass of a sample is related to the number of moles (n) present. By using the molar mass of the gas, we can convert moles to mass. Since our gas is hydrogen, the molar mass of the gas is 2.016 g/mol (don't forget that hydrogen gas is diatomic)

n = m/M ; n = moles, m = mass (g), M = molar mass (g/mol)

If we substitute "m/M" in for "n" into our ideal gas equation, we get:

PV = (m/M) RT

We can now use algebra to rearrange this equation to solve for m/V (density).

m/V = PM / RT

m/V = (.965 atm)(2.016 g/mol)/(0.0821 L*atm/mol*K)(324 K)

m/V = 0.0731 g/L

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Answer:

  x = 15

Step-by-step explanation:

You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

  U +V +W = 180°

  (3x -10)° +(6x +5)° +(4x -10)° = 180°

  13x -15 = 180 . . . . . . . divide by °, collect terms

  13x = 195 . . . . . . . add 15

  x = 15 . . . . . . . divide by 13

The value of x is 15.

The ratio of rainy days to total days written as a percent will be 75%.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.

Since in the last 24 days, it rained 18 days.

Number of rainy days = 18.

Number of total days = 24

The ratio of rainy days to total days written as a percent will be:

= Number of rainy days / Total days × 100

= 18/24 × 100

= 3/4 × 100

= 75%

Therefore, the ratio is 3:4 which is 75%.

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Standard deviation will be √3.3516 .

To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².

After that , we have to calculate the Xbar by using

Xbar = ∑fiXi / N

for which we need the value of fi , Xi and N

N = 100

fiXi = 6478

we have calculated the values from the given data ,

Therefore ,

Xbar = 6478 / 100

= 64.78

Var(X) = αx² - ∑fiXi² / N - (Xbar²)

= 419980 / 100 - (64.78)²

= 4199.80 -4196.4484

=3.3516

Thus,

standard deviation ax = √var(X)

= √3.3516

Therefore , the standard deviation will be  √3.3516

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A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

Who is economist?

An economist is an expert who studies the relationship between society's resources and their production or output. Economists study societies ranging from small communities to whole nations to the global economy.

Economists expert opinions and research inform the design of a variety of policies, including interest rates, tax laws, employment programs, international trade agreements and corporate strategy.

The work of economists is incredibly diverse. Conduct surveys and collect data. Analyze data using mathematical models, statistical methods, and software. Present your research results in reports, tables, and graphs. Interpreting and forecasting market trends. Advises businesses, governments and individuals on economic matters. Proposing solutions to economic problems. Write articles for scientific journals and other media.

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

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k² + 10k + 8 is the sum of (3k² + 2k - 3) + (- 2k² + 8k + 11).

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. Mathematicians employ the action of addition to combine numbers. The sum of the given numbers is the outcome of addition, or the total of the inputted numbers. For instance, when we add the numbers 2 and 3, we get the number 5. Here, we added the two numbers 2 and 3 to obtain the result, which is 5.

Given

Polynomials

(3k² + 2k - 3) + (- 2k² + 8k + 11)

Adding the polynomials with same exponents

3k² + 2k - 3 - 2k² + 8k + 11

3k² - 2k² + 2k + 8k - 3 + 11

k² + 10k + 8

k² + 10k + 8 is the sum of (3k² + 2k - 3) + (- 2k² + 8k + 11).

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Answer:

Step-by-step explanation:

The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.

Answer:

-1/2x + y - 8 = 0

Step-by-step explanation:

To write the equation of a line in slope-intercept form, we need to know the slope of the line and the coordinates of a point on the line. We are given that the line has a slope of -1/2 and passes through the point (10, 8), so we can use the point-slope formula to write the equation of the line.

The point-slope formula for a line is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line. Substituting the given values into the formula, we get:

y - 8 = -1/2(x - 10)

Next, we can distribute the -1/2 to get:

y - 8 = -1/2x + 5

Finally, we can rearrange the terms to get the equation in standard form, Ax + By = C, where A, B, and C are integers:

-1/2x + y - 8 = 0

Thus, the equation of the line in Ax + By = C form is:

-1/2x + y - 8 = 0

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Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.

A system of equations, also called simultaneous equations, is two or more equations solved concurrently.

We can use any of the following methods to solve simultaneous equations:

In this situation, after forming the equations, we can use substitution and elimination methods to solve them.

Racetrack charge per lower seat = $85

Racetrack charge per upper seat = $60

Racetrack charge per field ticket = $35

Let lower seats = x

Let upper seats = 3x

Let field tickets = y

4x + y = 22,800 ... Equation 1

y = 22,800 - 4x ...Equation 3

85x + 60(3x) + 35y = 948,000

85x + 180x + 35y = 948,000 ... Equation 2

Substitute Equation 3 in Equation 2 to eliminate y:

85x + 180x + 35(22,800 - 4x) = 948,000

85x + 180x + 798,000 - 140x = 948,000

125x = 948,000 - 798,000

125x = 150,000

x = 1,200

Determining the number of seats:

Seats in the Lower section = 1,200

Seats in the Upper section = 3,600 (1,200 x 3)

Field tickets, y = 22,800 - 4x

y = 22,800 - 4(1,200)

= 18,000

Check:

85x + 180x + 35y = 948,000

85(1,200) + 180(1,200) + 35(18,000) = 948,000

102,000 + 216,000 + 630,000 = 948,000

948,000 = 948,000

Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.

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The probability of the sum of the numbers comes up on the facing dice add up to 3 while rolling two fair six sided dice is equal to ( 1/ 18).

As given in the question,

Number of six sided fair dice rolled = 2

Total number of outcomes of each dice = 6

Total number of outcomes of rolling two six sided fair dice = 36

Outcomes are:

( 1,1), (1,2)...(1,6),( 2,1), (2,2)...(2,6), ( 3,1), (3,2)...(3,6), ( 4,1), (4,2)...(4,6), ( 5,1), (5,2)...(5,6), ( 6,1), (6,2)...(6,6)

Sum of facing up dice add upto 3 are

( 1,2) , (2,1) only

Number of favorable outcomes = 2

Required probability = 2/36

                                = 1/18

Therefore, the required probability of the sum of facing up dice add upto 3 is equal to (1/18).

The given question is incomplete, I answer the question in general according to my knowledge:

Roll two fair 6-sided dice. what is the probability that the sum of the numbers on the dice facing up add up to 3?

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Answer:

u=94 Hope that helps. Mark as brainliest it helps

The solution to the systems of equations is (4,1). Option C. is the answer

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included

Given the: equations {(y=x²-2x+4), (y=3x):}

y= x²-2x+4 and y = 3x

substitute y = 3x into y= x²-2x+4. That is:

y= x²-2x+4

3x =  x²-2x+4

x²-2x -3x+4 = 0

x²-5x+4 = 0

By factoring:

x²-4x -1x+4 = 0

x(x-4) -1(x-4) = 0

(x-4)(x-1) = 0

x-4 = 0 or x-1 = 0

x= 4 or x = 1

Thus, the solution is (4,1)

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When the largest value of a data set is doubled, c) The interquartile range increases.

The average of the numbers is the mean. Calculating is simple: add up all the numbers, then divide by the total number of numbers. When the sample maximum and minimum are subtracted, the range of a set of data is the difference between the largest and smallest values. It uses the same units as the data to express itself.

A high standard deviation in a normal distribution denotes that values are typically far from the mean, while a low standard deviation denotes that values are grouped closely around the mean.

The difference between the third and the first quartile is defined by the interquartile range. The partitioned values known as quartiles divide the entire series into four equally sized segments. There are thus three quartiles.

Find the median (middle value) of the lower half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.

In this case, there'll be an increase in the IQR. Therefore, the correct option is C.

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Answer: I believe the answer is triangles b and e

Step-by-step explanation:

Translations preserve side length and the do not rotate they only move right and left and/or up and down. Therefor f is out because the sides get larger and a is out because it would be a reflection of the xaxis and d is out because it would a reflection over the yaxis. C and g are both rotations. This is why only B and E are translations of triangle y.

I hope this helps and makes sense! Let me know!

By solving the equation we get ,t = ± 7 using concept of square roots.

How to find the square roots ?

Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.

For example, 2 is the square root of 4, and this is expressed as √4 = 2.

We know that every squared number has two square roots one is positive and another is negative.

In given que,

given condition is t squared minus 49 = 0

Form of equation is ax^ 2 = c.

given condition can also be written as t^2 - 49 = 0

                                                          i.e. t^2 = 49

where a = 1

x = t

c = 49

So, the square root are 7 and -7.

So, equation become t = ± 7.

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When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

let length be l and width be w.

l=3w+8

l*w=256

(3w+8)*w=256

3w²+8w=256

3w²+32w-24w-256=0

3w(w-8)+32(w-8)=0

(3w+32)(w-8)=0

w=-32/3, 8

w=8 inch

l=3*8+8

l=32 inch

The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.

To know more about area,

https://brainly.com/question/22469440

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