How can you write the prime factorization and find the greatet common factor and the leat common multiple of two number?

The annual interest rate of Niyati's invested to accumulate the accrued amount is 10%.

The formula for calculating compound interest is expressed as;

A = P( 1 + r )^t

Where A is accrued amount, P is principal , r is interest rate and t is time.

Given the data in the question;

To determine the annual interest rate, plug the given values into the equation and solve for r.

A = P( 1 + r )^t

r = (A/P)^1/t - 1

r = (( $1,210 / $1,000 )^1/2 ) - 1

r = (( 1.21 )^1/2 ) - 1

r  = 1.1 - 1

r = 0.1

Now, convert rate as percentage.

r = 0.1 × 100%

r = 10%

Therefore, the annual interest rate is 10%.

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Answer:

1 < x ≤ 6 is the solution

Step-by-step explanation:

Given

6 < x + 5 ≤ 11

Solution

Subtract 5 from the 3 terms. You do this so you can isolate x

6 - 5 < x + 5 - 5 ≤ 11 - 5

1 < x≤ 6

x lies between 1 and 6.

The equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.

What is the ratio?

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)

Luigi uses 39 mozzarella pearls for every 6 pizzas they make.

So the equivalent ratio would be 39/6

                                                     = 13:2

And similarly, Luigi uses 13 mozzarella pearls for every 4 pizzas they make.

So the equivalent ratio would be 13/4

                                                     = 13:4

Hence, the equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.

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Answer:

0.00896057348

Step-by-step explanation:

maybe I think I read it right but don't count on me

Answer: 1/4

Step-by-step explanation:  If you divide them both you get 0.25 and that's just 1/4.  Hope it helps.

The periodic interest rate for an account that is billed monthly with an APR of 32.99% will be 2.74%

Periodic interest rate is rate of interest over a short period of time. It is found by dividing APR ( annual percentage rate ) by the period of time given to us.

In this question it is given to us that the account is billed monthly so

periodic interest rate = 32.99 / 12

= 2.74%

Therefore periodic interest rate will be 2.74 for this account.

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The  slope of the line passes through the point (40,89) and (28,7) is   [tex]\frac{41}{6}[/tex].

What is slope?

It is possible to determine a line's direction and steepness by looking at its slope. Without using a compass, determining the slope of lines in a coordinate plane can assist forecast whether the lines are parallel, perpendicular, or none at all. The slope of any line can be computed using any two distinct locations on the line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

Here the given points are

[tex](x_1,y_1)=(40,89)\\(x_2,y_2)=(28,7)[/tex]

Now using slope formula ,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = [tex]\frac{7-89}{28-40}[/tex]

=> slope m=[tex]\frac{82}{12}[/tex]

=> slope m = [tex]\frac{41}{6}[/tex]

Hence slope of the line passes through the point (40,89) and (28,7) is   [tex]\frac{41}{6}[/tex].

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First Dave picks his swimming day, then his running day, and then his biking day. Since each activity is different, the order in which he selects the days matters. Therefore the number of selections is P(7, 3).

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 1/2.

Here,

He does 3 activities in 7 days,

P(7,3) is the ways to select the schedule.

Dave chooses his swimming, running, and biking days in that order. The sequence in which he chooses the days is important because each activity is distinct. Consequently, P is the number of choices (7, 3).

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The maximum value is; +√21 and the minimum value is; -√21

Function is a type of relation, or rule, that maps one input to specific single output.

We are given that

f(x,y,z) = x² + y² + z²

g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

Using Lagrange multipliers as follows;

df/dx = λg/dx,

df/dy = λg/dy.

df/dz = λg/dz

Thus, df/dx = 2x, df/dy = 2y, df/dz = 2z

dg/dx = 4x³,  dg/dy = 4y³, dg/dz = 4z³

So, df/dx = λg/dx

2x = 4λx³     (1)

df/dy = λg/dy

2y = 4λy³           (2)

df/dz = λg/dz

2z = 4λz³           (3)

From (1) 4λx³ - 2x = 0

2λx³ - x = 0

x(2λx² - 1) = 0

Now solving; x = 0 or (2λx² - 1) = 0

2λx² = 1

x = ±1/√(2λ)

since x ≠ 0

From (2) 4λy³ - 2y = 0

2λy³ - y = 0

y(2λy² - 1) = 0

Now solving, y = 0 or (2λy² - 1) = 0

2λy² = 1

y = ±1/√(2λ) since y ≠ 0

From (3) 4λz³ - 2z = 0

2λz³ - z = 0

z(2λz² - 1) = 0

now solving, z = 0 or (2λz² - 1) = 0

2λz² = 1

z = ±1/√(2λ) since z ≠ 0

Then we have g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

(1/√(2λ))⁴ + (1/√(2λ))⁴ + (1/√(2λ))⁴ - 7 = 0

3 (1/√(2λ))⁴ = 7

(1/√(2λ))⁴ = 7/3

1/√(2λ) = ⁴√7/3

√(2λ) = ⁴√3/7

2λ = √3/7

λ = 1/2(√3/7)

Since we know that x = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Also, y = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

and, z = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Now Substituting x,y and z into f(x,y,z) we have;

f(x,y,z) = (⁴√7/3)² + (⁴√7/3)² + (⁴√7/3)² = 3(⁴√7/3)² = 3(√7/3) = √(7 × 3) = ±√21

Hence, the maximum value is +√21 and the minimum value is -√21

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a. The number of students that this school is going to have to enroll abroad in the year 2001 is 150

b. In the 2018 academic year, it can be said that the school would also have to enroll 468 students in the school

a. The equation is as follows:

y = 123.1 * (1.069)^x

The value of x would be years that have changed.

To get the value of x we would have to find the differences that lies in the two years.

Hence

2001 - 1998 = 3

We would place the value of x in the equation

y = 123.1(1.069)³

Then

y = 150.4

This is approximately 150.

In conclusion, There would be 150 students enrolled in the school, according to estimates, in 2001.

b. For the year 2018

We would have to carry out similar calculation

x = 2018 - 1998

This would give us  20 years difference

Place x = 20 in the equation

y = 123.1(1.069)²⁰

y = 467.5

This is approximately

y ~ 468

468 would be enrolled in the school in 2018.

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Atleast 212 meal tickets need to sold to raise atleast $2,000 as fund.

Given:

Meal tickets for 8.50 per dinner

Donation = $200 donation

To raise at least = $2000

To find the number of meal tickets to be sold for raise at least $2000

Now, According to the question:

Based on the given condition:

$(8.50 x n + 200) = $2,000

=> 8.5n + 200 = 2,000

=> 8.5n = 2,000 - 200

=> 8.5n = 1,800

n = 1800/8.5

n = 211.76

n ≅ 212 {as tickets sold in integers }

Hence, Atleast 212 meal tickets need to sold to raise atleast $2,000 as fund.

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a = -2 is the value of linear equation .

What are examples of linear equations?

Step 1 - Write the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 2 - rewrite the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 3 - Take the LCM.

3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4

Step 4 - Further simplify the above expression

3a - 6 - a - 2/a² - 4 = 6a/a² - 4

Step 5 - Cancel out the denominator of both sides and then further simplify.

2a - 8 = 6a

a = -2

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The complete question is -

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.

3/a + 2 − 6a/a2 − 4 = 1/a − 2

Answer:

Step-by-step explanation:

According to triangle proportionality theorem we have equal ratios:

The value of x will be 6 units.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown is figure.

Now,

By the definition of triangle proportionality theorem, we get;

⇒(6x - 1 - 14)/14 = (15 - 6)/6

Solve for x as;

⇒ (6x - 15)/14 = 9/6

⇒ 6x - 15 = 9×14/6

⇒6x - 15 = 21

⇒ 6x = 21 + 15

⇒ 6x = 36

⇒ x = 6 units

Thus, The value of x will be 6 units.

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The complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

From the question, we have the following equation:

f(x) = 3ˣ

From the table of values, we have the following x values

x = -2, -1, 0, 1 and 2

Substitute x = -2, -1, 0, 1 and 2 in the equation f(x) = 3ˣ

When x = -2

f(-2) = 3⁻² = 1/9

When x = -1

f(-1) = 3⁻¹ = 1/3

When x = 0

f(-1) = 3⁰ = 1

When x = 1

f(1) = 3¹ = 3

When x = 2

f(2) = 3² = 9

Hence, the complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

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The value of n is 1, compound interest of the end of year.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is calculated by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/4)4t

where S= Amount at the end of n years = 3445.51

P = Principal = 2400

r = Rate of interest = 0.075

n = 1 as interest is compounded annually

Try to find it's value by solving. The number of years will be provided.

Hence the value of n is 1.

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Answer:

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent.

The minimum unit cost is 8099.

Given:

A supply company manufactures copy machines. the unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function.

C(x)=0.8x^2-208x+21,619

derivative of C(x):

C'(x) = 0.8*2 x - 208+0

0 = 1.6 x - 208

1.6x = 208

divide by 1.6 on both sides

x = 208/1.6

= 208/16/10

= 208*10/16

= 2080/16

= 1040/8

= 520/4

= 260/2

x = 130

C(130) = 0.8*130^2-208*130+21619

= 16900*0.8 - 27040 + 21619

= 13520 - 5421

= 8099

Therefore the minimum unit cost is 8099.

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150cm² is the area of the given parallelogram.

So we understand that Rectangles are parallelograms.

They have the same formula for finding the perimeter and area.

Therefore, 150cm² is the area of the given parallelogram.

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AC is not perpendicular to XZ, because the slope of AC is -1 and the slope of XZ is 2/3. Therefore, the correct answer options are:

B. Is not

A. -1

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For the slope of AC, we have the following:

Point at A = (-1, 3)

Point at C = (4, -2)

Slope, m of AC = (-2 - 3)/(4 - (-1))

Slope, m of AC = (-2 - 3)/(4 + 1)

Slope, m of AC = -5/5.

Slope, m of AC = -1.

For the slope of XZ, we have the following:

Point at X = (12, 2)

Point at Z = (6, -2)

Slope, m of XZ = (-2 - 2)/(6 - 12)

Slope, m of XZ = -4/-6.

Slope, m of XZ = 2/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1 × 2/3 = -1

-2/3 = -1 (False).

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The largest Volume of the box possible is 4000 cm³ .

In the question ,

it is given that

the box has a square base ,

let the length and width of the box = "x" , because it is a square

let the height of the box [tex]=[/tex] h

the total surface area of the box = 1200

also the total  surface area with open top is = x² + 4xh

So , x² + 4xh = 1200

h = (1200 - x²)/4x

According to the question ,

the volume of the box = x²h

Substituting the value of h = (1200 - x²)/4x ,

we get ,

Volume = x² × (1200 - x²)/4x

V = (1/4)(1200x - x³)

to Maximize the volume dV/dx = 0

(1/4)(1200 - 3x²) = 0

1200 - 3x² = 0

3x² = 1200

x² = 400

x = -20 , +20

length cannot be in negative , hence x = 20 ,

So , Volume = (1/4)[1200(20) - 20³]

= 4000 cm³

Therefore , The largest Volume of the box possible  is 4000 cm³ .

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Answer:

0.375

Step-by-step explanation:

The final polynomial equation after synthetic division is [tex]x^5-3x^4-81x+243[/tex]

We need to solve;

Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.

The polynomial equation given is;

[tex]\left(x^4-81\right)\left(x-3\right)[/tex]

By using synthetic division;

⇒ [tex]x^4x+x^4\left(-3\right)-81x-81\left(-3\right)[/tex]

    [tex]x^5-3x^4-81x+243[/tex]

→ The required final equation in descending powers of x is [tex]x^5-3x^4-81x+243[/tex] .

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For a lower tail test, the p-value is the probability of obtaining a value for the test statistic as small as or smaller than that provided by the sample. For an upper tail test, the p-value is the probability of obtaining a value for the test statistic as large as or larger than that provided by the test statistic.

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. The p-value serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

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The scores of geography, economics and science are 38, 76, 80 respectively.

Let Yakubu scored x marks in geography.

Given that the score of him in economics is twice of the score of him in geography.

So, his score in economics = 2x

Again it is given that, the score in science is 4 more than the score in economics.

So the score in science = 2x+4

According to question the combined total score is 194. So the suitable equation is,

x+2x+2x+4 = 194

Solving the equation we get,

5x+4 = 194

5x = 194-4

5x = 190

x = 190/5

x = 38

So the score in geography = 38

the score in economics = 2x = 2*38 = 76

the score in science = 2x+4 = 2*38+4 = 76+4 = 80

Hence the scores of geography, economics and science are 38, 76, 80 respectively.

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The value of x is 7 and the value of y is 37. These values of x and y results in congruence.

For the two triangles, Δ LMN and Δ PQR,

Side LM = Side PQ,

Side LN = Side PR

Side MN = Side QR

⇒ Δ LMN and Δ PQR are congruent by (S.S.S : side side side) property

Since both the triangles are congruent to each other. There corresponding angles will be equal.

i.e. ∠ L = ∠ P, ∠ N = ∠ R and ∠ Q = ∠ M.

⇒ ∠ L = ∠ P

⇒ 3x + 24 = 8x - 11

⇒ 24 + 11 = 8x - 3x

⇒ 5x = 35

⇒ x = 7

In Δ PQR, sum of all angles is 180°

⇒ ∠P + ∠Q + ∠R = 180°

⇒ (8x - 11)° + 84° + ∠R = 180°

⇒ (8×7 - 11)° + 84° + ∠R = 180°

⇒ 45° + 84° + ∠R = 180°

⇒ 129° + ∠R = 180°

⇒ ∠R = 180° - 129° = 51°

We know that ∠N = ∠R

⇒ (2x + y) = 51

⇒ (2×7) + y = 51

⇒ y = 51 - 14 = 37

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an=an-1+6, written in explicit formula when a = 9 is aₙ = 9n+5

An explicit formula is given as aₙ= a + (n - 1) d

where,

aₙ = nth term of the arithmetic sequence

a = the first term of the arithmetic sequence

d = the common difference

Given: aₙ = an-1+6 ;a1= 9

Substitute a = 9 into the equation:

aₙ = 9n-1+6

aₙ = 9n+5

Therefore, an=an-1+6, when a = 9 written in explicit formula, is aₙ = 9n+5

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Answer:

45c−20c2

Step-by-step explanation:

have great day

The line parallel to line AB will have the same slope with different

y-intercepts.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know lines parallel to each other have the same slope with a different y-intercept.

Suppose the line AB has an equation y = mx + b.

∴ The line parallel to line AB will have an equation y = mx + c.

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Answer:

y=1/2x-3

Step-by-step explanation: if you are using edmentum this is correct.

The inverse of the given function is, h^(-1)(x) = (x - 8)/6.

What is inverse of function?

What a function's inverse function is F is a function that reverses what F did. The inverse of f is represented by f-1 if it exists and only if f is a bijective function.

Consider, the given function

h(x) = 6x + 8

Let,

y = 6x + 8

Replace x with y,

x = 6y + 8

Solving the equation for y,

x - 8 = 6y

y = (x - 8)/6

Replace y with h^(-1)(x),

So,

h^(-1)(x) = (x - 8)/6.

Hence the inverse of the given function is, h^(-1)(x) = (x - 8)/6.

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