Solve for r²
1
S= Ar^2h

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 7900\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 7900\left(1+\frac{0.023}{1}\right)^{1\cdot 5} \implies A=7900(1.023)^5\implies A \approx 8851.26[/tex]

By using linear equations, The winning team scored 3 less 3s than the losing team.

What are linear equations?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

For winning team

let x=no. of 2s and y=no. of 3s

Therefore, these linear equations will be formed

x+y=50

2x+3y=114

After solving these we get x=36 and y=14

For losing team

let a=no. of 2s and b=no. of 3s

Therefore, these linear equations will be formed

a+b= 48

2a+3b=113

After solving these we get a=31 and b=17

Difference between 3s scored=17-14

Difference between 3s scored=3

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Answer: 9y-4

Step-by-step explanation:

13y-4y=9y

7-11=-4

Answer:

13y+7-11-4y

13y-4y+7-11

9y-4 ans

Step-by-step explanation:

first combine the like terms along with their front sign

then sbtract 13y by 4y ,after subtract 7 from 11

[ here 7 have (+) and 11 have (-) before itself

according to the rule,(+) + (-) = (-)

hence we have to subtract 7 from 11 and put the (-) before answer]

but put sign (-) before the answer because we should always put that sign before answer which have more value

Answer:

The answer is 685 km hopefully I understood your question and helped you ☻

Step-by-step explanation:

710 km - 25 = 685

The zeros of this polynomial are (1, 0), (2, 0), and (0, 4).

The zeros of the polynomial can be determined by setting the equation equal to zero and solving for the roots.

For example, if the polynomial is given as [tex]ax^{2}[/tex] + bx + c, then the zeros can be determined by solving the equation [tex]ax^{2}[/tex] + bx + c=0.

Step 1: To determine the zeros of the polynomial, set the polynomial equal to 0 and solve for x.

f(x) = [tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0

Step 2: Factor the polynomial to solve for x.

[tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0

x([tex]x^{2}[/tex] - 3x + 4) = 0

Step 3: Factor the quadratic equation.

x(x - 1)(x - 2) = 0

Step 4: Set each factor equal to 0 and solve for x.

x = 0, x = 1, x = 2

Step 5: Plug each x-value into the original equation to determine the corresponding y-value for each zero.

When x = 0, y = 4

When x = 1, y = 0

When x = 2, y = 0

Step 6: The coordinate points of the zeros are (1, 0), (2, 0), and (0, 4).

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It is not possible to conclude a causal relationship from this study alone. This is because the study only shows a correlation between eating large amounts of bananas and being bitten by mosquitoes, it does not demonstrate that one causes the other. There could be other factors that are not controlled for in the study that could be the true cause of the relationship, such as people who eat more bananas also spend more time outdoors. To establish a causal relationship, further research would be needed such as a randomized control trial.

To determine a causal relationship between eating bananas and being bitten by mosquitoes, a randomized controlled trial could be conducted. This type of study would involve randomly assigning participants to two groups: one group would eat a large amount of bananas, while the other group would eat a smaller amount of bananas. The number of mosquito bites each participant receives would be recorded and compared between the two groups.

If the group that ate a large amount of bananas had a significantly higher rate of mosquito bites than the group that ate a smaller amount of bananas, it would suggest that eating bananas may cause an increase in the number of mosquito bites.

Additionally, other variables that could influence the result should be controlled or measured, such as time spent outdoors, skin type, or use of mosquito repellent.

It's important to note that even if the study shows a correlation between eating bananas and being bitten by mosquitoes, it doesn't mean that the banana causes the bites, there could be other factors that are not controlled for in the study that could be the true cause of the relationship.

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The number of centimetres in the 1 yard will be 9.144 cm.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that:-

Metric System Units

1 inch = 2.54 centimetres

1 foot = 0.3048 meters

1 mile = 1.61 kilometres

1 yard = 3 feet

1 yard = 36 inches

First, we will calculate 1 yard to feet.

1 yard = 3 feet

1 feet = 0.3048 meters

1 feet = 3.048 centimeters

1 yard = 3 x 3.048 centimeters

1 yard = 9.144 centimeters

Hence, the length of 1 yard in cm is 9.144 cm.

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The value of x and y is -10 and 5 respectively in the given equations.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first linear equation is - x + 3y = 5

The second linear equation is - -3x - 2y = 20

On evaluating individually the equation obtained is -

-3x - 2y + x + 3y = 20 + 5

-2x + y = 25

Multiply equation (1) with 3 -

3(x + 3y) = 5 × 3

3x + 9y = 15.....(3)

Adding equation (3) and (2) -

-3x - 2y + (3x + 9y) = 20 + 15

-3x - 2y + 3x + 9y = 35

-2y + 9y = 35

7y = 35

y = 35/7

y = 5

Substituting the value of y in equation (1) -

x + 3y = 5

x + 3(5) = 5

x + 15 = 5

x = 5 - 15

x = -10

Therefore, the value of x and y is -10 and 5 respectively.

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Hey Mate,

Answer is (4,3),

Thank you .

Considering the figure the side length x is solved to be 6.6

Information given from the question is interpreted as

√11 = adjacent

x = hypotenuse

The side x  is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The side x is calculated using cos, CAH

cos 60 = Adjacent / hypotenuse

cos 60 = √11  / x

x =  √11  / cos 60

x = 6.633

x = 6.6 to the nearest tenth

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Answer:

B) Horizontal Asymptote

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values get larger or smaller. The end behavior of a rational function is determined by the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the function will approach a horizontal asymptote as the x-values get larger or smaller. If the degree of the numerator is greater than the degree of the denominator, the function will not have a horizontal asymptote.

Triangle ABC is similar to triangle FGH.

And the value of the x is  22.5 centimeters.

Those triangles that looks the same but different in sizes.

And in the similar triangle,

the corresponding sides in proportion to each other and corresponding angles are equal to each other.

Given:

Triangle ABC is similar to triangle FGH.

That means, the corresponding sides of the triangles are in proportion to each other.

That means,

13.5/9 = 18/12 = x/15

Now,

18/12 = x/15

x = 270/12

x =22.5 centimeters

Therefore, the value of the x is 22.5 centimeters.

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The height of the mountain is 10000ft.

Now, According to the question:

A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base.

The snow covers 1,200,000 square feet of part of the mountain.

We know that:

Area of triangle = 1/2 × base × height

Area of a triangle = 1/2 × 2.4 h × h

1200000 = 2.4[tex]h^2[/tex]/2

cross multiply

1200000 × 2 = 2.4[tex]h^2[/tex]

2400000  = 2.4[tex]h^2[/tex]

Divide both sides by 2.4

[tex]h^2[/tex] = 2400000/2.4

[tex]h^2[/tex] = 1000000

h = √1000000

h = 1000  ft.

The height of the mountain = 1000 ft. + 9000 ft. = 10000 ft.

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Answer:

13.99 + 5.75 + 3.29 + 7.35 = 30.38

30.38 - .65 - 3.00 = 26.73

Step-by-step explanation:

Hope this helps! =D

Answer:

$26.73

Step-by-step explanation:

razor = $13.99 - $3.00(rebate) = $10.99

refill pack of razor blades = $5.75

shaving cream = $3.29 - $0.65(coupon) = $2.64

lotion = $7.35

The graph of the function is added as an attachment and the function values are y = 4 for all x values

From the question, we have the following parameters that can be used in our computation:

y=1-3sin(3/2)Theta

Express properly

So, we have the following representation

y = 1 - 3sin(3/2π)

Next, we create a plot of the graph (see attachment)

From the graph, we can see that the function is a horizontal line at y = 4

This means that for all x values, the y value is constant at 4

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The decrease in Kaitlin's investment account is 7%, which is calculated by multiplying the initial $5200 by 0.07.

This gives a decrease of $364. The amount in her account at the end of the year is the initial $5200 minus the decrease of $364, which equals $4836.

This can be expressed algebraically as:

Let x = amount in Kaitlin's account at the end of the year

Initial Amount (x) = 5200

Decrease (%) = 0.07

Decrease in Dollars = x * 0.07

Decrease in Dollars = 5200 * 0.07

Decrease in Dollars = 364

Amount in Account at the End of the Year = 5200 - 364

Amount in Account at the End of the Year = 4836

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Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

Given: Taylan sold 7 total frames, with the number of plastic frames being less than twice the number of wooden frames

Let x = number of wooden frames

Since the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation to represent this:

x + (x * 2) < 7

2x < 7

x < 7/2

x = 3

Therefore, Taylan sold 3 wooden frames and 5 plastic frames.

Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

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The addition of the two expression is 4a + 23

The term called expression in math is defined as the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Here we know that the following expression are known.

=> 14 - 3a

=> 7a - 9

Now, we have to perform the addition operation on it.

Then the expression can be written as

=> (14 - 3a) + (7a + 9)

Now, we have to combine the similar term of the expressions, then we get,

=> (14 + 9) + (-3a + 7a)

When we simplify this one then we get,

=> 23 + 4a

When we write it as the standard form, then we get,

=> 4a + 23.

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Mr. and Mrs. Zeta want to make sure that their baby's monogram, which consists of the first, middle, and last initials, is in alphabetical order with no letters repeated. We may utilize the idea of permutations to determine the number of possible monograms.

A permutation is a way to arrange a group of things in a particular sequence. In this instance, we are examining the alphabet's set of letters (from A to Z), and we are trying to determine how many different ways there are to arrange them so that the monogram is composed entirely of unique letters.

The breakdown of the computation is as follows:

There are 26 different alternatives for the first initial (A to Z).

Since the monogram must be in alphabetical sequence, the letter for the second initial must appear after the first initial. There are so 25 possibilities left (the letters that come after the first initial in the alphabet).

There are 24 possibilities left for the final initial (the remaining letters that come after the second initial in the alphabet).

By multiplying the alternatives for each initial, we can calculate the total number of possible monograms using the basic counting principle:

26 x 25 x 24 = 15,600

Because they must be in alphabetical order and contain no repeating letters, there are 15,600 number of monograms are possible .

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The radius is increasing at rate of [tex]\frac{10}{36\pi } \\[/tex]

What is volume ?

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

As we know Volume of sphere V=

[tex]V=\frac{4}{3} \pi r^3\\dv/dt=6\\Given\\radius=3cm\\[/tex]

so, we need to find dr/dt

Since there is no t in our equation. So differentiate using chain rule

[tex]\frac{dv}{dt} =\frac{dv}{dr} *\frac{dr}{dt} \\[/tex]

Since, in question it is given dv/dt=6

[tex]6=\frac{dv}{dr} .\frac{dr}{dt} \\[/tex]

To find dv/dr differentiate

 [tex]4/3\pi r^3\\dv/dr(\frac{4}{3} \pi r^3)=4\pi r^2\\6=4\pi r^2\frac{dr}{dt} \\[/tex]

Dividing

[tex]\frac{10}{4\pi (3)^2} =dr/dt\\dr/dt=\frac{10}{36\pi } \\[/tex]

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The radius is increasing at rate of 10/36π

What is volume ?

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

As we know Volume of sphere V= 4/3 πr³

dv/dt =6

Given  r = 3 cm.

so, we need to find dr/dt

Since there is not in our equation. So differentiate using chain rule

dv/dt =dv/dr * dr/dt

Since, in question it is given dv/dt=6

6 =dv/dr * dr/dt

To find dv/dr differentiate

dv/dr (4/3πr³) = 4πr²

6 = 4πr² dr/dt

Finally,

dv/dt = 10/36π

Hence, The radius is increasing at rate of 10/36π

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A ring with a idempotent not equal to 0 or 1 is 3 and 4.

Make (R,+) a domain that is integral.

As a commutative ring with two elements, R, ab = 0 when either an or b are equal to zero.

If a ∈ R is an idempotent element, then a ≠ 0,a ≠ 1 will result.

[tex]a^{2}[/tex] = a

We can take multiple of 1 because the same number return if we multiply 1 to any number.

[tex]a^{2}[/tex] = a·1

Subtract a·1 on both side, we get

[tex]a^{2}[/tex] - a·1 = 0

Taking a common

a(a -1) = 0

(a -1) = 0 or a =0

R has no zero divisors.

So, a = 1 or a = 0

As a result, the only idempotent elements in the integral domain R are 0 and 1.

A ring that is not equal to 0 or 1 and is idempotent.

A ring with respect to addition and multiplication is the set R = 0 through 5.

Let 3 ∈ R,

[tex]3^{2}[/tex] = 6+3 = 0+3 = 3

Let 4 ∈ R.

[tex]4^{2}[/tex] = 16 = 12+4 = 2

Hence, 3 and 4 are idempotent elements other than 0 and 1

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The complete question is:

An element x in a ring is called an idempotent if [tex]x^2[/tex] = x. Prove that the only idempotents in an integral domain are 0 and 1. Find a ring with an idempotent x not equal to 0 or 1.

The length of the altitude is 10. 4 yards

The formula for the perimeter of an equilateral triangle is expressed as;

P = 3a

Where;

Substitute the values

36 = 3a

Divide the value by the coefficient  of a

a = 36/3

a = 12 yards

Using the Pythagorean theorem, we get;

12² = h² + 6²

Find the square values

144 = h² + 36

collect like terms

h² = 108

Find the square root

h = 10. 4 yards

Hence, the value is  10. 4 yards

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The least possible value for the mode is D=11

Let M be the median

According to the question, the two largest integers are M+2

Let a and b be the two smallest integers such that a<b

Accordingly, the sorted list can be concluded as a,b, M, M+2, M+2

Since the median is 2 greater than their arithmetic mean, we have,

{a+b+M+(M+2)+(M+2)/5 }+2 =M

OR, a+b+14=2M

Note that a+b must be even.

We minimize this sum so that the arithmetic mean, the median, and the unique mode is minimized.

Let a=1 and b=3

from which M=9 and

M+2=11

Therefore, The least possible value for the mode is D=11

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The end behavior of the radical function represented by this graph is option C. As x decreases in value, f ⁡ ( x ) increases in value. As x increases in value, f ⁡ ( x ) decreases in value.

A radical function is a type of mathematical function that includes a radical symbol, such as a square root sign (√) or cube root sign (3√), in its equation.

The graph of a radical function is a curve that may open upward or downward, depending on the specific function. For example, the graph of the square root function, y = √x, starts at the point (0,0) and extends upward and to the right, creating a "V" shape. As the input (x) increases, the output (y) also increases, but at a decreasing rate.

Therefore, the correct answer is as given above

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Dupes's age is 14 year and Olu's age is 11 year now.

What is linear algebraic equations?

Unknown quantities can often be determined using linear algebra. Among linear algebra's practical uses are the following: to calculate time, distance, or speed. used by linear maps to translate a three-dimensional image into a two-dimensional plane.

Mathematical structures that can be closed under addition and scalar multiplication are the focus of this area of study, which also encompasses the theory of linear equation systems, matrices, determinants, vector spaces, and linear transformations.

Assume that Dupe is x years old and Olu is y. We may create two linear algebraic equations using the given data:

x + y = 25

(x - 8) = 2(y - 8)

This system of linear equations can be transformed into the following by using a little algebraic trickery:

x + y = 25

x - 2y = -8

To obtain x = 14 and y = 11, construct an augmented matrix and use either Gaussian elimination or Gauss-Jordan elimination.

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The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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The mean ,median ,mode and range of 75 55 68 44 82 28 19 31 75 36 59 93 48 are:

mean = 49.7

media = 55

mode=75

Range=74

The concept that can be used here is mean median and mode.

We will need to arrange the value from the lowest to the biggest as :

75 55 68 44 82 28 19 31 75 36 59 93 48

19 28 31 36 44 48 55 59 68 75 75 82 93

The mean can be calculated by adding all numbers in the data set and then dividing by the number of values in the set.

= (19+ 28+ 44 +48+55+ 59+ 68+ 75+ 75+ 82+ 93 )/13 =646/13= 49.7

Median = (n + 1)/2th value

Where n = numner of the given digits which is 13

= (13 + 1)/2th value

= 7th value

=55

Mode = is the number that occurs most often = 75

Range = highest value - lowet value = 93-19 =74

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The answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.

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