( Look at picture) Thx btw

The amount invested in the two different bank accounts which has a simple interest of $ 560 is $ 2000 and $ 4000 respectively

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as SI

The value of SI = $ 560

Now , the total amount A = $ 6000

Let the first bank account be A

Let the second bank account be B

The amount invested in the bank account A be = P

The amount invested in the bank account B be = ( 6000 - P )

The rate of interest of bank account A = 8 %

The rate of interest of bank account B = 10 %

Now ,

The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

The SI of bank account A = ( P x 8 x 1 ) / 100

The SI of bank account A = 8P/100

And ,

The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

The SI of bank account A = [ ( 6000 - P ) x 10 x 1 ] / 100

The SI of bank account A = ( 60000 - 10P ) /100

And , the total SI = $ 560

So ,

8P/100 +  ( 60000 - 10P ) /100 = 560

Multiply by 100 on both sides of the equation , we get

8P + 60000 - 10P = 56000

On simplifying the equation , we get

-2P = -4000

Divide by -2 on both sides of the equation , we get

P = $ 4000

So , the amount invested in bank account A = $ 4000

And , the amount invested in bank account B = $ 2000

Hence , the amount invested is $ 4000 and $ 2000 respectively

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Answer:

You will need 3 [tex]\frac{11}{15}[/tex] cups of sugar.

Step-by-step explanation:

1 1/3 x 2 4/5

another name for 1 is 3/3

3/3 + 1/3 = 4/3

Another name for 1 is 5/5

5/5 + 5/5 + 4/5 = 14/5

[tex]\frac{4}{3 }[/tex] x [tex]\frac{14}{5}[/tex] = [tex]\frac{56}{15}[/tex]

I can break 56 into 15 + 15 + 15 + 11

[tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{11}{15}[/tex]  another name for [tex]\frac{15}{15}[/tex] is 1

1 + 1 + 1 + [tex]\frac{11}{15}[/tex]

3 [tex]\frac{11}{15}[/tex]

Answer:

Step-by-step explanation:

The three numbers are 50, 40, and 27.

We can solve this equation by setting up a system of equations.

Let x be the first number, y be the second number, and z be the third number.

x + y + z = 117

y = x - 10

z = (1/2)x + 2

Substituting the equation for y into the first equation, we get:

x + (x - 10) + (1/2)x + 2 = 117

2x - 8 = 117

2x = 125

x = 62.5

Substituting this value of x into the other equations, we get:

y = x - 10 = 62.5 - 10 = 52

z = (1/2)x + 2 = (1/2)62.5 + 2 = 32.5 + 2 = 34.5

Rounding these values, the three numbers are 50, 40, and 27.

The number which is lesser than its square is 12/11

When a number is multiplied by itself, the result is a square number. For instance, 25 is a square number as it is composed of 5 lots of 5, or 5 × 5. 

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.

The numbers are

9/10 , 12/11 , 15/16 and 13/13

The squares are

81/100, 144,121, 225/256, 1

here

81/100 < 9/10 abd

225/256 < 15/16

144/121 > 12/11

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Gina sold more than twice as many TVs as Ethan, because 19 > (2 * 8)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Ethan sold exactly eight TVs this quarter.

Ethan TV = 8

Gabriel sold more TVs than Ethan, hence:

Gabriel TV (G) > 8

Gabriel TV > 8

Gina sold exactly three more TVs than Gabriel and Ethan combined

Gina TV = Gabriel TV + 8 + 3

Gina TV > 8 + 8 + 3

Gina TV > 19

Frank sold exactly twice as many TVs as Gina, hence:

Frank TV = 2 * Gina TV

Frank TV > 2 * 19

Frank TV > 38

Gina sold more than twice as many TVs as Ethan.

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well,  the number is really "x", which oddly enough is the 100%.

we also know that 3/4% of "x" is 24, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\[1em] 24&\frac{3}{4} \end{array}\implies \cfrac{x}{24}~~ = ~~\cfrac{100}{~~ \frac{3 }{4 } ~~}\implies \cfrac{x}{24}=\cfrac{400}{3} \\\\\\ 3x=9600\implies x=\cfrac{9600}{3}\implies x=3200[/tex]

Answer:

\frac{27}{17}+\frac{28}{17}i

Step-by-step explanation:

Answer:

Step-by-step explanation:

A line of reflection can be represented by a line of dashes that is used to reflect a geometric shape or figure over it.

A line of reflection can be represented by a line of dashes, which is the mirror line. When a shape is reflected over it, the shape is flipped over the line in a 180-degree angle, creating a mirror image of the original shape.

For example:

(Picture attached)

In this example, the horizontal line represented by the dashes is the line of reflection. If a shape is reflected over this line, it would create a mirror image of the original shape.

Please note that this representation is only for visualization purposes and it's not a mathematical representation.

The number of different sequences of tosses could there have been, if the number of tosses was even 1/2

You should understand that the tosses involves a sequence which is an array of numbers in a particular order

The question reads thus How many different sequences of tosses could there have been, if the number of tosses was even.

Number of tosses = 12

The tosses are 1,2,3,4,5,6,7,8,9,10,11,12 = 12 Times

The even numbers are

2,4,6,8,10,12 = 6 times

The Probability of the toss is 6/12

Therefore the number of tosses equals 1/2

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Answer:

-2 is not a solution of the inequality 6g - 14 > 21.

Step-by-step explanation:

To determine if -2 is a solution of the inequality 6g - 14 > 21, we need to substitute -2 for g in the inequality and see if it is true.

6g - 14 > 21

6(-2) - 14 > 21

-12 - 14 > 21

-26 > 21

This inequality is not true. Because -26 is not greater than 21.

[tex]6g-14 > 21[/tex]

Substitute -2 for g:

[tex]6(-2)-14 > 21[/tex]

[tex]-12-14 > 21[/tex]

[tex]-26 > 21[/tex]

-2 is not a solution because -26 is not greater than 21.

Therefore , the solution of the given problem of elevation comes out to be

X = 21.23°.

When it is between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.

Here,

Given :  tan X = P/ B

tan X = 68 / 175

X  = tan⁻¹ (68 /175)

X = 21.23

Therefore , the solution of the given problem of elevation comes out to be

X = 21.23°.

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The p-value for right tailed test based on the information will be 0.2147.

The p-value, under the assumption that the null hypothesis is true, is the likelihood of obtaining results from a statistical hypothesis test that are at least as extreme as the observed results. The p-value provides the smallest level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by stronger evidence when the p-value is lower.

In this case, the survey was done to test the claim that 20% of adult Americans believe that the lottery is the path to riches. The hypothesis test of H0: p=.2 versus Ha: p>.2 resulted in 0.79 for a right-tailed test

The Z statistic given to be =0.79 for a right tailed test. Here, by looking aththe distribution table, the p value for Z=0.79 for one tail test is 0.2147.

So, we do not reject null hypothesis and then conclude that data does not provide sufficient evidence that the proportion of Americans who believe path to riches is the lottery is greater than 0.2

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The survey methods that would result in a valid random sample of the community include:

Option E. All of the above is correct.

Simple random sampling involves selecting a random sample of participants from a larger population using a random number generator or a random sampling software. This method ensures that every member of the population has an equal chance of being selected.

Stratified random sampling involves dividing the population into smaller groups or strata based on certain characteristics, such as age, gender, income, etc. A random sample is then selected from each stratum. This method is useful when the population is heterogeneous and you want to ensure that the sample is representative of the entire population.

Systematic sampling involves selecting participants at regular intervals from a list of the population. This method is useful when the population is ordered, such as a list of customers.

Cluster sampling involves selecting a random sample of clusters or groups from the population, and then sampling individuals within those clusters. This method is useful when the population is geographically dispersed or it's difficult to obtain a complete list of the population. So Lily can use any of these survey methods to come up with a sample of the community.

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Options for this question include:

The gain percentage is 12.5%

First, let`s find the Cost price (C.P) of the sofa.

Let C.P of the sofa be x.

Now, according to the question:

x+ 7% of x=Rs.3852

x + (7/100 * x) = 3852

x + 0.07x = 3852

1.07x = 3852

x=3852/1.07,

x = Rs 3600.

Now the dealer sells it for Rs 4050.

so, the Formula for gain% is=(Selling price-Cost price/Cost price)x100

Gain %= (4050-3600/3600)x100

Gain%=(450/3600)x100

Gain%=(450/36)

i.e = 12.5%.

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Answer:

The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = 2750, r = 0.035, n = 4 (because interest is compounded quarterly) and t = 7 (because we are trying to find the balance after 7 years).

So the formula becomes:

A = 2750(1 + 0.035/4)^(4*7)

By plugging the number into the formula we can find the final amount after 7 years

A = $3,974.23

So the amount of money in the account at the end of 7 years is $3,974.23, rounded to the nearest hundredth.

The length of RZ is obtained as follows:

RZ = 11.5.

From the kite given by the image at the end of the answer, the segment lengths are given as follows:

Segments WX and WZ are congruent, hence segment WZ has the length given as follows:

WZ = 14.

Then the length of RZ is obtained considering a right triangle, for which:

The Pythagorean Theorem states that the length of the hypotenuse squared is equals to the sum of the lengths squared of the sides.

Considering the Pythagorean Theorem, the length RZ is obtained as follows:

x² + 8² = 14².

[tex]x = \sqrt{14^2 - 8^2}[/tex]

x = 11.5.

RZ = 11.5.

The problem is given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

Q1)

A toffee costs $0.15 + $0.10 = $0.25

If you buy 15 candies, it will cost you 15* $0.15 = $2.25

If you buy 12 toffees, it will cost you 12* $0.25 = $3.00

So buying 15 candies is $3.00 - $2.25 = $0.75 cheaper than buying 12 toffees.

Q2)

The original price of two tennis rackets is $120 x 2 = $240

The original price of three cans of tennis balls is $15 x 3 = $45

So the original price of two tennis rackets and three cans of balls is $240 + $45 = $285

By buying two tennis rackets and three cans of balls at the sale price of $255, you save $285 - $255 = $30 off the original price.

The square root of 625 is 25 and the square root of 25 is 5. Therefore, option A and F are the correct answers.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

A) [tex]625^{\frac{1}{2}[/tex]

= [tex](25^2)^{\frac{1}{2}[/tex]

= 25

F) 25

= 5

Therefore, option A and F are the correct answers.

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Answer: The equation for the translation of x2 + y2 = 64 three units to the left and two units down is:

(x − 3)2 + (y − 2)2 = 64

Step-by-step explanation:

This is known as the standard equation of a circle centered at (3, 2) with a radius of 8.

When translating a shape, we need to change the center point of the shape. If we want to translate 3 units to the left and 2 units down, it means that we need to change the center point of the shape from the origin to (3, 2). This can be achieved by subtracting 3 from x and subtracting 2 from y in the equation of the circle. This results in (x - 3)2 + (y - 2)2 = 64, which is the equation for the translated circle.

Answer: (x - 3)^2 + (y - 2)^2 = 64.

Step-by-step explanation:

This is because to translate a point or a function in the x-axis by a certain value we need to add or subtract the value from the x variable. To translate in the y-axis we need to add or subtract the value from the y variable. In this case, we are translating it three units to the left, so we subtract 3 from x, and two units down so we subtract 2 from y.

The amount that will be realized after 7years is $3459.5

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Amount in Compound interest is given as:

A = P(1+r/n)^nt

Where A is the amount

P is the principal

t is the duration and

n is the period of compoundment

r is the rate

n= ¼, r = 3.5/100 = 0.035

therefore A = 2750(1+0.035/0.25)^0.25×7

A = 2750( 1+0.14)^1.75

A= 2750(1.14)^1.75

A = 2750×1.258

A = $3459.5

Therefore the amount after 7 years is $3459.5

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a) 5-5 is a numerical expression

b) c-5 is a variable expression where, variable is c

c) 8÷x+9 is a variable expression where, variable is x

d) 100·6 is a numerical expression

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Staff at the learning center can teach whole groups of students who need extra help or focus on working one-on-one with a specific child. They work on improving knowledge of academic subjects like biology as well as skills like reading comprehension.

Learning centre instructors work in programmes that assist at-risk students in strengthening their academic skills. Learning centre instructors can work for a private or public learning centre. Learning centre instructors work with students to teach them valuable skills and academic subjects no matter where they work.

Learning centre instructors can teach large groups of students who require extra assistance or work one-on-one with a specific child. They work on improving academic knowledge, such as biology, as well as skills, such as reading comprehension.

They are in charge of creating the overall curriculum and training programme. Learning centre instructors must also have excellent classroom management skills as well as patience in order to work with students who are experiencing difficulties.

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{5}{x}[/tex] - [tex]\frac{2}{x^2}[/tex] = 2

multiply through by x² ( x ≠ 0 ) to clear the fractions

5x - 2 = 2x² , that is

2x² = 5x - 2 ( subtract 5x - 2 from both sides )

2x² - 5x + 2 = 0 ← in standard form

(2x - 1)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 2 = 0 ⇒ x = 2

since x₁ < x₂ , then

x₁ = [tex]\frac{1}{2}[/tex] and x₂ = 2

Then

3x₁ + x₂

= 3 × [tex]\frac{1}{2}[/tex] + 2

= [tex]\frac{3}{2}[/tex] + 2

= [tex]\frac{3}{2}[/tex] + [tex]\frac{4}{2}[/tex]

= [tex]\frac{7}{2}[/tex]

Answer:

¥4050

Step-by-step explanation:

The exchange rate given is ¥81 to 1 US dollar.

1 US = ¥81.

You are trying to solve for the amount of yen it will cost if the equivalent is $50.

Multiply $50 US, with ¥81 (as it is the exchange rate):

$50 * (¥81/$1) = ¥4050

¥4050 is your answer.

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Answer: yes, it is

Step-by-step explanation:

Answer:4

Step-by-step explanation:

Answer:no

Step-by-step explanation:

Answer:

Step-by-step explanation:

.

The best way for Anthony to plan his garden is to create a rectangular plot. He can use the side of the barn as one side of the rectangle, and then measure out the other three sides. The total length of the three sides will be 176 feet. He can divide this into two sides that are 88 feet long and two sides that are 44 feet long. This will give him a rectangular plot that is 176 square feet.

Once Anthony has the dimensions of the plot, he can build a fence around it to protect it from rabbits. He can use a variety of materials such as wood, wire, or plastic mesh to build the fence. The fence should be at least four feet tall and buried at least six inches deep to be effective. If he chooses to use wire, he should use thick, galvanized wire to make sure that the rabbits cannot chew through it.

Once the fence is in place, Anthony can begin planting his garden. He should also consider adding a layer of mulch or straw around the outside of the fence to discourage the rabbits from digging underneath it. With the right planning and protection, Anthony should be able to enjoy a successful garden.

Answer: 4

Step-by-step explanation: Amplitude has to do with how high and low the function goes according to the midline. The midline for this function is at -3. The maximum point is 1, and the minimum point is -7. The function goes up 4 units and down 4 units

Answer:

Amplitude = 4

Step-by-step explanation:

The amplitude of a sinusoidal function is the height (vertical distance) from the midline to the peak (or trough).

To calculate the amplitude, simply divide the vertical distance between the maximum and minimum y-values by 2.

From inspection of the given graph:

Therefore:

[tex]\implies \sf Amplitude = \dfrac{1-(-7)}{2}=\dfrac{8}{2}=4[/tex]

Answer:

third option

Step-by-step explanation:

Instead of having a constant rate of change, the third option does not as it goes up by 1 then 3 then 5