The area of a square floor on a scale drawing is 36 square centimeters, and the scale drawing is 1 centimeter:3 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?

David has $165 more money than Charles after 1 year of investment with an annual return of 5.4%.

The Simple Interest (S.I.) formula is a way to figure out how much interest will accrue on a given principal sum of money. Have you ever run out of pocket money and borrowed money from your siblings? Or perhaps lent him? What occurs when you take out a loan? You put the money to the use for which you originally borrowed it. When your parents give you pocket money for the following month, you return the money at that time. This is how lending and borrowing operate at home.

The investment is made as simple interest as the returns are calculated at the end of the year.

The simple interest is given by:

SI = PRT

For Charles:

P = $5000

R =0.021

T = 1

SI = (5000)(0.021)(1)

SI = $105

Total amount = 5000 + 105 = $5105.

For David:

P = $5000

R = 0.054

T = 1

SI = (5000)(0.054)(1)

SI = 270

Total amount = 5000 + 270 = $5270.

Thus, the difference between the two investment is:

A = 5270 - 5105

A = 165.

Hence, David has $165 more than Charles after 1 year of investment with an annual return of 5.4%.

Learn more about simple interest here:

https://brainly.com/question/25845758

#SPJ1

(4x³- 4 + 7x) - (2x³ - x - 8) is equivalent to expression 2x³ + 8x + 4. Option B

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x)  is equivalent to expression 3x⁴ - 3x² + 5x - 7. Option D

(x² - 2x) (2x + 3) is equivalent to expression 2x³ - x² - 6x. Option A

From the information given, we have that the expressions are;

(4x³- 4 + 7x) - (2x³ - x - 8)

expand the bracket, we have;

4x³ - 4 + 7x - 2x³ + x + 8

collect the like terms, we have;

2x³ + 8x + 4

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x)

expand the bracket, we have;

-3x² + x⁴ + x + 2x⁴ - 7+ 4x

collect the like terms

3x⁴ - 3x² + 5x - 7

(x² - 2x) (2x + 3)

expand

2x³ + 3x² - 4x² - 6x

2x³ - x² - 6x

Learn more about equivalent expression at: https://brainly.com/question/4344214

#SPJ1

Answer: 25 times 50 = 1,250 inches every inch is 50 miles on the second map

Step-by-step explanation: hope i could help you

Answer: Observational Study

Natalie is observing the people who step on the seal, and counting each one through a tally system or frequency table. By frequency table, I mean that she may have each row represent a different day, and at the very bottom is the total count (the sum of everything in the frequency column).

Natalie is not conducting an experiment because she doesn't have two groups (treatment vs control) and she's not directly interacting with the people she's observing. This also means she's not conducting a survey either. That would involve her having to ask each student to fill out a form, or answer questions.

Given the below equation;

Collecting like terms, we'll have;

Then, we'll multiply both sides by -1 to give us the below answer;

Therefore, the required number is 6.

Answer:

Step-by-step explanation:

x+9

Let x, be 4

4+9=13

given condition,

x+9<4x

4+9<4(4)

13<16

The answer is:

Work/explanation:

Our inequality is:

\(\sf{x+9 < 4x}\)

Flip it

\(\sf{4x > x+9}\)

Solve

\(\sf{4x-x > 9}\)

Combine like terms

\(\sf{3x > 9}\)

Divide each side by 3

\(\sf{x > 3}\)

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

For similar questions on possible value

https://brainly.com/question/21237643
#SPJ11

Here, m∠GHI=72° and m∠LMN=108°. Therefore, option B is the correct answer.

Given that, m∠GHI=6x° and m∠LMN=9x°.

We need to find the measure of each angle.

Supplementary angles are thus a set of angles that complete each other to form 180°. Supplementary angles are those angles that sum up to 180°.

Now, 6x°+9x°=180°

⇒15x°=180°

⇒x°=12°

Thus, m∠GHI=6×12°=72° and m∠LMN=9×12°=108°.

Therefore, option B is the correct answer.

To learn more about the supplementary angles visit:

https://brainly.com/question/17000619.

#SPJ1

Answer:

y= - 1/3x - 7/3

Step-by-step explanation:

Answer:

0.125 cubic feet

Step-by-step explanation:

Since the container has a shape of a cube with a measure of its side 0.5 ft, then;

Volume of the container, V = \(s^{2}\)

where s is the measure of its side.

s = 0.5 ft, then;

V = \((0.5)^{3}\)

    = 0.125

V = 0.125 cubic feet

The cubic feet of slime that would fit in the container is 0.125.

1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

Learn more on Volume on https://brainly.com/question/27710307

#SPJ1

Answer: supplement <17

Step-by-step explanation:

1. 17 is greater

2. supplement is smaller

Answer:

\(y = {(x - 4)}^{2} - 1\)

Step-by-step explanation:

\(y = a(x - h)^{2} + k\)

We know the value of h and k.

\(y = a(x - 4)^{2} - 1\)

The graph passes through (2,3). Therefore, substitute x = 2 and y = 3.

\(3 = a {(2 - 4)}^{2} - 1\)

Solve for a.

\(3 = a {( - 2)}^{2} - 1 \\ 3 = 4a - 1 \\ 3 + 1 = 4a \\ 4 = 4a \\ \frac{4}{4} = a \\ 1 = a\)

Therefore, a = 1. Rewrite the equation.

\(y = 1 {( x - 4)}^{2} - 1 \\ y = {(x - 4)}^{2} -1\)

Answer Check

Substitute x = 2 and y = 3 in the equation.

\(3 = {(2 - 4)}^{2} - 1 \\ 3 = {( - 2)}^{2} - 1 \\ 3 = 4 - 1 \\ 3 = 3\)

The equation is true for (2,3). Therefore, the answer is —

\(y = {(x - 4)}^{2} - 1\)

Answer:

a

   The  90%  confidence interval is  \(52561.13 < \mu < 57540.8\)

b

Confidence interval for the population men between $52561.13  up to $57540.8

Step-by-step explanation:

From the question we are told that

   The sample size is  \(n = 25\)

     The  sample mean is  \(\= x = \$ 55,051\)

     The standard deviation is  \(\sigma = \$ 7,568\)

Given that the confidence level is  90% then the level of confidence is mathematically represented as

             \(\alpha = 100 -90\)

              \(\alpha = 10\%\)

             \(\alpha = 0.10\)

Next we obtain the critical value of \(\frac{\alpha }{2}\) from the normal distribution table the values is  

               \(Z_{\frac{\alpha }{2} } = 1.645\)

Generally the margin of error is mathematically  represented as

               \(E = Z_{\frac{ \alpha }{2} } * \frac{ \sigma }{\sqrt{n} }\)

substituting values

               \(E = 1.645 * \frac{ 7568}{ \sqrt{ 25} }\)

             \(E = 2489.9\)

The 90% confidence interval is mathematically evaluated as

       \(\= x -E < \mu < \= x +E\)

substituting values

     \(55051 - 2489.8 < \mu < 55051 + 2489.8\)

     \(52561.13 < \mu < 57540.8\)

Answer:

A

Step-by-step explanation:

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

Learn more about axioms here:

https://brainly.com/question/2857184

#SPJ8

The area of trapezoid DEFG having coordinates D (2, 3), E (4, 3), F (6, 1), and G (2, 1) is found to be  12 square units.

The diagram is attached for the question.

Area of trapezoid DEFG = 1/2(sum of parallel sides)*height

Area of trapezoid DEFG = 1/2*(2 + 4)*4

Area of trapezoid DEFG = 12 square units

Thus, the area of trapezoid DEFG having coordinates D (2, 3), E (4, 3), F (6, 1), and G (2, 1) is found to be  12 square units.

To know more about the trapezoid, here

https://brainly.com/question/1410008

#SPJ1

The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

Know more about congruent angles,

https://brainly.com/question/28262429

#SPJ1

To make a regular polygon with 96 sides we can take a circle as a starting point and divide it into 96 equal sides.

To create a regular polygon with 96 sides, we must take into account that all its sides must be equal, so we can take a circumference as a starting point. In this case, the circumference has 360°, so we must divide this into 96 parts and the result would be the distance between the edges of the polygon.

In this case, we must make a circle with a protractor and mark every 3.75°, when we have completed this procedure in the entire circumference we will have a regular polygon with 96 sides.

Learn more about polygons at: https://brainly.com/question/24464711

#SPJ1

The simplified solution of the linear equation is determined as -18v - 5t = 4.

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 given equation is a linear equation;

6(-3v+1)=5(2+t)

The solution to the given linear equation is calculated as follows;

6(-3v + 1) = 5(2 + t)

open the brackets by multiplying with the coefficients

-18v + 6 = 10 + 5t

collect similar terms together

-18v - 5t = 10 - 6

-18v - 5t = 4

Thus, the simplified solution of the linear equation is determined as -18v - 5t = 4.

Learn more about linear equations here: https://brainly.com/question/14323743

#SPJ1

Answer:

Step-by-step explanation:

D

The p-values for the observed values of the test statistic are 0.0094, 0.0628, 0.0228, 0.032 and 0.4404.

To calculate the p-value for each observed value of the test statistic, we need to find the area under the standard normal distribution curve to the right of each z-score. This is because the alternative hypothesis is one-tailed, with the inequality sign pointing to the right (i.e., H1: µ > µ0). Here are the steps to calculate the p-value for each observed value:

For z0 = 2.35, the area to the right of the z-score can be found using a standard normal distribution table or calculator. The area is 0.0094, which is the p-value.

For z0 = 1.53, the area to the right of the z-score is 0.0628, which is the p-value.

For z0 = 2.00, the area to the right of the z-score is 0.0228, which is the p-value.

For z0 = 1.85, the area to the right of the z-score is 0.0322, which is the p-value.

For z0 = -0.15, the area to the right of the z-score is 0.5596. However, since the alternative hypothesis is one-tailed with the inequality sign pointing to the right, we need to subtract this area from 1 to get the p-value. Therefore, the p-value is 1 - 0.5596 = 0.4404.

To know more about p-value:

https://brainly.com/question/30461126

#SPJ4

Answer:

The test statistic value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

Step-by-step explanation:

Step(i):-

Given mean of the population (μ) =  $183,000

Given mean of the sample (x⁻)  = $198,000

Given standard deviation of the sample (S) =  $65,000.

Mean of the sample size 'n' = 51

level of significance  α = 0.05

Step(ii):-

Null hypothesis : H₀ : There is no significance difference between the means

Alternative Hypothesis :H₁: There is  significance difference between the means

Test statistic

             \(t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

           \(t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }\)

          t =  1.64

Step(iii)

Degrees of freedom  ν = n-1 = 51-1 =50

t₀.₀₅ =  2.0086

The calculated value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

Final answer:-

There is no significance difference between the means

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

Answer: x=10

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

when we see something like 7x-3=67, we have to get x alone. the first step is to always cancel out the constant (the number that does not have a variable such as x connected to it). so to make -3 equal to 0 we have to add 3. what we do to one side we have to do to the other so after adding 3 on each side we get 7x=70. now here, we still have to get x alone. 7x means 7 times x so to undo this we have to do the opposite and divide each side by 7. 7 divided by 1 (and 1x is 1 times x which is just x so now we have x alone yaay) and 70 divided by 7 is 10. so x = 10.

I hope this helped :))

Answer:

Step-by-step explanation:

1st 10 days - 8 GB

2nd 10 days - 8 GB

3rd 10 days - 8 GB

________________

30 days    -  24 GB

Answer:

10.5 miles.

Step-by-step explanation:

If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)

We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.

Answer:

10 1/2

Step-by-step explanation:

divide 7/10 which is 0.7 then multiply that by 5 which is 3.5

then divide 4/10 which is 0.4 then multiply that by 5 which is 2, but add 5 which is 7.

then combine all of that together which is 3.5+7= 10.5

then convert that into a fraction which is 10 1/2

Answer:

B. 28.27

Step-by-step explanation:

The volume of the figure that is composed of two rectangular prisms is: 146 cubic in.

The volume of a rectangular prism = (length)(width)(height).

The figure can be decomposed into two rectangular prisms. Find the volume of each of the prisms.

Volume of rectangular prism 1:

Length of the prism = 8 in.

Width of the prism = 7 in.

Height of the prism = 1 in.

Volume of rectangular prism 1 = (8)(7)(1) = 56 in.³

Volume of rectangular prism 2:

Length of the prism = 10 in.

Width of the prism = 9 in.

Height of the prism = 1 in.

Volume of rectangular prism 1 = (10)(9)(1) = 90 in.³

Volume of the figure = 90 + 56 = 146 cubic in.

Learn more about volume of rectangular prism on:

https://brainly.com/question/12917973

#SPJ1

The graph of the equation y=-3/5+3 will be a straight line

The graph of a straight line is always straight.  The equation is written in slope intercept for where -3/5 is the

The form of an equation in slope intercept form is y=mx+c

Here, m=-3/5

c=3

To draw the line, from the point 3 on the x-axis, rise negative 3 and run 5

The draw the line for form a straight line

Note that the formula for slope is

S=rise/run

In conclusion, the equation forms a straight line.

Learn more about equation of a line on https://brainly.com/question/21511618

#SPJ1