Veronica used this figure in her proof of the Pythagorean theorem.

Answer:

QT = 108 m

Step-by-step explanation:

the diagonals of a rectangle are congruent and bisect each other, so

QS = PR = 216 , then

QT = [tex]\frac{1}{2}[/tex] QS = [tex]\frac{1}{2}[/tex] × 216 = 108 m

Answer: 108

Step-by-step explanation:

diagonals of a rectangle are equal in length

∴ PR = QS = 216

Diagonals of a rectangle bisect each other

=> QT = QS = [tex]\frac{QS}{2} \\= > \frac{216}{2}\\ = 108[/tex]

The idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population is referred to as Alternative Hypothesis.

Alternative Hypothesis:

In statistical hypothesis testing, the alternative hypothesis is one of the statements proposed in the hypothesis test. In general, the purpose of a hypothesis test is to show that, given the conditions, there is sufficient evidence to support the reliability of the alternative hypothesis rather than the sole assertion in the test (the null hypothesis) . It is usually consistent with research hypotheses because it is generated from literature reviews, previous studies, etc. However, in some cases the research hypothesis is consistent with the null hypothesis.

In statistics, the alternative hypothesis is often denoted by Ha or H1. Hypotheses are formulated to compare them in statistical hypothesis testing. In the field of inferential statistics, two competing hypotheses can be compared for their explanatory and predictive power.

For scalar parameters, there are four main types of alternative hypotheses:

Learn more about Alternative Hypothesis:

https://brainly.com/question/27335001

#SPJ4

The function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0

What are factors?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Factors can be found using either division or multiplication. Rules of divisibility can also be applied.

Given, the factors of a function are (x+1), (x-1) and (x-4)

We know that if the factors of a function are (x-a) and (y-b), it would mean that the function is (x-a)(y-b) = 0

Similarly, taking the above factors given in a function, the function would be:

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

⇒ (x²-1)(x-4)=0

⇒ x³-4x²-x+4 = 0

Hence, the function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0

To know more about factors visit:

brainly.com/question/29128446

#SPJ1

Answer:

f(20) = 10

Step-by-step explanation:

The best option is to Convert it to a decimal and multiply is the best way to describe rate in simple interest formula. The correct option is A.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.

Simple Interest (S.I.) is a method for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.

Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount. The correct option is A.

Learn more about interest on:

https://brainly.com/question/25793394

#SPJ1

Answer:

B and C

Step-by-step explanation:

(5⁷)¹¹ = 5⁷⁷

5⁹ × 5² = 5¹¹

Answer:

[tex] {5}^{12} \times {5}^{6} and \: \frac{ {5}^{24} }{ {5}^{6} } \\ option \: b \: and \: c[/tex]

Step-by-step explanation:

[tex] {a}^{b} \times {a}^{c} = {a}^{(b + c)} \\ \frac{ {a}^{b} }{ {a}^{c} } = {a}^{(b - c)} [/tex]

[tex] {5}^{12} \times {5}^{6} = {5}^{(12 + 6} = {5}^{18} \\ \frac{ {5}^{24} }{ {5}^{6} } = {5}^{(24 - 6)} = {5}^{18} [/tex]

Answer: Mode: 180

Quartiles:

Q1 --> 149

Q2 --> 165.5

Q3 --> 178

Mean: 162.944....

Median: 165.5

Step-by-step explanation:

The model to show the cost of the shirt is x+49.95=79.16. Therefore, the cost of shirt is $29.21.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Jeremy spent a total of $79.16 on a shirt and one pair of jeans.

Let the cost of shirt be x.

The jeans cost is $49.95

Now, the cost of shirt + the cost of jeans = Total cost

⇒ x+49.95=79.16

⇒ x=79.16-49.95

⇒ x=$29.21

Therefore, the cost of shirt is $29.21.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ1

Answer:

Step-by-step explanation:

35/90 gets devided by 5

7/18

3/36 gets devided by 3

1/12

Answer:35/90 = 7/18

            3/36=1/12

Step-by-step explanation:

for 35/90 you divide both sides by 5 giving you 7/18 and 3/36 you divde both by 3 giving you 1/12.

Hope this helped

The expression that is equivalent to −6(b − 7) is: B. -6b + 42.

Expressions that are equivalent to each other will give the same value when simplified and solved in their simplest forms.

Simply put, two expressions will be equivalent if they have the same number of terms or they will give the same quantity when you plug in the values of all the variables that are given in the expressions.

Given the expression, -6(b - 7), the steps below shows how we can simplify to determine the expression that is equivalent to it

-6(b - 7) [given]

Open the parentheses by using the distributive property of equality, which involves multiplying each of the terms within the parentheses by the term outside of the parentheses:

-6(b) -6(-7) [distributive property]

-6b + 42

-6b + 42 is the equivalent expression of -6(b - 7).

Thus, the answer is: B. -6b + 42.

Learn more about equivalent expression on:

https://brainly.com/question/24734894

#SPJ1

The addends 4, _ 37 + 1,28_ is completed so there will be need to regroup to add.

the addends. 4, 837 + 1,287

the sum is 6124

Regrouping refers to rearranging numbers into groups according to place value to assist kids in handling greater numbers.

When performing operations like addition and subtraction on two-digit integers or bigger, regrouping is the process of forming groups of tens. Regrouping refers to the process of performing an operation by rearranging groups in place value.

Using regrouping for the addition problem

addend 4 8 3 7

addend  1 2 8 7

sum                 4

                    1      regrouped to tens column

addend 4 8 3 7

addend  1 2 8 7

sum              2 4

                1         regrouped to hundreds column

addend 4 8 3 7

addend  1 2 8 7

sum           1 2 4

             1              regrouped to thousands column

addend 4 8 3 7

addend  1 2 8 7

sum        6 1 2 4

the sum is 6124

Learn more on regrouping at:

https://brainly.com/question/29637833

#SPJ1

Answer:

6400

Step-by-step explanation:

We have 1 + 3 + 5 + ... + 155 + 157 + 159.

We can use Gauss's strategy.

Since we are adding 80 numbers, there are 40 pairs. Each pair adds up to 1 + 159 = 160. (Notice that 3 + 157, 5 + 155 = 160)

Thus, because there are 40 pairs and each pair adds up to 160, we have 160 * 40 = 6400.

I hope this helps!

The probability that the next respondent questioned would say they plan to vote is 0.59.

What is probability?

The ratio of the number of favorable outcomes to the total number of outcomes of an event is defined as probability.

We know that the probability of an occurrence =the number of favorable outcomes divided by the total number of events.

Given that, 315 respondents stated they planned to vote, while 217 said they did not.

Now, the probability of voting is:

P(voting)=315(315+217)

= 315/532

= 0.59

As a result, the likelihood that the next respondent questioned would say they plan to vote is 0.59.

The probability that the next respondent questioned would say they plan to vote is 0.59.

To learn more about the Probability, go to:

brainly.com/question/11234923.

#SPJ4

Answer:

15 c m.

Step-by-step explanation:

120 divided by 8 =15

Answer: The Value has increased by 800%

Step-by-step explanation:

Answer: Reduction: 1/3

Step-by-step explanation:

Remember that if you are dilating it to be larger, it will be a whole number. If it is less than one, then it is dilating to be smaller.

Answer: Reduction 1/3.

Step-by-step explanation: When a shape is transformed into a smaller version of the original, it's a reduction. Reductions are less than 1 so the answer I provided above is what you're looking for.

Have a great day! :)

Answer: B

Step-by-step explanation:

If you chose D it would be wrong because you have to remember that the two negatives cancel out!

The three cut pieces should be 10 inches, 20 inches, and 40 inches  for the shortest, middle-sized and longest respectively

This is a word problem. We need to understand the sentence in order to translate it correctly.

To find the length of each of the three cut pieces, we can use the given information to set up a system of equations.

Let L, M and S be the length of the longest, middle-sized and shortest piece respectively

So we can set up the following equation:

L = 2M

S = M-10

L + M + S = 70

2M + M + (M - 10) +  = 70

We can combine like terms to get:

4M - 10 = 70

4M = 80

We can divide both sides by 4 to get:

M = 20

Therefore, the length of the middle-sized piece is 20 inches.

Since L = 2M

L =  2 × 20 inches = 40 inches.

Since S = M - 10

S = 20 - 10 = 10 inches.

Therefore, the three cut pieces should be 10 inches, 20 inches, and 40 inches for the shortest, middle-sized and longest respectively

Learn more about word problems here:

brainly.com/question/1781657

#SPJ1

The expression that represent the area of the cabin for rectangular floor plan is 2w² + 5w.

What is the area of rectangular shape?

In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.

Given that the length of a cabin is equal to 5 feet more than twice the width.

Assume that the width of the cabin be w.

Then the mathematical expression of twice the width is 2w.

Then the mathematical expression of 5 feet more than twice the width is 2w + 5.The length of the cabin is 2w + 5 feet.

The area of rectangular shape is product of length and width.

The area of the cabin is (2w + 5)w

Apply distributive property:

= 2w × w + 5 × w

= 2w² + 5w

To learn more about expression click on below link:

https://brainly.com/question/11516438

#SPJ1

His present age is 36 years.

Let his present age = x

Given,

2(x − 12) = x +12

2x - 24 = x + 12

2x - x =  12 + 24

x = 36

Therefore, his present age is 36 years.

To know more about the Calculation of ages, please refer to the link below:

brainly.com/question/24338087

The slope of the linear relationship is 15.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). The slope of a line tangent to a function's graph in differential calculus is determined by the derivative of that function and serves as a representation of the function's instantaneous rate of change with regard to changes in the independent variable. The slope of a tangent line in the graph of a position function, which plots the distance travelled by an object against the passage of time, corresponds to the object's instantaneous velocity.

Given

A linear relationship is given.

y₁ = -9

y₂ = 6

x₁ = 0

x₂ = 1

Slope:

m = y₂ - y₁/x₂ - x₁

m = 6 + 9/1 - 0

m = 15/1

m = 15

The slope of the linear relationship is 15.

To learn more about slope, visit:

https://brainly.com/question/3605446

#SPJ1

Answer:

Slope = 15

Step-by-step explanation:

Now we have to,

→ find the slope of linear relationship.

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Coordinates we use from table,

→ x1 = 0, y1 = -9

→ x2 = 1, y2 = 6

Then the required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (6 -(-9))/(1 - 0)

→ m = (6 + 9)/1

→ m = (15)/1

→ [ m = 15 ]

Hence, the required slope is 15.

(3) Isosceles triangle Theorem

(8) Same side Interior angle Theorem

(2) Triangle sum Theorem

(1) Vertical angle Theorem

(7) Alternate exterior angle Theorem

(5)Corresponding angle Postulate

(6)Alternate exterior angle Theorem

(4) Triangle midsegment Theorem

What is isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Isosceles triangle Theorem: A triangle's opposite angles are also congruent if its two sides are.

Same side Interior angle Theorem:

The same side interior angles are additional when two parallel lines are cut by a transversal.

Triangle sum Theorem:

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

Vertical angle Theorem:

When two straight lines collide, two sets of linear pairs with identical angles are created.

Alternate exterior angle Theorem:

The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.

Corresponding angle Postulate:

The related angles are equivalent if a transversal cuts two parallel lines.

Alternate exterior angle Theorem:

The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.

Triangle midsegment Theorem:

The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.

To learn more about theorem and postulate, click on below link:

https://brainly.com/question/26142429

#SPJ1

Answer:

the answer is g = (7 - 3e) / (4 - 9e)

Step-by-step explanation:

The subject of an equation is the value or values being solved for. An equation typically consists of two parts: an expression on the left side of an equal sign and an expression on the right side of the equal sign.

The given equation subject of equation is 3e + 4g = 7 + 9eg

Subtraction of 9eg from both sides of the equation

3e + 4g - 9eg = 7 + 9eg - 9eg

3e + 4g - 9eg = 7

Subtract 3e on both sides of the equation

3e + 4g - 9eg - 3e = 7 - 3e

4g - 9eg = 7 - 3e

Factorize g on left side of the equation,

g (4 - 9e) = 7 - 3e

Then divide (4 - 9e) on both sides of the equation,

g = (7 - 3e) / (4 - 9e)

To learn more about equation refer to:

https://brainly.com/question/22688504

#SPJ1

Answer:191

Step-by-step explanation:

65x2=130

130+61=191

A. The equation that represents the balance is, 2x + 3 = 15.

B. Each box contains, x = 6 apples.

Given the problem above, to write an equation that would represent the balance, we would assume both sides of the balance are separated by the equal sign, "=".

Therefore, let the unknown number of apples in each box be be represented as x.

A. Apples in the two boxes would be 2x, the total apples on the left of the balance would be expressed as:

2x + 3

On the right, we have 15 apples, therefore, the equation that represents the balance is: 2x + 3 = 15

B. Solve to find x, the number of apples in each box:

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

x = 12/2

x = 6

This means that there were 6 apples in each box.

Learn more about equations on:

https://brainly.com/question/25678139

#SPJ1

The probability that extra unleaded gas was requested is 35%.

To find the probability that the next customer requested extra unleaded gas, we need to first find the total probability that any customer requests extra unleaded gas.

Since 35% of customers request extra unleaded gas, the probability that a customer requests it is 35%. Of those customers, 30% fill their tanks, so the probability that a customer requesting extra unleaded gas fills their tank is 30%.

Therefore, the probability that a customer requesting extra unleaded gas fills their tank is (35%) * (30%) = 0.105, or about 10.5%.

This is the probability that the next customer requested extra unleaded gas and fills their tank. To find the probability that the next customer simply requested extra unleaded gas, regardless of whether they fill their tank or not, we need to add the probabilities of them requesting extra unleaded gas and either filling or not filling their tank.

The probability that the next customer requested extra unleaded gas and filled their tank is 0.105, as we calculated above. The probability that the next customer requested extra unleaded gas and did not fill their tank is (35%) * (70%) = 0.245, or about 24.5%.

To find the total probability that the next customer requested extra unleaded gas, we need to add these two probabilities: 0.105 + 0.245 = 0.35, or 35%. This is the probability that the next customer requested extra unleaded gas.

To learn more about probability,

visit; brainly.com/question/29381779

#SPJ4

I think

it should be 200 as it's the first common multiple of 20 40 and 25

Answer: e = 9.16

Step-by-step explanation: Although it's not necessary, I would first get rid of the decimals by multiplying both sides of the equation by 100.

That gives is 100e + 5 = 921 which has no decimals.

Now just subtract 5 from each side to get 100e = 916 and

dividing both sides by 100 from here, e = 9.16.