find the area of this triangle

Answer:

  QR = 20

Step-by-step explanation:

You want the measure of side QR of isosceles triangle PQR with congruent sides PQ and QR marked 5x and 3x+8, respectively.

The sides of the isosceles triangle are congruent, so we have ...

  PQ = QR

  5x = 3x +8

  2x = 8 . . . . . . . subtract 3x

  x = 4 . . . . . . . divide by 2

  QR = 3x +8 = 3(4) +8 = 20 . . . . . . find the length of QR

The measure of QR is 20 units.

__

Additional comment

You will recognize that the segment QS is both the altitude and median of the triangle. That means the triangle is isosceles, so symmetrical about QS.

If you need a formal proof, you can observe that QS is congruent to itself, so the two right triangles are congruent by LL (or SAS).

It will take 11 years for the investment to exceed £7000 if £5200 is invested over a year at a compound interest rate of 2.8%.

The addition of interest to the principal of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It occurs when interest is reinvested, added to the lent capital instead of being paid out, or the borrower is required to pay it, resulting in the next period's interest being generated on the principal amount plus any accumulated interest.

In contrast to simple interest, which does not compound since past interest is not added to the current period's principal, compound interest allows for the accumulation of interest from prior periods.

We solve this problem by using compound interest.

Given,

£5200 is invested over a year at a compound interest rate of 2.8%.

£7000. 1.028 = 5 200 x 5200 × 1.028¹¹ = 7045.76 2.

So, number of years=11

Therefore, It will take 11 years for the investment to exceed £7000.

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The system of equations that should be used is the second one:

-15 = 5A

10 = -2A + B

Here we have the following equation:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}[/tex]

If we multiply and divide the first therm in the right side by (5x - 2) we will get:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A*(5x - 2)}{(5x - 2)^2} + \frac{B}{(5x - 2)^2}[/tex]

The numerators must be equal, then we can write:

-15x + 10 = A*(5x - 2) + B

-15x + 10 = A*5x - 2A + B

Then we can write two equations, one that has x as a factor and other that does not, these are:

-15 = 5A

10 = -2A + B

That is the system of equations.

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Answer:

B.

Step-by-step explanation:

took unit test

The df would equal in the chi-square statistic for this test is found as 4.

The formula for the chi-square (X²) statistic is;

(X²)  = ∑(O - E)²/E

For the given question-

The answer to the query is;

We would determine whether two qualities, A and B, under examination are independent or not using the chi-square test.

Taking that as a given, the null hypothesis H0: The two factors are unrelated.

Now, the degrees of freedom in the independence test using chi-square is,

v = (r-1) (s-1) (s-1).

r = 3 and s = 3.

The degree of freedom are;

ν =  (r-1) (s-1) = (3-1) (3-1) = 2×4

ν  = 4

Consequently, let test statistic be,

(X²)  = ∑(O - E)²/E

Consequently, df would equal in the chi-square statistic for this test is found as 4.

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13) y= 3/5 x +2

14) y= x + 2

The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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The kids' judgments of the significance of excellent nutrition in the food given may vary based on the students' ages and, consequently, on school level, making this variable an useful one to stratify the survey on.

Each sample has an equal chance of being picked when using the random sampling sampling approach. It is intended that a sample picked at random will be a fair reflection of the entire population. Two different approaches to sampling exist: Random selection is a key component of probability sampling, which enables you to draw robust statistical conclusions about the entire group. Non-probability sampling incorporates non-random selection based on practicality or other factors, making it simple to gather data.

The student's degree of education is one potential stratification factor. Depending on the kids' ages and, thus, on their academic ability, the students' judgments of the significance of nutritious meals may vary. In contrast to middle school and high school pupils, elementary school children may place different values on the food that is offered.

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Variance is the only meaningful measure of the central location for a categorical variable.

Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance is a measure of dispersion, or how far apart from the mean a group of data is from one another.

Descriptive statistics, statistical inference, hypothesis testing, the goodness of fit, and Monte Carlo sampling are just a few of the concepts that make use of a variance. In the sciences, where statistical data analysis is widespread, a variance is a crucial tool.

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For an saving account in a bank, With the given value of the rate 'r' and the compounding period 'n' , The AER on the saving account is given by :

AER = [tex](1+\frac{r}{n})^{n} -1[/tex] .

The interest rate on a savings account or investment product with multiple compounding periods is known as the annual equivalent rate (AER). The next interest payment will be based on the marginally higher account amount, and AER is computed under the presumption that any interest paid is included in the balance of the principle payment.

The main benefit of AER is that it takes compounding effects into account, making it the real rate of interest.

Unfortunately, the AER is typically not mentioned when investors are comparing various investment possibilities. Investors are required to perform the calculations themselves.

n= compounding periods.

r= rate

Annual Equivalent Rate (AER) = [tex](1+\frac{r}{n})^{n} -1[/tex]

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Vertical angles are two angles that are opposite each other and share a common vertex. Adjacent angles are two angles that share a common side and vertex.

To find the measure of an unknown angle using these relationships, you can use the vertical angle theorem which states that if two angles are vertical, then they have equal measure. For example, if angle A and angle B are vertical angles, then angle A = angle B.

Example:

Given: Angle A = 40°

Find the measure of angle B

Solution:

Since angle A and angle B are vertical angles, then angle A = angle B

Therefore, the measure of angle B = 40°

An angle is created when two straight lines or rays intersect at the same point. The point where all points converge is known as an angle's vertex. The Latin word angulus, which meaning "corner," is where the term "angle" comes from.

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Answer:

The end behavior of the function f(x) = 2^-xsin3x is that it approaches 0 as x approaches positive infinity and approaches infinity as x approaches negative infinity.

Step-by-step explanation:

if the sum of two digits is divided by the sum of the digits, the number is  80.

Generally, Let the two digits of the number be x and y. The number can be written as 10x + y.

We are given that (x+y)/(x+y) = 6, which means that x + y = 6x + 6y.

Subtracting x + y from both sides, we get 5x = 5y. Therefore, x = y.

We are also given that the number is 9 greater than the number formed by reversing the digits, which means that 10x + y = 9 + 10y + x.

Combining like terms, we get 9x = 8y, or x = 8/9y.

Substituting this expression for x into the equation x = y, we get 8/9y = y, which means that y = 0.

Therefore, the number is 10x + y = 10 * (8/9y) + 0 = 80.

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Answer:

c 5

Step-by-step explanation:

2=10

1=5

5+5=10

hope this helps by now

Answer:

Blue: 1/5

Step-by-step explanation:

To find the rate of change you use your slope formula which is y2-y1 over x2-x1.

You'd set your equation and you'd get 4-2 over 20-10. You solve and you get 2/10 and because it isn't one of the answer choices you have to simplify it. To simplify it you find the common number they both share and they both share 2 so you divide both by 2. 2 divided by 2 is 1 and 10 divide by 2 is 5. So then the rate of change or slope is 1/5.

Under the null hypothesis, the expected number of strongly opposed juniors is 50.

The term null hypothesis refers the typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

Here we have given that suppose we wish to test the null hypothesis that there is no association between student year in school and student opinion.

And we need to find under the null hypothesis, what is the expected number of strongly opposed juniors.

Here let us consider there are 100 students.

Then according to the given statement, there is no association between student year in school and student opinion.

Which refers that half of them are supported and half of them are opposed.

Therefore, the expected value is 50.

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Answer:

153°

Step-by-step explanation:

Angle EHG is a right angle, so it measures 90°.

The measures of angles EHF and FHG add to 90°.

m<EHF + m<FHG = 90°

m<FHG = 27°

m<EHF + 27° = 180°

m<EHF = 153°

To calculate the amount of commission that Nancy Bell earned last month, we can use the following formula:

Commission = Sales * Commission Rate

In this case, the sales are $59,400 and the commission rate is 14%, so the commission is:

Commission = $59,400 * 14% = $8,356

To calculate Nancy's gross pay, we can add her salary to her commission:

Gross Pay = Salary + Commission

Gross Pay = $1,710 + $8,356 = $10,066

Therefore, Nancy earned $8,356 in commission and her gross pay was $10,066.

Answer: 890 downloads the high-quality version

Step-by-step explanation:

Let x be the number of downloads of the high-quality version

1420-x be the number of downloads of the standard version

So, we have the equation

4.5x + 2.7(1420-x) = 5436

4.5x + 3834 - 2.7x = 5436

1.8x + 3834 = 5436

Subtract 3834 on both sides

1.8x = 1602

x = 890

Answer:

Step-by-step explanation:

you get a tutor

" BRAINLY TUTOR "

press that link

Answer:

1 Green Sack = 2

1 Red Sack = 2

1 Elf Mask = 8

1 Christmas List = 5

Step-by-step explanation:

g=Green sack

r= Red sack

e = Elf mask

c = Christmas list

What would happen is the result would increase by a factor of 2. The result of dividing the fractions will be 4.

From the question, we are to determine what would happen if we divide by 2/5 instead of 4/5

That is,

We are to carry out the division operation

1 3/5 ÷ 2/5

Evaluating

1 3/5 ÷ 2/5

8/5 ÷ 2/5

8/5 × 5/2

= 8/2

= 4

The answer increased by a factor of 2.

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Examining the triangles, the length of side QT is 2.5

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

The solution is worked out using sides SQ and QR, then ST and TU

(12 + QT) / 18 = 12 / 6(QT)

let QT = x

(12 + x) / 18 = 12 / 6x

cross multiplying

6x(12 + x) = 18 * 12

72x + 6x² = 216

6x² + 72x - 216

x = 2.5 OR -14.4

take the positive value x = 2.5

The length of QT is 2.5

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The probability that a randomly chosen person from the given population makes a purchase is [tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] *0.25.

We can calculate the probability in the following way,

Let the total population of visitors visiting to the online shopping site be P.

The estimated odds of visitors making a purchase on the online shopping website are 0.25

P(E)=0.25 and n=P

We know that the probability mass function is also known as p.m.f. of Binomial Distribution with parameters n and P.

P(X=x) = [tex]\left(\begin{array}{ccc}n\\x\end{array}\right){p^x}[/tex]* [tex](1-p)^{(1-x)}[/tex] ; 0 < p < 1 And x=0,1,2,3,...

Probability of one randomly chosen visitor making a purchase= P(x=1)

=[tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] 0.25^1 * 0.75^0

=[tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex]*0.25

Therefore, the Probability of a random visitor making a purchase depends on the value of the population and is equal to [tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] * 0.25

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Answer:

804.063 is the answer

Step-by-step explanation:

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The midrange for the data items in the given frequency distribution is 30.5.

Generally, To find the midrange for the data items in the given frequency distribution, we need to calculate the midpoint of each score range. The midpoint of a range is calculated by taking the average of the lower and upper bounds of the range.

For the first score range (29-30), the lower bound is 29 and the upper bound is 30, so the midpoint is (29 + 30) / 2 = 29.5.

For the second score range (30-31), the lower bound is 30 and the upper bound is 31, so the midpoint is (30 + 31) / 2 = 30.5.

Therefore, the midrange for the data items in the given frequency distribution is 30.5.

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Answer:

The equation intersects the x or y axis a total ot three times:

(-1.5,0), (5,0), and (-15,0).

Step-by-step explanation:

I will assume that the "all points of intersection" refers to the intersection of the line with the x and y axes.  One can find those points by either a mathematical or graphing approach.

    We and to find all points that have a zero for either the x or y coordinate:  (0,y) and (x,0)

(x,0):  Solve  p(x)=(2x+3)(x-5) for p(x) = 0:

  0=(2x+3)(x-5)

 (2x+3)=0 and (x-5)=0

 (2x+3)=0

2x=-3

x= - 1.5    (-1.5,0)

and

  (x-5)=0

X=5     (5,0)

--

(0,y):  Solve  p(x)=(2x+3)(x-5) for p(x)  for x=0:

p(x) = (2x+3)(x-5)

p(x) = (2*0+3)(0-5)

p(x) = (3)*(-5)

p(x) = -15       (-15,0)

See the attached graph.  The points of intersection can be located, as shown.  They match the values obtained mathematically, but a free graphing utility (DESMOS) makes graphing a pleasant chore.

all squares are parallelogram but all parallelogram are not squares

Answer:

d. 4x − 5y = 27x + 6y = 10

I hope my answer helps you.

Answer:

To have 4 times as many apples as bananas, Amadou could have bought 4 apples for every 1 banana, or 8 apples for every 2 bananas, or 16 apples for every 4 bananas.

4 apples : 1 banana

8 apples : 2 bananas

16 apples : 4 bananas

We can use the fact that the total cost of the apples and bananas was $9 to determine the number of apples and bananas that Amadou bought. Since each apple costs $1, Amadou bought 9 apples if he bought no bananas, or 7 apples if he bought 2 bananas, or 5 apples if he bought 4 bananas.

9 apples : 0 bananas

7 apples : 2 bananas

5 apples : 4 bananas

Therefore, the possible combinations of apples and bananas that Amadou could have bought are 9 apples and 0 bananas, 7 apples and 2 bananas, or 5 apples and 4 bananas.

Answer:

x=5, y=2 | Equations: 4x+y=22 (or see below) and 12x-5y=50

Step-by-step explanation:

Here's my attempt:

First Equation:

Because triangles ΔSTU and ΔXYZ are congruent, then we can say that:
m∠S = m∠X
m∠T = m∠Y
m∠U = m∠Z

We know that m∠X = 130°, and that m∠X = m∠S, so m∠S = 130°

We also know that the sum of angles in a triangle = 180°

We also know the rest of the angles in ΔSTU: 28° and (4x+y)°

So, we can say that ∠S + ∠T + ∠U = 130+28+4x+y = 180 (we can remove the degree sign)

Now, you can either enter this as it is or simplify it: ❗

130+28+4x+y=180

4x+y+158=180

4x+y=22

Second Equation:

We can do the same thing as for the first equation and get the angles of ΔXYZ:

∠X = 130, ∠Y = 8x-6y, ∠Z = 4x+y

Then, add them and set it to 180:

130+8x-6y+4x+y=180

Simplify:

12x-5y+130=180

12x-5y=50

To solve for x and y:

Now, we have to solve the systems.

Let's start with the first one:

4x+y=22

Isolate y:

y=22-4x (Equation 1)

Then, we plug it into the second equation:

12x-5y=50

12x-5(22-4x)=50

12x-110+20x=50

32x=160

x=5

So we got x, but to find y, we need to plug in x into Equation 1 (where we isolated y

y=22-4x

y=22-4(5)

y=22-20

y=2

We have both our x and y values

That was my attempt, hope it helped!