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Write an informal proof for each of the following problems.

1.) Triangles QRS and XYZ are congruent. Answer the following quesions:
a.) Write the relaionship between the sides for these two triangles.
b.) Write the relaionships between the angles of these two triangles.
c.) If side QS is equal to 16 and XZ is equal to 3x – 20, ind x.

Answer:

A, C, E

Step-by-step explanation:

8 X 9 = 72  yes
8 x  5 = 35 no it equals 40
8 x 6 = 48 yes
8 x 7 = 65 no it equals 56
8x 3 = 24 yes

Answer: 65%, 195 children

Step-by-step explanation: To get this, we just do 100-35 to get 65 percent. We can calculate this further, and do 300*0.65, and we get 195. Thus, there were 195 children.

Answer:

There was 195 people.

Step-by-step explanation:

You divide and subract.

Answer:

scalene right

Step-by-step explanation:

all side are opposite and there is a 90% so that makes it right

Answer:

you multiply the length and height, then, you figure out what you multiply to get the volume by dividing the product of the length and height multiplied.

Step-by-step explanation:

ex: kyle

2x3=6

6x?=12

6/12=2

The solution with the lesser x is -10 and the solution with the greater x is -2.

The given function is f(x) = (x+6)² - 16.

To find the zeros of the function, we need to set f(x) equal to zero and solve for x.

0 = (x+6)² - 16

Adding 16 to both sides, we get:

16 = (x+6)²

Taking the square root of both sides, we get:

±4 = x+6

Subtracting 6 from both sides, we get:

x = -6 ± 4

Therefore, the zeros of the function are x = -10 and x = -2.

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Answer:

Step-by-step explanation:

Please see diagram attached.

Moon A and C are 100,000km + 10,000 = 110,000km from center of planet.

So they are 110,000 + 110,000 = 220,000km apart.

Answer:

Step-by-step explanation:

AC is 220000km according to the drawing:

Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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Answer:

Multiply 3 by 5

Step-by-step explanation:

the P and M in PEMDAS because there’s multiplication inside the parentheses

5 + 3(5) - 4.2

a. the principal (loan amount) is $5000, the rate is 8.25%, and the time is 9 months (expressed in years as 9/12). b. the student will have to pay $306.25 in interest, and the future value of the loan will be $5306.25.

a. The student must pay $306.25 in interest.

To calculate the amount of interest, we can use the formula for simple interest:

Interest = Principal × Rate × Time

In this case, the principal (loan amount) is $5000, the rate is 8.25%, and the time is 9 months (expressed in years as 9/12).

Plugging in these values into the formula, we can calculate the interest amount the student must pay.

b. The future value of the loan is $5306.25.

To find the future value, we add the interest amount to the principal amount.

The future value is calculated using the formula:

Future Value = Principal + Interest

By substituting the values of the principal ($5000) and the interest ($306.25), we can find the future value of the loan.

Therefore, the student will have to pay $306.25 in interest, and the future value of the loan will be $5306.25.

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In order to start a small​ business, a student takes out a simple interest loan for ​$ 5000 for 9 months at a rate of 8.25 ​%.

a. How much interest must the student​ pay?

b. Find the future value of the loan.

Given the diagram below

Introducing 'a', as shown above, it can be observed that

It can also be observed that

It can also be observed that

Substitute for y to get z

Hence, the value of y is 34°, while z is 119°.

The fraction 2/3 satisfies this condition. We can confirm this by cross-multiplying 2/3 and 4/5. The result is (2 * 5) and (3 * 4), which simplifies to 10 and 12, respectively. Since 10 is less than 12, we can see that 2/3 is indeed less than 4/5.

The fraction that goes in the blank is 2/3. To understand why, let's compare the given fractions step by step.

We start with 1/2 and -< 4/5. Here, -< is used as a symbol to represent the less than sign (<). To compare fractions, we need to make sure they have a common denominator. The common denominator of 2 and 5 is 10.

So, we rewrite the fractions with a common denominator: 1/2 = 5/10 and 4/5 remains as 4/5.

Now, let's compare 5/10 and 4/5. We can do this by cross-multiplying. Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction.

Cross-multiplying 5/10 and 4/5, we get (5 * 5) and (4 * 10), which simplifies to 25 and 40, respectively.

Since 25 is less than 40, we can conclude that 5/10 is less than 4/5. Therefore, the blank should be filled with a fraction that is greater than 5/10 but less than 4/5.

Out of the given options, the fraction 2/3 satisfies this condition. We can confirm this by cross-multiplying 2/3 and 4/5. The result is (2 * 5) and (3 * 4), which simplifies to 10 and 12, respectively. Since 10 is less than 12, we can see that 2/3 is indeed less than 4/5.

In conclusion, the fraction that goes in the blank is 2/3.

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Answer:

0

Step-by-step explanation:

\(\frac{rise}{run}\) =\(\frac{-6-(-6)}{6-7}\)=\(\frac{0}{-1}\)=0

The total amount Jimmy will save in summation notation will be:

The total amount Jimmy will save is determined as follows:

For the first week, Jimmy will save $3 * 1 = $3

For the second week, Jimmy will save $3 * 2 = $6

For the third week, Jimmy will save $3 * 3 = $9

For n number of weeks, Jimmy will save 3 * n = $3n

The total amount saved in the first three weeks using summation notation = ∑($3, $6, $9)

The total amount saved in the first three weeks = $18

Therefore, the amount Jimmy will save = $18 + $3n

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The integer that represents the difference in high temperature from Monday to Tuesday is 38.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The high temperature on Monday was -14 degrees.

On Tuesday the high temperature was 24 degrees.

The temperature difference between Monday and Tuesday.

= Temperature on Tuesday - Temperature on Monday

= 24 - (-14)

= 24 + 14

= 38

Thus,

The integer that represents the difference in high temperature from Monday to Tuesday is 38.

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To find the sum of the squared differences, you first need to calculate the mean of the data set. Then, you need to subtract the mean from each score to get the difference. Finally, you need to square each difference and add them all together to get the sum of the squared differences.

Here are the steps to find the sum of the squared differences:

1. Calculate the mean of the data set by adding up all the scores and dividing by the number of scores.
2. Subtract the mean from each score to get the difference.
3. Square each difference.
4. Add up all the squared differences to get the sum of the squared differences.

For example, if the data set is {1, 2, 3, 4, 5}, the mean is (1+2+3+4+5)/5 = 3. The differences are (-2, -1, 0, 1, 2), and the squared differences are (4, 1, 0, 1, 4). The sum of the squared differences is 4+1+0+1+4 = 10.

So, the sum of the squared differences for this data set is 10.

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Answer:

9.6miles per hour

Step-by-step explanation:

2/3＝40min

32/5 /40＝0.16

0.16miles per min

0.16*60＝9.6

Step-by-step explanation:

he jogs 3 2/5 miles in 2/3 of an hour.

3 2/5 miles are 17/5 miles.

now, to get mph as speed unit, we need to bring the 2/3 hour to 1 hour.

we need to multiply 2/3 by a factor to get 1

2/3 × x = 1

2x = 3

x = 3/2

since we have to multiply the denominator of the ratio by 3/2, we also need to multiply the numerator by the same value to keep the overall value of the ratio/fraction the same.

17/5 / 2/3 × 3/2 / 3/2 = (17/5 × 3/2) / (2/3 × 3/2) =

= ((17×3)/(5×2)) / ((2×3)/(3×2)) =

= (51/10) / 1 = 51/10 = 5.1 mph

so, his jogging speed is 5.1 mph.

Answer:

148.91

Step-by-step explanation:

hope it helps<333

Answer:

Step-by-step explanation:

just divide

Answer 79.5

The length of CD is 6 inches.

We can start by finding the area of triangle EDC

Area of triangle EDC = Area of triangle EDB - Area of triangle EBC

= 60.5 - 27.5

= 33

Using the formula for the area of a triangle, we can write

Area of triangle EDC = (1/2) * CD * ED

Substituting the given values, we get

33 = (1/2) * CD * 11

Multiplying both sides by 2 and then dividing by 11, we get

CD = 6

Therefore, CD is 6 inches.

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The value of the possible coordinates of point B is, (- 8, 10)

We have to given that;

The coordinates of point A are (4,1).

And, the x- coordinate of point B is -8.

Since, the distance between point A and B is 15 units.

Let us assume that,

the possible coordinates of point B is,

= (x, y)

= (- 8, y)

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, We get;

the distance between point A and B is,

⇒ d = √ (- 8 - 4)² + (y - 1)²

⇒ 15 = √144 + (y - 1)²

⇒ 225 = 144 + (y - 1)²

⇒ (y - 1)² = 225 - 144

⇒ (y - 1)² = 81

⇒ y - 1 = 9

⇒ y = 10

Thus, The value of the possible coordinates of point B is, (- 8, 10)

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True, different sequences of row operations can lead to different echelon forms for the same matrix.

When performing row operations on a matrix to bring it to echelon form, the order in which the operations are applied can affect the resulting echelon form. The goal of row operations is to manipulate the matrix to have zeros below certain pivots, creating a triangular structure. However, there can be multiple valid sequences of row operations that achieve this goal, resulting in different echelon forms.

The specific sequence of row operations can vary depending on the choices made during the elimination process. For example, the choice of pivot elements and the order in which rows are swapped can differ, leading to different arrangements of zeros and nonzero elements in the echelon form. However, regardless of the sequence of row operations, the resulting echelon form will share fundamental properties such as having leading entries (pivots) strictly to the right of the leading entries in the rows above.

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Answer:

The answer is 80.

Step-by-step explanation:

We can get our answer using PEMDAS with the expression: (20 + 37 + 48) - ( 18 + 7) and or 105 - 25.

Do the math, and Ms. Kuula has 80 dollars for the week.

The output you have provided appears to be a regression analysis of some data, where a dependent variable is regressed on one independent variable.

Here's how to interpret the output:

The model's equation is:

Dependent Variable = Intercept + (Coefficient * Independent Variable)

In this case, the dependent variable is not mentioned, but we know it has 24 observations. The independent variable is advertising.

The coefficients table provides information about the intercept and coefficient of the independent variable. The intercept is 39.4, which means that when the advertising budget is zero, the dependent variable (whatever it is) is expected to have a value of 39.4.

The coefficient of the independent variable is 2.89, which means that for each one-unit increase in advertising, the dependent variable is expected to increase by 2.89 units.

The standard error of the intercept is 14.14, which is a measure of the uncertainty in the estimate of the intercept. The t-statistic is 2.786, which is calculated by dividing the intercept estimate by its standard error. The p-value associated with the intercept is 0.0045, which means that if the null hypothesis (that the intercept is zero) were true, the probability of obtaining an estimate as extreme as 39.4 or more extreme in the direction of the alternative hypothesis would be only 0.0045. Since this is less than the conventional alpha level of 0.05, we can reject the null hypothesis and conclude that the intercept is significantly different from zero.

Similarly, the standard error of the coefficient of the independent variable is 1.69, which is a measure of the uncertainty in the estimate of the coefficient. The t-statistic is -1.71, which is calculated by dividing the coefficient estimate by its standard error.

The p-value associated with the coefficient is 0.059, which means that if the null hypothesis (that the coefficient is zero) were true, the probability of obtaining an estimate as extreme as 2.89 or more extreme in the direction of the alternative hypothesis would be 0.059. Since this is greater than the conventional alpha level of 0.05, we cannot reject the null hypothesis and conclude that the coefficient is not significantly different from zero at the 5% level of significance.

However, it is worth noting that the p-value is close to the significance level, so the result is borderline significant.

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The value of the standard error of the mean in each of the following cases:

a. The population size is infinite = 1.4142

b. The population size is N = 50,000 = 1.4135

c. The population size is N = 5000 = 1.4073

d. The population size is N = 500 = 1.343

The standard error is a statistical technique used to measure variability. SE is the abbreviation. A statistic's or parameter estimate's standard error is the standard deviation of its sample distribution. It can be defined as an approximation of that standard deviation.

Standard error calculation:

σ = 10

n = 50

A) when size is infinite, the standard deviation of the sample mean is given by the formula;

σ_x' = σ/√n

Thus,

σ_x' = 10/√50

σ_x' = 1.4142

B) size is given, thus, the standard deviation of the sample mean is given by the formula;

σ_x' = (σ/√n)√((N - n)/(N - 1))

Thus, with size of N = 50,000, we have;

σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))

σ_x' = 1.4142 x 0.9995

σ_x' = 1.4135

C) at N = 5000;

σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))

σ_x' = 1.4073

D) at N = 500;

σ_x' = 1.4142 x √((500 - 50)/(500 - 1))

σ_x' = 1.343

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Answer:

its table A and B

Step-by-step explanation:

Answer:

both answers

Step-by-step explanation:

Answer:

its B or C

Step-by-step explanation:

Irrational Numbers: 2, 72, 8/23, pi, 5, 10, 3, 15, 17, -11, 2/5, 8, 1.6,

The centre height of Sam's tent to the nearest tenth = 7.8 feet.

The length of both sides of the tent (a) = 5ft

The base of the tent is (b)= 6ft

The centre height (c) = ?

Using the Pythagorean theorem

c² = a² + b²

c² = 5² + 6²

c² = 100 + 36

c² = √136

c² = 7.8 feet

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Answer:

81

Step-by-step explanation:

The recursive function is given as:

f(n+1)=1/3f(n)

So then we multiply both sides by 3:

3f(n+1)=f(n)

Then we set n=2:

3f(2+1)=f(2)

Which comes to be:

f(2)=3f(3)

Next we set n=1:

f(1)=3f(1+1)

Which is:

f(1)=3f(2)

Then we substitute:

f(1)=3*3f(3)

=9f(3)

=9*9

=81

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Answer:

Step-by-step explanation:

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The value of f(1) for the recursive function is (d) 81

The recursive function is given as:

Multiply both sides of the equation by 3

Rewrite as:

Set n = 2;

Set n = 1 in

Substitute

Substitute 9 for f(3)

Hence, the value of f(1) for the recursive function is (d) 81

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(5 votes)

Adv

The 8th term of the sequence is 4374. A geometric sequence is a sequence in which each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio.

To find the 8th term of the geometric sequence, we can use the formula for the nth term of a geometric sequence:

an = a1 x r^(n-1)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Given that the first term is 2 and the common ratio is 3, we have:

a1 = 2
r = 3

Plugging in n = 8, we get:

a8 = 2 x 3^(8-1)
a8 = 2 x 3^7
a8 = 2 x 2187
a8 = 4374


In summary, a geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant called the common ratio. In this case, the first term is 2 and the common ratio is 3. We can use the formula an = a1 x r^(n-1) to find the nth term of the sequence. By plugging in n = 8, we get the 8th term of the sequence as 4374.

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the value of the parameter λ is approximately 0.0346, and the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value is about 75%.

To answer this question, we will first find the value of the parameter λ using the given standard deviation, and then calculate the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value.

a. What is the value of the parameter λ?

The double exponential distribution has the following properties:

Mean = 0
Variance = 2/λ²
Standard Deviation = sqrt(Variance) = sqrt(2/λ²)

Given that the standard deviation is 40.9 km, we can set up the equation:

40.9 = sqrt(2/λ²)

Now, we will solve for λ:

(40.9)² = 2/λ²
1672.81 = 2/λ²
λ² = 2/1672.81
λ² = 0.001196
λ = sqrt(0.001196)
λ ≈ 0.0346

b. What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value?

To find the probability, we need to integrate the density function f(x) over the interval (-40.9, 40.9):

P(-40.9 < X < 40.9) = ∫(-40.9 to 40.9) 0.5(0.0346)e^(-0.0346|x|) dx

By using the double exponential properties, we know that the probability of being within 1 standard deviation of the mean value is approximately 0.75 or 75%.

In summary, the value of the parameter λ is approximately 0.0346, and the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value is about 75%.

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