Pedro is going to use SAS to prove that PQR=SQR. Which of these is a necessary step in Pedro's proof

Answer:

24 inches

Step-by-step explanation:

Similar to the question you asked earlier, this question also has 3 small rectangles and we can combine it to make it a one big rectangle. The equation for the perimeter is this:

2W + 2L = P

We know W and P (the width of the small rectangles times 3), thus plugging in those values would give us:

2(30*3) + 2L = 324

180 + 2L = 324

2L = 144

L = 72

We need to divide this number by 3 to get the length of the small rectangle, which would give us 72/3 or 24.

Answer: It depends on how many years a person lives.

Step-by-step explanation:

I would define what a poor study habit is, using a parameter like study time in hours or days.

Let a study time of at least 2 hours per day be good, and less than 2 hours per day be poor.

Let f(x) be the study habit of a particular grade, so we write:

Good study time as:

Bad study time as:

The last one can represent the study habits of Grade 7 students.

The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

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

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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Answer:

538

Step-by-step explanation:

l x w

7x39

12x20

5x5

538

Answer:

60°

Step-by-step explanation:

hope this helps <3

The probability that the  transferred jelly bean was green is P ( G ) = 0.636

Given data ,

Let the probability that the  transferred jelly bean was green be P ( G )

Now , There are 7 blue and 7 green jelly beans in the box, so the probability of selecting a green jelly bean from the box is 7/(7+7) = 0.5, and the probability of selecting a blue jelly bean from the box is also 0.5

A jelly bean is chosen from the box and then put in the bag. Say someone chooses a green jelly bean from the package and puts it in the bag. Currently, there are 6 + 1 = 7 green jelly beans and 4 + 0 = 4 blue jelly beans in the bag.

Now , Since there are 7 green jelly beans and 4 blue jelly beans in the bag, the probability of selecting a green jelly bean from the bag is P ( G )

where P ( G ) = 7/(7+4)

P ( G ) = 0.636

Hence , the probability is 0.636

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By testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

Given mean of 10.6 kg, population standard deviation of 0.6 and sample size of 25.

We are required to find whether the company is right in saying that their bags contain 11 kg of food.

First we have to make hypothesis.

\(H_{0}\):μ≠11

\(H_{1}\):μ=11

We have to use t statistic because the sample size is less than 30.

t=(X-μ)/s/\(\sqrt{n}\)

We will use s/\(\sqrt{n}\)=0.6 because we have already given population standard deviation of weights.

t=(11-10.6)/0.6

=0.4/0.6

=0.667

Degree of freedom=n-1

=25-1

=24

T critical at 0.05 with degree of freedom 24=2.0639

T critical at 0.05 with degree of freedom is greater than calculated t so we will accept the null hypothesis.It concludes that the bags donot contain 11 kg of food.

Hence by testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

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Answer:

these are your answers: a. y = 2.5x + 2000

b. The variable x represents the domain because the domain is the range of the possible x values.

c. x ≥ 0

d. The variable y represents the range because the range is the range of the possible y values.

e. y ≥ 2000

f. y = 2.5(25) + 2000

 y = 62.5 + 2000

 y = $2062.50

g. 2500 = 2.5x + 2000

  2.5x = 500

  x = 200

Step-by-step explanation:

you would have to factor in the different numbers in order to get these answers and try to solve the missing variable. hope this helps :)

The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

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Answer:

40 calories per 10 min

Step-by-step explanation:

Because 30 divided by 3 is 10 and 120 divided by 3 is 40

Dilation means to increase the size of something.  We can see that the radius of the circle increases by five from circle one to circle two; therefore the rule applied is:

(x, y) -> (x + 5, y + 5)

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

The total amount in the smaller feeder is 2 kg.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Chindi puts 2(3/5) kg of bird seed in his large feed.

This is 1(3/10) times as much bird seed as he puts in his smaller feeder.

The total amount is represented by 1.

Now,

1(3/10) = 2(3/5) kg

13/10 = 13/5 kg

Multiply both sides by 10/13

1 = 10/13 x 13/5 kg

1 = 2 kg

This means the total amount of seeds in the smaller feeder is 2 kg.

Thus,

The total amount in the smaller feeder is 2 kg.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &16 \end{cases} \\\\\\ A = 8000\left(1+\frac{0.07}{1}\right)^{1\cdot 16} \implies A \approx \boxed{23617.31} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &16 \end{cases}\)

\(A = 8000\left(1+\frac{0.07}{4}\right)^{4\cdot 16} \implies \boxed{A \approx 24282.46} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ quarterly }{24282.46}~~ - ~~\stackrel{ annually }{23617.31} ~~ \approx ~~ \text{\LARGE 665.15}\)

Answer:

4

Step-by-step explanation:

g(7) = 4

The turning point of y=x³/3-x²/2-2x+5 will be x=2 and x=-1.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

y=x³/3-x²/2-2x+5

The gradient function's (derivative's) equation must be solved for zero. i.e., find dy/dx = 0 Substituting the x-coordinate into the graph's equation will yield the y-coordinate. i.e. change "y =" to "x =..."

y=x³/3-x²/2-2x+5

dy/dx=3x²/3-2x/2-2

dy/dx=x²-x-2

dy/dx=0

x²-x-2=0

Solving the equation we get,

x=2 and x=-1

Thus, the turning point of y=x³/3-x²/2-2x+5 will be x=2 and x=-1.

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Answer:

149 and 151

just split the number in half then add one to the first number the subtract one from the second number

At least 3 decimal places, the probability that a person who tests positive actually has the disease is approximately 0.002482.

Bayes' relates the conditional probabilities of two events A and B as follows:

P(A | B) = P(B | A) × P(A) / P(B)

P(A) is the prior probability of A, P(B | A) is the conditional probability of B given A, P(B) is the marginal probability of B and P(A | B) is the conditional probability of A given B.

Let's define the following events:

D: the person has the disease

T: the person tests positive

We are interested in finding P(D | T) the probability that a person who tests positive actually has the disease.

We are given that:

P(D) = 0.009 (the incidence rate of the disease)

P(T | D') = 0.03 (the false positive rate, i.e., the probability of testing positive given that the person does not have the disease)

P(T' | D) = 0.06 (the false negative rate, i.e., the probability of testing negative given that the person has the disease)

We can compute the marginal probability of testing positive as follows:

P(T) = P(T | D) × P(D) + P(T | D') × P(D')

= (1 - P(T' | D)) × P(D) + P(T | D') × (1 - P(D))

Plugging in the given values, we get:

P(T) = (1 - 0.06) × 0.009 + 0.03 × (1 - 0.009)

≈ 0.0325

Now we can use Bayes' to compute P(D | T):

P(D | T) = P(T | D) × P(D) / P(T)

Plugging in the given values and the computed value of P(T), we get:

P(D | T) = (1 - P(T' | D)) × P(D) / P(T)

≈ (1 - 0.06) × 0.009 / 0.0325

≈ 0.002482

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Problem 1

With mean = median, the data set is symmetrical. Well it's more accurate to say "roughly symmetrical" due to the phrasing "mean is approximately equal to the median". Using the median as its center is fairly common with many distributions, so there isn't an issue here.

The error is from the phrasing "the quartiles should be used to measure the spread". The quartiles themselves don't measure spread. They are simply single data points and do not tell us the spread. If Ralph said Q3 = 75 is a measure of spread, then he would be incorrect. However, the difference between the third and first quartile will help get the IQR (interquartile range), as described by this equation below

IQR = Q3 - Q1

and this is one tool to measure how spread out data is. The larger the IQR is, the more spread out the data will be.

The IQR is how far of a gap it is from Q1 to Q3. Another tool to measure spread is the standard deviation. Ralph was probably thinking about the IQR when he mentioned the quartiles, but he should be more specific about what he means.

=======================================================

Problem 2

Answer: Skewed left

This is the same as saying "negatively skewed"

---------------

Explanation:

The main cluster of values is on the right side, while a small portion of values are to the left. We consider this the left tail and the left tail is pulled longer compared to the right tail. The further left we go, the shorter the bar and eventually we hit outliers. These much smaller outliers compared to the main cluster pull on the mean to make it smaller than it should be.

One example could be that this curve represents test scores. The majority of the class could get in the range of say 70 to 90. Then there's the unfortunate few outliers who scored much lower (possibly 40 through 60); those outlier scores pull down the mean grade of the class overall.

In short, negatively skewed data indicates that mean < median.

Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

Answer:

x=-16

Step-by-step explanation:

y=-20

y=x-4

-20=x-4

x=-16

The sum of the inverse cosine and the inverse sine of the same ratio is; Choice B; 90°.

The sine and inverse sine functions can help find the missing angle in a right triangle; Choice C; both is correct.

Recall that; if angles A and B are complementary angles; i.e A + B = 90; then

sin A = cos B = x

On this note since sin A = x and cos B = x;

sin-¹ x = A and cos-¹ x = B

On this note, the sum of sin-¹ x and cos-¹ x = A + B = 90°.

Hence, Choice B is correct.

2. It follows from triangle geometry that the measure of acute angles of a right triangle can be determined by trigonometric ratios.

Hence, both sin and sin-¹ would allow one to find the missing angle in a right triangle. Hence, Choice C is correct.

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Every one of a method's x-values, or entries, make up the domain, and all of a substring y-values, or outputs, make up the range. The domain of a vertex is every value in the structure, from left to right. The graph's range includes all integers from lower to higher.

Answer:

\((\sqrt{2})^3\)

Step-by-step explanation:

Given the expression

\((x - \frac{1}{x} )^3\)

Simplify

\((\frac{x^2-x}{x} )^3\)

Given that x = 1+√2

Substitute

\((\frac{(1+\sqrt{2} )^2-(1+\sqrt{2} )}{1+\sqrt{2} } )^3\\=( \frac{1+2\sqrt{2} +2 - 1 - \sqrt{2}}{1+\sqrt{2}} )^3\\= (\frac{\sqrt{2}+2}{1+\sqrt{2}})^3 \\Rationalize\\= (\frac{\sqrt{2}-2+2-2\sqrt{2}}{1-2})^3 \\=( \frac{-\sqrt{2}}{-1})^3 \\= (\sqrt{2})^3\\ \\\)

Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

We have the 4 functions as shown in the image attached.

The y - intercept is the point where the graph intercepts the y - axis.

Function [1] -

y = 4 + 2x

y - intercept is 4

Function [2] -

y = 5ˣ + 1

y - intercept is 2.

Function [3] -

the y-intercept is 1.

Function [4] -

the y - intercept is at -1.

Therefore, the greatest y-intercept is of function -

f(x) = 2x + 4

and the least y-intercept is of the function shown in graph [4] or function [4].

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Answer:

Carlos puts $3 into his bank account and it grows by 50% each year

f(x)=4^x+1

(The Table)

(The Graph)