(L8) Apply the 45º-45º-90º Triangle Theorem to find the length of a leg of a right triangle if the length of the hypotenuse is 102.

The two inequalities that define the shaded region in the diagram are:

y ≥ 4 and y < x

For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥"  because the shaded region is to the left and the boundary line is solid.

The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:

y ≥ 0(x) + 4

y ≥ 4

For the dashed line:

m = change in y / change in x = 1/1 = 1

b = 0

the inequality sign to use is: "<"

Substitute m = 1 and b = 0 into y < mx + b:

y < 1(x) + 0

y < x

Thus, the two inequalities are:

y ≥ 4 and y < x

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The correct answer is B) She is 95% confident that the true mean length of this species after five weeks of life is between 8.5 and 11.9 inches.

The 95% confidence interval (CI) is a range of values that we are 95% confident contains the true population parameter (in this case, the mean length of the fish species after five weeks of life). The supervisor cannot say with certainty that 95% of all fish of this species are between 8.5 and 11.9 inches long (A), as the CI only pertains to the mean length. She can also not say with certainty that 95% of all fish of this species that are five weeks mature are between 8.5 and 11.9 inches long (D), as the sample was randomly selected and may not represent the entire population.

The correct answer is B, as she is 95% confident that the true mean length of this species after five weeks of life is between 8.5 and 11.9 inches. This means that if she were to repeat the experiment many times and construct a CI for each sample, 95% of those intervals would contain the true population mean. Finally, option C is similar to option B and could also be considered correct.

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Answer:

C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.

Step-by-step explanation:

An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.

In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.

What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.

Answer:The answer is C

Step-by-step explanation:I did the test.

Answer:

400

Step-by-step explanation:

Tge 6 in the tens place is greater than 5, so you round the 3 up to 4.

If the number that determines where you round is 5 or more, round up.

So 366 rounded to the hundreds place is 400.

The answer is 400.

Happy to help!!! :)

The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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Answer:

Step-by-step explanation:

We have indication of:

Missing information is just confirmation that both of them are right triangles

This is:

Correct answer option is B

Step-by-step explanation: 6.7 x 10^1 = 67

The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Next three terms are -8, 16 and -32

Step-by-step explanation:

We are given the sequence:-

1, -2, 4, ...

We want to find next three terms:-

1, -2, 4, a4, a5, a6, ...

Since the sequence is geometric because it has common ratio;-

-2/1 = -2

4/-2 = -2

Our common ratio is -2.

General Term of Geometric

\( \displaystyle \large{a_n = a_1 {r}^{n - 1} }\)

Our first term or a1 is 1

Our common ratio or r is -2

Therefore:-

\( \displaystyle \large{a_n =1 {( - 2)}^{n - 1} }\)

Since we want to find next three terms which are a4,a5 and a6. Substitute n = 4,5 and 6 in.

Finding a4

\( \displaystyle \large{a_4 = 1 {( - 2)}^{4 - 1} } \\ \displaystyle \large{a_4 = 1 {( - 2)}^{3 } } \\ \displaystyle \large{a_4 = 1 {( - 8)} } \\ \displaystyle \large{a_4 = - 8}\)

Finding a5

\( \displaystyle \large{a_5 = 1 {( - 2)}^{5 - 1} } \\ \displaystyle \large{a_5 = 1 {( - 2)}^{4 } } \\ \displaystyle \large{a_5= 1(16)}\\ \displaystyle \large{a_5 = 16}\)

Finding a6

\( \displaystyle \large{a_6= 1 {( - 2)}^{6- 1} } \\ \displaystyle \large{a_6 = 1 {( - 2)}^{5 } } \\ \displaystyle \large{a_6 = 1( - 32)}\\ \displaystyle \large{a_6 = - 32}\)

Answer:

x = 4 mm

y = 15 mm

Step-by-step explanation:

x = 12 mm / 3 = 4 mm

y = 3 × 5 mm = 15 mm

Answer:

-93

Step-by-step explanation:

This is just.a matter of using a couple of integration rules and plugging in then using order of operations.

Difference rule and constant multiple rule will be used here.

3(-17)-7(6)

-51-42

-93

Answer:

\(\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = -93\)

General Formulas and Concepts:

Calculus

Integration

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                       \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \int\limits^6_4 {f(x)} \, dx = -17\)

\(\displaystyle \int\limits^6_4 {g(x)} \, dx = 6\)

\(\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx\)

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Stochastic simulations use random variables or probability distributions to model uncertainty in the system being simulated.

The type of simulation that is defined over a theoretically infinite time frame is called a "steady-state simulation".

In a steady-state simulation, the system being modeled is assumed to have reached a stable state where the behavior of the system does not change over time. The simulation is then run for a long period of time, allowing the outputs to converge to a steady state. The quantities to be estimated are defined over this theoretically infinite time frame.

On the other hand, terminating simulations have a fixed end time, and the simulation is terminated when that time is reached. Discrete simulations model systems where the state changes only at discrete points in time. Stochastic simulations use random variables or probability distributions to model uncertainty in the system being simulated.

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Answer:

Center ( 4 , -2) and r = 6

Step-by-step explanation:

x² - 8x + y² + 4y - 16 = 0

x² - 8x  + y² + 4 y = 16

x²- 2*4x + y² + 2 *2y = 16

(x² - 2*4x + 16 ) - 16 + (y² + 2*2y + 4) -4 = 16

(x - 4)² + (y + 2)² = 16 + 16 + 4

(x - 4)² + (y -[-2])² = 36

(x- 4)² + ( y - [-2] )² = 6²

Compare with (x - h)²+ (y - k)² = r²

Center ( 4 , -2) and r = 6

Based on the given expressions, the ones which canot be used to find the volume of the box or rectangular-prism is/are:

a)16 + 4 + 3

b)7 x 16

What is rectangular-prism?

A cuboid, also known as a rectangular prism, is a three-dimensional solid form or figure with six faces (two top and bottom faces and four lateral faces). The prism's faces are all rectangular and are divided into three pairs by their similarity. Based on its three dimensions, it has a volume and a surface area. The sum of the surfaces of each of its six sides represents the overall surface area.The total area of all of its side faces or four walls makes up the lateral surface area. Its volume can be calculated by multiplying the base area by the height.The volume of cuboid is given by area of base times height or length times width times height.

The given dimensions of the box:

Length=16 feet

Width=4 feet

Height=3 feet

Therefore the volume of cuboid can be written as LWH:

Volume=L.W.H

            =16 . 4 . 3

            = 64 . 3

             =16 . 12  

             =48 . 4

In this way the volume of cuboid will be 192 cubic feet

The expressions which will represent the volume of box:

a)12 x 16

b)16 x 4 x 3

c)3 x 64

d)48 x 4

And expressions which will not represent the volume of box:

a)16 + 4 + 3

b)7 x 16

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Refer to the attachment for the complete question.

Answer:

here it the answer

Step-by-step explanation:

hope it helps

The estimated cost for one student to purchase the ingredients for s'mores at the camp store is $2.10.

To estimate the cost for one student, we can divide the total cost for 15 students by the number of students. Given that the ingredients cost $31.50 for 15 students, we can calculate the cost for one student as follows:

Cost for 1 student = Total cost for 15 students / Number of students

Cost for 1 student = $31.50 / 15

Cost for 1 student ≈ $2.10

Therefore, the estimated cost for one student to purchase the ingredients for s'mores at the camp store is approximately $2.10. This calculation assumes that the cost is evenly distributed among the students and that the quantity of ingredients per student remains constant.

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Answer:

Therefore, the approximate monthly payment is $548.85

Step-by-step explanation:

The amount of student loans Erica currently has = $34,006.00

The duration over which Erica is to pay back the loan = 7 years

The annual interest rate for the loan = 9.1%

Therefore, we have the geometric sequence formula is given as follows;

\(A_n = P( 1 + r)^n - M \times \left [ \dfrac{(1 + r)^n-1}{r} \right ]\)

Where;

M = The monthly payment

P = The initial loan balance = $34,006.00

r = The annual interest rate = 9.1%

n = The number of monthly payment = 7 × 12 = 84

Aₙ = The amount remaining= 0 at the end of the given time for payment

Substituting the values into the above formula, , we get;

\(0 = 34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} - M \times \left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]\)

\(M = \dfrac{34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} }{\left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]} \approx 548.85\)

Therefore, the approximate monthly payment = $548.85

Answer:

Slope is 1/2

Step-by-step explanation:

1/2 is a fraction not a integer.

For every change of 1 y there is a change of 2 x

In the above case, the possible point system will be:

1st choice vote: 4 points

2nd choice vote: 2 points

In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:

Lets say:

1st choice vote: 4 points

2nd choice vote: 2 points

Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.

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Answer: The answer is (264)×(261)(525), because (264)×(261) are the possibilities for choosing 4 red cards and 1 black card from a deck of 52 cards, while (525) are the possibilities for choosing 5 cards from a deck of 52 cards.

So, your first solution is almost correct. On why your second solution is wrong, you'll have to explain your thought process.

Step-by-step explanation:

Answer:

9,202.77

Step-by-step explanation:

This is off of g/o/o/g//l/e/// btw hope this helped

Answer:

1/7

Step-by-step explanation:

4/28

= 4 * 1 is 4

= 4 * 7 is 28

So, 4/28 simplified is 1/7

Answer:

1/7 is the answer

Answer: 60 degrees

Step-by-step explanation:

An interior angle of a polygon and its corresponding exterior angle are supplementary (add to 180 degrees).

The box and whisker plot that represents the data given is option D (see attachment below).

The box and whisker plot that represents a data set will display the five-number summary of the data, which include minimum and maximum values, upper quartiles and lower quartiles, and the median of the data.

Given the data set, 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30, the five-number summary that would be displayed on the box and whisker plot include:

Minimum: 6 (at the beginning of the whisker to the left)

First Quartile: 13 (at the beginning of the edge of the box)

Median: 21 (at the middle line on the box)

Third Quartile: 27 (at the end of the edge of the box)

Maximum: 30 (at the end of the whisker to the right)

Therefor, the box and whisker plot would be the option D (see image below).

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The scatterplot between a predictor variable and an outcome with a non-linear relationship would not form a straight line, but rather a curved or nonlinear shape.

In linear regression, we assume that there is a linear relationship between the predictor variable and the outcome. However, this assumption may not hold in all cases, and there may be cases where the relationship between the two variables is not linear.

In such cases, a straight line may not be a good fit for the data, and a non-linear model may be more appropriate. In a scatterplot, a non-linear relationship would be indicated by a curve or a nonlinear shape rather than a straight line.

Examples of non-linear relationships include exponential, logarithmic, and polynomial relationships. It is important to identify and account for non-linear relationships when modeling data to ensure accurate and valid results.

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To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Step-by-step explanation:

Lets translate this word problem into math.

"Latoya's annual salary is $26,000" = We start with the number 26,000

"A total of $7352.24 will be deducted for taxes and health insurance" = It's the number we started with "deducted" (minus) 7352.24

"She will receive her paycheck monthly in 12 equal installments" = Our number will be divided by 12

"How much will she get paid with each paycheck?" = "Find answer pls thx"

To put it all together...

\(\frac{26,000-7,352.24}{12}\)

Now all we have to do is solve!

\(\frac{26,000-7,352.24}{12}\)

\(\frac{18,647.76}{12}\)

\(1,553.98\)

Answer:

Latoya will get paid $1,553.98 with each paycheck.