What are the values of the interior angles?

Round each angle to the nearest degree.
A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º
B) m∠X = 120º, m∠Y = 15º, m∠Z = 30º
C) m∠X = 145º, m∠Y = 18º, m∠Z = 36º

What Are The Values Of The Interior Angles?Round Each Angle To The Nearest Degree.A) MX = 131, MY = 16,

Answers

Answer 1

We can see here the values of the interior angles will be: A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º.

What is interior angle?

An interior angle is an angle created between two adjacent sides of a polygon. To put it another way, it is the angle created by two polygonal sides that have a shared vertex.

Sum of interior angles of a triangle = 180°

[tex]2p + \frac{1}{4} p + \frac{1}{2} p = 180[/tex]

11p/4 = 180°

p = 720°/11

m∠X = 2p = 2 ×  720°/11 = 130.9 ≈ 131°

m∠Y = [tex]\frac{1}{4} p[/tex] = 1/4 × 720°/11 = 16.3 ≈ 16°

m∠Z = [tex]\frac{1}{2} p[/tex] = 1/2 × 720°/11 = 32.7 ≈ 33°

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Related Questions

Find the derivative of f(x) = -2x^3 by the limit process…

Answers

Answer:

f'(x) = -6x^2

f'(-5) = -150

f'(0) = 0

f'(√17) = -102

a rectangular prism with a volume of 20 in^3 is dialited with a scale facotr of 2. what is the volume of the new figure?

Answers

The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.

In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.

Volume of rectangular prism = length x width x height

20 = l x w x h

Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.

New length = 2 x l

New width = 2 x w

New height = 2 x h

Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:

Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)

Simplifying this expression, we get:

Volume of new rectangular prism = 8 x (l x w x h)

We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:

Volume of new rectangular prism = 8 x 20 in³

Volume of new rectangular prism = 160 in³

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Given that x is a positive integer less than 100, how many solutions does the congruence x+13=55 (mod 34) have?

Answers

The congruence x + 13 ≡ 55 (mod 34) simplifies to x ≡ 12 (mod 34). There are three solutions for x less than 100 that satisfy this congruence.

The given congruence is x + 13 ≡ 55 (mod 34). Simplifying this, we get x ≡ 12 (mod 34).

We need to find the number of solutions for x that are less than 100 and satisfy this congruence.

The general solution for the congruence x ≡ 12 (mod 34) is x = 12 + 34k, where k is an integer.

The solutions that are less than 100 are obtained when k = 0, 1, or 2.

Thus, the number of solutions is 3.

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. If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2

Answers

By linear equality , g >1.5 is must be true.

What are equality and inequality along a line?

Equal (=) is the symbol used in linear equations. Example. Using the inequality symbols (>,, is greater than or equal to, and is less than or equal to), linear inequalities are expressed.

                          x - 5 > 3x - 10 is an illustration of a linear inequality. As the larger than symbol is employed in this inequality, the LHS is strictly greater than the RHS. After being solved, the inequality appears as 2x 5 x (5/2).

If h> 3 and h - 2g= 0

H=2g

2g>3

g >1.5

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under the normal distribution, if the mean of the distribution of raw scores is equal to 100, then its equivalent z-score is equal to

Answers

The equivalent z-score for a raw score of 115 under a normal distribution with a mean of 100 and a standard deviation of 15 is 1.

Under the normal distribution, if the mean of the distribution of raw scores is equal to 100 and the standard deviation is known, we can use the z-score formula to calculate the equivalent z-score for any given raw score.

The z-score formula is given by:

z = (x - μ) / σ

where x is the raw score, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the corresponding z-score.

Since the mean of the distribution is 100, we have μ = 100. To calculate the z-score, we need to know the standard deviation of the distribution or have information about the distance of the raw score from the mean in terms of standard deviations.

If we assume that the standard deviation is 15, which is a common value used in educational testing, and the raw score is 115, then the corresponding z-score would be:

z = (115 - 100) / 15 = 1

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ab and bc are perpendicular lines find the value of x of 25

Answers

Answer:

If the time is 3:45 how many minutes is it slow or fast

Line AB contains point A(1, 2) and point B (−2, −1). Find the coordinates of A′ and B′ after a dilation with a scale factor of 5 with a center point of dilation at the origin

Answers

The coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.

How to find dilated coordinate of A and B?

To find the coordinates of the points A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we can use the following formula:

[tex]$$(x', y') = (5(x - 0), 5(y - 0)) = (5x, 5y)$$[/tex]

where (x, y) are the original coordinates of the point, and (x', y') are the new coordinates after the dilation.

For point A(1, 2), the new coordinates A' are:

[tex]$$(x_A', y_A') = (5(1), 5(2)) = (5, 10)$$[/tex]

Therefore, the coordinates of point A' are (5, 10).

For point B(-2, -1), the new coordinates B' are:

[tex]$$(x_B', y_B') = (5(-2), 5(-1)) = (-10, -5)$$[/tex]

Therefore, the coordinates of point B' are (-10, -5).

Therefore, the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.

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PLEASE HELP ME!!! Type the correct answer in each box. Use T for true and F for false.
Complete the truth table for the contrapositive of a conditional statement.
р
T
T
LL
LL
q
T
F
T
LL
P→q
T
F
T
T
~9~p

Answers

The answer will of given mathematical logic will be T F T T F respectivelly.

What fundamental ideas underlie mathematical logic?

A negation, conjunction, and disjunction are the fundamental mathematical logics. The symbols for negation, conjunction, and disjunction in mathematical logic are "," "," and "v," respectively.

What is the purpose of mathematical logic?

Logical proofs frequently employ mathematical logic. Proofs are legitimate arguments that establish the veracity of mathematical assertions. A series of statements make up an argument. The conclusion is the last assertion, and the premises are all the statements that came before it (or hypothesis).

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The complete truth table is shown in the below diagram.

≈ q → ≈ p: True  False  True  True

Define the conditional statement for contrapositive?

The contrapositive of a conditional statement is a new conditional statement that is formed by negating both the hypothesis (the "if" part) and the conclusion (the "then" part) of the original statement, and switching their positions. The truth table for the contrapositive of a conditional statement has the same number of rows as the truth table for the original statement.

For example, if the original statement is "If it is raining, then the ground is wet", then the contrapositive would be "If the ground is not wet, then it is not raining."

According to the given table the contrapositive of a conditional statement q and p is defines as;

True

False

True

True

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Elizabeth works as a server in coffee shop, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work. 25 g 20 15 10 6 0 0 l0 15 20 Tip Amounts (dollars a. Write a few sentences to describe the distribution of tip amounts for the day shown. b. One of the tip amounts was S8. If the S8 tip had been S18, what effect would the increase have had on the following statistics? Justify your answers. i. The mean: ii. The median:

Answers

a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.

b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.

a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.

b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.

ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.

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show that the properties of a probability distribution for a discrete random variable are satisfied.

Answers

The properties of a probability distribution for a discrete random variable ensure that the probabilities assigned to each possible value of the variable are consistent with the axioms of probability and allow for meaningful inference and prediction.

The properties of a probability distribution for a discrete random variable are.

The probability of each possible value of the random variable must be non-negative.

The sum of the probabilities of all possible values must equal 1.

The probability of any event A is the sum of the probabilities of the values in the sample space that correspond to A.

These properties are satisfied because the probabilities of each possible value of a discrete random variable are defined in such a way that they are non-negative and sum to 1. Additionally, any event A can be expressed as a collection of possible values of the random variable, and the probability of A is then computed as the sum of the probabilities of those values.

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Question 2
State the probability that a randomly selected, normally
distributed value lies between
a) o below the mean and o above the mean (round to
the nearest hundredths)
b) 20 below the mean and 20 above the mean (round
to the nearest hundredths)

Answers

The probability of a randomly selected, normally distributed value lying between 20 below the mean and 20 above the mean is 0.9545 (rounded to the nearest hundredth).

What is the fundamental concept of probability?

A number between zero and one represents the probability that an occurrence will take place. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.

We can calculate the probabilities of a randomly chosen value falling between different z-scores using the provided standard normal distribution table.

a) The probability of a value being 0 below or above the mean is the same as the probability of a value being -1 to 1 standard deviations from the mean. According to the standard normal distribution table, the probability of a z-score between -1 and 1 is 0.6827. As a result, the probability of a randomly chosen, normally distributed value falling between 0 below and 0 above the mean is 0.6827. (rounded to the nearest hundredth).

b) The probability of a value falling between 20 and 20 standard deviations from the mean is the same as the probability of a value falling between -20/10 and 20/10 standard deviations from the mean (since the standard deviation is 10). According to the standard normal distribution table, the probability of a z-score between -2 and 2 is 0.9545. As a result, the probability of a randomly chosen, normally distributed value falling between 20 below and 20 above the mean is 0.9545. (rounded to the nearest hundredth).

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[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25} } } )[/tex]


find the value of y ~ ​

Answers

The simplification of the given expression

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

is y = 7

How to simplify expressions?

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

find the square root of 25

[tex]y =( \sqrt{47 + \sqrt{9 - 5} } [/tex]

simplify root 9 - 5

[tex]y = ( \sqrt{47 + \sqrt{4} } [/tex]

find the square root of 4

[tex]y = ( \sqrt{47 + 2)} [/tex]

Add root 47 and 2

[tex]y = ( \sqrt{49} )[/tex]

Find the square root of 49

y = 7

Therefore, the solution to the given expression is y = 7

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to calculate the workload of a resource that serves different flow unit types, one must know which of the following?

Answers

The workload of the resource is 20.5 units.

To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.

For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:

Workload = (10*2 + 8*1 + 5*3) / 2

       = 41 / 2

       = 20.5 units

Therefore, the workload of the resource is 20.5 units.

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Complete question

What are the flow unit types that the resource is serving?

For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).

Answers

Answer: (f⋅g)(1) = 10.

Step-by-step explanation:

To find (f⋅g)(x), we need to multiply the two functions f(x) and g(x) together. This can be done by multiplying each term of f(x) by each term of g(x), and then combining like terms. We get:

(f⋅g)(x) = f(x) * g(x)

= (-7x+3) * (3x^2 - 4x - 1)

= -21x^3 + 28x^2 + x - 3x^2 + 4x + 1

= -21x^3 + 25x^2 + 5x + 1

To find (f⋅g)(1), we can substitute x=1 into the expression for (f⋅g)(x):

(f⋅g)(1) = -21(1)^3 + 25(1)^2 + 5(1) + 1

= -21 + 25 + 5 + 1

= 10

Therefore, (f⋅g)(1) = 10.

0.0125 inches thick
Question 4
1 pts
The combined weight of a spool and the wire it carries is 13.6 lb. If the weight of the spool is 1.75 lb.,
what is the weight of the wire?
Question 5
1 pts

Answers

In linear equation, 11.85 pounds is the weight of the wire.

What is  linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Total weight of pool having 16 wires     =13.6 pounds

Weight of the pool                                 =1.75

Therefore the weight of the wire alone = 13.6 - 1.75

                                                             =  11.85 pounds

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What is the meaning of "the homotopy classes of paths from x to x in a space X"?

Answers

The homotopy classes of paths from x to x in a space X refer to a set of equivalence classes of continuous paths that start and end at the same point, x, in the space X, where equivalence is defined in terms of homotopy.

What is the homotopy about?

In other words, for any two paths, there exists a continuous transformation (called a homotopy) between them such that the endpoints remain fixed. Two paths are said to be homotopic if they can be continuously deformed into each other while keeping their endpoints fixed. The set of all paths that are homotopic to each other forms an equivalence class.

The homotopy classes of paths from x to x are important in algebraic topology, as they provide a way to study the topological structure of a space by analyzing the properties of the paths within it. They can also be used to define higher algebraic structures such as the fundamental group and higher homotopy groups.

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2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Question 1
Part A

Which equation can be solved to predict the number of times Harris will spin a sum less than 10?

A) 3/500 = x/15

B) 12/500 = x/15

C) 12/15 = x/500

D) 3/15 = x/500

QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?

_______

Answers

Accοrding tο the data, the answers tο Questiοns 1 and 2 are: Harris shοuld anticipate spinning a sum οr less 10 apprοximately 367 times and a tοtal that is 10 οr larger apprοximately 133 times.

What are a fοrmula and an equatiοn?

Yοur example is an equatiοn since an equatiοn that's any statement with an equal's sign. The usage οf equatiοns in mathematical expressiοns is widespread because mathematicians adοre equal signs. An equatiοn is a cοllectiοn οf guidelines fοr prοducing a specific οutcοme.

Part A: Tο calculate the likelihοοd that Harris will spinning a sum οr less 10, multiply the οverall number οf spins by the chance οf οbtaining a sum οr less 10. The οutcοmes οf the first spinner's spin are 1, 2, and 3, while the results οf the secοnd spinner's spin are 4, 5, 6, 7, and 8. Hence, the amοunts οr less 10 are:

1 + 4 = 5

1 + 5 = 6

1 + 6 = 7

1 + 7 = 8

1 + 8 = 9

2 + 4 = 6

2 + 5 = 7

2 + 6 = 8

2 + 7 = 9

3 + 4 = 7

3 + 5 = 8

3 + 6 = 9

There are 11 amοunts that cοuld be less than ten. The number οf successful results divided by the entire number οf pοssibilities, which is 11/15, represents the likelihοοd οf receiving a payοut οf less than 10 in a single spin. Harris will therefοre spin a tοtal less than 10 times, and the equatiοn tο estimate this is:

11/15 = x/500

After finding x, we οbtain:

x = (11/15) x 500

x = 366.67, which rοunds up tο 367

Sο, Harris shοuld expect tο spin a sum less than 10 abοut 367 times.

Part B: Tο determine hοw frequently Harris shοuld anticipate spinning a sum οf ten οr mοre, we can deduct the times that he shοuld anticipate spinning a sum lοwer than ten frοm the οverall number οf spins:

500 - 367 = 133

Therefοre, Harris shοuld expect tο spin a sum that is 10 οr greater abοut 133 times.

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My little cousin needs help with this can anyone help please.

I’m busy with my tests and I don’t have the time to explain.

Answers

Answer:

I don't knowI am sorry I will let someone else answer

Step-by-step explanation:

-0.1x^2+10=0

find the x

Answers

x = 10 and x = -10.

Answer:

x = ±10

Step-by-step explanation:

1) Subtract 10 from both sides.

[tex]-0.1 \times x^2=-10[/tex]

2) Divide both sides by -0.1.

[tex]x^2=\frac{-10}{-0.1}[/tex]

3) Simplify [tex]\frac{-10}{-0.1}[/tex] to 100.

[tex]x^2=100[/tex]

4) Take the square root of both sides.

[tex]x=\pm \sqrt{100}[/tex]

5) Since 10 * 10 is 100, the square root of 100 is 10.

[tex]x=\pm10[/tex]

do you mind helping me with this?

Answers

Answer:

125

Step-by-step explanation:

We Take

625 / 5 = 125

So, the answer is 125

The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 104 parts are
produced, the cost is $324. What is the average cost per part?
OA $0.23 per part
B. $6 per part
OC. $0.17 per part
OD. $7 per part

Answers

Answer:

B. $6 per part

Step-by-step explanation:

The average cost per part can be computed as follows

Average Cost = (324-300)/(104-100)

= 24/4

=$6

Answer: B. $6 per part

What the values of angles B and C?

Answers

The value of b is 73° as opposite angles of congruent sides are equal in an isosceles triangle.

What dοes a math angle mean?  

An angle is created by cοmbining twο rays (half-lines) that have a cοmmοn terminal. The angle's vertex is the latter, while the rays are alternately referred tο as the angle's legs and its arms.

What is fundamental angle?

An angle within a shape that has the shape's base as οne οf its sides is knοwn as the base angle οf a shape in geοmetry. Cοnsider the triangle in the image as an example. We can οbserve that the triangle's base side is made up οf an angle B side and an angle C side. As a result, the triangle's base angles are angles B and C.

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Baker School's hockey games are 60 minutes long. Nico played for 30 minutes of the last game. What percent of the game time did Nico play?
Pick the model that represents the problem.

Answers

Dude he played for 1/2 of the game half of 60 is 30.

50%.

I'm I missing something?

If the area of one side of this cube is 25 cm^2
2
, what is the area of the whole surface of the cube?




cm^2
2

Answers

Answer:

150 cm2

Step-by-step explanation:

Given side of cube's area = 25. Since Side's a square,

Edge^2 = 5^2 = 5 cm

Total surface area: 6*a² = 6*5*5 = 150 cm2


The population of a certain city was 3,846 in 1996. It is expected to decrease by about 0.27% per year. Write an exponential decay function, and use it to approximate the population in 2022.

Answers

Answer:

To write an exponential decay function for this situation, we can use the formula:

P(t) = P₀e^(rt)

where:

P(t) = the population at time t

P₀ = the initial population

r = the annual rate of decrease (as a decimal)

t = time in years

We are given P₀ = 3,846 and r = -0.0027 (since the population is decreasing).

To approximate the population in 2022, we need to find t, the number of years from 1996 to 2022. That is:

t = 2022 - 1996 = 26 years

Now we can plug in the values we have:

P(t) = 3,846 e^(-0.0027t)

To find P(2022), we plug in t = 26:

P(26) = 3,846 e^(-0.0027(26))

≈ 3,200.62

Therefore, we can approximate the population of the city in 2022 to be about 3,201 people.

Answer:

3,101

Step-by-step explanation:

Please hit brainliest if this helped!

To write an exponential decay function for the population of the city, we can use the formula:

P(t) = P₀e^(-rt)

where P(t) is the population at time t, P₀ is the initial population, r is the decay rate, and e is the base of the natural logarithm.

In this problem, P₀ = 3,846 and r = 0.0027 (0.27% expressed as a decimal). We want to find the population in 2022, which is 26 years after 1996.To use the formula, we need to convert 26 years to the same time units as the decay rate. Since the decay rate is per year, we can use 26 years directly. Therefore, the exponential decay function for the population is:

P(t) = 3,846e^(-0.0027t)

To find the population in 2022 (t = 26), we substitute t = 26 into the function:

P(26) = 3,846e^(-0.0027*26) ≈ 3,101

Therefore, the population in 2022 is approximately 3,101.

Let me know if this helped by hitting brainliest! If you have any questions, comment below and I"ll get back to you ASAP.

can someone please help me asap!!! ill mark brainlistt...

Answers

Answer:

Step-by-step explanation:

To solve this problem, we can use the formula for the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given the length of two sides of the triangle (the legs) and we need to find the length of the hypotenuse.

Let's label the sides of the triangle:

The shorter leg is the vertical side opposite the angle marked 55 degrees, so let's call it "a".

The longer leg is the horizontal side adjacent to the angle marked 55 degrees, so let's call it "b".

The hypotenuse is the side opposite the right angle, so let's call it "c".

Using trigonometry, we can determine the value of "a" and "b":

a = b * tan(55°) (since tangent = opposite/adjacent, we solve for opposite which is "a" in this case)

a = 100 * tan(55°) = 100 * 1.428 = 142.8

b = 100

Now, we can use the Pythagorean theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2

c^2 = 142.8^2 + 100^2

c^2 = 20484.84 + 10000

c^2 = 30484.84

c = sqrt(30484.84)

c ≈ 174.6

Therefore, the length of the hypotenuse is approximately 174.6 units (the units are not given in the problem, but we can assume they are consistent with the units used for the given values of "a" and "b").

The problem does not specify the orientation or scale of the graph, but we can assume that it is a right triangle with the angle marked 55 degrees in the upper left corner.

The vertical side (the shorter leg) of the triangle should be labeled with a length of approximately 142.8 units (assuming the units used for the problem are consistent with the values given for "a" and "b"). The horizontal side (the longer leg) should be labeled with a length of 100 units.

The hypotenuse (the side opposite the right angle) should be drawn as a diagonal line connecting the endpoints of the vertical and horizontal sides. The hypotenuse should be labeled with a length of approximately 174.6 units.

The angle marked 55 degrees should be labeled as such, and the other two angles of the triangle (the right angle and the angle opposite the longer leg) should be labeled accordingly.

Change the following equation of a line into slope-intercept form.
y + 4 = 2x

Answers

Answer:

Step-by-step explanation:

[tex]y=2x-4[/tex]    (slope-intercept form is [tex]y=mx+b[/tex] where m=gradient

                     and b is where line intercepts y-axis)

Ciara throws four fair six-sided dice. The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6 Work out the probability that at least one of the dice lands on an even number.

Answers

The likelihood that one or more of the dice will land on an even number is 1296.

How does probability work?

The likelihood of an event is quantified by its probability, which is a number. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The likelihood of an event increasing with probability of occurrence.

According to the given information:

Four 6-sided dice are rolled what is the probability that at least two dice show least 2 die the same.

For 2 of the same: 5×5×642) =900

For 3 of the same: 5×643) =120

For 4 of the same: 644) =6

Combined: 900+120+6=1026

Total possibilities: 64=1296

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The probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

We can solve this problem by finding the probability that all four dice land on odd numbers and then subtracting this probability from 1 to get the probability that at least one of the dice lands on an even number.

The probability that one dice lands on an odd number is 3/6 = 1/2, and the probability that all four dice land on odd numbers is:

(1/2) × (1/2) × (1/2) × (1/2) = 1/16

Therefore, the probability that at least one of the dice lands on an even number is:

1 - 1/16 = 15/16

So the probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.

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12. Reason A data set is represented by the box plot shown. Between which two values would the middle 50% of the data be found? Explain.

Answers

The middle 50% data of the boxplot will be calculated between the value of 7 to 14.

Explain about the box plot?The variation in information is shown using a boxplot, which is a standardized method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum"). It can reveal information about your outliers' values. Boxplots can also show you exactly securely your data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.

The data set ranges are:

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Divide the given data in 4 quartiles Qs;

Q1 = 4 - 6

Q2 = 7 - 10

Q3 = 11 - 14

Q4 = 15 - 17

Thus, 50% data will be lying in Q2 and Q3.

Range - 7 - 14

Thus, the middle 50% data of the box plot will be calculated between the value of 7 to 14.

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construct shear and bending diagrams for the following beams. show your equations used to create the plots. p p p p l/2 l/4 l/4 p p p l/3 l/3 l/3

Answers

The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.

To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:

Leftmost section (0 ≤ x ≤ L/4)

Second section (L/4 < x ≤ L/2)

Third section (L/2 < x ≤ 5L/12)

Fourth section (5L/12 < x ≤ 7L/12)

Rightmost section (7L/12 < x ≤ L)

We can use the equations for shear and bending moments to create the plots:

For section 1: 0 ≤ x ≤ L/4

The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.

For section 2: L/4 < x ≤ L/2

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.

For section 3: L/2 < x ≤ 5L/12

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.

For section 4: 5L/12 < x ≤ 7L/12

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.

For section 5: 7L/12 < x ≤ L

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.

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