Calculate the perimeter of the shape below. Show ur work! TYSM!!

The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.

In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ

where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.

To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.

We have , a = 5 , b = 12 , c= 13

cos α =( 12² + 13² - 5² )/2×12×13= 288/312

=> α = cos⁻¹(0.923 ) = 22.63°

cos β = (5² + 13² - 12² )/2×13×5 = 50/130

=> β = cos⁻¹(5/13) = 67.38°

cos γ = (12² + 5² - 13² )/2×12×5= 0

=> γ = cos⁻¹(0) = 90°

Hence, the required angles are 90°, 22.63°, 67.38°.

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Answer:

a. 5

i need to write 20 characters.

To calculate P(X ≥ 2), we need to standardize the variable X. First, we find the standard deviation of X by taking the square root of the variance: σ = √(25) = 5.

Then, we calculate the z-score for the value 2 using the formula z = (X - μ) / σ, where μ is the mean of X. Plugging in the values, we get z = (2 - 10) / 5 = -1.6. We can then look up the probability corresponding to this z-score in the standard normal distribution table or use a calculator. P(X ≥ 2) is equal to 1 minus the probability of X being less than 2, which can be written as P(X ≥ 2) = 1 - P(X < 2). By looking up the z-score of -1.6 in the table, we find that the probability is approximately 0.0548. Therefore, P(X ≥ 2) ≈ 1 - 0.0548 ≈ 0.9452.

To plot the histogram of Y = FX(X), we need to generate random samples from the distribution of X and compute the corresponding values of the distribution function FX. Since X is a normally distributed random variable, we can use a random number generator to generate samples from the normal distribution with mean 10 and variance 25. We then apply the distribution function FX to each sample to obtain the corresponding values of Y. By plotting the histogram of Y with a sample size of n = 1000, we can observe the shape of its distribution. If the histogram of Y closely resembles a uniform distribution on the interval [0, 1], it suggests that Y follows a uniform distribution. Conversely, if the histogram of Y deviates significantly from a uniform distribution, it indicates that Y does not follow a uniform distribution. Comparing the histogram of Y with the histogram of a uniform distribution on [0, 1], we can draw conclusions about the distribution of Y.

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Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

Let's calculate the final amount paid by Alice and Jeff for their purchases.

Alice:

Jeff:

So, Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

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The posssble number of boats build up by builder with 9 pounds of wood and 6 ounces of glue are three.

The ratio of two objects is defined as their relative size expressed as the quotient of one divided by the other. Wood needed to make mini boat

= 1 pounds

Glue needed to make one mini boat

= 2 ounces (oz)

Boat builder has 9 pounds of wood and 6 ounces of glue. We have to determine how many boats are build by boat builder. Ratio of wood to glue to make a boat = 1 : 2, i.e, 1 pounds of wood and 2 ounces of glue used for one mini boat.

Available wood to glue ratio = 9 : 6

You have 3 pounds of wood to build 3 boats, leaving 6 pounds and 6 ounces of glue. So the possible boat build number here is 3.

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Answer:

20-pounds

Step-by-step explanation:

If you multiply $27.50 by 2 then you get $55.00

($27.50*2=$55.00)

Answer:

2 pounds of meat

Step-by-step explanation: if you do 27.50 times 2 you get 55

the square root of 1728 is 41.57.

Answer:

41.57 is the answer.

Answer:

I hope it will be -20 please mark me brainleast

Answer:

To find out how much the TV is worth now, we need to apply the depreciation rate of 9% to the original price for 8 months:

First, let's calculate the value after the first month:

Value after 1 month = $2740 - (9% of $2740) = $2501.40

Now, let's calculate the value after 2 months:

Value after 2 months = $2501.40 - (9% of $2501.40) = $2275.80

We can continue this process for 8 months to find the current value:

Value after 3 months = $2071.67

Value after 4 months = $1888.81

Value after 5 months = $1725.10

Value after 6 months = $1579.92

Value after 7 months = $1452.16

Value after 8 months = $1339.53

Therefore, the TV is worth $1,339.53 now.

The ladder's base travels away from the property at a rate of -2.16 ft/s, whereas the peak of the staircase is 5 feet above the ground.

Let x = elevation in floors and bottom of the ladder.

Let y = the distance between the ladder's bottom and top.

The point of focus, x = 5 ft,

\(\frac{dy}{dx}\) = 2 ft/sec.

While x and y fluctuate as the ladder descends, the hypotenuse of a right-angled triangle illustrated remains constant at 10 feet. As a result, the Pythagorean theorem extends:

x² + y² = (13)² = 169

The derivative among both sides of the equation is about time. Keep in mind the chain rule.

\(\frac{d}{dt}\)(x² + y²) = \(\frac{d}{dt}\)(169)

2x\(\frac{dx}{dt}\) + 2y\(\frac{dy}{dt}\) = 0

The value of \(\frac{dy}{dt}\) at x = 5 and \(\frac{dx}{dt}\) = 2 ft/sec,

So,

2x\(\frac{dx}{dt}\) + 2y\(\frac{dy}{dt}\) = 0

2y\(\frac{dy}{dt}\) = -2x\(\frac{dx}{dt}\)

\(\frac{dy}{dt}\) = (-x ÷ y)\(\frac{dx}{dt}\)

Through the Pythagorean theorem, the value of y is somewhere at the instant when x = 5.

(5)² + y² = 169

25 + y² = 169

y² = 144

y = 12

Substituting all of the known values into the equation \(\frac{dy}{dt}\) = (-x ÷ y)\(\frac{dx}{dt}\),

\(\frac{dy}{dt}\) = (-13 ÷ 12) × 2

\(\frac{dy}{dt}\) = -2.16 ft/s

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Explanation:

I'm assuming the equation is \(y = \frac{5}{7}x\) which is the same as writing y = (5/7)x.

If so, then the constant of proportionality is the fraction out front: The value 5/7 is the coefficient of the term (5/7)x.

All direct proportion equations are of the form y = kx, where k is the constant of proportionality.  Another example would be y = 12x and this time k = 12.

Answer:

hi

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

it does add up to more then 60

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

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The measure of ∠B = 189°

Here it is given that

∠A = (5x + 24)° and ∠B = (6x - 5)°

∠A and ∠B are vertical angles

Since vertical angles are always equal so

      ∠A = ∠B

5x + 24 = 6x - 5

add +5 on both sides, we get

5x + 24 + 5 = 6x - 5 + 5

     5x + 29 = 6x

add -5x on both side, we get

   5x - 5x + 29 = 6x - 5x

   x = 29

Now put the value of x in 6x - 5

6 × 29 - 5 = 189

The measure of ∠B = 189°

According to the vertical angle theorem, the vertical angles that are created when two lines intersect are congruent. There are equal amounts of vertical angles. For instance, if a, b, c, and d are the four angles created by two intersecting lines and a, b, and c are vertically opposed to d and c, respectively, then a, b, and c are congruent to d.

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Answer:

rational

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

Rational numbers are numbers you can use in a ratio, basically things like negative/regular numbers, and fractions, decimals! Since you have a decimal negative number, it would be rational. It can't be Irrational because only numbers that are complicated

{ π, √10, and 1,271971910...)

(a) To find the probability that only one machine is in working condition after two days, we need to determine the probability of transitioning from state (1, 1) to state (1, 0) after two days.

From the transition probability matrix, we see that to transition from (1, 1) to (1, 0) in one day, both machines need to remain operational, which has a probability of (1 - p) * (1 - p) = (1 - p)^2.

Therefore, the probability of transitioning from (1, 1) to (1, 0) after two days is ((1 - p) * (1 - p))^2 = (1 - p)^4.

(b) To find the expected number of days until both machines are down, given that currently both machines are operational, we need to consider the transition probabilities from state (2, 0) to state (0, 1).

From the transition probability matrix, we see that to transition from (2, 0) to (0, 1) in one day, both machines need to fail, which has a probability of p * p = p^2.

Therefore, the expected number of days until both machines are down, given that both machines are currently operational, is 1 / (p^2).

(c) To find the steady-state probabilities, we need to solve the equation πP = π, where π is the row vector of steady-state probabilities and P is the transition probability matrix.

Solving this equation will give us the steady-state probabilities for each state (i, j). Since the given matrix is not provided, it is not possible to calculate the exact steady-state probabilities without the specific values of the transition probabilities.

(d) To determine the percentage change in the long-run average benefit per day if p changes from 0.3 to 0.2, we would need to know how the revenue R TL is related to the probability p. Without this information, it is not possible to calculate the percentage change.

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If the average rate of change is 18, then the value of the x is √(13/5). Then the correct option is B.

It's an average of how far the functions changed per unit throughout that time period.

Let f be the function given by f(x) = x³ + 5x.

Then the value in the closed interval [1,3] will be

The instantaneous rate of change will be

\(f'(x) = 3x ^2 + 5\)

Then the average rate of change will be

\(= \dfrac{f(3) - f(1)}{3-1} \\\\= \dfrac{(3^3 + 5\times 3) - (1^3 + 5 \times 1)}{3-1}\\\\= 18\)

Then we have

3x² + 5 = 18

Then the value of x will be

\(\begin{aligned} \rm 3x^2 + 5 &= 18\\\\\rm x &= \sqrt{\dfrac{13}{3}} \end{aligned}\)

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The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomials are given below.

10x⁶ + 20x⁴ - 15x² and 5x²

The factor of the polynomial 10x⁶ + 20x⁴ - 15x² will be given as,

10x⁶ + 20x⁴ - 15x² = (5x²) · (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be given as,

⇒ (10x⁶ + 20x⁴ - 15x²) ÷ (5x²)

⇒ [(5x²) · (2x⁴ + 4x² - 3)] ÷ (5x²)

⇒ (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

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Answer:

0.6% of the people had a mild allergic reaction.

Step-by-step explanation:

Given that:

Number of people who tried hair care products = 6000

Number of people who had reaction = 36

Percent of people = \(\frac{Number\ of\ people\ with\ reactions}{Total\ number}*100\)

Percent of people = \(\frac{36}{6000}*100\)

Percent of people = 0.6%

Hence,

0.6% of the people had a mild allergic reaction.

Answer:

A

Step-by-step explanation:

On a number line, I would start at 32 and then go left on the number line 17 spaces.  This would land me at positive 15.

Explanation

We are given the following:

We are required to determine the surface area of a cylinder. This can be achieved by using the formula:

Hence, the answer is 301.44m².

The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.

Given an equation,

$2.21 + 8% tax = $2.3868

This is an equation which relates the cost including the percentage of tax.

When 2.21 is added to the tax amount, we get $2.3868.

2.21 + (0.08 × 2.21) = 2.3868

Here it is not mentioned up to what decimal we have to round the figure.

If 2.3868 is rounded to the nearest whole number, it becomes 2.

If 2.3868 is rounded to the tenth, it becomes 2.4.

If 2.3868 is rounded to the hundredth, it becomes 2.39.

Hence the rounded amount to the nearest tenth is $2.4.

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The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

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Therefore ,There is sufficient evidence to support the claim that the results contradict Mendel's theory.

Mendelian inheritance is the term used to describe certain patterns of how features are passed down from parents to offspring. Gregor Mendel, an Austrian monk, developed these broad patterns through his countless pea plant studies in the 19th century.

Here,

n=307+77+98+18=500

k=4

O1=307

O2=77

03=98

04=18

\(\alpha =0.05\)

The null hypothesis claims that the population proportions are the same as those indicated (9:3:3:1).

\(H_{0}\): P1=9/16, P2=3/16,P3=3/16 & P4=1/16

In contrast to the null hypothesis, the alternative hypothesis states:

\(H_{\alpha }\): At least one of the peas is different.

E1=nP1=4297*9/16=281.25

E2=nP2=4297*3/16=93.75

E3=nP3=4297*3/16=93.75

E4=nP4=4297*1/16=31.25

The  subtotals are the squared differences between the observed and expected frequencies, divided by the expected frequency.

Next, the sum of the  subtotals represents the test-value: statistic's

\(x^{2} =\)∑\(\frac{O-E}E^{2}\)=\(\frac{(307-281.25)^{2}}{281.25} + \frac{(77-93.75)^{2}}{93.75} + \frac{(98-93.75)^{2}}{93.75} + \frac{(18-31.25)^{2}}{31,25}\)

=11.16

The number of categories has shrunk by 1 to reflect the degrees of freedom:

The P-value is the likelihood of getting the test statistic's value or a more extreme result. The number (or range) in the column heading of the chi-square distribution table in the appendix that contains the \(x^{2}\) value in the row df=k-1=4-1=3

0.01<P<0.025

If the P-value is less than or equal to the significance level, then the null hypothesis is rejected:

P<0.05=>Reject \(H_{0}\)

Therefore, The claim that the outcomes defy Mendel's theory is sufficiently supported by the available data.

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​

Answer:

less than

Step-by-step explanation:

Answer:

n ≤ 25

Step-by-step explanation:

n - 8 ≤ 17

n - 8 (+8) ≤ 17 (+8)

n ≤ 25

n ≤ 25 is your answer

Hope this helps <3

The p-value for this hypothesis test is 0.0272 when rounded to four decimal places.

To find the p-value for the hypothesis test, we need to calculate the test statistic and compare it to the critical value or use it to find the p-value from the appropriate distribution.

In this case, we are testing the null hypothesis H₀: μ = 21 against the alternative hypothesis H₁: μ ≠ 21, where the sample size is n = 81, the sample mean is \(\bar x\) = 19.00, and the population standard deviation is σ = 8.1.

The test statistic for this hypothesis test is the z-score, which is calculated using the formula:

z = (\(\bar x\) - μ) / (σ / √n)

Substituting the given values:

z = (19.00 - 21) / (8.1 / √81)

= -2 / (8.1 / 9)

= -2.2222

Now, to find the p-value, we need to find the probability of observing a test statistic as extreme or more extreme than -2.2222 under the null hypothesis.

Since the alternative hypothesis is two-sided (μ ≠ 21), we will calculate the p-value as the probability of the test statistic being greater than 2.2222 or less than -2.2222.

Using a standard normal distribution table or a statistical software, we find that the area under the curve to the left of -2.2222 is approximately 0.0136. Since this is a two-sided test, we double this probability to get the p-value:

p-value = 2 * 0.0136

= 0.0272

Therefore, the p-value for this hypothesis test is 0.0272 when rounded to four decimal places.

The complete question is:

Find the p-value for the following hypothesis test.

H₀: μ=21, H₁ : μ ≠ 21,n=81,  \(\bar x\) =19.00,  σ = 8.1

Round your answer to four decimal places.

p =?

the tolerance is +/-2%

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