Please help!
Geometry
If mZAOC = 31°, mZBOC = 2x + 10, and mZAOB = 4x - 15, find the degree measure of ZBOC and ZAOB.

The diagram is not to scale.

A step by step explanation would be greatly appreciate :(

Yes, the function satisfies the Mean Value Theorem conditions.

To determine if the function satisfies the hypotheses of the Mean Value Theorem (MVT) on the given interval [0, 2], we need to check two conditions:

Continuity: The function\(f(x) = 5x^2 − 2x + 4\) must be continuous on the closed interval [0, 2].

Differentiability: The function f(x) = \(5x^2 − 2x + 4\) must be differentiable on the open interval (0, 2).

Let's check each condition:

Continuity: The function f(x) = \(5x^2 − 2x + 4\) is a polynomial function, and all polynomial functions are continuous on their entire domain. Therefore, f(x) = 5x^2 − 2x + 4 is continuous on the interval [0, 2].

Differentiability: To check differentiability, we need to verify that the derivative of the function f(x) = \(5x^2 − 2x + 4\) exists and is continuous on the open interval (0, 2).

The derivative of f(x) = \(5x^2 − 2x + 4\) is:

f'(x) = 10x - 2

The derivative is a linear function, and linear functions are differentiable everywhere. Therefore, f(x) = \(5x^2 − 2x + 4 i\)s differentiable on the open interval (0, 2).

Since the function f(x) =\(5x^2\)− 2x + 4 is both continuous on the closed interval [0, 2] and differentiable on the open interval (0, 2), it satisfies the hypotheses of the Mean Value Theorem on the given interval [0, 2].

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Answer:

b=5

Step-by-step explanation:

the answer is in the image above

Answer:

5

Step-by-step explanation:

The Pythagorean Theorem states that a^2 + b^2 = c^2 for right triangles where a and b are the legs and c is the hypotenuse.

In the image, b and 12 are legs and 13 is the hypotenuse, so b^2 + 12^2 = 13^2 -> b^2 = 13^2 - 12^2 = 169 - 144 = 25 -> b = 5

I hope this helps! :)

To calculate the p-value, we need to use a one-tailed t-test since we're interested in the probability of getting a sample mean greater than 12.10 oz.

First, we need to calculate the t-statistic:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

t = (12.15 - 12.10) / (0.05 / sqrt(25))

t = 3.1623

Next, we need to find the degrees of freedom, which is the sample size minus one:

df = 25 - 1 = 24

Using a t-distribution table with 24 degrees of freedom and a significance level of 0.01, we find that the critical value is 2.492.

Since the calculated t-value (3.1623) is greater than the critical value (2.492), we can reject the null hypothesis and conclude that there is evidence that the mean volume is greater than 12.10 oz.

To find the p-value, we need to calculate the probability of getting a t-value greater than 3.1623 with 24 degrees of freedom:

p-value = P(t > 3.1623) = 0.0028 (calculated using a t-distribution table or software)

Therefore, the p-value is 0.0028, which is less than the level of significance (0.01), indicating strong evidence against the null hypothesis.

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The survey methods that will produce a simple random sample of 60 students in a high school is: Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.

Simple random sampling is a type of probability sampling where the researcher randomly chooses a subset of participants from a population. Each part of the population has the same chance of being selected. Then, data is collected from as large a percentage as possible of the random subset.

The American Community Survey is an example of simple random sampling. In order to gather detailed data on the population of the US, the Census Bureau officials randomly choose 3.5 million households a year and use variety of methods to make them sure to fill out the survey.

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Answer:

2/9

Step-by-step explanation:

The sum of two numbers is 5/9 can be expressed as:

\(\displaystyle \large{x+y=\dfrac{5}{9}}\)

One of the numbers is 1/3. Find the other - this means that either x or y is 1/3 but that doesn’t matter as we can either let x = 1/3 or y = 1/3 via property:

\(\displaystyle \large{x+y = y+x}\)

Hence, let x = 1/3:

\(\displaystyle \large{\dfrac{1}{3}+y=\dfrac{5}{9}}\)

Solve for y - subtract both sides by 1/3:

\(\displaystyle \large{\dfrac{1}{3}-\dfrac{1}{3}+y=\dfrac{5}{9}-\dfrac{1}{3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1}{3}}\)

We know that we can only evaluate the fractions if both have same denominator so what we have to do is to multiply 1/3 by 3 for both top and bottom:

\(\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1\cdot 3}{3\cdot 3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{3}{9}}\\\displaystyle \large{y=\dfrac{2}{9}}\)

Therefore, the other number is 2/9

Answer:

The other number is 2/9

Step-by-step explanation:

"a" is the other number

The equation:

\(a+\frac{1}{3} =\frac{5}{9}\)

Then

\(a=\frac{5}{9} -\frac{1}{3} =\frac{15-9}{27} =\frac{6}{27}\)

simplifying the fraction:

\(a = \frac{2}{9}\)

Hope this helps

Answer: if you do length x width x height you should get 64 cm

Step-by-step explanation:

Answer:

21 - 8 = x

21 - 8 = 13

Step-by-step explanation:

because you send a total of 21, and you send 8, just do 21 - 8 and thats how many text messages she sends

The smallest number of kilometers that each must run is 6 kilometers.

From the information, Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers and at the end of the month, they realize that they have run the same total number of kilometers.

It should be noted that the question simony had to do with finding the least common multiple. This will be:

Multiple of 3 = 3, 6, 9, 12

Multiple of 6 = 6, 12

The least common multiple is 6.

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Answer:

y= -1+5x

Step-by-step explanation:

a) The maximum error in the calculated area of the disk =  23.87 cm²

b) The relative error is: 0.0211 and the percentage error is 2.11%

Let us assume that r represents the radius of the circular disk and A represents the area.

Here, the radius of a circular disk is given as 19 cm

So, r = 19 cm

and the radius has a maximum error in measurement of 0.2 cm.

So, dr = 0.2

The area of the circular disk would be,

A = πr²            ..........(1)

A = π × 19²

A = 361π cm²

Differentiating equation (1) with respect to r,

dA = 2πr × dr

dA = 2 × π × 19 × 0.2

dA = 7.6π

dA = 23.87 cm²

So, the maximum error in the calculated area is: 23.87 cm²

Now we find the relative error.

R = dA/A

R = 7.6π / 361π

R = 0.0211

And the percentage error would be:

P = relative error × 100

P = 0.0211 × 100

P = 2.11%

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Distance is increasing with a speed of 0.2 Miles/Min

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time in Minutes      Distance in Miles

0                              0.0

2                              0.4

4                              0.8

6                              1.2

8                              1.6

Here, Myra’s distance is increasing as time increase with a constant Speed.

Now, In every 2 mins distance traveled = 0.4 Miles

Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min

Thus, Distance is increasing with a speed of 0.2 Miles/Min.

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Answer:

  (c)  The domain and range of the graph are the same.

Step-by-step explanation:

You want to identify the correct statement about the domain and range of the square root function f(x) = √x.

The square root is defined for all non-negative numbers.

The values of the square root function will not be negative.

The appropriate description of the domain and range is ...

  The domain and range of the graph are the same.

The area of the sector is evaluated to be equal to 9π square meters

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For the area of circle 72π m²;

πr² = 72π m²

r² = 72 m²

hence the area of the sector is calculated as follows:

area of the sector = (45°/360°) × π × 72 m²

we simplify by multiplication and division

area of the sector = 1/8 × π × 72 m²

area of the sector = π × 9 m²

area of the sector = 9π m².

Therefore, the area of the sector is evaluated to be equal to 9π square meters

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T he linear equation for the monthly cost of a dance company member is Cost = 10x + 12. Using this equation, we can calculate the total monthly cost for a member with a specific number of lessons, as well as determine the number of lessons a member had if their cost is given.

To find the linear equation for the monthly cost of a dance company member based on the number of lessons they have, we can use the information given about two members and their corresponding costs. By setting up a system of equations, we can solve for the flat monthly fee and the cost per lesson. With the linear equation, we can then determine the total monthly cost for a member with a specific number of lessons. Additionally, we can find the number of lessons a member had if their cost is given.

a) Let's denote the flat monthly fee as "f" and the cost per lesson as "c". We can set up two equations based on the information given:

For the member with 7 lessons:

7c + f = 82

For the member with 11 lessons:

11c + f = 122

Solving this system of equations, we can find the values of "c" and "f" that represent the cost per lesson and the flat monthly fee, respectively. In this case, "c" is $10 and "f" is $12.

Therefore, the linear equation for the monthly cost of a member as a function of the number of lessons they have is:

Cost = 10x + 12, where x represents the number of lessons.

b) To find the total monthly cost for a member who wants 16 lessons, we can substitute x = 16 into the linear equation:

Cost = 10(16) + 12 = $172.

Thus, the total monthly cost for a member with 16 lessons is $172.

c) To find the number of lessons a member had if their cost is $142, we can rearrange the linear equation:

142 = 10x + 12

130 = 10x

x = 13.

Therefore, the member had 13 lessons.

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Answer:

Step-by-step explanation:

x=first number; y=second number

x+y=85

y-4=2x

Solve-

y=85-x

(85-x)-4=2x

81=3x

x=27

Plug in-

(27)+y=85

y=58

The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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Answer:

The answer is -14 .

Step-by-step explanation:

Using BODMAS rule.... at first solve the bracketed problem... then you wm get your answer!

Answer: i think x

Step-by-step explanation:

x squared is x multiplied by x so doing the square root just gets rid of the square

As per the trigonometric substitution the value of the integrals are

a) ∫ x² + 4 / x² dx is 2 tan θ

b) ∫ (16 - 9x²) / x² dx is (4/3) sec θ

c) ∫ (5x² - 3) / x² dx is (1/√3)tanθ

Let's take a look at the given integrals:

a) ∫ x² + 4 / x² dx

For this integral, we can use the trigonometric substitution x = 2tanθ. This substitution simplifies the integral and allows us to solve it using trigonometric identities.

b) ∫ (16 - 9x²) / x² dx

To solve this integral, we can use the trigonometric substitution x = (4/3)secθ. This substitution simplifies the expression under the integral sign and allows us to use trigonometric identities to solve the integral.

c) ∫ (5x² - 3) / x² dx

For this integral, we can use the trigonometric substitution x = (1/√3)tanθ. This substitution simplifies the integral and allows us to use trigonometric identities to solve it.

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The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.

According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.

To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.

Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.

Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.

Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.

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Answer:

5

Step-by-step explanation:

Because the 2 sides and 2 other sides and bottom

Answer:

The prism has 5 faces

Step-by-step explanation:

A face is a side of a polygon.

~theLocoCoco

Answer:

$108.79

Step-by-step explanation:

49.45÷5=9.89

9.89=the cost for 1 video game

9.89×11=108.79

(11=the used video games)

The answer would be $108.79 for 11 used video games.

Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.

It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.

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Answer: Your answer is 21.21

Step-by-step explanation: To figure it out you need to know the radius which is half of the diameter and if the diameter is 3 the radius is 1.5 and then I just solved Using this equation.

V = π r² h = π x 1.5² x 3 = 21.20575

Hope I helped :D

Answer:

6

Step-by-step explanation:

In the first step I simply took 25 away from 76, as she already has 25 tickets meaning she needs 51 more.

than I divided 51 by 8, which would tell us the number of visits she needs to make

It's the 4th option.

Step-by-step explanation:

Corresponding angles are congruent, so x =43. I hope this helps, have a great day!

The charge on capacitor C2 is 3.24μC.

Given: Capacitance of capacitor C1=7.00μF and Capacitance of capacitor C2=6.00μF

(a) Equivalent capacitance of the system.

Using the formula for capacitance when capacitors are in parallel: C = C1 + C2C = 7.00μF + 6.00μFC = 13μF

Thus, the equivalent capacitance of the system is 13μF.

(b) Charge on each capacitor:

We know that charge stored by the capacitor is given by the formula Q = CV.

Calculating the charge on capacitor C1Q1 = C1V1

Where V1 is the potential difference across capacitor C1V1 = V

The total charge in the system should be equal and thus:

Q = Q1 + Q2

Where Q is the total charge.Q2 = Q - Q1Q2 = CV - C1V

The potential difference V = V1 + V2

Applying the formula V = V1 + V2

We have V = Q/C 1+ Q/C 2Q

= VC 1C 2/ C 1+ C 2Q

= (7.00μF x 6.00μF)V / 7.00μF + 6.00μFQ

= 42.0 V / 13.0μFQ

= 3.23 μC

Thus, the charge on capacitor C1 is 3.23μC.Q2 = 3.23μC - 6.00μF x V2V2

= Q2 / C2V2 = 3.23μC / 6.00μFV2

= 0.54 VQ2 = C2V2Q2

= 6.00μF x 0.54VQ2

= 3.24 μC

Thus, the charge on capacitor C2 is 3.24μC.

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1)The pdf of U is f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

2)U follows a gamma-distribution with parameter a = 3/2 or a = 1/2.

3)x = (y²/2) and dx = y dy using exponential distribution

We can rewrite the integral as:

I(1/2) = ∫₀^∞ y exp(-y²) dy

       = 1/2 ∫₀^∞ exp(-u/2) du

This is the same as the integral for f(u) when u = 1/2.

Therefore, we have:

I(1/2) = V1

(1) For U = Z², we can use the method of transformations.

Let g(z) be the transformation function such that

U = g(Z)

   = Z².

Then, the inverse function of g is given by h(u) = ±√u.

Thus, we can apply the transformation theorem as follows:

f(u) = |h'(u)| g(h(u)) f(u)

     = |1/(2√u)| exp(-u/2) for u > 0 f(u) = 0 otherwise

Therefore, the pdf of U is given by:

f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

(2) We are given that f(1/2) = VT, where V is a constant.

We can substitute u = 1/2 in the pdf of U and equate it to VT.

Then, we get:VT = (1/(2√(1/2))) exp(-1/4)VT

                            = √2 exp(-1/4)

This gives us the value of V.

Now, we can use the pdf of the gamma distribution to find the parameter a such that the gamma distribution matches the pdf of U.

The pdf of the gamma distribution is given by:

f(u) = (u^(a-1) exp(-u)/Γ(a)) for u > 0 where Γ(a) is the gamma function.

We can use the following relation between the gamma and the factorial function to simplify the expression for the gamma function:

Γ(a) = (a-1)!

Thus, we can rewrite the pdf of the gamma distribution as:

f(u) = (u^(a-1) exp(-u)/(a-1)!) for u > 0

We can now equate the pdf of U to the pdf of the gamma distribution and solve for a.

Then, we get:

(1/(2√u)) exp(-u/2) = (u^(a-1) exp(-u)/(a-1)!) for u > 0 a = 3/2

Therefore, U follows a gamma distribution with parameter

a = 3/2 or equivalently,

a = 1/2.

(3) We need to show that I(1/2) = V1.

Here, I(1) = ∫₀^∞ exp(-x) dx is the integral of the exponential distribution with rate parameter 1 and V is a constant.

We can use the change of variables y = √(2x) to simplify the expression for I(1/2) as follows:

I(1/2) = ∫₀^∞ exp(-√(2x)) dx

Now, we can substitute y²/2 = x to obtain:

x = (y²/2) and

dx = y dy

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Answer:

A basket ball being held

Step-by-step explanation:

Hope this helps you out