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Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?
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The shaded area of the portion as shown in the diagram is 78.04 cm².

Area is the region bounded by a plane shape.

To calculate the shaded area of the portion, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Complete question: A 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm. Calculate the area of the shaded portion.

The interest that Tamika will be charged in interest after 24 months of borrowing $5,000 at 8% simple interest per year is $800.

Simple interest is the interest system that computes interest only on the principal for each period.

Unlike the compound interest system, simple interest does not charge interest on accumulated interest and the principal.

The principal loan amount borrowed by Tamika = $5,000

The interest rate per year = 8%

The loan period = 24 months = 2 years (24/12)

Simple Interest = Principal x Rate x Period

= $800 ($5,000 x 8% x 2)

Thus, for borrowing $5,000 for 24 months of 2 years, Tamika would pay a simple interest of $800.

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Tamika is seeking a loan with a simple interest rate of 8% per year. If she wants to borrow $5,000, then how much will she be charged in interest after 24 months?

Answer:

Distance that car B travels =1.2× distance that car A travels

=1.2×221.5=265.8 km

Answer:

car B travels a distance of 265.8 km during the same time.

Step-by-step explanation:

Car A travels 221.5 km at a given time.

To find the distance traveled by car B, which is 1.2 times the distance traveled by car A, we can multiply the distance of car A by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, car B travels a distance of 265.8 km during the same time.

i. The sample mean and median for the data for the two companies are 8.1 and 8.25 respectively.

ii. The line graph of the data is illustrated below.

iii. Yes, The steel rods supplied by Company B may be more flexible than those supplied by Company A.

iv. If you are looking for steel rods with higher flexibility, I would recommend Company B based on the higher median, the apparent differences in the box and whisker plot, and the confidence interval indicating a higher mean flexibility for their rods.

For Company A, the sample mean can be calculated by adding all the values and dividing by the number of values:

Mean of Company A = (9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0) / 10 = 8.1

To find the median, we first need to arrange the data in ascending order:

6.5, 6.7, 6.8, 7.0, 8.0, 8.5, 8.7, 8.8, 9.2, 9.3

Since there are an even number of values, the median is the average of the two middle values:

Median of Company A = (8.0 + 8.5) / 2 = 8.25

For Company B, the sample mean can be calculated similarly:

Mean of Company B = (11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6) / 10 = 10.2

Arranging the data in ascending order, we get:

9.6, 9.7, 9.8, 9.9, 10.1, 10.2, 10.2, 10.2, 11.0, 11.1

Since there are an odd number of values, the median is the middle value:

Median of Company B = 10.2

Next, let's plot the data for both companies on the same chart and observe any apparent differences. We can use a box and whisker plot to do this.

Looking at the box and whisker plot, we can see that the median of Company B (represented by the line in the middle of the box) is higher than the median of Company A. Additionally, the box for Company B is taller than the box for Company A, indicating that the range of values for Company B is greater than that of Company A. These observations suggest that the steel rods supplied by Company B may be more flexible than those supplied by Company A.

To determine if there is a significant difference between the means of the two companies, we can use a 90% confidence interval of the mean. This interval gives us a range within which we can be 90% confident that the true population mean lies.

Using a t-distribution with 18 degrees of freedom (10 + 10 - 2), we can find the 90% confidence interval for the difference between the means of the two companies. The formula for the confidence interval is:

Difference in means ± (t-value x standard error of difference in means)

The t-value for a 90% confidence interval with 18 degrees of freedom is approximately 1.734.

Now, we can calculate the margin of error by multiplying the t-value (1.734) by the standard error:

Margin of Error = 1.734 * 0.393 ≈ 0.682

Finally, we can construct the 90% confidence interval for the difference in means as:

Difference in means ± Margin of Error

Calculating the difference in means (mean of Company B - mean of Company A), we have:

Difference in means = 10.2 - 8.1 = 2.1

Therefore, the 90% confidence interval is:

2.1 ± 0.682

This means that we can be 90% confident that the true population mean difference between the two companies' steel rods lies between 1.418 and 2.782.

Based on this analysis, we can conclude that Company B tends to supply steel rods that are more flexible compared to Company A. However, it's important to note that this study was conducted on a small sample size, so further investigation with larger sample sizes would be beneficial to confirm the findings.

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695 divided by 70=9.92 hours

Answer:

17

Step-by-step explanation:

11+6=17

(a) The exact value of sin B is 6 / 12.53

(b) The exact value of tan A is 11 / 6

(c) The exact value of cos A is 6 / 11

The value of sin (B), cos (A) and tan (A) is calculated by applying trigonometry ratio as follows;

The trigonometry ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The value of the hypotenuse side of the right triangle is;

L = √ (6² + 11²)

L = 12.53

(a) The exact value of sin B is;

sin B = 6 / 12.53

(b) The exact value of tan A is;

tan A = 11 / 6

(c) The exact value of cos A is;

cos A = 6 / 11

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The function limit of f(x) as x approaches 2 is 67 and the limit of f²(x) as x approaches 2 is 4489.

The function f(x) can be rewritten as:

f(x) = (5x³ + 3x² - x)/(x+2)

Using direct substitution, we see that f(2) is undefined, as the denominator of the function becomes 0.

To evaluate the limit, we can use L'Hopital's rule:

[tex]\lim_{x \to 2\[/tex] f(x) = lim x→2 (5x³ + 3x² - x)/(x+2)

= [tex]\lim_{x \to 2\[/tex] (15x² + 6x - 1)/(1)

= (15(2)² + 6(2) - 1)/(1)

= 67

To find the limit of f²(x) as x approaches 2, we can simply square the limit:

f(x) = [tex]\lim_{x \to 2\}[/tex]f²(x)

= [tex]\lim_{x \to 2[/tex] f²(x)  

= 67²

= 4489

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Answer:

Y=-10x+1 with x being -5

y = -10 *-5 +1

y = -50+1

y =-49

[tex]x=\textit{gallons of solution at 10\%}\\\\ ~~~~~~ 10\%~of~x\implies \cfrac{10}{100}(x)\implies 0.10 (x) \\\\\\ y=\textit{gallons of solution at 60\%}\\\\ ~~~~~~ 60\%~of~y\implies \cfrac{60}{100}(y)\implies 0.6 (y) \\\\\\ \textit{150 gallons of solution at 50\%}\\\\ ~~~~~~ 50\%~of~150\implies \cfrac{50}{100}(150)\implies 75 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{gallons}{quantity}&\stackrel{\textit{\% of gallons that is}}{\textit{fertilizer only}}&\stackrel{\textit{gallons of}}{\textit{fertilizer only}}\\ \cline{2-4}&\\ \textit{Sol'n of 10\%}&x&0.10&0.10x\\ \textit{Sol'n of 60\%}&y&0.60&0.60y\\ \cline{2-4}&\\ mixture&150&0.5&75 \end{array} \\\\\\ \begin{cases} x + y = 150\\\\ 0.10x+0.60y=75 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=150}\implies y=150-x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 2nd equation}}{0.10x+0.60y=75}\implies \stackrel{\textit{substituting on the 2nd equation from above}}{0.10x+0.60(150-x)=75} \\\\\\ 0.10x+90-0.60x=75\implies 90-0.50x=75\implies 90=0.50x+75 \\\\\\ 15=0.50x\implies \cfrac{15}{0.50}=x\implies \boxed{30=x}\hspace{5em}\stackrel{ 150~~ - ~~30 }{\boxed{y=120}}[/tex]

Answer:

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

We know that area is the product of two dimensions.

Hence we consider the square of the scale factor when comparing areas of similar figures.

The surface area of solid B is k² times the surface area of solid A:

Substitute and calculate:

The function that has a greater slope and greater y-intercept than the linear function represented in the table is,

⇒ y = 3x + 7.5

We have to given that;

The table below represents a linear equation.

Now, The equation of line is,

Take two points (- 1, 5) and (1, 9)

⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)

⇒ y - 5 = 4/2 (x + 1)

⇒ y - 5 = 2 (x+ 1)

⇒ y - 5 = 2x + 2

⇒ y = 2x + 7

Hence, By options,

The function that has a greater slope and greater y-intercept than the linear function represented in the table is,

⇒ y = 3x + 7.5

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An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (50.25 - 2)/(5 - 0)

Slope (m) = 48.25/5

Slope (m) = 9.65.

At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 9.65(x - 0)

y = 9.65x + 2

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Answer: 116.985 mm2

Step-by-step explanation:

Answer: We can use Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male. Bayes' theorem states:

P(A|B) = P(B|A) * P(A) / P(B)

where A and B are events, P(A|B) is the conditional probability of event A given that event B has occurred, P(B|A) is the conditional probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this case, we want to find P(grad degree | male), which is the probability that an applicant has a graduate degree given that they are male. Using Bayes' theorem, we have:

P(grad degree | male) = P(male | grad degree) * P(grad degree) / P(male)

We are given that 134 applicants are male, and 40 of those males have a graduate degree. Therefore:

P(male | grad degree) = 40 / total number of applicants with a graduate degree

We are not given the total number of applicants with a graduate degree, but we can find it using the fact that 40 applicants are male and have a graduate degree, and that there are 134 male applicants in total. Therefore:

total number of applicants with a graduate degree = 40 / (40/134) = 118.33 (rounded to the nearest whole number)

Next, we need to find the prior probability of having a graduate degree, P(grad degree). We can use the total number of applicants and the number of applicants with a graduate degree to calculate this probability:

P(grad degree) = number of applicants with a graduate degree / total number of applicants = 118 / 300 = 0.3933 (rounded to four decimal places)

Finally, we need to find the prior probability of being male, P(male). This probability can be calculated similarly:

P(male) = number of male applicants / total number of applicants = 134 / 300 = 0.4467 (rounded to four decimal places)

Now, we can substitute these values into Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male:

P(grad degree | male) = (40 / 118) * 0.3933 / 0.4467 = 0.332 (rounded to three decimal places)

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they are male, is approximately 0.332 or 33.2%.

Step-by-step explanation:

Answer:

  117

Step-by-step explanation:

You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).

The cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.

  u×v = (12)(11) -(-3)(-5) = 132 -15

  u×v = 117

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Answer:

a. 3x = 23-2

3x = 21

x = 21÷3

x = 7

b. 5x - 2 = 4

5x = 4+2

5x = 6

x = 6÷5

x = 1.2

c. 3x = 23-2

3x = 21

x = 21÷3

x = 7

d. 7 = 2x+0.5x

7 = 2.5

x = 2.5÷7

x = 2.8

1. It would be better to use the median to describe the data set.

2. It would be better to use the median to describe the data set.

3. It would be better to use the mean to describe the data set as the average salary of the workers is to be calculated.

4. It would be better to use the mean to describe the data set as the average test grade of the class is to be calculated.

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The projection of (v + w) onto u is (-8 √(2)i + 6 √(2)j).

Now, let's consider the given vectors u = - i + j, v = 8i - 2j, and w = - 4j. The question asks us to find the projection of vector v + w onto the vector u, denoted as proj_u(v + w). To find this projection, we need to use the dot product between the two vectors.

First, we need to calculate v + w, which is (8i - 2j) + (-4j) = 8i - 6j. Next, we calculate the dot product of u and (v + w):

u · (v + w) = (-i + j) · (8i - 6j)

= -8i + 6j - 8i + 6j

= -16i + 12j

The dot product measures the similarity between two vectors, and in this case, it gives us the component of (v + w) that is parallel to u. To find the projection of (v + w) onto u, we need to divide this component by the magnitude of u:

proj_u(v + w) = (u · (v + w)) / ||u||

= (-16i + 12j) / √(2)

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We need to use equations C and D:

C. 4 ÷ 12 = 1/3

D. 16 ÷ 12 = 4/3

We need to divide the total amount of pasta by 12. Therefore, we need to use equations C and D:

C. 4 ÷ 12 = 1/3

D. 16 ÷ 12 = 4/3

Equation C shows that each serving is 1/3 of a pound

Equation D shows that Mariana can make 4/3 servings

Therefore, Mariana can make 4/3, or approximately 1.33, servings of 12 pounds each.

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Answer:

can i get a picture\

Step-by-step explanation:

thanks

Answer:

Step-by-step explanation:

1:4

Using the relationship of distance, time and speed, the speed of the boat in still water is 8mi/hr

To determine the speed of the boat in still water, we can write an equation to represent this.

The speed as it travels upstream = x - 2

The speed as it travels downstream = x + 2

The total distance travelled by the boat = 15 + 15 = 30mi

Let's write an equation to represent this;

15/(x - 2) + 15/(x + 2) = 4

simplifying this;

15(x + 2) + 15(x - 2) = 4(x - 2)(x + 2)

15x + 30 + 15x - 30 = 4x² - 16

30x = 4x² - 16

4x² - 30x - 16 = 0

Solving for x;

x = -0.5, 8

But since the speed can't be negative, the speed is 8 mi/hr

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The probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.

The number of successes in a certain number of independent trials is modelled by the binomial distribution, which has just two potential outcomes for each trial, commonly referred to as "success" and "failure."

We can solve this problem by using the binomial distribution formula:

[tex]P(X=k) = (n\ choose\ k) * p^k * (1-p)^{(n-k)[/tex]

where:

P(X=k) is the probability of getting exactly k automobiles that fail the emissions test

n is the number of automobiles being tested, in this case, n = 10

k is the number of automobiles that fail the emissions test

p is the probability of a single automobile failing the emissions test, in this case, p = 0.05

Using this formula, we can calculate the probability of getting exactly k failures for k = 0, 1, 2, ..., 10, and then add up these probabilities to get the probability of getting at least one failure.

The probability of getting exactly k failures is:

[tex]P(X=k) = (10\ choose\ k) * 0.05^k * 0.95^{(10-k)[/tex]

Using a calculator or statistical software, we can calculate these probabilities:

[tex]P(X=0) = (10 choose 0) * 0.05^0 * 0.95^10 = 0.5987\\P(X=1) = (10 choose 1) * 0.05^1 * 0.95^9 = 0.3151\\P(X=2) = (10 choose 2) * 0.05^2 * 0.95^8 = 0.0746\\P(X=3) = (10 choose 3) * 0.05^3 * 0.95^7 = 0.0119\\P(X=4) = (10 choose 4) * 0.05^4 * 0.95^6 = 0.0013\\P(X=5) = (10 choose 5) * 0.05^5 * 0.95^5 = 0.0001\\[/tex]

[tex]P(X=6) = (10 choose 6) * 0.05^6 * 0.95^4 = 0.0000\\P(X=7) = (10 choose 7) * 0.05^7 * 0.95^3 = 0.0000\\P(X=8) = (10 choose 8) * 0.05^8 * 0.95^2 = 0.0000\\P(X=9) = (10 choose 9) * 0.05^9 * 0.95^1 = 0.0000\\P(X=10) = (10 choose 10) * 0.05^10 * 0.95^0 = 0.0000\\[/tex]

The probability of getting at least one failure is:

[tex]P(X > =1) = 1 - P(X=0) = 1 - 0.5987 = 0.4013[/tex]

Therefore, the probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.

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Answer:

10. 120 Degrees 12. 60 Degrees

Step-by-step explanation:

#12. Since CAD is 30, and BAD is a 90 degree angle, angle BAF is 60 degrees. Since BAF is 60 degrees and FAE and BAF are vertical angles, they have the same angle measure. 60 Degrees.

#10. Since BAF is 60, and FAE and BAF are on a line, we can do 180-60 to get the measure in degrees of that angle. FAE = 120 Degrees.

Answer:

Step-by-step explanation:

10. somewhere between 126 and 129, i feel its 128

12. between 60 and 65

The factor of 2xy + 30x^2 - xy - 16y^4 - yx - 5x^2 is 25x2−16y4=(5x+4y2)(5x−4y2)

We are given that;

2xy + 30x^2 - xy - 16y^4 - yx - 5x^2

Now,

Combine like terms by adding or subtracting the coefficients of the same variables. For example, 2xy - xy - yx = 0xy, and 30x^2 - 5x^2 = 25x^2. The polynomial becomes:

25x2−16y4

Check if there is a common factor for all the terms. In this case, there is no common factor other than 1, so we cannot use the greatest common factor method.

Check if the polynomial is a difference of two squares, which means it has the form a2−b2. In this case, we can see that both terms are perfect squares: 25x2=(5x)2 and 16y4=(4y2)2. Therefore, we can use the difference of two squares formula:

a2−b2=(a+b)(a−b)

Substituting a=5x and b=4y2, we get:

25x2−16y4=(5x+4y2)(5x−4y2)

Check if each factor can be further factored using any of the methods. In this case, neither factor can be further factored, so we are done.

Therefore, by factorization the answer will be 25x2−16y4=(5x+4y2)(5x−4y2)

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Answer:

No solution.

Step-by-step explanation:

To solve this problem, all you have to do is graph the lines and see where they intersect.

This is what you would do to solve a normal problem. However, these lines are parallel this means that the solution to these lines is no soultion

Answer:

Would buy Would not

again buy again Total

Aalora 77 16 93

Mederac 48 23 71

Total 125 39 164

71/164 = 43.3% of the customers purchased Mederac.

So the group that accounts for about 43% of the respondents is the percentage of the customers who purchased Mederac.

Answer:

When you divide 781.253 by 100, you get 7.81253 as the result.

The digit 2 is in the hundredths place in the dividend 781.253. Since we are dividing by 100, which has two decimal places, we move the decimal point two places to the left in the dividend to get the quotient.

Therefore, the digit 2 is in the ten-thousandths place in the quotient 7.81253.