Find the area of the circle. Round your answer to the nearest hundredth. Use $3.14$ or $\frac{22}{7}$
for $\pi$ .

area: about
ft2

Circle with center C and point D. Triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

What is construction?

In the context of geometry, construction refers to the process of creating geometric figures or shapes using only a compass and straightedge (also called a ruler). The goal of construction is to create accurate and precise geometric figures using only these two tools and a given set of instructions.

To construct an equilateral triangle DEF with points E and F on circle C, we will follow the following steps:

Step 1: Draw a circle with center C and point D on it.

Step 2: Draw a line through points C and D. This line will be the base of our equilateral triangle DEF.

Step 3: Construct the perpendicular bisector of line CD. This can be done by drawing two circles with centers at C and D, both with radius greater than half the length of CD. The two circles will intersect at two points, and the line passing through these two points will be the perpendicular bisector of CD.

Step 4: Let G be the intersection point of the perpendicular bisector and circle C that is closest to point D. Draw lines from G to points C and D. These lines will intersect circle C at points E and F, respectively.

Step 5: Check that the length of CE is equal to the length of CF. This can be done using a compass and ruler.

Step 6: Finally, draw lines from points E and F to point D. The resulting triangle DEF will be equilateral.

To prove that triangle DEF is equilateral, we can show that DE = EF = FD. We already know that CE = CF from step 5. Since C is the center of the circle, CE = CF = CD. By construction, angle ECD and angle FCD are both 60 degrees, since they are inscribed angles that intercept the same arc.

Therefore, triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

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If  circumference of a circle is 7π cm then area of circle is 38.465 square centimeter

The circumference of a circle is 7π cm

We have to find the area of the circle

To find area we have to know the radius

Circumference = 2πr

7π= 2πr

r=7/2

= 3.5 cm

Area of circle = πr²

=3.14×(3.5)²

=3.14×3.5×3.5

=38.465 square centimeter

Hence, if  circumference of a circle is 7π cm then area of circle is 38.465 square centimeter

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The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.

The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.

Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.

Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.

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Probable and certain both speak about something that may (or may not) happen in the future, but probable and possible speak about future possibilities in different ways.

‘Probable’ is high up on the scale of probability.  If something is probable, then there is a high chance that something will happen.  We can imagine that ‘probable’ is around 80% and up on the scale of probability.

If something is possible, it doesn’t mean it’s probable.  However, if something is probable then it’s possible too.  And if this confuses you then you’re probably in the right place.  

Probable and certain are both on a scale of probability.  Probability is the level of possibility or chance that something will happen or will be true in the present or future.  

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Answer:

8 weeks

Step-by-step explanation:

Ok, so the equation given is y=8x+40

If the school needs 104 cabinets in total, we have to find x, the number of weeks to complete this order.

We can input 104 as y as that's the total:

104=8x+40

We have to isolate x, so first, subtract 40 from both sides

64=8x

Next, divide both sides by 8

8=x

So, it will take 8 weeks to fulfill this order.

Answer:

three hundred five thousanths

Step-by-step explanation:

The proportion of cherry tomatoes that are rejected based on their diameter is 0.0033. (option a).

To use the CDF, we need to standardize the diameter values using the z-score formula:

z = (x - μ) / σ

where z is the z-score, x is the diameter value, μ is the mean diameter, and σ is the standard deviation.

For tomatoes with a diameter of at most 15 mm, we have:

z = (15 - 22) / 2.5 = -2.8

For tomatoes with a diameter of at least 30 mm, we have:

z = (30 - 22) / 2.5 = 3.2

Next, we use the z-table to find the area under the Normal distribution curve that corresponds to these z-scores. For a z-score of -2.8, the area is 0.0026. For a z-score of 3.2, the area is 0.9993.

Finally, we add these two areas together to get the total proportion of rejected tomatoes:

proportion = 0.0026 + (1 - 0.9993) = 0.0033

Hence the correct option is (a).

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Problem 1: The best approximation for finding the price of an individual product is (b) Marginal Cost. This is because marginal cost represents the cost of producing one additional unit of the product. Problem 2: You get profit when (c) Revenue is more than cost. When the revenue generated from selling products is greater than the cost of producing those products, you will have a positive profit.

For problem 1, the best approximation for finding the price of an individual product would be the Marginal Cost. This is because it takes into account the additional cost of producing one more unit of the product, which directly affects the price.

For problem 2, the correct answer would be c) When Revenue is more than cost. This is because profit is calculated by subtracting the cost of producing the product from the revenue earned from selling it. If the revenue is higher than the cost, then there is profit. If the cost is higher than the revenue, then there is a loss. When the cost is equal to the revenue, there is no profit or loss, just a break-even point. Therefore, option d) "All of them" is incorrect.

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Using the formula for the perimeter of a triangle, x + (2x+5) + (2x-4) = 73. Solving for x, so the first side is 18 inches, the second side is 41 inches, and the third side is 32 inches.

Perimeter is the total distance around the outside of a closed two-dimensional shape, such as a polygon or a circle. It is found by adding the lengths of all the sides of the shape.

An equation is a mathematical statement that shows the equality of two expressions or values, often with one or more variables that can be solved for.

According to the given information :

Let the first side of the triangle be x.

Then, the second side is 2x + 5, and the third side is 2x - 4, according to the given conditions.

The perimeter of the triangle is the sum of the lengths of its sides, so we can write:

x + (2x + 5) + (2x - 4) = 73

Simplifying the equation:

5x + 1 = 73

5x = 72

x = 14.4

Therefore, the first side of the triangle is 14.4 inches, the second side is 2(14.4) + 5 = 33.8 inches, and the third side is 2(14.4) - 4 = 24.8 inches.

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By probability, the likelihood that a candidate chosen at random played an electric guitar and wore sequins is 0.3.

Using probabilities, one can determine how likely something is to occur.. It is represented by a number between 0 and 1, with 1 denoting a certain event and 0 an impossibility.

For instance, you can get either heads or tails when you flip a coin. There is only one way to get heads and two outcomes, hence the probability of receiving heads is 0.52.

The likelihood that a competitor played an electric guitar is 0.8, the likelihood that they were wearing sequins is 0.4, and the combined likelihood that they both played an electric guitar and wore sequins is 0.91.

The following formula can be used to determine the likelihood that a competitor chosen at random played an electric guitar and wore sequins:

P(A and B) equals P(A) times P(B|A)

where there are two events, A and B.

In this instance, A stands for the competitor who played an electric guitar, and B is for the person who wore sequins.

P(A) is known to equal 0.8. and P(B) = 0.4.

We also know that P(A or B) = 0.9.

Using the following equation to determine the likelihood of two events occurring together:

P(A or B) = P(A) + P(B) - P(A and B)

we can find P(A and B):

P(A and B)

           = 0.8 + 0.4 - 0.9

           = 0.3

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According to the given information, we know that:

Force (F) is constant

Mass (m) of the first object is 4 kg, and its acceleration (a) is 13 m/s².

Using Newton's second law of motion, we know that:

F = m*a

Solving for the force (F) acting on the first object:

F = m*a = 4 kg * 13 m/s² = 52 N

Now, if the same force acts upon an object with a mass of 26 kg, we can use the same equation to find its acceleration (a):

F = m*a

a = F/m

a = 52 N / 26 kg = 2 m/s²

Therefore, the acceleration of the second object is 2 m/s².

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On solving the provided question, we can say that As a result, we lack sufficient data at the hypothesis 0.01 level to declare that Josiah's new strategy has increased his driving speed.

A null hypothesis is a statistical hypothesis that states that a certain collection of observations has no statistical significance. Hypotheses are examined using sample data to determine their viability. It is also known as "zero" and is represented by the symbol H0. Researchers begin with the assumption that there is a relationship between the variables. The null hypothesis, on the other hand, asserts that there is no such link. Although the null hypothesis may not appear to be significant, it is an important component of research.

Part A: The following are the hypotheses for Josiah's test:

There is no statistically significant change in the average speed of Josiah's hits utilising the old and new techniques. In scientific notation: H0 = 1 - 2 = 0, where 1 represents the population mean speed of hits using the old approach and 2 represents the population mean speed of hits using the new technique.

Alternative hypothesis: There is a substantial difference in the average speed of Josiah's hits when employing the old and new techniques, with the new technique producing a faster average speed. In mathematical terms: Ha: 1 - 2 0.

Part B: We'll use a t-test because we're comparing two means and don't know the population standard deviation. We will assume that the sample sizes are big enough for the Central Limit Theorem to apply, and that the sample means have a normal distribution. We also suppose that the two samples are independent, which means that the speed of one strike is independent of the speed of the other.

Part C: To run the test, we must compute the test statistic and compare it to the critical value with 44 degrees of freedom (n1 + n2 - 2).

The test statistic is calculated as follows:

[tex]t = (x1 - x2 - 0) / (s / \sqrt(n1 + n2 - 2))[/tex]

where x1 represents the sample mean speed using the old approach, x2 represents the sample mean speed using the new technique, s represents the pooled standard deviation, and n1 and n2 represent the sample sizes.

When we plug in the values, we get:

[tex]t = (82 - 83.2 - 0) / (4.6 / \sqrt(45)) = -2.06[/tex]

At the 0.01 significance level, the critical value for a one-tailed t-test with 44 degrees of freedom is -2.681. We cannot reject the null hypothesis since our test statistic (-2.06) is bigger than the crucial threshold.

As a result, we lack sufficient data at the 0.01 level to declare that Josiah's new strategy has increased his driving speed.

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Over the weekend, I went hiking. I had hiked 1 3/4 miles when I came to a trail fork. I turned to the right. I continued hiking for another 2 1/2 km till I arrived at the lookout. I hiked for A) 4 1/4 miles to get there.

In this question, we have been given that the person first hikes for 1 3/4 miles and then for 2 1/2 miles, so we will first convert them into mixed fractions and we will add the fractions.

Total miles hiked to get there = 1 3/4 miles + 2 1/2 miles

= 7 / 4 miles + 5/2 miles

= (7 + 10) / 2 miles

= 17 / 2 miles

= 4 1/4 miles

If the denominators of two fractions are the same (such fractions are said to be similar fractions), they can be added directly. If the denominators are different (such fractions are known as unlike fractions), we must change the denominators and then add the fractions.

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Skewness measures the magnitude, degree, and direction of asymmetry in a distribution. It is an important tool for describing and understanding the shape of data distributions.

Skewness is a measure of the asymmetry of a distribution. It is a statistical measure that indicates the degree to which a distribution deviates from the symmetry of a normal distribution. Skewness can be either positive or negative, or it can be zero, indicating no skewness.

Magnitude, The magnitude of skewness is determined by the degree of asymmetry in the distribution. The larger the magnitude of skewness, the more asymmetrical the distribution is. A small magnitude indicates a distribution that is close to symmetric.

Degree, The degree of skewness is the extent to which the distribution deviates from symmetry. Positive skewness indicates a distribution with a longer right tail than left, while negative skewness indicates a distribution with a longer left tail than right.

Direction, The direction of skewness is the direction of the longer tail of the distribution. If the tail is to the right, the distribution is positively skewed, and if the tail is to the left, the distribution is negatively skewed.

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Answer:

In (-3)^2, Henry multiplied -3 by 2. That is not correct. (-3)^2 = (-3)(-3) = 9. Additionally, a^3 • a^4 = a^7, and so

[tex] {( - 5ab)}^{3} \times {( - 3 {a}^{2} {b}^{2} )}^{2} [/tex]

[tex] {( - 5)}^{3} {a}^{3} {b}^{3} \times ( { - 3)}^{2} {a}^{4} {b}^{4} [/tex]

[tex]( - 125 \times 9) {a}^{7} {b}^{7} = 1125 {a}^{7} {b}^{7} [/tex]

The second staff member receives ₦40,000.

In mathematics, a ratio is a comparison of two or more quantities of the same kind or unit. It is expressed as the quotient or fraction of one quantity to another. Ratios are used to compare and express the relationship between different quantities, such as distance, time, weight, or money.

To solve this problem, we need to first determine the total ratio of the ages of the three staff, which is 18 + 20 + 22 = 60.

Next, we need to calculate the share of each staff member by multiplying their age ratio with the total amount of money collected:

The first staff member's share = (18/60) x ₦120,000 = ₦36,000

The second staff member's share = (20/60) x ₦120,000 = ₦40,000

The third staff member's share = (22/60) x ₦120,000 = ₦44,000

Therefore, the second staff member receives ₦40,000.

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Answer:

We can start by calculating the total amount of money earned per week:

$12.50/hour x 25 hours/week = $312.50/week

To find out how many weeks it will take to earn $3,437.50, we can set up a proportion:

Total amount earned / Amount earned per week = Number of weeks

$3,437.50 / $312.50/week = 11 weeks

Therefore, it will take 11 weeks to earn $3,437.50 working 25 hours per week at a rate of $12.50 per hour.

Answer:

32m

Step-by-step explanation:

area= L×B

L= 10m ×2 =20m

B= 6m×2 =12m

Area= 20m + 12m = 32m

I'm confused what's being asked here...but if you're looking for someone to check it then:

The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.

And the correlation is positive

The linear function that represent the situation is as follows:

f(x) = 27x + 254

A function relates input and output values.

Julia has 254 dollars. Each week she saves an additional 27 dollars .

Therefore, the function that models the amount of money Julia has  after x week can be represented as follows:

The function is a linear function. A linear function can be represented in the form as follows:

y = mx + b

where

Therefore,

f(x) = 27x + 254

where

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The surface area of the trapezoid is calculated to be equal to 731 square feet

area of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel base. Also the trapezoid have four rectangle sides and two same trapezoid sides.

A = 10ft

B = 13ft

height = 7ft

area of two trapezoid side = 2[1/2 × (10 + 13) ft × 7 ft = 161 ft²

area of rectangle with length 15ft and width 8ft = 8 ft × 15 ft = 120 ft²

area of rectangle with length 15ft and width ft = 15 ft × 105 ft = 105 ft²

area of rectangle with length 15ft and width 13ft = 15 ft × 13 ft = 195 ft²

area of rectangle with length 15ft and width 10ft = 15 ft × 10 ft = 150 ft²

surface area of the trapezoid = 161 ft² + 120 ft² + 105 ft² + 195 ft² + 150 ft² = 731 ft².

Therefore, the surface area of the trapezoid is calculated to be equal to 731 square feet

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The number of planes of symmetry the prism has will be 2. Then the correct option is B.

A prism is made from four identical cubes.

Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.

The number of planes of symmetry the prism has will be given as,

The plane divides the shape T into two halves and the plane is perpendicular to the shape T.

The plane divides the shape T and the plane is parallel to the plane of the paper.

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The period for the following graph is 90 degrees. So correct option is C.

In mathematics, a period is a specific type of repetition in a function or a sequence. A period is the smallest positive value of a constant T for which a function or a sequence f(x + T) = f(x) for all x.

Periods are used to describe the behavior of functions and sequences that exhibit a repeating pattern. The length of the period determines the frequency of the pattern, and it is often used to describe the periodicity of functions in various applications, such as signal processing, harmonic analysis, and Fourier series.

For example, the sine function sin(x) is periodic with a period of 2π. This means that sin(x + 2π) = sin(x) for all x. Similarly, the cosine function cos(x) is also periodic with a period of 2π. Other common examples of periodic functions include the tangent function, cotangent function, and exponential function.

In addition to their applications in mathematics, periods also have practical applications in fields such as physics, engineering, and computer science, where they are used to model periodic phenomena such as waves and oscillations.

Overall, periods are an important concept in mathematics and are used to describe the repeating patterns that are found in many mathematical functions and sequences.

The period for the following graph is 90 degrees.

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The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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The interior angles measure 160° and the exterior measure 200°

The sum of the interior angles of a polygon of n sides is:

(n - 2)*180

here n = 18

(18 - 2)*180 = 2880

divide that by the number of sides

2880/18 = 160°

That is the measure of each interior angle, and the exteriors are such that the sum is 360, then:

a + 160 = 360

a = 360 - 160 = 200

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The statement "If the size of a sample is at least 30, then you can use a z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution." is true because  when the sample size is at least 30, the Central Limit Theorem applies and the sampling distribution of the sample mean can be approximated by a normal distribution.

If the size of a sample is at least 30, the Central Limit Theorem (CLT) applies, which states that the distribution of sample means is approximately normal, regardless of the underlying distribution of the population, as long as the sample size is sufficiently large.

When the sample size is at least 30, the sampling distribution of the sample mean can be approximated by a normal distribution, and z-scores can be used to calculate probabilities of sample means falling in a given interval.

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Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.

Toshi's prediction was that he would perform the card trick successfully 95% of the time. This means that out of 100 card tricks, he expects to perform the trick successfully in 95 of them. We can represent this mathematically by:

P(success) = 0.95

This is the probability of success for one card trick.

Toshi actually performed the card trick 30 times and was successful in 24 of them. We can represent this as:

P(actual success) = 24/30 = 0.8

This is the proportion of successful card tricks that Toshi actually performed.

To compare Toshi's prediction with his actual results, we can use probability theory. The probability of getting exactly x successes in n trials when the probability of success is p is given by the binomial distribution formula:

P(x) = (n choose x) * pˣ * [tex](1-p)^(n-x)[/tex]

In this case, we can use the formula to calculate the probability of getting exactly 24 successes in 30 trials if Toshi's prediction of 95% success rate is accurate. This is given by:

P(24 successes) = (30 choose 24) * 0.95²⁴ * 0.05⁶ ≈ 0.0045

This means that if Toshi's prediction is accurate, the probability of getting exactly 24 successes in 30 trials is very low (less than 0.5%).

Therefore, we can conclude that Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

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