Angle C is inscribed in circle O.
AB is a diameter of circle O.
What is the measure of A?

The frequency distribution of lottery winners of age between 19 and 40 is 7, and 3.32% of lottery winners are 70 years or older.

To find the frequency of lottery winners of age between 19 and 40, we need to add the frequencies of the age groups [20,29] and [30,39].

Frequency of lottery winners between 20 and 29 years old = 2

Frequency of lottery winners between 30 and 39 years old = 5

Frequency of lottery winners between 19 and 40 years old = 2 + 5 = 7

Therefore, the frequency of lottery winners of age between 19 and 40 is 7.

To find the percentage of lottery winners who are 70 years or older, we can use the cumulative relative frequency. We know that the cumulative relative frequency for the age group [70,79] is 0.9668, which means that 96.68% of the lottery winners are 70 years old or younger. Therefore, the percentage of lottery winners who are 70 years or older is:

100% - 96.68% = 3.32%

So, 3.32% of lottery winners are 70 years or older.

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Answer:

Adults = 300

Step-by-step explanation:

The correct Numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:

9 x 4 + (3 − 2)

To solve this expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Evaluate the subtraction inside the parentheses:

3 − 2 = 1

Step 2: Rewrite the expression with the simplified value:

9 x 4 + 1

Step 3: Perform the multiplication:

9 x 4 = 36

Step 4: Add the products:

36 + 1 = 37

Therefore, the correct numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

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The remote interior angles of ∠1 are ∠2 and ∠6.

Corresponding angles in a triangle are those angles which are contained by a congruent pair of sides of two similar (or congruent) triangles.

The remote interior angles of ∠1 is determined by applying the principle of corresponding angles as shown below;

∠1 = ∠2 ( vertical opposite angles are equal )

∠1 = 180 - ∠5 ( corresponding angles  are equal )

180 - ∠5  = ∠ 6 ( vertical opposite angles are equal )

So we can conclude that, ∠1 = ∠6.

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Answer:

Whole numbers, and rational numbers

Step-by-step explanation:

Answer:

C. ⅓ × (8 + 7) + 12

Step-by-step explanation:

Let's translate each statement given to numerals and symbols first:

Twelve => 12

One-third => ⅓

Sum of 8 and 7 => (8 + 7)

Representing this statement altogether will be:

⅓ of (8 + 7) = ⅓ × (8 + 7)

If 13 is added, we would get:

⅓ × (8 + 7) + 12

Answer:

Option C, 3x = 30

Step-by-step explanation:

Cuz both angles are vertical angels and therefore congruent to each other.

Hope this helps!

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

The preferred measure of central tendency for the following data is Mode.

Given,

Number of males = 57

Number of females = 23

The preferred measure of central tendency for the given data is Mode.

Mode

The mode is the number in a set of numbers that appears the most often. The mean of a set of numbers is the sum of all the numbers divided by the number of values in the set.

To find the mode manually, arrange the numbers in ascending or descending order, then count how often each number appears. The number that appears most often is the mode. It's now easy to see which numbers appear most often

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Answer:

Please read the explanation!

Step-by-step explanation:

Hi! I will try to do my very best with helping you. Because there is not an example that goes along with this question, I will give my own.

Lets say we have triangle ABC in quadrant II. The Points are:

A: (-5,1)

B: (-3,5)

C: (-1,1)

If we plot that than we have a triangle. And when we reflect anything, not just a triangle, we would need to basically flip it over and mirror the image. The triangle will move, but it is the same triangle as it was before. All that has happened is that is was married to the otherside.

If you are a bit confused think of when you are in front of a mirror.

So let's reflect it over the y-axis.

When in doing so, you need to make sure that the x in (x, y) is changed into a positive number. We need to make sure that we know that quadrant I has positive x-axis.

So,

A becomes (5,1)

B becomes (3,5)

C becomes (1,1)

And if you plot that it should be flipped or reflected like a mirror image.

I really hope this helped!

Answer:

73in to the nearest inch

Step-by-step explanation:

r=d/2

r=25.3/2

r=11.6cm

C=2πr

C=πd

C=22/7×25.3

C=72.51

C=73 to the nearest inch

The answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

A combination of numbers, variables, and operators that represents a quantity or mathematical relationship is called an expression.

First, divide sextillion (10²¹) by nonmillion (10⁶) to get 10¹⁵.

Next, multiply 10¹⁵ by 10,000 to get 10¹⁹.

Subtract 200 million (2 x 10⁸) from 10¹⁹ to get 9.9998 x 10¹⁸.

Finally, add 5,000 to get the result of approximately 9.9998 x 10¹⁸ + 5,000 = 9.9998 x 10¹⁸ + 0.0005 x 10¹⁸ = 9.9998 x 10¹⁸.

Therefore, the answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

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Answer:

37

Step-by-step explanation:

the equation is /a^2 + b^2 =c

so 12^2=144 and 35^2=1225

144+1225=1413

the square root of 1413 is equal to 37

The smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

To compute this, first convert 5 to binary and base-4:

5 in binary: 101

5 in base-4: 11

Since 11 is the same in both bases, the next number that would be a palindrome in both bases is 11.

To find the base 10 number of this palindrome, we convert 11 from binary and base-4 to base 10:

11 in binary: 1011

11 in base-4: 111

Therefore, the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-11}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-3)}}}\implies \cfrac{-16}{5+3}\implies \cfrac{-16}{8}\implies -2\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-2}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-5-2(x+3)\implies y-5=-2x-6\implies y=-2x-1\)

To solve for x at an angle, you must first understand what type of angle you are working with. If the angle is a right angle, you can use the Pythagorean theorem to solve for x. If the angle is an obtuse angle, you can use the law of cosines to solve for x. If the angle is an acute angle, you can use the law of sines to solve for x.

To solve for x at a right angle using the Pythagorean theorem, you must have the lengths of the two neighboring sides of the triangle. The sum of the squares of the two sides is equal to the square of the hypotenuse, according to the Pythagorean theorem. By rearranging the components and solving for x, this equation may be used to find x.

To use the law of cosines to solve for x at an obtuse angle, you must know the lengths of all three sides of the triangle. According to the law of cosines, the square of one side's length equals the sum of the squares of the other 2 sides minus twice the product of the other 2 sides multiplied by the cosine of the obtuse angle. You can use this equation to solve for x by rearranging the terms and solving for x.

To apply the law of sines to solve for x in an acute angle, you should first know the lengths of the triangle's two sides as well as the acute angle's measurement. According to the law of sines, the ratio of one side's length to the sine of the opposite angle equals the ratio of the other side's length to the sine of the acute angle. By rearranging the terms and solving for x, you may use this equation to solve for x.

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Answer:

Step-by-step explanation:

"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.

The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,

we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)

= 13.8 ± (1.96 × 1.088)

= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13

= 15.9313.8 - 2.13

= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].

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Answer:

Step-by-step explanation:

find the area of ​​the big rectangle and add the double area of ​​a triangle, they are the same so it is as if you have the area of ​​both

[(4+4+4)*5] + (4*3.5)=

8 * 5 + 14 =

40 + 14 =

51m²

The total number of students in the seminar is 258, with 98 boys and 160 girls given a ratio of 8:5 between boys and girls.

We can begin by using the given ratio of boys to girls, which is 8:5, and the information that there are 160 girls to find the number of boys in the seminar.

If the ratio of boys to girls is 8:5, then we can say that for every 8+5=13 students, there are 8 boys and 5 girls.

To find the number of boys, we can set up a proportion

8/13 = x/160

where x is the number of boys.

Simplifying this proportion, we get

x = 8/13 × 160

x = 98.46

Therefore, the number of boys in the seminar is approximately 98.

To find the total number of students in the seminar, we can add the number of boys and girls

Total number of students = Number of boys + Number of girls

Total number of students = 98 + 160

Total number of students = 258

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Answer:

only the circle graph

Step-by-step explanation:

Answer:

Only the graph

Step-by-step explanation:

Im not an expert or anything but the chart only shows numbers, which aren't useful, but the circle shows, under the 80-89, 44.4%, which is the useful one. hope that helps you

Answer:

D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)

Step-by-step explanation:

hope this helps

Answer:  D has the largest perimeter

Step-by-step explanation:

The top numbers of fractions describe the vertex and  the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.

A.

P = 2(11) + 2(3)

P = 22+6

P=28

B.

P = 2(4) + 2(9)

p = 8 +18

P = 26

C.

P = 2(5) + 2(9)

P = 10 +18

P = 28

D.

P =  2(8) + 2(7)

P = 16 +14

P = 30

Both Mathew and James are exerting the same amount of force, which is 400 newtons.

Force is a measure of the interaction between two objects and is expressed in newtons (N). In this case, both Mathew and James are exerting a force of 400 newtons. The weight of the sled and the tree stump, both weighing 200 lbs, does not affect the force exerted by Mathew and James.

The weight of an object is the force exerted on it due to gravity. In this context, the weight of the sled and the tree stump is the same, 200 lbs. However, when comparing forces, we consider the amount of force applied by an individual, which is independent of the weight of the object being pushed or lifted.

Therefore, Mathew and James are exerting the same amount of force, which is 400 newtons.

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Answer:

-1 = 4

0 = -2

1 = -8

5 = -32

Step-by-step explanation:

trust

Answer:

(a) \(x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}\)

(b) \(x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}\)

Step-by-step explanation:

It is given that \(0\leq x\leq 2\pi\).

(a)

\(\sqrt{2}\sin 2x=1\)

\(\sin 2x=\dfrac{1}{\sqrt{2}}\)

\(\sin 2x=\dfrac{\pi}{4}\)

\(2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}\)     \([\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]\)

\(x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}\)

(b)

\(\csc^2 x-\csc x-2=0\)

\(\csc^2 x-2\csc x+\csc x-2=0\)

\(\csc x(\csc x-2)+1(\csc x-2)=0\)

\((\csc x+1)(\csc x-2)=0\)

\(\csc x=-1\text{ or }\csc x=2\)

\(\sin x=-1\text{ or }\sin x=\dfrac{1}{2}\)         \([\because \sin x=\dfrac{1}{\csc x}]\)

\(x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}\)

Therefore, \(x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}\).

Answer: (0,.5)

x is 0 because it is the value where point F and line D are the closest. And y = .5 because both 3 and -2 are 2.5 units away from (0,.5).

Answer:

\(P(B|A)=0.565\)

Step-by-step explanation:

Call A to the event that represents a red light at the first traffic light

Then, call B the event that represents a red light at the second traffic light.

Then we know that:

P(A∩B) = 0.35

P(A) = 0.62

Then the probability that the second light is red because the first one is red is:

\(P(B|A)=\dfrac{P(A \ and \ B)}{P(A)}\)

Then:

\(P(B|A)=\dfrac{0.35}{0.62}\)

\(P(B|A)=0.565\)

There is a 56.5% chance that the second light is in red

Answer:

u = 10ft

Step-by-step explanation:

7ft x 8ft = 56. 560 ÷ 56 = 10.
Therefore, u = 10ft