Which choice names a chord of circle F?

FE

BA

A and F

FD

The ratio of the sides' lengths of a triangle with sides of 30-60-90 is:

short leg : long leg : hypotenuse = 1 : √3 : 2

Consequently, the triangle's short leg's measurement is 8.

A triangle is a 3-sided shape with 3 vertices. The angles of the triangle are formed by the connection of the 3 sides end to end at a single point. The triangle's three angles sums up to 180 degrees.

Triangles can be divided into three varieties based on the lengths of their sides, which are:

Scalene.

Isosceles.

Equilateral.

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Answer:

17 people surveyed own a cat.

Step-by-step explanation:

Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.

d = 4c

d + c + 15 = 100

4c + c + 15 = 100

5c + 15 = 100

5c = 85

c = 17

Check:

The number of dog owners is 4 * 17, or 68.

68 + 17 + 15 = 100

Answer:

The total length of the two straight parts is 80 m x 2 = 160 m.

So, the length of the curved part of the track is 400 m - 160 m = 240 m.

Let the radius of the curved part of the track be "r".

Since there are two curves, each of length "l", in the track, the total length of both curves is 2l.

The length of one curved part can be given by the formula:

l = 2πr, where π is pi (approximately equal to 3.14).

So, 2l = 2 x 2πr = 4πr.

Therefore, 4πr = 240 m.

Dividing both sides by 4π, we get:

r = 240 m / (4π) = 240 / (4 x 3.14) = 15 m.

Hence, the radius of the curved part of the track on both sides is 15 m.

B. East Meets West: Natives’ Perspectives is most likely a compare-and-contrast essay because it is directly comparing the perspectives of people from the East and West coasts. The other titles are more descriptive or subjective in nature, rather than focused on comparing and contrasting two different things.

Beth's rate of travel is 2.2 meters per second and Amy's line is steeper

From the question, we have the following parameters that can be used in our computation:

The table of values

See attachment for the graph

From the graph, we have

Beth's rate of travel = 2.2 meters per second

This is so because from the graph:

As x increases by 1. y increases by 2/2

Here, we have

Amy's rate of travel = 75/30 meters per second

Evaluate

Amy's rate of travel = 2.5 meters per second

The higher the rate, the steeper the line

This means that Amy's line is steeper

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The amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that :

Cost of speaker = $35

Cost per song = $195

Sales tax rate = 8.25%

Expression to obtain the amount of sales tax on entire purchase : 0.0825(35+ 195s)

Using distributive law to expand the expression :

0.0825(35+ 195s)

= 2.8875+16s

Hence, the amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s

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The probability of flipping a heads on the coin and rolling a 5 on the die is 1/12 if a coin is flipped and die is rolled once.

The sample space for the coin toss is  {H,T}, so there are two possible outcomes. The favorable one is  H.

The probability of flipping a heads on the coin is equal to 1/2.

Die has six faces, meaning six possible outcomes, but we’re only interested in one of those outcomes: that roll of a 5. That means that only 1 in 6 outcomes is desirable and we can write it as  1/6

The probability of rolling a 5 on the die is equal to 1/6.

Since a coin is flipped and die is rolled independently, the joint probability is a product of above probabilities.

Therefore, the probability of flipping a heads on the coin and rolling a 5 on the die equals

[tex]\frac{1}{2} \times \frac{1}{6}\\= \frac{1}{12}[/tex]

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Answer:

First, we need to find the area of Site A and Site B. The area of a rectangle is found by multiplying its length and width, so:

Site A: 60 m x 40 m = 2400 m^2

Site B: 45 m x 40 m = 1800 m^2

Next, we need to find the perimeter of each site, which is the distance around the edges of the rectangle. The perimeter is found by adding up the lengths of all four sides, so:

Site A: 2 x (60 m + 40 m) = 2 x 100 m = 200 m

Site B: 2 x (45 m + 40 m) = 2 x 85 m = 170 m

Finally, to find the total amount of rope needed, we add up the perimeters of both sites:

200 m + 170 m = 370 m

So, we need a total of 370 meters of rope to rope off both sites.

Answer:350

ITS NOT 370

Answer:

minimum is $14.40

maximum is $18

she can get 9 ice cream cups

Step-by-step explanation:

The surface area is changing at a rate of approximately 2.94 square meters per second when the volume is 36 cubic meters and the balloon is being inflated at 3 cubic meters per second.

Volume of a sphere in terms of its radius = V = (4/3)π[tex]r^3\\[/tex]     .......(1)

Differentiating on both sides,                       [tex]\frac{dV}{dt}[/tex] = 4π[tex]r^{2}[/tex][tex]\frac{dr}{dt}[/tex]      .......(2)      

r = radius of the sphere.

Spherical balloon is being inflated at a rate of 3 cubic meters per second.

[tex]\frac{dV}{dt}[/tex] = 3 [tex]m^3/sec[/tex]

Volume is 36 cubic meters.

V = 36 [tex]m^3[/tex]

From equation (1), [tex]r^3[/tex] = [tex]\frac{3V}{4\pi }[/tex]

                              [tex]r^3[/tex] = [tex]\frac{3*36}{4*\pi }[/tex]

                              [tex]r^3\\[/tex] = [tex]8.59^1^/^3[/tex]

                               r = 2.04 meters

Substituting this in equation (2),  [tex]\frac{dr}{dt}[/tex]  =   [tex]\frac{dV}{dt}[/tex] / 4π[tex]r^{2}[/tex]

                                                     [tex]\frac{dr}{dt}[/tex]  =   3/(4π[tex]2.04^{2}[/tex])

                                                     [tex]\frac{dr}{dt}[/tex]  =   0.05737 m/sec

Now, surface area of sphere = A = 4π[tex]r^{2}[/tex]

Differentiating on both sides,

Rate of change of surface area  [tex]\frac{dA}{dt}[/tex] = [tex]8\pi r\frac{dr}{dt}[/tex]

                                                       = 8* 3.14* 2.04* 0.05737

                                                       = 2.94 [tex]m^2/sec\\[/tex]

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Answer:

Step-by-step explanation:

In a density curve, the proportion of data is represented by the option B) area under the curve and correct classification of shapes of density curves is option E)

A density curve is a curve on a graph that represents the distribution of values in a dataset.

A density curve, also called a density function, is a graphical representation of the relative frequency distribution of a continuous random variable. The type of distribution most commonly represented by a density curve is the normal distribution, but any distribution of a continuous variable may be represented by a density curve.

Normal distribution curve is a bell shaped curve obtained for the distribution having maximum frequency near the central value of distribution and the frequency gradually tapering off symmetrically on both side.so, All → Symmetric → Bell → Normal

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The probability of getting two odd numbers or two even numbers is 50%, since there are an equal number of odd and even numbers.

There are 6 possible outcomes when rolling two dice:

(1,1), (1,2), (2,1), (2,2), (1,3), (3,1).

The probability of getting two odd numbers is

2/6, or 1/3.

The probability of getting two even numbers is also

2/6, or 1/3.

Therefore, the probability of getting either two odd numbers or two even numbers is 2/3.

The probability of getting two odd numbers or two even numbers is 50%. This is because there are an equal number of odd and even numbers, so each outcome is equally likely. This means that the probability of getting two odd numbers or two even numbers is the same as the probability of getting one odd number and one even number. In both cases, the probability is 50%, since each outcome is equally likely. Therefore, the probability of getting two odd numbers or two even numbers is 50% as there are an equal number of odd and even numbers. This is because all possible outcomes are equally likely, and there are an equal number of odd and even numbers, so the probability of getting either two odd numbers or two even numbers is the same.

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Answer:

Let's assume that the cost of each box of cookies is "x" dollars.

Based on the given information, Gail sold a total of 3 + 4 + 1 = 8 boxes of cookies this week, and Mr. Millbrook gave a $7 donation. Therefore, the total amount of money collected this week is:

8x + 7

Since we know that Gail sold 10 boxes of cookies last week and collected the same amount of money, we can set up an equation:

10x = 8x + 7

Solving for x, we get:

2x = 7

x = 3.50

Therefore, each box of Girl Scout cookies costs $3.50.

Step-by-step explanation:

The point that divides a segment into two congruent segments is called the midpoint. Therefore, the answer is B) midpoint.

In geometry, a midpoint is a point that divides a line segment into two equal parts. It is the point on the line segment that is equidistant from both endpoints. The midpoint is important in geometry as it can be used to construct other geometric figures, such as perpendicular bisectors, which are lines that pass through the midpoint of a line segment and are perpendicular to it. For example, if we have a line segment AB, the midpoint M is the point that is exactly halfway between A and B, such that AM = MB. This can be found by drawing a perpendicular bisector of AB, which is a line that passes through the midpoint M and is perpendicular to AB. The perpendicular bisector will intersect AB at the midpoint M. It is important to note that the midpoint is not a bisector, ray, or point on a line. A bisector is a line, segment, or ray that divides an object into two congruent parts, while a ray is a part of a line that extends infinitely in one direction. The midpoint is simply the point that divides a line segment into two equal parts, and it is denoted by a symbol, such as a small vertical line with a hat on top, or by labeling the midpoint as a letter, such as M in the example above

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The recipe requires two-thirds of a cup of milk, and Sam needs 1/3 cup of milk to make 5 banana pancakes.

What is the proportion?

A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.

The recipe for 20 banana pancakes requires 2/3 cup of milk.

To find out how much milk is needed for 5 pancakes, we can use proportion. We can set up a proportion that relates the amount of milk needed to the number of pancakes:

(milk needed) / 2/3 cup = 5 pancakes / 20 pancakes

Simplifying the right side of the equation, we get:

(milk needed) / 2/3 cup = 1/4

To solve for the milk needed, we can cross-multiply:

milk needed = (2/3 cup) * (1/4) = 1/3 cup

Therefore, Sam needs 1/3 cup of milk to make 5 banana pancakes.

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Step-by-step explanation:

h represents the number of hours

15 represents the initial price for bike rentals

0.75h represents that for every hour, the price of bike rentals increases by 0.75

Answer:

8a3

Step-by-step explanation:

volume of cube = Lcube

one side=length of cube

so

volume of cube= L3

=2a3

= 2A × 2A × 2A

If the similar sides and angles of two triangles are proportionate, then the triangles are similar.

We must assess if two triangles have the same shape but perhaps different sizes in order to determine their similarity. The triangles are similar if their corresponding sides are proportionate. The triangles are not comparable if they are not proportionate. We only need to determine whether two triangles' respective sides are proportionate if we are given two triangles and are aware that their corresponding angles are congruent.

In conclusion, in order to establish whether two triangles are comparable, we must look at both the proportionality of the respective sides and the congruency of the corresponding angles. The triangles are similar if both requirements are satisfied, and we can create a similarity assertion by using the matching triangle vertices.

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Answer:

The sum of all numbers between 1 and 100 that are divisible by 4 or 7 can be found by using the concept of multiples. First, let's find all the multiples of 4 between 1 and 100. These are 4, 8, 12, 16, ..., 96. To find the number of multiples of 4 between 1 and 100, we can divide 100 by 4 and round down to the nearest whole number. That gives us 25. So, we have 25 multiples of 4 between 1 and 100.

Next, let's find all the multiples of 7 between 1 and 100. These are 7, 14, 21, 28, ..., 98. To find the number of multiples of 7 between 1 and 100, we can divide 100 by 7 and round down to the nearest whole number. That gives us 14. So, we have 14 multiples of 7 between 1 and 100.

Now we need to add up all the multiples of 4 and 7, but we have to make sure not to count any number twice, since some numbers may be divisible by both 4 and 7. For example, 28 is divisible by both 4 and 7. To avoid double counting, we need to find the multiples of 4 * 7 = 28. These are 28, 56, 84. There are 3 multiples of 28 between 1 and 100. So, we subtract these 3 numbers from the sum of all multiples of 4 and 7.

Finally, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is:

(4 + 8 + 12 + ... + 96) + (7 + 14 + 21 + ... + 98) - (28 + 56 + 84)

= (4 * 25) + (7 * 14) - (28 * 3)

= 100 + 98 - 84

= 114

So, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is 114.

To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.

The down payment refers to the initial cash payment for the purchase of an item on mortgage.

The down payment is required by the financier to evaluate the buyer's financial readiness.

The cost of the new home = $300,000

Down payment = 20% or $60,000 ($300,000 x 20%)

Mortgage loan required = $240,000 ($300,000 - $60,000)

Bank quoted interest rate = 4.75%

Desired interest rate = 4.5%

Difference in interest rate = 0.25% (4.75% - 4.5%)

Rate of buy down of the quoted interest per point = 0.125%

The number of points to buy down the interest rate = 2 (0.25/0.125)

The cost of each point = 1% of $240,000 = $2,400

The total cost of 2 points = $4,800 ($2,400 x 2)

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The volume of a cylinder can be calculated as π * radius^2 * height. In this case, the radius is 0.5 ft and the height is 25 ft, so the volume is:

π * 0.5^2 * 25 = 19.63 cubic feet

So the cost of the utility pole would be 19.63 * $25.81 = $509.24

Rounding to the nearest cent, the cost of the utility pole would be $509.24, which can be rounded to $509.00.

Answer:

A semicircle can be drawn by first drawing a diameter of a circle, which is a line segment connecting two points on the circumference that passes through the center of the circle. Then, the semicircle can be constructed by drawing an arc that is half of the circumference of the circle and connecting the ends of the arc to the endpoints of the diameter.

A quarter circle can be drawn in a similar way, but instead of drawing an arc that is half of the circumference, you would draw an arc that is a quarter of the circumference. To do this, you would need to find the central angle that subtends the arc and divide it by 4. The quarter circle can then be constructed by drawing an arc with this central angle and connecting the ends of the arc to the endpoints of a radius of the circle, rather than the diameter.

In both cases, you can use a compass or a protractor to accurately draw the arcs.

The most precise of the measures given 44mm. Hence option B is the correct answer.

The closeness of measured values is referred to as precision. We require the lowest scale attainable to measure in order to measure a value accurately.

Different scales of measures are presented to us. Any of these scales can be used to calculate the distance between two places. But we need to utilize the lowest scale in order to acquire an exact measurement. The millimetre (mm) is the lowest used scale in the options, making the measurement

Thus for the given options the smallest and the precise measure is obtained at 44mm.

Hence option B is the correct answer.

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To prove QR ~ SR, Use SAS to show triangle PRQ is congruent to

triangle PRS.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given,  PR bisects ZQPS, PQ = 12 units, and PS = 12 units

Now, The two triangles formed PQR and PSR share the same side PR.

Also m∠SPR = m∠QPR, Therefore these two triangles are congruent, and hence QR ~ SR

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The average rate of change over the interval [3,4] is given as follows:

3.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The numeric values for the ends of the interval are given as follows:

Then the change in the output is of:

32 - 29 = 3.

The change in the input is of:

4 - 3 = 1.

Hence the rate is of:

r = 3/1

r = 3.

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Answer:

2.0333

Step-by-step explanation:

log 108

Express 108 in terms of 2 & 3.

108 = 2 * 2 * 3 * 3 * 3 = 2² * 3³

log 108 = log 2² * 3³ = log 2² + log 3³ [Using Product Law]

= 2log 2 + 3log 3 [Using Power Law]

Now put the values of log 2 & log 3:

2log 2 + 3log 3

= 2*0.3010 + 3*0.4771

= 0.6020 + 1.4313

= 2.0333