A high school track is shaped as a rectangle with a half circle on either side. A rectangle has a length of 96 meters and width of 35 meters. 2 semicircles with diameters of 35 meters are on each end of the rectangle. Jake plans on running four laps. How many meters will Jake run? Use 3.14 for Pi. 301.9 m 823.6 m 1,207.6 m 1,647.2 m

Answer:

if the parabola is positive it would be facing up

Step-by-step explanation:

Answer:

pointed upward

Step-by-step explanation:

The coefficient of the quadratic term, a, determines how wide or narrow the graphs are, and whether the graph turns upward or downward. A positive quadratic coefficient causes the ends of the parabola to point upward.

Answer:

-19/248

Step-by-step explanation:

Answer:

If you still need the answer I think it's B

Step-by-step explanation:

The total surface area of the solid is 1466.4 square millimeters.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The rectangular prism has a total surface area of:

2lw + 2lh + 2wh

= 2(16)(11) + 2(16)(10) + 2(11)(10)

= 352 + 320 + 220

= 892 square millimeters.

The triangular prism has a total surface area of:

2B + Ph

= 2(0.5bh) + (perimeter of base)h

= 2(0.5(11)(8)) + (11 + 8 + sqrt(11² + 8²))(16)

= 88 + 478.4

= 566.4 square millimeters.

Therefore,

The total surface area of the solid is:

892 + 566.4

= 1458.4 square millimeters,

which rounded to one decimal place is 1466.4 square millimeters.

Thus,

The total surface area of the solid is 1466.4 square millimeters.

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Answer:

D. 75x+160<760

Step-by-step explanation:

The reason is 75 has to be a variable because it changes with time. The fee is a fixed rate that will not change no matter the time. All of these values must be less than 760 meaning the variable and constant must be less than (<) 760

y = 5x

and x = y/5

you can then put any value for x and y and it will make sense

Answer:

11.31 mph

Step-by-step explanation:

60' = 1°

48'=x°

X = 48/60

X = 0.8°

Hence 70°48' = 70.8°

θ = 90°-70.8°

θ = 19.2°

Sin 19.2 = bc/34.4

Bc = sin 19.2 × 34.4

Bc = 0.32866×34.4

BC = 11.31 mph

By using the combination formula to calculate the number of unique ways a group can be formed, we find that a coach can divide her 9-player squad into three equal groups in 5600 ways.

The student's question is about a concept in mathematics called combinations. A combination is a selection of items without regard to the order in which they are selected. In this particular problem, the tennis coach is dividing her 9-player squad into three equal groups. The number of ways this can be done uses the formula for combinations (nCr) where n equals the total number of items (in this case, players) and r equals the number of items being chosen at a time (in this case, the number of players in each group).

First, the coach can choose the first trio from the nine players using the combination formula 9C3. The second trio is chosen from the remaining 6 players, so this uses the formula 6C3, and for the third trio, which is chosen from the remaining 3 players, the formula is 3C3. Multiplied out, 9C3 x 6C3 x 3C3 equals 280 x 20 x 1 which is 5600. Therefore, there are 5600 unique ways the coach can divide her 9-player squad into three 3-player groups with each player in only one group.

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Answer:

42 cents per peach and 68 cents per apple

Answer:

-1,048,572

Step-by-step explanation:

Please mark brainliest :)

The teacher can choose four students to present the project out of seven in 35 different ways. This is calculated using the combination formula in combinatorics, a concept in mathematics.

The question involves the concept of combinatorics in mathematics, specifically the combination formula. The combination formula is used when the order of selection does not matter. In this case, the teacher is selecting 4 students out of 7 to present the project, and the order in which the students are chosen is irrelevant.

To calculate the number of ways the teacher can choose four students out of seven, we use the combination formula which is C(n, r) = n! / [(n-r)!r!], where:

Applying this to our scenario, n = 7 (total number of students), and r = 4 (students to be chosen to present). Plugging the values into the formula gives us C(7, 4) = 7! / [(7-4)!4!] = 35. So, there are 35 ways the teacher can choose four students to present the project.

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The teacher can choose 4 students to present the project in 35 ways.

The teacher needs to choose 4 students out of a group of 7 to present the project.

To find the number of ways to choose 4 students from a group of 7, we use the combination formula.

The formula for combinations is C(n, r) = n! / (r! * (n-r)!), where

n is the total number of students and

r is the number of students to be chosen.

Substituting n = 7 and r = 4 into the formula, we get

C(7, 4) = 7! / (4! * (7-4)!) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1 * 3 * 2 * 1) = 35.

Therefore, there are 35 ways for the teacher to choose 4 students to present the project.

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Final answer:

To find the value of x for the given sequence, we must ensure the median remains 14. Since the median is the average of the third and fourth numbers in an ordered list of six numbers, x must be 16 because 9, 10, 12, 16, 20, 25 gives us a median of 14 (12 + 16 = 28; 28 / 2 = 14).

Explanation:

The student is asking to find the value of x in a sequence of numbers given that the median is 14. First, we place all the numbers in order: 9, 10, 12, x, 20, 25. Since there are six numbers, the median will be the average of the third and fourth numbers.

To have a median of 14, the sum of the third and fourth numbers must be 28 (since 14 = (third number + fourth number) / 2). Therefore, if the third number is 12, x must be 16 because 12 + 16 = 28.

The value of x that makes the median of the set equal to 14 is 16.

Answer:

A and D I did it on edge:

There are 720 different ways for 7 students to sit at a circular table for a debate, calculated using permutation principles by fixing one seat and arranging the remaining six students (6!).

The question asks about the number of different ways 7 students can sit at a circular table for a debate, which involves a mathematical concept called permutations. Since a circular arrangement means that the starting point is not fixed, we have to consider one position as fixed to avoid repeating identical seating arrangements caused by rotation. Therefore, with one student fixed, we have 6 seats left to arrange the remaining 6 students. This scenario is a permutation problem without repetition and can be calculated using the factorial operation (6!).

So, the calculation would be:

Therefore, there are 720 different ways the 7 students can sit at the table for the debate.

Answer:

500 cm²  

Step-by-step explanation:

You haven't presented any diagrams, so I assume the prism has the dimensions shown below.

Then the dimensions of the original piece of cardboard are as in the second figure.

The area of the cardboard is the same as the lateral area of the triangular prism.

The formula for the area of a rectangle is  

A = lw

 l = 9 cm + 9 cm + 7 cm = 25 cm

w = 20 cm

A = 25 cm × 20 cm = 500 cm²

The area of the piece of cardboard is 500 cm².

Answer:

6/81

there are 9 marbles and 3 are green so 3/9 and 2 are red so2/9 then times to get 6/81

Answer:

C is the answer

Step-by-step explanation:

If you graph them on a line the outcome will be a straight line making it functional and a proportion

The required set of ordered pairs are (0, 1), (1, 3), (2, 9), (3, 27). The correct option is (D).

An exponential function can be represented as y = aˣ. When x = 0, y = a⁰ = 1. The range of an exponential function is from zero to infinity for a > 0.

It is clear from the given options that, only options (B) and (D) satisfies the general expression y = aˣ at x = 0.

Now, both these options can be examined one by one as follows,

Option (B),

The ordered pairs are given as (0, 1), (1, 2), (2, 5), (3, 10).

Substitute the values in the general expression y = aˣ, first two pair are satisfied for a = 2 but the remaining two are not.

Option (D),

The ordered pairs are given as (0, 1), (1, 3), (2, 9), (3, 27).

Substitute the values in the general expression y = aˣ, all the pairs are satisfied for a = 3.

Thus, the correct option is found.

Hence, the set of ordered pairs which could be generated by an exponential function are (0, 1), (1, 3), (2, 9), (3, 27).

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Answer:

C

Step-by-step explanation:

16 times 2 equals 32, 52 minus 32 equals 20.

Answer:

80 degrees

Step-by-step explanation:

Congruent triangles have congruent corresponding sides and angles

The true statement is (c) yes, because of ASA or AAS

Start by adding the angles of the triangles

[tex]\mathbf{\theta = 98 + 35 + 47}[/tex]

[tex]\mathbf{\theta = 180}[/tex]

The angles add up to 180 degrees,

This means that, the triangles have congruent corresponding angles and a congruent corresponding side

Hence, the triangles are congruent by AAS or ASA.

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Answer:

Yes, because of ASA or ASA

Step-by-step explanation:

Tooken note so their right trust me

Answer:

D 64

Step-by-step explanation:

f(x) = 4^x

Let x = 3.

f(3) = 4^3

    = 4*4*4

   = 64

Answer:

Option A. 2

Step-by-step explanation:

From the question given, we were told that the total outcome in event A is 5.

Now if region 2 is 6, 7 or 8, as given in the other options, it therefore means that the total out in event A will be more than 5. So region 2 must be 2 in order to satisfy the event A.

Further more, considering the diagram, event B is bigger than event A. With this idea we can give the summary in diagram as follow:

Region 1 => 3 outcomes

Region 2 => 2 outcomes

Region 3 => 4 outcomes

Region 4 => 6 outcomes

Total => 15 outcomes

Now we can see that the total outcome correspond to the total outcome of 15 given in the question.

Therefore, region 2 has 2 outcome

Given the information, we can determine that B has 4 outcomes, but the number of outcomes specifically in region 2 cannot be found without additional information.

Let's break down the given information one piece at a time. The sample space (S) consists of 15 equally likely outcomes. Out of these, we know that 5 outcomes are in region A, and 6 outcomes neither belong to event A nor to event B.

Since events A and B are independent, they do not share outcomes. Now, we can calculate the number of outcomes in event B by subtracting the outcomes not belonging in A or B and belonging in A from the total outcomes. Hence, there are 15 - 5 - 6 = 4 outcomes in event B.

However, the question requires us to find outcomes in the second region (2). Since the regions were not specified concerning events A and B, we cannot identify the precise number of outcomes in region 2. Therefore, we cannot accurately answer the question with the given information.

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Step-by-step explanation:

- 4x2 - 80x - 400

- 4x2 - 40x - 40x - 400

-4x( x + 10) - 40(x + 10)

(x + 10) and ( - 4x - 40) are the factors

Answer:

Shannon's expression:

[tex]\frac{4.2 \times 10^{9} }{1.4 \times 10^{4} }[/tex]

Kristoph's expression:

[tex]\frac{4.2 \times 10^{2} }{1.4 \times 10^{-3} }[/tex]

Notice that both expression has the same coefficient numbers: 4.2 and 1.4. That means to have the same results, we just need to have the same powers.

Without dividing the complete expression, you can observe that both powers are the same, because each you subtract 9-4 = 5, and 2-(-3) = 5, both gives the same exponent to the power of 10.

Therefore, both expression give the same result, because they have the same numbers and the same powers.

Let's solve the division to have the result in scientific notation.

Shannon's expression:

[tex]\frac{4.2 \times 10^{9} }{1.4 \times 10^{4} }=3 \times 10^{9-4}=3 \times 10^{5}[/tex]

Kristoph's expression:

[tex]\frac{4.2 \times 10^{2} }{1.4 \times 10^{-3} }=3 \times 10^{2-(-3)}=3 \times 10^{5}[/tex]

The standard form refers to each number written without the power. To do so, we need to move the decimal points the number of spots as the exponent demands. Notice that the exponent is 5, that means, we need to move the decimal point 5 spots to the right.

[tex]3 \times 10^{5}=300000[/tex]

Therefore, the standard value of the expressions is 300,000.

The quotient is close to 4

A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.

Given that, two mixed fractions, [tex]8\frac{1}{6}[/tex]  and [tex]1\frac{7}{8}[/tex]

Converting the mixed numbers to improper fraction: we get,

49/6 and 15/8

Divide: 49/6 : 15/8

= 49/6 · 8/15

= 49 · 8/6 · 15

= 392/90

= 2 · 196/2 · 45

= 196/45

= [tex]4\frac{16}{45}[/tex]

Hence, The quotient is close to 4

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Answer:

49.13 in

Step-by-step explanation:

circle circumference: 25.13

rectangle perimeter: 24

total: 49.13

The perimeter of the figure to the nearest hundredth. is 28.56 in.

To find the find the perimeter of the figure we'll add the sides of square and the circumference.

Perimeter of figure = 2 × Perimeter of semicircle + 2 × side of square + 2 × side length after excluding semicircle

Radius of semicircle = 4/2 = 2 in.

Perimeter of semicircle

= π r

= 3.14 × 2

= 6.28 in.

Side of square = 6 in.

Side length after excluding semicircle = 6 - 4 = 2 in.

Perimeter of figure

= 2 × Perimeter of semicircle + 2 × side of square + 2 × side length after excluding semicircle

= 2 × 6.28 + 2 × 6 + 2 × 2

= 12.56 + 12 + 4

= 28.56 in.

Answer:

40 cm

Step-by-step explanation:

a square has 4 equal length sides, to get area you multiply two of those sides, 10 x 10 = 100, so each side is 10cm long, adding all of the sides together gets you 40cm.

Answer:

40cm

Step-by-step explanation:

We know that the formula for area of a square is side length squared or [tex]s^2[/tex]

In this case, [tex]s^2=100[/tex]. So we can go through the following steps in order to solve for s

[tex]s^2=100\\\sqrt{s^2} =\sqrt{100} \\\\s=10[/tex]

If one side equals 10, and we know all squares have 4 equal sides, then we can multiple 10 * 4 or add 10+ 10 + 10 + 10.

Our outcome is 40!

Answer:

We divided the figure into 1 triangle and 3 rectangles (as shown in attached pic).

Adding up the area of them, we get the total area:

A = area of triangle + area of 3 rectangles

   =  base x height/2 + length1 x width1 + length2 x width2 + length3 x width3

   = 6 x (2 + 11 + 5 - 4 -3)/2 + 2 x 2 + 11  x (5 + 2) + 5 x 9

   = 159 (m2)

Hope this helps!

:)

Step 1) Split the figure into separate shapes

Triangle: 6 x 11

Small square: 2 x 2

Large rectangle (center): 16 x 7

Medium rectangle (bottom): 2 x 5

Step 2) Find the area of each shape

Triangle: A = 6 x 11 x 1/2 = 33

Small square: A = 2 x 2 = 4

Large rectangle (center): A = 16 x 7 = 112

Medium rectangle (bottom): A = 2 x 5 = 10

Step 3) Add the areas together

A = 33 + 4 + 112 + 10 = 159 square meters

Hope this helps! :)

Answer:

358,000,000 BTU's.

Step-by-step explanation:

Given that the radius is equal to 5 ft. and we need to find the volume of sphere~we can use the following formula. Additionally, we will use 3.14159 to be more accurate in this case...

[tex]V =\frac{4}{3} \pi r^3\\V=\frac{4}{3} (3.14159)5^3\\V=4.18878667(125)\\V=523.6[/tex]

So the volume is 523.6 cubic ft!

To convert this to gallons...

[tex]\\1 ft^3 = 7.48052 gal\\523.6 ft^3 = 3916.8 gallons[/tex]

The final step is to multiply this amount by the original 91,500 BTU, when we do this we get...

[tex]3916.8*91500=358387200[/tex]

The nearest million from this number is 358,000,000!

Final answer:

To determine the number of BTUs a spherical storage tank provides, find the tank's volume in gallons by converting from cubic feet, then multiply by 91,500 BTU per gallon and round to the nearest million BTUs.

Explanation:

To calculate the number of BTUs a spherical storage tank can provide, given in gallons, we first need to know the tank volume in cubic feet. Let's assume the student provides this volume. Since 1 cubic foot is equivalent to approximately 7.48 gallons of liquid, we divide the volume in cubic feet by 7.48 to find the number of gallons of propane the tank can hold. Each gallon of propane yields approximately 91,500 BTU.

To find the total BTUs, we use the following steps:

Calculate the number of gallons in the tank by multiplying the volume in cubic feet by 7.48.

Multiply the number of gallons by 91,500 BTU per gallon to get the total BTUs in the tank.

Round the result to the nearest million BTUs, as the question asks.

For example, if a spherical storage tank has a volume of 100 cubic feet, the number of gallons it can hold would be 100 cubic feet * 7.48 gallons/cubic foot = 748 gallons. Then, the total BTUs would be 748 gallons * 91,500 BTU/gallon = approximately 68,442,000 BTU, which would then be rounded to 68 million BTUs.

Answer:

100; 14400

Step-by-step explanation:

Volume = base * height

a) Base = 4 * 2.5/2 = 5

Height = 20

That makes volume  = 5 * 20 = 100

b) Base = 36 * 16/2 = 288

Height = 50

That makes the volume = 288 * 50 = 14400

Answer:

100, 14400

Step-by-step explanation:

Answer:

The answer is GF  

Step-by-step explanation:

Because Your question did not mention GF and it asked for which line it didn't  

mention.