A rectangle has a diagonal of 100 feet as shown in the picture below Which of the following lengths could be the base and height of the rectangle?
A. Base = 80 feet; Height = 60 feet
B. Base = 8 feet; Height = 6 feet
C. Base = 50 feet; Height = 50 feet
D. Base = 75 feet; Height = 25 feet

Answer:

176 children and 105 adults.

Explanation:

Let's call x the number of children and y the number of adults.

If 281 people entered the park, we can write the following equation

x + y = 281

If they collected 684 dollars, we can write the following equation

1.5x + 4y = 684

because it cost $1.5 for children and $4 for adults.

Now, we have the following system of equations

x + y = 281

1.5x + 4y = 684

First, we need to solve the first equation for y, so

x + y = 281

x + y - x = 281 - x

y = 281 - x

Then, replace this expression on the second equation

1.5x + 4y = 684

1.5x + 4(281 - x) = 684

1.5x + 4(281) - 4(x) = 684

1.5x + 1124 - 4x = 684

-2.5x + 1124 = 684

Finally, we can solve the equation for x

-2.5x + 1124 - 1124 = 684 - 1124

-2.5x = -440

-2.5x/(-2.5) = -440/(-2.5)

x = 176

So, the value of y is equal to

y = 281 - x

y = 281 - 176

y = 105

Therefore, they admitted 176 children and 105 adults.

To prove that triangle FGE and triangle IJH we need information like the two sides of each triangle and the included angle to be congruent.

To prove two triangles are similar by the SAS is that you need to show that two sides of one triangle are proportional to two corresponding sides of another triangles, with the included corresponding angles being congruent.

For the SAS postulate you need two sides and the included angle in both triangles.

Side-Angle-Side (SAS) postulate:-

If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS postulate relate two triangles and says that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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Answer:

The correct answer is Yes, because there is enough water in the cooler for about 81 cups total which is C.

Step-by-step explanation:

The water available, (approximately 81 cups) is more than the number of cups required (76 cups). Therefore, option C is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a cylindrical cooler that has a radius of 6 inches and a height of 20 inches.

Here, volume of cylindrical cooler =πr²h

= 3.14×6²×20

= 3.14×36×20

= 2260.8 cubic inches

A cone has a dimensions diameter 4.4 inches and height 5.5 inches.

Here, volume of cup = 1/3 πr²h

= 1/3× 3.14×(4.4/2)²×5.5

= 28 cubic inches

So, number of cups = 2260.8/28

= 80.74

≈ 81

The number of cups required for each of the 38 player to have two full cups is, Cups = 38 × 2 = 76 cups

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

During practice, the Northwood football team drinks water from a cylindrical cooler that has a radius of 6 inches and a height of 20 inches. Players use conical paper cups, as shown below. A cone has a dimensions diameter 4.4 inches and height 5.5 inches.

If the water cooler is filled completely, can each of the 38 players have two full paper cups of water during practice? Explain 4.4 in.

A) No, because there is enough water in the cooler for about 3 cups total.

B) No, because there is enough water in the cooler for about 59 cups total 5.5 in.

C) Yes, because there is enough water in the cooler for about 81 cups total.

D) Yes, because there is enough water in the cooler for about 2,261 cups total.

Answer:

==========================================================

Reason:

For any triangle, the inside angles always add to 180 degrees.

(angle1)+(angle2)+(angle3) = 180

(6x+13)+(79)+(6x+4) = 180

(6x+6x)+(13+79+4) = 180

12x+96 = 180

12x = 180-96

12x = 84

x = 84/12

x = 7

Then use this to compute angle A.

A = 6x+13 = 6*7+13 = 42+13 = 55 degrees

If you wanted, you can compute the other angle as well

6x+4 = 6*7+4 = 42+4 = 46 degrees

Then as a check:

(angle1)+(angle2)+(angle3) = (55)+(79)+(46) = 180

which confirms the answer.

A perfect positive correlation means that every time factor A occurs, factor B also occurs.

In statistics, correlation refers to the relationship between two variables. A perfect positive correlation means that as one variable increases, the other variable also increases in a consistent and linear manner.

In the case of a perfect positive correlation, every time factor A occurs (increases), factor B also occurs (increases) simultaneously. The occurrence of factor B is directly and consistently related to the occurrence of factor A.

For example, let's consider the relationship between studying time and exam scores. If there is a perfect positive correlation between these two factors, it means that every time a student spends more time studying, their exam scores also increase in a predictable and proportional manner.

It's important to note that a perfect positive correlation does not necessarily imply causation. While the two variables are strongly associated, it does not indicate that one variable directly causes the other. Correlation simply describes the relationship between the variables.

In summary, a perfect positive correlation means that whenever factor A occurs, factor B also occurs, demonstrating a consistent and linear relationship between the two variables.

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Answer:

-3, -2.5, -3/4, 0.8, 2.5, 6 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 = 0.5

6 = 6

6 + 0.5 = 6.5

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

1/4 = 0.25

-1/4 = -0.25

-3/4 = -0.75

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

Hope this helps! <3

Answer:

3940 is the correct answer

Answer:

  a) 48 gigabytes

  b) 250 minutes, or 4 hours 10 minutes

Step-by-step explanation:

For D(t) = 75 -0.3t modeling the number of remaining gigabytes to download after t minutes, you want to find D(90) and t such that D(t) = 0.

  D(90) = 75 -0.3·90 = 48

After 90 minutes, 48 gigabytes are left to download.

The time required to complete the entire download is given by ...

  0 = 75 - 0.3t

  0 = 250 -t . . . . . divide by 0.3

  t = 250 . . . . . . add t

It will take 250 minutes, or 4 hours 10 minutes to download the entire game.

__

Additional comment

The attached calculator screen shows conversion to hours and minutes. Hours, minutes, seconds are computed "base-60" the same way that Degrees, minutes, seconds are computed "base-60". 250 minutes is converted to hours by dividing by 60 min/hour. We can use the →DMS function of the calculator to show decimal or fractional hours in hours : minutes : seconds. In this use of that function, degrees represents hours.

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A plane flies for 1.6 hours at 140 mph on a bearing of 30°, then turns and flies for 2.8 hours at the same speed on a bearing of 120°. We need to find the distance of the plane from its starting point.

To find the distance of the plane from its starting point, we can break down the problem into two components: the horizontal distance and the vertical distance.

In the first leg of the flight, the plane flies for 1.6 hours at 140 mph on a bearing of 30°. This means the horizontal component of the distance is given by d₁ = 1.6 * 140 * cos(30°) and the vertical component is given by d₂ = 1.6 * 140 * sin(30°).

In the second leg of the flight, the plane flies for 2.8 hours at the same speed on a bearing of 120°. Again, we calculate the horizontal component as d₃ = 2.8 * 140 * cos(120°) and the vertical component as d₄ = 2.8 * 140 * sin(120°).

To find the total distance from the starting point, we add the horizontal components and the vertical components:

Total distance = sqrt((d₁ + d₃)² + (d₂ + d₄)²).

Evaluating this expression will give us the distance of the plane from its starting point.

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Answer:

B

Step-by-step explanation:

Complete the sentence for your layer. (1 point)

The troposphere is the region that starts at Earth's surface and ends between 0 km and 12 km

above Earth.

The upper crust is the region that starts at Earth's surface and ends between 0 km and 50 km

below Earth's surface.

Use the temperature equation to find the temperature range for your layer.

The temperature equation is not specified in the question. Please provide the temperature equation for me to solve this question.

What is the temperature at the end of your layer that is farthest from the surface? (1 point)

Without knowing the layer specified in the question, I cannot provide the temperature at the end of the layer that is farthest from the surface.

For the layer you selected, the temperature ranges from the temperature at Earth's surface to

the temperature at the end of the layer that is farthest from the surface.

If the cost for 10 ounce of organic blueberry is $2. 70, the cost of 30 ounce of organic blueberry is represented by the equation x = 20y + 2.70 where y is the cost in dollars for one ounce of organic blueberry.

As x is the cost in dollar for 30 ounce of organic blueberry. For y is the cost in dollars for one ounce of organic blueberry, then

x = 30y + c

where c is the fixed cost

We know for 10 ounce of organic blueberry it costs $2.70. That is

2.70 = 10y + c

c = 2.70 - 10y

So x = 30y + 2.70 - 10y

x = 20y + 2.70

-- The question is incomplete, the complete question is as follows--

"The cost for 10 ounce of organic blueberry is $2. 70 which equation can be used to determine x the cost in dollars, for 30 ounces of organic blueberries.?"

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The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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Based on the given information, we cannot prove that △EFG and △KLM are similar using the SSS or SAS similarity theorems. The correct answer is option D) No, they cannot be proven similar by SSS or SAS.

To determine if the triangles △EFG and △KLM can be proven similar using the SSS (Side-Side-Side) or SAS (Side-Angle-Side) similarity theorems, we need to compare their corresponding sides and angles.

SSS Similarity Theorem states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

SAS Similarity Theorem states that if two corresponding sides of two triangles are proportional, and the included angles are congruent, then the triangles are similar.

Let's examine the given information:

Side lengths of △EFG: EF = 18, EG = 24, FG = 15.

Side lengths of △KLM: KL = 6, KM = 8, LM = 5.

By comparing the side lengths, we can see that they are not proportional. For example, the ratio of EF/KL is 18/6 = 3, while the ratio of EG/KM is 24/8 = 3. Therefore, the corresponding sides of △EFG and △KLM are not proportional, which means we cannot establish similarity using the SSS theorem.

Now, let's consider the SAS theorem. For this, we also need to compare the included angles.

Angles of △EFG: ∠EFG, ∠EFG, ∠EGF.

Angles of △KLM: ∠KLM, ∠KML, ∠KLM.

The given information states that ∠EFG and ∠KLM are congruent. However, we don't have any information about the other angles. Without knowing the congruency of the remaining angles, we cannot establish similarity using the SAS theorem

Option D.

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Answer: Its C

Step-by-step explanation:

The money spent to fill up the tank with gas was $32.90

An equation is an expression that shows the relationship between two or more numbers and variables.

Lou's car had 4.6 gallons of gas in the 14-gallon tank. To fill the tank:

Amount of gas needed = 14 gallon - 4.6 gallon = 9.4 gallons

Lou filled the tank costing 3.50 per gallon, hence:

Total cost = $3.50 * 9.4 gallons = $32.90

The money spent was $32.90

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Answer:

its  A & B, x<50

Step-by-step explanation:

atmost means till 50.

atleast means more than 50.

The number sentence that states that x is at most 50 is option B: x ≤ 50.

In mathematical notation, the symbol "≤" means "less than or equal to." So, x ≤ 50 translates to "x is less than or equal to 50."

This means that x can be any value that is less than 50 or exactly 50.

Option A (x < 50) would mean "x is less than 50," excluding the value 50 itself.

Option C (x = 50) would mean "x is equal to 50," but it doesn't include any values less than 50.

Option D (x > 50) would mean "x is greater than 50," excluding the value 50 itself.

Option E (x ≥ 50) would mean "x is greater than or equal to 50," which includes values greater than 50, but it doesn't allow any values less than 50.

So, the correct choice to state that x is at most 50 (including the value 50) is option B: x ≤ 50.

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To determine examples with a net torque of zero about the axis perpendicular to the page and extending from the center of the puck, we need to consider the conditions for torque equilibrium.

Torque is the rotational equivalent of force, and it depends on the force applied and the lever arm distance. To have a net torque of zero, the sum of the torques acting on an object must balance out. In this case, the axis is perpendicular to the page and extends from the center of the puck.

The applied forces must have equal magnitudes but act in opposite directions, creating a balanced couple. Without specific examples provided, it is not possible to determine the scenarios with a net torque of zero. The examples would need to be given in terms of the forces applied, their magnitudes, and the corresponding lever arm distances.

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Answer:

0.00264

Step-by-step explanation:

(3.3x10^-4)x(8x10^0)

(3.3x1/100000)x(8x1)

0.00033x8

0.00264

hope this helps

brainliest?

Answer:

2.64 x 10⁻-3

0.00264

Bryce worked a total of 53 3/8 hours during the week.

To calculate the total number of hours Bryce worked for the week, we need to add up the hours worked on each individual day.

On Monday, Bryce worked 8 hours. On Tuesday, Bryce worked 4 14 hours, which is equivalent to 4 * 24 + 14 = 110 hours. On Wednesday, Bryce worked 6 1/8 hours, which is equivalent to 6 + 1/8 = 49/8 hours. On Thursday, Bryce worked 7 14 hours, which is equivalent to 7 * 24 + 14 = 182 hours. Finally, on Friday, Bryce worked 8 18 hours, which is equivalent to 8 * 24 + 18 = 210 hours.

To find the total number of hours Bryce worked for the week, we add up the hours worked on each day: 8 + 110 + 49/8 + 182 + 210 = 53 3/8 hours.

Therefore, Bryce worked a total of 53 3/8 hours during the week.

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The probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.

The quantity of occurrences of an event is referred to as its frequency. The concept of relative frequency is experimental rather than theoretical. It is experimental, therefore if we repeat the trials, we can get different relative frequencies. To determine the frequency, we must first:

Number of occurrences for the entire population

Frequency count for a particular demographic segment

If we know the two frequencies mentioned above, we can use the following formula to get the relative frequency probability. A subgroup's formula is as follows:

Subgroup Count / Overall Count: Relative Frequency

Given that, a player hits the bullseye with a dart 8% of the time.

The probability of hitting the dart is = 8/100.

Now, the probability of hitting the bullseye if the dart is thrown 40 times is:

p = 40 (8/100) = 3.2 times = 3 times.

Hence, the probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.

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Answer:

Yes

Step-by-step explanation:

If she writes 8 pages a day for 4 days a week, in the first week, she will have already written 32 pages which she would only need one more day.

4 x 8 = 32

32 + 8 = 40

That gives her time to edit and revise :)

Hope this makes sense

Answer:

31

Step-by-step explanation:

1. Replace the variables with numbers

8(5)-(9)

2.Conduct order of operations

8(5)-9           -->     40-9    ---> 31

Answer:

31

Explanation:

Trust

Answer:

same volume

Step-by-step explanation:

5X4X3=60, 3X4X5=60

Answer:

ok for this problem lets subtract 25 for 100 to get 75 so know we know we have to multiple 20 by 0.75 to get 15 dollars for the reduced price

Answer:

0.0625 miles

Step-by-step explanation:

There is a faster way but this way makes more sense

1/4 miles = 440 yards

440/4 (since 4 people)

110 yards per person

Put back into miles

Everyone ran 0.0625 miles

The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:

D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.

The mean of the sampling distribution of p is of:

0.388.

The standard deviation of the sampling distribution of p is of:

0.0184.

The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:

As long as these two conditions are respected:

The values of the parameters in this context are given as follows:

N = 30000, n = 700, p = 0.388.

Hence the conditions are:

Then the shape is approximately normal and option D is correct.

The mean of the distribution is of:

\(\mu = p = 0.388\)

The standard error of the distribution is of:

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184\)

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To find the maximum area of the lawn that can be watered by the sprinkler, we can use the formula for the area of a circle:

A = πr^2

Given that the radius of the sprinkler's spray is 22ft, we can substitute this value into the formula:

A = 3.14 * (22)^2

A ≈ 3.14 * 484

A ≈ 1519.76

Rounded to the nearest tenth, the maximum area of the lawn that can be watered by the sprinkler is approximately 1519.8 ft^2.\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

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Answer:

The numbers that when multiplied give 15 and when added give -12 are -3 and 5. Multiplying -3 by 5 gives -15, and adding -3 and 5 gives -8.

Explanation:

To find the numbers that when multiplied give 15 and when added give -12, we need to find two numbers that multiply to give -15 and add to give -12. One pair of numbers that satisfy these conditions is -3 and 5. When multiplied, -3 and 5 give -15, and when added, -3 and 5 give -8.

(a) For the null hypothesis, we would use the claim that the average weight of a healthy 3-month-old colt is equal to 60 kg, that is,

H0 : μ = 60 kg.

(b) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg, that is,

H1: μ < 60 kg.

(c) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is greater than 60 kg, that is, H1: μ > 60 kg.

(d) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is different from 60 kg, that is, H1: μ ≠ 60 kg.

(e) For the test in part (b), the area corresponding to the p-value would be on the left of the mean because the alternate hypothesis is one-tailed and represents a left-tailed test.

For the test in part (c), the area corresponding to the p-value would be on the right of the mean because the alternate hypothesis is one-tailed and represents a right-tailed test.

For the test in part (d), the area corresponding to the p-value would be on both sides of the mean because the alternate hypothesis is two-tailed and represents a two-tailed test.

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