Basketballs cost 24$. a physical education teacher spent 312$ on basketballs for the school.

Which equation can be used to determine the number (n) of basketballs the physical education teacher purchased?

A. 24+n=312
B. 24/n =312
C. 24n= 312
D. 24 =312-n
URGENT!!!

Answer:

To calculate the volume of soil needed, we first convert the dimensions of the backyard to feet:

Length = 70 ft

Width = 60 ft

Depth = 4 in = 4/12 ft = 1/3 ft

Volume = Length x Width x Depth

Volume = 70 ft x 60 ft x (1/3) ft

Volume = 1400 ft³

Option 1: Bags of topsoil

Each bag of topsoil contains 3 ft³ of soil, so the number of bags needed is:

Number of bags = Volume / Bag size

Number of bags = 1400 ft³ / 3 ft³ per bag

Number of bags = 467 bags

The total cost of bags of topsoil is:

Cost = Number of bags x Cost per bag

Cost = 467 bags x $2.50 per bag

Cost = $1167.50

Option 2: Bulk topsoil

The volume of topsoil needed is 1400 ft³, which is equivalent to:

Volume = 1400 ft³ / 27 ft³ per yd³

Volume = 51.85 yd³ (rounded to two decimal places)

The cost of bulk topsoil is:

Cost = Volume x Cost per yd³ + Delivery fee

Cost = 51.85 yd³ x $22.00 per yd³ + $20.00 delivery fee

Cost = $1153.70

Therefore, buying bulk topsoil is less expensive than buying bags of topsoil. The cost of bulk topsoil is $1153.70, while the cost of bags of topsoil is $1167.50

Answer:

Bulk is less expensive

Step-by-step explanation:

First convert inches to feet:  4 in x 1 ft/12 in =0.333 ft

Volume of topsoil needed = 70 x 60 x 0.333 = 1400 ft³

Bagged topsoil:   1400 ft³ x $2.50/3 ft³ = $1166.67

Bulk: 1400 ft³ x 1 yd³/27 ft³ x $22.00/yd³ + $20 = $1160.74

Bulk is just a little cheaper

The surface area of the right rectangular prism 280 yd².

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The surface area of a rectangular prism is expressed as;

S.A = 2( wl + hl + hw )

Where w is the width, h is height and l is length.

From the diagram:

Length l = 6 yd

Width w = 5 yd

Height = 10 yd

Plug the values into the above formula:

S.A = 2( wl + hl + hw )

S.A = 2( 5×6 + 10×6 + 10×5 )

S.A = 2( 30 + 60 + 50 )

S.A = 2( 90 + 50 )

S.A = 2( 140 )

S.A = 280 yd²

Therefore, the surface area is 280 square yards.

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Thus, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%.

To calculate the confidence interval of the proportion smeared in 200 sheets of paper inspected for smeared ink, we can use the formula:

Confidence Interval = sample proportion ± (critical value) x (standard error)

The sample proportion is the number of sheets containing smeared ink divided by the total number of sheets inspected, which is 17/200 = 0.085.

The critical value for a 99% two-sided confidence interval with 200 observations can be found using a t-distribution table or calculator, and is approximately 2.576.

The standard error can be calculated as the square root of [(sample proportion) x (1 - sample proportion) / sample size], which is the square root of [(0.085) x (1 - 0.085) / 200] = 0.028.

Plugging in these values, we get:

Confidence Interval = 0.085 ± (2.576) x (0.028)
Confidence Interval = 0.085 ± 0.072
Confidence Interval = (0.013, 0.157)

Therefore, with 99% confidence, we can say that the proportion of smeared ink in the 200 sheets of paper inspected falls between 1.3% and 15.7%. This means that we are 99% confident that the true proportion of smeared ink in the population of printed sheets falls within this range.

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This prompt is about rounding figures up. We can conclud t that where the above are given, both lists are not in the same order.

  To round up the first order to the second decimal place we have:

Rounding the second batch of cheese and ordering them from the least to greatst, we have:

Hence, we can submit that they are both not in the same eorder.

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The conditional probability of A given B (P(A|B)) is 1/6, or approximately 0.167.

Conditional probability is the probability of an event occurring given that another event has already occurred.

It is denoted by P(A|B), where A and B are events, and P(A|B) represents the probability of event A occurring given that event B has already occurred

The formula for conditional probability is:

P(A|B) = P(A and B) / P(B)

To find the conditional probability of A given B (P(A|B)), we can use the formula
P(A|B) = P(A ∩ B) / P(B)
We are given:
P(A) = 0.5 (probability of event A occurring)
P(B) = 0.6 (probability of event B occurring)
P(A ∩ B) = 0.1 (probability of both A and B occurring)
Now, we can plug in the given values into the formula:
P(A|B) = 0.1 / 0.6
P(A|B) = 1/6.

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Rounding to the nearest minute, the athlete's trip will take approximately 96 minutes.

Let's start by drawing a diagram to better visualize the situation:

        A     x     D         C

        o-----x------------x

              |            |

              |            |

              |            |

              |            |

              |            |

              |            |

              B            |

              o------------o

Here, point A is where the athlete starts, point B is where she comes ashore due to the current, point C is her intended destination on the shoreline, and point D is the point where she switches from rowing to running.

From the diagram, we can see that the distance AB is 3 miles, and the distance AC is 3 + 1/2 = 3.5 miles.

We can use the Pythagorean theorem to find the distance BC:

[tex]BC^2 = AB^2 + AC^2[/tex]

[tex]BC^2 = 3^2 + 3.5^2[/tex]

[tex]BC^2 = 12.25[/tex]

BC = sqrt(12.25)

BC = 3.5

So the distance the athlete needs to travel on foot is 3.5 miles.

Let's first calculate the time it takes for her to row to point D:

Time to row to D = Distance / Speed

Time to row to D = 1/2 / 2

Time to row to D = 1/4 hours

Next, let's calculate the time it takes for her to run from D to C:

Time to run to C = Distance / Speed

Time to run to C = 3.5 / 4

Time to run to C = 7/8 hours

Now, we need to find the time it takes her to travel from B to C.

We can use the law of sines to find the angle between AB and BC:

sin(28) / 3 = sin([tex]\theta[/tex]) / 3.5

sin(theta) = 3.5 * sin(28) / 3

sin(theta) = 0.5407

theta = arc sin(0.5407)

theta = 33.15 degrees

Therefore, the angle between AB and BC is approximately 33.15 degrees.

We can use this angle and the distance BC to find the distance the athlete actually traveled from B to C:

Distance traveled from B to C = BC * sin([tex]\theta[/tex])

Distance traveled from B to C = 3.5 * sin(33.15)

Distance traveled from B to C = 1.925 miles

Finally, we can calculate the total time of the trip:

Total time = Time to row to D + Time to run to C + Time to travel from B to C

Total time = 1/4 + 7/8 + (1.925 / 4)

Total time = 0.25 + 0.875 + 0.48125

Total time = 1.60625 hours

To convert this to minutes, we can multiply by 60:

Total time = 1.60625 * 60

Total time = 96.375 minutes.

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To find the area of the resulting surface when the given curve y = 1/4x^2 - 1/2 ln(x) is rotated about the y-axis, we can use the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from a to b

Here, a = 3 and b = 5.

First, we need to find the derivative of y with respect to x (dy/dx):

y = 1/4x^2 - 1/2 ln(x)
dy/dx = (1/4 * 2x) - (1/2 * 1/x) = x/2 - 1/(2x)

Now, let's plug this into the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (x/2 - 1/(2x))^2)] dx from 3 to 5

We will now integrate the expression within the brackets with respect to x from 3 to 5. This might be challenging to solve analytically, so we may need to use a numerical integration method or a calculator to find the exact value.

Once the integration is completed, you will obtain the surface area of the curve when rotated about the y-axis.

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Answer:

a) a square number:64

b) a multiple of 13:65

c) a factor of 186:62

d)the prime number:61,67

Answer:

  h = 10 13/14 units

Step-by-step explanation:

You want the height from the side of length 14 of a parallelogram with side length 17 and height 9.

The area of a parallelogram is the same, no matter which side is used as the "base". This means ...

  A = bh = 17(9) = 14(h)

  h = 17·9/14 = 10 13/14 . . . . units

Answer:

1. Neither would yield the lower tax.

2. (not sure yet about how much)

3. and there is not really a marriage penalty.

ADF

Thats not the answer those are just my favorite letters

Answer: tan 47/1 = x/.5 = x = .53618

Step-by-step explanation:

The graph of the exponential function across the interval is attached below

To graph the function y = 3ˣ over the interval 1 ≤ x ≤ 2, you can follow these steps:

Choose a suitable scale for the x-axis and y-axis. Since the function grows rapidly, you may need to use a logarithmic scale on the y-axis to show the entire graph.

Plot some key points of the function. To do this, you can choose some values of x within the given interval and calculate the corresponding values of y. For example:

When x = 1, y = 3^1 = 3

When x = 1.5, y = 3^1.5 = 5.2

When x = 2, y = 3^2 = 9

Connect the plotted points with a smooth curve. Since the function is exponential, the curve will be a smooth upward curve that gets steeper and steeper as x increases.

Label the axes and add any necessary annotations or markings. For example, you may want to label the plotted points with their coordinates or add gridlines to help read off values from the graph.

Kindly find the attached graph below

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Answer:

True

hope it helps :) !!!

Answer:

the answer is true, it's the objects net is the same as the surface area.

Answer: 5 3/4 feet

Step-by-step explanation:

The original perimeter of the room is:

2(length + width) = 2(13 ft + 8 ft) = 42 ft

After the length and width are increased by "x" feet, the new perimeter becomes 53 1/2 ft.

So, we can write the equation:

2(length + x + width + x) = 53 1/2 ft

Simplifying the equation, we get:

2(length + width + 2x) = 53 1/2 ft

But we know that the original perimeter of the room was 42 ft, so:

2(length + width) = 42 ft

Substituting this into the above equation, we get:

42 ft + 2x = 53 1/2 ft

Subtracting 42 ft from both sides, we get:

2x = 11 1/2 ft

Dividing both sides by 2, we get:

x = 5 3/4 ft

Therefore, the length and width of the room were both increased by 5 3/4 feet

Answer:

the required answer is 1 and -5

Answer:

6(15) + 25x = w

Step-by-step explanation:

6h would be the babysitting money, and since we know the hours, h, we replace the variable with the constant, 15, to get 6 * 15, or 6(15).

25x represents that each week, x, you earn $25.

Put this all together to get the answer above.

The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

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The solution to the initial value problem is [tex]y = (3 - e^x)/(e^x - 1)[/tex]. The domain of this solution is all values of x except x = ln(3).

A method for resolving specific kinds of first-order ordinary differential equations is called variable separation. It entails moving the equation's terms so that those involving the independent variable x are on the other side and those involving the dependent variable y are on the one side. In order to arrive at a general solution, we can then integrate both sides with respect to their respective variables. The name of the method comes from the fact that the variables on either side of the equation are separated.

The given differentiation is given as:

[tex]dy/dx = 9e^{x - y}[/tex]

Separating the variables we have:

[tex]dy/(9e^{x - y}) = dx[/tex]

Now, integrating on both sides we have:

[tex]\int dy/(9e^{x - y}) = \int dx[/tex]

Using partial fraction decomposition we have:

[tex]\int [1/(3-y) - 1/(3e^{x-y})] dy = x + C[/tex]

Integrating each term we have:

[tex]ln|3-y| - ln|3e^{x-y}| = x + C\\ln|3-y| - ln (\|y-3e^x\| = x + C\\ln|(3-y)/(y-3e^x)| = x + C\\(3-y)/(y-3e^x) = ke^x[/tex]

, where k is a constant of integration

We can solve for y:

[tex]y = (3ke^x + 3)/(ke^x + 1)[/tex]

Now, for the initial condition y = 4 and x = 0 we have:

[tex]4 = (3k + 3)/(k + 1)\\4k + 4 = 3k + 3\\k = -1[/tex]

Hence, the solution to the initial value problem is [tex]y = (3 - e^x)/(e^x - 1)[/tex].

Now, the domain of this solution is all values of x except x = ln(3)

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The acceleration acquired by the object of mass 12 Kg and is pushed with a force of 12 N, is given by 5/3 m/s².

We know that from the first law of Newton's Law that,

F = m*a

where 'F' is applied force; 'm' is mass of object and 'a' is acceleration.

Let the acceleration acquired by the object be 'A'.

Mass of the object is (m) = 12 Kg

The force applied (F) = 20 N

So from Newton's First Law of Motion we get,

F = m*a

20 = 12*A

A = 20/12

A = 5/3

Hence the acceleration will be 5/3 m/s².

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The question is in another language. The question is in English will be -

''What is the acceleration acquired by an object that has a mass of 12 Kg and is pushed with a force of 20N?''

Answer:

A correct option is option (b).

Given,

Trigonometric ratios:

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The given triangle is right angle triangle then

Now, calculate the angles.

Again,

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Step-by-step explanation:

Answer: If the daffodil start at 1 inch on day one, and only 1 day has passed, it will grow half of what it would in 2 days because half of 2 is 1. So the current height 1 inch + how much it will grow in one day (1.5 inches) = the final height (2.5 inches) Hope this helps :D

Step-by-step explanation:

If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The area of a rectangle is calculated by multiplying its length and width. If the dimensions of a rectangle are multiplied by a factor of k, then the new area of the rectangle is equal to k times the original area.

In this case, the dimensions of the original rectangle are multiplied by 1/2, which means that the new length and width of the rectangle are 1/2 times the original length and width. Therefore, the new area of the rectangle is equal to (1/2) times the original length multiplied by (1/2) times the original width. This can be simplified to 1/4 times the original area. Therefore, the area of the new rectangle is one-fourth of the area of the original rectangle.

Therefore, If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.

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Going from top left to right then bottom left to right

Answers:

1st. answer: 94

2nd. answer: 82

3rd. answer: 142

4th answer: 88.2

5th. answer: 130

6th. answer: 178

(also I relearned how to do triangles)

(I'm going to follow you so if you have any more questions I can help)

in general, to perform a hypothesis test comparing the means of two independent samples using the critical value method, you would follow these steps:

State the null and alternative hypotheses. For example, the null hypothesis could be that there is no difference in means between the two populations (i.e., H0: µ1 - µ2 = 0), and the alternative hypothesis could be that there is a significant difference in means (i.e., Ha: µ1 - µ2 ≠ 0).

Determine the level of significance, α, which represents the probability of rejecting the null hypothesis when it is actually true. For example, if α = 0.05, then there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).

Calculate the test statistic. The most common test statistic for comparing the means of two independent samples is the t-test. The formula for the t-test is:

t = (x1 - x2) / [s^2pooled/n1 + s^2pooled/n2]^0.5

where x1 and x2 are the sample means, s^2pooled is the pooled variance (calculated using the two sample variances and sample sizes), and n1 and n2 are the sample sizes.

Determine the critical value(s) from the t-distribution table based on the degrees of freedom (df) and level of significance (α). The degrees of freedom for a two-sample t-test is calculated as:

df = n1 + n2 - 2

Compare the test statistic to the critical value(s). If the absolute value of the test statistic is greater than the critical value(s), then reject the null hypothesis; otherwise, fail to reject the null hypothesis.

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The amount it will cost to recarpet the the whole room is $891.12

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

For example, the area of a circle is given as: A = πr², where r is the radius and π is constant.

The room takes the shape of a rectangle, therefore,

Area of the room = l× w, where l is the length and w is the width.

Area = 3×8 = 24 m²

The cost of 1m² = $33.38

therefore the cost for 24m²

= 24× 33.8

= $801.12

therefore the cost to recarpet the room is $801.12

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Answer:

53b - 7b - 6b + 1 with b = 25 simplifies to 1001.

Step-by-step explanation:

To simplify 53b - 7b - 6b + 1 with b = 25, we substitute 25 for b and simplify the expression as follows:

53b - 7b - 6b + 1 = 53(25) - 7(25) - 6(25) + 1

= 1325 - 175 - 150 + 1

= 1001

Therefore, 53b - 7b - 6b + 1 with b = 25 simplifies to 1001.