A group of friends were working on a student film that had a budget of $1400. They used 23% of their budget on equipment. How much money did they spend on equipment?

Step-by-step explanation:

Given eqn

y=1/3x+4

1/3x-y+4=0

eqn of line perpendicular to the given eqn.,

x+1/3y+k=0

since the reqd. line contains the point (2,-3)

2+1/3 (-3)+k=0

2-1+k=0

k=-1

so

x+1/3y-1=0

1/3y=1-x (in slope intercept form)

The volume of the resulting solid is approximately 904.78 cubic units.

To find the volume of the resulting solid, we can subtract the volume of the smaller ball (the hole) from the volume of the larger ball. The volume of a sphere is given by the formula:

where V is the volume, r is the radius of the sphere, and π is approximately equal to 3.14.

Using this formula, we can find the volume of the larger ball:

We can then find the volume of the smaller ball (the hole):

Subtracting the volume of the smaller ball from the volume of the larger ball gives us the volume of the resulting solid: 4188.79 cubic units - 113.04 cubic units = approximately 904.78 cubic units. This is the volume of the resulting solid.

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From the tally chart and line plot, it can be concluded that the most common number of books read by Hannah and her classmates last month was 2, and the median number of books read was 1.5.

Number is a mathematical object used to count, measure and label. It is a symbol or set of symbols used to represent a numerical quantity. It can also be used to represent a quantity in an equation or other mathematical expression. Numbers can be written using different number systems, such as the decimal system, the binary system and the hexadecimal system. They are also related to arithmetic operations such as addition, subtraction, multiplication, division and exponentiation.

Tally Chart:

Books Read: 0 |  |
Books Read: 1 |  |  |  |
Books Read: 2 |  |  |  |  |  |
Books Read: 3 |  |  |  |  |  |  |  |
Books Read: 4 |  |  |  |  |  |  |

Line Plot:

0 |  |
1 |  |  |  |
2 |  |  |  |  |  |
3 |  |  |  |  |  |  |  |
4 |  |  |  |  |  |  |

The line plot shows that the most common number of books read by Hannah and her classmates was 2. The least common number of books read was 0, with only 1 student reading 0 books. The next least common number of books read was 1, with 4 students reading 1 book. The third most common number of books read was 3, with 5 students reading 3 books. The fourth most common number of books read was 4, with 4 students reading 4 books.

To calculate the median number of books read, the data points from the line plot must be arranged in numerical order. This would be 0, 1, 2, 3, 4. Since there are an even number of points, the median is the average of the two middle numbers, which is 1.5.

From the tally chart and line plot, it can be concluded that the most common number of books read by Hannah and her classmates last month was 2, and the median number of books read was 1.5. This data suggests that many students were reading 2 books last month, but some students were reading fewer than 2 books.

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Answer:

Step-by-step explanation:

8. 7.5 Goes up by 2.5.

9. 7.3 Goes down by 2.1

10. 116/3

Answer:

8- 7.5

9-7.3

10-38 \(\frac{2}{3}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation being shown in the question is the absolute value of x. Absolute values when graphed show up as a V-shaped graph pointing upwards. This is because whatever value is passed as an input will output a positive, regardless of whether the input is positive or negative. Meaning that both 4 and -4 will output 4. That is why the graph is a V-shaped because the outputs repeat for both positive and negative inputs. In this case since the negative is outside the absolute value brackets the positive value given from the absolute value of the input will be turned into a negative. So this will cause the V-shape graph to be reflected across the x-axis. As seen in the attached picture below.

Answer: This is the correct answer
I just took the test. :)

Step-by-step explanation:

:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.

During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.

According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes

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Answer:

The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours

The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours

since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Step-by-step explanation:

The given parameters are;

The elapsed time by which Ms. Croft missed the boat = 5 hours

The speed of the cruise ship = 528 mi/day

The speed of the speedboat = 100 miles in 2.5 hours

The speed of the helicopter = 90 mph

The time it would take Ms. Croft to arrive at the harbor = 3.5 hours

Therefore, we have;

The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph

The location of the cruise after the first 5 hours = 5 × 22 = 110 miles

The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph

By traveling with a speed boat

The time at which Ms. Croft will intercept the cruise ship is given by the following relation;

40 mph × t = 22 mph × t + 110 miles

Which gives;

40 mph × t - 22 mph × t = 110 miles

18 mph = 110 miles

t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours

By taking the helicopter, we have;

Upon arrival at the harbor, after 3.5 hours, we find

90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles

90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles

68 mph × t = 77 miles + 110 miles = 187 miles

t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours

The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours

Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

The doctor used inductive reasoning because the doctor used various observations to come up with a final conclusion.

As per the average, the distance of planes at 2:45pm is 678 miles.

First, let's talk about the concept of "average." When we say a plane is traveling at an average speed of 428 mph, that means it may be going faster or slower at different points in its journey, but the overall average speed over time is 428 mph.

To find out how far apart the planes are at 2:45pm, we need to know how far each plane has traveled by that time. Since the first plane left at 1:00pm and it is now 2:45pm, it has been flying for 1 hour and 45 minutes. To find out how far it has traveled, we can use the formula:

distance = speed x time.

So, distance = 428 mph x 1.75 hours = 749 miles.

The second plane left 15 minutes later, so it has been flying for 1 hour and 30 minutes by 2:45pm.

To find out how far it has traveled, we can use the same formula:

distance = speed x time.

So, distance = 452 mph x 1.5 hours = 678 miles.

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Answer:

Step-by-step explanation:

= 1,521

Answer:

1521

Step-by-step explanation:

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Opposite angles of ABCD are congruent if and only if ABCD is a parallelogram. The diagonals of ABCD bisect each other if and only if ABCD is a parallelogram.

(a) Given ABCD is a quadrilateral. If ABCD is a parallelogram, then AB || CD and BC || AD. Also, opposite angles are congruent and it can be proven using proposition 29 of Euclid's first 29 propositions. Using the converse of the above, If opposite angles of ABCD are congruent, then AB || CD and BC || AD. So ABCD is a parallelogram, which is proved using proposition 28 of Euclid's first 29 propositions. Hence it is proved that opposite angles of ABCD are congruent if and only if ABCD is a parallelogram.

(d) Given ABCD is a quadrilateral. The diagonals AC and BD of a quadrilateral ABCD bisect each other if and only if ABDE is a parallelogram. So, it is proved using proposition 29 of Euclid's first 29 propositions that diagonals of ABCD bisect each other if and only if ABCD is a parallelogram. Hence it is proved that the diagonals of ABCD bisect each other if and only if ABCD is a parallelogram.

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Answer:

2 13/20

Step-by-step explanation:

Answer:

2 13/20

Step-by-step explanation:

we can split up 2.65 into a whole number and a decimal

2.65

= 2 + 0.65      (note that 0.65 = 65/100)

= 2 + 65/100

= 2 65/100   (we can see that both numerator and denominator are multiples of 5, hence we can try to simply by dividing both numerator and denominator by 5)

= 2 (65÷5) / (100÷5)

= 2 13/20   (answer)

Answer:

84

Step-by-step explanation:

7/10 of them likes math and there are 240 student in total

240 / 10 = 24 and 24*7 = 168 student likes math if half of them are girls

then there are 84 girls that likes  math.

The given expression is an iterated triple integral of a function over a region defined by the equation 9 - x^2 - y^2 = 0. The task is to evaluate the triple integral ∭∭∭(√(9 - x^2) + √(x^2 + y^2 + z^2)) dz dy dx.

To evaluate the triple integral, we need to break it down into three separate integrals representing the three variables: z, y, and x. Since the region of integration is determined by the equation 9 - x^2 - y^2 = 0, we can rewrite it as y^2 + x^2 = 9, which represents a circular region centered at the origin with a radius of 3.

We start by integrating with respect to z, treating x and y as constants. The innermost integral evaluates the expression √(x^2 + y^2 + z^2) with respect to z, giving the result as z√(x^2 + y^2 + z^2).

Next, we integrate the result obtained from the first step with respect to y, treating x as a constant. This involves evaluating the integral of the expression obtained in the previous step over the range of y-values defined by the circular region y^2 + x^2 = 9.

Finally, we integrate the result from the second step with respect to x over the range defined by the circular region.

By performing these integrations, we can find the value of the triple integral ∭∭∭(√(9 - x^2) + √(x^2 + y^2 + z^2)) dz dy dx.

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To determine the number of tokens Frank bought, we need to set up an equation using the given information. Frank spent $2 for every 11 tokens and spent a total of $16 on tokens.

Let t be the total number of tokens Frank bought. We know that for every 11 tokens, he spent $2. So, we can express the relationship between the amount spent and the number of tokens as follows:

(amount spent) = (cost per token set) × (number of token sets)

Since Frank spent $2 for every 11 tokens, the cost per token set is $2, and the number of token sets is t/11. Therefore, the equation can be written as:

$16 = $2 × (t/11)

Alternatively, we can also use the equation:

t = (11/2) x ($16/$2)

Simplifying this expression gives us:

t = 11 x 8

t = 88

This equation can be used to determine t, the number of tokens Frank bought at the arcade.

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The resulting output array would be {16, 8, 29, 22, 43, 28}.

To perform a 1D convolution, we need to flip the mask m and then slide it over the array n, multiplying the corresponding elements and adding the products.

First, we need to pad the array n with zeros to handle the ghost elements. We need to add two zeros at the beginning and one zero at the end to ensure that all elements in the mask m have corresponding elements in the array n.

n_padded = {0, 0, 4, 1, 3, 2, 3, 0}

Now we flip the mask m.

m_flipped = {4, 1, 2}

Next, we slide the mask over the padded array and perform the multiplication and addition.

output[0] = m_flipped[0]*n_padded[0] + m_flipped[1]*n_padded[1] + m_flipped[2]*n_padded[2] = 0 + 0 + 16 = 16

output[1] = m_flipped[0]*n_padded[1] + m_flipped[1]*n_padded[2] + m_flipped[2]*n_padded[3] = 0 + 4 + 4 = 8

output[2] = m_flipped[0]*n_padded[2] + m_flipped[1]*n_padded[3] + m_flipped[2]*n_padded[4] = 16 + 1 + 12 = 29

output[3] = m_flipped[0]*n_padded[3] + m_flipped[1]*n_padded[4] + m_flipped[2]*n_padded[5] = 8 + 6 + 8 = 22

output[4] = m_flipped[0]*n_padded[4] + m_flipped[1]*n_padded[5] + m_flipped[2]*n_padded[6] = 29 + 2 + 12 = 43

output[5] = m_flipped[0]*n_padded[5] + m_flipped[1]*n_padded[6] + m_flipped[2]*n_padded[7] = 22 + 6 + 0 = 28

Therefore, the resulting output array would be {16, 8, 29, 22, 43, 28}.

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Time = 3 hours

Money earned = $45

3 hours = $45

1 hour = ?

Cross Multiply

1 hour x $45 / 3 hours

= $15

Time = 10 hours

Money earned = $150

The amount of money Carl earns per hour is calculated as:

10 hours = $150

1 hour = ?

Cross Multiply

1 hour x $150 / 10 hours

= $15

Therefore, the amount of money Carl earns per hour is $15

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Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Answer:

4. (−4, 6), slope −2. eSolutions Manual - Powered by Cognero. Page 1. 4-2 Writing ... 4. (−4, 6), slope −2. SOLUTION: Find the y-intercept. Write the equation in ... Write an equation in slope-intercept form to find the total cost C for p people. b. ... b. Plot points and draw a line through them. c. Solve for G when t = 17.

Answer: The bottom right I did that

I hope it helps you can you mark me as Brainliest please

Answer:

p = 16

Step-by-step explanation:

(p + 2) - 4 = 14

We can just drop the parentheses:_

p + 2 - 4 = 14

p - 2 = 14

Add 2 to both sides:-

p - 2 + 2 = 14 + 2

p = 16

Answer:

Step-by-step explanation:

the answer is c

Step-by-step explanation:

Let the first side is x, second side is (x+1) and the third sie is (x+2). The perimeter of the triangle is 114 cm.

It means,

x+x+1+x+2=114

3x+3=114

3(x+1)=114

x+1=38

x=37

So, first side is 37 cm

Second side is 37+1=38 m

Third side is 37+2=39 m

Hence, this is the required solution.

The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

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The final expression is given as ln|S| = 8t / √πS(0) + ln|S(0)|.

A spherical weather balloon is being inflated at a rate of 5 cm/s. If we want to express the surface area of the balloon as a function of time t (in seconds), then we have to use the formula for the surface area of a sphere which is given as S = 4πr².

Here, the radius of the balloon is increasing at the rate of 5 cm/s.

So we can say that dr/dt = 5 cm/s, where dr is the rate of change of radius with respect to time.

We can differentiate the formula of surface area of the sphere w.r.t time, we get: dS/dt = d/dt (4πr²) => dS/dt = 8πr (dr/dt)We know, r = (1/2)Sqrt(S/π)So, we can substitute the value of r in the above expression, dS/dt = 4πS (ds/dt) / Sqrt(πS)

On simplifying this, we get: dS/dt = 4S (ds/dt) / √πSNow, if S = S(0) at t = 0, then we can integrate both sides of the equation to get the surface area of the balloon as a function of time t.S(0) is the initial surface area of the balloon.

Substituting, we get:∫ dS/S = ∫ 4(dt/√πS(0))We get:ln|S| = 8t / √πS(0) + CWhere C is the constant of integration.At t = 0, S = S(0),

so we get:ln|S(0)| = CBy substituting this value of C in the above expression, we get:ln|S| = 8t / √πS(0) + ln|S(0)|

On simplifying this expression, we get the surface area of the balloon as a function of time t.

We derived the expression of surface area of the balloon as a function of time t when the radius of the balloon is increasing at the rate of 5 cm/s. We used the formula of surface area of a sphere and the derivative of radius w.r.t time to derive the expression of surface area. The final expression is given as ln|S| = 8t / √πS(0) + ln|S(0)|.

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The correctanswer is-the percentage of the pieces that will meet the length specs is 98.78%.

The given data may be a random variable that takes after the normal distribution with mean μ=64 and standard deviation σ=0.1

The required value is to discover the rate of the pieces that will meet the length specs which is between 63.76 and 64.24 inches.

To find the required percentage, standardize the given limits as follows: Lower Limit: (63.76 - μ) / σ= (63.76 - 64) / 0.1 = -2.4

Upper Limit: (64.24 - μ) / σ= (64.24 - 64) / 0.1 = 2.4

Using the Standard Normal Distribution Table, the probability that the value will fall between -2.4 and 2.4 is found to be 0.9878.

The required percentage is then found by multiplying the probability by 100, which is: Percentage = 0.9878 x 100% = 98.78%

Therefore, the percentage of the pieces that will meet the length specs is 98.78%.

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