If 50% of 600 is 300, what is 75% of 600​

the total amount of oil that leaks out over the entire time interval [0, 120].

integral ∫₀¹₂₀ r(t) dt represents the total amount of oil that leaks from the tank in 120 minutes.

To see why, consider the definition of an integral. If we divide the interval [0, 120] into small subintervals of width Δt, then the amount of oil that leaks out during each subinterval is approximately r(t)Δt. Summing up all these small amounts over the entire interval gives:

Σᵢ r(tᵢ) Δt

where tᵢ is the midpoint of the i-th subinterval. As we take the limit as the subinterval width goes to zero, this sum becomes the integral:

∫₀¹₂₀ r(t) dt

which represents the total amount of oil that leaks out over the entire time interval [0, 120].

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Answer:

#6 is 17 days

Step-by-step explanation:

This is how I answered it

1) 2750 = 550 + 125x

2) subtract 550 from each side

2750-550=2200

so the left over equation is:

2200 = 125x

3) divide each side by 125 to get x by itself

2200÷125= 17.6

4) you are left with: x = 17 days

The solution to the initial value problem is y(t) = (1/2) * [sin(t) + cos(t)], where y(0) = y''(0) = y'''(0) = 0 and y'(0) = 1.

To solve the initial value problem using Laplace transforms, we'll first take the Laplace transform of both sides of the differential equation. Then we'll solve for the Laplace transform of the unknown function y(t), denoted as Y(s). Finally, we'll find the inverse Laplace transform of Y(s) to obtain the solution y(t).

Given the initial value problem:

y^(4)(t) - y(t) = 0,

y(0) = y''(0) = y'''(0) = 0,

y'(0) = 1.

Taking the Laplace transform of both sides, we get:

s^4Y(s) - s^3 - s^2 - s - 1 + Y(s) = 0.

Combining like terms, we have:

(s^4 + 1)Y(s) - (s^3 + s^2 + s + 1) = 0.

Now, we can solve for Y(s):

Y(s) = (s^3 + s^2 + s + 1) / (s^4 + 1).

To find the inverse Laplace transform of Y(s), we need to decompose the rational function into partial fractions. The denominator s^4 + 1 can be factored as (s^2 + i)(s^2 - i), where i is the imaginary unit.

Using partial fractions, we can write Y(s) as:

Y(s) = A/(s^2 + i) + B/(s^2 - i).

To find the values of A and B, we can multiply both sides by the denominator (s^4 + 1):

(s^3 + s^2 + s + 1) = A(s^2 - i) + B(s^2 + i).

Expanding and equating coefficients, we get the following system of equations:

A + B = 1 (coefficients of s^3 term)

A - B = 1 (coefficients of s^2 term)

A = B = 0 (coefficients of s and constant terms)

Solving this system of equations, we find A = B = 1/2.

Therefore, Y(s) can be expressed as:

Y(s) = (1/2) / (s^2 + i) + (1/2) / (s^2 - i).

Now, we can find the inverse Laplace transform of Y(s) to obtain the solution y(t).

Taking the inverse Laplace transform, we have:

y(t) = (1/2) * [sin(t) + cos(t)].

Hence, the solution to the initial value problem is y(t) = (1/2) * [sin(t) + cos(t)], where y(0) = y''(0) = y'''(0) = 0 and y'(0) = 1.

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The roots of quadratic equations:

In this question we need to determine sixteen cases of quadratic equations, whose roots should be determined. This can be done by following procedure:

Now we proceed to show the solution to each case:

Case 1

b² - 4 = 0

b² = 4

b = ± 4

Case 2

4 · a² - 1 = 0

4 · a² = 1

a² = 1 / 4

a = ± 1 / 2

Case 3

2 · x² = 21 + 11 · x

2 · x² - 11 · x - 21 = 0

2 · [x² - (11 / 2) · x - 21 / 2] = 0

2 · [x² - (11 / 2) · x + 121 / 16] = 2 · (121 / 16) + 2 · (21 / 2)

2 · (x - 11 / 4)² = 289 / 8

(x - 11 / 4)² = 289 / 16

x - 11 / 4 = ± 17 / 4

x = 11 / 4 ± 17 / 4

Case 4

2 · n² = 32

n² = 16

n = ± 4

Case 5

5 · x² = 3 · x + 92

5 · x² - 3 · x - 92 = 0

5 · [x² - (3 / 2) · x - 92 / 5] = 0

5 · [x² - (3 / 2) · x] = 5 · (92 / 5)

5 · [x² - (3 / 2) · x + 9 / 16] = 5 · (92 / 5 + 9 / 16)

5 · (x - 3 / 4)² = 1517 / 16

(x - 3 / 4)² = 1517 / 80

x - 3 / 4 = ± √(1517 / 80)

x = 3 / 4 ± √(1517 / 80)

Case 6

4 · x² = 7 · x + 92

4 · x² - 7 · x - 92 = 0

4 · [x² - (7 / 4) · x - 23] = 0

4 · [x² - (7 / 4) · x + 49 / 64] = 92 + 49 / 64

4 · (x - 7 / 8)² = 5937 / 64

x - 7 / 8 = ± √(5937 / 256)

x = 7 / 8 ± √(5937 / 256)

Case 7

5 · k² = - 7 · k + 138

5 · k² + 7 · k - 138 = 0

5 · [k² + (7 / 5) · k - 138 / 5] = 0

5 · [k² + (7 / 5) · k] = 5 · (138 / 5)

5 · [k² + (7 / 5) · k + 49 / 100] = 5 · (138 / 5 + 49 / 100)

5 · (k + 7 / 10)² = 2809 / 20

k + 7 / 10 = ± √(2809 / 100)

k = - 7 / 10 ± √(2809 / 100)

Case 8

m² - 88 = 3 · m

m² - 3 · m - 88 = 0

m² - 3 · m - 352 / 4 = 0

m² - 3 · m = 352 / 4

m² - 3 · m + 9 / 4 = 361 / 4

(m - 3 / 2)² = 361 / 4

m - 3 / 2 = ± √(361 / 4)

m = 3 / 2 ± √(361 / 4)

Case 9

4 · n² - 7 = 12 · n

4 · n² - 12 · n = 7

4 · (n² - 3 · n + 9 / 4) = 7 + 9

4 · (n - 3 / 2)² = 16

n - 3 / 2 = ± 4

n = 3 / 2 ± 4

Case 10

6 · n² - 2 · n = 140

6 · [n² - (1 / 3) · n] = 140

6 · [n² - (1 / 3) · n + 1 / 36] = 140 + 1 / 6

6 · (n - 1 / 6)² = 841 / 6

n - 1 / 6 = ± 841 / 36

n = 1 / 6 ± 841 / 36

Case 11

4 · p² = 64

p² = 16

p = ± 4

Case 12

6 · v² - 10 · v = 84

6 · [v² - (5 / 3) · v] = 84

6 · [v² - (5 / 3) · v + 25 / 36] = 84

6 · (v - 5 / 6)² = 84

(v - 5 / 6)² = 14

v - 5 / 6 = ± 14

v = 5 / 6 ± 14

Case 13

3 · r² - 77 = - 10 · r

3 · r² + 10 · r = 77

3 · [r² + (10 / 3) · r] = 77

3 · [r² + (10 / 3) · r + 25 / 9] = 77 + 25 / 9

3 · (r + 5 / 3)² = 718 / 9

(r + 5 / 3)² = 718 / 27

r + 5 / 3 = ± √(718 / 27)

r = - 5 / 3 ± √(718 / 27)

Case 14

5 · x² - 11 · x = - 6

5 · [x² - (11 / 5) · x + 121 / 100] = - 6 + 5 · (121 / 100)

5 · (x - 11 / 10)² = 1 / 20

(x - 11 / 10)² = 1 / 100

x - 11 / 10 = ± √(1 / 10)

x = 11 / 10 ± √(1 / 10)

Case 15

2 · n² = 11 · n + 6

2 · n² - 11 · n = 6

2 · [n² - (11 / 2) · n] = 6

2 · [n² - (11 / 2) · n + 121 / 16] = 6 + 2 · (121 / 16)

2 · (n - 11 / 4)² = 169 / 8

(n - 11 / 4)² = 169 / 16

n - 11 / 4 = ± 13 / 4

n = 11 / 4 ± 13 / 4

Case 16

4 · x² = 100

x² = 25

x = ± 5

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a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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The derivative of the function is f'(x) = -2x + 2, the critical number is x = 1, the absolute minimum value is 5 at x = 5, and the absolute maximum value is 16 at x = 1.

The derivative of the function f(x) = 15 + 2x - x^2 on the interval [0, 5] is f'(x) = -2x + 2. The critical number of the function is x = 1. The absolute minimum value of f on the interval is 5 at x = 0, and the absolute maximum value is 16 at x = 1.

To find the derivative of the function, we differentiate each term of the function with respect to x. The derivative of 15 is 0 since it is a constant. The derivative of 2x is 2, and the derivative of x^2 is 2x. Adding these derivatives together, we get f'(x) = 2 - 2x.

To find the critical numbers, we set the derivative equal to zero and solve for x: -2x + 2 = 0. Simplifying, we find x = 1 as the critical number.

To determine the absolute maximum and minimum values of f on the interval [0, 5], we evaluate the function at the endpoints and the critical number. At x = 0, f(0) = 15 + 2(0) - 0^2 = 15, and at x = 5, f(5) = 15 + 2(5) - 5^2 = 5. At the critical number x = 1, f(1) = 15 + 2(1) - 1^2 = 16. Comparing these values, we find that the absolute minimum value of f is 5 at x = 5, and the absolute maximum value is 16 at x = 1.

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Answer:

Hope This Helps <3

Step-by-step explanation:

4-8 +2 = -11

6-3-7 = -4

1 +4-6 =  -1

2-7+6 = 1

The required answer is the equation of the line that passes through (-1, -8) and is perpendicular to x + 3y = 6 is y = 3x - 5.

Explanation :

find the equation of the line that passes through (-1, -8) and is perpendicular to x + 3y = 6.
Step 1: Find the slope of the given line (x + 3y = 6).
Rewrite the equation in the form y = mx + b:
3y = -x + 6
y = (-1/3)x + 2
The slope (m) of the given line is -1/3.
Step 2: Find the slope of the perpendicular line.
For two lines to be perpendicular, their slopes are negative reciprocals of each other. So, the slope (m') of the perpendicular line is the negative reciprocal of -1/3:
m' = 3
We can rearrange this equation to the slope-intercept form y = (-1/3)x + 2. The slope of any line perpendicular to this line will be the negative reciprocal of (-1/3), which is 3. Now that we know the slope,
Step 3: Use the point-slope form (y - y1 = m'(x - x1)) and the given point (-1, -8) to find the equation of the perpendicular line:
y - (-8) = 3(x - (-1))
y + 8 = 3(x + 1)
Step 4: Rewrite the equation in the form y = mx + b:
y = 3x + 3 - 8
y = 3x - 5
So, the equation of the line that passes through (-1, -8) and is perpendicular to x + 3y = 6 is y = 3x - 5.

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The sum of the measures of angle A and angle B is 90 degrees. To determine the value of x, we need to set up an equation based on the given information.

Angle A is given as (5x + 10) degrees, and angle B is given as 3x degrees.

According to the problem, the sum of angle A and angle B is 90 degrees. We can write this as an equation:

(5x + 10) + 3x = 90

Combining like terms, we have:

8x + 10 = 90

Subtracting 10 from both sides:

8x = 80

Dividing both sides by 8:

x = 10

Therefore, the value of x is 10.

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(a) The expression for a Riemann sum of a function f on an interval [a, b] is Δx = (b-a)/n

(b) If f(x)⩾ 0, then the geometric interpretation of a Riemann sum is infinity

(c) If f(x) takes on both positive and negative values, then the geometric interpretation of a Riemann sum is infinity

Riemann sums are an important tool in calculus for approximating the area under a curve. They are used to estimate the value of a definite integral, which represents the area bounded by the curve and the x-axis on a given interval. In this explanation, we will discuss the expression for a Riemann sum, its notation, and its geometric interpretation.

(a) Expression for a Riemann sum:

A Riemann sum is an approximation of the area under a curve using rectangles. We divide the interval [a, b] into n subintervals, each of length Δx=(b−a)/n. The notation used to represent this is:

Δx = (b-a)/n

(b) Geometric interpretation of a Riemann sum when f(x)⩾ 0:

If f(x) is always non-negative, the Riemann sum represents an approximation of the area between the curve and the x-axis on the interval [a, b].

Each rectangle has a positive area, which contributes to the overall area under the curve. The sum of the areas of the rectangles approaches the true area under the curve as the number of subintervals n approaches infinity.

(c) Geometric interpretation of a Riemann sum when f(x) takes on both positive and negative values:

When f(x) takes on both positive and negative values, the Riemann sum represents the net area between the curve and the x-axis on the interval [a, b].

Each rectangle may have a positive or negative area, depending on the sign of f(xi).

The positive areas represent regions where the curve is above the x-axis, and the negative areas represent regions where the curve is below the x-axis.

In conclusion, Riemann sums are used to approximate the area under a curve on an interval [a, b]. The expression for a Riemann sum involves dividing the interval into n subintervals and approximating the area under the curve using rectangles.

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The simplified expression of the perimeter of the triangle is 3.75x - 7.

A triangle is a a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The perimeter of a triangle is the sum of the whole three sides.

Therefore, the simplified expression that represents the perimeter of the triangle is as follows:

Hence, the three sides of the triangle are as follows;

Hence,

perimeter of the triangle = 1.5x - 3 + 1.5x - 3 + 0.75x - 1

perimeter of the triangle = 1.5x + 1.5x + 0.75x - 3 - 3 - 1

perimeter of the triangle = 3.0x + 0.75x - 7

perimeter of the triangle = 3.75x - 7

Therefore, the simplified expression is 3.75x - 7

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Answer:

8, 10, 15, 16, 17, 17, 22

16 is the median

Step-by-step explanation:

Answer:

median is 16

Step-by-step explanation:

Answer:

10

13

15

17

22

Step-by-step explanation:

the first 5 terms will be 1,2,3,4 and 5.

I guess...

Answer:

a1 = 10

a2 = 13

a3 = 16

a4 = 19

a5 = 22

Step-by-step explanation:

Substitute in the value of  n  to find the  n

th term.

a1 = 3 (1) + 7

3 + 7 = 10

a2 = 3 (2) + 7

6 + 7 = 13

a3 = 3 (3) + 7

9 + 7 = 16

a4 = 3 (4) + 7

12 + 7 = 19

a5 = 3 (5) + 7

15 + 7 = 22

good luck, hope this helps :)

The probability that 75% or more of the women in the sample have been on a diet is approximately 0.063.

Sample size of a SRS of 267 college women has been given. It is stated that 70% of college women have been on a diet within the past 12 months and we are asked to find the probability that 75% or more of the women in the sample have been on a diet.

To find the required probability, we can use the binomial distribution since we have a sample with a binary outcome. Let X be the number of women in the sample who have been on a diet in the past 12 months. Then X follows a binomial distribution with n = 267 and p = 0.7.

The probability that 75% or more of the women in the sample have been on a diet can be found as follows:

P(X ≥ 0.75n) = P(X ≥ 200.25) ≈ 1 - P(X ≤ 200)

We use the normal approximation to the binomial distribution to estimate this probability.

μ = np = 267 × 0.7 = 186.9

σ = √(np(1 - p)) = √(267 × 0.7 × 0.3) ≈ 8.71

P(Z ≥ (200.25 - 186.9)/8.71) ≈ P(Z ≥ 1.526) = 1 - 0.937 = 0.063 (using a standard normal table)

Therefore, the probability that 75% or more of the women in the sample have been on a diet is approximately 0.063.

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What is the quotient?

StartFraction (negative 3) Superscript 0 Over (negative 3) squared EndFraction

Negative 9

StartFraction 1 Over 9 EndFraction

StartFraction 1 Over 9 EndFraction

9  

Answer:1/9

(-3)^0= 1

Answer:

A = 2k + 8

Step-by-step explanation:

so if Abby read 8 more then twice what Kristen read

she read 2k + 8 books

k = Kristen

A = Abby

Answer:

the answer is 5 lists

hope this helps

x+(12+x)=44

2x+12=44

2x=32

x=32/2

x=16  

The two numbers are 16, 28  

Hope I helped :)

Answer:

you can't find the square root of a negative

Step-by-step explanation:

A - Growth (25%)

B- Growth (75%)

C - Growth

D - Growth (100%)

E - Growth (99%)

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

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Answer:Sally would have 2 apples left

Step-by-step explanation:Because 4-2=2 so she gave 2 away so she has 2 left.

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Using the concepts of probability, we got that  0.063 is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time

We know very well that probability is defined as the fraction of number of favorable outcomes to the total number of outcomes.

Here, we are rolling a 6-faced dice.

Getting 3 on the top face of dice is same as the any number getting from 1 to 6 on the top face of the dice.

So, every number has equal probability to come on the top face,  therefore the probability of getting 3 on the top face of dice is (1/6)

Now, similarly total number of marbles in the bag=6 blue +3 black+8 orange marble=17 marbles.

Now, picking one marble from 17 marble is can be done in \(^1^7C_1\)  ways, similarly  choosing 1 blue marble from 6 marble can be done in \(^6C_1\) ways.

So, probability of picking 1 blue marble randomly=6/17

Now, the probability of picking 1 blue marble from 17 marbles along with rolling dice probability is given by =(6/17)×(1/6)=(1/17)=0.063

Hence, the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time is 0.063

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the depth perception cue based on the observation that parallel lines converge in the distance is that the depth perception cue based on the observation that parallel lines converge in the distance is known as linear perspective. This is a monocular cue, meaning it can be perceived with just one eye.

When looking at a scene, our brain uses the visual information provided by our eyes to determine depth and distance. Linear perspective is a cue that relies on the way that objects appear to shrink in size and converge towards a vanishing point as they move further away from the viewer. This is why parallel lines, such as the sides of a road or railway tracks, appear to meet at a point in the distance.

Linear perspective is a powerful visual cue that allows us to accurately perceive depth and distance in a scene. It is commonly used in art and architecture to create a sense of depth and realism, and is a crucial component of our visual perception.

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Answer:

I rounded to 1,591 rolls of toilet paper can fit. I have the big rolls so I may fit less than the average roll.

Step-by-step explanation:

87.96 SA Per roll

140,000 Volume for the closet.

No, because AB is 2/5 the length MN but CD is 1/3 the length QP.  

What is Dilation transformation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

Enlargement is the term used when a dilatation results in a bigger picture.

Reduction occurs when a dilatation results in a smaller picture.

Comparing the corresponding sides, the length of AB is 4. The length of MN is 10.  This makes their ratio 4/10 = 2/5.

The length of CD is 2. The length of QP is 6.  this makes their ratio 2/6 = 1/3.

The ratios of the sides are not the same, so the figure is not proportional and is therefore not a dilation.

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The one that belongs where the "x" is is "Oxygen is used up."

Answer:

Answer: D. 31⅔

\({ \rm{ \frac{2}{5} \: hours = 12 \frac{2}{3} \: ft {}^{2} }} \\ \\ { \rm{1 \: hour = ( \frac{5}{2} \times 12 \frac{2}{3}) \: {ft}^{2} }} \\ \\ = { \rm{ \frac{5}{2} \times \frac{38}{3} }} \\ \\ = { \rm{ \frac{95}{3} }} \\ \\ = { \rm{31 \frac{2}{3} }}\)

Answer:

3. 0

4. (0.5,1)

7. 0

Step-by-step explanation:

too lazy to calculate the rest liao