I will give brainliest to the fastest answer and correct!

The standard equation of the parabola is:

The focus of the parabola, (h, f) = (-3, 3)

The directrix: y = 0

The equation of a parabola is of the form:

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix

f - k = k - y

3 - k = k - 0

k + k = 3 + 0

2k = 3

k = 3/2

Substitute k = 3/2, f = 3, and h = -3 into the equation above

This can be further simplified as:

Therefore, the standard equation of the parabola is:

Answer:

The function f(x) = cos^2x + sin^2x is not a straight line, but rather a constant function that always evaluates to 1 for any value of x.To see why this is the case, recall the trigonometric identity that states that the square of the cosine of an angle added to the square of the sine of the same angle equals 1:cos^2x + sin^2x = 1Since this identity holds for all values of x, it follows that f(x) = 1 for all x. Therefore, the graph of this function is a horizontal line at y = 1, not a straight line.

Step-by-step explanation:

Answer:

5000 lbs

Step-by-step explanation:

if there ae 8 boxes and each one has the weight of 625 you will need to ultiply 8 by 625 and that will be 5000 pounds

Answer:

88 inches

Step-by-step explanation:

Divide the shape into 2 shapes and add all side lengths.

20+8+8+16+12+24=88

Answer:

The answer is $55 =$4x * $2y

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

if it is higher the 3 as you stated it would most likely be b because of it being higher than three so prosecss of elimination you would get b

The stretch of an exponential decay function is y = 2(1/5)ˣ

From the question, we have the following parameters that can be used in our computation:

The list of exponential functions

An exponential function is represented as

y = abˣ

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/5)ˣ

Hence, the exponential decay function is y = 2(1/5)ˣ

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Complete question

Which is a stretch of an exponential decay function?

Of(x) = -(5)ˣ

Of(x) = 5(2)ˣ

O fix) = 2(1/5)ˣ

The question asks us to find the volume of the solid when a region bounded by the given lines is rotated around the y-axis.

Here's how we can do it:

First, we need to sketch the region. The region is a parabola y = 3x^2 bounded by y = 10 and x = 0 (y-axis).

The sketch of the region is given below: Sketch of the region

Then, we need to rotate this region around the y-axis to obtain a solid. When we do so, we get a solid as shown below:

Solid obtained by rotating the region

We need to find the volume of this solid. To do so, we can use the washer method.

According to the washer method, the volume of the solid obtained by rotating a region bounded by

y = f(x), y = g(x), x = a, and x = b about the y-axis is given by:

\($$\begin{aligned}\pi \int_{a}^{b} (R^2 - r^2) dx\end{aligned}$$\)

where R is the outer radius (distance from the y-axis to the outer edge of the solid), and r is the inner radius (distance from the y-axis to the inner edge of the solid).

Here, R = 10 (distance from the y-axis to the top of the solid) and r = 3x² (distance from the y-axis to the bottom of the solid).Since we are rotating the region about the y-axis, the limits of integration are from y = 0 to y = 10 (the height of the solid).

Therefore, we need to express x in terms of y and then integrate.

To do so, we can solve y = 3x²  for x:

\($$\begin{aligned}y = 3x^2\\x^2 = \frac{y}{3}\\x = \sqrt{\frac{y}{3}}\end{aligned}$$\)

Therefore, the volume of the solid is:

\($$\begin{aligned}\pi \int_{0}^{10} (10^2 - (3x^2)^2) dy &= \pi \int_{0}^{10} (10^2 - 9y^2/4) dy\\&= \pi \left[10^2y - 3y^3/4\right]_{0}^{10}\\&= \pi (1000 - 750)\\&= \boxed{250 \pi}\end{aligned}$$\)

Therefore, the volume of the solid obtained by rotating the region bounded by y = 3x² , y = 10, and x = 0 about the y-axis is 250π cubic units.

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Given function: y = 3x², y = 10, x = 0,

The region is bounded by y = 3x², y = 10, and x = 0 about the y-axis.To calculate the volume of the solid formed by rotating the region bounded by y = 3x², y = 10, and x = 0 about the y-axis, we must first create a sketch and then apply the formula for volume.

Let's begin the solution:

Solve for the intersection points of the equations:y = 3x² and y = 10 3x² = 10 x² = 10/3 x = ± √(10/3)y = 10 and x = 0 These values will be used to create the sketch.

Sketch:The figure that follows is the region bounded by the curves y = 3x², y = 10, and x = 0, and it is being rotated around the y-axis.
[asy] import graph3; size(250); currentprojection=orthographic(0.7,-0.2,0.4); currentlight=(1,0,1); draw(surface((3*(x^2),x,0)..(10,x,0)..(10,0,0)..(0,0,0)..cycle),white,nolight); draw(surface((3*(x^2),-x,0)..(10,-x,0)..(10,0,0)..(0,0,0)..cycle),white,nolight); draw((0,0,0)--(12,0,0),Arrow3(6)); draw((0,-4,0)--(0,4,0), Arrow3(6)); draw((0,0,0)--(0,0,12), Arrow3(6)); label("$x$",(12,0,0),(0,-2,0)); label("$y$",(0,4,0),(-2,0,0)); label("$z$",(0,0,12),(0,-2,0)); draw((0,0,0)--(9.8,0,0),dashed); label("$10$",(9.8,0,0),(0,-2,0)); real f1(real x){return 3*x^2;} real f2(real x){return 10;} real f3(real x){return -3*x^2;} real f4(real x){return -10;} draw(graph(f1,-sqrt(10/3),sqrt(10/3)),red,Arrows3); draw(graph(f2,0,2),Arrows3); draw(graph(f3,-sqrt(10/3),sqrt(10/3)),red,Arrows3); draw(graph(f4,0,-2),Arrows3); label("$y=3x^2$",(2,20,0),red); label("$y=10$",(3,10,0)); dot((sqrt(10/3),10),black+linewidth(4)); dot((-sqrt(10/3),10),black+linewidth(4)); dot((0,0),black+linewidth(4)); draw((0,0,0)--(sqrt(10/3),10,0),linetype("4 4")); draw((0,0,0)--(-sqrt(10/3),10,0),linetype("4 4")); [/asy]

We can see that the region is a shape with a height of 10 and the bottom of the shape is bounded by y = 3x². We may now calculate the volume of the solid using the formula for the volume of a solid obtained by rotating a region bounded by curves about the y-axis as follows:V = ∫aᵇA(y) dywhere A(y) is the area of a cross-section and a and b are the bounds of integration.

In this instance, the bounds of integration are 0 and 10, and A(y) is the area of a cross-section perpendicular to the y-axis. It will be a circular area with radius x and thickness dy, rotating around the y-axis.  The formula to be used is A(y) = π x².

By using the equation x = √(y/3), we can write A(y) in terms of y as A(y) = π (y/3). Hence,V = π ∫0¹⁰ [(y/3)]² dy = π ∫0¹⁰ [(y²)/9] dyV = π [(y³)/27] ₀¹⁰ = π [(10³)/27] = (1000π)/27

Therefore, the volume of the solid obtained by rotating the region bounded by y = 3x², y = 10, and x = 0 about the y-axis is (1000π)/27 cubic units.

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The statement which identifies Melissa’s error and the correct answer is; Melissa added incorrectly. The correct answer is 4.5°F

New temperature = Initial temperature + (Change in temperature per × Number of hours)

= -20.5°F + (5°F × 5)

= -20.5°F + (25°F)

= 4.5°F

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Answer:

C

Step-by-step explanation:

The conditional probability that a student is studying Spanish given that he or she is studying some language other than English is 0.634.

What is conditional probability?

Conditional probability is a metric for determining the likelihood of an event happening provided that another event has already happened.

According to the given question:

From the image we can see the probability of studying different languages.

Given probability of studying no languages is P(none) = 0.59

From this we can find the probability of studying another language using complement rule = 1 - P(none) = 1 - 0.59 = 0.41

It is given probability of studying Spanish P(Spanish) = 0.26

So the conditional probability of studying Spanish

= P(Spanish) / P(Studying another language)

= 0.26/0.41 = 0.634

Therefore  the conditional probability that a student is studying Spanish given that he or she is studying some language other than English is 0.634.

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Answer:

10/12 also 5/6

Step-by-step explanation:

Answer:

10/12 or the simplified version 5/6

Step-by-step explanation:

you have to multiply 2/3 by the reciprocal of 4/5 which is 5/4

so you write down 2/3 times 5/4 (just multiply across so it's 2x5 over 3x4)

2x5=10 and 3x4=12

10 is the numerator and 12 is the denominator

simplify if the problem calls for it by dividing the top and bottom numbers by 2

Answer:

Yes, Osvoldo met his goal of getting at least 30% of his carbs from whole grains.

Step-by-step explanation:First, we need to find out what 30% of 220 grams of carbohydrates is. To do that, we multiply 220 by 0.3 (which is the same as 30%). That gives us 66 grams of carbohydrates that should come from whole grains.

Next, we need to see how many grams of carbohydrates Osvoldo actually ate from whole grains. That's 555 grams.

Finally, we just need to compare the two numbers. Since 555 is greater than 66, Osvoldo met his goal of getting at least 30% of his carbs from whole grains.

Answer:

y=26 over3

Step-by-step explanation:

-2/3+y=8

y-2/3=8

add 2/3 to both sides

y-2/3+2/3=8+2/3

Simplify:

y=26 over3

The limit of the sequence bn is ln(1.7)*e^(0) = ln(1.7). Therefore, the limit of the sequence bn is ln(1.7) or approximately 0.5306.

To use the given fact and l'Hopital's rule to compute the limit of the sequence bn = (n)*1.7, we can rewrite the sequence as bn = (n)/(1/1.7) and use the fact that the limit of n/(1/1.7)^n is 0 as n approaches infinity (since the exponential term grows much faster than n).

Applying l'Hopital's rule, we can take the derivative of the numerator and denominator separately to get:

bn = (n)/(1/1.7)^n = (1)/(1/1.7)^n-1/(1/1.7)

Taking the derivative of the numerator and denominator yields:

= -ln(1/1.7)/(1/1.7)^n

= ln(1.7)/(1/1.7)^n

Since the limit of (1/1.7)^n approaches infinity as n approaches infinity, we can use the given fact to conclude that the limit of the sequence bn is ln(1.7)*e^(0) = ln(1.7). Therefore, the limit of the sequence bn is ln(1.7) or approximately 0.5306.

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Answer:

y = 4/3x -11

Step-by-step explanation:

y = -3/4 x - 8

This is in slope intercept form  

y = mx+b where the slope is -3/4

We want a slope that is perpendicular

Take the negative reciprocal

-1 ( -3/4) = 4/3

The slope of the line that is perpendicular is 4/3

Using the slope intercept form of a line is

y = mx+b

y = 4/3x+b

Substituting the point into this equation

-3 = 4/3(6) +b

-3 = 8+b

Subtract 8 from each side

-3-8 = b

-11 =b

y = 4/3x -11

The required measures are :

the length of the rectangle is equal to 5 + x = 5 + 5 = 10 inches

the breadth of the rectangle = x = 5 inches

Given that perimeter of the rectangle is equal to 30 inch

Let the width be x

thus the length will become 5 + breadth = 5 + x

As we know that the perimeter of rectangle can be calculated by the formula

perimeter = 2 ( length + breadth )

perimeter = 2 ( 5 + x + x )

30 = 10 + 2x + 2x

Bringing the like terms together and we will get

30 - 10 = 4x

this implies

20 = 4x

On dividing 4 on both sides and we will get

5 = x

Thus the length of the rectangle is equal to 5 + x = 5 + 5 = 10 inches

And the breadth of the rectangle = x = 5 inches

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Answer:

324?

Step-by-step explanation:

a. You will pay $24.b. People might think that 25% off followed by 30% off is 55% off because they are adding the two percentages together.

However, this is not correct. When you take multiple discounts, you need to multiply the percentages together. In this case, the overall percentage is 42.5%.To calculate the final price, we can use the following formula:

Final price = Original price * (1 - Discount 1) * (1 - Discount 2)

Where:

The final price is the price you will pay

The original price is the price of the item

Discount 1 is the first discount

Discount 2 is the second discount

In this case, the original price is $40, the first discount is 25%, and the second discount is 30%.

Final price = $40 * (1 - 0.25) * (1 - 0.30)

Final price = $24

As you can see, the final price is $24. This is because the overall percentage is 42.5%.

People might think that 25% off followed by 30% off is 55% off because they are adding the two percentages together. However, this is not correct. When you take multiple discounts, you need to multiply the percentages together. In this case, the overall percentage is 42.5%.

To convince people that 25% off followed by 30% off is not 55% off, you can use the following analogy. Imagine that you have a $100 bill and you take 25% off. This means that you will have $75 left. Now, imagine that you take another 30% off of the $75. This means that you will have $52.50 left. As you can see, the overall percentage is not 55%. It is 42.5%.

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Answer:

The distance between the points is approximately 6.4

Step-by-step explanation:

The given coordinates of the points are;

(2, -2), and (6, 3)

The distance between two points, 'A', and 'B', on the coordinate plane given their coordinates, (x₁, y₁), and (x₂, y₂) can be found using following formula;

\(l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}\)

Substituting the known 'x', and 'y', values for the coordinates of the points, we have;

\(l_{(2, \, -2), \ (6, \, 3) } = \sqrt{\left (3-(-2) \right )^{2}+\left (6-2 \right )^{2}} = \sqrt{5^2 + 4^2} = \sqrt{41}\)

Therefore, the distance between the points, (2, -2), and (6, 3) = √(41) ≈ 6.4.

Answer:

The fourth option - t = 3, y = 5

Step-by-step explanation:

-8 + t becomes -5, thus t is 3 since -8 + 3 = -5.

-12 becomes -2y - 2, so we can set these equal to each other as -2y - 2 = -12 and solve from there. Add 2 to both sides, -2y = -10, then divide by -2 on both sides, y = 5.

The value of t is 3.

the value of y is 5.

please see the attached picture for full solution

hope it helps

Good luck on your assignment

Answer:

115.52 m³

Step-by-step explanation:

As per given question we have provided that :

We need to find the volume of cylinder :

Substituting all the given values in the formula to find the volume of cylinder :

\({\longrightarrow{\sf{Volume_{(Cylinder)} = \pi {r}^{2}h}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} = \pi{(3.8)}^{2}8}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} = \pi{(3.8 \times 3.8)}8}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} = \pi{(14.44)}8}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} = \pi \times 14.44 \times 8}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} = \pi \times 115.52}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)} = 115.52 \pi \: {m}^{3}}}}\)

\({\star\underline{\boxed{\sf{\pink{Volume_{(Cylinder)}} = \purple{115.52 \pi \: {m}^{3}}}}}}\)

Hence, the volume of cylinder is 115.52 m³.

\( \rule{200}2\)

Answer:

It will add 20

Step-by-step explanation:

If the mean is 50, we can make the guess that maybe there are 10 children with all 50. If we add 20 then the mean becomes 70.

Answer

3.7 or approximately 4 gallons

Step-by-step explanation:

7x2=14 total liters.

3.78 liters=1 gallon

14/3.78= 3.7 gallons

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

A negative correlation means that as the x variable decreases, the y variable tends to decrease as well. In other words, there is an inverse relationship between the two variables.

A negative correlation indicates that when the value of one variable decreases, the value of the other variable also tends to decrease. It implies an inverse relationship between the two variables. For example, if we consider the variables "temperature" and "ice cream sales," a negative correlation would mean that as the temperature decreases, the sales of ice cream also tend to decrease.

To determine the strength of a negative correlation, we can calculate the correlation coefficient, often denoted by "r." The correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation. The closer the value of "r" is to -1, the stronger the negative correlation between the variables.

In summary, a negative correlation suggests that as the x variable decreases, the y variable tends to decrease as well. It signifies an inverse relationship between the two variables. The strength of the negative correlation can be measured using the correlation coefficient, where values closer to -1 indicate a stronger negative correlation.

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Answer: y=-3x+5

Step-by-step explanation:

6x+2y=10

Solve for y

2y=-6x+10

y=-3x+5

Answer: y = -3x + 5

Step-by-step explanation:

Slope intercept form is y = mx + b so all you need to do is put the equation into that format.

6x + 2y = 10

2y = 10 - 6x

y = -3x + 5

Answer:

Step-by-step explanation:

Step-by-step explanation:

Familiarize yourself with perfect squares in the neighborhood of 140:

10^2 = 100

11^2 = 121

12^2 = 144

Note that 140 is much closer to the perfect square than it is to the perfect square 121.  The value of √140 must lie closer to 12 than to 11.

Place a point on the number line about 3/4 of the way from 11 to 12.