5 cups of grape juice to 2 cups of apple juice
find the unit rate

Answer:

R = $ 40

Step-by-step explanation:

Answer:

$40 dollars

i ready

Answer:

Step-by-step explanation:

(-3,1) (5,3)

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{3-1}{5-(-3)}\\\\=\frac{2}{5+3}\\\\=\frac{2}{8}\\\\=\frac{1}{4}[/tex]

= 0.25

The correct value of the h function is; h= -9.8t² + 45t + 1

Answer:

Using the discriminant, no real solution exists and the baseball will not hit the roof.

Step-by-step explanation:

We are told the height is expressed as;h= -9.8t² + 45t + 1

Also that the Astrodome has a maximum height of 63.4 m

Thus, to find out if the baseball hit at a velocity of 45 m/s will hit the roof, we'll replace h with 63.4m.

Thus;

63.4 = -9.8t² + 45t + 1

Subtract 63.4 from both sides to give;

-9.8t² + 45t + 1 - 63.4 = 0

-9.8t² + 45t - 62.4 = 0

Using quadratic formula, we have;

t = -45 ± √{(45² - (4 * (-9.8) * (-62.4)}

t = -45 ± √(2025 - 2446.08)

t = -45 ± √(-421.08)

The discriminant is -421.08

This value is less than 0.

Thus, no real solution exists and the baseball will not hit the roof.

Answer:

C (x,-y)

Step-by-step explanation:

Answer:

x,-y

Step-by-step explanation:

It cannot transform across x axis unless it goes down to negative y.

In a graph we have 4 areas to fit a description of reflect accross an axis.

As this was x axis it can only be reflection negative y or reverse.

We cannot reverse this as the object has the positive y side of x

The image is the reflection or the transformation, and so this image is now negative y.

x-y= x object | y image = positive x = negative y.

Answer:

50

Step-by-step explanation:

The inside of a triangle equals 180 and so you subtract the other two values(100 and 30) to 180 and you get 50.

Answer:

50

Step-by-step explanation:

The sum of the angles of a triangle add to 180

A+B+C = 180

A + 100+ 30 = 180

A + 130= 180

Subtract 130 from each side

A+130-130= 180-130

A = 50

Answer:

Step-by-step explanation:

Given:

The volume of a cylinder is 30π cubic units.

A cone shares the same base.

The height of the cone is twice the height of the cylinder.

We need to determine the volume of the cone.

Height of the Cone:

Let h denote the height of the cylinder.

Let H denote the height of the cone.

Since, it is given that, the height of the cone is twice the height of the cylinder, we have;

H=2h

Volume of the cylinder:

The formula to determine the volume of the cylinder is

V=πr^2h

Since, volume of the cylinder is 30π , we get;

30π=πr^2-------(1)

Volume of the cone:

The formula to determine the volume of the cone is

v=1/3πr^2H

Substituting H=2h , we get;

v=1/3πr^2(2h)

v=1/3πr^2h

Substituting equation (1), we get;

V=2/3(30π)

v=20π

Thus, the volume of the cone is 20π

Answer:

The answer is 20pi

Step-by-step explanation:

Answer:

35x+5=10

Step-by-step explanation:

Answer:

B and C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A= very light

B= heavy

C= REALLY HEAVY

Answer:

y = f(x + 90)

Step-by-step explanation:

f(x)=Acos(Bx+C)+D,

A is the amplitude: A = 1

B is the 360/period: 360/360 = 1

D is the mean line: y = 0

f(-270) = 0

sin(x + C) = 0

-270 + C = -180

C = 90

y = f(x + 90)

Answer:

The two numbers are 5 and 12, the lesser is 5.

5 is the lesser number, therefore the answer. Hope this helped! :D

Answer: A, (y-1)^2/49-x^2/81=1

The given equations are both hyperbola equations with the center shifted to (0,1). They represent different graphs due to differences in their denominators. Hyperbola equations result in a graph of two separate curves, each one a mirror image of the other.

The equations (y-1)^2/49-x^2/81=1 and (y-1)^2/7-x^2/9=1 are both in the form of the hyperbola equation. This type of equation represents a graph that consists of two separate curves, each one a mirror image of the other, positioned about a central point called the center of the hyperbola. In these particular equations, the center of the hyperbola is shifted from the origin to the point (0,1).

Hyperbola equations are generally in the form (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/a^2 - (x-h)^2/b^2 = 1

However, even though these equations are in the form of hyperbolas, they do not represent identical graphs. In the first equation, the y term is divided by 49 and the x term by 81, whereas in the second, these denominators are 7 and 9. These denominator values affect the shape and orientation of the hyperbolae, leading to different graphical representations for each equation.

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Answer:

Tn = 64-4n

Step-by-step explanation:

The nth term of an AP is expressed as:

Tn = a+(n-1)d

a is the common difference

n is the number of terms

d is the common difference

Given the 6th term a6 = 40

T6 = a+(6-1)d

T6 = a+5d

40 = a+5d ... (1)

Given the 20th term a20 = -16

T20 = a+(20-1)d

T20 = a+19d

-16 = a+19d... (2)

Solving both equation simultaneously

40 = a+5d

-16 = a+19d

Subtracting both equation

40-(-16) = 5d-19d

56 = -14d

d = 56/-14

d = -4

Substituting d = -4 into equation

a+5d = 40

a+5(-4) = 40

a-20 = 40

a = 20+40

a = 60

Given a = 60, d = -4, to get the nth term of the sequence:

Tn = a+(n-1)d

Tn = 60+(n-1)(-4)

Tn = 60+(-4n+4)

Tn = 60-4n+4

Tn = 64-4n

Answer:

360 x 1/10 = 360/10 simplify is 36

36 degrees is 1/10

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

1.) not safe

2.)

[tex]18 \sqrt{3} [/tex]

Step-by-step explanation:

1.) given the length of the ladder = 15ft.

and the height to the top of ladder when leaned against a wall is 14.8ft. This all forms a right triangle.

with what we are given we can solve for the angle it creates from the ground to the leaned ladder by using the SOHCAGTOA. Whike we do this keep in mind its not safe for a ladder to create an angle more than 70 degrees.

in this case if we are solving for the angle where the height is opposite we will use SOH. because we know the oposite and the hyp. Sin(theta) = opp/hyp

[tex] \sin(theta) = \frac{14.8}{15} [/tex]

[tex]sin^{ - 1} ( \frac{14.8}{15} ) = 81 \: degrees[/tex]

therefore not safe.

2.)

your givin 90 and 60. remember all interior angles add up to 180.

therefore 30 would be the unknown angle.

knowing that we use the chart at the top.

across from 30 is 6. so we put that by x. (remember we are doing this to find the height for our area of a triangle formula = base time height devide by 2.)

we need to find the height so since we kmow what x is we know what is across from 60 which is

[tex]6 \sqrt{3} [/tex]

so we plug that into our formula for area of triangle and u should get 18

[tex] \sqrt{3} [/tex]

The area of the bedroom is 40 square feet, 10 square feet less than the area of the kitchen.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Given, Gavin is moving into a new apartment that has a kitchen with an area of 50 square feet.

Also given that the area of the kitchen is 10 square feet more than the area of the bedroom.

Let, The area of the bedroom be 'x' square feet.

Therefore, x + 10 = 50.

x = 50 - 10.

x = 40 square feet.

So, The area of the bedroom is 40 square feet.

learn more about rectangles here :

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Final answer:

The area of the bedroom is 40 square feet, calculated by subtracting 10 square feet from the kitchen's area of 50 square feet.

Explanation:

To find the area of the bedroom, we start with the area given for the kitchen, which is 50 square feet. The problem states that the kitchen is 10 square feet larger than the bedroom. Therefore, to find the area of the bedroom, we subtract the difference from the kitchen area.

Area of bedroom = Area of kitchen - 10 square feet

Area of bedroom = 50 square feet - 10 square feet

Area of bedroom = 40 square feet

The height of the cone (h) is approximately 12.8 centimeters to the nearest tenth of a centimeter.

To find the height of the cone (h) to the nearest tenth of a centimeter, we can follow these steps:

Calculate the radius (r) of the base:

The formula for the circumference of a circle is C = 2πr.

We are given the base circumference C = 44 cm.

Solving for r, we get: r = C / (2π) ≈ 7.07 cm (round to two decimal places).

Use the Pythagorean theorem to find the height (h):

The Pythagorean theorem states that a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

In this case, the slant height (16.2 cm) is the hypotenuse, and the radius (7.07 cm) and the height (h) are the legs.

Therefore, we can write the equation: 16.2² = 7.07² + h².

Solve for the height (h):

Rearranging the equation to isolate h, we get: h² = 16.2² - 7.07² ≈ 163.97 cm².

Taking the square root of both sides, we get: h ≈ 12.8 cm.

Round the height to the nearest tenth of a centimeter:

Rounding 12.8 cm to the nearest tenth gives us: h ≈ 12.8 cm (to the nearest tenth).

Therefore, the height of the cone (h) is approximately 12.8 centimeters to the nearest tenth of a centimeter.

Final answer:

The height of the cone is calculated using the base radius, found from the given base circumference, and applying the Pythagorean theorem with the slant height as the hypotenuse. The height comes out to be approximately 14.6 cm.

Explanation:

To calculate the height of the cone (h) given its slant height and base circumference, we first need to find the base radius (r) using the formula for the circumference of a circle: C = 2πr. Given that the base circumference is 44 cm, solving for r we get:

r = C / (2π)
 = 44 cm / (2 * 3.1416)
 ≈ 7 cm

Next, we use the Pythagorean theorem in the right-angled triangle formed by the radius, slant height, and the height of the cone. The slant height is the hypotenuse of the triangle, 16.2 cm in this case, and the opposite side to the angle at the cone's base is the height we need to find.

Using the formula h = √(slant height)^2 - (radius)^2, we substitute the values into the equation:

h = √(16.2 cm)^2 - (7 cm)^2
 = √262.44 cm^2 - 49 cm^2
 = √213.44 cm^2
 ≈ 14.6 cm

Therefore, the height of the cone, rounded to the nearest tenth, is 14.6 cm.

Answer:

2s = 16

Step-by-step explanation:

In the choir, there are 16 altos and s sopranos.

Let the number of altos be a.

=> a = 16

There are twice as many sopranos as altos.This means that:

a = 2s

Since the number of altos, a, is 16, the equation that represents this situation is:

2s = 16

An equation representing the number of sopranos in a choir, given the number of altos is s = 2 x 16, which simplifies to s = 32.

The question asks us to write an equation to represent the number of sopranos in a choir based on the number of altos. Given that there are 16 altos and the number of sopranos is twice as many, we can represent the number of sopranos as s. The relationship between the altos and sopranos can be expressed mathematically as s = 2 × 16. Therefore, the equation that represents this situation is s = 32, where s stands for the number of sopranos in the choir.

Answer: B.) x = 6

Step-by-step explanation:

Pythagoras Theorem a^2 +b^2 =c^2

Additionally divide 8 by 2 since it's an isosceles triangle and it's in the middle.

[tex]\sqrt{52}[/tex] ^2 - 4^2= x^2

52 - 16 = x^2

x^2 = 36

Square root both sides = 6

Answer: Tanyia lives 18 miles away from the airport.

Step-by-step explanation: First, I took $3.25(initial fee) away from $25.40(starting amount) which equals $22.15. Then, I subtracted -$9.35(How much money Tanyia had after the taxi ride)from $22.15 which came out to $31.50. Lastly, I divided $31.50 by $1.75(cost per mile) which came out to 18.

Hope this helps!

Answer:

Point C

Step-by-step explanation:

Answer:

3. C

Step-by-step explanation:

X before Y

We can solve it, but we can't actually use the interactive system they want you to use.  Let's see if we can guide you through it.

My guess is you can control the lines by dragging the two points on the line.

Let's make the green line y = 2x + 3

When x=0 we get y=3, point (0,3).   That's the y intercept, 3 up on the y axis.  Drag one green point there.

When x=2 we get y=7, point (2,7), two to the right, seven  up.  Drag the other green point there.   The green line is now y = 2x + 3.

Similarly the red line is made y = -3x + 3.    When x=0, y=3, point (0,3).  [Surprise!]   When x=2, y=-3, point (2,-3).  Drag the red points to (0,3) and (2,-3).

We already saw where they meet, at (0,3), x=0, y=3, the y intercept of both lines.

Answer: x=0, y=3

Final answer:

To rearrange the equation so x is the independent variable, add 4y to both sides and then divide by -5 to solve for x.

Explanation:

To rearrange the equation so x is the independent variable, we need to isolate x on one side of the equation. Let's start by adding 4y to both sides of the equation:

-5x - 4y + 4y = -8 + 4y

-5x = 4y - 8

Next, divide both sides of the equation by -5 to solve for x:

x = (4y - 8) / -5

So, the rearranged equation with x as the independent variable is:

x = (-4y + 8) / 5

Therefore, as per the explaination above,  the answer to the required question is x = (-4y + 8) / 5

Answer:

That makes no sense because there is no A and those measurements are not clear.

Step-by-step explanation:

Answer:

x = -1

y = -9

Step-by-step explanation:

7x - 3y = 20

7x - 3(5х – 4) = 20

7x - 15x + 12 = 20

-8x = 20 - 12

x = 8/-8

x = -1

7x - 3y = 20

7(-1) - 3y = 20

-7 - 3y = 20

-3y = 20 + 7

-3y = 27

y = 27/-3

y = -9

Answer:

60

Step-by-step explanation:

AB is 4 of 5 parts BC is i of 5 parts

75 divided by 5 = 15

75 minus 15=60

Answer:

The radius of a cone is the radius of its circular base. You can find a radius through its volume and height. Multiply the volume by 3.

Step-by-step explanation:

Answer:

The probability that [tex] \\ P(x<85)[/tex] is, approximately, 0.3594 or about 35.94% (or simply 36%).

Step-by-step explanation:

Firstly, we have to know that the random variable, in this case, is normally distributed. A normal distribution is completely determined by its two parameters,  namely, the population mean and the population standard deviation. For the case in question, we have a mean of [tex] \\ \mu = 89[/tex], and a standard deviation of [tex] \\ \sigma = 11[/tex].

To find the probability in question, we can use the standard normal distribution, a special case of a normal distribution with mean equals 0 and a standard deviation that equals 1.

All we have to do is "transform" the value of the raw score (x in this case) into its equivalent z-score. In other words, we first standardize the value x, and then we can find the corresponding probability.

With this value, we can consult the cumulative standard normal table, available in most Statistics textbooks or on the Internet. We can also make use of technology and find this probability using statistical packages, spreadsheets, and even calculators.

The corresponding z-score for a raw score is given by the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

And it tells us the distance of the raw score from the mean in standard deviations units. A positive value of the z-score indicates that the raw value is above the mean. Conversely, a negative value tells us that the raw score is below the mean.

With all this information, we are prepared to answer the question.

The corresponding z-score

According to formula [1], the z-score, or standardized value, is as follows:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

From the question, we already know that

x = 85

[tex] \\ \mu = 89[/tex]

[tex] \\ \sigma = 11[/tex]

Thus

[tex] \\ z = \frac{85 - 89}{11}[/tex]

[tex] \\ z = \frac{-4}{11}[/tex]

[tex] \\ z = -0.3636 \approx -0.36[/tex]

Consult the probability using the cumulative standard normal table

With this value for z = -0.36, we can consult the cumulative standard normal table. The entry for use it is this z-score with two decimals. This z-score tells us that the raw value of 85 is 0.36 standard deviations below from the population mean.

For z = -0.36, we can see, in the table, an initial entry of -0.3 at the first column of it. We then need to find, in the first line (or row) of the table, the corresponding 0.06 decimal value remaining. With this two values, we can determine that the cumulative probability is, approximately:

[tex] \\ P(x<85) = P(z<-0.36) = 0.3594[/tex]

Then, [tex] \\ P(x<85) = 0.3594[/tex] or, in words, the probability that [tex] \\ P(x<85)[/tex] is, approximately, 0.3594 or about 35.94% (or simply 36%).

Remember that this probability is approximated since we have to round the value of z to two decimal places (z = -0.36), and not (z = -0.3636), because of the restrictions to two decimals places for z of the standard normal table. A more precise result is [tex] \\ P(x<85) = 0.3581[/tex] using technology, shown in the graph below.

Notice that, in the case that the cumulative standard normal table does not present negative values for z, we can use the next property of the normal distributions, mainly because of the symmetry of this family of distributions.

[tex] \\ P(z<-a) = 1 - P(z<a) = P(z>a)[/tex]

For the case presented here, we have

[tex] \\ P(z<-0.36) = 1 - P(z<0.36) = P(z>0.36)[/tex]

[tex] \\ P(z<-0.36) = 1 - 0.6406 = P(z>0.36)[/tex]

[tex] \\ P(z<-0.36) = 0.3594 = P(z>0.36)[/tex]

Which is the same probability obtained in the previous step.

The graph below shows the shaded area for the probability of  [tex] \\ P(x<85)[/tex] finally obtained.  

Final answer:

To find P(x<85), calculate the z-score and use the standard normal distribution to find the cumulative probability. Susan's z-score for her final exam is 2, meaning her performance was significantly above the average. The central limit theorem helps to analyze the mean of large sample sizes, while binomial distributions apply to scenarios such as analyzing a basketball player's field goal completion rate.

Explanation:

Finding Probability in a Normal Distribution

To find the probability P(x<85) when the number of points scored by each team in the NHL at the end of the season is normally distributed with a mean (μ) of 89 and a standard deviation (σ) of 11, we use the standard normal distribution. First, we calculate the z-score for x=85, which is the value for which we want to find the cumulative probability. The z-score is calculated using the formula z = (x - μ) / σ. Substituting the given values, we get z = (85 - 89) / 11 = -0.3636. Then we look up this z-score in the standard normal distribution table or use a calculator or software to find the cumulative probability associated with this z-score.

To express the number 13.7 in terms of the mean and standard deviation of the given data, you would use the formula for the z-score again.

If Susan's biology class has a mean final exam score of 85 and a standard deviation of 5, and Susan scored a 95 on her final exam, her z-score would be z = (95 - 85) / 5 = 2. This means Susan's score is 2 standard deviations above the mean, indicating she performed significantly better than the average student.

When dealing with sample sizes larger than one, the central limit theorem tells us that the sampling distribution of the sample mean will tend to be normal regardless of the shape of the population distribution, especially as the sample size increases (typically n > 30 is considered large enough). This is reflected in the examples involving the estimation of mean final exam scores and calculating probabilities with a sample size of 55.

The probability distribution question for the basketball player's shots would involve the binomial distribution, where the probability of success is given by the player's field goal completion rate. The mean and standard deviation for this binomial distribution can be calculated using the formulas for a binomial distribution.