Dan is calculating the volume of two cylinders. Cylinder A has a radius of 2 feet and a height of 4 feet. Cylinder B also has a height of 4 feet, but the radius has been doubled. Which statement best describes the relationship between the volumes of the two cylinders? A) When the radius is doubled, the resulting volume is half the original volume. B) When the radius is doubled, the resulting volume is 2 times the original volume. C) When the radius is doubled, the resulting volume is 4 times the original volume. D) When the radius is doubled, the resulting volume is 8 times the original volume.

Answer:

6:40

Step-by-step explanation:

The statement which is true about the dilation is:

                        [tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]    

We know that the dilation transformation changes the size of the original figure but the shape is preserved.

The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.

The ratio of the corresponding sides of the two figure are equal.

i.e.

                 [tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]

No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.

Therefore, the null hypothesis would be:

H₀: µ₁ - µ₂ = 0

where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Now, We test this null hypothesis against the alternative hypothesis that the mean score on campus 1 is higher than on campus 2:

Hₐ: µ₁ > µ₂

Hence, if there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the mean scores of campus 1 and campus 2.

Thus, No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.

Therefore, the null hypothesis would be:

H₀: µ₁ - µ₂ = 0

where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.

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Answer:

9

Step-by-step explanation:

Answer with explanation:

Pottery is on a Kiln.

Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).

Unit of time is second, minute and hour.

Rate of change of temperature of the pottery over time can be written as

     [tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]

Internationally , Kelvin is used as S.I unit of Temperature.

So,Yanin can use

  [tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]

 as Rate of change of temperature of the pottery over time.

Answer:

Sunglasses

Step-by-step explanation:

Answer:

0.05

Step-by-step explanation:

Given :

Hair Color Boys Girls

Black          4                 5

Blonde          4                  6

Brown          10                 8

Red                  2                   1

Solution :

Since ware required to find the probability that a student is a boy with red hair.

Total no. of boys with red hair = 2

Total no. of students = 4+4+10+2+5+6+8+1=40

Thus the probability  that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]

⇒[tex]\frac{2}{40}[/tex]

⇒[tex]\frac{1}{20}[/tex]

⇒[tex]0.05[/tex]

Hence the probability that a student is a boy with red hair is 0.05

The student initially had 42 ounces of rice, bought 58 more for a total of 100 ounces. These were divided into 10 portions, so each portion will contain 10 ounces of rice.

This problem is a basic arithmetic question. The student starts with 42 ounces of rice and then adds 58 more ounces, for a total of 100 ounces. She then divides these 100 ounces into 10 equal portions. The key here is to understand the concept of division, which basically means splitting up a total amount (100 ounces) evenly into a certain number of parts (10 portions). To do this, simply use the operation of division: 100 divided by 10 equals 10. Thus, each portion will contain 10 ounces of rice.

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Answer:

Favorable Outcomes

Step-by-step explanation:

The equation of the line with a slope of -3/5 and a y-intercept of 7/10 is y = (-3/5)x + (7/10).

To write an equation of a line with a given slope (m) and y-intercept (0,b), we use the slope-intercept form of a linear equation which is y = mx + b. In this case, the slope is -3/5 and the y-intercept is 7/10.

Substituting these values into the slope-intercept formula, the equation of the line is y = (-3/5)x + (7/10).

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Answer:

The zeros to the quadratic equation are:

[tex]x= -4+\sqrt{\frac{41}{2}}\\\\x= -4-\sqrt{\frac{41}{2}}[/tex]

Step-by-step explanation:

A quadratic function is one of the form [tex]f(x) = ax^2 + bx + c[/tex], where a, b, and c are numbers with a not equal to zero.

The zeros of a quadratic function are the two values of x when [tex]f(x) = 0[/tex] or [tex]ax^2 + bx +c = 0[/tex].

To find the zeros of the quadratic function [tex]f(x)= 2x^2 + 16x -9[/tex] , we set [tex]f(x) = 0[/tex], and solve the equation.

[tex]2x^2+16x\:-9=0[/tex]

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\mathrm{For\:}\quad a=2,\:b=16,\:c=-9:\quad x_{1,\:2}=\frac{-16\pm \sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}\\\\x=\frac{-16+\sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}= -4+\sqrt{\frac{41}{2}}\\\\x=\frac{-16-\sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}= -4-\sqrt{\frac{41}{2}}[/tex]

(a) Calculate the standard error of the sample proportion.

(b) Determine the z-score for the sample proportion.

(c) Find the p-value for the given z-score.

To find the standard error, z-score, and P-value for the given test, follow these steps:

(a) Calculate the standard error using the formula:

[tex]\[ \text{Standard error} = \sqrt{\frac{p \times (1 - p)}{n}} \][/tex]

Given [tex]\( p = 0.50 \) (the population proportion) and \( n = 100 \) (the sample size), substitute these values into the formula:[/tex]

[tex]\[ \text{Standard error} = \sqrt{\frac{0.50 \times (1 - 0.50)}{100}} \]\[ = \sqrt{\frac{0.50 \times 0.50}{100}} \]\[ = \sqrt{\frac{0.25}{100}} \]\[ = \sqrt{0.0025} \]\[ = 0.05 \][/tex]

(b) Calculate the z-score using the formula:

[tex]\[ \text{z-score} = \frac{\text{sample proportion} - \text{population proportion}}{\text{standard error}} \]Given that the sample proportion is \( 0.47 \), substitute this value along with the previously calculated standard error into the formula:\[ \text{z-score} = \frac{0.47 - 0.50}{0.05} \]\[ = \frac{-0.03}{0.05} \]\[ = -0.6 \][/tex]

(c) Finally, find the P-value using a z-table or statistical software corresponding to the calculated z-score. The P-value represents the probability of observing a sample proportion at least as extreme as the one obtained, assuming the null hypothesis is true.

The quadratic equation 3x² − 15x + 20 = 0 has a radicand of -15, indicating no real solutions. The equation 3x² + 5x − 8 = 0 can be solved using the quadratic formula, yielding solutions of x = 1 and x = -8/3.

For the quadratic equation 3x² − 15x + 20 = 0, the radicand can be found as part of the quadratic formula process, which is b^2 - 4ac. Here, a=3, b= -15, and c=20. Substituting these values in, we get the radicand as (-15)² - 4(3)(20) = 225 - 240 = -15. Since the radicand is negative, this indicates that the equation has no real solutions; the solutions are complex numbers.

To solve the equation 3x² + 5x − 8 = 0, we will use the quadratic formula, x = −b ± √(b^2 - 4ac) / (2a), since we have a quadratic with a, b, and c all non-zero. Substituting a=3, b=5, and c= -8, we find the radicand to be (5)² - 4(3)(-8) = 25 + 96 = 121. Calculating further, x = (-5 ± √121) / 6, which simplifies to x = (-5 ± 11) / 6. Thus, we have two solutions: x = (11 - 5) / 6 = 1 and x = (-5 - 11) / 6 = -16/6 = -8/3.

Answer:

She's right the answer is a horizontal stretch.

There is a unique solution for a triangle with A=30 degrees, a=20 units, and b=16 units. By using the Law of Sines, sin(B) is computed as 0.4. Since there is no obtuse angle with the same sine, there is only one possible angle B, leading to one possible triangle.

To determine the number of possible solutions for a triangle with A=30 degrees, a=20 units (side opposite angle A), and b=16 units (another side), we need to apply the Law of Sines and explore the possible cases. According to the Law of Sines:

a/sin(A) = b/sin(B)

For the given values, we have:

20/sin(30 degrees) = 16/sin(B)

Calculating sin(B) gives us:

sin(B) = 16 * sin(30 degrees) / 20 = 8/20 = 0.4

Now, if sin(B) is less than 1, which it is in our case, there are two possible scenarios:

B is acute: There will be one solution for B, meaning B could be angle whose sine is 0.4.

B is obtuse: We must also check if there is a possible obtuse angle that also has a sine of 0.4. However, since the sine function is positive and less than or equal to 1 for angles between 0 and 180 degrees and it's symmetric with respect to 90 degrees, there can't be an obtuse angle with the same sine value as an acute angle.

Therefore, we only have one possible angle B, which implies we have a unique solution for the triangle.

Additionally, we should check whether side b is larger than the altitude from A; otherwise, there would be no solution for the triangle. To do this, we can use the extended Law of Sines to calculate the diameter (D) of the triangle's circumcircle:

D = a / sin(A)

And thus, the altitude (h) from A would be:

h = D * sin(B)

If b > h, we have a valid triangle and a unique solution.

There is exactly one possible solution for a triangle with the given side lengths a = 20, b = 16, and angle A = 30°.

To determine the number of possible solutions for a triangle given the side lengths a, b, and the angle A, we can use the Law of Sines. The Law of Sines states:

[tex]\[\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\][/tex]

where:

a, b, c - side lengths of the triangle

A, B, C - angles opposite to the respective sides

Given:

A = 30°

a = 20

b = 16

[tex]\[\frac{a}{\sin(A)} = \frac{b}{\sin(B)}\][/tex]

[tex]\[\frac{20}{\sin(30^\circ)} = \frac{16}{\sin(B)}\][/tex]

sin (B) = [tex]\frac{16 \times \sin(30^\circ)}{20}[/tex]

         = [tex]\frac{16 \times 0.5}{20}[/tex]sin

         = [tex]\frac{8}{20}[/tex]

         = 0.4

To find the angle B, we take the inverse sine:

B = [tex]\sin^{-1}(0.4)[/tex]

B = 23.58°

C = 180° - A - B

C = 180° - 30° - 23.58°

C = 126.42°

Now, let's check if the side lengths satisfy the triangle inequality theorem:

a + b > c

20 + 16 >

36 > c

Since 36 is greater than c, the triangle inequality theorem is satisfied.

So, there is exactly one possible solution for a triangle with the given side lengths a = 20, b = 16, and angle A = 30°.

Solution:

Independent Events:

Consider an experiment of Rolling a die, then getting an even number and multiple of 3.

Total favorable outcome = {1,2,3,4,5,6}=6

A=Even number = {2,4,6}

B=Multiple of 3 = {3,6}

A ∩ B={6}

P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]

P(A ∩ B)=[tex]\frac{1}{6}[/tex]

So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)

Hence two events A and B are independent.

Option (c). the outcome of one event does NOT determine the outcome of the other event

Answer:

C on edge or the outcome of one event does NOT determine the outcome of the other event

Step-by-step explanation:

Using synthetic division and the Remainder Theorem, we find that P(a) for P(x) when a=2 is P(2)=4, which is the remainder of the synthetic division.

To find P(a) for the given polynomial P(x)=x⁴+3x³-6x²-10x+8 when a=2, we can use synthetic division. The Remainder Theorem states that the remainder of the division of a polynomial by a linear divisor (x - a) is equal to P(a).

Let's perform the synthetic division:

The synthetic division should look like this:

The final number in the bottom row is the remainder, which is also P(2). So, P(2)=4.