make r the subject of the formula: V=PI Rsquared H

Answer:

last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

Looks like we both struggle with geometry

The probability of selecting two blue marbles without replacement is 1/6, and the probability of selecting three blue marbles without replacement is 1/35. The fewest number of marbles that must have been in the bag before any were drawn is 36.

Let's assume there are x marbles in the bag. The probability of selecting two blue marbles without replacement can be calculated using the following equation: (x - 1)/(x) * (x - 2)/(x - 1) = 1/6. Simplifying this equation gives (x - 2)/(x) = 1/6. Solving for x, we find x = 12.

Similarly, the probability of selecting three blue marbles without replacement can be calculated using the equation: (x - 1)/(x) * (x - 2)/(x - 1) * (x - 3)/(x - 2) = 1/35. Simplifying this equation gives (x - 3)/(x) = 1/35. Solving for x, we find x = 36.

Therefore, the fewest number of marbles that must have been in the bag before any were drawn is 36.

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Answer:

two games must be won by the team

Step-by-step explanation:

Let the no. of games played by x, since  team

does not lose any more games.

Then total game won = 6+x

total game lost = 4

win: loss = 6+x : 4

given ratio of win and loss = 2:1

6+x : 4 = 2: 1

6+x = 8

=> x = 8-6 = 2

Thus, two games must be won by the team

then total win will be = 6+2 = 8

and loss = 4

ration of win : loss = 8:4 = 2:1

Answer: x= 95° ;  y= 35°

Step-by-step explanation:

If J II K (symmetrical), then x°= 180°- 85°

                                            x°= 95°

In addition to this, because the J II K lines are symmetrical:

                               (5y-90)°= 85°

                              5y°- 90° = 85°

                                       5y°= 85°+ 90°

                                      5y° = 175°

                                  5y°/ 5 = 175°/5

                                          y°= 35°

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

f(2) = -40

Step-by-step explanation:

Just substitute x=2 into the function:

f(x) = 2x³ - 3x² - 18x - 8

f(2) = 2(2)³ - 3(2)² - 18(2) - 8

f(2) = 2(8) - 3(4) - 36 - 8

f(2) = 16 - 12 - 44

f(2) = 4 - 44

f(2) = -40

Answer:

9 scoops

Step-by-step explanation:

3 scoops = 45g

3/45 scoops = 1g

3/45*135 scoops = 135g = 9 scoops

Answer:

∠ 2 = 160° , ∠ 3 = 10°

Step-by-step explanation:

The opposite angles of a rhombus are congruent , then

∠ 2 = ∠ 1 = 160°

The triangle has 2 congruent sides and is isosceles with base angles being congruent , then

∠ 3 = \(\frac{180-160}{2}\) = \(\frac{20}{2}\) = 10°

Answer:

m∠3 = 10° || m∠2 = 160°

Step-by-step explanation:

if  m∠1 =  160°

then m∠2 = 160°

The triangle is isosceles.

therefore

m∠3 + m∠3 + 160° = 180°

2 m∠3 = 180° - 160°

2 m∠3 = 20°

m∠3 = 10°

Answer:

The second one

Answer:

no solutions.

Step-by-step explanation:

2x - 3y = 1

-4x + 6y = -4

Simplifying our second equation, we get:

-4x + 6y. =-4

-2x + 3y = -2

2x - 3y = 2

From here, we can see that this system of equationis has no solutions because, how can 2x - 3y be equal to both 1, and 2???

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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The answer is option C: 109 shares. If the broker charges a set free of $7 per transaction. If the shares are worth $7.69/sh and you have $850 to invest 109 shares can you purchase.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To calculate the number of shares you can purchase, you need to subtract the broker's fee from the total amount you have to invest and then divide that by the share price:

$850 - $7 = $843 (the amount available to purchase shares)

$843 ÷ $7.69/share = 109.48

Since you cannot purchase a fraction of a share, you would be able to purchase 109 shares.

Therefore, the answer is option C: 109 shares.

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Answer:

14.45

Step-by-step explanation:

The original slope's reciprocal will be the opposite of the perpendicular slope. To determine the intercept, b, enter the supplied point and the new slope into the slope-intercept form (y = mx + b). Rewrite the following equation in standard form: ax + by = c.

The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

The slope is m and the y-intercept is b in the equation y=mx+b in slope-intercept form. Some equations can also be rewritten so that they resemble slope-intercept form. For instance, y=x can be written as y=1x+0, resulting in a slope and y-intercept of 1 and 0, respectively.

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Answer:

the second one on the top right

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

You can tell by where the line crosses the y-intercept as a positive, and the direction in which the line is going tells you it has a negative slope

The conclusion regarding the publisher's claim is that it is incorrect if the potential advertiser rejects the null hypothesis. A newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis.

What is a null hypothesis?

The null hypothesis is a fundamental idea in inferential statistics that represents the null assumption. It's frequently utilized to compare datasets and decide whether any differences between them are real or just by chance.

It is also called H0. It is the default theory that no difference exists between two tested populations or data sets.

A hypothesis test is a way of deciding whether the data supports or disproves the null hypothesis. If the null hypothesis is incorrect, it is referred to as a Type I error. If it is true and the data leads to its rejection, it is known as a Type II error.

Thus, after performing the test at the 0.02 level of significance, if the potential advertiser decides to reject the null hypothesis, the publisher's claim is incorrect.

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Answer:

  1

Step-by-step explanation:

The given ratio will be the remaining factor of 343 after factors of 7 have been removed. The value of interest is that factor, modulo 7.

  343 = 7·7·7 = 7³

The value of k is the power of 7 in the factorization of 343, so we have ...

  k = 3

and ...

  343/7³ = 1

The remainder when this ratio is divided by 7 is ...

  1 mod 7 = 1

The remainder when 343/7^k is divided by 7 is 1.

Answer: A not a triangle

Step-by-step explanation:

Answer:

Slope = \(-1\)

y-intercept = \(-2\)

Slope-intercept equation: \(y=-1x-2\)

Step-by-step explanation:

Let \(m\) equal slope.

Start with:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

For Point (0,-2):

\(x_1=0\), \(y_1=-2\)

For Point (-5,3):

\(x_2=-5\), \(y_2=3\)

Let's substitute those values in.

\(m=\frac{3-(-2)}{-5-0}\)

Rewrite.

\(m=\frac{3+2}{-5-0}\)

Combine like terms.

\(m=\frac{5}{-5}\)

Simplify.

\(m=-1\)

__

Let \(b\) equal the y-intercept.

Since we have our slope, let's format an equation as:

\(y=mx+b\)

Substitute.

\(y=-1x+b\)

We can use either point for this next part, let's use point (-5,3).

Since the numbers are representatives of both \(x\) & \(y\), we can substitute:

\(3=-1(-5)+b\)

Multiply.

\(3=5+b\)

Subtract \(5\) from both sides of the equation.

\(-2=b\)

Let's rewrite.

\(b=-2\)

__

Now that we have both our slope & y-intercept, let's put this into slope-intercept form.

\(y=mx+b\)

Substitute.

\(y=-1x-2\)

Answer: 5.7 (rounded)

Step-by-step explanation: The formula to find the diagonal of a square is \(\sqrt{2\) * a, where a is a side length on the square. Since we are solving for half of a diagonal, we use this formula and divide our result by two. We start by multiplying root 2 by 8 and we get 11.31371, next we divide by two and we get 5.656855 which is 5.7 when rounded.

The salt will acquire octahedral hole. Thus option B is correct .

Given,

\(r^{+} = 165\\ r^{-} = 297\)

Now,

Find the coordination number ,

Radius ratio = \(r^{+} / r^{-}\)

Substitute the values of radius of salt to get the coordination number .

Radius ratio = 165/297

Radius ratio = 0.556 .

If the radius ratio is between 0.414 and 0.732

Range of radius ratio : 0.414 < r < 0.732

Then coordination number is 6 . If the coordination number is 6 then it will acquire octahedral void .

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5.4p +13.1 = −2.6p+3.5 .

5.4p + 2.6p = 3.5 -13.1

8.0p = -9.6

p = -9.6 / 8

p = -1.2

The function that takes an input, adds 2, and then multiplies by 3 is a linear function with two operations: addition and multiplication. It can be represented by the equation y = 3(x + 2), where x is the input and y is the output.

To describe the function that adds 2 to the input and then multiplies by 3, we can break it down into two steps. First, we add 2 to the input, which can be represented by (x + 2). This expression ensures that the input is increased by 2.

The next step is to multiply the result by 3. Multiplying the expression (x + 2) by 3 gives us 3(x + 2). This step ensures that the increased input is further multiplied by 3.

Combining the two steps, we have the equation y = 3(x + 2), where y represents the output of the function. This equation indicates that the input (x) is first incremented by 2 and then multiplied by 3 to produce the final output (y).

Therefore, the function that takes an input, adds 2, and then multiplies by 3 can be described by the equation y = 3(x + 2).

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The probability that all 6 flips result in heads is 1/64

The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0

For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64

P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64

Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.

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The probability is approximately 52.54% or 31/59 when randomly choosing an element from the given subarray.

The probability of randomly selecting an array element within the subarray A[[n/2]], A[[n/2] + 1], ..., A[n] depends on the size of the subarray and the total number of elements in the array. In this case, n is given as 59.

The subarray A[[n/2]], A[[n/2] + 1], ..., A[n] includes the elements starting from the middle element, A[29], up to the last element, A[59]. Since the array has 59 elements, the subarray consists of 31 elements.

To determine the probability, we divide the size of the subarray (31) by the total number of elements in the array (59). Therefore, the probability is given by 31/59.

In decimal form, this probability is approximately 0.5254, which can be expressed as a percentage as approximately 52.54%.

Hence, the probability of randomly choosing an array element within the subarray A[[n/2]], A[[n/2] + 1], ..., A[n] when n = 59 is approximately 52.54%

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The probability that a randomly selected student is taking exactly one language class is 0.5045 or approximately 50.45%.

1. This is calculated by subtracting the number of students taking two or more classes from the total number of students, and then dividing by the total number of students.

2. To calculate this probability, we start by finding the total number of students taking at least one language class. This can be calculated by adding the number of students in each language class, and then subtracting the students who are taking multiple classes to avoid double counting. So, the total number of students taking at least one language class is: 42 + 32 + 29 - 13 - 8 - 10 + 4 = 76

3. Next, we can find the number of students taking exactly one language class by subtracting the students taking two or more classes from the total number of students taking at least one class. So, the number of students taking exactly one language class is: 76 - 13 - 8 - 10 + 4 = 49

4. Finally, we can calculate the probability of selecting a student taking exactly one language class by dividing the number of students taking exactly one class by the total number of students. So, the probability is: 49/111 ≈ 0.5045 or approximately 50.45%.

5. In summary, the probability of selecting a student taking exactly one language class is 0.5045 or approximately 50.45%. This probability is calculated by subtracting the number of students taking multiple classes from the total number of students, and then dividing by the total number of students. The calculation involves avoiding double counting of students taking multiple classes.

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