In a solid cube made up of smaller black and white cubes. The black and white cubes are at alternate places of the larger cube. How many black cubes are there in the above arrangement?

The area between the large loop and the enclosed small loop of the curve r=24cos(3) is approximately 8.75 square units.

To find the area between the large loop and the enclosed small loop, we need to first determine the values of θ where the loops occur. The polar equation r=24cos(3) has two loops, with the smaller loop enclosed within the larger one. The smaller loop occurs when cos(3)=0, which happens when theta is a multiple of π/6. The larger loop occurs when r=0, which happens when cos(3)=-1/2 or when theta is a multiple of π/3. To calculate the area between the loops, we can integrate the area of the sector between two adjacent θ values and subtract the area of the smaller loop from the larger loop. This gives us an approximation of 8.75 square units for the area between the loops. The actual value can be obtained by using calculus to calculate the definite integral of the difference in the areas of the two loops.

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Answer:

Explanation;

Here, we want to get the probability of rolling either a 6 or an even number

If we roll a die, there are 6 possible results, that is 1 to 6

The number of 6 we have is 1. So the probability of rolling a 6 will be 1/6

The even numbers we have are 2,4,6.

The probability of rolling a even number is the count of even numbers divided by the total count of numbers

We have this as 3/6

Since we have or as the condition, we will have to add the two probabilities from above

We have this as:

Answer:

$6 left

Step-by-step explanation:

since she saved up for 10 weeks= 3*10
$30-$24(price of the shirt)

=$6

Answer:

Step-by-step explanation:

since its a horizontal parabola opening to the right we use a formula for the directrix

 x=h-p 4p=5/4 p=5

X= -3 v(h,k)=(2,0)

 The integral \(\int {ln(x^{14})/x^2\ dx\) converges to \(f'(x) = (14/x^3) - (2/x^{15}) = (14x^{12} - 2)/x^{15}\)

To determine if the integral \(\int {ln(x^{14})/x^2 dx\)converges or diverges, we can use the integral test.

The integral test states that if f(x) is a continuous, positive, and decreasing function for x ≥ a, then the improper integral ∫a to infinity f(x) dx converges if and only if the infinite series ∑a to infinity f(n) converges.

Let \(f(x) = ln(x^{14})/x^2\). Then,

\(f'(x) = (14/x^3) - (2/x^{15}) = (14x^{12} - 2)/x^{15}\)

f'(x) is positive for x > 0, so f(x) is a decreasing function for x > 0. Also, since \(ln(x^{14}) \leq x^14\ for\ x > 0\), we have

\(0 \leq f(x) = ln(x^{14})/x^2 \leq x^{12}\ for\ x > 0\).

The integral \(\int\limits^{\infinity}_1 {x^{12}} \, dx\) converges (by the p-test with p = 12 > 1), so by comparison, the integral \(\int\limits^{\infinity}_1 {f(x)} \, dx\) converges.

Therefore, the integral \(\int {ln(x^{14})/x^2} dx\) converges.

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Answer: 4)90˚

Step-by-step explanation:

(90˚ is more towards the middle

A regular octagon is a shape with 8 congruent sides.

The minimum angle of rotation is 45 degrees

The number of sides of a regular octagon is:

\(\mathbf{n = 8}\)

The total angle at the center of the regular octagon is:

\(\mathbf{\theta = 360}\)

So, the minimum angle of rotation is calculated as follows:

\(\mathbf{\alpha = \frac{\theta}{n}}\)

This gives

\(\mathbf{\alpha = \frac{360}{8}}\)

\(\mathbf{\alpha = 45}\)

Hence, the minimum angle of rotation is 45 degrees

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Answer:

Just simply look up how to find the volume of a prism and the answer will immediately come to your head you'll get the right answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(3(* + 4) - 2 (1 - 1);\\\\3(\times +4)-2(1-1)\\\\3\left(4\right)-2\left(1-1\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=3\times \:4-2\left(1-1\right)\\\\3\times \:4=12\\2\left(1-1\right)=0\\\\=12-0\\\\=12\)

The group of volunteers can make a total of 200 masks out of 25 yards of fabric.

To calculate the number of masks that can be made, we divide the total amount of fabric (25 yards) by the amount of fabric required per mask (1/8 yard). To do this, we first convert the fraction 1/8 to decimal form, which is 0.125. Then, we divide the total fabric (25 yards) by the fabric required per mask (0.125 yards). This can be done by dividing 25 by 0.125, which equals 200. Therefore, the group of volunteers can make a total of 200 masks out of 25 yards of fabric. Each mask requires 1/8 yard of fabric, so dividing the total fabric by the fabric required per mask gives us the total number of masks that can be made.

Calculation steps:
1. Convert the fraction 1/8 to decimal form: 1/8 = 0.125.
2. Divide the total fabric (25 yards) by the fabric required per mask (0.125 yards):
  25 / 0.125 = 200.


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To use the normal approximation for a test of two proportions, n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2) must all be greater than or equal to 5.

This is because the normal distribution assumes that the sample size is large enough to approximate the binomial distribution, and the rule of thumb is that each cell (n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2)) should have at least 5 expected counts. If any of these cells have fewer than 5 expected counts, then the normal approximation is not reliable and a more appropriate test should be used. It is important to note that this is just a rule of thumb, and other factors such as the size of the effect and the desired level of significance should also be considered when deciding on a statistical test.

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To verify the identity sin(θ) / 1-cos^2θ = cosθ, we start by manipulating the left-hand side of the equation using trigonometric identities. We can use the Pythagorean identity cos^2θ + sin^2θ = 1 to rewrite the denominator as 1-sin^2θ. Then, using the reciprocal identity sinθ/cosθ = tanθ, we can simplify the left-hand side to 1/cosθ.

We can start by manipulating the left-hand side of the equation using trigonometric identities:

sin(θ) / (1-cos^2θ)

= sin(θ) / sin^2θ (using the Pythagorean identity cos^2θ + sin^2θ = 1)

= 1/cosθ (using the reciprocal identity sinθ/cosθ = tanθ)

Now, we can simplify the right-hand side using the definition of cosine:

cosθ = cosθ/1 (multiplying numerator and denominator by 1)

= sin^2θ/cosθsinθ (using the definition of sine and cosine: sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse)

= sinθ/sin^2θ (using the Pythagorean identity cos^2θ + sin^2θ = 1)

= 1/cosθ (using the reciprocal identity sinθ/cosθ = tanθ)

Therefore, we have shown that:

sin(θ) / (1-cos^2θ) = cosθ

The identity is verified.

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Among the given alternatives, the following option accurately describes the expected frequencies for a chi-square test: They can contain fractions or decimal values.

The answer is B.

A chi-square test is a statistical method used to measure the relationship between two categorical variables. The null hypothesis for a chi-square test is that there is no relationship between the variables.

The expected frequency (EF) is the number of times an outcome is expected to occur during a trial based on probabilities. In a chi-square test, the expected frequencies are calculated based on probabilities and sample sizes.

The expected frequency can be a fraction or a decimal, and it is determined by multiplying the row total and column total of each cell by the overall total and dividing it by the total number of observations.

The chi-square test statistic is calculated by comparing the observed frequencies to the expected frequencies. The test statistic is then compared to a critical value in a chi-square distribution table to determine whether to accept or reject the null hypothesis.

Hence, the answer of the question is B.

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It can be expect approximately 7.61 inches of rain for the rest of the month of April.

To determine how much more rain can be expected for the rest of the month, we need to calculate the total rainfall recorded for the three days and subtract it from the average rainfall for April.

The total rainfall recorded for the three days is:

1.25" + 0.7" + 3.09" = 5.04"

The average rainfall for April is given as 12.65".

To find how much more rain can be expected for the rest of the month, we subtract the total recorded rainfall from the average rainfall:

12.65" - 5.04" = 7.61"

Therefore, you can expect approximately 7.61 inches of rain for the rest of the month of April.

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The correct question is:

Neil recorded the amount of rain that fell over the course of 3 days in April on one day he recorded 1.25" on day 2 he recorded 0.7" and on day 3 he recorded 3.09" the average rainfall for April is 12.65" how much more rain can you expect this month?

To evaluate the expression ∫x f(x) f''(x) dx, we need the information about f'(x) and f''(x). Given that f'(1) = -1, f'(5) = 3, f''(1) = 4, and f''(5) = 7, we can compute the integral using the Fundamental Theorem of Calculus.

The Fundamental Theorem of Calculus states that if F(x) is an antiderivative of f(x), then ∫a to b f(x) dx = F(b) - F(a). In this case, we have the function f(x) and its derivatives f'(x) and f''(x) evaluated at specific points.

Since we don't have the function explicitly, we can use the given information to find the antiderivative F(x) of f(x). Integrating f''(x) once will give us f'(x), and integrating f'(x) will give us f(x).

Using the given values, we can integrate f''(x) to obtain f'(x). Integrating f'(x) will give us f(x). Then, we substitute the values of x into f(x) to evaluate it. Finally, we multiply the resulting values of x, f(x), and f''(x) and compute the integral ∫x f(x) f''(x) dx.

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i tried my best hope this helps:)

The height of the tree can be found by establishing a proportional relationship between the heights and the shadows of the tree and Cameron and the height of the tree to the nearest hundredth of a meter is 2.40 m.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Therefore, we will establish a proportion to find the height of the tree.

Cameron height = 1.85 m

Tree shadow = 21.55 m

Cameron shadow length = 16.6 m

height of the tree = x

Therefore,

1.85 / x = 16.6 / 21.55

16.6x = 21.55 × 1.85

x = 39.8675 / 16.6

x = 2.40165662651

x = 2.40 m

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When two variables vary directly they follow the next:

k is a constant.

Use the given data: when x=48, y=36 o find the value of k:

Then, x and y vary directly following the next equation:

Use the equation above to find x when y=18:

Answer:

(30.00)

Step-by-step explanation:

(30.00) is the correct answer for your question/ statement you have asked. the answer is (30.00) again.

Answer:

Step-by-step explanation:

7x times 6x = 42x^2 - 7x

A possible solution to the equation cos(x+2)=sin(3x) is x = 22 degrees

The correct answer is an option (C)

Consider a trigonometric equation,

cos(x+2) = sin(3x)

For value x = 0.5 degrees,

cos(x + 2) = cos(2.5)

                = 0.999

and sin(3x) = sin(1.5)

                 = 0.026

For x = 1 degree,

cos(x + 2) = cos(3)

                =0.9986

sin(3x) = sin(3)

           = 0.052

For x = 22 degrees

cos(x + 2) = cos(24)

                = 0.913

sin(3x) = sin(66)

           = 0.913

for x = 44 degrees,

cos(x + 2) = cos(46)

                = 0.69

sin(3x) = sin(132)

           = 0.743

Therefore, the solution to an equation cos(x+2) = sin(3x) is x = 22 degrees

The correct answer is an option (C)

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The expression x² + 8x + 16 represents the area of the square.

The area of the square is defined as the product of the length and width.

Given data as:

A square has a side length of (x+4)

The area of the square = (x+4)(x+4)

The area of the square = (x+4)²

The area of the square = x² + 2(x)(4) + 4²

The area of the square = x² + 8x + 16

Hence, the expression x² + 8x + 16 represents the area of the square.

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No cost price is given hence its not possible to calculate the actual answer.But don't worry I will simplify the equation till end that you can get the answer in fractions of sec

Solution:-

Let the Cost price be x

Mark up percent=40%

Now

Mark up=

\(\\ \sf\longmapsto 40\%\:of\:x\)

\(\\ \sf\longmapsto \dfrac{40}{100}\times x\)

\(\\ \sf\longmapsto \dfrac{40x}{100}\)

\(\\ \sf\longmapsto 0.04x\)

Just multiply The CP by 0.04 to get the answer

The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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Answer:

x is = 25° by complimentary angles

Answer:

D

Step-by-step explanation:

Answer:

the y coordinates are opposite numbers

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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Answer:4.5

Step-by-step explanation:

Using the tangent-secant theorem, where x is the length of a tangent line segment in a circle, and we find that x is equal to 24 cm.

The given problem involves finding the value of x, which is the length of a line segment in a circle. We are given two lengths: 8 cm and 2 cm, and we need to use the tangent-secant theorem to solve for x.

The tangent secant theorem states that if a tangent and a secant line intersect at a point outside a circle, then the product of the length of the secant and its external part is equal to the square of the length of the tangent. In this case, the 8 cm line segment is the secant and the 2 cm line segment is the external part.

Using this theorem and the given values, we can set up the following equation:

2(x + 8) = \(8^2\)

Expanding the left side, we get:

2x + 16 = 64

Subtracting 16 from both sides, we get:

2x = 48

Dividing both sides by 2, we get:

x = 24

Therefore, x is equal to 24 cm.

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Answer:

4 toppings

Step-by-step explanation:

22-12=10

2.50*?=10

2.50*4=10

4 toppings

Answer:

12+(2.50x)

12+(2.50*4)

12+(10)

22

Step-by-step explanation:

x stands for number of toppings