If sin(A+B)=sinAcosB+cosAsinB and cos(A−B)=cosAcosB+sinAsinB, find the values of (i) sin75 ∘
and (ii) cos15 ∘

The probability that the customer will pick neither the chocolate chip topping nor the walnut topping is 0.6.

Probability refers to the chance of occurrence of an event.

Let E be an event. Then, the probability of E = P(E)

=> P(E) = \(\frac{Number Of Favourable Outcomes Of Event E}{Total Number Of Outcomes}\)

Given: The probability that the customer will take both toppings = 0.4

We know that the total probability of an event occurring = 1.

Thus, the probability that the customer will take neither the chocolate chip toppings nor the walnut toppings = 1 - 0.4 = 0.6

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To answer this question, we are assuming that the triangle is a right triangle, with sides (legs), a = 0.84m, and b = 0.63m.

Then, we can use the Pythagorean Theorem as follows:

Then, we have:

• c is the hypotenuse

• a, b the given legs of the right triangle

Now, to solve the equation for c, we need to take the square root from both sides of the equation:

Therefore, c = 1.05m. The result was already given in three significant figures.

In summary, the measure of the hypotenuse of the given right triangle is 1.05m.

Step-by-step explanation:

1 / (1/120 + 1/60) = 40 minutes.

Answer:

The answer is 3.

Step-by-step explanation:

Plug in, combine, solve.

\(m = - 3 \\ {m}^{2} + 5m + 9\\ ( - 3)^{2} + 5( - 3) + 9 \\ 9 + 5( - 3) + 9 \\ 9 - 15 + 9 \\ - 6 + 9 \\ 3\)

The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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To find the length of the rectangular piece of wrapping paper, we need to use the given information that the perimeter is 90cm and the width is 20cm.
The formula for the perimeter of a rectangle is P = 2(length + width).

Given that the perimeter is 90cm and the width is 20cm, we can plug these values into the formula:
90cm = 2(length + 20cm)
To find the length, we need to isolate it on one side of the equation. We can do this by first dividing both sides of the equation by 2:
45cm = length + 20cm
Next, we can subtract 20cm from both sides of the equation to isolate the length:
45cm - 20cm = length
Simplifying, we get:
25cm = length
Therefore, the length of the rectangular piece of wrapping paper is 25cm.

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Answer:

Step-by-step explanation:

The root is the fractional part of an exponent and the power is the upper part of the exponent fraction

1)    \(\sqrt{x^{3} } = x^{\frac{3}{2} }\)

2)    \(17^{\frac{1}{5} } =\sqrt[5]{17}\)

3)   \(\sqrt[5]{y^{3} } = y^{\frac{3}{5} }\)

4)   \(z^{\frac{2}{3} } =\sqrt[3]{z^{2} }\)

Answer:

There are 24 outcomes in the sample space.

Step-by-step explanation:

Suppose that we have some events, such that each one of these events has a given number of outcomes.

If we have an experiment where we perform all of these events, the total number of possible outcomes is equal to the product between the number of outcomes for each one of the events.

Let's apply this to our case.

Here we have two events:

Rolling a standard number cube: 6 outcomes

Spinning a spinner with 4 equal sections: there are 4 outcomes.

Then the total number of outcomes in the sample space is the product:

C = 6*4 = 24 outcomes.

There are 24 outcomes in the sample space.

If the “x” for this equation is meaning to multiple, the exact answer is: -31/7

If the “x” is a variable then the equation would be 10/7 - 45x/7

Answer:

4x_2y=5

4x=5+2y

x=5+2y/5

now, y=3x_1

putting value of x in second question

In this way you can do

Answer:

$1.50

Step-by-step explanation:

9/6=1.5

1.5=1.50

One hotdog cost $1.50

Answer:

$1.50

Step-by-step explanation:

$9 > 6h

? > 1h

9/6 = $1.50

For one hotdog, the price is $1.50

The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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Answer:

Step-by-step explanation:

if you multiplied a number by 3, you would get 51. If you want to solve for x, divide on both sides of the equal sign.

51/3 = 3x/3

17=x

Answer: 17

Step-by-step explanation: X is your variable, you need to find what X equals

In this case you can divide

51/3= 17

You can plug in your result to check your work. If the equation is true, it is  correct

Since 51= 3 x 17, or 3 x 17= 51, this is correct

Answer:  The middle school has 652 students.

Step-by-step explanation:  Divide the number of student in the high school by 4.5

\(\frac{2934}{4.5}\) = 652

Answer:

Lin lives 1 1/20 miles away from school

Step-by-step explanation:

1 3/10 becomes 1 6/20

1/4 becomes 5/20

1 6/20 - 5/20

= 1 1/20

Answer:

(6,-4)

Step-by-step explanation:

The answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.

The Hardy-Weinberg equilibrium is a method for determining the frequency of certain genetic traits in a population. The following are the frequencies of the red hair (r) and non-red hair (R) alleles in the Norwegian population, according to the question: A) The total frequency of alleles is 1. If red hair (r) is found in approximately 4% of the people in Norway, then the frequency of the R allele must be 0.96 or 96%. R = 0.96 r = 0.04 B) The frequency of hetero zygotes in a population can be determined by multiplying the frequency of the R allele by the frequency of the r allele and then multiplying that number by 2.

Heterogeneous genotype = 2pq Here, p represents the frequency of the R allele, and q represents the frequency of the r allele. p = R = 0.96 q = r = 0.04 Therefore, 2pq = 2(0.96 x 0.04) = 0.077, or approximately 8%. C) In order for a child to have red hair, both parents must carry the r allele. If both parents are homozygous for the R allele, there is no chance that their child will have red hair. This means that the proportion of matings that cannot result in a child with red hair is (0.96 x 0.96) = 0.9216 or 92.16%.

Therefore, the answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.

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The function y=x²+5x-6 has a minimum value. All real numbers are included in the function's domain. The function has a range of y ≤ 12.25, the correct option is (c).

The parabola has a minimum value and widens upwards since the x² term's coefficient is positive.

To find the minimum value, we can use the formula for the x-coordinate of the vertex:

x=-b/2a=-5/(2 × 1)=-2.5.

Plugging this value into the equation, we get

y=(-2.5)²+5(-2.5)-6=-12.25.

Therefore, the function has a minimum value of -12.25.

The function is a polynomial, which means it is defined for all real numbers.

Since the function has a minimum value of -12.25, the range of the function is all real numbers less than or equal to -12.25, i.e., {y ≤ 12.25}.

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The complete question is:

Consider the equation y=x^(2)+5x-6. Determine whether the function has a maximum or minimum value. State the maximum or minimum value. What are the domain and range of the function

a. minimum; 0; D: (all real numbers); R: {all real numbers}

b. maximum; 0; D (all real numbers); R: {y <-0}

c. minimum; -12.25; D (all real numbers); R: {y <-12.25}

d. maximum; -12.25; D {x <- 2.5}; R: {all real numbers}

The WACC for Company A is approximately 0.564 or 56.4%.

To calculate the weighted average cost of capital (WACC) for Company A, we need to consider the cost of debt and the cost of equity, weighted by their respective proportions in the company's capital structure.

Given information:

Debt proportion (D/V) = 26%

Equity proportion (E/V) = 100% - 26% = 74%

Before-tax cost of debt (r_d) = 3.2%

Risk-free rate (r_f) = 1.1%

Market risk premium (RPM) = 6%

Beta (β) = 0.9

Marginal tax rate (T) = 30%

The formula to calculate WACC is as follows:

WACC = (D/V) * r_d * (1 - T) + (E/V) * r_e

To calculate the cost of equity (r_e), we can use the Capital Asset Pricing Model (CAPM):

r_e = r_f + β * RPM

Plugging in the given values:

r_e = 1.1% + 0.9 * 6% = 1.1% + 5.4% = 6.5%

Now, let's calculate WACC:

WACC = (0.26) * 3.2% * (1 - 0.30) + (0.74) * 6.5%

WACC = 0.0832 + 0.481

WACC ≈ 0.5642

Rounding to three decimal places, the WACC for Company A is approximately 0.564 or 56.4%.

Please note that the WACC represents the average rate of return required by both debt and equity investors to finance the company.

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we can conclude that there is significant evidence to support the claim that μ is less than 10.

We need to compare the test statistic with the critical value to determine whether to reject or fail to reject the null hypothesis. Since the test statistic (-2.50) is less than the critical value (-1.645), we can reject the null hypothesis at the 5% level of significance.

The conclusion is that there is sufficient evidence to support the alternative hypothesis Ha: μ < 10. This means that the sample data suggests that the true population mean is less than 10, and we can reject the possibility that the population mean is greater than or equal to 10.

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Answer:A samantha will save 45$ because the two sales will combine for 75% off the original cost.

Step-by-step explanation:

I took the test hope this helps

Answer:  

Option B

(B) Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction

Step-by-step explanation:

The probability that the event that the second part is defective will be 0.0564.

From the information, the bin of 50 manufactured parts contains 3 defective parts and 47 nondefective

Therefore, the probability of having a defective and non defective parts will be:

= 47/50 × 3/50

= 0.94 × 0.06

= 0.0564

Therefore, the probability that the event that the second part is defective will be 0.0564.

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The following data shows the daily production of cell phones. 7, 10, 12, 15, 18, 19, 20. Mean The formula for finding the mean is: mean = (sum of observations) / (number of observations).

Therefore, the mean for the daily production of cell phones is: Mean = (7+10+12+15+18+19+20) / 7

= 101 / 7

Mean = 14.43

Variance The formula for finding the variance is: Variance = (sum of the squares of the deviations) / (number of observations - 1) Where the deviation of each observation from the mean is: deviation = observation - mean First, calculate the deviation for each observation:7 - 14.43

= -7.4310 - 14.43

= -4.4312 - 14.43

= -2.4315 - 14.43

= 0.5718 - 14.43

= 3.5719 - 14.43

= 4.5720 - 14.43

= 5.57

Now, square each of these deviations: 56.25, 19.62, 5.91, 0.33, 12.75, 20.9, 30.96 The sum of these squares of deviations is: 56.25 + 19.62 + 5.91 + 0.33 + 12.75 + 20.9 + 30.96

= 147.72

Therefore, the variance for the daily production of cell phones is: Variance = 147.72 / (7-1) = 24.62 Standard deviation ) Mean = 14.43b) Variance per Day = 24.62c) Standard Deviation = 4.96

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Answer:

6164

Step-by-step explanation:

Answer:

1. Yes, 34+12=46

2.No, 22-9=13

3. Yes, 6*9=54

4. Yes, 39/3=13

5. k=4 7+4=11

6. p=37 37+24=13

7. h=23 23+16=7

8. m=13/30 2/5+13/30=5/6

9. w+15=190 w=175

i hope this helps:)

Answer:

x = 0 and y = -4

Step-by-step explanation:

2x + y = -4...................................(i)

-3y = 2x + 12................................(ii)

from (i)

2x+y=-4

=> y=-4-2x

again from (ii)

-3y=2x+12

=> -3(-4-2x)=2x+12

=> 12+6x=2x+12

=> 6x-2x=12-12

=> 4x=0

=> x= 0

now,

y=-4-2(0)

=> y=-4-0

=> y=-4

Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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