Mrs vilakazi is a retired consumer studies educator .she owns a small business of selling different types of cakes including scones.the cost price for ingredients plus water and electricity is r0,53 per scone .she sells scones at r2 ,00 each . calculate the profit mrs vilakazi will make if she bakes 204 scones and sells 171.​

The value of f(g(x)) is x^2 + 1/x

A function is an expression that describes the relationship between an independent variable and dependent variable.

Given the functions;

f(x) =

\( \sqrt[3]{x} \)

g(x) =

\( \frac{ x+ 1}{ {x}^{3} } \)

How to determine the function

Substitute the value do x as the value of the function g(x)

f(g(x)) =

\( \sqrt[3]{ \frac{x + 1}{ {x}^{3} } } \)

Find the cube root of the expression

f(g(x)) =

\( \frac{ {x}^{3} + {1}^{3} }{x} \)

Find the cube of the values

f(g(x)) =

\( \frac{ {x}^{3} + 1 }{x} \)

Divide through by x, we have;

f(g(x)) = x^2 + 1/x

Thus, the value of f(g(x)) is x^2 + 1/x

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Answer:

30°

Step-by-step explanation:

Use that

-the sum of angles in a triangle is 180° and that

-vertical angles are congruent ( angle x and the missing angle in the bottom triangle are vertical)

x= 180-75 -75 = 30°

Answer:

9

Step-by-step explanation:

Calculate the absolute difference of the 2 points, that is

| - 7 - 2 | = | - 9 | = 9 , or

| 2 - (- 7) | = | 2 + 7 | = | 9 | = 9

Answer:

9

Step-by-step explanation:

You count Down from -7

ex -7,-6,-5

until you get to zero. While doing this the member the amount of times that you counted a number. You should have counted 7. Then you add 2. You could also add 7 and 2 right away.

(Note, if you add 7 and 2 right away, makes sure 7 is a positive number.)

From the probability distribution for the number of defective items in a random sample, the expected value of X is 2.82.

To calculate the expected value of X, we need to multiply each possible value of X by its corresponding probability and sum them up.

The expected value of X, denoted as E(X) or μ, is calculated using the formula:

E(X) = ∑ (x * p(x))

where x represents each possible value of X and p(x) represents the corresponding probability.

In this case, the probability distribution for X is given as follows:

x: 0 1 2 3 4

p(x): 0.1 0.15 0.13 0.07 0.55

To calculate the expected value, we perform the following calculations:

E(X) = (0 * 0.1) + (1 * 0.15) + (2 * 0.13) + (3 * 0.07) + (4 * 0.55)

E(X) = 0 + 0.15 + 0.26 + 0.21 + 2.2

E(X) = 2.82

The expected value represents the average value or mean of the probability distribution. In this case, it represents the average number of defective items we expect to find in a random sample based on the given probabilities.

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Simplifying it down:

(10/6)*4

40/24

Therefore, there are 1.455511e+23 ways 17 employees can be chosen from 200 employees and 4.652950e+19 ways 17 employees can be chosen from 144 non-minorities.

(a) Use technology to find the number of ways 17 employees can be chosen from 200.

Therefore, the number of ways 17 employees can be chosen from 200 is 1.455511e+23.

(b) Use technology to find the number of ways 17 employees can be chosen from 144 non-minorises.

The total number of non-minority employees is 200 – 56 = 144.

Thus, the number of ways 17 employees can be chosen from 144 non-minorities is 4.652950e+19.

(c) The probability that the committee contains no minority members is given as:

P(committee with no minorities) = (number of ways to choose 17 non-minorities from 144) / (number of ways to choose 17 employees from 200)

Therefore, P(committee with no minorities) = (4.652950e+19) / (1.455511e+23) = 0.03195

(d) As we can see, the probability that the committee contains no minority members is very low. It implies that the committee selection is most likely not based on random chance. A committee that was chosen at random would be expected to have a much higher probability of containing minority members.

Therefore, there are 1.455511e+23 ways 17 employees can be chosen from 200 employees and 4.652950e+19 ways 17 employees can be chosen from 144 non-minorities. The probability of selecting a committee with no minority members is 0.03195, which is quite low. This implies that the committee selection is not random.

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Answer:

(-2, 1)

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

2/1=2 (look at the picture to see how I got the numbers)

It's negative because it's going down from the left

( ° ▽ ° )

Answer:P is 3

Step By step explanation:

p+2p−3=6

3p-3 =6

P=3

The solutions to the given expressions is given below.

To add the rational expressions, we need to have a common denominator, which is 5x in this case. Thus,

12/5x + 3/5x = (12+3)/5x = 15/5x = 3/x

So, the sum of the two rational expressions is 3/x.

To subtract the rational expressions, we need to have a common denominator, which is 9x^2 in this case. Thus,

\(x/9x^2 - 3/9x^2 \\= x/9x^2 - (3x)/9x^2 \\= (x-3x)/9x^2 = -2x/9x^2\\ = -2/x^2\)

So, the difference of the two rational expressions is -2/x².

To subtract the rational expressions, we need to have a common denominator, which is (x-2) in this case. Thus,

\(\frac{7}{(x-2)} - \frac{3x}{(x-2)} = \frac{7-3x}{(x-2)}\)

To combine these two rational expressions, we need to first find a common denominator, which is (x-2)^2. Thus,

\(\frac{7(x-2)}{(x-2)^2} - \frac{3x(x-2)}{(x-2)^2} =\frac{ (7x-14-3x^2)}{(x-2)^2}\)

So, the difference of the two rational expressions is \((7x-14-3x^2)/(x-2)^2\).

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The test statistic for the sample is calculated using the formula for testing the difference in proportions of two independent samples. The p-value is determined based on the test statistic and the assumption of a normal distribution as an approximation for the binomial distribution.



The decision is made by comparing the p-value to the significance level (α), and the final conclusion is drawn based on the decision made.
To calculate the test statistic for the sample, we use the formula:
test statistic = (p1 - p2) / √[(p1(1-p1)/n1) + (p2(1-p2)/n2)]
where p1 and p2 are the sample proportions, and n1 and n2 are the respective sample sizes.
For this test, we do not use the continuity correction and approximate the binomial distribution with the normal distribution. The test statistic is computed using the given values of 444 successes and 132 failures for the first sample, and 585 successes and 186 failures for the second sample.
The p-value is then determined based on the test statistic and the assumption of a normal distribution. It represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.
To make a decision, we compare the p-value to the significance level (α). If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.
The final conclusion is drawn based on the decision made. If the null hypothesis is rejected, there is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proportion. If the null hypothesis is not rejected, there is not sufficient evidence to warrant rejection of the claim.

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Answer:

4th option

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= \(\sqrt{16x^4}\) - (3x² - 3x - 5)

= 4x² - 3x² + 3x + 5 ← collect like terms

= x² + 3x + 5

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

Answer:

Congruent

Step-by-step explanation:

Answer:

Congruent figures -------

Answer:

Step-by-step explanation:

All that making a list does is creates a visible step by step instruction manual on what needs to be done in order to solve the math problem that needs to be solved. Lists are extremely helpful and can be used in every single math problem, for example....

15x - 25 = 275

See making a list isolates the problem into an easy to read instruction manual.

Answer: n=-3 and n=3/2

Step-by-step explanation:

To solve the expression, we want to find the values of n. Since there are no common factors in 2, 3, -9, we directly multiply the "a" and "c" values.

2×(-9)=-18

This means, we want to find two numbers that multiply to -18 and adds to 3. This can also be known as the cross method.

We will find that 6 and -3 multiply to -18, and adds to 3.

In our box method, we want to find the common factors.

|2n²|6n|

|-3n|-9|

Note: Just pretend the lines line up and form a square box, with a term in each box.

After finding that is in common between the boxes, we get (n+3)(2n-3)=0

To solve, we set each factor equal to 0.

n+3=0

n=-3

2n-3=0

2n=3

n=3/2

Answer:

17.5

Step-by-step explanation:

x(x-4)=140

2x=140/4

2x=35

x=35/2

x=17.5

This statement ''The proportion in the body of a normal distribution can never be less than 0.50.'' is false because the proportion in the body of a normal distribution can be less than 0.50, depending on the location of the mean and the spread of the distribution.

In fact, for a normal distribution with a mean of μ and standard deviation of σ, approximately 68% of the area under the curve falls within one standard deviation of the mean (i.e., between μ - σ and μ + σ), which means the proportion in the body of the distribution is about 0.68.

The remaining 32% is split evenly between the tails of the distribution, which means the proportion in each tail is about 0.16.

So, the proportion in the body of the distribution is greater than 0.50.

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Answer:

-0.1402

Step-by-step explanation:

Let's calculate the price impact of a 50-basis point (0.50%) interest rate change using a linear approximation for a 10-year, 7% semi-annual coupon bond priced at $97.50.

Step 1: Calculate the current yield:

Current yield = Coupon payment / Current price

Coupon payment = Face value * Coupon rate

Coupon payment = $100 * 0.07 = $7

Current yield = $7 / $97.50 = 0.0718 (or 7.18%)

Step 2: Calculate the Macaulay duration:

Macaulay duration = [(Time until Cash Flow) * (Cash Flow)] / [Current Price * (1 + Yield per period)]

The bond has 20 semi-annual periods, and the cash flow is the coupon payment of $7.

Macaulay duration = [(1 * $7) + (2 * $7) + ... + (20 * $7)] / [$97.50 * (1 + 0.0718)]

Using the formula for the sum of an arithmetic series, we can simplify the Macaulay duration calculation:

Macaulay duration = (20 * ($7 * 21)) / ($97.50 * 1.0718)

Macaulay duration = 2940 / 104.8375

Macaulay duration ≈ 28.0344

Step 3: Estimate the price impact:

Price impact ≈ -Macaulay duration * Interest rate change

Price impact ≈ -28.0344 * 0.005

Price impact ≈ -0.1402

Therefore, the estimated price impact of a 50-basis point interest rate change for the given bond is approximately -0.1402, implying a decrease in the bond price.

Answer:

13 blocks per hour

Step-by-step explanation:

52/4=13

hope this is helpful

Answer:

13 blocks per hour

Step-by-step explanation:

52/4 = 13

He was walking really slow apparently

The correct explanation for preferring the mean over the median as a measure of center is option 3: The mean is the same as the median for symmetric data.

The mean over the median as a measure of center is that the mean takes into account all values in a data set, making it more representative of the data as a whole. On the other hand, the median only considers the middle value(s), and is less sensitive to outliers. This means that extreme values in a data set have less impact on the median than they do on the mean. However, if the data set is skewed or has outliers that significantly affect the mean, the median may be a better measure of central tendency. In summary, the choice between the mean and the median depends on the characteristics of the data set being analyzed and the research question being asked.
In symmetric data, the mean and median provide the same central value, giving an accurate representation of the data's center. However, it's important to note that the mean is more sensitive to outliers than the median, which might affect its accuracy in skewed data sets.

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Answer: The answer is 7(9 + 5)=98

7x9=63

7x5=35

63+35=98

Step-by-step explanation: 63+35=98

Answer:

9(7+35)

Step-by-step explanation:

don't really have a step-by-step so I hope u don't fail

approximately 667.4 square inches of the traffic cone needs to be painted orange.

The traffic cone can be approximated as a frustum of a right circular cone, where the top of the frustum is the opening of the cone and the bottom of the frustum is the base of the cone. The area to be painted is the lateral surface area of the frustum, which can be calculated using the slant height and the generatix.

The generatrix is the distance between the tip of the cone and the edge of the frustum. We can use the Pythagorean theorem to find it:

generatrix = sqrt(slant height^2 - (diameter/2)^2)

generatrix = sqrt(29^2 - (14/2)^2)

generatrix = sqrt(783)

The lateral surface area of the frustum can be calculated using the generatrix and the slant height:

lateral surface area = pi * (generatrix + slant height) * (diameter/2)

lateral surface area = pi * (sqrt(783) + 29) * (14/2)

lateral surface area ≈ 667.4 square inches

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\(\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5\)  is the difference.

What is an expression?

⇒ An expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

Calculation :

⇒   \(\frac{3x^{2} }{(x^{2} -7x+10)}- \frac{5x} {x-2}\)

⇒   \(\frac{3x^{2} }{(x-2)(x-5)}- \frac{5x} {x-2}\)

⇒1/(x-2) [(3x²-5x{x-5})/(x-5)]

⇒1/(x-2) [(3x²-5x²+25x)/(x-5)]

⇒1/(x-2) [ (-2x²+25x)/(x-5)]

⇒\(\frac{-2x^{2} +25x }{(x-2)(x-5)}\)

at x=2 and x=5 the denominator becomes zero If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.

⇒   \(\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5\) is the difference

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The total surface area that Lisa would need to cover is 2 times the sum of the areas of the top and bottom faces plus 2 times the sum of the areas of the side faces.

To calculate the total surface area that Lisa would need to cover, we need to consider all the faces of the block.

Assuming the block is a rectangular prism, it will have six faces: a top face, a bottom face, and four side faces.

Let's denote the length, width, and height of the block as L, W, and H, respectively.

Top and Bottom Faces:

The top and bottom faces have dimensions of L × W each, so their combined area is 2 × (L × W).

Side Faces:

The side faces consist of four rectangles, two with dimensions of L × H and two with dimensions of W × H. So, the combined area of the side faces is 2 × (L × H) + 2 × (W × H).

Now, we can calculate the total surface area by summing up the areas of all the faces:

Total Surface Area = 2 × (L × W) + 2 × (L × H) + 2 × (W × H)

Therefore, the total surface area that Lisa would need to cover is 2 times the sum of the areas of the top and bottom faces plus 2 times the sum of the areas of the side faces.

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Answer:

i think 220

Step-by-step explanation:

because if he swim 250 then 30 less it would be 220