Sarah is a psychologist at an practise. she earns a basic salary of R3000 per month as well as 20% commission on income up to R 5000. She receives an additional 10% bonus on top of the normal commission rate on earning above R 5000. If Sarah did work to the value of R 12000 ,how much did she earn in total???​

Answer:

y = 5x - 35

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

m = 5

The y-intercept is located at (0, -35)

So, the equation is y = 5x - 35

Answer: y=5x-35

Step-by-step explanation:

The formula I believe you are looking for would be y=mx+b. M is your slop and B is your y-intercept. Since the slope is already given, you would fill in the rest of the formula with that and the (x,y) you were provided, and it should look like this:

5=5(8)+b.

Then you solve that for b as follows:

5=5(8)+b

5=40+b

-35=b

Therefore the equation would be y=5x-35

Answer:

The square root of 20 is approximately between 4 and 5.

To find this, you can estimate the square root of 20 by finding the square root of the closest perfect squares, which are 16 (4^2) and 25 (5^2):

√16 = 4

√25 = 5

Since 20 is closer to 25 than 16, we know that the square root of 20 must be closer to 5 than to 4. Therefore, the square root of 20 lies between 4 and 5.

The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.

a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.

(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:

Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.

Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.

(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:

Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50

Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.

(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.

Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the

average monthly rent is at least $1,300. As a result, the answer is "No."

(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.

A 92% confidence interval has a z-score of 1.75. (to two decimal places).

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The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.

In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.

Next, we need to find the derivative of x = √y with respect to y, which is:

dx/dy = 1/2√y

Substituting this into the formula for the surface area, we get:

Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy

Simplifying the expression inside the square root, we get:

Surface Area = 2π ∫[0,4] √(y+(1/4)) dy

We can evaluate this integral using the power rule of integration, which gives:

Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴

Simplifying further, we get:

Surface Area = 2π [2/3(17/4)^(3/2)]

Surface Area ≈ 54.33 square units

Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.

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Complete Question:

How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?

The best chart to represents changes in the stock portfolio over the last 12 months by financial advisor is shown by option 1. a line chart.

The best type of chart to use to show how a stock portfolio has changed over time is a line chart.

A line chart can show the trend in the portfolio's value over the 12-month period.

Which is useful for identifying patterns and changes in performance.

A histogram is used to show the distribution of a single variable.

While a pie chart is used to show the proportion of a whole made up by different parts.

A bar chart is useful for comparing different categories or groups.

However, for tracking changes in a single variable over time, a line chart is the most appropriate choice.

Therefore, the best chart for financial advisor to show changes in stock portfolio over the last 12 months is given by option 1. a line chart.

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Step-by-step explanation:

h(-2) = 25

h(-1) = 5

h(0) = 1

h(1) = 1/5

h(2) = 1/25

Answer:

0.03

Step-by-step explanation:

So we can tell that our population parameter is p-hat = 0.637, which is 0.03 apart from the upper and lower bounds of the confidence interval. This means that 0.03 is our margin of error, or how much room there is for error.

319 is the correct answer.

Whenever two variables are correlated, we assume that one variable is the cause of the observed effect from the other variable.

It is a false statement,

Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. These two separate variables are theoretically influenced by the same outside factors because they travel in the same direction.

Whenever two variables are correlated, we assume that one variable is the cause of the observed effect from the other variable.

It is a false statement,

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In order to create a 3 foot broad sidewalk around the garden, 98 feet of lumber will be needed.

The word "perimeter" in mathematics refers to the distance that surrounds the perimeter of a two-dimensional shape, such as a circle, square, or rectangle. It represents the total length of the shape's edges. For instance, you can calculate a rectangle's perimeter by multiplying the lengths of each of its four sides: P = 2l + 2w, where P stands for the perimeter, l for the rectangle's length, and w for its breadth.

given

We must multiply each dimension of the garden by the sidewalk's width to determine the overall length of the perimeter in order to determine the walk's perimeter.

The garden's revised measurements, including the 3-foot-wide sidewalk that surrounds it, are as follows:

Length = (17 + 2(3)) feet.

width = 20 + 2 (3) = 26 feet.

The sum of the four edges defines the walk's perimeter:

Width is equal to 98 feet (23 + 23 + 26 + 26).

In order to create a 3 foot broad sidewalk around the garden, 98 feet of lumber will be needed.

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James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.

Prοbability is a measure οf the likelihοοd οf an event οccurring. It is a numerical value between 0 and 1, where 0 means the event is impοssible and 1 means the event is certain tο οccur. Fοr example, the prοbability οf flipping a fair cοin and getting heads is 1/2 οr 0.5.

Tο calculate the tοtal cοst in Singapοre dοllars, we need tο cοnvert the US dοllars tο Singapοre dοllars using the given exchange rate, and then add the twο cοsts tοgether.

The cοst οf the item in Singapοre dοllars is:

75 USD * 1.65 SGD/USD = 123.75 SGD

The shipping and handling cοst in Singapοre dοllars is:

39 USD * 1.65 SGD/USD = 64.35 SGD

The tοtal cοst in Singapοre dοllars is the sum οf these twο cοsts:

Tοtal cοst = 123.75 SGD + 64.35 SGD = 188.10 SGD

Therefοre, James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.

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Step 1: Let the two numbers be x and y

Step 2: Since we know the difference between the two numbers is 6, that means x = y + 6

Step 3: We also know the sum of the two numbers is 10, so x + y + 6 = 10

Step 4: Simplifying, we get 2y + 6 = 10

Step 5: Subtracting 6 from both sides, we get 2y = 4

Step 6: Dividing both sides by 2, we get y = 2

Step 7: Finally, we can use the first equation (x = y + 6) to solve for x, so x = 8

Therefore, the two numbers are 8 and 2.

Answer:

A≈1.83m²

Step-by-step explanation:

Using the formulas

A=πr2C=2πr

Solving forAA=C24π=4.824·π≈1.83346m²

Answer:

1.83 (approximate)

Step-by-step explanation:

First, we need to find the radius of the circle.

Using the formula:

[tex]C=2 \pi r[/tex]

We have to reorganize terms:

[tex]r=\frac{C}{2\pi}[/tex]

[tex]\frac{4.8}{2 \times \pi}[/tex]

r ≈ 0.76

Now we have the radius and the circumference in order to find the area.

Use the formulas:

[tex]A= \pi r^2[/tex]

[tex]C=2 \pi r[/tex]

A = C^2/4[tex]\pi[/tex]  = 4.8^2 / 4 * pi = 1.83

The correct answer to the given question is:

Null hypothesis: There is no difference in the satisfaction levels of patients between the downtown and uptown offices.

Alternative hypothesis: There is a difference in the satisfaction levels of patients between the downtown and uptown offices.

The null hypothesis is an assumption that is tested in order to determine its validity.

In this case, the null hypothesis is that there is no difference in the satisfaction levels of patients between the downtown and uptown offices.

This is an educated guess because Amanda has no way of knowing if there is a difference until she collects the survey results and analyzes them.

The alternative hypothesis is the opposite of the null hypothesis. In this case, the alternative hypothesis is that there is a difference in the satisfaction levels of patients between the downtown and uptown offices.

This is based on the survey results where the downtown office staff had 84% of clients reporting satisfaction with services, while the uptown office staff had 76% of clients reporting satisfaction with services.

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Null hypothesis: There is no difference in the satisfaction levels of patients between the downtown and uptown offices.

Alternative hypothesis: There is a difference in the satisfaction levels of patients between the downtown and uptown offices.

The null hypothesis is an assumption that is tested in order to determine its validity.

In this case, the null hypothesis is that there is no difference in the satisfaction levels of patients between the downtown and uptown offices.

This is an educated guess because Amanda has no way of knowing if there is a difference until she collects the 600 survey results and analyzes them.

The alternative hypothesis is the opposite of the null hypothesis.

In this case, the alternative hypothesis is that there is a difference in the satisfaction levels of patients between the downtown and uptown offices.

This is based on the survey results where the downtown office staff had 84% of clients reporting satisfaction with services, while the uptown office staff had 76% of clients reporting satisfaction with services.

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Answer: $2,162.06

Step-by-step explanation:

To calculate the total monthly payment to the bank, we need to add up the monthly mortgage payment, the monthly portion of the semi-annual property tax bill, and the monthly portion of the annual homeowner's insurance bill.

First, we need to find the monthly portion of the semi-annual property tax bill. To do this, we divide the semi-annual property tax bill by 6 (since there are 6 months in half a year):

Monthly property tax payment = Semi-annual property tax bill / 6

Monthly property tax payment = $3,239 / 6

Monthly property tax payment = $539.83

Next, we need to find the monthly portion of the annual homeowner's insurance bill. To do this, we divide the annual homeowner's insurance bill by 12 (since there are 12 months in a year):

Monthly homeowner's insurance payment = Annual homeowner's insurance bill / 12

Monthly homeowner's insurance payment = $980 / 12

Monthly homeowner's insurance payment = $81.67

Now we can add up the monthly mortgage payment, the monthly property tax payment, and the monthly homeowner's insurance payment to find the total monthly payment to the bank:

Total monthly payment = Monthly mortgage payment + Monthly property tax payment + Monthly homeowner's insurance payment

Total monthly payment = $1,711.22 + $539.83 + $81.67

Total monthly payment = $2,332.72

Therefore, the Dotkoms pay the bank $2,332.72 each month.

Answer:

Step-by-step explanation:

Using proportions, it is found that they pay the bank $2332.72 each month.

What is a proportion?

A proportion is a fraction of a total amount.

Using proportions, it is found that they pay the bank $2332.72 each month.

What is a proportion?

A proportion is a fraction of a total amount.

Their payments are given by:

Monthly mortgage of $1,711.22.

Semi-annual property tax bill is $3,239, that is, it is paid every 6 months, hence 3239/6 = $539.83.

Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.

A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.

For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.

Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.

To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.

The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.

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Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)

b) The experimental probability is given by:

[tex]P(A)= \frac{32}{150} =0.2133[/tex]

[tex]P(B)= \frac{38}{150} =0.2533[/tex]

[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.  

The value of 3302 mod 385 is 51179.

To use Fermat's little theorem to compute the expression, we need to first identify two relatively prime numbers that we can use as the base and the modulus. Let's choose 2 and 384, respectively.

Then, we have:

2³⁸⁴ ≡ 1 (mod 385)

Multiplying both sides by 3302, we get:

2³⁸⁴ × 3302 ≡ 3302 (mod 385)

Now, we can use the Chinese remainder theorem to find the value of 2³⁸⁴ × 3302 mod 385.

From the part (a) of this question, we know that:

2³⁸⁴ ≡ 1 (mod 7)

2³⁸⁴ ≡ 1 (mod 5)

2³⁸⁴ ≡ 16 (mod 11)

Using the Chinese remainder theorem, we can combine these congruences to get:

2³⁸⁴ ≡ 166 (mod 385)

Substituting this into the expression we derived earlier, we have:

2³⁸⁴ × 3302 ≡ 166 × 3302 (mod 385)

Multiplying out, we get:

2³⁸⁴ × 3302 ≡ 51179 (mod 385)

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The frequency table is completed as follows

Number of books           frequency

0 - 9                                      1

10 - 19                                    10

20 - 29                                  9

A frequency table is a way of organizing data in a table that shows the number of times each value or category appears in a dataset.

The table lists the unique values or categories in one column, and the frequency (or count) of occurrences of each value or category in the dataset in another column.

In the table attached, the solution is achieved by examining the tally column

Each item in the tally column is counted to get the numbers in place of l

A B C and D

Examining the table, we can say that

A = 1

B = 5 + 5 = 10

C = 5 + 4 = 9

D = 3

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Answer:

Step-by-step explanation:

25.

[tex]cos 45=\frac{x}{18\sqrt{2} } \\\frac{1}{\sqrt{2}} =\frac{x}{18\sqrt{2} } \\x=\frac{18\sqrt{2}}{\sqrt{2}} \\x=18[/tex]

  26.

sin30=30/x

[tex]\frac{1}{2} =\frac{30}{x} \\x=30 \times 2=60[/tex]

The answer of the given question based on the  transformation from its parent function the explanation part is given below and The equation of the function is y = -2(x+3)².

In mathematics,  function is  relation between  set of inputs and  set of possible outputs with  property that each input is related to exactly one output. It is  rule that assigns to each input value exactly one output value. Functions can be represented in various ways, like algebraic expressions, graphs, tables, and words. They are used to model relationships between variables, to describe how one quantity depends on another, and to make predictions about future values. Functions are  important concept in many fields of mathematics, as well as in science, engineering, economics, and other areas where quantitative analysis is used.

a. The graph appears to be a reflection of the parent function f(x) = x² over the x-axis followed by a vertical stretch by a factor of 2 and a horizontal shift to the left by 3 units.

b. The equation of the function is y = -2(x+3)².

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Answer:

X=18

Step-by-step explanation:

Answer:

x = 3.5 units (nearest tenth)

Step-by-step explanation:

The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.  

Therefore, the formula for the ratio of the sides is x : x : x√2 where:

As the hypotenuse of the given right triangle is 5 units:

[tex]\implies x\sqrt{2} = 5[/tex]

To find the measure of x, solve for x:

[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x =3.5355339...[/tex]

[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]

Therefore, the length of side x to the nearest tenth is 3.5 units.

Answer:

Step-by-step explanation:

To find the zeros of the function, we set y to zero and solve for x:

y = (x+1)(x-2)(x-6) = 0

Setting each factor equal to zero and solving for x gives us the zeros:

x+1 = 0 or x-2 = 0 or x-6 = 0

x = -1, x = 2, x = 6

So the zeros of the function are -1, 2, and 6.

To graph the function, we can use the zeros and the leading coefficient to sketch a rough graph. The leading coefficient is positive, so the graph will open upward. The zeros are -1, 2, and 6, so the graph will intersect the x-axis at those points. We can also find the y-intercept by plugging in x = 0:

y = (0+1)(0-2)(0-6) = 12

So the y-intercept is (0, 12).

Using this information, we can sketch the graph:

The probability that a data value is between 46 and 47 in a normal distribution with mean 48 and standard deviation 2 is approximately A. 15.0%.

To solve this problem, we need to first standardize the given values using the standard normal distribution formula:

z = (x - μ) / σ

where z is the standardized value, x is the data value, μ is the mean, and σ is the standard deviation.

For x = 46:

z = (46 - 48) / 2 = -1

For x = 47:

z = (47 - 48) / 2 = -0.5

Next, we can use a standard normal distribution table or calculator to find the area under the standard normal curve between these two standardized values.

Using a calculator or table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = -0.5 is 0.3085.

Therefore, the area between z = -1 and z = -0.5 is:

0.3085 - 0.1587 = 0.1498

Finally, we can convert this area back to a probability by rounding to the nearest tenth of a percent:

0.1498 ≈ 15.0%

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Answer:

0 and 180 degrees.

Step-by-step explanation:

We can start by using a trigonometric identity to rewrite sin2x in terms of cos2x:

sin2x = 1 - cos2x

Substituting this into the given equation, we get:

cos2x = 1 + (1 - cos2x)

Simplifying this equation, we get:

2cos2x = 2

Dividing both sides by 2, we get:

cos2x = 1

Solving for x, we get:

2x = 0°, 360°x = 0°, 180°

Therefore, the solutions to the equation cos2x = 1 + sin2x in the interval 0° ≤ x ≤ 360° are x = 0° and x = 180°.

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[tex]\sqrt{2} = 1.414[/tex]. [tex]\sqrt{x3} = 1.732[/tex]. So, a rational number between those two would be [tex]1.5 (\frac{3}{2} )[/tex].

A rational number is any fraction with a non-zero denominator. Examples for rational numbers comprise 1/2, 1/5, 3/4, as well as other values. The number "0" also qualifies as a rational number since there are various ways to express it, including 0/1, 0/2, 0/3, etcetera.

Any number that can be expressed as a fraction and where the divisor (the bottom number) and the numerator (the total score) are both integers is considered a rational number. In other words, p/q, where both p and q both are integers and q 0, can be used to represent a rational number.

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Part A :  the probability that a randomly chosen recipient served in the army, navy, or marines is 0.993. Part : the probability that a randomly chosen recipient served in the Air Force is 0.0038.

Probability is a branch of mathematics that deals with the study of chance or randomness. It involves the measurement of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and it landing on heads is 0.5 or 50%, assuming a fair coin.

The total number of recipients in the pie chart is the sum of all the values: 2393 + 743 + 296 + 13 + 8 + 1 = 3454.

Part A: The number of recipients who served in the army, navy, or marines is 2393 + 743 + 296 = 3432. Therefore, the probability that a randomly chosen recipient served in the army, navy, or marines is:

P(Army or Navy or Marines) = (2393 + 743 + 296) / 3454 ≈ 0.993

Part B: The number of recipients who were civilians is 8. Therefore, the probability that a randomly chosen recipient was a civilian is:

P(Civilian) = 8 / 3454 ≈ 0.0023

Therefore, the probability that a randomly chosen recipient served in the Air Force is:

P(Air Force) = 13 / 3454 ≈ 0.0038.

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The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%

The shape of an equilateral triangle is an equilateral triangle.

The word "Equilateral" is formed by combining two words. H. "Equi" means equal, "lateral" means side.

Equilateral triangles are also called regular polygons or equilateral triangles because all sides are equal.

In geometry, an equilateral triangle is a triangle with all sides of equal length.

Three sides are equal, so three angles on the same side are equal. Therefore, it is also called an equilateral triangle with each angle of 60 degrees.

Like other types of triangles, equilateral triangles have formulas for area, perimeter, and height. 

According to our question-

AB=OA=BO= 9CM

ONQ-AOB/ONQ*100

PUTTING VALUES

60.3%

Hence, The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%

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Answer:

15.

The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.

So, the answer to the question "what is 5 divided by 1/3?" is
15!

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