A survey was done with 50 students currently taking Algebra 1 at Laurel Springs School. They were asked which they preferred - English or mathematics? Out of the 50 students, 30 were male. There were 35 students who preferred mathematics and out of those that preferred mathematics, 24 were male. Create a two way relative frequency table for the data. According to the table, would it be safe to assume that females prefer English and males prefer mathematics? Why or why not?
Answers
we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12).
HOW TO SOLVE THE QUESTION?
To create a two-way relative frequency table, we can use the following table:
| English | Mathematics | Total
--------|---------|-------------|-------
Male | x | 24 | 30
Female | y | 11 | 20
--------|---------|-------------|-------
Total | 35 | 35 | 50
Here, x and y represent the number of male and female students who preferred English, respectively.
To calculate the values for x and y, we can use the fact that there were 35 students who preferred mathematics, and 24 of them were male. Therefore, the number of females who preferred mathematics is 35 - 24 = 11. Since there are a total of 20 female students, the number of females who preferred English is 20 - 11 = 9. Similarly, the number of male students who preferred English is 30 - 24 = 6.
To calculate the relative frequencies, we can divide each cell by the total number of students (50). For example, the relative frequency of male students who preferred mathematics is 24/50 = 0.48.
The resulting two-way relative frequency table is as follows:
| English | Mathematics | Total
--------|---------|-------------|-------
Male | 0.12 | 0.48 | 0.60
Female | 0.18 | 0.22 | 0.40
--------|---------|-------------|-------
Total | 0.30 | 0.70 | 1.00
From this table, we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12). However, it would not be safe to assume that all females prefer English and all males prefer mathematics based on this data alone, as there may be individual variations and exceptions to this trend.
It's also important to note that the sample size is relatively small, with only 50 students surveyed, and may not be representative of the larger population. Further research with a larger and more diverse sample size would be needed to make more accurate conclusions about gender-based preferences in this population
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Related Questions
Find the area of the following figure with the indicated dimensions. Round your
answer to the nearest thousandth, if necessary.
10.2 cm
15.3 cm
7.5 cm
Answers
The area of the figure is approximately 86.325 square centimeters.
What is a triangle?A triangle is a shape with three sides and three angles. It is one of the basic shapes in geometry. Triangles can be classified according to the lengths of their sides as equilateral, isosceles and scalene triangles, and also according to their internal angles as right, acute and obtuse triangles.
To find the area of the trapezoid triangle , we need to first find the length of the other diagonal
Since the center line is perpendicular to both diagonals, it divides the trapezoid triangle into two right triangles, ABC and ABD.
Using the Pythagorean theorem, we can find the length of BD:
BD = [tex]\sqrt{(AB^2 + AD^2)}[/tex]
BD = [tex]\sqrt{(10.2^2 + 7.5^2)}[/tex]
BD = 12.654
Now, we can use the formula for the area of a trapezoid:
A = (1/2) * (AB + CD) * h
where h is the height of the trapezoid, which is the distance between the parallel sides AB and CD.
To find h, we can use the formula for the area of a triangle:
A = (1/2) * b * h
where b is the base of the triangle and h is its height.
We can use triangle ABD, which is a right triangle, to find the height h:
h = AD = 7.5
Now we can substitute the values into the formula for the area of a trapezoid:
A = (1/2) * (AB + CD) * h
A = (1/2) * (10.2 + 15.3) * 7.5
A = 86.325
Therefore, the area of the trapezoid triangle ABC is approximately 86.325 square centimeters.
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Please help will mark Brainly
Answers
The quadratic function on the graph is:
y = (-4/9)*(x - 3)^2 + 6
How to find the quadratic equation?Here we can see that we have a quadratic equation, remember that if the vertex is (h, k) and the leading coefficient is a, then we can write this as:
f(x) = a*(x - h)^2 + k
Here we can see that the vertex is at (3, 6), then we can write:
f(x) = a*(x - 3)^2 + 6
And we can see that the y-intercept is (0, 2), then we can write:
2 =a*(0 - 3)^2 + 6
2 = a*9 + 6
2 - 6 = a*9
-4/9 = a
Then the function is:
y = (-4/9)*(x - 3)^2 + 6
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which function has the same end behavior as f = -x -4 - 1?
Answers
The end behavior of the function f(x) = -1/x - 4 is given as follows:
As x -> ∞, f(x) -> -4.
How to obtain the end behavior of a function?The end behavior of a function refers to the behavior of the function as the input variable (usually denoted as "x") approaches positive or negative infinity. To obtain the end behavior of a function, we look at the highest degree term in the function, which will determine the general shape of the graph.
The function for this problem is defined as follows:
f(x) = -1/x - 4.
As x goes to infinity, the term 1/x goes to zero, hence the end behavior of the function is defined as follows:
f(x) = 0 - 4
f(x) = 4.
Missing InformationThe problem is incomplete, hence I found the end behavior of the function f(x) = -1/x - 4.
You should use the same procedure to find the end behavior of the function in your problem.
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Juan has already run 6 miles this month. He plans to run an additional 2.5 miles per day. At this rate, how many days will it take Juan to run 41 miles?
First, write an equation to represent the scenario above.
Next, solve the equation to show how many days it will take Juan to run 41 miles.
Be sure to show or explain all steps when solving the equation.
HINT: What math operation does the word 'per' tell us to perform? However much he has already run and what he plans to run will equal 41.
PLEASE EXPLAIN THIS I NEED TO SHOW WORK ON THIS.
Answers
The linear function that represents the above scenario is given as follows:
y = 6 + 2.5x.
The number of days needed to run 41 miles is given as follows:
14 days.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The parameters in the context of the problem have the values given as follows:
m = 2.5, as each day, Juan runs 2.5 additional miles.b = 6, as Juan has already ran 6 miles.Hence the function is modeled as follows:
y = 2.5x + 6.
The number of days needed to run 41 miles is given as follows:
2.5x + 6 = 41
x = 35/2.5
x = 14 days.
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The City of Dire Dewa started calendar year 2013 with General Fund cash of Br. 50,000 and fund balance (unassigned) of Br. 50,000. The Dire Dewa council approved the following General Fund budget for 2013:Estimated RevenuesProperty taxes …………………………………..Br.850,000Licenses and fees ………………………………….70,000Investment income …………………………………5,000 ……….. Br.925,000AppropriationsSalaries ………………………………… Br.800,000Utilities ……………………………………50,000Equipment …………………………………85,000……………….. 935,000Budgeted Decrease in Fund Balance …………………………… Br.10,000The following transactions and events occurred in 2013:i. Recorded the approved budget for the year.ii. Levied property taxes of Br.850,000. (The council assumed all property taxes would be collected in time to pay the year’s expenditures.)iii. Collected property taxes in the amount of Br.840,000 and licenses and fees of Br.70,000.iv. Invested Br.50,000 of available cash in a CD. Later in the year, redeemed the CD in full with interest of Br.2,000.v. Ordered police sedans for Br.80,000.vi. Received police sedans (with some extra bells and whistles) and an invoice for Br.82,000. (The Police chief liked the bells and whistles and approved the invoice for Br.82,000.) The invoice was subsequently paid. (Note: Record this purchase as capital outlay expenditure.)vii. Paid salaries of Br.770,000 and utility bills of Br.45,000.viii. During the last few days in December, Dire Dewar employees earned Br.25,000, which will be paid at the end of the pay period in early January 2014. Also, Dire Dewar received a utility bill for Br.4,000 for December 2013, which will be paid in January 2014.Use the preceding information to do the following:a. Prepare journal entries to record the foregoing transactions and events. b. Prepare a statement of revenues, expenditures, and changes in fund balance. c.Prepare balance sheet.
Answers
Answer:
Step-by-step explanation:
a. Journal Entries:
i. Budget Approval:
Debit: Appropriations - Salaries - Br. 800,000
Debit: Appropriations - Utilities - Br. 50,000
Debit: Appropriations - Equipment - Br. 85,000
Credit: Estimated Revenues - Property Taxes - Br. 850,000
Credit: Estimated Revenues - Licenses and Fees - Br. 70,000
Credit: Estimated Revenues - Investment Income - Br. 5,000
ii. Property Tax Levy:
Debit: Property Taxes Receivable - Br. 850,000
Credit: Property Taxes Revenue - Br. 850,000
iii. Collection of Revenues:
Debit: Cash - Br. 910,000
Credit: Property Taxes Receivable - Br. 840,000
Credit: Licenses and Fees Revenue - Br. 70,000
iv. Investment in CD:
Debit: Cash - Br. 50,000
Credit: Investments - Br. 50,000
v. Purchase of Police Sedans:
Debit: Equipment - Br. 80,000
Credit: Cash - Br. 80,000
vi. Payment for Police Sedans:
Debit: Equipment - Br. 2,000
Credit: Cash - Br. 82,000
vii. Payment of Salaries and Utility Bills:
Debit: Salaries Expense - Br. 770,000
Debit: Utilities Expense - Br. 45,000
Credit: Cash - Br. 815,000
b. Statement of Revenues, Expenditures, and Changes in Fund Balance:
Revenues:
Property Taxes Revenue - Br. 850,000
Licenses and Fees Revenue - Br. 70,000
Investment Income - Br. 2,000
Total Revenues - Br. 922,000
Expenditures:
Salaries Expense - Br. 800,000
Utilities Expense - Br. 50,000
Capital Outlay - Br. 82,000
Total Expenditures - Br. 932,000
Net Change in Fund Balance:
Revenues - Expenditures - Br. 10,000
Fund Balance:
Beginning Fund Balance - Br. 50,000
Net Change in Fund Balance - Br. 10,000
Ending Fund Balance - Br. 40,000
c. Balance Sheet:
Assets:
Cash - Br. 58,000
Investments - Br. 50,000
Property Taxes Receivable - Br. 10,000
Equipment - Br. 85,000
Total Assets - Br. 203,000
Liabilities:
None
Fund Balance:
Unassigned - Br. 40,000
Total Liabilities and Fund Balance - Br. 203,000
Write 762 in the base seven system
Answers
762 base 10 to base 7 is 2136 base 7
What are Base Numbers?
Base Numbers are the number of units, or numbers, we use in our counting system. The most common base number is ten because the digits 0-9 are used in the number system.
And it is a base-7 number system we would only use seven different digits, like 0-6.
How to determine this
By dividing the number 762 base 10 in base 7 until it can no more be divided in base 7.
First divide 762 /7 = 108 remainder 6
108/7 = 15 remainder 3
15/7 = 2 remainder 1
2/7 = 0 remainder 2
Where the remainders arranged in descending is the base system.
So, by arranging from the bottom
= 2136 base 7
Therefore, 762 base 10 is 2136 base 7
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1
Select the correct answer.
Over which interval of the domain is function h decreasing?
x < 1
(22,
√x + 3,
z ≥ 1
h(x) =
O A.
O B.
O C.
O D. (-∞0, ∞0)
(1, 00)
(-∞0, 1)
The function is increasing only.
Answers
Twο statement for this graph are true -
O The functiοn is increasing οn the interval (-∞, 0).
O The functiοn is increasing οn the interval (0, ∞).
What is the dοmain οf functiοn?A functiοn's parameters are a grοup οf values that can be plugged intο the dοmain οf the functiοn. This set οf data cοntains the x values fοr a functiοn like f. (x).
The term "range" refers tο the set οf numbers that the functiοn cοnsiders tο be valid. The functiοn οutputs this string οf values in respοnse tο the insertiοn οf an x value.
The functiοn h(x) = 3x is a linear functiοn (straight line) with a slοpe οf 3, and a y-intercept οf 0. The cοnstant, pοsitive slοpe means that h(x) will increase οver the interval (-∞, ∞).
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The complete question is -
Given the function h(x)=3x, which statement is true about h(x)?
O The function is decreasing on the interval (-∞, 0).
O The function is increasing on the interval (-∞, 0).
O The function is decreasing on the interval (0, ∞).
O The function is increasing on the interval (0, ∞).
The population of American IQ scores are normally distributed with a mean of 101 and a standard deviation of 17. If a random sample of 416 American IQ scores are selected, what sample average score would be the 33rd percentile for all such sample averages?
Answers
In the given problem, using central limit theorem, the sample average score that corresponds to the 33rd percentile of all such sample averages is 100.66.
How to Calculate the Average?To solve this problem, we need to use the central limit theorem, which states that the distribution of sample averages is approximately normal, regardless of the distribution of the population, as long as the sample size is sufficiently large.
The mean of the sample means is equal to the population mean, which is 101. The standard deviation of the sample means, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard error of the mean is:
SE = 17 / sqrt(416) = 0.831
To find the sample average score that corresponds to the 33rd percentile of all such sample averages, we need to find the z-score that corresponds to the 33rd percentile and then use it to calculate the sample average score.
The z-score corresponding to the 33rd percentile is given by:
z = invNorm(0.33) = -0.439
where "invNorm" is the inverse normal distribution function.
We can use the formula for the z-score of a sample mean:
z = (x - μ) / SE
Rearranging this formula, we get:
x = z * SE + μ
Substituting the values we have, we get:
x = -0.439 * 0.831 + 101 = 100.66
Therefore, the sample average score that corresponds to the 33rd percentile of all such sample averages is 100.66.
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The difference of –3.2 and the sum of a number and 19.1 is at most 14.2.
A: Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2
B: Negative 3.2 minus x + 19.1 less-than-or-equal-to 14.2
C: Negative 3.2 minus (x + 19.1) greater-than-or-equal-to 14.2
D: Negative 3.2 minus x + 19.1 greater-than-or-equal-to 14.2
Answers
Answer:
C
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The difference of –3.2 and the sum of a number and 19.1 is given as:
|-3.2 - (x + 19.1)| ≤ 14.2
Simplifying the left side of the inequality:
|-22.3 - x| ≤ 14.2
The absolute value of a number is always greater than or equal to 0, so we can split the inequality into two cases:
Case 1: -22.3 - x ≤ 14.2
-36.5 ≤ x
Case 2: -22.3 - x ≥ -14.2
-8.1 ≥ x
Combining the two cases, we get:
-36.5 ≤ x ≤ -8.1
Therefore, the correct option is:
A: Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2.
The answer to question 18 and 19
Answers
The circumference of the circle is 150.768 units.
The area of the circle is 1809.216 units squared.
How to find the area and circumference of a circle?The area and circumference of a circle can be found as follows:
Let's find the circumference of the circle as follows:
circumference of a circle = 2πr
where
r = radiusTherefore,
circumference of a circle = 2πr
r = 24 units
π = 3.141
Hence,
circumference of the circle = 2 × 3.141 × 24
circumference of the circle = 150.768 units
Let's find the area of the circle as follows:
area of the circle = πr²
area of the circle = 3.141 × 24²
area of the circle = 1809.216 units squared
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Find the slope of the tangent in the positive y-direction to the surface
z = 3x + 2y − 4exy at (6, 0, 14).
If z = x2 + 5x − 3y3,
find the following.
Answers
That the gradient gives the direction of steepest ascent, so the negative of the gradient gives the direction of steepest descent.
To find the slope of the tangent in the positive y-direction to the surface z = 3x + 2y − 4exy at (6, 0, 14), we need to find the partial derivative of z with respect to y and evaluate it at the point (6,0):
∂z/∂y = 2 - 4ex(6)
At (6,0), this becomes:
∂z/∂y = 2 - 4e(36) = -646.158
So the slope of the tangent in the positive y-direction at (6,0,14) is -646.158.
To find the following for z = x2 + 5x − 3y3:
a) The partial derivative of z with respect to x:
∂z/∂x = 2x + 5
b) The partial derivative of z with respect to y:
∂z/∂y = -9y2
c) The gradient of z:
∇z = (2x + 5)i - 9y2j
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Kiran says that -2 < -5 . do you agree with Kiran?b explain or shoe your reasoning
Answers
No, Kiran is incorrect. -2 is actually greater than -5, so the correct statement is -5 < -2.
What is number line?A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). The numbers to the left of zero are all negative whereas the numbers on the right of zero are all positive. As a result, we may argue that on a number line, the value of numbers grows as we approach towards the right. The numbers on the right are thus greater than the ones on the left, according to this statement.
No, Kiran is incorrect. -2 is actually greater than -5, so the correct statement is -5 < -2.
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Find a formula for the quadratic function depicted in the following graph.
f(x)=
Answers
Answer:
Step-by-step explanation:
Without the graph or any additional information, it is not possible to determine the formula for the quadratic function f(x). The graph provides visual information about the shape and characteristics of the function, but not enough details to determine the exact coefficients of the quadratic expression.
To find the formula for a quadratic function, we need to know three coefficients: a, b, and c. These coefficients are determined by the specific shape and features of the graph, such as the vertex, intercepts, and symmetry.
If you can provide more information about the graph, such as the coordinates of some key points or any additional characteristics, I can help you find the formula for the quadratic function f(x).
HELPP PLSS The following tree diagram represents the possibilities of two spins on a fair spinner
A. What are the number of outcomes in the sample space?
B. How many favorable outcomes for spinning the same color twice in a row?
C. How many favorable outcomes for spinning blue?
Answers
Therefore , the solution of the given problem of probability comes out to be rotating blue has two positive results.
What precisely is probability?Each of the procedure's criteria-based methods have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from zero to one, where 0 typically represents percentage and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.
Here,
A. The number of potential outcomes for each spin can be multiplied to determine the number of outcomes in the sample space. Since there are two potential outcomes for each spin in this scenario, there are a total of:
=> 2 x 2 = 4
There are four potential outcomes in the sample space as a result.
B. There are two of these branches: blue-blue and red-red. Therefore, spinning the same hue twice in a row has two positive results.
C. Counting the number of branches that lead to blue on either spin will allow us to determine how many good outcomes there are for spinning blue. These stems come in two varieties: blue-red and blue-blue. Therefore, rotating blue has two positive results.
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Find the value of x and please show work
Answers
After addressing the issue at hand, we can state that As a result, x equals triangle 180 degrees.
What precisely is a triangle?A polygon is a triangle with four or more sections. It is rectangular in shape. The edges of a triangle ABC are A, B, and C. Euclidean geometry yields a single plane and cube when the sides are not collinear. A polygon is formed when a triangle has three components and three angles. The corners of a triangle are the points at which the three edges meet. Triangle sides add up to 180 degrees.A polygon is a triangle with four or more sections. It is rectangular in shape. The edges of a triangle ABC are A, B, and C. Euclidean geometry yields a single plane and cube when the sides are not collinear. A polygon is formed when a triangle has three components and three angles. The corners of a triangle are the points at which the three edges meet. Triangle sides add up to 180 degrees.
To calculate x, we must use the fact that the sum of a triangle's interior angles is 180 degrees.
First, determine the size of angle B. Angle A is 60 degrees, and angle C is 75 degrees. So,
angle B = 180 minus angle A A - angle C angle B = 180 - 60 - 75 angle B = 45
D = 360 minus angle angle A angle B angle C angle D = 360° - 60° - 45° - 75° D is equal to 180 degrees.
angle E stands for angle. D\sangle E is equal to 180 degrees.
As a result, the value of x is:
x = the angle 180 degrees = E x
As a result, x equals 180 degrees.
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which expressions represent the product of t and 9
Answers
The expression that represents the product of t and 9 is 9t
How to determine the expressionThe product of t and 9 can be represented by the following expressions:
t * 99 * t9tAll three of these expressions represent the same thing: the result of multiplying t and 9 together.
The expression "t * 9" uses the multiplication operator (*) to indicate that t and 9 are being multiplied.
The expression "9 * t" is equivalent, as multiplication is commutative and the order of the factors doesn't affect the result.
The expression "9t" is a shorthand way of writing the product, using the distributive property of multiplication.
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Lol please help me , cant get this right!!!
Answers
To understand how to get that answer is by using the quadratic formula
−b±√b^2−4(a)(c)/2a
Hope this helps
oetz Corporation has gathered the following data on a proposed investment project (Ignore income taxes.): Investment required in equipment $ 34,000 Annual cash inflows $ 7,600 Salvage value of equipment $ 0 Life of the investment 15 years Required rate of return 10% The company uses straight-line depreciation on all equipment. Assume cash flows occur uniformly throughout a year except for the initial investment. The simple rate of return for the investment (rounded to the nearest tenth of a percent) is:
Answers
The simple rate of return for the investment (rounded to the nearest tenth of a percent) is: 0.1572 or 15.7%.
What is simple rate of return?Simple rate of return is a financial metric used to measure the profitability of an investment, calculated as the ratio of net income to the initial investment.
To calculate the simple rate of return for the investment, we need to first calculate the average annual net cash inflow.
Annual net cash inflow = Annual cash inflows - Annual depreciation expense
The annual depreciation expense can be calculated as:
Depreciation expense = (Initial cost - Salvage value) / Life of investment
Depreciation expense = ($34,000 - $0) / 15 years = $2,266.67 per year
Therefore, the average annual net cash inflow is:
Annual net cash inflow = $7,600 - $2,266.67 = $5,333.33
The simple rate of return can now be calculated as:
Simple rate of return = Average annual net cash inflow / Initial investment
Simple rate of return = $5,333.33 / $34,000 = 0.1572 or 15.7% (rounded to the nearest tenth of a percent)
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Melody is planning a raised bed for her vegetable garden. How many square feet of wood does she need to create the bed? Hint: There is no bottom on the bed
Answers
Step-by-step explanation:
To calculate the amount of wood needed to create a raised bed, you will need to know the dimensions of the bed.
Assuming the raised bed is rectangular, you will need to know the length and width of the bed, as well as the height of the bed.
Once you have these dimensions, you can calculate the surface area of the raised bed by multiplying the length and width of the bed together. This will give you the area of the bottom of the bed.
To calculate the total surface area of the bed, including the sides, you will need to multiply this area by 2 (since there are two sides) and add this to the area of the bottom.
So the formula for calculating the total surface area of the raised bed is:
Total surface area = (2 x length x height) + (2 x width x height) + (length x width)
Once you have this total surface area, you can then calculate how much wood you need by multiplying it by the thickness of the wood.
For example, if the total surface area of the bed is 100 square feet and you plan to use 2-inch-thick boards, you would need 200 cubic feet of wood.
It's worth noting that this calculation assumes that the raised bed has straight sides and right angles. If the bed has a more complex shape, the calculation will be more difficult.
Model the product of -4a and 3a-2b+4c using the rectangular array shown. Drag the expression to complete the array
Answers
The product of -4a and 3a-2b+4c is calculated as: -12a²+8ab-16ac.
Explain about the product of polynomial?Sums of terms of the form kxn, where k is any quantity as well as n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.
Have used FOIL method, Box method, and distributive property, multiply two polynomials. To multiply polynomials, you can employ one of three methods.
The polynomial's zeros must be located using a method of your choice, and the linear expression that produce those zeros must then be combined in order to describe the polynomial like a product of linear factors. After factoring, you will have to filter through the third degree polynomial.
The given polynomials are-
-4a and 3a-2b+4c
Formulation of rectangular array:
3a -2b 4c
-4a : -4a*3a -4a*(-2b) -4a*(4c)
-12a² 8ab -16ac.
Thus, the product of -4a and 3a-2b+4c is calculated as: -12a²+8ab-16ac.
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Bailey works at an athletic store. He earns $90 per day plus an 11% commission on his sales. On Thursday, Bailey has $500 in sides. How much money does Bailey earn on Thursday, including his commission
Answers
Answer:
Bailey earned approximately $499.99 on Thursday, including his commission
Step-by-step explanation:
Bailey's earnings on Thursday consist of his base pay plus his commission. His base pay is $90, and his commission is 11% of his sales.
Let's call Bailey's sales on Thursday "S". Then his commission is 0.11S.
We know that Bailey's total earnings on Thursday were $500. So we can write an equation:
$90 + 0.11S = 500$
To solve for S, we can subtract $90$ from both sides of the equation:
$0.11S = 410$
Then we can divide both sides by $0.11$:
$S = 3,727.27$
So Bailey's sales on Thursday were $3,727.27.
To find Bailey's total earnings, we can add his base pay and commission:
$90 + 0.11(3,727.27) \approx 499.99$
So Bailey earned approximately $499.99 on Thursday, including his commission.
Divide 42 apples in the ratio 3:4
Answers
Answer:
18:24
Step-by-step explanation:
We know
For every 7 apples, we divided to 3:4
To get from 7 to 42, we time 6. So, we take the ratio times 6 and get 18:24
Construct a polynomial function with the started properties. Third-degree, with zeros of −3 , − 1 , and 2 , and passes through the point (3,5)
Answers
Step 1: Convert zeros to factors of the polynomial.
If "k" is a zero, then (x-k) is a factor of the polynomial.
The allows us to convert zeros of -3, -1, and 2 into the factors (x+3)(x+1)(x-2).
So right now we have y= (x+3)(x+1)(x-2), but there's a missing piece, the leading coefficient of "a", so really we currently have
y = a · (x+3)(x+1)(x-2)
This is where the point (3,5) comes in. We need to substitute x=3 and y=5 into the equation above to find a.
5 = a · (3+3)(3+1)(3-2)
5 = a · (6)(4)(1)
5 = a · 24
5/24 = a
That's the full function:
f(x) = 5/24 (x+3)(x+1)(x-2)
Answer:
[tex]f(x)=\dfrac{5}{24}x^3+\dfrac{5}{12}x^2-\dfrac{25}{24}x-\dfrac{5}{4}[/tex]
Step-by-step explanation:
The zeros of a polynomial f(x) are the values of x which satisfy f(x) = 0.
If the polynomial function is degree 3 with 3 zeros, in factored form it can be written as f(x) = k(x - r₁)(x - r₂)(x - r₃) where r are the zeros and k ≠ 0.
Substitute the given zeros -3, -1 and 2 into the formula:
[tex]\implies f(x)=k(x-(-3))(x-(-1))(x-2)[/tex]
[tex]\implies f(x)=k(x+3)(x+1)(x-2)[/tex]
To find the value of k, substitute the given point (3, 5) into the function:
[tex]\begin{aligned}\implies f(3)&=5\\k(3+3)(3+1)(3-2)&=5\\k(6)(4)(1)&=5\\24k&=5\\k&=\dfrac{5}{24}\end{aligned}[/tex]
Therefore, the factored form of the polynomial function is:
[tex]\implies f(x)=\dfrac{5}{24}(x+3)(x+1)(x-2)[/tex]
To write in standard form, expand and distribute:
[tex]\implies f(x)=\dfrac{5}{24}(x^2+4x+3)(x-2)[/tex]
[tex]\implies f(x)=\dfrac{5}{24}(x^3+2x^2-5x-6)[/tex]
[tex]\implies f(x)=\dfrac{5}{24}x^3+\dfrac{10}{24}x^2-\dfrac{25}{24}x-\dfrac{30}{24}[/tex]
[tex]\implies f(x)=\dfrac{5}{24}x^3+\dfrac{5}{12}x^2-\dfrac{25}{24}x-\dfrac{5}{4}[/tex]
Downloading 30 songs from a music website costs £45. How much does it cost to download 15 songs? How much does it cost to download 45 songs?
Answers
Answer:
Download 15 songs cost £22.50
Download 45 songs cost £67.50
Step-by-step explanation:
We know
Downloading 30 songs from a music website costs £45.
45 / 30 = £1.5 for 1 song
Download 1 song = £1.50
How much does it cost to download 15 songs?
1.5 x 15 = £22.50
How much does it cost to download 45 songs?
1.5 x 45 = £67.50
So,
Download 15 songs cost £22.50
Download 45 songs cost £67.50
Write C/d = π.
Then show how this equation can be rewritten in two steps to write a formula for the circumference of a circle in terms of its radius.
Answers
The fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.
What is circumference οf a circle?The perimeter οf a circle οr ellipse is its circumference. That is, if the circle were οpened up and straightened οut tο a line segment, the circumference wοuld be the length οf the arc.
The equatiοn C/d = π relates the circumference (C) οf a circle tο its diameter (d) using the cοnstant pi (π).
we can use the relatiοnship between the diameter and the radius:
d = 2r
We can substitute 2r fοr d in the equatiοn C/d = π, giving us:
C/(2r) = π
We can then multiply bοth sides by 2r tο isοlate C:
C = 2πr
Therefοre, the fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.
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If the base is 7.5 cm and the height is 12.2cm and the width is 4.5cm what’s the area of the parallelogra?
Answers
Answer:
The formula gives the area of a parallelogram:
Area = base x height
Substituting the given values, we get:
Area = 7.5 cm x 12.2 cm
Area = 91.5 cm^2
Therefore, the area of the parallelogram is 91.5 square centimeters.
Step-by-step explanation:
Answer:
91.5 sq cm
Step-by-step explanation:
A=bh=7.5·12.2=91.5
(a) find the critical numbers of (if any), (b)
find the open interval(s) on which the function is increasing or
decreasing, (c) apply the First Derivative Test to identify all
relative extrema, and (d) use a graphing utility to confirm your
results
Answers
(a) OIne critical number that is x = 1
(b) Function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).
(c) at x = 1, this critical number corresponds to a relative minimum.
(d) The graph is given in the attachment.
What is derivative of function?The rate change of the function at a specific point
a) The values of x where the derivative of the function equals zero or does not exist.
f'(x) = -4x + 4
Setting f'(x) equal to zero gives:
-4x + 4 = 0
-4x = -4
x = 1
So the critical number is x = 1.
(b) we need to examine the sign of the derivative on either side of the critical number.
When x < 1, f'(x) is negative, indicating that the function is decreasing.
When x > 1, f'(x) is positive, indicating that the function is increasing.
Therefore, the function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).
(c) all relative extrema, we examine the sign of the derivative in the neighborhood of the critical number x = 1. Since f'(x) changes sign at x = 1, this critical number corresponds to a relative minimum.
(d) The graph is given in the attachment.
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you deposit $300 each month into an account earning 8% interest compounded monthly. how much will you have in the account after 30 years!
Answers
Answer:
$3,280.72
Step-by-step explanation:
300(1 + [tex]\frac{.08}{12}) ^{(12x30)}[/tex] = 3280.72
Helping in the name of Jesus.
The value of 'x' in the equation log(x-3) = 5 is A. 33 B. 32. C. 35. D. 34
Answers
Therefore , the solution of the given problem of equation comes out to be x = 100,003 is the value of x that fulfils the equation log(x-3) = 5.
What is an equation?It is standard practise in mathematical formulas to employ a single variable term to ensure agreement between competing claims. Equations, which are mathematical statements, are used to demonstrate the equality of many academic expression numbers. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the data from
y + 6.
Here,
By utilising the characteristics of logarithms, we can find x.
Beginning with the expression provided:
=> log(x-3) = 5
It can be rewritten in exponential form as follows:
=> 10^5 = x - 3
When we simplify this solution, we obtain:
=> x = 10^5 + 3
We can calculate that 105 = 100,000 by using a calculator, so:
=> x = 100,000 + 3 = 100,003
As a result, x = 100,003 is the value of x that fulfils the equation
log(x-3) = 5.
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Complete the sentences about simplifying this expression once you given a value for b. 24 + b/b + 24 x 53.72
Answers
Answer:
Step-by-step explanation:
To simplify the expression 24 + b/b + 24 x 53.72,
we first need to substitute the given value of b into the expression.
For example, if b is equal to 5, we can replace all instances of b with 5 to get 24 + 5/5 + 24 x 53.72.
Next, we can simplify the division by evaluating 5/5, which equals 1.
Then, we can multiply 24 and 53.72 to get a product of 1288.28.
Finally, we can add the simplified terms to get a final result of 1312.28.
Therefore, the simplified expression, given that b is equal to 5, is 1312.28.