5. A deli bought 45kg of tuna salad R1.48 per kg. In warm weather about 5kg usually spoil before they can be sold. What price per kg will give the desired profit of 40% of selling price?
The deli needs to sell the tuna salad at a price of R2.33 per kg to achieve a profit of 40% of the selling price after 5kg spoilage.
What price per kg will give the desired profit of 40% of selling price?A desired profit also known as target profit means expected amount of profit that the managers of a business expect to achieve by the end of a designated accounting period.
First, let's calculate the cost of the tuna salad the deli purchased:
= 45kg x R1.48/kg
= R66.60
How much tuna salad the deli has left after spoilage:
= 45kg - 5kg
= 40kg
To achieve a profit of 40% of the selling price, the selling price should be 140% of the cost price: which is:
= 140% of cost price
= 1.4 x R66.60
= R93.24
To find the price per kilogram, we divide the selling price by the remaining amount of tuna salad:
= Selling price / Remaining amount of tuna salad
= R93.24 / 40kg
= R2.33/kg
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Answer: 6 dolla per kg
Step-by-step explanation:
The mug is 5/8 full, the mug contains 3/4 of water find the capacity of the mug
The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).
What is capacity?It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.
In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.
Let the capacity of the mug be x.
Given,
Mug is 5/8 full and contains 3/4 of water
So, 5/8 of the mug is filled with water
Therefore,
5/8 of x = 3/4
(5/8 )x = (3/4)
x = (3/4) × (8/5)
x = (24/20)
x = 1.2
Therefore, the capacity of the mug is 1.2.
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Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval. (Round your answers to three decimal places. If an answer does not exist, enter DNE.)
Answer:
minimum: (0.345, -1.339)maximum: (0, 1)Step-by-step explanation:
You want the absolute extremes of f(x) = -x +cos(3πx) in the interval [0, π/6].
GraphThe attached graph shows the extremes to be ...
minimum: (0.345, -1.339)maximum: (0, 1)__
Additional comment
The x-value at the minimum is (π+arcsin(1/(3π)))/(3π) ≈ 0.344612473782. The corresponding y-value is about −1.33896758676.
write an inequality for x
Which best describes the relationship between the line that passes through the points (8, 2) and (3, 5) and the line that passes through the points (–3, –7) and (0, –12)?
A. parallel
B. same line
C. perpendicular
D. neither perpendicular nor parallel
The best line that represents the relation between the lines that passes through the points (8, 2) and (3, 5) and the line (-3, -7) and (0, -12) is a perpendicular line.
What are perpendicular lines?
In geometry, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90 ∘). The term ‘perpendicular’ originated from the Latin word ‘perpendicularis,’ meaning a plumb line. If two lines AB and CD are perpendicular, then we can write them as AB ⊥ CD.
To determine the relationship between the two lines, we can first find the slope of each line using the two-point formula:
Slope of the line passing through (8, 2) and (3, 5):
m1 = (5 - 2) / (3 - 8) = -3/5
Slope of the line passing through (–3, –7) and (0, –12):
m2 = (-12 - (-7)) / (0 - (-3)) = -5/-3 = 5/3
If the two lines are parallel, their slopes will be equal. However, -3/5 is not equal to 5/3. If the two lines are perpendicular, their slopes will be negative reciprocals of each other. That is,
m1 x m2 = -1
But, (-3/5) x (5/3) = -1, which means that the two lines are perpendicular.
Therefore, the correct answer is C. perpendicular.
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Pls help fast! Will get 20+ and brainliest
Answer:
a) 30 × .5 = 15 days
b) .2 + .1 = .3
1. What is the breakeven point in unit sales and dollars for each type of filter at the current sales mix?
For fau/cet filter:
The break-even point in unit sales is 28,571 units.The break-even point in dollar is $2,571,390.For pitcher-filter:
The break-even point in unit sales is 22,222 units.The break-even point in dollar is $2,444,420.How do we calculate breakeven point in unit sales and dollars?Let's start with the fau/cet model:
Contribution margin per unit = selling price - variable cost
Contribution margin per unit = $90 - $25
Contribution margin per unit = $65
Contribution margin ratio = contribution margin per unit / selling price
Contribution margin ratio = $65 / $90
Contribution margin ratio = 0.722
The sales mix is 2 faucet models for every 3 pitcher filters sold, so the contribution margin weighted average is:
= (2/5)($65) + (3/5)($90-$20)
= $42
Now we can calculate the break-even point in units for the faucet model:
= Total fixed costs / contribution margin per unit
= $1,200,000 / $42
= 28,571 units
For pitcher filter:
Contribution margin per unit = selling price - variable cost
Contribution margin per unit = $110 - $20
Contribution margin per unit = $90
Contribution margin ratio = contribution margin per unit / selling price
= $90 / $110
Contribution margin ratio = 0.818
Contribution margin weighted average:
= (2/5)($25) + (3/5)($90-$20)
= $54
Break-even point in units for pitc/her filter:
= Total fixed costs / contribution margin per unit
= $1,200,000 / $54
= 22,222 units
Break-even point in dollars for fau/cet model:
= 28,571 units x $90 per unit
= $2,571,390
Break-even point in dollars for pitc/her-filter:
= 22,222 units x $110 per unit
= $2,444,420
Full question "Multiproduct CVP and decision making. Crystal Clear Products produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet. The other is a pitcherfilter that only purifies water meant for drinking. The unit that attaches to the faucet is sold for $90 and has variable costs of $25. The pitcherfilter sells for $110 and has variable costs of $20. Crystal Clear sells two faucet models for every three pitchers sold. Fixed costs equal $1,200,000.
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(1/64)^(2/3)
SOLVE LAW OF INDICES
Answer:
To solve this problem, we can use the laws of indices, specifically the law that states that (a^m)^n = a^(m*n).
So, we have:
(1/64)^(2/3) = (1^(2/3))/(64^(2/3))
Since any number raised to the power of 1 is itself, we can simplify the numerator to just 1.
Now, we have:
(1/64)^(2/3) = 1/(64^(2/3))
To evaluate 64^(2/3), we can use the law of indices again, which states that a^(1/n) = nth root of a. In this case, we have:
64^(2/3) = (64^(1/3))^2 = 4^2 = 16
So, substituting this back into the original expression, we have:
(1/64)^(2/3) = 1/16
Therefore, (1/64)^(2/3) simplifies to 1/16.
Step-by-step explanation:
Answer:
Using the law of indices, we have:
(1/64)^(2/3) = (1^(2/3))/(64^(2/3))
Now we need to simplify the denominator by finding the cube root of 64:
64^(1/3) = 4
Substituting this value in the original expression, we get:
(1/64)^(2/3) = (1^(2/3))/(4^2)
Simplifying further, we have:
(1/64)^(2/3) = 1/16
Step-by-step explanation:
y=-x+8 4x+y=5
Help me pls
Answer: x = -1 and y = 9
Step-by-step explanation:
To solve this system of equations, we can use the substitution method.
First, solve the first equation for y:
y = -x + 8
Now, substitute this expression for y into the second equation and solve for x:
4x + y = 5
4x + (-x + 8) = 5 (substituting -x + 8 for y)
3x + 8 = 5
3x = -3
x = -1
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
y = -x + 8
y = -(-1) + 8
y = 9
Therefore, the solution to the system of equations is x = -1 and y = 9.
A person places $741 in an investment account earning an annual rate of 5.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe
rt
, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years.
The nearest cent, the amount of money in the account after 13 years is $2,094.18.
The formula for continuous compound interest is:
V = Pe^(rt)
where V is the value of the account after t years, P is the principal (initial amount) invested, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time period in years.
In this case, P = $741, r = 0.058 (since the annual interest rate is 5.8%), and t = 13. Substituting these values into the formula, we get:
V = 741e^(0.058*13)
Using a calculator, we can evaluate e^(0.058*13) to be approximately 2.8302. Then, we can multiply this value by 741 to get:
V = 741*2.8302
V ≈ $2,094.18
Therefore, to the nearest cent, the amount of money in the account after 13 years is $2,094.18.
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When 60% of a number is added to the number 160, the result is .
Any percentage can be written as that number divided by 100. As a decimal, you find that quotient. You can quickly divide any number by 10 by moving the decimal place to the left for every 0 in that multiple of 10. 100 has 2 zeros, so all you need to do to divide by 100 is to move the decimal place 2 places to the left. Therefore, 60% is .6 as a decimal.
Let's say the number we want to find is x. In word problems, "of" indicates multiplication, so 60% of our number would be 6x.
We then add our number to that, giving us .6x + x
We know the result is 160, so
.6x + x = 160
Since any number multiplied by 1 is itself, that x can be written as 1x.
.6x + 1x = 160
Now, we combine our like terms; we add the numbers in front of the x's (aka coefficients).
(.6 + 1)x = 160
1.6x = 160
We want x by itself. 1.6 is multiplied by our number, so to undo multiplication, we do division. This leaves us with
x = 160/1.6
x=100
Sarah spent 5 minutes painting. She spent twice as much time reading
as she spent painting. She spent 35 more minutes hiking than she
spent reading. How many minutes did she spend doing these three
activities?
After answering the provided question, we can conclude that So the total equation amount of time Sarah spent on these three activities is determined by how much time she spent reading.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x^2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.
Let's call Sarah's reading time "r" in minutes.
We can deduce from the problem:
Sarah painted for 5 minutes.
Because she spent twice as much time reading as she did painting,[tex]r = 2*5 = 10.[/tex]
She hiked for 35 minutes longer than she read, so [tex]h = r + 35.[/tex]
To calculate Sarah's total time spent on these three activities, simply add the times:
Time spent painting + time spent reading + time spent hiking = total time
Time total =[tex]5 + 10 + (r + 35)[/tex]
Time total = [tex]50 + r[/tex]
So the total amount of time Sarah spent on these three activities is determined by how much time she spent reading.
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=
For the cost and price functions below, find a) the number, q, of units that produces maximum profit; b) the price, p, per
unit that produces maximum profit; and c) the maximum profit, P.
C(q) = 70+ 15q; p=63-2q
a) The number, q, of units that produces maximum profit is q =
b) The price, p, per unit that produces maximum profit is p = $
c) The maximum profit is P = $
a) The number of units that produces maximum profit is q = 12.
b) The price per unit that produces maximum profit is p = $39.
c) The maximum profit is P = $386.
What is profit?
a) To find the number of units that produces maximum profit, we need to find the point where revenue equals cost. The revenue function is given by:
R(q) = pq = (63-2q)q = 63q - 2q²
The cost function is given by:
C(q) = 70 + 15q
The profit function is given by:
P(q) = R(q) - C(q) = (63q - 2q²) - (70 + 15q) = -2q² + 48q - 70
To find the number of units that produces maximum profit, we take the derivative of the profit function with respect to q, and set it equal to zero:
P'(q) = -4q + 48 = 0
Solving for q, we get:
q = 12
Therefore, the number of units that produces maximum profit is q = 12.
b) To find the price per unit that produces maximum profit, we substitute q = 12 into the price function:
p = 63 - 2q = 63 - 2(12) = 39
Therefore, the price per unit that produces maximum profit is p = $39.
c) To find the maximum profit, we substitute q = 12 and p = 39 into the profit function:
P = -2q² + 48q - 70 = -2(12)² + 48(12) - 70 = $386
Therefore, the maximum profit is P = $386.
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Round the solution up to the nearest whole number, if necessary.
A sample size that would give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years is 1,227.
How to determine the sample size?In Mathematics and Statistics, a sample size that would result in a standard deviation of 0.8 years can be calculated by using the mathematical equation (formula):
Sample size, n = (zσ/ME)²
Where:
n represents the sample size.z represents the z-score of the desired confidence level. σ represents the standard deviation of the population.ME represents the margin of error.By assuming a confidence level of 95% with a z-score of 1.96, we would substitute the given parameters into the formula for sample size as follows;
Sample size, n = (zσ/E)²
Sample size, n = (1.96 × 14.3/0.8)²
Sample size, n = (28.028/0.8)²
Sample size, n = (35.035)²
Sample size, n = 1,227.45 ≈ 1,227.
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Complete Question:
Suppose the standard deviation of the ages of all Florida panthers is 14.3 years. Let [tex]\bar{x}[/tex] be the mean age for a sample of a certain number of Florida panthers. What sample size will give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years?
Round the solution up to the nearest whole number, if necessary.
Find the value of V.
From the diagram the value of v is √6
How to solve for the value of v?You should recall that Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
Using the trigonometrical ratios, we have
Tangent = opposite /adjacent
This implies that
√2/1 = 2√3/v
cross and multiplying to have
v√2 = 2√3
Rationalizing the denominator and making v the subject of the formular we have
v = 2√3/√2 *√2/√2
v = 2√2/2
Therefore the value of v is √6
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solve for x: p(x)=x^3+6x^2+3x-10=0
Answer:
Step-by-step explanation:
P(x)=x³+6x²+3x-10=0
x³+2x²+4x²+8x-5x-10=0
x²(x+2)+x(x+2)-5(x+2)=0
(x+2)(x²+x-5)=0
either x+2=0,x=-2
or
x²+x-5=0
[tex]x=\frac{-1 \pm \sqrt{1^2-4 \times 1 \times(-5)} }{2 \times 1} \\=\frac{-1 \pm \sqrt{21} }{2} \\Hence ~x=\frac{-1+\sqrt{21} }{2} \\or\\x=\frac{-1 -\sqrt{21} }{2}[/tex]
In 1970, 11% of Americans completed four years of college
Answer:
Thank you for the statement. Is there a question or additional information you would like me to respond to?
Step-by-step explanation:
1383400691
Find the experimental probability that 3 of 4
children in a family are boys.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHH HTTH TTTT THTT HTHT
HHTT HHHT THHT HTTH TTHH
HTTT HTHT TTHH THTH HTHH
TTHT HTTT HTHT HHHT HHHH
Experimental Probability
What is 55 increased by 10%
Answer:
60.5
Step-by-step explanation:
Answer: 60.50
Step-by-step explanation:
.
I need helppppppppp please help me
A committee of ten health professionals has been selected to investigate the ethical conduct of some health workers in a health facility.A sub committees of four health professionals is to be selected out of the ten health professionals . Find how many ways this can happen
Answer:
Step-by-step explanation:
Functions for -4,-6,-9,-27/2,-81/2
The function of the sequence -4,-6,-9,-27/2,-81/2 is f(n) = -4(3/2)^(n - 1)
Identifying the function of the sequence
from the question, we have the following parameters that can be used in our computation:
-4,-6,-9,-27/2,-81/2
The above sequence is a geometric sequence
This is because it has a common ratio calculated as
r = -6/-4
So, we have
r = 3/2
The sequence is then represented as
f(n) = ar^n-1
So, we have
f(n) = -4(3/2)^(n - 1)
Hence, the function is f(n) = -4(3/2)^(n - 1)
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15. Mathew waxes a car twice as fast as Andrea. If Andrea takes 24 minutes to wax the car, how much
time will they take together to wax the same car?
A) 8 minutes
B) 18 minutes
C) 12 minutes D) 16 minutes
E) 10 minutes
According to the solving time will they take together to wax the same car 16 minutes
Define minutes?The minute is a unit of time usually equal to 160 (the first sexagesimal fraction) of an hour, or 60 seconds.
According to the given information:Let's assume that Andrea takes x minutes to wax the car. Then Mathew takes x/2 minutes to wax the same car since he waxes twice as fast as Andrea.
We know that Andrea takes 24 minutes to wax the car. So we can substitute this value in the equation and solve for x.
x = 24 * 2 = 48
So Andrea takes 48 minutes to wax the car alone.
Now we can use the formula:
1/x + 1/(x/2) = 1/t
where t is the time taken by both of them together to wax the same car.
Substituting x = 48, we get:
1/48 + 1/24 = 1/t
Solving for t, we get:
t = 16minutes
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Decompose and find the area of the composite figure
The composite figure has a total area of 102 square units (80 + 16 + 6 square units). Consequently, the composite figure has a 102 square unit area.
How can you calculate a composite figure's entire surface area?Composite things that are three dimensional (3D) are constructed from two or more separate pieces. Finding each item's outside surface area and adding the surface areas together will yield the surface area of a 3D composite object. Another way to divide it is into a top and a bottom.
We may divide the composite figure into smaller forms and sum up their areas to determine the area of the overall figure. Here is one method for breaking down the figure:
A rectangle and two triangles make up the figure.
The rectangle has an area of 80 square units since it is 10 units long and 8 units wide.
The two triangles have right triangles with four and six unit-long legs, respectively. The equation (base * height) / 2 may be used to calculate each triangle's area.
The area of the triangle on the left is (4 * 8) / 2 or 16 square units since its base is 4 units and its height is 8 units (the length of the rectangle).
The area of the triangle on the right is (6 * 2) / 2 or 6 square units because its base is 6 units and its height is 2 units (the distance between the bottom of the triangle and the bottom of the rectangle).
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Consider figures 1 and 2 shown on the coordinate plane. Figure 1 has been transformed to produce figure 2.
This transformation of figure 1 has been transformed to produce figure 2, can be described by (x' , y') = (x' -y')
What is transformation in geometry?Transformation describes how an item moves, particularly as they are shown on a coordinate plane.
There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or position. The four methods comprise
rotationdilationreflectiontranslationPre-Image refers to the item's shape before transformation, whereas Image refers to the object's ultimate location and shape.
The linked image's preimage and image may be examined to determine that reflection is the involved translation.
The transformation rule for reflection over the y-axis is as follows:
(x, y) → (x, -y)
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These are the questions I was talking about
Tim's score range would be between 20.2 - 56.25 and 20.2 + 56.25, or between -36.05 and 76.45. To find the percentage of games
a. To find the percentage of candy wrappers that would have between 3.4 and 3.6 ounces, we need to calculate the z-scores for each of the values:
[tex]z-score for 3.4 ounces = (3.4 - 3.5) / 0.16 = -0.625[/tex]
[tex]z-score for 3.6 ounces = (3.6 - 3.5) / 0.16 = 0.625[/tex]
Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers between these two values is approximately 47.70%.
b. To find the percentage of candy wrappers that would have less than 3.3 ounces, we need to calculate the z-score for this value:
[tex]z-score for 3.3 ounces = (3.3 - 3.5) / 0.16 = -1.25[/tex]
Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with less than 3.3 ounces is approximately 10.92%.
To find the percentage of candy wrappers with more than 3.62 ounces, we need to calculate the z-score for this value:
[tex]z-score for 3.62 ounces = (3.62 - 3.5) / 0.16 = 0.75[/tex]
Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with more than 3.62 ounces is approximately 22.77%.
c. To find how many of the 1358 packets made that day have between 3.35 and 3.65 ounces, we need to convert these values to z-scores:
[tex]z-score for 3.35 ounces = (3.35 - 3.5) / 0.16 = -0.9375[/tex]
[tex]z-score for 3.65 ounces = (3.65 - 3.5) / 0.16 = 0.9375[/tex]
Using a z-table or a calculator with a normal distribution function, we can find the percentage of candy wrappers between these two values, which is approximately 62.97%. To find how many packets this represents, we can multiply this percentage by the total number of packets made:
[tex]0.6297 * 1358 = 856 packets[/tex]
Therefore, approximately 856 packets made that day have between 3.35 and 3.65 ounces.
d. To find how many games Tim would have scored 22 points or more if he plays 32 games, we first need to calculate the z-score for this value:
[tex]z-score for 22 points = (22 - 20.2) / 25 = 0.072[/tex]
Using a z-table or a calculator with a normal distribution function, we can find the percentage of games with a z-score greater than or equal to 0.072, which is approximately 53.10%. To find how many games this represents, we can multiply this percentage by the total number of games:
[tex]0.5310 x 32 = 17 games[/tex]
Therefore, Tim would have scored 22 points or more in approximately 17 games out of 32.
e. To find how many games Tim would have scored within 2.25 standard deviations from his average if he plays 32 games, we first need to calculate 2.25 standard deviations:
[tex]2.25 x 25 = 56.25[/tex]
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Meredith drives 5 miles to the northeast, then 15 miles to the southeast, then 25 miles to the
southwest, then 35 miles to the northwest, and finally 20 miles to the northeast. How many miles is
Meredith from where she started?
A study of adult Americans conducted by the polling organization Ipsos asked each person in a sample whether he or she self-identified as an entrepreneur. The responses to the question were used to learn about the population of adult Americans who self identify as an entrepreneur.
(a) What is the question type? (i) Estimation (ii) Hypothesis Testing
(b) What is the study type? (i) Experimental data (ii) Sample data 1
(c) Type (Part 1): Is the data categorical or numerical? (i) Categorical (ii) Numerical
(d) Type (Part 2): How many variables? (i) one (ii) two (iii) more than two
(e) How many samples or treatments are there? (i) one (ii) two (iii) more than two
(f) M: What is the appropriate method for analysis of data? (Use Table 7.1 of Section 7.2 and your answer to the previous questions to complete.) (i) One-sample z confidence interval for a proportion (ii) One-sample z test for a proportion (iii) Two-sample z confidence interval for a difference in proportions (iv) Two-sample z test for a difference in proportions (v) One-sample t confidence interval for a mean (vi) One-sample t test for a mean (vii) Two-sample t or Paired t confidence interval for a difference in means (viii) Two-sample t or Paired t test for a difference in means (ix) ANOVA F Test (x) Multiple Comparisons
Hypothesis Testing ,Sample data , Categorical ,one variable ,one sample and sample z test for a proportion are the responses to the question were used to learn about the population of adult Americans who self identify as an entrepreneur.
(a) The question type in this study is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.
(b) The study type is sample data, as a sample of adult Americans was surveyed to learn about the population of adults who self-identify as entrepreneurs.
(c) The data is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.
(d) There is one variable in this study, as the responses to the question about self-identification as an entrepreneur are the only data collected.
(e) There is one sample in this study, as only one group of adult Americans was surveyed.
(f) The appropriate method for analyzing the data in this study is the one-sample z test for a proportion. This method is used when we have one categorical variable and want to test whether the proportion of a certain response differs significantly from a hypothesized proportion. In this case, the hypothesized proportion would be the proportion of adult Americans who self-identify as entrepreneurs. We would use the z-test to determine if the proportion of respondents who self-identify as entrepreneurs is significantly different from the hypothesized proportion. If the difference is significant, we can conclude that there is a difference between the sample and population proportions, and if the difference is not significant, we cannot reject the null hypothesis that the sample proportion is the same as the population proportion.
Overall, this study is using categorical data to learn about the proportion of adult Americans who self-identify as entrepreneurs. The appropriate method for analyzing this type of data is the one-sample z test for a proportion, which allows us to test whether the sample proportion is significantly different from the hypothesized population proportion.
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Please help me find the arc!!!
The length of the arc that is drawn in a circle of radius 14 cm and angle of arc 135° is approximately 32.67 cm.
What is an arc?An arc is a portion of a curve that is part of a circle. It is defined as a continuous portion of the circumference of a circle. In other words, an arc is a segment of a circle's circumference.
To find the length of an arc of circle, you can use the formula:
arc length = (angle of arc / 360) x (2 x π x radius)
Where π (pi) is a mathematical constant approximately equal to 3.14.
In this problem, the radius of the circle is given as 14 cm and the angle of the arc is 135°. So, By substituting these values in the formula, we get:
arc length = (135/360) x (2 x π x 14)
arc length = (3/8) x (2 x 3.14 x 14)
arc length = (3/8) x (87.92)
arc length = 32.67 cm (rounded to two decimal places)
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F.BF.1b Combine standard function types using arithmetic o
Give the equation for f(x) + g(x) given that
f(x) = x² - x + 1 and g(x) = 2x + 3
We can easily say that the following about this question:
Functions are polynomial expressions.Arithmetic operations are performed between coefficients of terms of the same degree. Coefficients of different degrees are written as they are, without being changed.[tex]f(x)=x^2-x+1[/tex] and [tex]g(x)=2x+3[/tex] can be combined as;
[tex]f(x)+g(x)=x^2+(2-1)x+(3+1)[/tex][tex]f(x)+g(x)=x^2+x+4[/tex]