Answers
The piecewise function forms of the absolute values are, respectively:
Case 1 (|(x - 19) + 11|)
x - 8 for x > 8
0 for x = 8
8 - x for x < 8
Case 2 (|14 - (x - 6)|)
- x + 22 for x < 22
0 for x = 22
x - 22 for x > 22
Case 3 (|14 - (6 - x)|)
x + 8 for x > - 8
0 for x = - 8
- x - 8 for x < - 8
How to rewrite absolute value functionsIn this problem we find three cases of absolute values represented in a single expression. Herein we need to determine an alternative form without "bar" operators.
This form is represented by a piecewise function derived from definition of absolute value:
|x - a| = x - a for x > a|x - a| = a - x for x < a|x - a| = 0 for x = a.Then, we find the following definitions for each of the three cases:
Case 1
|(x - 19) + 11| = |x - 8|
|x - 8| = x - 8 for x > 8
|x - 8| = 0 for x = 8
|x - 8| = 8 - x for x < 8
Case 2
|14 - (x - 6)| = |- x + 22|
|- x + 22| = - x + 22 for x < 22
|- x + 22| = 0 for x = 22
|- x + 22| = x - 22 for x > 22
Case 3
|14 - (6 - x)| = |x + 8|
|x + 8| = x + 8 for x > - 8
|x + 8| = 0 for x = - 8
|x + 8| = - x - 8 for x < - 8
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Related Questions
find surface area of cilinder with the radius of 9 and height of 14. make sure to put the correct exponents with answer.
Answers
The cylindrical has a surface area of 414 square units due to its 9-unit radius and 14-unit height.
what is cylinder ?A cylinder is a three-dimensional geometric form made up of two circular bases that are parallel to one another and are joined by a curved lateral surface. It can be pictured as a solid item with a constant circular cross-section along its entire length. The measurements of a cylinder, such as the radius and height of the circular bases, affect its characteristics. The surface area, volume, and horizontal surface area of a cylinder are some of its typical characteristics. Mathematical formulas can be used to determine these properties.
given
The following algorithm determines a cylinder's surface area:
[tex]A = 2\pi r^2 + 2\pi rh[/tex]
where r is the cylinder's base's radius, h is the cylinder's height, and (pi) is a mathematical constant roughly equivalent to 3.14.
Inputting the numbers provided yields:
[tex]A = 2\pi (9)^2 + 2\pi (9)(14)\\[/tex]
A = 2π(81) + 2π(126)
A = 162π + 252π
A = 414π
The cylindrical has a surface area of 414 square units due to its 9-unit radius and 14-unit height.
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The scale on a map is 1:320000
What is the actual distance represented by 1cm?
Give your answer in kilometres.
Answers
By answering the presented question, we may conclude that Therefore, 1 expressions cm on the map corresponds to a real distance of 3.2 km.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Scale 1:
320000 means that 1 unit on the map represents his 320000 units in the real world.
To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.
1 kilometer = 100000 cm
So,
1 unit on the map = 320000 units in the real world
1 cm on the map = (1/100000) km in the real world
Multiplying both sides by 1 cm gives:
1 cm on the map = (1/100000) km * 320000
A simplification of this expression:
1 cm on the map = 3.2 km
Therefore, 1 cm on the map corresponds to a real distance of 3.2 km.
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Question 8 Suppose that W is random variable. Given that P(W ≤6)=0.935 find the probability of it complement, P(W>6)
Answers
The required probability of W being greater than 6 is 0.065 or 6.5%.
What is Probability?A probability value represents the likelihood that an occurrence will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
According to question:The complement of an event A is the event that A does not occur. In this case, the event A is "W ≤ 6", and its complement is "W > 6".
We are given that P(W ≤ 6) = 0.935. Using the complement rule of probability, we can find the probability of W > 6 as follows:
[tex]$$P(W > 6) = 1 - P(W \leq 6)$$[/tex]
Substituting the given value, we have:
P(W > 6) = 1 - 0.935 = 0.065
Therefore, the probability of W being greater than 6 is 0.065 or 6.5%.
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What is the perimeter of the football field without the end zones?
Answers
Answer:
30623 yards
Step-by-step explanation:
Answer:
In the NFL, the perimeter of a football field, excluding the end zones, is 30623 yards. The field is how many feet wide... A football field in the United States is 120 yards long (including the end zones).
Step-by-step explanation:
Brainliest pls
describe all the x -values at a distance of 13 or less from the number 8 . enter your answer in interval notation.
Answers
The set of all x-values that are at a distance of 13 or less from the number 8 in the interval notation is given by [ -5, 21 ].
The distance between x and 8 is |x - 8|.
Find all the values of x such that |x - 8| ≤ 13.
This inequality can be rewritten as follow,
|x - 8| ≤ 13
⇒ -13 ≤ x - 8 ≤ 13
Now,
Adding 8 to all sides of the inequality we get,
⇒ -13 + 8 ≤ x - 8 + 8 ≤ 13 + 8
⇒ -5 ≤ x ≤ 21
Therefore, all the x-values which are at a distance of 13 or less from the number 8 represented in the interval notation as [ -5, 21 ].
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Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
Answers
The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.
The expression !(!(x < y) || (y != 5)) is equivalent to:
(x < y) && (y == 5)
To see why, let's break down the original expression:
!(!(x < y) || (y != 5))
= !(x >= y && y != 5) (by De Morgan's laws)
= (x < y) && (y == 5) (by negating and simplifying)
So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.
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Complete question:
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
(x < y) && (y != 5)
(x >= y) && (y == 5)
(x < y) || (y == 5)
(x >= y) || (y != 5)
pls helppppppp explain !!!
Answers
Answer:
x²
Step-by-step explanation:
[tex]{ \tt{ \frac{ {x}^{ - 3} . {x}^{2} }{ {x}^{ - 3} } }} \\ \\ \dashrightarrow{ \tt{x {}^{( - 3 + 2 - ( - 3))} }} \\ \dashrightarrow{ \tt{ {x}^{( - 3 + 2 + 3)} }} \: \: \: \: \\ \dashrightarrow{ \boxed{ \tt{ \: \: \: \: {x}^{2} \: \: \: \: \: \: }}} \: \: \: \: [/tex]
The retail price of a television set is $4,500. If the buyer pays by cash, the price is 10% below the retail price. If the set is bought on higher purchase, the buyer pays a down payment of $675 and 24 monthly installments of $212.50. Calculate for the television the:
cash price to the buyer, if he pays by cash.
amount payable.
outstanding balance.
hire purchase price.
interest.
difference between the hire purchase and the cash price.
percentage interest charged.
Answers
Cash price to the buyer, if he pays by cash:
The cash price would be 10% less than the retail price of $4,500:
Cash price = $4,500 - (10% * $4,500)
Cash price = $4,500 - $450
Cash price = $4,050
Amount payable:
If the buyer chooses to purchase the TV on higher purchase, the amount payable would be the sum of the down payment and the total amount of monthly installments:
Amount payable = Down payment + (24 * Monthly installment)
Amount payable = $675 + (24 * $212.50)
Amount payable = $5,175
Outstanding balance:
The outstanding balance would be the difference between the amount payable and the down payment:
Outstanding balance = Amount payable - Down payment
Outstanding balance = $5,175 - $675
Outstanding balance = $4,500
Hire purchase price:
The hire purchase price would be the sum of the down payment and the outstanding balance:
Hire purchase price = Down payment + Outstanding balance
Hire purchase price = $675 + $4,500
Hire purchase price = $5,175
Interest:
The interest charged on the hire purchase would be the difference between the hire purchase price and the cash price:
Interest = Hire purchase price - Cash price
Interest = $5,175 - $4,050
Interest = $1,125
Difference between the hire purchase and the cash price:
The difference between the hire purchase price and the cash price would be the interest charged:
Difference = Interest
Difference = $1,125
Percentage interest charged:
To calculate the percentage interest charged, we can divide the interest by the hire purchase price and multiply by 100:
Percentage interest charged = (Interest / Hire purchase price) * 100
Percentage interest charged = ($1,125 / $5,175) * 100
Percentage interest charged = 21.74%
Therefore, the cash price to the buyer is $4,050, the amount payable is $5,175, the outstanding balance is $4,500, the hire purchase price is $5,175, the interest charged is $1,125, the difference between the hire purchase and the cash price is $1,125, and the percentage interest charged is 21.74%.
Find the product of 3√20 and √5 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answers
Answer:
30, rational
Step-by-step explanation:
[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]
The result is rational because it can be written as a fraction of integers.
one ticket is drawn at random from each of the two boxes below: 1 2 6 1 4 5 8 find the chance that the both numbers are even numbers.
Answers
The chance that both numbers drawn are even numbers is 8/21.
The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.
The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.
By the multiplication rule of probability, the probability of drawing an even number from both boxes is
(4/7) × (2/3) = 8/21
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Consider the initial value problem y⃗ ′=[33????23????4]y⃗ +????⃗ (????),y⃗ (1)=[20]. Suppose we know that y⃗ (????)=[−2????+????2????2+????] is the unique solution to this initial value problem. Find ????⃗ (????) and the constants ???? and ????.
Answers
The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.
To find the solution to the initial value problem, we first need to solve the differential equation.
Taking the derivative of y(t), we get:
y'(t) = -2t + a
Taking the derivative again, we get:
y''(t) = -2
Substituting y''(t) into the differential equation, we get:
y''(t) + 2y'(t) + 10y(t) = 20sin(3t)
Substituting y'(t) and y(t) into the equation, we get:
-2 + 2a + 10(-2t + a) = 20sin(3t)
Simplifying, we get:
8a - 20t = 20sin(3t) + 2
Using the initial condition y(0) = 2, we get:
y(0) = -2(0) + a = 2
Solving for a, we get:
a = 2
Using the other initial condition y'(0) = 21, we get:
y'(0) = -2(0) + 2(21) + B = 21
Solving for B, we get:
B = -21
Therefore, the solution to the initial value problem is:
y(t) = -t^2 + 2t + 3sin(3t) - 1
Thus, we have e(t) = y(t) - 8, so
e(t) = -t^2 + 2t + 3sin(3t) - 9
and a = 2, B = -21.
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_____The given question is incomplete, the complete question is given below:
Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =
he is paid $22.60 an hour. He normally earns $904 each week. Last week he worked an extra 3 hours at time-and-a-half
his total income last week = $
Answers
Answer:
971.8
Step-by-step explanation:
A simple random sample of size n is drawn. The sample mean, x, is found to be 18.1, and the sample standard deviation, s, is found to be 4.1.
(a) Construct a 95% confidence interval about u if the sample size, n, is 34.
Lower bound: Upper bound:
(Use ascending order. Round to two decimal places as needed.)
Answers
In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
We use the following formula to create a confidence interval around the population mean u:
CI = x ± z*(s/√n)
where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.
Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.
CI = 18.1 ± 1.96*(4.1/√34)
CI = 18.1 ± 1.96*(0.704)
CI = 18.1 ± 1.38
Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.
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3. The total number of Democrats and Republicans in the US House of Reps during the 115th
year was 434. There were 46 fewer Democrats than Reps. How many were there of each
party?
Answers
Answer:
Step-by-step explanation:
subtract 434-46
Brendan buys items at a cost of $23 each and sells them at $56 each.
His profit per item is
Answers
A cube of sugar is 2cm wide. Calculate the number of cube in a box 720cm³
Answers
Answer:
V=lwh
=2×2×2=8
720÷8=90
90 cubes
I will mark you brainiest!
SSS is used to prove two triangles are congruent.
A) False
B) True
Answers
Answer:
A
Step-by-step explanation:
because___________________________________
Answer:
B) True
Step-by-step explanation:
SSS or Side-Side-Side is used to prove two triangles are congruent.
Bill buys candy that costs $5 per pound. He will spend at least $40 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Bill will buy. Write your answer as an inequality solved for p.
Answers
Answer: 5p = 40
Step-by-step explanation:
5 X p = 40
5/5 40/5
p = 8
Marcia Gadzera wants to retire in San Diego when she is 65 years old. Marcia is now 50 and believes she will need $90,000 to retire comfortably. To date, she has set aside no retirement money. If she gets interest of 10% compounded semiannually, how much must she invest today to meet her goal of $90,000?
Answers
Answer:
Step-by-step explanation:
We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where:
FV = future value of the annuity
PMT = payment (or deposit) made at the end of each compounding period
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:
Marcia wants to retire in 15 years (when she is 65), so t = 15
The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2
Marcia wants to have $90,000 in her retirement account
Substituting these values into the formula, we get:
$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)
Simplifying the formula, we get:
PMT = $90,000 / [(1.025)^30 - 1] / 0.025
PMT = $90,000 / 19.7588
PMT = $4,553.39 (rounded to the nearest cent)
Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.
3.4 3.2 3.3 5m 3.142 Radius of semi-circie = 5.5m Area of cir Au 35m YOGA TWEM Define the word Perimeter in this context. Calculate the length of the swimming pool. If the circumference of the semi-circle is 17 3m. Calculate tl. total perimeter of the swimming pool. Calculate the total area of the floor of the swimm You may use the given formu
Answers
In the context of a semi-circle, the perimeter refers to the total distance around the curved edge of the semi-circle. It is calculated by adding the length of the straight edge (diameter) to half the circumference of the semi-circle.
The total area of the floor of the swimming pool is 23.86 square meters.
How to calculate the valueThe diameter of the semi-circle is twice the radius, so the diameter is 2 × 5.5m = 11m.
Therefore, the perimeter of the semi-circle is:
Perimeter = Diameter + Circumference/2
Perimeter = 11m + 17.3m/2
Perimeter = 20.3m
The length of the swimming pool is equal to the perimeter of the semi-circle, which is 20.3 meters.
To calculate the total area of the floor of the swimming pool, we need to find the area of the semi-circle. The formula for the area of a semi-circle is:
Area = πr²/2
where π is a constant approximately equal to 3.14 and r is the radius of the semi-circle.
In this case, the radius is 5.5m, so the area of the semi-circle is:
Area = π(5.5m)²/2
Area = 47.71m²/2
Area = 23.86m²
Therefore, the total area of the floor of the swimming pool is 23.86 square meters.
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Radius of semi-circle = 5.5m Define the word Perimeter in this context. Calculate the length of the swimming pool. If the circumference of the semi-circle is 17 3m. Calculate the total area of the floor of the swimming pool.
What is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2?"
one half x (8 − 6) + 2
one half x (6 + 8 + 2)
one half x (6.08 − 2)
one half − (6.08 ÷ 2)
Answers
Answer: c
Step-by-step explanation: i dont have one
1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .
what is expression ?An expression, as used in computer programming, is a grouping of values, variables, operators, and/or function calls that the computer evaluates to produce a final value. For instance, the equation 2 + 3 combines the numbers 2 and 3 using the + operator to produce the number 5. Similar to this, the equation x * (y + z) produces a value based on the current values of the variables x, y, and z by combining the variables x, y, and z with the * and + operators.
given
In terms of numbers, the phrase "one-half the difference of 6 and 8 hundredths and 2" is expressed as follows:
1/2 x (6.08 - 2) (6.08 - 2)
1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .
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Question 7 (2 points)
A survey asked 1,000 people if they invested in Stocks or Bonds for retirement. 700
said they invested in stocks, 400 said bonds, and 300 said both.
How many invested in stocks or bonds?
Note: consider making a Venn Diagram to help solve this problem.
300
500
800
100
Answers
Answer: To solve this problem, we can use the formula:
Total = Stocks + Bonds - Both
where "Total" represents the total number of people who invested in either stocks or bonds.
Plugging in the given values, we get:
Total = 700 + 400 - 300
Total = 800
Therefore, 800 people invested in stocks or bonds.
Step-by-step explanation:
which piece of required information is missing from the following prescription?premarin tabs0.625 mg
Answers
The given prescription lacks important information about the frequency and route of administration. Knowing how often a medication should be taken and how it should be administered is crucial for ensuring that patients receive the appropriate dose and achieve the desired therapeutic effect.
Without the frequency information of how (e.g., orally, intravenously, etc.) and when (e.g., daily, twice daily, etc.) to take medicine on prescription, patients may take the medication incorrectly or miss doses, potentially leading to ineffective treatment or adverse effects.
Healthcare providers should always provide clear and complete instructions for medication use to ensure patient safety and optimal treatment outcomes.
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5. Jeni put a cake in the
oven at 2:30. If the
cake takes 1 hours
to bake, at what time
should it be taken
out of the oven? What the answer
Answers
Answer:
3:30
Step-by-step explanation:
We know
Jeni put a cake in the oven at 2:30. The cake takes 1 hour to bake.
What time should it be taken out of the oven?
We take
2:30 + 1 = 3:30
So, it should be taken out of the oven at 3:30
A box containing 5 balls costs $8.50. If the balls are bought individually, they cost $2.00 each. How much cheaper is it, in percentage terms, to buy the box as opposed to buying 5 individual balls?
Answers
Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.
The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.
To calculate the percentage difference, we can use the formula:
% difference = (difference ÷ original value) x 100%
In this case, the difference is $1.50, and the original value is $10.00.
% difference = ($1.50 ÷ $10.00) x 100%
% difference = 0.15 x 100%
% difference = 15%
Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.
Step-by-step explanation:
Tristan is going to invest $73,000 and leave it in an account for 18 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Tristan to end up with $104,000?
Answers
Answer:
2%
Step-by-step explanation:
Given,P = $73000
A = $104000
T = 18 years, Compounded annually.
To find: r%
Soln: By formula, A = 73000*(1+r/100)^18
=> (104/73)^1/18 = (100+r)/100
=> 1.0198 = 100+r/100
=> 101.98 -100 = r
=> 1.98 = r
To the nearest percent, 2 = r
Hence, Rate of interest = 2%
In the diagram below, IJK~LJK Find g. 5
Answers
In the diagram given IJK≅LJK ,the length cannot be negative, the only valid solution is g = 6. Therefore, the length of the segment KJ is 6 meters.
What is length?Length is a physical dimension that measures the distance between two points or the size of an object along one dimension.
It is commonly measured using standard units of length such as meters, feet, inches, and centimeters.
Given that KM is the bisector line of line IM and J is the bisector point on line IL. Two triangles are formed, △IJK and △LJK, on line IL in the upward and downward direction, respectively. We are given the lengths of IK, JN, LM, and KJ, and we need to find the value of g such that IJK≅LJK.
Since the two triangles are similar, their corresponding sides are proportional. Using the side proportionality theorem, we have:
KJ/LM = IJ/JL
Substituting the given values, we get:
g/10 = 5/(4+g)
Cross-multiplying, we get:
g(4+g) = 50
Expanding and simplifying, we get:
g²+ 4g - 50 = 0
Using the quadratic formula, we get:
g = (-4 ± √(4² + 4(50)))/2
g = (-4 ± √(256))/2
g = (-4 ± 16)/2
g = -10 or g = 6
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QUESTION THREE (30 Marks) a) For a group of 100 Kiondo weavers of Kitui, the median and quartile earnings per week are KSHs. 88.6, 86.0 and 91.8 respectively. The earnings for the group range between KShs. 80-100. Ten per cent of the group earn under KSHs. 84 per week, 13 per cent earn KSHs 94 and over and 6 per cent KShs. 96 and over. i. Put these data into the form of a frequency distribution and obtain an estimate of the mean wage. 15 Marks
Answers
Answer:
the answer would be 100 I guess
PLEASE HELP 30 POINTS!
Answers
Answer:
57
57
123
123
57
57
123
that's all.
Answer:
m<1 = 57°
m<2 = m<1 = 57°
m<3 = x = 123°
m<4 = x = 123°
m<5 = m<1 = 57°
m<6 = m<5 = 57°
m<7 = m<4 = 123°
Step-by-step explanation:
[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]
Work out x. Area=194
Please help due in 2 hourss
Answers
Step-by-step explanation:
Please mark as brainliest
