The cost to rent each chair is $1.5 and cost to rent each table is $6.5
Applications of systems of linear equationsFrom the question, we are to determine the cost to rent each chair and each table
Let c represent chair
and
t represent table
From the given information,
The total cost to rent 5 chairs and 3 tables is $27
That is,
5c + 3t = 27 ------------ (1)
Also,
The total cost to rent 2 chairs and 12 tables is $81
That is,
2c + 12t = 81 ---------- (2)
Now, solve the equations simultaneously
5c + 3t = 27 ------------ (1)
2c + 12t = 81 ---------- (2)
Multiply equation (1) by 2 and multiply equation (2) by 5
2 × [5c + 3t = 27 ]
5 × [2c + 12t = 81 ]
10c + 6t = 54 ------------- (3)
10c + 60t = 405 ------------- (4)
Subtract equation (4) from equation (3)
10c + 6t = 54
10c + 60t = 405
---------------------------
-54t = -351
t = -351/-54
t = 6.5
Substitute the value of t into equation (2)
2c + 12t = 81
2c + 12(6.5) = 81
2c + 78 = 81
2c = 81 - 78
2c = 3
c = 3/2
c = 1.5
∴ The cost of chair is $1.5 and cost of table is $6.5
Hence, the cost to rent each chair is $1.5 and cost to rent each table is $6.5
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A COUPLE PLAN TO HAVE SIX CHILDREN. HOW MANY POSSIBLE OUTCOMES ARE IN
THE SAMPLE SPACE?
Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6
What is probability?Probability is the likelihood or chance that an event will occur. Mathematically, the formula for calculating probability is expressed as:
Probability = expected outcome/Total outcome
Sample space is the total number of element in a given set of probability. The subsets if this sets are called event
Let the six children the couple plan to have ne 1, 2, 3, 4, 5,6 such that the sample space will be:
S = {1, 2, 3, 4, 5, 6}
Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6
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A large university has 24,000 students. A
randomly selected sample of 750 students
were surveyed and asked how far away
they live from the university. Of those
surveyed, 120 students live more than
500 miles away from the university.
Based on the survey results, estimate the
number of students who live within 500
miles of the university?
Answer:
23370 students live with in 500 miles of the university.
Step-by-step explanation:
large university students =24000
selected students = 750
surveyed students =120 lives far away from university.
students live with in 500mile=?
750-120=630
24000-630=23370
Suppose that Andrea told you that “Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me.” Is Andrea’s reasoning incorrect? If so, how can you help Andrea identify her misunderstanding?
Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
Using translation concepts, the transformations are described as follows:
Reflection over the x-axis.Shifted up 4 units.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
[tex]f(x) = 2^x[/tex]
The transformed function is:
[tex]g(x) = -2^x + 4[/tex]
We have that the transformations in this problem can be described as follows:
f(x) was multiplied by -1, hence it was reflected over the x-axis.4 was added to the function, hence it was shifted up 4 units.More can be learned about translation concepts at https://brainly.com/question/28098112
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the confidence interval for the population variance is
(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.
Find the confidence interval for population variance:The formula for finding the confidence interval for population variance is:
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.
Here it is given that,
confidence level = 1 - α = 0.98 significance level = α = 0.02standard deviation = 39 sample size n = 15degrees of freedom (n - 1) = 15 - 1 = 14α/2 = 0.02/2 = 0.01
1 - α/2 = 1 - 0.01 = 0.99
For (n - 1) degrees of freedom,
[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)
Using the formula we get,
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]
[tex]730.72 < \sigma^{2} < 4569.53[/tex]
The confidence interval for the population variance is (730.72, 4569.53)
Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.
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why kilogram is more appropriate unit than milligram?
Step-by-step explanation:
that question is fundamentally wrong.
"appropriate" completely depends on the situation and circumstances.
if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.
if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".
because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.
if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.
one of the acute angles of a right triangle is 36° find the other acute angles
Step-by-step explanation:
An acute angle is an angle less or equal to 90 degrees.
let the other angle be x.
x + 36 = 90
grouping like terms
X = 90 - 36
X = 54 degrees
Answer:
54
Step-by-step explanation:
= ∠A + ∠B + ∠C = 180o … [∵sum of the angles of a triangle is 180]
or 180 = 36 + 90 + ∠C
C=54
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder over the past 12 months are satisfied with their products. If there are 4 different brands of videocassette recorders made by the company, the best sampling strategy would be to use a
The best sampling strategy would be a stratified sample.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.
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Calculate the weight on earth of an object with a mass of 48kg
Answer: 470.4 N
Step-by-step explanation:
Concept:
1 kg on Earth = 9.8 N
Given information:
Mass = 48 kg
Find the weight on Earth
1 kg = 9.8 N
48 kg = 48 * 9.8 = [tex]\Large\boxed{470.4N\\}[/tex]
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In the following activity, match each pair of equivalent expressions(will give 50 points)
The length of a certain rectangle is 6 meters more than twice its width. What is the perimeter of the rectangle if the area of the rectangle is 260 square meters?
Answer:
Perimeter = 72 meters
Step-by-step explanation:
Let L be the length and W the width of the rectangle
We have the following relationship
L = 2W + 6
Area of the rectangle = LW = (2W+6)W by substituting for L
Area =
2W² + 6W =260 ==> 2W² + 6W -260 = 0
Dividing both sides by 2 yields
W² + 3W -130 = 0
This is a quadratic equation which can be solved using the formula for the roots of the equation ie the values of W which satisfy the above equation
However in this case it is easier to solve by factorization
W² + 3W -130
= W² + 13W - 10W - 130
= W(W + 13) -10(W + 13)
= (W+13)(W-10) = 0
This means W is either -13 or W = 10
Since W cannot be negative, we get W = 10 and
L = 2(10) + 6 = 26
Perimeter of a rectangle is given by
2(L + W) = 2(26 + 10) = 2(36) = 72 Answer
TIME REMAINING
51:31
What are the factors of x2 – 100?
(x – 50)(x + 50)
(x – 10)(x + 10)
(x – 25)(x + 4)
(x – 5)(x + 20)
Answer:
(b) (x -10)(x +10)
Step-by-step explanation:
The factorization of the difference of squares is a special form:
a² -b² = (a -b)(a +b)
ApplicationYour expression is recognizable as the difference of squares:
x² -100 = x -10²
Using the above form, the factorization is ...
= (x -10)(x +10) . . . . . . . . matches the second choice
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
How to determine the remainder?The function is given as:
f(x)=−2x3+x2−4x+1 is divided by x+3.
Set the divisor to 0
x + 3 = 0
Solve for x
x = -3
Calculate f(-3)
f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1
Evaluate the expression
f(-3)= 76
Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
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43. Which function has an x-intercept of 4?
A. f(x) =
= -√2x+4
B. f(x) = (x + 4)(x-7)
Soloct ono
C. f(x) = x² + 3x - 4
D. f(x)=x-4
Answer:
D
Step-by-step explanation:
When f(x) is equal to 0, x=4.
Please answer this question
Answer:
1 and 4
Step-by-step explanation:
x-1 = 0
x = 1
x^2 - 5x + 4
(x-4)(x-1) = 0
x can't be 1 or 4
Answer: 1 and 4
Step-by-step explanation:
1. To find excluded values, we need to make the denominator equal to zero.
x² - 5x + 4 = 0
2. Then we need to find the x the product of them was 4, but they add up to -5, which are -4 and -1. We get:
(x - 4)(x - 1) = 0
x - 4 = 0 x - 1 = 0
x = 4 x = 1
These two numbers will make the denominator equal to 0, the denominator cannot be equal to 0, so they are excluded numbers.
write the equations after translating the graph of y=|x+2| one unit to the right
write the equations after translating the graph of y=|x+2| one unit to the left
integer for 1,440 feet below sea level
At the beginning of this year, you went out and purchased $300 worth of gold coins. Every 3 months for the next 8 years, you purchase an additional $300 worth of coins. At the end of the first 3 years, the price of gold starts to come back down, and when you decide to cash out, your coins are only worth what you paid for them. What is the value of your account now?
Answer:
9900
Step-by-step explanation:
You start with 300, and add 300 32 times (once for every 3 months in 8 years).
[tex]300+9600=9900[/tex]
What is the least common multiple of 6x^2+39x-21 and 6x^2+54x+84?
12x² + 102x² + 114x - 84
Answer:
Solution Given:
1st term: 6x²+39x-21
Taking common
3(2x²+13x-7)
doing middle term factorization
3(2x²+14x-x-7)
3(2x(x+7)-1(x+7))
3(x+7)(2x-1)
2nd term: 6x²+54x+84
taking common
6(x²+9x+14)
doing middle term factorization
6(x²+7x+2x+14)
6(x(x+7)+2(x+7))
2*3(x+7)(x+2)
Now
Least common multiple = 2*3(x+7)(2x-1)(x+2)
2(x+2)(6x²+39x-21)
(2x+4)(6x²+39x-21)
2x(6x²+39x-21)+4(6x² + 39x-21)
12x³+78x² - 42x+4(6x² + 39x-21)
12x³+78x² - 42x + 24x² + 156x-84
12x³ + 102x²-42x + 156x - 84
12x² + 102x² + 114x - 84
Answer:
[tex]12x^3+102x^2+114x-84[/tex]
Step-by-step explanation:
Given polynomials:
[tex]\begin{cases} 6x^2+39x-21\\6x^2+54x+84 \end{cases}[/tex]
Factor the polynomials:
Polynomial 1
[tex]\implies 6x^2+39x-21[/tex]
[tex]\implies 3(2x^2+13x-7)[/tex]
[tex]\implies 3(2x^2+14x-x-7)[/tex]
[tex]\implies 3[2x(x+7)-1(x+7)][/tex]
[tex]\implies 3(2x-1)(x+7)[/tex]
Polynomial 2
[tex]\implies 6x^2+54x+84[/tex]
[tex]\implies 6(x^2+9x+14)[/tex]
[tex]\implies 6(x^2+7x+2x+14)[/tex]
[tex]\implies 6[x(x+7)+2(x+7)][/tex]
[tex]\implies 6(x+2)(x+7)[/tex]
[tex]\implies 2 \cdot 3(x+2)(x+7)[/tex]
The lowest common multiplier (LCM) of two polynomials a and b is the smallest multiplier that is divisible by both a and b.
Therefore, the LCM of the two polynomials is:
[tex]\implies 2 \cdot 3(x+7)(x+2)(2x-1)[/tex]
[tex]\implies (6x^2+54x+84)(2x-1)[/tex]
[tex]\implies 12x^3+108x^2+168x-6x^2-54x-84[/tex]
[tex]\implies 12x^3+102x^2+114x-84[/tex]
If you borrow $100 for 5 years at an annual interest rate of 8%, how much will you pay all together
Answer:
$140
Step-by-step explanation:
interest = 8x5 = 40
total = time + interest
total = 100 + 40 = $140
A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation? Question 5 options: A) The speed at which the car travels B) The distance the car has traveled C) The age of the car D) The number of hours the car has traveled
The dependent variable in this situation is; the speed at which the car travels.
Distance and speedSpeed of the car = 60 miles per hourSpeed = Distance / Time
The dependent variable in this situation is; the speed at which the car travels.
The independent variable; The distance the car has traveled.
What is dependent variable?This is the variable whose value depends on one or more variables in the equation.
Independent variable
This is the variable whose value is not dependent on any other in the equation.
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The length and width of a rectangle is 42cm and 28cm respectively. The ratio between the two
quantities is ____________.
Answer:
The ratio is 3 : 2.
Step-by-step explanation:
42 cm : 28 cm
= 21 : 14 (Divide both sides by 2)
= 3 : 2 (Divide both sides by 7)
The ratio between the length and width of the rectangle is 3:2.
We have,
The concept used here is the concept of ratio.
In mathematics, a ratio is a comparison of two quantities.
It expresses how many times one quantity contains another or how many times it is greater or smaller than the other quantity.
The ratio between the length and width of the rectangle can be found by dividing the length by the width:
Ratio = Length / Width
= 42 cm / 28 cm
= 7 x 6 / 7 x 4
Cancel out the common factor.
= 6/4
= 2 x 3 / 2 x 2
Cancel out the common factor.
= 3/2
Thus,
The ratio between the length and width of the rectangle is 3:2.
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PLS HELP ME ASAP I NEED THE ANSWER NOW BEFORE 5 mins PLS Help ME I WILL MARK BRAINLIST IF YOUR ANSWER IS CORRECT AND WAS ANSWERED 4 MIN AGO HELP ME PLSSS
The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 42 hours.
1 day
24 hours
12 hours 12 hours
1 and 1 over 4. days (wrong)
1 and 1 over 2. days
1 and 3 over 4. days
2 days
Answer:
42 - 24 = 18
18/24 = 3/4
the answer would be 1 and 3/4 days
Answer:
1 and 3 over 4 days
Step-by-step explanation:
Since 24 hours is 1 day all we have to do is divide 42 into 24 and see what the resulting fraction is
42/24 = 7/4 (reducing to lowest fraction)
7/4 = 1 3/4 days (7 ÷ 4 gives quotient 1 and remainder is 3)
Answer:
1 and 3 over 4 days
Given angle YMC = 170 degrees, find the measure of angle AMC.
Answer:
i think 10 because in triangle there is 180 and 180-170 = 10
Answer:
Step-by-step explanation:
hjhj
If 55 people enrolled in a psychology course but only 25 completed it, what percent of the students completed the course? (Round to the nearest tenth of a percent.)
Answer:
45%
Step-by-step explanation:
Simply, 25/55 which gives you 0.454545.
Convert that to a percentage and you get 45%
Four seniors and six juniors are competing for four places on a quiz bowl team.
What is the approximate probability that all four seniors will be chosen at random?
what’s the % ?
Answer:
.00476
Step-by-step explanation:
What is the length of S?
Answer:
c
Step-by-step explanation:
By the Pythagorean theorem,
[tex]28^2 + 15^2 = s^2 \\ \\ s^2 = 1009 \\ \\ s = \sqrt{1009}[/tex]
PLS HELP
Which functions have a range of {y e R-00 < y < 00}?
O f(x)
2x+3
Of(x) = x - 8
O f(x) = x² + 7x - 9
O f(x) = -4x + 11
O f(x) = -(x + 1)² - 4
=
Answer:
[tex]\displaystyle{1.) \ \ f(x) = \dfrac{2}{3}x-8}\\\\\displaystyle{2.) \ \ f(x) = -4x+11}[/tex]
Step-by-step explanation:
- Range is a set of all y-values in a set of coordinate points.
A linear equation or function always have range equal to set of real number because you can substitute f(x) as any numbers and you'll still be able to solve for x-variable.
An quadratic equation or function may have range equal to set of positive real number or negative real number depending whether if the coefficient of x² is in positive or negative but consider this:
Suppose we have f(x) = x², f(x) cannot be negative number because that'd make the equation not real. Therefore, a quadratic function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range.
For an exponential function, it's same as quadratic equation. It depends whether if a base is in negative or positive. You can consider like this:
Suppose we have [tex]\displaystyle{f(x)=2^x}[/tex], f(x) cannot be negative number because there are no x-values that make the equation true. Therefore, an exponential function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range as well.
Question 5
Find the interest rate for a principal of $6570 and charged $30105 in interest for 12 years.
The Formula is
I
PT
x 100
Take the interest divide by the principal
then divide by the years
then times by 100
Round your answer to 1 decimal place.
Answer:
R=i
Step-by-step explanation:
R=i×100÷p×t
r=30105×100÷6570×12
r=3010500÷78840
r=38.18
K
An employment agency specializing in temporary construction help pays heavy equipment operators $124 per day and general laborers $82 per day If thirty-seven people were hired
and the payroll was $3916, how many heavy equipment operators were employed? How many laborers?
The number of heavy equipment operators hired was?
The number of general laborers hired was?
Step-by-step explanation:
x = number of heavy equipment operators
y = number of general laborers
x + y = 37 (37 people were hired)
out if this we get e.g.
x = 37 - y
124x + 82y = 3916 (daily rate for each role, in total 3916)
now we use the first equation in the second :
124(37 - y) + 82y = 3916
4588 - 124y + 82y = 3916
672 - 42y = 0
672 = 42y
y = 16
x = 37 - y = 37 - 16 = 21
21 heavy equipment operators were hired.
16 general laborers were hired.