party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is $25. The total cost to rent 6 chairs and 5 tables is $49. What is the cost to rent each chair and each table?
The cost to rent each chair and each table is $2.75 and $6.50 respectively.
How to calculate the cost?The total cost to rent 2 chairs and 3 tables is $25. This will be:
2c + 3t = 25
The total cost to rent 6 chairs and 5 tables is $49. This will be:
6c + 5t = 49
2c + 3t = 25
6c + 5t = 49
6 × (2c + 3t = 25)
2 × (6c + 5t = 49)
12c + 18t = 150
12c + 10t = 98
Subtract
8t = 52
Divide
t = 52/8
t = 6.5
Cost to rent table = $6.50
Since 2c + 3t = 25
2c + 3(6.5) = 25
2c + 19.5 = 25
Collect like terms
2c = 25 - 19.5
2c = 5.5
c = 5.5/2
c = 2.75
Cost to rent chair = $2.75.
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Evaluate the expression.
−5 × (−8 − 6 ÷ −3)
Answer:
=30
Step-by-step explanation:
-5×(-8-6÷-3)-5×(-8+2)........as -6÷-3=2-5×-630Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students? 50 students 200 students 124 students 250 students
The number of students that chose band as an elective is 50
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic
let the total number of seats for choir be x and that for band be y
if there are 4 times as many seats as there in band then mathematically,
x = 4y.--------------------1
If there are 250 students, then, there would be 250 seats for the combined class.
so,
x + y = 250--------------2
substitute x = 4y in equation 2
4y + y = 250
5y = 250
y = 250/5
y = 50
In conclusion, 50 students can choose band.
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Martina is taxed at a rate of 25% for her federal taxes. Last year, she reduced her taxable income by contributing to a flexible savings plan in the amount of $2,700. If her
wages before the deduction were $68,000, how much did she save in federal taxes by using the FSA?
▸
Answer:
14300
Step-by-step explanation:
this is the answer that I got I hope it works
Saving of Martina in taxes = $675
What is FSA?A flexible spending account (FSA) is a type of savings account, usually for healthcare expenses, that sets aside funds for later use. It is also known as a flexible spending arrangement, is one of a number of tax-advantaged financial accounts, resulting in payroll tax savings.
Given,
Wages of Martina = $68000
Tax rate = 25%
Amount to flexible savings = $2700
Then saving in taxes = $2700 × 25/100
= $675
Hence, Martina saved $675 in taxes using FSA.
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Solve the inequality.
Question 1
3y≤−9
The solution is
The solution of the given inequality is y ≤ -3.
The given inequality is -
3y ≤ −9
We have to solve this given inequality.
Now, we have the inequality as -
3y ≤ −9
=> y ≤ -3
Thus, the solution of the given inequality is y ≤ -3.
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A continuous random variable is normally distributed. The probability that a value in the distribution is greater than 23 is 0.6784. Find the probability that a value in the distribution is less than 23.
The probability that are a normally distributed variable is less than 23 is 0.3216
What is normal distribution?The most significant probability distribution in statistics for independent, random variables is the normal distribution, sometimes referred to as the Gaussian distribution.
In statistical reports, its well-known bell-shaped curve is generally recognized.
While calculating for probability for normally distributed variables the relationship the relationship is written in the form
P > 23 = 1 - P < 23
0.6784 = 1 - P < 23
P < 23 = 1 - 0.6784
P < 23 = 0.3216
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You have a 64-ounce pitcher of tea.
After you pour as many 7-ounce cups of tea as possible, how much tea will be left
over?
Answer:
You can pour nine 7-ounce cups of tea (63 ounces) and be left with one ounce of tea.
Step-by-step explanation:
Dividing 64 by 7 and finding the remainder.
Apply the properties of operations to multiply the expression
The properties of operations to multiply the expression are commutative property, associative property, and distributive property.
Let us understand the properties of operations to multiplication:
The foundation of arithmetic is the Properties of Operations; we use them when performing computations and recalling basic facts.
There are basically three properties of operations to multiplication which are:
Commutative Property: The commutative property of multiplication states that the order in which values are multiplied does not matter and will result in the same answer. That is to say: a * b = b * aAssociative Property: The associative property of multiplication states that when three or more numbers are multiplied, the order in which the multiplication occurs has no effect on the answer. That is to say: (a * b) * c = a * (b * c)Distributive Property: Students are asked to create two groups of six (2 x 6) using connecting cubes and to locate two hidden facts inside the 2 x 6 such as 2 x 3 and 2 x 3. That is: 2 x 6 = 2 x 3 + 2 x 3.Thus, the properties of operations to multiply the expression are commutative property, associative property, and distributive property.
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5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.
1. What values make sense for n in this situation? What values don't make sense for n?
Using the pattern, n can represent the the increase of dots according to step.
In the given question we have to find what values make sense for n in this situation.
n is representing the number.
As we can see that there is a pattern given.
In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.
So if we see the pattern then according to number of step the dots increasing accordingly.
As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.
So, n can represent the the increase of dots according to step.
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Help. I'll mark as brainlist. I am always giving brainlist points.
Answer: 18 square unit
Step-by-step explanation:
We can divide the shape into two pieces.
a triangle and a square.
The square is 2*6=12 square unit
and the triangle is 1/2*6*2=6 square unit
So if we sum this up we get the answer
answer = 6+12 = 18 square unit
pls help I don't get the problem
Simplified form is the -(1+sinα).
Given in question,
[tex]cos^{2}[/tex]α/sinα-1
[tex]sin^{2}[/tex]α + [tex]cos^{2}[/tex]α = 1
[tex]cos^{2}[/tex]α = 1 - [tex]sin^{2}[/tex]α
[tex]cos^{2}[/tex]α/sinα-1 = (1 - [tex]sin^{2}[/tex]α ) / (sinα-1)
= (1-sinα)(1+sinα)/(sinα-1)
= (1-sinα)(1+sinα)/-(1-sinα)
= (1+sinα)/-1
= -(1+sinα)
Hence, in simplified form [tex]cos^{2}[/tex]α/sinα-1 = -(1+sinα)
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A pendant of gold alloy weighs 15/32 troy ounces. How many pendants can a jeweler make
from 5 5/8 troy ounces of gold alloy?
Solve the problem mathematically by finding the quotient.
The Jeweler makes the number of Pendants from the total weight of gold alloy = 12
The Jeweler has the total weight of gold alloy = 5 [tex]\frac{5}{8}[/tex] = 45/8 troy ounces.
Weight of a single gold alloy pendant = 15/32 troy ounces.
Jeweler makes the number of Pendants from the total weight of gold alloy = 45/8 ÷ 15/32.
Dividing Fractions by Fractions
We just learned how to divide fractions by taking the reciprocal. Now, let us see the method of dividing fractions by fractions with an example. Have a look at the formula of the division of a fraction by fraction given below. If x/y is divided by a/b, this implies,
x/y ÷ a/b
⇒ x/y × b/a (reciprocal of a/b is b/a)
⇒ xb/ya
Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators.
45/8 ÷ 15/32 = 45/8 × 32/15 = 12
∴ The value of 45/8 ÷ 15/32 = 12.
Hence the Jeweler makes the number of Pendants from the total weight of gold alloy = 12
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Which is bigger 21.17 or 2.117
Answer:
21.17
Step-by-step explanation:
If you were to round each number to the nearest whole number you would get :
21.17 ⇒ 21
2.117 ⇒ 2
Now the question is , which is bigger 21 or 2?
Now that is a very straightforward answer (21 in case your still lost)
Hope this helped and have a good day
Evaluate for A(12). Round your answer to the nearest hundredth.
The value the function A(12) is 2960.94
How to evaluate the function?From the question, we have the following function definition that can be used in our computation:
A(t) = 710e⁰°¹¹⁹⁺
To calculate the function A(12), we set t to 12
i.e. calculate A(t) when t = 12
This equation becomes
A(12) = 710e⁰°¹¹⁹ˣ¹²
Evaluate the products
A(12) = 710e¹°⁴²⁸
Evaluate the exponents
A(12) = 2960.94
Hence, the solution is 2960.94
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Is this column graph skewed or symmetrical?? and if skewed what way?
Answer:
skewed to the right
Step-by-step explanation:
look at the graph
divide it in half
if both the sides are not equal then it is skewed
then to find out which way it is skewed look which side has more.
Bob invested his savings in two investment funds. The amount he invested in Fund A was 3 times as much as the amount he invested in Fund B. Fund A returned a 5% profit and Fund B returned a 7% profit. How much did he invest in Fund B, if the total profit from the two funds together was $2200?
The amount that he invested in Fund B if the total profit from the two funds together was $2200 is $8,800.
How to find the amount invested?Let x represent the amount invested in Fund B
Let 3x represent the amount invested in Fund A
Hence,
.07x + .05(3x) = 2200
.07x + .15x = 2200
.25x = 2200
Divide both side by .25x
x = 2200/.25
x = $8,800 (invested in Fund B)
Fund A:
3x = 3(8,800)
3x = $26,400 (Invested in Fund A)
Therefore $8800 was invested in Fund B.
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Angles X and Y are supplementary. Angle X measures 127.42°, and angle Y measures (m − 12)°. Find m∠Y. anwsers 115.42° 74.84° 64.58° 52.58°
The measure of angle Y, m ∠Y, is 52.58°. The correct option is the last option 52.58°
Calculating the measure of an angleFrom the question, we are to determine the measure of angle Y.
From the given information,
Angles X and Y are supplementary angles.
NOTE: Supplementary angles are angles that sum up to 180°
Thus,
m ∠X + m ∠Y = 180°
Also,
From the given information,
Angle X measures 127.42°
That is,
m ∠X = 127.42°
Therefore,
127.42° + m ∠Y = 180°
m ∠Y = 180° - 127.42°
m ∠Y = 52.58°
Hence, the measure of the angle is 52.58°
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find the difference in centimetres between 5m and 465cm
Answer:
35 cm
Step-by-step explanation:
Jillian sells handmade t- Shirts and large purses; each tea shirt costs $15. Each Large purse goes for $59 and the cost of small purses is $32 each. In the first week she sold 4 t-shirts and 3 large purses and 9 small. In the second week she sold another 5 t-shirts, 7 large bags and 4 small ones. Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses. What was the exact amount she made in 3 weeks?
Jillian made the exact amount was $1598 in 3 weeks.
Each t-shirt costs $15.
Each Large purse goes for $59
And the cost of small purses is $32 each.
In the first week, she sold 4 t-shirts and 3 large purses, and 9 small ones.
Her earning in the first week = 4 × $15 + 3 × $59 + 9 × $32 = $525
In the second week, she sold another 5 t-shirts, 7 large bags, and 4 small ones.
Her earning in the second week = 5 × $15 + 7 × $59 + 4 × $32 = $616
Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses.
Her earning in the Last week = 8 × $15 + 3 × $59 + 5 × $32 = $457
The exact amount she made in 3 weeks = $525 + $616 + $457 = $1598
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**BRAINLIEST** TO WHOEVER ANSWERS CORRECTLY! PLEASE HELP ME!
- During a certain time of year, the daily temperature in a certain city, in degrees Celsius follows a periodic pattern. The graph below shows the temperature over two days, where time t is measured in hours after 12:00 a.m. (midnight) on the first day.
- Write an equation for the graph below in terms of Y (temperature in degrees Celsius) and T (time in hours) to represent the given context.
ANSWER SHOULD BE IN THIS FORM
y = ( a ) sin ( b ) (t - h) + k
GRAPH IS GIVEN BELOW PLEASE HELP ME OUT!
Answer:
y = A cos B(x - C) + D
Step-by-step explanation:
The equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -
y = √180 sin (π/12.5)(t - 25) + 12
What is the general equation of a sinusoidal wave?The sinusoidal wave is of the form -
y{x} = A sin (ωt - kx + Ф)
Given is that during a certain time of year, the daily temperature in a certain city (in degrees Celsius) follows a periodic pattern.
We can write the amplitude as -
A = √(18 - 12)² + (13 - 1)²
A = √(36 + 144)
A = √180 ... { 1 }
{K} = 12 ... { 2 }
The time taken to complete one complete wave is 25 hours. So, we can write -
{T} = 25 ... { 3 }
ω = 2π/T = 2π/25 = π/12.5
{ω} = π/12.5 ... { 4 }
So, we can write the equation as -
y = √180 sin (π/12.5)(t - 25) + 12
Therefore, the equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -
y = √180 sin (π/12.5)(t - 25) + 12
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Determine the vertex of the graph of the following parabola. f(x)=−(x+1)2−6
The vertex of the graph of the parabola is at the point (-1, -6)
How to find the vertex of the parabola?We know that for any parabola with a vertex at the point (h, k) and a leading coefficient a, can be written in vertex form as:
y = a*(x - h)^2 + k
In this case the parabola is:
f(x) = (-1)*(x + 1)^2 - 6
Comparing this with the general form, we can see that:
h = -1
k = -6
Then the vertex of the parabola is (-1, -6)
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I'm taking the math pert tomorrow I've failed it 2 times already I've been studying nonstop for the past two weeks and still feel like I'm going to fail any tips on how to pass ?
Can you solve please
Answer:
I'm assuming that you want to find x and y.
x = 18
y = 42
Step-by-step explanation:
Angle ACD = 138°
(5x + 2) + (2x + 10) = 138
7x + 12 = 138
7x = 126
x = 18
y + (5x + 2) + (2x + 10) = 180 (sum of adjacent angles on a straight line)
Substitute x = 18 into the equation.
y + 5(18) + 2 + 2(18) + 10 = 180
y + 90 + 2 + 36 + 10 = 180
y = 42
what do they mean, (Grade 10 real numbers)
X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.
So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.
So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.
Consider the polynomial function []
p
given by p(x)=5x3+8x2−3x+1
A(x)
. Evaluate the function at x=−2
x
.
The point N lies on the segment MP
Find the coordinates of N so that MN is 3/7
of MP.
M(-4,6)
N (?,?
P (17,-22)
The coordinates of N are (5,-6) so that segment MN is 3/7 of MP.
Given the coordinates of M is (-4,6) and the coordinates of P is (17,-22).
now we have to find the coordinates of N such that the MN : NP is 3:4 .
We will use the section formula:
The section formula states that:
[tex]{\displaystyle N=\left({\frac {mx_{2}+nx_{1}}{m+n}},{\frac {my_{2}+ny_{1}}{m+n}}\right)}[/tex]
Where the coordinates of the points are given and the ratio in which the points are divided is given.
Now we will substitute the values:
[tex]{\displaystyle N=\left({\frac {17\times 3+4\times -4}{3+4}},{\frac {3\times-22+4\times 6}{3+4}}\right)}[/tex]
Solving we get:
N=(5,-6)
The Section formula is used to determine the coordinates of things like the point that separates a line segment (internally or externally) into a particular ratio.
Both physics and mathematics regularly employ this formula. In mathematics, it is used to find the centroid and incenters of a triangle, but in physics, it is used to find the center of mass, equilibrium points, etc. The section formula is often used to find the midpoint of a line segment.
Therefore coordinates of N are (5,-6) so that MN is 3/7 of MP.
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A taxi ride cost a customer a total of \$13.73$13.73dollar sign, 13, point, 73, which included 4\%4%4, percent sales tax and then a \$1$1dollar sign, 1 surcharge. What was the subtotal before the surcharge and sales tax?
The subtotal before the surcharge and sales tax is $12.2
How to determine the subtotal amount?In this question, we have the following parameters
Total = $13.73
Sales tax = 4%
Surcharge = $1
The above parameters imply that:
Total = Subtotal * (1 + sales tax) + Surcharge
Substitute the known values in the above equation, so, we have the following representation
13.73 = Subtotal * (1 + 4%) + 1
This gives
Subtotal * (1 + 4%) = 12.73
Divide both sides by 1.04
Subtotal = 12.2
Hence, the subtotal is $12.2
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Tough question help asap
The function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Given,
The function; f(x) = 9 × 4ˣ
The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. coordinate's
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
We have to find the following function values;
f(-2) = 9 x 4⁻² = 9 x 0.0625 = 0.5625f(1/2) = 9 x 4^(1/2) = 9 x 2 = 18f(0) = 9 x 4⁰ = 9 x 1 = 9Learn more about functions here;
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help pleaseeeeee !!!
Answer:
[tex]\sqrt{6}, -\sqrt{6}[/tex]
Step-by-step explanation:
[tex]f(x)=x^3+3x^2-6x-18 \\ \\ =x^2(x+3)-6(x+3) \\ \\ =(x^2-6)(x+3) \\ \\ \implies (x^2-6)(x+3)=0 \\ \\ x=\pm \sqrt{6}, -3[/tex]
K
Assume that females have pulse rates that are normally distributed with a mean of μ-750 beats per minute and a standard deviation of e=125 beats per minute. Complete parts (a) through (c) below
B. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 69 beats per minute and 81 bears per minute
The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute, using the normal distribution and the central limit theorem, is of:
0.663 = 66.3%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for the problem are given as follows:
[tex]\mu = 75, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]
The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute is the p-value of Z when X = 81 subtracted by the p-value of Z when X = 69, hence:
X = 81:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (81 - 75)/6.25
Z = 0.96
Z = 0.96 has a p-value of 0.8315.
X = 69:
Z = (69 - 75)/6.25
Z = -0.96
Z = -0.96 has a p-value of 0.1685.
0.8315 - 0.1685 = 0.663 = 66.3%.
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