1. Janice donates 100 items of clothing to the Salvation Army. There were four times as many shirts as there were pants. How many shirts and pants did Janice donate? Write and solve a system of equations to answer the question.
2. Amy and Mike have 56 video games between them. Amy has 8 more games than Mike. How many games does each of them have? Write and solve a system of equations to answer the question.
Janice donated 20 pants and 80 t-shirts of clothing to the Salvation Army.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Given, Janice donates 100 items of clothing to the Salvation Army and the number of t-shirts were 4 times the number of pants.
Therefore, If the number of pants is 'x' then the number of t-shirts are '4x'.
So, x + 4x = 100.
5x = 100.
x = 20.
So, The number of pants are 20 and the number of t-shirts are 80.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
What is equation of a circle?We should know that a circle is a set of points on a circle that are equal from a fixed point
The standard form for finding the equation of a circle is expressed as;
(x-a)² + (y-b)² = b=r²
where; (a, b) is the center of the circle
r is the radius of the circle
Given the following
Diameter = 12 units
radius = 12/2 = 6 units
If the center lies on the y-axis, the center will be at (0, 3)
Therefore, Substituting into the formula, we will have (x-0)² + (y-3)² = 6² which is equivalent to x²+ (y-3)² = 36
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Use A Double Integral To Find The Volume Of The Solid Shown In The Figure.
_________ cu units
Without the specific function it is not possible to give you the exact solution and also without knowing the specific limits of the integral, it is not possible to evaluate the definite integral.
The solid in the figure is a rectangular prism with a cutout, the cutout is a cylinder with radius 2. The volume of the solid can be found by using a double integral.
The first integral represents the volume of the rectangular prism, and the second integral represents the volume of the cylinder cut out of it. The limits of the double integral are determined by the dimensions of the rectangular prism and the cylinder.
The volume of the rectangular prism = (x-coordinate max - x-coordinate min) * (y-coordinate max - y-coordinate min) * (z-coordinate max - z-coordinate min)
The volume of the cylinder = ∫∫[2<= [tex]\sqrt{x^{2} + y^{2} }[/tex] <= 2.5] dA
The limits of the double integral are determined by the dimensions of the rectangular prism and the cylinder
The x-coordinate min is 0, x-coordinate max is 4, y-coordinate min is 0, y-coordinate max is 6, z-coordinate min is 0, and z-coordinate max is 6.
The volume of the solid
= (4 - 0) * (6 - 0) * (6 - 0) - ∫∫[2<= [tex]\sqrt{x^{2} + y^{2} }[/tex] <=2.5] dA
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What value is missing from the table?
Answer: D - 14
Step-by-step explanation:
1 gallon = 2.15
So to find how many gallons is worth 30.10, divide by 2.15
30.10 ÷ 2.15 = 14
Answer:
Step-by-step explanation:
To find the required gallons of gas for 30.10$, you can use the following formula:
Required gallons of gas=Cost of required gallons of gas/cost of one gallon of gas
Here given that, the cost of required gallons of gas is 30.10$ and the cost of one gallon of gas is 2.15$
Now apply the formula:
Required gallons of gas = 30.10$/2.15$ = 14
Therefore, the required gallons of gas = 14
So 14 gallons of gas costs 30.10$
Option D is the correct answer.
The scale is 2 cm = 15 m. Find the length each measurement would be in a scale drawing of 180 m
The length of measurement would be in a scale drawing of 180 m is 24 cm.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, the scale is 2 cm = 15 m.
So, 1 m =2/15
A scale drawing of 180 m
Now, 180 m = 2/15 ×180
= 2×12
= 24 cm
Therefore, the length of measurement would be in a scale drawing of 180 m is 24 cm.
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The perimeter of a rectangular parking lot is 354 m . If the width of the parking lot is 83 m , what is its length?
The perimeter of a rectangle is given by the formula P = 2(L + W), where P is the perimeter, L is the length, and W is the width.
We know that the perimeter of the parking lot is 354 m, and the width of the parking lot is 83 m. We can use this information to find the length of the parking lot.
Substituting the known values into the formula, we get:
354 = 2(L + 83)
Simplifying the equation:
354 = 2L + 166
Subtracting 166 from both sides:
188 = 2L
Dividing both sides by 2:
L = 94
The length of the parking lot is 94 m.
Answer:
Step-by-step explanation:
Formula for perimeter = (2 * length) + (2* width) = Perimeter
2l + (83 * 2) = 354
2l + 166 = 354
2l = 354 - 166
2l = 188
l = 188/2
l = 94 m
Sara's dog is 5 years younger than Anna's dog. Let A represent Anna's dog and S represent Sara's dog. Complete the table using the equation S = A − 5.
Answer: c
Step-by-step explanation:
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.
In a study of a birth sex selection method used to increase the likelihood of a baby being born female, 2085 users of the method gave birth to 1019 males and 1066 females. There is about a 169
chance of getting that many babies born female if the method had no effect.
Because there is a 16% chance of getting that many babies born female if the method had no effect, the method
procedure that raises the likelihood of a baby born female from the approximately 50% rate expected by chance to the produced by this method.
(Round to the nearest integer as needed.)
So, this method
has statistical significance.
should be used to make conclusions.
has practical significance.
does not have practical significance.
4
%
couples would likely use a
Because there is a 16% chance of getting that many babies born female if the method had no effect, the method has no statistical significance. Hence couples would likely use a procedure that raises the likelihood of a baby born female from the approximately 50% rate expected by chance to the 51.13% produced by this method.
This means that the method has practical significance.
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected, meaning that the research study is not statistically significant.If it is less, it is rejected, meaning that the research study is statistically significant.The p-value for this problem is given as follows:
0.16.
As the p-value is greater than the standard significance level of 0.05, the method has no statistical significance.
The percentage of females born is given as follows:
1066/2085 x 100% = 51.13%.
As this percentage is an increase from the usual 50%, the method has practical significance.
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A shopper at a clearance sale is pleased to discover some bottles of hand lotion on sale for $2.49 each. The original price tags read $3.25. What is the discount percentage?
Round your answer to the nearest percent and include a percent sign
HELPPPPP PLEASE
Answer: The discount percentage is 23.4%
Step-by-step explanation:
The discount percentage can be calculated by taking the difference between the original price and the sale price, dividing that by the original price, and then multiplying by 100 to get a percentage.
In ordered pair, notations, right down the components of vector D
Expression answers to the nearest integer
So on solving the provided question, we can say that n the graphs we have A at origin; B at origin; C in 3rd quadrant; D in the 2nd quadrant
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here in the graphs we have
A at origin
B at origin
C in 3rd quadrant
D in the 2nd quadrant
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Find the indicated measure in LMNQ. Explain your reasoning
Answer:
29°
Step-by-step explanation:
In given parallelogram LMNQ, you want the measure of angle LMQ when angle MQN is given as 29°.
Alternate interior anglesAngles LMQ and MQN are alternate interior angles where transversal MQ crosses parallel lines LM and NQ. As such, they are congruent.
m∠LMQ = 29°
Cole has many cans of fruit and vegetables in her pantry. 1/4 of the cans are vegetables and 6/7 of the cans are fruit. What fraction of the cans are either fruit or vegetables?
Answer:
Fraction of fruit or vegetable cans = 13/28
Step-by-step explanation:
The fraction of the cans that are either fruit or vegetables is the sum of the fractions of the cans that are fruit and the cans that are vegetables. Since the fractions are for mutually exclusive categories, we can add the fractions of cans of fruit and the cans of vegetables to find the total fraction of cans that are either fruit or vegetables.
Fraction of fruit cans: 6/7
Fraction of vegetable cans: 1/4
Therefore,
Fraction of fruit or vegetable cans = 6/7 + 1/4 = (6 + 7)/(7*4) =13/28
Find the limit as (x,y) approach (0,0) pf the function (cos(xy) -1)/(x^2y^2)
The limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined.
We can see that the denominator [tex]x^2[/tex][tex]y^2[/tex] goes to 0 as (x,y) approaches (0,0), and that can cause the function to go to infinity. However, the numerator (cos(xy) -1) does not have a specific value as (x,y) approaches (0,0) the cosine function oscillates between -1 and 1 as xy approaches zero, and therefore it does not approach a specific value.
The term (x,y) → (0,0) means that x and y are approaching 0 independently. There are different paths in which x and y can approach zero. Hence, by the squeeze theorem, we can see that if we approach (x,y) to (0,0) along the path y = mx, where m is a nonzero constant, the function goes to infinity, but if we approach (x,y) to (0,0) along the path x = 0 or y = 0, the function goes to -1.
Therefore, the limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined, as the function does not approach a specific value along all paths.
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Determine if the relationship ship is an additive. If it is, make a equation to match.
Answer:
No it is not
Step-by-step explanation:
In an additive relationship, two quantities can be expressed as related to each other through addition. It can be written as y = x + a, where y is related to x through the addition of a constant, “a”.
In this scenario, the "a" is not constant
1+2=3, 5+3=8, and 9+4=13
the number is increasing by one each time
Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy created all the students in your math class for a week, how many meters could the truck drive?
(DUE TODAY)
(TYSM FOR YOUR TIME)
PLEASE SHOW FULL WORK:)
The figure shows an object O in front of a plane mirror. Determine from which locations A-D the object's image is visible.
O A O B O C O D
An object O is displayed in front of a plane mirror in the figure. The image of the object is visible from locations B and C.
An object's image is created by a plane mirror by reflecting light rays that originate from the object. The object and its image appear to be equally distant from the mirror because the image created by a plane mirror is imaginary, upright, and the same size as the object.
As light from the object enters the plane mirror, it reflects each beam in accordance with the Law of Reflection. At the intersection of the reflected beams' extensions, the image is visible.
Therefore, the location must be on the reflected ray's path for the image to be visible. Here, locations B and C are on the path of the reflected ray. So the image is visible in these locations. But not in locations A and D.
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Does each equation represent exponential decay or exponential growth?
Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
A = (0.97)t
y=3.7(0.2)t
y= 9/11(4)t
P=7/9(5/4)t
V=0.8(9)t
P=0.9(8.3)t
g(x) = 2.1(x)
Solving the provided question, we can say that Not exponential growth or decay (no exponent) G(x)=1.3(x)
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially.
The base of the exponentiation is the strongest indicator of whether an equation exhibits an exponential growth or decline.
It will be an exponential growth if the base is greater than 1.
It will be an exponential decay if the base is less than 1.
There won't be any exponential growth or decay if the function's exponent is zero.
Therefore: Decay exponential (base less than 1:
W = 9/8(3/5)t
f(t) = (3/4)t
L = 4.2(0.6)t
Exponential Growth (base larger than 1:
L = 0.25(12)t
W = 0.5(2.1)t
f(t) = 2/3(6)t
Not exponential growth or decay (no exponent):
G(x)=1.3(x)
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find the sum of the series. [infinity] (−1)n 8nx6n n! n = 0
Sum of the series will be (19/30)
Partial differentiation is the method of determining a function's partial derivative. By holding the other variable constant, one may use this method to get the partial derivative of a function with respect to one variable.
An equation having an unknown function of two or more variables and its partial derivatives with respect to these variables is known as a partial differential equation. A partial differential equation has the highest-order derivatives as its order. is a partial differential equation of order 2, as an illustration.
Ordinary differential equations, often known as ODEs, are equations for which only one variable's derivatives are considered. Consequently, there is just one independent variable. PDEs are equations that rely on the partial derivatives of a number of distinct variables.
Using partial fractions, we have
[tex]\frac{6}{(n+8)(n+10)}=\frac{A}{n+8}+\frac{B}{n+10}\\\\=\frac{A(n+10)+B(n+8)}{(n+8)(n+10)} \\\\ 6=A(n+8)+B(n+10)[/tex]
Put n=-8,
we have 6=0+2B=>B=3
Put n=-10,
we have 6=-2A =>A=-3
[tex]$$\begin{aligned}& \sum_{n=1}^{\infty} \frac{6}{(n+8)(n+10)}=\sum_{n=1}^{\infty}\left(\frac{3}{n+8}-\frac{3}{n+10}\right) \\& =3 \sum_{n=1}^{\infty} \frac{1}{n+8}-\frac{1}{n+10} \\& =3\left[\left(\frac{1}{9}-\frac{1}{11}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{11}-\frac{1}{13}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)+\ldots\right] \\& =3\left[\frac{1}{9}+\frac{1}{10}\right]=\frac{19}{30}\end{aligned}$$[/tex]
other terms will be cancelled out
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The correct question should be:
Find the sum of the convergent series: [tex]$$\sum_{n=1}^{\infty} 6 /(n+8)(n+10)$$[/tex]
A truck is traveling 30 mi ahead of a car at an average rate of 55 mph. The car is traveling at a rate of 63 mph. Let x represent the number of hours that the car and truck travel. Write an inequality to determine at what times the car will be ahead of the truck and graph the inequality to solve.
An inequality to determine at what times the car will be ahead of the truck is; 63x > 55x + 30
The graph of the inequality is attached and the solution is (3.75, 236.25).
How to graph Inequality problems?We are told that;
x represent the number of hours that the car and truck travel
The truck is traveling at an average rate of 55 mph. Thus, the expression 55x represents the distance the truck travels in x hours.
The car is traveling at a rate of 63 mph. Thus, the expression 63x represents the distance the car travels in x hours.
In the beginning, the truck was 30 miles ahead of the car. So, we need to solve the inequality:
63x > 55x + 30
Use technology to graph y = 63x and y = 55x + 30 gives us;
The intersection point is (3.75, 236.25)
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IF MNOP IS A RHOMUS FIND MP
MNOP is a rhombus then, the length of the segment MP = 49 unit.
What is a rhombus?One kind of parallelogram is the rhombus, which has four sides and four vertices.
The length of each side is the same as the length of the opposing angle.
Given:
A rhombus is given in the attached image.
In rhombus,
every side is equal in length.
That means,
the parallel sides are equal.
9x - 77 = 3x + 7
6x = 84
x = 14
So, 3(14) + 7 = 42 + 7 unit
That means, the side in rhombus = 49 unit.
Therefore, MP = 49 unit.
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The complete question is given in the attached image.
Situation #6
=
It is known that ΔTOP~ΔBUG. Also, TO = 16, TP = 20, OP = 30, and BG = 105.
6. What is the perimeter of ΔBUG?
The perimeter of Δ BUG with sides BG = 105, BU = 16 and UG = 30 is 151 units.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
It is given that ΔTOP ~ ΔBUG.
The lengths of sides of ΔTOP is - TO = 16, TP = 20, OP = 30.
The length of one side of ΔBUG is BG = 105.
Since ΔTOP is same as ΔBUG, so sides BU and UG will same as sides TO and OP respectively.
So, BU = 16 and UG = 30.
The formula for the perimeter of a triangle is -
P = a + b + c
Where, P is the perimeter and a, b, c are the sides of the triangle.
For ΔBUG -
P = BU + BG + UG
P = 16 + 105 + 30
P = 151
Therefore, the perimeter of ΔBUG = 151 units.
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what is synthetic division method
Fernando has $1,608 in an account. The interest rate is 1% compounded annually.
To the nearest cent, how much will he have in 5 years?
Answer:
$1688.40
Step-by-step explanation:
1% of 1608 = 16.08
16.08 (5) = 80.40
1608+ 80.40= 1688.40
use the triangle sum theorem to find 7x + 4x + x = 180
Answer: x = 15
Step-by-step explanation: Combine like terms
7 x plus 4 x plus x equals 180
12 x equals 180
2
Divide both sides by the same factor
12 x equals 180
the fraction with numerator 12 x and denominator 12 end fraction equals the fraction with numerator 180 and denominator 12 end fraction
3
Simplify
Solution
x equals 15
ILL GIVE BRAINLIEST IF CORRECT NEED HELP ASAP PLS
Answer:
A
Step-by-step explanation:
Answer: y = (3/4)x - (7/4).
Step-by-step explanation:
Subtract 3x from both sides of the equation. Divide both sides of the equation by -4. Simplify. We get that solving 3x - 4y = 7 for y gives y = (3/4)x - (7/4).
A scale model of a merry-go-round and the actual merry-go-round are similar.
a. How many times greater is the base area of the actual merry-go-round than the base area of the scale model? Explain.
The ratio of the corresponding lengths is w : 1. So, the ratio of the areas is y : 1 and the base area of the actual merry-go-round is z times greater than the base area of the scale model.
I will give you a brainliest if you answer this!!!
b. What is the base area of the actual merry-go-round in square feet?
The base area of the actual merry-go-round is x square feet.
Answer:
A mary go round I'm sorry I am middle school
Please help ASAP!! I will appreciate it
Answer: D
Step-by-step explanation:
Evelyn wants to enlarge a 5” x 7” photograph. She plans to enlarge it to fit a frame that is 16” x 20”. Will Evelyn’s photo retain the same proportions? Explain your reasoning.
Evelyn’s enlarged photo will not retain the same proportions as the original one.
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol "::" or "=".
Given,
Length of the original photograph L = 5''
Width of the original photograph W = 7''
Ratio between length and width of original photograph
L/W = 5/7
Length of the enlarged photograph L' = 16''
Width of the enlarged photograph W' = 20''
Ratio between length and width of enlarged photograph
L'/W' = 16/20 = 4/5
Comparing both ratios
L/W = L'/W'
5/7 ≠ 4/5
so, proportion is not same.
Hence, proportion of the enlarged photo is not same as the original photo.
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Solve for z.
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.
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.
.
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The value of the z is 6√6 units. The triangles follow similar triangle property.
What are similar triangles?
Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.
Consider △BDC and △ABC:
∠C = ∠C
∠ABC = ∠BDC = right angle
If two angles of a triangle are equal to two angles of another triangle, then third angle of the triangles also equal.
∠BAC =∠DBC
According to A-A-A rule △BDC and △ABC are similar to each other.
Thus the ratio of corresponding sides is also equal.
Therefore:
AB/BD = BC/DC = AC/ BC
Consider the last two ratios:
BC/DC = AC/ BC
z/12 = z/18
z² = 12 × 18
z² = 6×2×6×3
z = 6√6
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Marcella wants to earn a total of at least $4,000 per month. For each company, find the least number of office machines she would need to sell each month in order to meet this goal. Show your work.
Answer:
1540$!$($9$
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Marcella would need to sell at least 40 office machines each month to earn at least $4,000.
To find the least number of office machines Marcella would need to sell each month to earn at least $4,000, we need to know the price of each office machine and the commission she receives for each sale.
We can use following formula:
Total Earnings = (Number of Machines Sold) x (Price of Machine) x (Commission Rate)Rearranging this formula to solve for the number of machines sold, we get:
Number of Machines Sold = Total Earnings / (Price of Machine x Commission Rate)Plugging in the values we know:
Number of Machines Sold = 4000 / (1000 x 0.1)
Number of Machines Sold = 4000 / 100
Number of Machines Sold = 40
Therefore, Marcella would need to sell at least 40 office machines each month to earn at least $4,000.
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