Answer:
To find out how many paddle balls will be in each hopper, you can divide the total number of paddle balls by the number of hoppers.
paddle balls ÷ hoppers = paddle balls per hopper
2798 ÷ 40 = 69.95
So there will be approximately 69.95 paddle balls in each hopper. Since it's not possible to put 0.95 of a paddleball in a hopper, you can round it to the nearest whole number. This means each hopper will have 70 paddleballs.
Step-by-step explanation:
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
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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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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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.
Find the following cardinalities:
a. A when A= {5, 6, 7, 8, ..., 35}.
b. A when A= {xEZ: -2 ≤ x ≤ 90}.
c. An B| when A= {x EN: x ≤ 31} and B = {x EN: x is prime}
Therefore , the solution of the given problem of set A when A= {5, 6, 7, 8, ..., 35}.
What does the math set mean?In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.
Here,
The set A contains integers between 5 and 35, inclusive. So, the cardinality of set A is the number of integers between 5 and 35, which is 35-5+1 = 31.
b. A when A= {xEZ: -2 ≤ x ≤ 90}.
The set A contains all integers between -2 and 90, inclusive. So, the cardinality of set A is the number of integers between -2 and 90, which is 90-(-2)+1 = 93.
c. An B| when A= {x EN: x ≤ 31} and B = {x EN: x is prime}
The set A contains all the natural numbers less than or equal to 31. The set B contains all the prime numbers less than or equal to 31. There are 15 prime numbers less than or equal to 31: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. So, the cardinality of set B is 15.
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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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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
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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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 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]
Pedro has a tax-free savings account (TFSA) with a balance of
$2350.00. His interest is earned at a rate of 2.10%, compounded monthly. If he
contributes $400.00 to the TFSA at the end of every month, how long will it take
him to save $15 000.00?
You can hold qualified investments like cash, stocks, bonds, mutual funds in a TFSA and can withdraw contributions as well as the interest, capital gains, and dividends earned in the account at any time1, without paying taxes
What is the use of TFSA?Any individual that is a non-resident of Canada who has a valid SIN and who is 18 years of age or older is also eligible to open a TFSA. However, any contributions made while a non-resident will be subject to a 1% tax for each month the contribution stays in the account.A TFSA allows you to set money aside in eligible investments and watch those savings grow tax-free throughout your lifetime. Interest, dividends, and capital gains earned in a TFSA are tax-free for life.The single biggest benefit of a TFSA is that growth of all assets within it are tax-free: this includes interest, dividends and capital gains. You won't pay a penny in income tax even when you withdraw from your account or sell the assets inside the TFSATo know more about tax visit:
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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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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
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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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).
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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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
Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42? l'll give brainiest
Answer: x3 +y3 20
Step-by-step explanation:
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
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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Listed below are the lead concentrations (in mg/g) measured in different samples of a medicine. What do the results suggest about the safety of this medicine? What do the decimal values of the listed amounts suggest about the precision of themeasurements?
O 18.5
O 14.5
O 20.5
O 7.5
O 18
O 8.5
O 8
O 9.5
O 15
The results suggest that the lead concentrations in the medicine samples are relatively low, as all of the values are below 20 mg/g. However, it would be necessary to compare these values to a standard, such as the acceptable limit of lead in medicine set by a regulatory body, in order to determine if the medicine is considered safe.
The decimal values of the listed amounts suggest that the measurements were precise, as they are all reported to one decimal place. It means that the measurement was done with a precision of 0.1. In addition to that, the measurements are consistent and close to each other, which also indicates that the measurements were precise.
It's important to keep in mind that precision and accuracy are different things. Precision refers to the degree of reproducibility of a measurement, while accuracy refers to the degree of closeness of a measurement to the true value. In this case, the measurements are precise but it's not specified if the measurements are accurate or not.
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what is synthetic division method
Jean joined a gym. It costs $60 per month and $2 per hour of boxing classes. Write an expression to represent the total cost of his gym, including the boxing classes for a month. Then determine how much it would cost him, if he spent 19.5 hours in gym class that month.
Answer:
y= 60+ 2x and if he spent 19.5 hours then he would pay $99 for that month
Step-by-step explanation:
$60 PER MONTH + $2 per hour of boxing classes
X represents the total hours he had the boxing classes
equation: y= 60+ 2x
if he spent 19.5 hours in boxing class
plug in 19.5 hours to X
99 = 60+ 2(19.5) = 60 + 39
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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A car is purchased for $22,500. After each year, the resale value decreases by 30%. What will the resale value be after 4 years?
Use the calculator provided and round your answer to the nearest dollar.
On solving the provided question, exponents, resale value be $5339 after 4 years.
Exponents in math: what are they?The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) means 2 x 2 x 2 = 8. and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
y = cn^x
y is the new price, c is the starting price, n is the rate of increase (or decrease), and x is the number of years. I won't bore you with the various names this exponent use has in calculus and economics.
In our instance:
By calculating how much of the price will remain, we can determine n.
1.00 — 0.25 = 0.75
f(x) = (22500)(0.75)^x
f(5) = (22500)(0.75)^5
=5339.35
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Please help ASAP!! I will appreciate it
Answer: D
Step-by-step explanation:
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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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:
I need help ASAP
Look at the image below
Answer:
2 only
Step-by-step explanation:
Answer:2 and 4
Step-by-step explanation:
if you divide 164 by all the numbers you only get whole numbers when you divide it by 2 and 4 not 3 and 6
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