Answer:
I'm sorry but your question is not clear. Can you please provide more context or clarify what you are asking?
prove by mathematical induction that the sum of the cubes of the first n positive integers is equal to the square of the sum of these integers
The formula for the sum of cubes of the first n natural numbers is:
(1³+2³+3³+ ... + n³) = (1 + 2 + 3 + ... + n)²
Let us consider:
A(n)=1³+2³+⋯+n³--------(1)
B(n)=(1+2+⋯+n)²---------(2)
Now plug the numbers in the above equations(1)&(2) then,we get:
A(1)=B(1)=1
A(2)=B(2)=9
A(3)=B(3)=36
A(4)=B(4)=100
A(5)=B(5)=225
So both A and B are polynomials of degree at most 4 on n, and they coincide at 5 points.
Hence A(n) = B(n) for all n.
In general, p(n) is a polynomial of degree d on n,
∑kn=1 P(k)
is defined as a polynomial of the degree of d+1 on n. This trick will help solve every single issue involving the summation of polynomials, and then find the value on d+2 points, and we will determine the sum for all n.
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in a positive number of two digits, the sum of the digits is 15, if the digits are interchanged, the number is increased by 9. Find the number.
Answer:
the number is 78
Step-by-step explanation:
call x is the tens digit (0<x<9)
y is the unit digit (0[tex]\leq[/tex]y[tex]\leq[/tex]9)
we have:
10y+x=[tex]\oveline{yx}[/tex] (1)
10x+y= [tex]\overline{xy}[/tex] (2)
acording (1),(2) and the topic we have: (10y+x)-(10x+y)=9 ⇔9y-9x=9
⇔y-x=1 (3)
and x+y=15 (4)
from (3), (4) we have a system of equation
[tex]\left \{ {{y-x=1} \atop {x+y=15}} \right.[/tex]
⇔[tex]\left \{ {2y=16} \atop {x+y=15}} \right.[/tex]
⇔[tex]\left \{ {{y=8} \atop {x+8=15}} \right.[/tex]
⇔[tex]\left \{ {{y=8} \atop {x=7}} \right.[/tex] (conditions are satified)
the number is 78
what expressions are equivalent to 4x4x4x4x4
Answer:
4^5 = 1024
Step-by-step explanation:
Although there are many treatments for bulimia nervosa, some subjects fail to benefit from treatment. In a study to determine which factors predict who will benefit from treatment, Wendy Baell and E.H. Wertheim found that self-esteem was one of the important predictors. The mean and standard deviation of posttreatment self-esteem scores for n = 21 subjects were
= 26.6 and s = 7.4, respectively. Find a 95% confidence interval for the true posttreatment self-esteem scores.
95% CI for the true posttreatment self-esteem score is:
(24.47, 28.73)
The formula for calculating a 95% confidence interval for the mean self-esteem score is as follows:
(standard deviation/square root of sample size) * (mean (critical value)
The standard deviation of a set of data is a measure of its spread or dispersion. It denotes the average deviation of individual values in a data set from the data set's mean.
A low standard deviation indicates that the data points are close to the mean, whereas a high standard deviation indicates that the data points are scattered across a wide range.
For a normal distribution and a 95% confidence level, the critical value is 1.96.
As a result, the 95% confidence interval for the mean posttreatment self-esteem score is as follows:
26.6 ± 1.96 * (7.4/sqrt(21)) = 26.6 ± 2.13
As a result, the 95% CI for the true posttreatment self-esteem score is:
(24.47, 28.73)
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P(A or B)=P(A) + P(B)-P(A and B)
P(A and B)=P(A)xP(B|A)
P(B|A)=P(A and B)
P(A)
In a Pew poll of American voters, almost 80% of Democrats say the government
shutdown is a "very serious problem for the country, while just 35% of Republicans feel
the same. 54% of the people polled were Democrats and 46% were Republicans.
(a) Overall, what percentage of American voters say the government shutdown is a
"very serious" problem for the country?
%
Answer=
(b) Set up a 2x2 probability table. Round all percentages to 2 decimal places.
Democrat
Republican
Total
Serious
P(A and B)=P(A)x P(B) (if independent)
Not Serious
Total
%
%
%
%
%
%
%
%
%
Answer:For part (a), the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" can be calculated as follows:
P(A) = 54% (probability of being a Democrat)
P(B|A) = 80% (probability of saying the shutdown is a "very serious problem" given that the person is a Democrat)
P(A and B) = P(A) * P(B|A) = 54% * 80% = 43.2%
P(B) = 35% (probability of saying the shutdown is a "very serious problem" for Republicans)
P(A|B) = (P(A and B) / P(B)) = (43.2% / 35%) = 123.14%
P(A or B) = P(A) + P(B) - P(A and B) = 54% + 35% - 43.2% = 45.8%
Therefore, the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" is 45.8%.
For part (b), the 2x2 probability table can be set up as follows:
Serious Not serious Total
Democrat 43.2% 6.8% 50%
Republican 10.5% 35.5% 46%
Total 53.7% 42.3% 100%
Step-by-step explanation:
Heather saved $20 a week. This was 5% of her salary. What was Heather’s weekly salary?
Answer:
$400
Step-by-step explanation:
Here is my crack at it:
To find Heather's weekly salary, we can set up an equation using the information given. Let's call Heather's weekly salary "x".
According to the problem, $20 is 5% of her salary, so we can write this as an equation:
$20 = 0.05x
Now we can solve for x by dividing both sides by 0.05:
x = 400$
So Heather's weekly salary was $400.
Heather’s weekly salary would be 400$.
If heather saved $20 a week. This was 5% of her salary. Heather’s weekly salary would be
Given, $20 = 5%
As we know, the total salary will be 100 %
If 5% = $20
then, 100% = $400 (multiplying both the sides by 20)
Thus, Heather’s weekly salary was 400$.
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The formula T=2pi sqrt(L/32) gives the time it takes in seconds, T, for a pendulum to make one full swing back and forth, where L is the length of the pendulum, in feet. To the nearest foot, what is the length of a pendulum that makes one full swing in 1.9 s?
The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.
As per the given data, the given formula is:
[tex]$T=2 \pi \sqrt{\left(\frac{L}{32}\right)}[/tex] gives the time it takes in seconds.
Where,
T is the time it takes for a pendulum to make one full swing back and forth (in seconds).
L is the length of the pendulum, in feet.
Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.
Substitute the given parameters into the formula will give;
[tex]$1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}[/tex]
Now divide both sides by 2π.
[tex]$ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\[/tex]
[tex]$ 0.3024=\sqrt{\left(\frac{L}{32}\right)}[/tex]
Then taking square on both sides.
[tex]$ (0.3024)^2=\frac{L}{32} \\[/tex]
0.09144576 = [tex]$\frac{L}{32}[/tex]
Later multiply both sides by 32.
2.9262 = L
The approximate value of the length of a pendulum:
L ≈ 3
Therefore, the length of a pendulum is about 3 feet.
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If f ( x ) = x 2 + 2 x − 3 and g ( x ) = x 2 − 9 , find ( f g ) ( 4 ) and ( f + g ) ( 4 ) . ( f g ) ( 4 ) is , and ( f + g ) ( 4 ) is .
(Photo)
Pls help…
Answer:
3
28
Step-by-step explanation:
The expression (f/g) (4) is equal to f(4) / g(4).
f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21
g(4) = 4^2 - 9 = 16 - 9 = 7
So, (f/g) (4) = 21 / 7 = 3.
The expression (f + g) (4) is equal to f(4) + g(4).
f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21
g(4) = 4^2 - 9 = 16 - 9 = 7
So, (f + g) (4) = 21 + 7 = 28.
what 2n boys are divided into two equal subgroups, find the probability that the two tallest are in the same subgroup?
The probability that the two tallest are in the same subgroup is given as follows:
2/n².
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
In this problem, we have that:
There are 2n boys.They are divided into two equal groups, hence each group has n students.For each student, the probability of belonging to a group is given as follows:
1/n.
Hence the probability that the two tallest are in the same subgroup is obtained as follow:
2 x 1/n x 1/n = 2/n².
The multiplication by 2 is because there are two groups.
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need help
please help me
The shaded region in the graph represents the possible solution sets to the inequality.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the inequality -
x² + 15 ≥ 23
The given inequality is -
x² + 15 ≥ 23
Refer to the graph attached.
The shaded region represents the possible solution sets to the inequality above.
Therefore, the shaded region in the graph represents the possible solution sets to the inequality.
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Heeeelp just need to find
(f+g)(2)=
===========================================
Work Shown:
[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (\text{x}+3)+(\text{x}^2-2)\\\\(f+g)(\text{x}) = \text{x}^2+\text{x}+1\\\\(f+g)(2) = 2^2+2+1\\\\(f+g)(2) = 4+2+1\\\\(f+g)(2) = 7\\\\[/tex]
----------------------------
Another approach:
[tex]\begin{array}{lll}f(\text{x}) = \text{x}+3& & g(\text{x}) = \text{x}^2-2\\f(2) = 2+3 & \text{ and } & g(2) = 2^2-2\\f(2) = 5 & & g(2) = 2\\\end{array}\\\\\\\text{Therefore, } (f+g)(2) = f(2)+g(2) = 5+2 = 7[/tex]
Solve the triangle:
Answer: 101.6
Since we are trying to find the sides of both the triangles, we will need to use the Sin, Cos, & Tan trigonometry functions. There are 3 equations:
[tex]Sin (Angle) = \frac{Opposite}{Hypotenuse} \\Cos (Angle) = \frac{Adjacent}{Hypotenuse} \\Tan (Angle) = \frac{Opposite}{Adjacent}[/tex]
For this triangle shown in the picture, we can infer that the 88 is OPPOSITE to the 60° and 30° angles. So we already have the opposite, and since we are trying to find the adjacent, we will use the formula that consists both opposite and adjacent, which is the following:
[tex]Tan(Angle) = \frac{Opposite}{Adjacent}[/tex]
Since [tex]x[/tex] is only a part of the long triangle, we will subtract the small triangle's side from the big one, which will give us [tex]x\\[/tex].
We can input our values to solve each triangle's side lengths.
(You have to use the calculator for these)
Small one:
[tex]Tan(60) = \frac{88}{Adjacent}\\Adjacent = \frac{88}{Tan(60)}\\Adjacent = \frac{88\sqrt{3} }{3} = 50.807 (3 d.p)[/tex]
Big one:
[tex]Tan(30) = \frac{88}{Adjacent} \\Adjacent = \frac{88}{Tan(30)} \\Adjacent = 88\sqrt{3} = 152.420 (3d.p)[/tex]
Now, to calculate [tex]x[/tex] , we will subtracat the small one from the big one like this: (it is better to input the values with the surds and not the real numbers for accurate marks and calculations)
[tex]88\sqrt{3} - \frac{88\sqrt{3} }{3} = 101.6 (1 d.p)[/tex]
That is the answer. If you did not understand it completely, please reach me back and I will help you :)
A math and science museum recently installed a door that features a stained glass topper as shown. What is the are
a of the topper?
The area of the topper will be 24 square units.
What is the area of the rectangle?A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
The area of the glass topper will be:-
Area = Length x Width
Area = 6 x 4
Area = 24 square units
The image of the glass topper is attached with the answer below.
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Use the graphs to evaluate the expressions below
Answer:
5,4,2,0
Step-by-step explanation:
f(g(4))=5
g(f(3))=4
f(f(2))=2
g(g(5))=0
The value of composition function is:
1. f(g(4)) = 5
2. g(f(3)) = 4
3. f(f(2)) = 2
4. g(g(5)) = 0
To find the value of function focus on the graph of the function.
1. f(g(4))
From the graph of g(x), when x= 4 the value of y is 2.
So, g(4) = 2
Now, the value of f(g(4))
f(g(4))= f(2)
= 5.
2. g(f(3))
From the graph of f(x), when x= 3 the value of y is 0.
So, f(3) = 0
Now, the value of g(f(3))
g(f(3))= g(0)
= 4.
3. f(f(2))
From the graph of f(x), when x= 2 the value of y is 5.
so, f(2)= 5
Now, the value of f(f(2))
f(f(2)) = f(5)
= 2
4. g(g(5))
From the graph of g(x), when x= 5 the value of y is 3.
so, g(5)= 3
Now, the value of g(g(5))
g(3) = 0
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Math ready Unit 5 lesson 3 task 10 part 1 BurgerRama Cartoon Dolls answer key to 4
Based on the information in the table, a graph can be created to relate the number of Supply Dolls and Demand Dolls with respect to the sale value.
How to create a graph with the information from the table?To create a graph with the information in the table, we must identify what information should go on the x-axis and the y-axis. In this case, we are being asked to locate the sale value on the x axis and on the y axis we must locate the number of units supplied and demanded.
Based on this information, we can infer that at a lower sale price, more dolls are demanded, but not as many are supplied. On the contrary, when the price is higher ($4.00) more dolls are supplied but not as many are demanded. This means that the relationship is inversely proportional.
Note: This question is incomplete because there is some misinformation. Here is the complete information:
Task.
Joan King is marketing director for the BurgeRama restaurant chain. BurgerRama has decided to have a cartoon-character doll made to sell at a premium price at participating BurgerRama locations. The company can choose from several different versions of the doll that sell different prices. King's problem is to decide which selling price will best suit the needs of BurgerRama's customers and store managers. King has data from previous similar promotions to help her make a decision.
1. Use the data from the table above to plot points representing selling price and supply price on a graph. (Selling Price of Each Doll should appear on the x-axis, and Number of Dolls Per Week per Store should appear on the y-axis). Draw the line through the data points and write the word "Supply on this line.
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Can someone answer this pls
-3y + 4 – 2 + 6y
Answer: 3y + 2
Step-by-step explanation: First, you can organize the equation into -3y + 6y + 4 - 2. Then, you get 3y + 2. :)))))
Find the area of the shaded portion.
Answer:
3a^2
Step-by-step explanation:
one way of answering this question is by finding the area of the whole shape, including the non-shaded shape, then taking away the area of the non-shaded shape from the whole thing, leaving you the area of the shaded shape
Step-by-step
find the area of the whole shape
2a x 2a
= 4a^2 (or 4a to the power of 2)
Now that we have the area of the whole shape, we must find the area of the non-shaded shape and take it away from 4a^2, we do this by
a x a
= a^2 (or a to the power of 2)
now we minus the non-shaded shape away from the total area
4a^2 - a^2
= 3a^2 (or 3a to the power of 2)
How would the break-even period in this scenario change if you lived in another state? Research another state’s minimum coverage requirement and calculate the break-even period you calculated above for that state’s minimum coverage requirements. Assume that all other variables (premium, deductible, etc.) are the same. Specify the state you researched and its minimum coverage requirements in your answer.
The break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.
What is meant by break-even period?In business accounting, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company within a specified time period.
To calculate the break-even point in units use the formula:
Break-Even point (units) = Fixed Costs ÷ (Sales price per unit – Variable costs per unit) or in sales dollars using the formula: Break-Even point (sales dollars) = Fixed Costs ÷ Contribution Margin.
Insurance Requirements the part of a commercial contract in which the types and minimum amounts of insurance the parties agree to provide in connection with their performance of the contract are specified.
A break even point is used in multiple areas of business and finance. In accounting terms, it refers to the production level at which total production revenue equals total production costs. In investing, the break even point is the point at which the original cost equals the market price.
Therefore, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.
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which of the following statements is true? a single variance clearing account is used to accumulate the individual variances.
The variance clearing account is used to accumulate individual variances until they can be allocated to their respective variance accounts, and the formula used to calculate the variance clearing account is the sum of all the individual variances, plus the beginning balance of the account.
A variance clearing account is a temporary ledger account used to accumulate individual variances such as direct labor cost, direct material cost, and overhead cost. The variance clearing account is used to collect all the individual variances in one account until it can be allocated to its respective variance accounts. This account has a debit side and a credit side. The debit side of the variance clearing account is used to accumulate all the unfavorable variances, while the credit side is used to accumulate all the favorable variances.
The formula used to calculate the variance clearing account is the sum of all the individual variances, plus the beginning balance of the account. This can be expressed as follows:
Variance Clearing Account = Beginning Balance + Sum of All Individual Variances
For example, if the beginning balance of the variance clearing account is $500, and the sum of all individual variances is $400, the balance in the variance clearing account would be $900 ($500 + $400). This balance can then be allocated to the respective variance accounts.
The variance clearing account is used to accumulate individual variances until they can be allocated to their respective variance accounts, and the formula used to calculate the variance clearing account is the sum of all the individual variances, plus the beginning balance of the account.
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Patricia decides to buy a pair of boots for $90.00. She was willing to pay $120.00. When her friend Cecilia sees the boots, she loves them and thinks they are worth $170.00. So she offers Patricia $145.00 for the boots, and Patricia accepts. Patricia and Cecilia are both thrilled with the exchange.
The total surplus received by both Patricia and Cecilia is $
Suppose that Patricia purchased the boots from Marie’s Boutique. Marie and other boutique owners in town are upset that customers like Patricia buy boots at their stores, and then resell them for a higher price. Marie and the other owners convince the city government to pass a law preventing such resale. Assuming the law is successful, how much surplus is lost if Patricia cannot sell the boots to Cecilia?
The total surplus received by both Patricia and Cecilia is $55.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
Patricia decides to buy a pair of boots for $90.00. She was willing to pay $120.00.
And, Her friend Cecilia sees the boots, she loves them and thinks they are worth $170.00. So she offers Patricia $145.00 for the boots, and Patricia accepts.
Hence, Consumer surplus is the difference between the willingness to pay of a consumer and the price of the good.
Consumer surplus = willingness to pay – price of the good
Consumer surplus received by Patricia = $120 - $90 = $30
Consumer surplus received by Cecilia = $170 - $145 = $25
Thus, Sum of the surpluses = $30 + $25 = $55
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find the equation of the slant asymptote of the function f(x)=x2+x+2/x+3
Answer:
[tex]y=x-2[/tex]
Step-by-step explanation:
The slant, or oblique asymptote, is found by taking the quotient of the two polynomials and disregarding the remainder:
-3 | 1 1 2
____ -3_6
1 -2 | 8
Hence, our slant asymptote is [tex]y=x-2[/tex]
An inch is exactly 2.54
centimeters.
Write an equation to convert the number of inches x
to the corresponding length in centimeters.
Enter the equation in the box.
Answer:
x * 2.54 = centimeters
Step-by-step explanation:
The equation to convert inches to centimeters is as follows:
x inches * 2.54 cm/inch = y centimeters
Where x is the number of inches and y is the equivalent length in centimeters.
To elaborate, the conversion factor between inches and centimeters is 2.54 cm/inch, meaning that for every inch there are 2.54 centimeters. To convert from inches to centimeters, we simply multiply the number of inches by the conversion factor. This gives us the equivalent length in centimeters.
Describe how you would obtain an equation in one variable to solve the system by substitution. 3x+5y=25 x-2y=-6
Solve for x in one of the equations and substitute it into the other equation.
To solve the system of equations 3x + 5y = 25 and x - 2y = -6 using substitution, we first solve for x in one of the equations. Let's solve for x in the second equation: x = 2y + 6. Next, we substitute this expression for x into the first equation: 3(2y + 6) + 5y = 25. This gives us 6y + 18 + 5y = 25, which simplifies to 11y + 18 = 25. Finally, we subtract 18 from both sides to obtain 11y = 7, and divide both sides by 11 to find y = 7/11. Now that we have y, we can substitute it back into either equation to find x.
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The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
this is a homeeork problem
rv X = the length of a randomly selected Atlantic cod
g) What length do 57% of all Atlantic cod have more than?
Round your answer to two decimal places in the first box.
Put the correct units in the second box.
The z score is -0.18 and 57 % of all Atlantic cod have more than 49.23 cm in length and
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P
Now , the equation will be
The observed value of be x
The mean of the sample μ = 49.9 cm
The standard deviation of the sample σ = 3.74 cm
Now , z-score is calculated using the formula:
z = (x - μ)/σ
And , the length of 57% of all Atlantic cod have more than is calculated by
Now , the z score with a p value of 0.43 is
z = -0.18
Substituting the values in the equation , we get
-0.18 = ( x - 49.9 ) / 3.74
Multiply by 3.74 on both sides of the equation , we get
-0.6732 = x - 49.9
Adding 49.9 on both sides of the equation , we get
x = 49.2268 cm
Hence , 57 % of all Atlantic cod have more than 49.2268 cm in length and the z score is -0.18
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Which of the following is true about graphical data? a) All graphs should start at the origin. b) An equation of the best-fit line of data can be used to estimate untested values. c) All data on a graph should be linear. d) Graphical correlations always have a positive relationship. e) The x-values of a graph can be estimated based on the y-values.
An equation of the best-fit line of data can be used to estimate untested values. Graphical data can be used to show relationships between variables, but those relationships do not have to be linear and do not always have a positive relationship.
Graphical data is a way of visually representing information in a way that can be easily understood. It is often used to determine relationships between variables, such as the relationship between prices and sales. Graphical data can be used to show correlations, even if the relationship is not linear. An equation of the best-fit line of data can be used to estimate untested values, which can be useful in predicting future values. The x-values and y-values of a graph can both be estimated based on the data presented, and do not necessarily need to start at the origin. Graphical correlations can have both positive and negative relationships, depending on the data presented. Graphical data can be a powerful tool for understanding relationships between data points.
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A
28⁰
78⁰
B
C
F
ABCD is a circle with centre O. BCF is a
straight line. Angle CBD = 28° and angle FCD
= 78°. What is the size of angle BAC?
(A) 28° (B) 50⁰ (C) 74°
(D) 78°
The size of angle BAC in the given circle is 50°
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Since, no figure is given, we will draw a circle according the given information, [attached in the solution]
So, we get a circle with center O, having chords, BC, which is extended to F, DC and AB,
We have, Angle CBD = 28° and angle FCD = 78°
Therefore,
∠ DCB = 180° - ∠ DCF [Linear pair]
∠ DCB = 180° - 78°
∠ DCB = 102°
In Δ DCB,
∠ DCB + ∠ BCD + ∠ BDC = 180°
∠ BDC = 180° - (102°+28°)
∠ BDC = 50°
Since, the angles made by the same chord are equal in measure,
Therefore,
∠ BDC = ∠ BAC
Therefore,
∠ BAC = 50°
Hence, the size of angle BAC in the given circle is 50°
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For each team, find the unit rate games per loss.
The unit rate for the games per loss are:
Jules’ Rules unit rate = 3 or 3/1
Pink sox unit rate = 4 or 4/1
Go - Girl unit rate = 4 or 4/1
High- 5s unit rate = 9 or 9/1
How to find the unit rate?Unit rate = Games/Losses
Jules’ Rules unit rate = 36/12
Jules’ Rules unit rate = 3 or 3/1
Pink sox unit rate = 68/17
Pink sox unit rate = 4 or 4/1
Go- Girls unit rate = 52/13
Go - Girl unit rate = 4 or 4/1
High-5s unit rate = 72/8
High- 5s unit rate = 9 or 9/1
Therefore the Jules’ Rules unit rate 3, Pink sox unit rate 4, Go - Girl unit rate 4, High- 5s unit rate 9.
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The cost of a newspaper subscription
includes a discounted initial week. Beatriz
pays $55 for 7 weeks of the newspaper
subscription and $100 for 12 weeks.
As a result, the original discounted price is $1 while the weekly normal price is $9.
How does arithmetic work with discounts?The fundamental formula for calculating a reduction is to increase the initial price by the provided percentage rate in decimal form. We must deduct the reduction from the initial price to determine the item's sale price.
From the given information, we have:
d + 6x = 55 (discounted price for 7 weeks)
d + 11x = 100 (discounted price for 12 weeks)
We can solve this system of equations by eliminating d. Subtracting the first equation from the second, we get:
5x = 45
Dividing both sides by 5, we get:
x = 9
Substituting x = 9 into one of the equations, we can solve for d. Using the first equation, we get:
d + 6(9) = 55
d + 54 = 55
d = 1
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What’s the right answer
Answer:
Cosine (cos)
Step-by-step explanation:
Sine, Cosine, and Tangent have their own properties.
Cosine is adjacent over hypotenuse. We have the angle of 59, the line adjacent is 17 and the hypotenuse is x. You could also do it for the right angle.
Let $\triangle ABC$ be a right triangle, and let $H$ be the point on side $\overline{AB}$ so that $\overline{CH} \perp \overline{AB}.$
[asy]
// Coordinates for 3-4-5 triangle
pair A = (5, 0);
pair B = (0, 0);
pair C = (1.8, 2.4);
pair H = foot(C, A, B);
draw(A--B--C--cycle);
draw(rightanglemark(B, C, A));
draw(C--H);
draw(rightanglemark(C,H,A));
label("$A$", A, E);
label("$B$", B, W);
label("$C$", C, N);
label("$H$", H, S);
label("$x$", midpoint(B--H), S);
label("$y$", midpoint(A--H), S);
label("$h$", midpoint(C--H), E);
label("$a$", midpoint(B--C), NW);
label("$b$", midpoint(A--C), NE);
[/asy]
Prove that
\[(x + h)^2 + (y + h)^2 = (a + b)^2.\]
The Proof of ( x + h)² +( y + h)² = (a + b)² is shown below.
What is Similarity?In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.
Given:
BHC and BCA are similar
HC / BC = CA / BA
so, h / a = b / ( x + y) ........... (1)
Working with your expansion
x² + h² = a² and
y² + h² = b²
So, subtracting out the equal parts we are left with
2xh + 2yh = 2ab ..........(3) divide through by 2
xh + yh = ab
h( x + y) = ab which we can rearrange as
h / a = b / ( x+ y)..............(2)
Since this is equal to (1) and it's just a rearrangement of (3) adding all the other equal parts of the expansion shows that
(x² + h²) + (y² + h²) + ( 2xh + 2yh) = a²+ b²+ 2ab
( x² + 2xh + h²) + ( y² + 2yh + h²) = ( a + b)²
( x + h)² + ( y + h)² = (a + b)²
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