The values of x and y such that the table represents a function are given as follows:
x = 8, y = 7.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
The input-output pairs for the function in this problem are given as follows:
An input of 6 is mapped to an output of 6.An input of 3 is mapped to an output of 8.An input of 9 is mapped to an output of 12.An input of 7 is mapped to an output of 8.Hence the x-value can only by 8 or 12, and we choose y = 8, while the y-value is free, hence we choose y = 7.
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Two step equations that equal 23
HELP!!
show you're work please...
The height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.
How to evaluate for the height of the trapezoidarea of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel bases.
we shall represent the height of the trapezoid with the letter h so that:
21 cm² = 1/2 × (5 + 9) cm × h
21 cm² = 1/2 × 14 cm × h
21 cm² = 7 cm × h
divide through by 7 cm
h = 21 cm²/7 cm
h = 3 cm
Therefore, the height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 4 people took the trip. She was able to purchase coach tickets for $140 and first class tickets for $1000. She used her total budget for airfare for the trip, which was $2280. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought = ___
The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.
Let us assume the number of coach tickets purchased is x.
And the number of first-class tickets purchased is y.
Now,
Including Sarah, a total of 11 people took the trip.
Thus,
[tex]x + y = 11 [/tex]
The cost of coach tickets and first-class tickets are $210 and $1200 respectively.
The total budget for airfare for the trip is $10,230.
Therefore,
210x + 1200y = 102309
21x + 120y = 1023
Solving both the equations, we get.
x=3
y=8
Thus, The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.
What is the answer of this p³+10+m-m if m=8 and p=3 equal
Given:-
p=3m=8Solution:-
p³+10+m-m
put the value of p nd m in eqⁿ :
( 3 )³ + 10 + 8 - 827 + 10 + 8 - 827 + 1037━━━━━━━━━━━
hope it helps⸙
The value of expression at m = 8 and p = 3 is,
⇒ 37
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ p³ + 10 + m - m
Now,
Put m = 8 and p = 3 in above expression, we get;
⇒ p³ + 10 + m - m
⇒ 3³ + 10 + 8 - 8
⇒ 27 + 10
⇒ 37
Thus, The value of expression at m = 8 and p = 3 is,
⇒ 37
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Identify the discriminant value of the quadratic equation m² + 18m + 17 = 0.
Answer:
Step-by-step explanation:
The discriminant value (denoted by Δ) of a quadratic equation in the form of ax² + bx + c = 0 is given by the expression b² - 4ac.
For the quadratic equation m² + 18m + 17 = 0, a = 1, b = 18, and c = 17. Substituting these values into the expression for the discriminant, we get:
Δ = b² - 4ac
Δ = (18)² - 4(1)(17)
Δ = 324 - 68
Δ = 256
Therefore, the discriminant value of the quadratic equation m² + 18m + 17 = 0 is 256.
2. Big Money Bank has an offer for new customers: if you deposit
$5,000 in a savings account, you will earn 6.5% simple interest
over the first 10 years.
C. At the town savings bank a new customer earns $2950 in simple interest on a $5000 deposit over the first 10 years what rate of interest does that bank pay
Answer:
We can use the simple interest formula to find the rate of interest that the town savings bank pays:
Simple Interest = Principal x Rate x Time
where Principal is the initial deposit, Rate is the interest rate, and Time is the time period.
We know that the Principal is $5000, the Simple Interest earned over the first 10 years is $2950, and the Time is 10 years. Substituting these values into the formula, we get:
$2950 = $5000 x Rate x 10
Simplifying the equation, we get:
Rate = $2950 / ($5000 x 10)
Rate = 0.059 or 5.9%
Therefore, the town savings bank pays an interest rate of 5.9% on its savings accounts.
Please Help ASAP - 100 pts + Brainliest if the answer is correct!
Answer:
a. aₙ=(aₙ₋₁ x 0.98) + 1150
I WILL GIVE BRANLIST ONLYNOF YOUR RIGHT
Determine the scale factor used to create the image
A 1/2
B 2
C 1/4
D 4
Answer:
Step-by-step explanation:
b
6 of 8
? Work out the area of the shaded shape.
5m
3m
T
6m
2m
2m
Suppose a recent government report indicates that 6% of the labor force is Asian. Of the individuals in the labor force who are Asian, 5% are unemployed. Among the individuals in the labor force who are not Asian, 6% are unemployed. Let be the event that a randomly selected member of the labor force is Asian and let be the event that a randomly selected member of the labor force is unemployed. Determine (∣) , the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed. Express your answer as a percentage with no decimal places.
Answer:
The probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98%
Step-by-step explanation:
We want to find the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed, which can be written as P(A|U). Using Bayes' theorem, we have:
P(A|U) = P(U|A) * P(A) / P(U)
We are given P(A) = 0.06 (6% of the labor force is Asian), P(U|A) = 0.05 (among Asians in the labor force, 5% are unemployed), and P(U|not A) = 0.06 (among non-Asians in the labor force, 6% are unemployed).
To find P(U), we can use the law of total probability:
P(U) = P(U|A) * P(A) + P(U|not A) * P(not A)
We know P(A) = 0.06, so P(not A) = 1 - P(A) = 0.94.
Therefore,
P(U) = 0.05 * 0.06 + 0.06 * 0.94 = 0.0602
Now we can substitute all the values into Bayes' theorem:
P(A|U) = 0.05 * 0.06 / 0.0602 = 0.0498
So the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98% (rounded to the nearest percentage with no decimal places).
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Answer:
a) Area of inner square = 58 cm²
b) Area of inner square = (2x² - 2xy + y²) cm²
Step-by-step explanation:
To calculate the area of a square, multiply the length of one of its sides by itself. This can be expressed as A = s², where A is the area and s is the side length of the square.
To calculate the area of a triangle, halve the product of its base and height. This can be expressed as A = (1/2)bh, where A is the area, b is the base and h is the height of the triangle.
The easiest way to calculate the area of the inner square is to subtract the areas of the 4 congruent triangles from the area of the outer square.
[tex]\hrulefill[/tex]
Part a)The outer square has a side length of 10 cm. Therefore its area is:
[tex]\implies \sf A_{outer\;square} = 10^2 = 100 \; cm^2[/tex]
Each corner triangle has a height of 3 cm and a length of (10 - 3) cm.
Therefore, the area of one triangle is:
[tex]\implies \sf A_{triangle}=\dfrac{1}{2} \cdot 7 \cdot 3=10.5\;cm^2[/tex]
Therefore, the area of the inner square is:
[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=\sf 100-(4 \cdot 10.5)\\&=\sf 100-42\\&=\sf 58\; cm^2\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Part b)The outer square has a side length of y cm. Therefore its area is:
[tex]\implies \textsf{A$_{\sf outer\;square}$} = y^2 \; \sf cm^2[/tex]
Each corner triangle has a height of x cm and a length of (y - x) cm.
Therefore, the area of one triangle is:
[tex]\begin{aligned}\implies \sf A_{triangle}&=\dfrac{1}{2} \cdot (y-x) \cdot x\\\\&=\dfrac{1}{2}x(y-x)\;\sf cm^2\end{aligned}[/tex]
Therefore, the area of the inner square is:
[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=y^2-4\left(\dfrac{1}{2}x(y-x)\right)\\\\&=y^2-2x(y-x)\\\\&=y^2-2xy+2x^2\\\\&=(2x^2-2xy+y^2)\; \sf cm^2\end{aligned}[/tex]
Please answer this for me quick i have another one
The value of the fraction x/y is 3/25 and option b is the correct answer.
What are fractions?An expression for a portion of a whole is a fraction. In general, the whole can be any particular object or value, and the fraction might be a piece of any quantity out of it.
The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.
The given equation is:
5x + y / y = 8/5
Divide the terms individually at the left side of the equation:
5x/y + y/y = 8/5
5 (x/y) + 1 = 8/5
5 (x/y) = 8/5 - 1
5 (x/y) = 3/5
x/y = 3/25
Hence, the value of the fraction x/y is 3/25 and option b is the correct answer.
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Confidence intervals are constructed to estimate the population parameter (like the mean) a specified proportion of the time. The upper and lower interval estimates are often described as the
The upper and lower interval estimate are often describe as associated with a specific level of confidence.
What is Interval Estimate?In statistics, interval estimate is the process of determining the interval, or range of values, within which a parameter—such as the mean (average) of a population—is most likely to fall.
The interval encompassing a population parameter is determined by computing the statistic from values obtained from a random sample chosen from the population and by using the understanding (derived from probability theory) of how accurately sample properties reflect those of the full population.
The possibility that the estimated confidence interval estimate will include the genuine population parameter is frequently referred to as the confidence level.
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A ball that is thrown upward follows the path h(t)=-t^2+8t+32, where h(t) represents the height of the ball above the ground at time t, and t represents the time since the ball was thrown. How high above the ground did the ball reach? show work
Answer:
Step-by-step explanation:
To find the maximum height of the ball, we need to find the vertex of the parabolic function h(t) = -t^2 + 8t + 32. The vertex represents the highest point of the parabolic curve.
The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = -1 and b = 8, so we have:
x = -b/2a = -8/(2(-1)) = 4
Therefore, the vertex occurs at time t = 4.
To find the y-coordinate of the vertex, we evaluate the function at t = 4:
h(4) = -4^2 + 8(4) + 32 = 16 + 32 = 48
Therefore, the ball reaches a maximum height of 48 feet above the ground.
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What's the best place to eat at? (Restaruant, Fast Food, Buffet, Cafe, etc.)
Answer:
Step-by-step explanation:
Me personally, I think buffets are the best because you can take as music food as you much, without being charged for much! But thats only for some buffets. If you go to a chinese buffet, they might lower the price allowing you to get as much food as you please!
Weber Jewelry advertised a diamond necklace for $572.95 and a gold pendant for $113.76. The state tax is 6.5 percent and the city tax is 0.5 percent. What is the total purchase price?
Therefore, the total purchase price is $734.78.
What are profits?Profit is the financial gain obtained by subtracting the cost (or expenses) of producing and selling goods or services from the revenue generated from their sale. In other words, profit is the amount of money that is left over after all expenses have been paid, including the cost of goods sold, operating expenses, taxes, and any other costs associated with running a business.
Profit can be calculated using the following formula:
Profit = Revenue - Cost
by the question.
To calculate the total purchase price, we need to calculate the tax and add it to the sum of the prices of the diamond necklace and the gold pendant.
The tax on the diamond necklace is:
572.95 * 0.065 = 37.24
The tax on the gold pendant is:
113.76 * 0.065 = 7.40
The total tax is the sum of these two taxes:
37.24 + 7.40 = 44.64
We also need to add the city tax, which is 0.5 percent of the total price:
(572.95 + 113.76) * 0.005 = 3.43
The total purchase price is the sum of the prices of the diamond necklace and the gold pendant, the state tax, and the city tax:
572.95 + 113.76 + 44.64 + 3.43 = 734.78
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A hardware store sells nylon rope for $0.89/yd. A lumber yard sells the same rope for $0.94/m.
a) Which store sells the rope for a lower price? Explain your answer.
b) How much money would Jim save if he purchased 650 ft. of the less expensive rope, before taxes?
pls complete a and b!!
Therefore , the solution of the given problem of unitary method comes out to be 14.7 dollars before taxation, assuming he bought 650 feet of the cheaper rope.
What is an unitary method?The job can be completed by bringing together what was learned and applying this variable technique, that also includes all supplementary data from two people that utilized a specific tactic. To put it another way, if the desired outcome materialises, either the entity stated in the calculation will be recognised, or both expression essential processes will truly skip the colour. For forty pencils, a refundable charge of Rupees ($1.01) might be required.
Here,
To evaluate the prices, we need to use the same units.
Since 0.9144 metres make up one yard, we can convert the cost of the rope at the hardware shop to dollars per metre as follows:
=> 0.89 dollars/yard * 1 yard/0.9144 meters = 0.97 dollars/meter
b) We must change the units to yards or metres in order to evaluate the costs of 650 feet of rope. 650 feet is equivalent to 3 yards, which is:
=> 650 feet x 3 feet per yard = 216.67 yards
The hardware store's price for the cord is:
=> 192.5 dollars ($0.89/yard x 216.67 yards)
At the timber yard, the price of the rope is:
=> (216.67 yards * 0.9144 meters/yard) * 0.94 dollars/meter = 177.8 dollars.
Jim would therefore save:
=> 192.5 dollars - 177.8 dollars = 14.7 dollars.
before taxation, assuming he bought 650 feet of the cheaper rope.
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Which is the following not true?
What are the x- and y-intercepts of f(x) - 3x - 4?
The x- and y-intercepts as required to be determined in the task content are; (-4/3, 0) and (0, -4).
Which points represent the x- and y-intercepts of the function?As evident in the task content; the given function is; f(x) = - 3x - 4.
The x-intercept represents the value of x when f(x) = 0.
0 = -3x - 4
3x = -4
x = -4 / 3.
The y-intercept represents the value of f(0); hence, we have that;
f (x) = -3(0) - 4
f(0) = -4.
Ultimately, the points which correctly represents the x- and y-intercepts are; (-4/3, 0) and (0, -4).
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Gwen owes a total of $4,522.50 on revolving credit accounts that have total limits of $7,950.00. Calculate the amount she needs to pay on her debt to reduce her revolving credit accounts to reach a 25% debt-to-credit ratio.
The amount that she needs to pay on her debt to reach a 25% debt-to-credit ratio is given as follows:
$2,535.
How to obtain the amount that she needs to pay?The amount that she needs to pay on her debt reach a 25% debt-to-credit ratio is obtained applying the proportions in the context of the problem.
She has a credit limit of $7,950.00, hence 25% of her credit limit is obtained as follows:
0.25 x 7950 = $1987.5.
She current has $4,522.50 on debts, hence the amount that she needs to pay for the debts to be reduced to $1987.5 is given as follows:
4522.5 - 1987.5 = $2,535.
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4.4 ×10 with the power of 3=
After answering the presented question, we can conclude that The answer for the following expression will be as follows [tex]4.4 X 10^3 = 4400[/tex]
what is expression ?In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.
The answer for the following expression will be as follows
[tex]4.4 X 10^3 = 4400[/tex]
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Find m1 if m5 =142 and m4=65
The value of m∠1 is 103°. The solution has been obtained by using the angle sum property.
What is the angle sum property?
The angle sum property of a triangle states that the sum of the three internal angles of a triangle is 180 degrees.
We are given that m∠5 = 142° and m∠4 = 65°.
Since m∠5 and m∠2 lie on a straight line so, they form a linear pair.
So,
⇒ m∠5 + m∠2 = 180°
⇒ 142° + m∠2 = 180°
⇒ m∠2 = 38°
We know that sum of angles of a triangle is 180°.
So,
⇒ m∠3 + m∠4 + m∠2 = 180°
⇒ m∠3 + 65° + 38° = 180°
⇒ m∠3 + 103° = 180°
⇒ m∠3 = 77°
Now, since m∠3 and m∠1 lie on a straight line so, they form a linear pair.
So,
⇒ m∠3 + m∠1 = 180°
⇒ 77° + m∠1 = 180°
⇒ m∠1 = 103°
Hence, the value of m∠1 is 103°.
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The complete question and the figure has been attached below.
Question: Find m∠1 if m∠5 = 142° and m∠4 = 65°.
The figure consists of a right triangle and an eighth of a circle. Find the area of the shaded region. 22/7 for pie.
The area of the shaded region of the composite shape is: 21.03 cm²
How to find the area of the shaded region?The formula for the area of a triangle is:
Area = ¹/₂ * base * height
Thus:
Area of given triangle = ¹/₂ * 14 * 14 = 98 cm²
Area of sector is given by the formula:
θ/360 * πr²
Area of sector = 45/360 * π * 14 * 14
= 76.97 cm²
Thus:
Area of shaded portion = 98 cm² - 76.97 cm² = 21.03 cm²
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HELP ASAP WILL GIVE 100 POINTS AND BRAINLYEST IF YOU DON"T ANSWER WITH THE INTENT TO ANSWER CORRECTLY I WILL REPORT YOU
how to complete borrowings in a cash budget
For every pound of warming gas produced by agriculture, how many pounds of gas are produced by transportation?
1.0
1.3
2.0
2.7
3.0
It is observed that 3 out of every 5 drills made at an oil-drilling site strike oil. The results from 50-simulation trials of the model showed 1 out of 5 drills
are guaranteed to strike oil. What is the hypothesis, and based on the results from the simulation trials, what should be concluded about the
hypothesis?
A. The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.
B. The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, it can be concluded that the hypothesis is
correct.
C. The hypothesis is that at least 3 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.
D. The hypothesis is that at least 3 out of 5 drills will strike oil. Based on the results from the simulation trials, it can be concluded that the hypothesis is
correct.
The hypothesis is that at least 1 out of 5 drills will strike oil. Based on the results from the simulation trials, the hypothesis should be rejected.
How do I find the lengths of sides that are cut by an altitude? (right triangle, the sides that the arrows are pointing at)
The length of line JC is 20 miles.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of sides of triangle.
To find the length of line JC, which is the hypotenuse of the right triangle JSC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
In this case, we have:
JS² + SC² = JC²
Substituting the given values, we get:
12² + 16² = JC²
144 + 256 = JC²
400 = JC²
Taking square root both sides, we get:
JC = √400
JC = 20
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Help!!
Question
Callie is buying fence for two triangular sections of her garden.
How much fence would she need for triangle DFG ?
Enter your answer in the box.
ft
Callie will need a total of 112 feet of fence for the triangle DFG.
How to find the amount of fence needed.We can find the amount of fence needed by finding the relationship between both triangles and find the missing side.
The sum of all the sides of the triangle will be known as the perimeter of the triangle. we can use this knowledge to find the amount of fence needed.
Both triangles are similar and are in the ratio of 1:7To find the missing side of triangle DFG, we multiply the corresponding side of triangle BAC by 7 to find the missing side.
This will give us 7 x 7 = 49ft
To find the amount of fence needed for triangle DFG we add all the sides of triangle DFG which will be 49 + 35 + 28.
The total will be 112ft.
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Consider the following function.
p(x)=2−29x
Step 1 of 2 : Find the slope and the y-intercept. Express the intercept as an ordered pair. Simplify your answer.
The slope of the function is -29 and the y-intercept is the point (0, 2).
What is function ?
In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range).
To find the slope and y-intercept of the function p(x) = 2 - 29x, we can write it in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
So, by comparing p(x) = 2 - 29x with y = mx + b, we can see that:
m = -29 (the coefficient of x)
b = 2 (the constant term)
Therefore, the slope of the function is -29 and the y-intercept is the point (0, 2).
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