There is no table provided to reference, but the equation that represents a linear relationship between X and Y is:
y = mx + b
where m is the slope of the line and b is the y-intercept. The equation can also be written as:
y = b + mx
where b is the y-intercept and m is the slope. The equation represents a straight line on a graph, where the slope determines the steepness of the line, and the y-intercept is the point where the line crosses the y-axis. To write the equation for the table of X and Y values, we need to determine the slope and y-intercept from the given data.
From a set of 10 cards numbered 1 to 10, two cards are drawn at random without replacement". What is the probability that both numbers are even?
Therefore, the likelihood of getting two even numbers without substitution from a deck of 10 cards with digits 1 through 10 is 2 out of 9.
The probability calculation is what?In most cases, the probability is described as the ratio of positive results compared with all occurrences in the survey region. The formula for probability of recurrence is P(E) = (The total amount of instances that are positive occurrences). (Sample space).
There are 5 even numbers in the set of 10 cards: 2, 4, 6, 8, and 10. The probability of drawing an even number on the first draw is 5/10, or 1/2. After the first card is drawn, there are 4 even numbers remaining in the set of 9 cards.
So the probability of drawing another even number on the second draw, given that the first card was even and was not replaced, is 4/9.
To find the probability of both events occurring (drawing an even number on the first draw and another even number on the second draw), we multiply the probabilities:
P(both even) = (1/2) x (4/9) = 2/9
Therefore, the probability of drawing two even numbers from a set of 10 cards numbered 1 to 10 without replacement is 2/9.
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THINK
12. SOLVE
EXPLAIN
SHORT RESPONSE During a vacation,
Alice went fly-fishing. She rented a
driftboat.
Rick's Rental
fishing rod
driftboat
$12
$8/hour
If she spent a total of $96, write and
solve an equation to find how many
hours she rented the boat.
Answer:
The equation to represent the situation is 96 = 12 + 8x and the number of hours she rent the boat is 10.5 hours.
How to find the number of hours she rented the boat?During a vacation, Alice went fly-fishing. She rented a drift boat. Rick's Rental fishing rod drift boat cost $12 plus $8/hour.
She spent a total of 96 dollars. The equation to solve the situation can be calculated as follows:
Hence,
y = 12 + 8x
where
y = total costx = number of hours spentTherefore,
96 = 12 + 8x
8x = 96 - 12
8x = 84
divide both sides by 8
x = 84 / 8
x = 10.5 hours
Therefore,
hours she rented the boat = 10.5 hours
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In a survey of women in a certain country (ages 20−29), the mean height was 63.7 inches with a standard deviation of 2.75 inches. Answer the following questions about the specified normal distribution.
(a) What height represents the 95th percentile?
(b) What height represents the first quartile?
a) The height that represents the 95th percentile is approximately 68.1 inches.
b) the height that represents the first quartile is approximately 65.5 inches.
Percentile and Quartile Heights(a) To find the height that represents the 95th percentile, we need to find the z-score that corresponds to this percentile and then use that to find the corresponding height.
The z-score for the 95th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.95, so the area to the right is 0.05. From the standard normal distribution table, the z-score corresponding to an area of 0.05 is approximately 1.645.
Now we can use the formula for z-scores to find the corresponding height:
z = (x - mu) / sigma
where x is the height we want to find, mu is the mean height (63.7 inches), sigma is the standard deviation (2.75 inches), and z is the z-score we just calculated (1.645).
Rearranging the formula, we get:
x = mu + z * sigma
Plugging in the values, we get:
x = 63.7 + 1.645 * 2.75 ≈ 68.1
Therefore, the height that represents the 95th percentile is approximately 68.1 inches.
(b) To find the height that represents the first quartile, we need to find the z-score that corresponds to the 25th percentile and then use that to find the corresponding height.
The z-score for the 25th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.25, so the area to the right is 0.75. From the standard normal distribution table, the z-score corresponding to an area of 0.75 is approximately 0.67.
Using the formula for z-scores and the same values for mu and sigma, we get:
x = mu + z * sigma = 63.7 + 0.67 * 2.75 ≈ 65.5
Therefore, the height that represents the first quartile is approximately 65.5 inches.
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pls hellpppppppppppppp!!!
Answer:
x = 52
Step-by-step explanation:
The angle x is vertical angle to the 52° angle. Meaning they have the same measurement.
Looking at the options, the answer is x = 52.
Rosa is in the 25% tax bracket and How much will her tax bill be reduced if she makes a $600 contribution to charity?
Answer:
Her contribution to charity reduces her taxable income by $600, Thus, her tax liability will be reduced by 28% of $ 600, and she comes under 28%
Step-by-step explanation:
Let f(x)=1/4x^3+x−1 . What is the value of (f−1)′(x) when x = 3?
For the given expression the value of [tex](f^{-1})'(3)[/tex] ≈ 0.052.
What is expression?
In mathematics, an expression is a combination of numbers, variables, operators, and symbols that represents a mathematical quantity or relationship.
To find the derivative of the inverse function, we use the formula:
[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))[/tex]
First, we need to find the inverse function [tex]f^{-1(x)[/tex]. To do that, we can solve for x in terms of f(x):
[tex]f(x) = (1/4)x^3 + x - 1\\y = (1/4)x^3 + x - 1\\x^3 + 4x - 4 = 4y\\x^3 + 4x - 4 = 4f^{-1}(x)\\f^{-1}(x) = (x^3 + 4x - 4) / 4[/tex]
Now, we can find the derivative of the inverse function:
[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))\\(f^{-1})'(3) = 1 / f'(f^{-1}(3))[/tex]
To find [tex]f^{-1}(3)[/tex], we plug in x = 3 into the expression for [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(3) = (3^3 + 4(3) - 4) / 4 = 8.75[/tex]
To find [tex]f'(f^{-1}(3))[/tex], we plug in [tex]f^{-1}(3) = 8.75[/tex] into the expression for f'(x):
[tex]f'(8.75) = (3/4)(8.75)^2 + 1 = 19.2031[/tex]
Now we can find the derivative of the inverse function at x = 3:
[tex](f^{-1})'(3) = 1 / f'(f^{-1}(3))\\(f^{-1})'(3) = 1 / f'(8.75)\\(f^{-1})'(3) = 1 / 19.2031[/tex]
[tex](f^{-1})'(3)[/tex] ≈ 0.052
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Find the value of w and x in the following diagram zoom in
5
32⁰
W
6
to
Round your answers to the nearest hundredth.
The values of the side w and the angle x are 2.649 and 26. 206 degrees respectively.
How to determine the valueIt is important to note that there are different types of trigonometric identities are;
sinetangentcosinesecantcosecantcotangentFrom the image shown, we have;
Using the sine identity
sin θ = opposite/hypotenuse
sin 32 = w/5
find the value
w = 2. 649
To determine the value of angle x , we have;
Using the sine identity
sin x = w/6
sin x = 2. 649/6
sin x= 0. 4416
Take the sine inverse
x = 26. 206 degrees
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Simultaneous Equations
y=x-2
y=3x+5
Hello and regards kiann09.
So the solution of the equation is:
x = - 7/2y = - 11/2Step-by-step explanation:y = x - 2
y = 3x + 5
We substitute the given value of y into the equation y = 3x + 5.
x - 2 = 3x + 5
We solve the equation for x.
x - 2 - 3x = 5
We move the variable to the left side and change its sign.
The sign of the variable must be changed because, in the process of "moving the variable", we are adding its opposite to both sides.
x - 2 - 3x = 5
Now we move the constant to the right hand side and change its sign.
x - 3x = 5 + 2
We group like terms.
-2x = 5 + 2 ⇒ We add the numbers ⇒ -2x + 7
We must divide both sides by -2.
x = - 7/2
We substitute the given value of x into the equation y = x - 2.
y = (-7/2)-2
We solve the equation for y. We write all the numerators above the common denominator.
y = -(7 + 4)/2
y = - 11/2
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What is the area of the real object that the scale drawing models? Scale factor. 1:5 Area = 10 square cm Scale drawing Real object
Answer:
D. 50 square centimeters
what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Answer:
D. An Energy source, a recipient, and a connection
the sum of
44+45+46+47+...+131
Answer:313:)
Step-by-step explanation:
Which of the following is a way your bank can make money? A Your bank can charge you a fee for using an ATM from another bank. B Your bank can charge an annual or monthly fee just for having an account. C Your bank can charge fees if your balance goes below a certain amount. D all of the above
Answer:
D. All of the above
Step-by-step explanation:
Your bank can incur additional revenue by charging you for all of those things
Helppopppppppppppp image below
The value of angle Y (m∠Y) in the given parallelogram is determined as 112⁰.
What is the value of angle Y?The value of angle Y is determined by applying the principle of a quadrilateral for the given parallelogram as shown below.
The adjacent angles of a parallelogram are supplementary, that is they add up to 180 degrees, while the opposite angles are equal or congruent.
From the given diagram angle W = angle Y (opposite angles)
angle W + angle Z = 180 (adjacent angles )
angle W = 180 - angle Z
angle W = 180 - 68
angle W = 112
Therefore, angle Y (m∠Y) = 112⁰.
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If 9x+10=20
, what is the value of 18x+1
?
Answer:
21
Step-by-step explanation:
9x + 10 = 20
9x = 10
x = 10/9
What is the value of 18x + 1?
18(10/9) + 1
= 20 + 1
= 21
So, the value of 18x + 1 is 21
Susan placed an order for a drum set priced at $71.28, cluding the taxes. The drum set is 30% off. 30% of $71.28, which means .3 x 71.28, is $21.39 off. How much does Susan have to pay in total?
Answer:
Step-by-step explanation:
take 71.28-21.39
Answer:
If the drum set is 30% off, this means that Susan only needs to pay 70% of the original price. We can calculate this using the following formula:
Total price = Original price x (1 - Discount rate)
where the discount rate is the percentage discount expressed as a decimal. In this case, the discount rate is 30% or 0.3. Substituting in the given values, we get:
Total price = $71.28 x (1 - 0.3)
Total price = $71.28 x 0.7
Simplifying, we get:
Total price = $49.896
However, we also know that Susan got a discount of $21.39. This means that she only needs to pay:
Total price - Discount = $49.896 - $21.39
Total price - Discount = $28.506
Therefore, Susan has to pay $28.506 in total.
It snowed 3 inches on Monday and 0.5 inches on Tuesday. How much did it snow on Monday and Tuesday combined?
Answer: It snowed 3.5 inches on Monday and Tuesday combined.
Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow
Hope this helped!
How do you write the standard form for 2 hundreds 9 tens and 18 ones
The standard form as: 298
What is standard form?
Standard form is a way of writing numbers a little differently for instance
The number "2 hundreds 9 tens and 18 ones" can be written in standard form as:
298
In standard form, we write the digits in the place value of their corresponding powers of 10. In this case, the digit 2 is in the hundreds place (10)², the digit 9 is in the tens place (10), and the digit 8 is in the ones place (10^0).
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Which triangles are similar?
a.
25
6
12
b.
16
8
25
ن
d.
3
25
6
Triangles (a) and (d) are similar because they have the same corresponding angles.
What are triangles ?
A triangle is a closed two-dimensional plane figure with three straight sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles are one of the basic shapes in geometry and can be classified into different types based on their side lengths and angle measurements. Some of the common types of triangles include equilateral triangles (where all sides and angles are equal), isosceles triangles (where two sides and two angles are equal), and scalene triangles (where no sides or angles are equal). Triangles have many applications in mathematics, science, and engineering, including in trigonometry, geometry, and physics.
According to the question:
Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. In other words, if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Additionally, if the ratio of the lengths of the corresponding sides of two triangles is constant, then the triangles are similar. This ratio is called the scale factor of similarity.
Therefore, triangles (a) and (d) are similar because they have the same corresponding angles.
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Q) Which triangles are similar given below?
a. 25,6, 12
b. 16, 8, 25
c. 3,25, 6
Rhonda just got promoted in her job as a physical therapy assistant. She will now earn $20.70 per hour. This is 115% of her hourly salary before her promotion. What was her hourly salary before her promotion?
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
what is unitary method ?Finding a single unit value and applying it to ratio and proportional problem solving is known as the unitary method in mathematics. It is frequently employed in order to resolve issues involving either direct proportion, inverse proportion, or both. In the unitary technique, the ratio of the quantities' corresponding unit values is used to indicate the relationship between the quantities. The desired value is then achieved by multiplying or dividing the unit value, as necessary.
given
Let x be the hourly wage Rhonda received prior to her promotion.
The issue states that her new hourly wage is equal to 115% of her previous wage:
20.70 = 1.15x
We can divide both sides by 1.15 to find x:
x = 20.70 / 1.15
x = 18
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
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monica is a chef at golden corral and works 35 hours a week at $15 her total deductions is $475 what is her monthly pay after deductions
Answer:
Step-by-step explanation:
To find Monica's monthly pay after deductions, we need to first calculate her gross pay (before deductions) for the week:
Gross pay = hours worked x hourly rate
Gross pay = 35 hours x $15/hour
Gross pay = $525
Since we know that her total deductions for the week are $475, we can calculate her net pay (after deductions) for the week:
Net pay = Gross pay - total deductions
Net pay = $525 - $475
Net pay = $50
To find her monthly pay after deductions, we need to multiply her weekly net pay by the number of weeks in a month. Since there are approximately 4.33 weeks in a month, we can round up to 4.5 weeks to be safe:
Monthly pay = weekly net pay x number of weeks in a month
Monthly pay = $50 x 4.5
Monthly pay = $225
Therefore, Monica's monthly pay after deductions is $225.
What is the measure of ∠b
Answer:
26
Step-by-step explanation:
triangle=180
81 + 73= 154
180 - 154= 26
Answer:
∠m = 26
Step-by-step explanation:
We know that the sum of the interior angles in a triangle is added up to 180°.
Accordingly,
∠81 + ∠73 + ∠m = 180°
Combine like terms.
∠154 + ∠m = 180°
Subtract 154 from both sides.
∠m = 26
The number 325 is equal to a square number multiplied by a prime number.
a) What are these two numbers?
What is an equation for the linear relationship in slope-intercept form?
y = ? x + ?
Answer:
y = -4x + 5
Step-by-step explanation:
y = mx + b
From the graph, we see the line intersects the y-axis at 5, so the y-intercept, b, is 5.
y = mx + 5
slope = m = rise/run
rise = up and down
run = left and right
We go up 4 units from the lower point to the upper point. That is a rise of 4 units. Then we go left 1 unit. That is a run of -1.
slope = m = 4/(-1) = -4
y = mx + 5
y = -4x + 5
Un camino recto que continua para siempre en ambas direcciones es un
Answer: una linea
Step-by-step explanation:
18 points for this help asap
Answer: m=1/-7
Step-by-step explanation:
2-1/-3-4=1/-7
I don't know if it can be simplified or not
Please Help ASAP (sequence question)
The sequence goes like this: 1, .5, .33, .25, ____, _____, ______
Please fill out the next three terms and write a function for the sequence
f(x)=_____
Answer: .2, .14, .125
Step-by-step explanation:f(x)=1/x or 1/n
A photographer is arranging 3 puppies in a row for a photo. There is one black puppy (B), one tan puppy (T) and one white puppy (W). Which list shows all the possible arrangements of the puppies?
Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.
What is a number arrangement?The number of possible arrangements or orders for a set of items is known as the arrangement number, sometimes known as the permutation number or simply as the permutation.
The following is the accurate list of all conceivable pup arrangements:
BTW, BWT, TBW, TWB, WBT, WTB
This is due to the fact that the puppies' order is important, thus we may utilize permutations to discover every potential configuration. There are 3 pups to place in a row, which results in a total of 3! = 6 combinations. We can categories them as follows:
1. BTW
2. BWT
3. TBW
4. TWB
5. WBT
6. WTB
Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.
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Write a quadratic function in standard form to represent the data in the table.
Therefore, the quadratic function in standard form that represents the data in the table is: y = 1/2 x² - 5/2 x + 5.
What is function?A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.
Here,
To write a quadratic function in standard form, we need to use the general form of the quadratic equation:
y = ax²+ bx + c
where a, b, and c are constants. We can use the values in the table to find these constants.
When x = 2, y = 3
When x = 4, y = 1
When x = 6, y = 3
When x = 8, y = 9
When x = 10, y = 19
Substituting these values into the quadratic equation, we get:
3 = 4a + 2b + c
1 = 16a + 4b + c
3 = 36a + 6b + c
9 = 64a + 8b + c
19 = 100a + 10b + c
We can now use these equations to solve for a, b, and c. One way to do this is to use a matrix equation:
|16 4 1| |a| |1|
|36 6 1| |b| = |3|
|64 8 1| |c| |9|
Using a calculator or matrix software, we can solve for a, b, and c:
a = 1/2
b = -5/2
c = 5
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Create a real-word mathematical problem as an equation that can be solved using all three properties
Thus, we should order two large pizzas, that will cost $22, to serve a group of 12.
What do you mean by cost?Costs in accounting are the dollar amounts paid for materials, labor, services, goods, equipment, and other purchases made for use by a company or even other accounting entity. This sum is listed as the price on invoices and is recorded as an expense of asset cost basis in bookkeeping records.
Solution:
Let x be the quantity of pizzas ordered.
12 x 2 = 24 slices are required because a large pizza contains 8 slices per slice.
As a result, the necessary quantity of pizzas is:
[tex]x\geq 3(x-1) \leq x[/tex]
In order to find the best price, we must reduce the total cost, that is determined by:
C(x) = 15x plus 5(x - 1) (x - 1) - 15
Using the cost function's derivative in relation to x, we may calculate:
C'(x) = 20 - 10[tex]/(x-1)^2[/tex]
Finding the critical points by setting the derivative to zero yields the following results:
20 - 10[tex]/(x-1)^2[/tex] = 0
Simplishing, we obtain:
[tex](x-1)^2[/tex]= 2
By solving for x using square root of the both sides, we arrive at:
x = 1 ± √2
The ideal quantity to order is two pizzas because x has to be an integer.
By adding x = 2 to the cost function, we can determine the total cost:
C(2) = 15(2) + 5(2 - 1) - 15 = 22
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there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream. What is the constant of proportionality in terms of vanilla to chocolate.
Answer: 2:3
Step-by-step explanation: