The equation of the diagonal curve is y = -0.07x + 3.15.
What is slope-intercept form?Y = mx + b, where m is the line's slope and b is the y-intercept, or the value of y at the point where the line meets the y-axis, is the formula for a linear equation in the slope-intercept form. This form is helpful in determining a line's equation since it offers a straightforward way to do it utilising the slope and the y-intercept, two crucial pieces of information. The y-intercept reveals the beginning point of the line, whereas the slope provides the rate of change of the line, or how much the y-value changes for every change in the x-value.
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the value (-5, 3.5) and (5, -3.2):
m = (-3.2 - 3.5) / (5 - (-5)) = -0.7 / 10 = -0.07
Using the equation of line:
y = mx + b
3.5 = (-0.07)(-5) + b
b = 3.5 - 0.35 = 3.15
Hence, the equation of the diagonal curve is y = -0.07x + 3.15.
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15 POINTS At a grocery store, a bag of 12 red apples cost $10.80 and a bag of 6 green apples costs $6.90. Which statement below is true?
A The cost per apple is the same.
B The cost per red apple is greater than the cost per green apple.
C The cost per green apple is greater than the cost per red apple.
AnswerC The cost per green apple is greater than the cost per red apple.
Step-by-step explanation: ok so first find the cost of one red apple 10.80/12=0.9 ok now find the cost per green apple 6.90/6=1.15 ok well 0.9<1.15 so a green apple is more expensive than a red apple
PLEASE ANSWER!! Scientists released 6 rabbits into a new habitat in year 0. Each year, there were four times as many rabbits as the year before. How many rabbits were there after x years? Write a function to represent the scenario. PLS ANSWER SOMEONE I NEED HELPPP
:(((
Answer: d
Step-by-step explanation:
Answer:
y=3
Step-by-step explanation:
y=x so y=3x
another equation for y = 8x + 7
If a United States dollar is worth $0.87 in European currency (euros), how much is $100 in Euros worth in United States money, to the nearest cent? Show ALL work and steps to get full credit!
The value of $100 in euros is $87.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Worth of 1 United States dollar is $0.87 in euros.
To find the value of $100 in Euros, use ratio property,
1 United States dollar = $0.87 in euros
100 United States dollar = $87 in euros.
The value of $100 in euros is $87.
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A line passes through (2, –1) and (8, 4).Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.
y – 2 = 5/6 (x + 1); –5x + 6y = 17
y + 1 = 5/6 (x – 2); –5x + 6y = –16
y – 1 = 5/6 (x – 2); –5x + 6y = 16
y + 1 = 5/6 (x + 2); –5x + 6y = –16
The equation in point slope form and standard form are as follows:
y + 1 = 5 / 6(x - 2)- 5x + 6y = - 16How to write equation in point slope form and standard form?The line passes through (2, -1) and (8, 4). The equation of the line in point slope form and standard form can be represented as follows;
Therefore, in point slope form,
y - y₁ = m(x - x₁)
where
m = slopeTherefore,
slope = m = 4 + 1 / 8 - 2
m = 5 / 6
Hence, using (2, -1)
y + 1 = 5 / 6(x - 2)
In standard form,
y + 1 = 5 / 6 x - 10 / 6
y - 5 / 6 x = - 10 / 6 - 1
y - 5 / 6 x = - 8 / 3
multiply through by 6
6y - 5x = - 16
Therefore,
- 5x + 6y = - 16
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Find the volume of radius 7 cm in diameter of 12 cm in 3.14
The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.
To find the volume of a sphere with a radius of 7 cm, we can use the formula:
V = (4/3) * π * r^3
where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.
The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:
V = (4/3) * π * (6 cm)^3
V = (4/3) * 3.14 * (6 cm)^3
V = (4/3) * 3.14 * 216 cm^3
V = 904.32 cm^3
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Given the figure above, if
Answer:
67
Explanation:
the angle labeled 10 which is =113 and the angle labeled 11 are co interior angles.
co interior angles add upto 180 therefore to get the value of the angle labeled 11 you subtract 113 from 180 which gives you 67
the angle labeled 11 which is =67 and the angle labeled 8 are alternate angles. Alternate angles are equal therefore the value of the angle labeled 8 which you've been asked to give is 67
A survey of 200 homeless persons showed that 35 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans. Let z0.05 = 1.65.
The 90% confidence interval for the proportion of homeless persons who are veterans is (0.110, 0.240) based on a sample of 200.
To build a 90% certainty span for the extent of destitute people who are veterans, we really want to compute the standard blunder of the example extent and afterward duplicate it by the basic worth of the standard typical dispersion relating to the picked certainty level (1.65 for 90% certainty). Involving the recipe for the standard blunder of an example extent, we get a standard mistake of 0.032. Then, at that point, we work out the lower and upper limits of the certainty span by deducting and adding the result of the standard mistake and the basic worth to the example extent, individually. Consequently, the 90% certainty span for the extent of destitute people who are veterans is (0.110, 0.240), implying that we are 90% sure that the genuine extent of destitute people who are veterans falls inside this reach.
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HELLLP khan academy !! due tonight
Equation of the line is y = -(1/3)x+5
The figure shows a straight line of which two points and thereby the slope can be found out.
Equation of a line is in the slope-intercept form is,
y = mx +c,
where m is the slope of the line and c is the y-intercept of the line.
From the figure, two points on the line are, (0,5) and (3,4).
Then slope = (4-5)/(3-0)
= -1/3
Now y-intercept, c is the y-co-ordinate when x = 0.
From the figure, when x = 0, y = 5
So y-intercept, c = 5.
Thus the equation of the line is, y = -(1/3)x+5
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find the p-value (to two significant digits) for the following test. h0: μ ≤ 0, h1: μ > 0, σ = 1, z = 1.5 hint: the population follows the standard normal distribution.
The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.
It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5
To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.
Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).
Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).
So, the p-value for the given test is 0.067 (rounded to two significant digits).
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determine whether f'(0) exists. Explain
f(x) = {x sin (1/x) x ≠ 0
{ 0 x = 0
we can conclude that f'(0) does not exist because the limit of the difference quotient as x approaches 0 does not exist.
To determine whether the derivative of f(x), denoted as f'(0), exists at x = 0, we need to check if the limit of the difference quotient exists as x approaches 0.
The difference quotient formula for the derivative is:
f'(a) = lim (h->0) [(f(a + h) - f(a))/h]
In this case, we need to evaluate f'(0), so our formula becomes:
f'(0) = lim (h->0) [(f(0 + h) - f(0))/h]
Substituting the definition of f(x) into the formula, we have:
f'(0) = lim (h->0) [(0 + h * sin(1/(0 + h)) - 0)/h]
Simplifying the expression further, we get:
f'(0) = lim (h->0) [h * sin(1/h)/h]
Canceling out h in the numerator and denominator, we have:
f'(0) = lim (h->0) [sin(1/h)]
Now, as h approaches 0, the value 1/h approaches infinity. As sin(1/h) oscillates between -1 and 1 for all non-zero values of 1/h, the limit of sin(1/h) as h approaches 0 does not exist.
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Suppose that you are headed toward a plateau 60 m high. If the angle of elevation to the top of the plateau is 20°, how far are you from the base of the plateau?
The plateau ismeters away
(Do not round until the final answer. Then round to two decimal places as needed)
PLEASEEE HELP 83 POINTS TO WHOEVER GET IT RIGHT!!!
Answer:
164.85 m
Step-by-step explanation:
You have a right triangle with 60 as the side opposite the 20° angle and you are looking for the adjacent side to that angle.
The trig function to use is the tangent of an angle = opp/adj
Let x = distance from you to the base of plateau
So, tan 20 = 60/x
x tan 20 = 60
x = 60/tan 20
x = 164.85 m
You must memorize the definitions all of the trig functions so you can do a problem like this one. OK?
A vending machine that takes only dimes and
quarters contains 30 coins, with a total value of
$4.20. How many of each coin are there?
Find the solution to the system
of equations.
435H
4
1
-4-3-2-1 1 2 3 4
y=-x
1234
-1
-2
-3
y=2x+B
-4
([?], [])
Enter
Answer:
(-1,1)
Step-by-step explanation:
See attached worksheet.
what is the answer to 4x+8
Answer:
×=-2
Step-by-step explanation:
4×+8=0
4x= -8
therefore;
x= -2
(For 160,000 it takes 18ms to sort each half. Then merging together the two sorted halves with 80,000 numbers in each of them takes 40-218 = 4 ms. For 320,000 elements, it will take 240 to sort each half and 24 to merge the sorted halves with 160,000 numbers in each, for the total of 240+8 = 88 ms.)
For a larger input size of 320,000 elements, it will take 240 ms to sort each half and 24 ms to merge the sorted halves, resulting in a total time of 264 ms.
The given information describes the time required for sorting and merging operations on two different input sizes. For 80,000 elements, it takes 18 ms to sort each half, resulting in a total of 36 ms for sorting. Merging the two sorted halves with 80,000 numbers in each takes 40 - 18 = 22 ms.
When the input size is doubled to 320,000 elements, the sorting time for each half increases to 240 ms, as it scales linearly with the input size. The merging time, however, remains constant at 4 ms since the size of the sorted halves being merged is the same.
Thus, the total time for sorting and merging 320,000 elements is the sum of the sorting time (240 ms) and the merging time (4 ms), resulting in a total of 264 ms.
Therefore, based on the given information, the total time required for sorting and merging 320,000 elements is 264 ms.
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the hypotenuse of a right triangle is 11 inches. if one leg is 10 inches, find the degree measure of each angle
The measure of angles are
∠A = 24.61 degrees∠B = 90 degrees∠C = 65.39 degreesThe length of the hypotenuse of the right triangle = 11 inches
The length of the one leg = 10 inches
Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square
Then the equation will be
The length of the other leg = \(\sqrt{11^2-10^2}\)
= \(\sqrt{121-100}\)
= 4.58 inches
Therefore AC = 11 inches
AB = 10 inches
BC = 4.58 inches
The angle B = 90 degrees
Consider the angle A
cos θ = Adjacent side / hypotenuse
cos θ = 10 /11
θ = 24.61 degrees
Consider the angle C
cos θ = Adjacent side / Hypotenuse
cos θ = 4.58 / 11
θ = 65.39 degrees
Hence, the measure of angles are
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Joseph removes gallon of white paint from a can. Then he addsgallon of blue paint to the can. Write and evaluate an addition expression to find the overall increase or decrease in the amount of paint in the can.
Answer:
-1+1
Step-by-step explanation:
cause takes out one gallon then adds one
Answer:
its not -1+1 NOT HELPFUL
Step-by-step explanation:
hi how is your day
Can anyone help with this?
Answer: D. 4x² + 3/2x - 7
Step-by-step explanation:
Which of the following is the quotient of the rational expressions shown
below?
2x^3/x+5 divided by x-5/3x-1
Answer:
6x^4 - 2x^3/ x^2 - 25
Step-by-step explanation:
On A
you are starting a small cupcake business. the expenses in the first month costs $155. you plan to charge $3.50 per cupcake. you would like to have a profit of atleast $250. write and solve an inequality that represents the number of cupcakes, c, that you need to sell
What can you about the value of a if the equation y=ax^2-8 has no solutions? Plz explain!
Answer:
If a is negative or zero there are no real solutions
Step-by-step explanation:
y=ax^2-8
Set equal to zero to find the solution
0 =ax^2-8
Add 8 to each side
8 = ax^2
Divide by a a cannot be zero or we cannot divide by it
8/a = x^2
Take the square root of each side
sqrt(8/a) = sqrt(x^2)
We need 8/a to be positive for it to have real solutions
That means a has to be positive
If a is negative or zero there are no real solutions
The distance between the diagonally opposite corners of a rectangular card is 12. 6cm. The height of the card is 4cm. What is the area of the card?
Give your answer in cm(2) to 1 d. P
The area of the card is approximately 48 cm².
To find the area of the rectangular card, we need to know its length and width. Since we are given the height (4cm), we can consider the diagonal as the hypotenuse of a right-angled triangle, where the height is one side and the width is the other side. We can use the Pythagorean theorem to find the width.
Let's denote the width as x. According to the Pythagorean theorem, we have:
x^2 + 4^2 = (12.6)^2
Simplifying the equation:
x^2 + 16 = 158.76
x^2 = 142.76
x ≈ 11.94 cm (rounded to two decimal places)
Now that we have the width, we can calculate the area of the card by multiplying the width by the height:
Area = width × height
≈ 11.94 cm × 4 cm
≈ 47.76 cm²
≈ 48 cm² (rounded to one decimal place)
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Steve is tossing a normal quarter. He tosses the quarter 20 times and it lands on heads 16 times. If Steve tosses the quarter again, what is the probability that it lands on tails? Input your answer in fraction form.
Answer:
1/5
Step-by-step explanation:
16 out of the 20 times landed on heads, making 4/20 times it landed on tails.
16 divided by 20 is .8 which turns into 80%
100% - 80% = 20%
To simplify into a fraction:
80/100 is equivalent to 4/5 when divided by 20, leaving 1/5 to complete the fraction which later totals to 100%
Answer:
the answer is 1/2
Step-by-step explanation:
i just did it
The Andersons are buying a paddle
boat for $540. They plan to pay in four
equal payments. How much will their
payments be?
Answer:
$135 each
Step-by-step explanation:
Since they plan to pay in 4 equal payments and the total is $540, you'd divide 540 ÷ 4 and it will give you $135
Answer:
135
Step-by-step explanation:
540/4=135
hope this helps :3
if it did pls mark brainliest
possible points: 7.14 question the student council is selecting officers for the next school year from the 7 freshmen, 4 sophomores, and 6 juniors that are running for the 5 officer positions available. at least three officers must be juniors. how many different possibilities are there for the 5 different officer positions?
The 5 separate possibility that officer seats may be filled in 336 different ways.
7 + 4 + 6 = 17 students are running for the 5 officer positions. If at least 3 of the 5 positions must be filled by juniors, there are 6 ways to choose which 3 juniors will fill these positions.
Then there are 7 + 4 - 3 = 8 remaining students 3 juniors and 5 from the remaining sophomores and freshmen to fill the remaining 2 positions.
There are 8 ways to choose the first of these 2 positions and 7 ways to choose the second, so there are a total of 6 × 8 × 7 = 336 ways to choose the officers.
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if we put a marble in 10 ml of water how can we find its volume
please answer
i will mark brainliest
Answer: See below
Step-by-step explanation:
This relates to the usage of water displacement.
Have the 10 ml of water ready in a measuring flask (or any container that has a scale)Put the marble into the waterObserve how much did the water riseSubtract the current water level by the original 10 mlThe final answer would be the volume.------------------------------------------------------------------------
EXTRA (Only for advanced purposes, if you do not understand, it is totally fine)
Refer to the attachment below to finish the question.
Assuming the water levels are integer,
The original water level is 13.33 mlAfter the rock is put in, the water level is raised to 30 mlThen, we do the fourth step which is subtraction
30 - 13.33 = 16.66 mlHope this helps!! :)
Please let me know if you have any quesitons
graph the absolute value of each number on a number line-5,-4,-3,-2,-,1,0,1,2,3,4,5
Note that the Absolute Values of the above numbers will be:
5,4,3,2,1,0,1,2,3,4,5. Since positive values cannot be represented on the Negative spectrum of the Coordinate system, we are left with 0,1,2,3,4,5 which means is represented by 0 ≤ x ≤ 5. See the attached Number Line.
What is a Number Line and why is it important?
A number line is a graphical representation of numbers on a line, where each point corresponds to a unique real number. It is important for understanding numerical concepts and operations visually.
The absolute value of a number is the distance of the number from zero, regardless of its sign. It is represented as a positive number and is important for understanding the magnitude of a quantity or a distance between two points on a number line.
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What is the degree of polynomial 5x³ 4x² 7x?
The degree of polynomial in 5x³ 4x² 7x is 3, since the highest power of variable is 3.
What is degree of polynomial?The degree of polynomials, which determines the maximum number of solutions a function could have and how frequently a function will cross the x-axis on a graph, is one of the key ideas in mathematics. Polynomials are also important because they help us understand how functions can be represented mathematically. In the equation involving polynomials, it has the highest exponential power.
In a polynomial equation, a variable's greatest power is its degree. Only the terms with variables are taken into consideration when calculating a polynomial function's degree. The polynomials degree can be determined by looking at the variable term's highest exponential power.
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if 12-3n = -7n-4(n +5), what is 32-5n
Answer:
52
Step-by-step explanation:
12-3n=-7n-4(n+5)
Step 1: distribute
12-3n=-7n-4n-20
Step 2: Combine like terms
12-3n=-11n-20
Step 3: Move N to one side
12-3n=-11n-20
+11n +11n
12+8n=-20
Step 4: Get normal numbers to the other side
12+8n=-20
-12 -12
8n=-32
Step 5: Take away the number infront of N by dividing each side by the number of Ns
8n=-32
/8 /8
n= -4
Step 6: Plug N into: 32-5n
32-5(-4)
Step 7: Get rid of parenthesis by multiplying. Negative times Negative is positive.
32+20
Step 8: Finish the problem
Answer is 52