Answer:
y =1 /2 x+ 5
Step-by-step explanation:
Answer:
y=1/2x+5
graph the points and do the change of y over the change of x to get slope
the 5 is y intercept when you connect the two points where the line touches the y axis the y point is the y- intercept
W (t) models the daily water level (in cm) at a pond in Arizona, t days after the hottest day of the year. Here, t is entered in radians:
w(t) = 15 cos ((2pi / 365)t) + 43
What is the first time after the hottest day of the year that the water levels is 30 cm?
Answer:
152 days
Step-by-step explanation:
Given:
w(t) = 15 cos ((2π / 365)t) + 43
To find first time after the hottest day of the year that the water levels is 30 cm, substitute with w(t) = 30 and solve for t
30 = 15 cos ((2π / 365)t) + 43
30 - 43 = 15 cos ((2π / 365)t)
15 cos ((2π / 365)t) = -13
cos ((2π / 365)t) = -13/15
(2π / 365)t = cos⁻¹ (-13/15) = 150.07° ≈ (5/6) π
t = (365/2) * (5/6) ≈ 152 days
So, the first time after the hottest day of the year that the water levels is 30 cm is after 152 days
The water level reaches 30 cm approximately 125.3 days after the hottest day of the year. This was calculated by setting the given equation equal to 30 cm, isolating the variable, and using inverse cosine to solve in terms of radians.
Explanation:The given equation represents a cosine function, w(t) = 15cos(2π / 365)t + 43, which models the water level in a pond. Here, 15 is the amplitude, and 43 is the vertical shift, indicating the average water level is 43 cm. To find the first time after the hottest day of the year that the water level is 30 cm we first set w(t) equal to 30 and solve this for t:
30 = 15cos((2π / 365)t) + 43,
Subtract 43 from both sides to get:
-13 = 15cos((2π / 365)t),
Next, divide both sides by 15 to get:
-13/15 = cos((2π / 365)t),
Now, use the inverse cosine function, or arccos, to solve for the argument (2π / 365)t, which is in radians:
(2π / 365)t = arccos(-13/15).
Thus, t = (365 / 2π) * arccos(-13/15). This equation can be solved using a calculator that provides results in radians. The solution is approximately 125.3 days after the hottest day of the year.
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An artist wishes to make a painting in the shape of a golden rectangle, based on the theory that this shape is the most pleasing to
the average customer. If the canvas has an area of 108 in? what would be the dimensions of the canvas? Round to the nearest
inch.
a 17 x 11
C 9 x 12
b. 11 x 12
d. 6 x 10
Please select the best answer from the choices provided
Mark this and return
Save and Exit
Next
Submit
The dimensions of the canvas would be approximately 11 inches by 7 inches.
Explanation:To determine the dimensions of the canvas, we need to find the side lengths of the golden rectangle. A golden rectangle is a rectangle in which the length is approximately 1.618 times the width. The formula for the area of a rectangle is length multiplied by width. Given that the area of the canvas is 108 square inches, we can set up the equation: length x width = 108. Using the golden ratio, we can express the length in terms of the width as length = 1.618 x width.
Substituting this expression for length in the equation, we get (1.618 x width) x width = 108. Solving for the width, we find width ≈ 6.68 inches. Rounding this to the nearest inch, the width is 7 inches. Substituting this value back into the expression for length gives us length ≈ 11.31 inches, which rounds to 11 inches.
Therefore, the dimensions of the canvas are approximately 11 inches by 7 inches. The correct answer choice is a. 17 x 11.
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If you wish to show that two triangles are similar, which statement(s) is correct? You may choose more than one correct answer.
It is enough to show that all three pairs of corresponding sides are in the same ratio.
It is not enough to have information about only sides or only angles.
It is enough to show that two pairs of corresponding angles are congruent.
It is enough to show that two pairs of corresponding sides are in the same ratio.
It is enough to show that one pair of corresponding angles is congruent.
Answer:
It is enough to show that all three pairs of corresponding sides are in the same ratio.
It is enough to show that two pairs of corresponding angles are congruent.
Step-by-step explanation:
If you know that the corresponding sides have the same ratio, then both triangles will be similar (SSS Similarity)
If 2 corresponding angles are congruent, you know the 3rd one is too (Triangle Angle Sum) which makes the triangles similar (AA Similarity)
Alexis surveys three different samples of 20 students selected randomly from the population of 492 students in the seventh grade about their choice for class president. In each sample, Elijah receives the least amount of votes. Alexis infers that Elijah will not win the election. Is her inference valid? Explain.
Answer:
i think her inference i invalid
Step-by-step explanation:
i think this because she only surveyed a very small population of the seventh graders and the more data the more accurate your prediction will be. Hope that helps.
A)The number of students in the seventh grade who would be expected to prefer math to science are: 128
B) The true statement about the inference is (c) Yes, this is a valid inference because he took a random sample of the neighborhood
What is sample?A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population.
here, we have,
A) Given that, the total number of students in seventh grade are: 150 students.
Now he took a sample of 25 students and find that the 85% of the sample prefers math to science.
This means that out of the sample the number of students who prefer math to science is:
= 85 / 100 x 25
= 21.25
Now, out of the total seventh graders the number of students who prefer math to science is:
21.25 x 150 / 25 = 127.5 ≈ 128
B) From the question, we understand that:
Mark draws a random sample of 20 addresses from all 80 of the neighborhood addresses.
The above selection is a random sampling technique
Therefore, the true statement about the inference is (c) Yes, this is a valid inference because he took a random sample of the neighborhood
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complete question:
Ben takes a random sample of 25 students in his seventh-grade class and finds that 85% of the sample prefers math over science. There are 150 students in the seventh grade. Based on the sample proportion, about how many students in the seventh grade would be expected to prefer math over science?
25
85
150
128
Mark wants to know how many families in his neighborhood plan to attend the neighborhood party. He puts all 80 of the neighborhood addresses in a hat and draws a random sample of 20 addresses. He then asks those families if they plan to attend the party. He finds that 20% of the families plan to attend the party. He claims that 20% of the neighborhood families would be expected to attend the party. Is this a valid inference?
No, this is not a valid inference because he asked only 20 families
No, this is not a valid inference because he did not take a random sample of the neighborhood
Yes, this is a valid inference because he took a random sample of the neighborhood
Yes, this is a valid inference because the 20 families speak for the whole neighborhood
Sunil is solving the quadratic equation by completing the square. 6x2 + 24x + 5 = 0 6x2 + 24x = –5 What should Sunil do next? Isolate the variable x2. Isolate the constant. Factor 6 out of the variable terms. Subtract 24x from both sides of the equation.
Answer:
Factor 6 out of the variable terms.
Step-by-step explanation:
6x^2 + 24x + 5 = 0
6x^2 + 24x = –5
Factor out the 6 on the left hand side
6 (x^2 +4x) = -5
Answer:
FACTOR IS 6
Step-by-step explanation:
What is the value of x
It depends on your Divisor, Product, or Value. There is just not a gaven value for X or X=0
Based on the data represented in the box plots, which football player had greater success during the 10 games?
Nasir was more successful because he had the greatest number of yards in one game.
Aaron was more successful because he had the greater total spread.
Nasir was more successful because he had the greater measure of center.
Aaron was more successful because he had an outlier.
Answer is C.
Based on the data represented in the box plots, the football player that had greater success during the 10 games is C. Nasir was more successful because he had the greater measure of center.
What is a box plot?It should be noted that a box plot simply means a method for graphically demonstrating the spread of a data.
In this case, based on the data represented in the box plots, the football player that had greater success during the 10 games is that Nasir was more successful because he had the greater measure of center.
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I need assistance on this question
Answer:
The solution is (1,2) plz give branliest
Step-by-step explanation:
The solution is where the point intersect
Is 100,60,50 a right triangle
Answer:
I dont think so because a right triangle should have a 90 degree
Fill in the blank with the correct response.
Fifty-four out of 72 is
a0%.
Answer:
3/4
Step-by-step explanation:
Answer:
Your answer would be 75%, or 3/4
Step-by-step explanation:
A bag contains 8 blue marbles, 15 red marbles, 10 yellow marbles, and 3 brown marbles. If a marble is randomly selected, what is the probability that it will be BROWN? Please select one answer. I REALLY NEED HELP!!!!!
Answer:
1/12
Step-by-step explanation:
8 blue marbles
15 red marbles
10 yellow marbles
3 brown marbles
So let's add them up
8+15+10+3
=36
Probability of picking brown marbles
3/36
Divide both by 3
1/12
So the probability of picking brown is 1/12
What is the volume of a cylinder with base radius 3 and height 6?
Either enter an exact answer in terms of or use 3.14 for and enter your answer as a decimal.
cubic units
Answer:
the volume of the cylinder is about 169.646
Step-by-step explanation:
V= 3.14 r^2 h = 3.14 × 3^2 × 6 = 169.646
what is the slope of the line that passes through points (-1,5) and (2,3)
Answer:
-2/3
Step-by-step explanation:
The slope of a line can be found using the formula change in y coordinate divided by change in x coordinate (rise over run). SO, first you find the difference in y: 3-5 which is equal to -2, then divide it by change in x (2--1 / 2+1 = 3), giving an answer of -2/3.
Which statements are true about y Less-than-or-equal-to 8 and its graph? Check all that apply.
y = 0 is part of the solution set.
y = 8 is part of the solution set.
y = 10 is part of the solution set.
There is an open circle on the graph at 8.
There is a closed circle on the graph at 8.
The arrow on the graph points left.
The arrow on the graph points right.
When the inequality sign is </> (less than/greater than), the dot is an open circle.
When the inequality sign is ≤/≥ (less than or equal to/greater than or equal to), the dot is a closed circle.
y = number that is a solution/makes the inequality true
y ≤ 8 (y is any number less than or equal to 8)
#1: y = 0 is part of the solution set.
Yes because if you substitute/plug in 0 into "y" in the inequality, since y = 0:
0 ≤ 8 0 is less than 8.
#2: y = 8 is part of the solution set.
Yes because if you plug it into the inequality:
8 ≤ 8 8 is equal to 8
#3: y = 10 is part of the solution set.
No because if you plug it into the inequality:
10 ≤ 8 10 is not less than or equal to 8
#4: There is an open circle on the graph at 8.
No because the inequality sign is ≤, so there should be a closed circle on 8.
#5: There is a closed circle on the graph at 8.
Yes because the inequality sign is ≤
#6: The arrow on the graph points left.
Yes because if the arrow is pointing left then the numbers are decreasing, and y is any number less than or equal to 8.
#7: The arrow on the graph points right.
No because if the arrow is point right then the numbers are increasing, but y is not a number greater than 8.
Your answer is the 1st, 2nd, 5th, and 6th option
To solve the problem first we need to understand the Inequality Signs.
Inequality SignIn an inequality sign there is a dot(circle) present, but whether the circle is open or closed depends, upon the inequality sign.
If the inequality sign is less than(<) or greater than(>), the dot is an open circle.
whereas, if the inequality sign is less than or equal to (≤) and greater than or equal to(≥), the dot is a closed circle.
The correct options are A, B, E, and F.
ExplanationGiven statements to us,
A.) y = 0 is part of the solution set.
B.) y = 8 is part of the solution set.
C.) y = 10 is part of the solution set.
D.) There is an open circle on the graph at 8.
E.) There is a closed circle on the graph at 8.
F.) The arrow on the graph points left.
G.) The arrow on the graph points right.
Solutions
We know that the number line is always decreasing number or negative towards the left while positive towards the right.
Therefore, y≤8 means, y is true for any value less than and equal to 8, which will give a closed circle on the graph, and the arrow will be pointing toward the left.
Now looking at the options we have,
A.) y = 0 is part of the solution set.
The statement is true as the y value is less than 8.
B.) y = 8 is part of the solution set.
The statement is true as the y value is equal to 8.
C.) y = 10 is part of the solution set.
The statement is false as the y value is greater than 8.
D.) There is an open circle on the graph at 8.
The statement is false as the inequality sign given is less than or equal to (≤).
E.) There is a closed circle on the graph at 8.
The statement is true as the inequality sign given is less than or equal to (≤).
F.) The arrow on the graph points left.
The statement is true as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
G.) The arrow on the graph points right.
The statement is false as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
Hence, the correct options are A, B, E, and F.
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find the sum of 997 + 992 + 987 +...+ 257 +252
Answer:
93,675
Step-by-step explanation:
We see that the given sequence is an arithmetic sequence with first term 997, common difference -5, and last term 252.
The number of terms in the sequence (n) can be found from the formula for the n-th term:
an = a1 +d(n -1)
(an -an)/d +1 = n
(252 -997)/(-5) +1 = n = 150
The sum of these terms is the average of the first and last terms, multiplied by the number of terms:
S150 = (997 +252)/2·150 = 93,675
The sequence sum is 93,675.
Organize the given volumes of cubes as either a perfect cube or not-perfect cube.
900m3
Perfect cubes
Not-perfect cubes
9m
8m3
343m
1,000m
300m
Answer:
343m3,8m3,1000m3 for Perfect squares
300m3,9m3,900m3 for Not-perfect squares
Step-by-step explanation:
Did an assignment on edge
Answer: answer in the picture
Step-by-step explanation:
At store #1 for $625 you can buy 25 pair of shoes. At store #2 you can buy 33 pairs of shoes for 800. Which store has the best deal on shoes? How do you know?
Answer:
store #2 is the better deal
Step-by-step explanation:
In store #1 you need to take the total cost $625 and divide it by 25 to get your pere item cost
625/ 25 = 25
In store #2 do the same
800/ 33 = 24.24
so store two is the better deal as per item cost is lower
Conor earns $9 an hour for yard work.He raked leaves 1 afternoon and earned $29.25. How many hours did he rake leaves? How much money does he get each minute?
Answer:
29.25 divided by 9 is 3.25 so this is equavilent to 3 hours and 15 minutes
he makes 0.15 per minute 9 divided by 60 is 0.15
Name the types of angles shown.
J
Check all that apply.
I
A. straight angle
B. right angle
O
c. complementary angles
D. supplementary angles
Answer:
All except complementary angle.
Step-by-step explanation:
Complementary angles equal 90 degrees.
Answer:
all is correct
Step-by-step explanation:
because a right angle, complementary angle and 90% angle are the same thing and a supplementary angle and straight angle are 180% so all answers are correct
I. There is a gap in the Potato Chips group
II. There is a gap in the Tortilla Chips group
III. The range is greater for the Potato Chips group
Which of the statements are true?
A) I only
B) II only
C) I and II
D) III only
Answer:
C) I and II
There is a gap in the Potato Chips group for the stem "14" and the Tortilla Chips group for the stem "12"
Answer:
its c
Step-by-step explanation:
i got it right on usatestprep
The chance that Rachel will win a prize is 21 over 50. Write this probability as a decimal and as a percent.
Answer:
.42 or 42%
Step-by-step explanation:
21/50 is equal to .42 which is the decimal answer. To get percent multiply the decimal by 100, and you get 42%.
Answer:
42%
0.42
Step-by-step explanation:
21/50 x2 = 42/100
The coach carried footballs to practice 8 times this year. Each time, he brought:
17 footballs
13 footballs
28 footballs
29 footballs
13 footballs
31 footballs
21 footballs
13 footballs
What was the median number of footballs?
(to find the median put the numbers from least to greatest the find the middle number)
im asking because i always get it wrong ;-; thanks!
Answer:
19
Step-by-step explanation:
Median is the middle number when they are lined up from smallest to largest
13,13,13,17,21,28,29,31,
There are 8 numbers
13,13,13,17, | 21,28,29,31,
The middle is here
Add up the two numbers on either side and divide by 2
(17+21) /2
19
Answer:
19 footballs
Step-by-step explanation:
First sort the data
13 13 13 17 21 28 29 31
Median is: (17+21)/2
38/2 = 19
What is the volume of a cylinder, in cubic feet, with a height of 7 feet and a base
diameter of 18 feet? Round to the nearest tenths place
Answer:
1781.29
Sorry, no explanations
Answer:
V= 1781.3
Step-by-step explanation:
That’s the correct answer.
Determine the slope of the line that passes though the points (2,-5) and (4,3).
Answer: slope = 2
Step-by-step explanation:
The formula for calculating slope is given as :
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
[tex]x_{1}=2[/tex]
[tex]x_{2}=4[/tex]
[tex]y_{1}=-5[/tex]
[tex]y_{2}=3[/tex]
substituting into the formula , we have :
[tex]m = \frac{3-(-5)}{4-2}[/tex]
[tex]m = \frac{8}{2}[/tex]
[tex]m = 2[/tex]
Therefore : slope = 2
The sum of two numbers is 41. The smaller number is 17 less than the larger number. What are the numbers?
The graph shows the function f(x) = |x-hl + k. What is the
value of K?
k=-2.5
k=-1
k=1
k= 2.5
Answer:
Step-by-step explanation:
While the h portion of that absolute value represents the side to side movement, the k represents the up and down. The pointy part of the graph (the vertex) is lowered from its position at y = 0 to y = -2.5
So k = -2.5
The correct value of k is k = -2.5. Hence, option a is correct.
To find the value of k for the function f(x) = |x - h| + k, you can use one of the given points, as all points lie on the graph of the function.
Let's use the point (1, -2.5) with coordinates (x, y).
Plug these coordinates into the function:
-2.5 = |1 - h| + k
Now, you need to find k:
-2.5 = |1 - h| + k
To isolate k, you can solve for k:
k = -2.5 - |1 - h|
Now, let's check which option fits this equation based on the given points:
For h = 1 (as in the point (1, -2.5)), you get:
k = -2.5 - |1 - 1| = -2.5 - 0 = -2.5
So, the correct value of k is k = -2.5.
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Make x the subject of the formula.
y = ax2 +b
Answer:
x = ± [tex]\sqrt{\frac{y-b}{a} }[/tex]
Step-by-step explanation:
Given
y = ax² + b ( subtract b from both sides )
y - b = ax² ( divide both sides by a )
[tex]\frac{y-b}{a}[/tex] = x² ( take the square root of both sides ), thus
x = ± [tex]\sqrt{\frac{y-b}{a} }[/tex]
Write all expressions that are equivalent to 8x + 16.
Answer:
There are an infinite number of expressions equivalent ot 8x+16, but a few are:
2(4x+8)
4(2x+4)
8(x+2)
Answer:
2(4x+8)
4(2x+4)
8(x+2)
Step-by-step explanation:
Model the following problem with a quadratic equation. Then solve.
Find the length of a side of a square with an area of 108 ft2.
Answer:
10.3923
Step-by-step explanation:
Answer:
6sqrt3
Step-by-step explanation:
To find the area of a square, we simply square the length of its side!
We can represent the length of the side by x; therefore, the area of the square would be x squared, or x^{2}.
Then, we solve!
x^{2} = 108, so we find the square root of 108.
108 = 2^2 * 3^3
So sqrt{2*2*3*3*3}
We can take the 2^2 and 3^2 out of the square root, so outside, it becomes 2 * 3, or 6.
The 3 is still inside the square root, leaving us with 6sqrt3.
Hope that helps!
How do u do this? Pls help me!!
Answer:
8.6 but im not sure.
Step-by-step explanation:
5 squared + 7 squared = 74 square root = 8.6
We have to find what "x" is greater than and less than.
(7-5)<x<(5+7) = 2 < x < 12
To be able to form a triangle, the sides can't be too small or big.
To find "x", use the formula above.