Final answer:
The range of the function y = -x^2 + 1 is all real numbers less than or equal to 1, represented as ]-∞, 1].
Explanation:
The range of the function y = -x^2 + 1 refers to the set of all possible values that y can take as x varies over all real numbers. Since the function is a downward-opening parabola (due to the negative coefficient of x^2), the maximum value of y is at the vertex of the parabola. The vertex, in this case, occurs at x=0, which gives us the maximum y value of y = 1. As x moves away from zero in either direction, the value of y decreases and approaches negative infinity. Hence, the range of this function is ]-∞, 1], or all real numbers less than or equal to 1.
What are the period and amplitude of the function?
A) period 3, amplitude 1.5
B) period 3, amplitude 3
C) period 4, amplitude 1.5
D) period 4, amplitude 3
Answer:
Option: A is the correct answer.
A) Period: 3 , amplitude : 1.5
Step-by-step explanation:
We know that Period of a function is the smallest value such that the function repeats after a fixed time.
and also the amplitude of the function is the height above or below the mid-line.
After looking at the graph we see that the period of the function is: 3
Since the function is repeating itself after every x=3.
Also, the mid-line of the function is: y= -0.5.
Hence, the height above the mid-line is: 1+0.5 = 1.5
Hence, amplitude= 1.5
Anyone know this geometry question?
Sam is making a histogram of the height in inches of all 250 students in his grade. The shortest person is 48 inches and the tallest is 60 inches. How wide should his x-axis intervals be? A) 2 B) 5 C) 8 D) 12
Answer:
The answer is A) 2.
Step-by-step explanation:
The best way would be to use intervals of 2.
We know that the shortest persons 48 inches and the tallest 60 inches.
The difference between the tallest person and the shortest is:
60 - 48 = 12 inches
Since the difference is small, we might use intervals smaller than 12 because if we used intervals of 12, we wouldn't know for sure the heights of the other students, and we would have to estimate their heights.
Using intervals of 8 would be the same, we would have to estimate the heights of most students.
Using 5 , would also not be a good choice because 5 is not a multiple of 48, 60 or 12, therefore, that
Therefore, 2 would be the best option, as you don't have to estimate and the intervals would match the shortest and tallest height.
The base of a triangular prism is a right triangle with hypotenuse 10 m long and one leg 6 M. If the height of the prism is 12 M, what is the volume of the prism
You want to determine the height of the screen at a drive-in movie theater. You use a cardboard square to line up the top and bottom of the screen structure. The vertical distance from the ground to your eye is 5.7 feet and the horizontal distance from you to the screen is 11 ft. The bottom of the screen is 6 feet from the ground. Approximate the height of the screen to the nearest tenth.
The height of the screen is about_______ feet
The height of the drive-in movie theater screen can be determined using proportions and similar triangles. The total height of the screen is found to be 11.7 feet.
Explanation:To find the height of the screen, you'll need to use similar triangles, as the triangle formed by your line of sight to the top and bottom of the screen is similar to the triangle formed by the screen and the ground. The proportion of the vertical distance from your eye to the ground and the horizontal distance from you to the screen is equal to the proportion of the height of the screen and the horizontal distance from you to the screen. Hence, you can calculate the height of the screen using a cross-multiplication.
So, we have the equation: 5.7/11 = h/11, where h is the height of the screen from your eye level. Solving this gives us h=5.7 feet. Thus, the total height of the screen is the height from the ground to your eye level plus the height of the screen from your eye level. So, the total height = 5.7 feet + 6 feet = 11.7 feet.
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I don’t really get how to do this?
Help me I don’t understand this
It takes 636363 minutes for 444 people to paint 999 walls. how many minutes does it take 777 people to paint 444 walls? minutes
9) If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?
Mrs. rifkin had 84 oranges. 24 of her oranges were rotten; the rest were either ripe or unripe. there were 18 more ripe oranges than unripe oranges. find the ratio of the number of ripe oranges to the number of rotten oranges to the number of unripe oranges.
If you take 5 quizzes and get scores of 95%, 95%, 80%, 85%, and 75%, how would you find your mean quiz score?
The mean of the quiz scores is given by the equation M = 86 %
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the mean of the quizzes be represented as M
Now , the equation will be
Let the number of quizzes be n = 5
Let the scores of each quizzes be represented by set A
Set A = { 95% , 95%, 80%, 85%, 75% }
So , the mean of the quizzes M = sum of the quizzes / number of quizzes
Substituting the values in the equation , we get
The mean of the quizzes M = ( 95% + 95% + 80% + 85% + 75% ) / 5
The mean of the quizzes M = ( 430/5 )
The mean of the quizzes M = 86 %
Therefore , the value of M is 86 %
Hence , the mean of the quizzes is 86 %
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The coach attempts to determine an association between shirt size and hat size. Which is most likely true?
Answer:
There is likely an association because 0.8 is not similar to ≈ 0.33.
Similar triangles ABC and PQR are located on the coordinate plane. The sin A = sin P = 7 over 8. If triangle PQR is translated 3 units to the left and dilated by a scale factor of two, what is the resulting value of sin P?
negative 7 over 8
4 over 5
7 over 8
14 over 16
Question 2)
If the tan of angle x is 4 over 3 and the triangle is dilated to be two times as big as the original, what would be the value of the tan of x for the dilated triangle?
8 over 6
4 over 3
8 over 3
The tan value cannot be determined for the dilated triangle.
Question 3
If the sin of angle x is 3 over 7 and the triangle is dilated to be three times as big as the original, what would be the value of the sin of x for the dilated triangle?
3 over 7
6 over 14
9 over 21
The sin value cannot be determined for the dilated triangle.
PLEASE HELP ME FIND THE VALUE OF X
25 POINTS
Answer:
the answer is x = 9 cm
Step-by-step explanation:
A students is taking a 5-question
a. True
b. False quiz and guesses at each question. find the probability that the student will get all questions correct. find the probability that the student will get no questions correct.
The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.
Emma enjoys flying kites. her red kite has a maximum altitude of 117.46 meters, and her black kite has a maximum altitude of 362.26 feet. one foot is the same as 0.3048 meters. which kite has a higher maximum altitude, and how many feet higher is it?
Answer:
Red kite has maximum altitude with 23.1 feet higher.
Step-by-step explanation:
Given : Emma enjoys flying kites. her red kite has a maximum altitude of 117.46 meters, and her black kite has a maximum altitude of 362.26 feet.
one foot is the same as 0.3048 meters.
To find : Which kite has a higher maximum altitude, and how many feet higher is it?
Solution :
First we have to convert meter into feet.
We have given, 1 feet = 0.3048 meters.
[tex]1 \text{ meter }=\frac{1}{0.3048} \text{ feet}[/tex]
So, red kite has a maximum altitude of 117.46 meters
In feet, red kite has a maximum altitude of
[tex]117.46\text{ meter }=\frac{117.46}{0.3048}=385.36 \text{ feet}[/tex]
Now, Red kite has a maximum altitude of 385.36 feet
Black kite has a maximum altitude of 362.26 feet.
385.36>362.26 feet.
Difference is 385.36-362.26=23.1 ft.
Therefore, Red kite has maximum altitude with 23.1 feet higher.
I NEED HELP ON THIS EQUATION PLEASE (:
Rebecca is planting an orange grove that covers 32 acres she uses the same amount of ground space for each tree Rebecca plants 15 trees in a section of the grove that measures 250 feet by 25 feet what is the population density of this section of the grove use 1 acre= 43,560 square feet
Solve for m -20+14m=10m+16
The perimeter of the rectangle below is 90 units. find the length of side vy . write your answer without variables.
the length of side VY is equal to the height, which is 19.4 units. The formula for the perimeter of a rectangle is given as `2 * (base + height)`.
It's correctly stated that the base of the rectangle is `3y + 1`, and the height is `2y + 3`. The perimeter is given as `90 units`.
To find the dimensions, we set up an equation using the formula for the perimeter:
90 = 2 * [(3y + 1) + (2y + 3)]
This equation represents that the perimeter is equal to twice the sum of the base and height.
The equation is then simplified:
90 = 2 * [5y + 4]
By dividing both sides by 2, it becomes:
5y + 4 = 45
Solving for y:
5y = 45 - 4
5y = 41
y = 41 / 5
y = 8.2 units
So, the value of y is correctly determined as 8.2 units.
With the value of y known, the base and height expressions are evaluated:
Base: `3y + 1 = 3 * 8.2 + 1 = 24.6 + 1 = 25.6 units`
Height: `2y + 3 = 2 * 8.2 + 3 = 16.4 + 3 = 19.4 units`
The dimensions of the rectangle are correctly calculated as follows:
Base: 25.6 units
Height: 19.4 units
It's also mentioned that the length of side VY is equal to the height, which is 19.4 units.
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How do I solved this question. 1/3c=3/8;c=3/4
Demarco wants to find the angle measures of this parallelogram. He knows that the first step is to find the value of x. Which of these equations will result in the correct value of x?
A. x + 15 = 6x + 4
B. 7x − 19 + 2x − 8 = 180
C. 7x − 19 = x + 15
D. 6x + 4 + 7x − 19 = 180
Answer:
B
Step-by-step explanation:
imagine math
Isabel deposits $6,000 into an account that earns 1.5% interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years? Compound interest formula:mc002-1.jpg t = years since initial deposit n = number of times compounded per year r = annual interest rate (as a decimal) P = initial (principal) investment V(t) = value of investment after t years
After 4 years, with an initial deposit of $6,000 at a 1.5% annual interest rate compounded monthly, Isabel will have approximately $6,370.07 in her account.
Calculating Compound Interest
To calculate the amount of money Isabel will have in her account after 4 years with an initial deposit of $6,000 at an annual interest rate of 1.5% compounded monthly, we can use the compound interest formula:
V(t) = P(1 + r/n)nt
P = principal amount (initial investment) = $6,000
r = annual interest rate (as a decimal) = 0.015
n = number of times the interest is compounded per year = 12
t = number of years the money is invested or borrowed for = 4
Substituting these values into the formula, we get:
V(4) = $6,000(1 + 0.015/12)12(4)
This simplifies to:
V(4) = $6,000(1 + 0.00125)48
Calculating the value inside the parentheses first:
1 + 0.00125 = 1.00125
Then raising it to the 48th power gives us:
1.0012548 ≈ 1.061678
Multiplying this by the principal:
V(4) ≈ $6,000 × 1.061678 ≈ $6,370.07
After 4 years, Isabel's account will have approximately $6,370.07.
Answer:$6,370.07
Step-by-step explanation:
A cylinder has a radius of 10m and a 8m. What is the exact volume of the cylinder?
160 TT m3
80 TT m3
800 TT m3
18 TT m3
Write an equation in intercept form of the parabola that passes through the point (1,32) and has x-intercepts −7 and 3?
The correct equation of the parabola in intercept form is [tex]2 (x+2)^2 -50[/tex].
To derive this equation, we will use the fact that the parabola passes through the given point (1,32) and has x-intercepts at -7 and 3.
[tex]y = k*(x+7)(x-3)[/tex]
[tex]y = k *(x^2 + 4x - 21)[/tex]
[tex]32 = k ( 8 * -2)32 = -16* kk = 32/-16 = -2[/tex]
[tex]y = -2(x+7)(x-3)[/tex]
[tex]= -2(x^2 + 4x - 21)[/tex]
[tex]= -2(x^2 +4x ) -42[/tex]
[tex]= 2(x^2 + 4x + 4) - 42 - 8[/tex]
[tex]= 2 (x+2)^2 -50[/tex]
Draw a box plot for the data:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
The solution is: The box plot is attached.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
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What is the interquartile range of this data? 6 7 8 9 Box-and whisker plot titled Temperatures in Celsius ranging from 12 to 48 with the five number summary from left to right 18, 25, 28, 33, and 42
What is the interquartile range of this data? 6 7 8 9 Box-and whisker plot titled Temperatures in Celsius ranging from 12 to 48 with the five number summary from left to right 18, 25, 28, 33, and 42
Solution:
The problem is not clear.
But, considering data set is:
18,25,28,33,42
So, if we consider the data set, Interquartile Range is the difference of Quartile3-Quartile1
IQR=Q3-Q1
To find, Q1 and Q3. Let us find the median, or, Q2 first.
Median is the middle term of the data set.
So, Median, Q2=28
Q1 is the median of first half of the data set. That is, 18,25,28
So, Lower Quartile, Q1=25
Q3 is the median of second half of data set. That is, 28, 33,42
So, Upper Quartile, Q3=33
IQR=Q3-Q1
=33-25=8
Answer: IQR=8
If we consider data set: 6,7,8,9
Median, Q2=[tex] \frac{(7+8)}{2}=\frac{15}{2} [/tex]=7.5
Lower Quartile, Q1=6.25
Upper Quartile, Q2=8.75
IQR=Q3-Q1=8.75-6.25=2.5
IQR=2.5
I need help! Math question
There is a spinner with 11 equal areas, number 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 5 and a multiple of 2?
The probability that the result is a multiple of 5 and a multiple of 2 is 6/11
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For this case, we're given that:
Spinner has 11 parts, numbered 1, 2, .... , 11P(result of spin is multiple of 5 or multiple of 2) = To find.Take E = Event of spinner's spin resulting in multiple of 5 or multiple of 2
S = results of Sample
Then, favorable results (in favor of E) are: 2,4,5,6,8,10 (total 6 in count)
All possible results are 1, 2, ... , 11 (total 11 in count)
Thus, we get:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{6}{11}[/tex]
Thus, the probability that the result is a multiple of 5 and a multiple of 2 is 6/11
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In a spinner numbered 1 through 11, there is only one number (10) that is both a multiple of 5 and a multiple of 2. As there are 11 possible outcomes in a single spin, the probability of spinning and landing on 10 is 1/11.
Explanation:The subject of this question is mathematical probability. Given that there is a spinner with 11 equal areas numbered 1 through 11, we are asked to find the probability of landing on a number that is both a multiple of 5 and a multiple of 2 when the spinner is spun once.
Firstly, we identify the numbers which are both multiples of 5 and 2 between 1 and 11. In this case, only one such number exists, which is 10. Hence, there is only one favorable outcome. The total number of outcomes are 11 (as the spinner has 11 equal areas).
Probability is defined as 'number of favorable outcomes' divided by the 'total number of outcomes'. In this case, since there is 1 favorable outcome (i.e. landing on '10') and 11 possible outcomes (any of the numbers 1 to 11), the probability is therefore 1/11.
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