A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t^2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent?
The axis of symmetry of a quadratic function indicates the time at which the soccer ball reaches its maximum height in this case.
The axis of symmetry of a quadratic function represented by [tex]h(t) = -16t^2 + 48t,[/tex] where t is time in seconds, is given by the formula t = -b / 2a. In this case, a = -16 and b = 48, so the axis of symmetry is
t = -48 / (2*(-16))
= 1.5 seconds.
The axis of symmetry represents the time at which the soccer ball reaches its maximum height. For this parabolic motion, the ball will rise until it reaches this time, at which point it will start to fall back down.
At t = 1.5 seconds, the ball is at the peak of its trajectory.
The axis of symmetry is useful because it gives us the time at which the event (in this case, reaching the maximum height) happens, and it is a line that divides the parabola into two symmetrical halves.
Suppose that 29% of all residents of a community favor annexation by a nearby municipality. The probability that in a random sample of 50 residents at least 35% will favor annexation is
Let us say that,
X = the number of residents in the sample who favor
annexation.
X has a distribution which follows a binomial curve with parameters:
n=50 and p=0.29
Calculating for mean:
Mean of X = n * p = 50 * 0.29
Mean of X = 14.5
Calculating for standard deviation:
Standard deviation of X = sqrt(n * p * (1 - p))
Standard deviation of X = 3.2086
Now we are to find the probability that at least 35% favour
annexation:
35% * 50 = 17.5 residents
Normal approximation can be applied in this case since sample size is greater
than 31. Therefore,
Required Probability:
P(X>=17.5) = 1 - P(X<17.5)
1 - P(z<(17.5-14.5)/3.2086) = 1 - P(z<0.9350) = 1- 0.825106 = 0.174894
Answer:
0.175 or 17.5%
The probability that at least 35% of a sample of 50 residents favor annexation is approximately 0.1469.
To solve this problem, we are dealing with a situation where we need to find the probability that at least 35% of a random sample of 50 residents favor annexation, given that the true population proportion is 29%.
Let's denote:
- ( p = 0.29 ) as the population proportion favoring annexation.
- ( n = 50 ) as the sample size.
We are interested in finding [tex]\( P(X \geq 0.35 \times 50) \),[/tex] where ( X ) follows a binomial distribution[tex]\( X \sim \text{Binomial}(n=50, p=0.29) \).[/tex]
First, calculate [tex]\( 0.35 \times 50 \):[/tex]
[tex]\[ 0.35 \times 50 = 17.5 \][/tex]
Since we can't have half a person favoring annexation, we take the ceiling of 17.5, which is 18. So, we need to find [tex]\( P(X \geq 18) \).[/tex]
To find this probability, we can use the cumulative distribution function (CDF) of the binomial distribution or an appropriate normal approximation. Here, due to large ( n ) and ( p), we can use the normal approximation to the binomial distribution.
1. **Calculate mean and standard deviation for normal approximation:**
- Mean (( mu )) of the binomial distribution: ( mu = np = 50 x 0.29 = 14.5 )
- Standard deviation[tex](\( \sigma \)) of the binomial distribution: \( \sigma = \sqrt{np(1-p)} = \sqrt{50 \times 0.29 \times 0.71} \approx 3.34 \)[/tex]
2. **Approximate using normal distribution:**
Convert [tex]\( X \geq 18 \)[/tex] to the corresponding normal distribution:
[tex]\[ Z = \frac{18 - 14.5}{3.34} \approx 1.05 \][/tex]
3. **Find the probability using the standard normal distribution:**
[tex]\[ P(X \geq 18) \approx P\left(Z \geq \frac{18 - 14.5}{3.34}\right) = P(Z \geq 1.05) \][/tex]
Using standard normal distribution table or calculator,
[tex]\[ P(Z \geq 1.05) \approx 0.1469 \][/tex]
Therefore, the probability that in a random sample of 50 residents at least 35% will favor annexation is approximately [tex]\( \boxed{0.1469} \).[/tex]
to get an a in a course you must have an average of at least 90 on four tests that are worth 100 points each. Your scores on the first three tests were 87, 92,
and 84 set up and solve an inequality to find the range of the score that you need on the last test to get a course grade of "A"
To get an A in the course, you need to score at least 97 on the last test.
Explanation:To find the range of scores needed on the last test to get an A in the course, we need to set up and solve an inequality. Let's assume that the score on the last test is x. The average of the four tests must be at least 90, so the sum of the scores on the first three tests (263) plus the score on the last test (x) divided by 4 must be greater than or equal to 90.
(87 + 92 + 84 + x)/4 ≥ 90
Combine like terms: (263 + x)/4 ≥ 90
Multiply both sides of the inequality by 4: 263 + x ≥ 360
Subtract 263 from both sides of the inequality: x ≥ 97
Therefore, you need to score at least 97 on the last test to get a course grade of 'A'.
If i am in 8th grade what year will I graduate
A proposed null hypothesis states that there is no difference in the population mean heights of males of two neighboring towns. The sample mean difference is found to be 10 cm, and the standard deviation of the difference of the sample means is 6 cm. Which statement is true? The null hypothesis must be rejected if we choose the 68% confidence level. The null hypothesis must be rejected if we choose the 95% confidence level. The null hypothesis must be rejected if we choose the 99.7% confidence level. The null hypothesis must be rejected if we choose the 100% confidence level. NextReset
9 - 12n 2 + 4n 3 - 7n
For a number X, 40% of X is what percentage of 60% of X?
The 40 percent of x is 66.67% of 60 percent of x
Percentage is a way of expressing a fraction or a proportion as a number out of 100. It is often denoted by the symbol "%".
Let x be the number we are considering.
1. 40% of x is equal to 0.40x.
2. 60% of x is equal to 0.60x.
To do that, set up the following expression:
Percentage=0.40x/ 0.60x * 100
Now, cancel out the common factor x:
Percentage = (0.40)/ (0.60) * 100
= (2/3) * 100
= 200 / 3
= 66.67 %
So, 40% of x is 66.67% of 60% of x.
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Bernard works as a courier delivering and picking up packages for a shipping company. Three of the communities on his route form an isosceles right triangle as shown in the figure. There are approximately 68 miles between Old Mill and Clarksville and between Clarksville and Hamilton. Approximately how many miles are there between Old Mill and Hamilton? Round your answer to the nearest mile if necessary.
Jupiter has a mass that is approximately___ times greater than Venus's.
I just need numbers 23 and 24
in a fish tank, 6/7 of the fish have a red stripe on them.if 18 of the fish have red stripes, how many total fish are in the tank?
How to represent 57.036 using fractions
[tex] 57.\underbrace{036}_{3}=\dfrac{57036}{1\underbrace{000}_{3}}=\dfrac{57036:4}{1000:4}=\dfrac{14259}{250} [/tex]
Which equation represents the line that passes through (–8, 11) and (4, 7/2)?
A. y = -5/8x + 6
B. y = -5/8x + 16
C. y = -15/12x – 49
D. y = -15/12x + 71
WHATS THE ANSWER?????????
The formula for the volume of a cylinder with a height of 5 units is V(r)=(5)(pi)(r^2) where r is the radius of the cylinder. What is the domain and range of this function?
Answer:
D=(-∞,∞) Range = [0, ∞)
Step-by-step explanation:
V(r) =5πr²
Firstly we have to work with π as ≈ 3.14 so that we can make it better, by doing this we reveal it more clearly its quadratic form
V(r)= 15.71r²
As there is no restriction algebraically speaking. The Domain is all the Real Line. This is a Total Function.
As for the Range, since any negative value plugged into x² will turn into a positive one we'll only have positive results for y to each entry of x. So the Range is f(x) ≥0
As you can check it below.
Joe flips the disc shown below 15 times:
A disc with two layers is shown. The top layer is shaded in a darker shade of gray, and the lower section of the disc is white.
What is the probability that the 16th flip will result in the disc landing white side up?
Xavier has $23.50 in his savings account. He deposits $35 every week. His mother also deposits $20 into the account every time Xavier washes the car. His savings account balance can be shown with the following expression: 20c + 35w + 23.50 Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points) Part B: If Xavier saves for 12 weeks and washes the car 3 times, how much will he have in his account? Show your work to receive full credit. (4 points) Part C: If Xavier’s mother deposited $25 after each car wash, would the coefficient, variable, or constant in the expression change?
A line has a slope of -3/4 and passes through the point (–5, 4). Which is the equation of the line?
a)y=-3/4x+1/4
b)y=-3/4x+4
c)y=-3/4x-2
d)y=-3/4x-1/4
Final answer:
The correct equation of a line with a slope of -3/4 that passes through the point (-5, 4) is y = (-3/4)x + 31/4. However, none of the answer choices provided match this equation.
Explanation:
To find the equation of a line with a slope of -3/4 that passes through the point (–5, 4), you can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Plugging in our values we get:
y - 4 = (-3/4)(x - (-5))
This simplifies to:
y - 4 = (-3/4)x - (-3/4)*(-5)
Which further simplifies to:
y - 4 = (-3/4)x + 15/4
To find the y-intercept, we put the equation in slope-intercept form, y = mx + b, by adding 4 to both sides:
y = (-3/4)x + 15/4 + 4
y = (-3/4)x + 15/4 + 16/4
So the final equation is: y = (-3/4)x + 31/4
Looking at the answer choices, there is a mistake in the options provided because none of the options match y = (-3/4)x + 31/4. It's important to convey this discrepancy to the student.
diana rode her stateboard at a average speed of 12mph what was her speed in feet per hour
Answer:
63,360 ft/h
Step-by-step explanation:
Who traveled the furthest
A line passes through (9, –9) and (10, –5). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers
Final answer:
a. The equation for the line in point-slope form is y + 9 = 4(x - 9), with a slope of 4.
b. The equation can be rewritten in standard form as 4x - y = 45.
Explanation:
a. To write the equation for the line in point-slope form, we need to determine the slope (m) and one point on the line (x1, y1).
The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1).
Taking the points (9, -9) and (10, -5), we can substitute the values into the formula to get m = (-5 - (-9)) / (10 - 9) = 4 / 1 = 4.
Now we can use the formula y - y1 = m(x - x1) with the point (9, -9) to get y - (-9) = 4(x - 9). Simplifying, we have y + 9 = 4x - 36.
b. To rewrite the equation in standard form, we need to bring the equation to the form Ax + By = C, where A, B, and C are integers.
Starting from the point-slope form, we can expand and simplify the equation to get y + 9 = 4x - 36 becomes y = 4x - 45.
To make all the coefficients integers, we can multiply the equation by 5 to get 5y = 20x - 225, rearrange the terms as -20x + 5y = -225, and divide every term by -5 to get the standard form 4x - y = 45.
evaluate 5x^2-3x+2 for x=-3
Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 2 and a horizontal side of 6. The other triangle has a vertical side of 10 and a horizontal side of 30. Could the hypotenuses of these two triangles lie along the same line?
two million, four hundred and two dollars overdrawn; write this using a negative number.
A woman rides a bicycle for 3 hours and travels 51 kilometers. Find the angular velocity of the wheel if the radius is 30 centimeters
Which product is less than 99 (look at pic) please answer
Answer: 10 / 11 × 99
Step-by-step explanation:
The first one is; 16/15 × 99 = 1584/15 = 105.6
Its greater than 99
The second one is; 12/7 × 99 = 1188/7 = 169.71
The value is greater than 99
The fourth one is; 20/20 × 99 = 1980/20 = 99
The value is equal 99
The third one is; 10/11 × 99 = 990/11 =90
The value is less than 99
Therefore the product of 10/11 ×99 is less than 99
x y
0 3
1 1
2 -1
Which equation represents the data in the table shown?
A) y = -2x
B) y = 2x + 3
C) y = -2x + 3
D) y = -2x - 3
Answer:
Option C - [tex]y=-2x+3[/tex]
Step-by-step explanation:
Given : Table of data
x y
0 3
1 1
2 -1
To find : Which equation represents the data in the table shown?
Solution :
To find the equation we need to check all the points satisfying the equation or not.
A) [tex]y=-2x[/tex]
Put x=0
[tex]y=-2(0)=0[/tex]
Not satisfied
B) [tex]y=2x+3[/tex]
Put x=0
[tex]y=2(0)+3=3[/tex]
Put x=1
[tex]y=2(1)+3=5[/tex]
Not satisfied
C) [tex]y=-2x+3[/tex]
Put x=0
[tex]y=-2(0)+3=3[/tex]
Put x=1
[tex]y=-2(1)+3=1[/tex]
Put x=2
[tex]y=-2(2)+3=-1[/tex]
All points satisfied.
D) [tex]y=-2x-3[/tex]
Put x=0
[tex]y=-2(0)-3=-3[/tex]
Not satisfied
Therefore, The required equation satisfying all the points of the table is [tex]y=-2x+3[/tex]
So, Option C is correct.
Juana can use the expression 64 divided by 4 to determine
A. 4% of 64.
B. 10% of 64.
C. 25% of 64.
D. 50% of 64.
Answer:
it is a 4% of 64
Step-by-step explanation:
What are the possible numbers of positive real, negative real, and complex zeros of f(x) = 6x3 − 3x2 + 5x + 9?
CORRECT OR FASTEST GET BRAINLIEST!!!!!! A standard showerhead in Marty's house dispenses 7 gallons of water per minute. Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x How much water does Marty save each day with the change in showerheads if he uses the shower for 8 minutes each day? the option choices are
4, 12, 32, 53
Answer: 32 gallons
Step-by-step explanation:
Given: Previous rate of dispensing water= 7 gallons per min
If Marty use 8 min showerhead then
Total amount of water dispensed= [tex]7\times8= 56\ gallons[/tex]
After Marty changed the showerhead to energy saving with equation
y=3x, where y is the amount of water dispensed as a function of the number of x minutes for the new showerhead.
When we put x=8 minutes, we get total amount of water dispensed=[tex]3\times8= 24\ gallons[/tex]
Water saved by Marty = 56-24 = 32 gallons
Hence, Marty save 32 gallons each day.
What is the value of the expression 30 divide -6
A. -180
B. -5
C. 5
D. 24
GIVING BRAINLIEST TO CORRECT ANSWER
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression 30 divide -6 will be -5.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that we need to divide the integer 30 with a negative integer, therefore, -6. If the given condition is written in the form of an expression then we can write it as,
30 ÷ (-6)
Writing the expression in the form of a fraction,
= 30/(-6)
Break 30 into factors to cancel it out,
= (6 × 5) / (-6)
Cancelling 6 from both the numerator and the denominator
= 5/-1
= -5
Hence, the value of the expression 30 divide -6 will be -5.
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Final answer:
The correct option is (B) -5. The expression 30 divide -6 results in -5 after dividing the absolute values and applying the negative sign from the original divisor.
Explanation:
The value of the expression 30 divide -6 is obtained by performing the division of 30 by -6. Division by a negative number yields a negative result. Therefore, the calculation would be:
Take the absolute value of both numbers: 30 (positive) and 6 (positive).
Divide the absolute values: 30 \/ 6 = 5.
Attach the negative sign to the result because the original divisor was negative: -5.
The correct answer is -5, which corresponds to option B.