the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot) with time.
To find the maximum altitude attained by the rocket, we need to find the vertex of the function h(t). We can do this by taking the derivative of the function and setting it equal to 0.
h'(t) = -32t + 300
Setting h'(t) = 0, we get
-32t + 300 = 0
32t = 300
t = 300/32
hence the time t ≈ 9.375
Now, we can substitute the value of t in the original equation h(t) to get the maximum altitude attained by the rocket.
h(9.375) = -16(9.375)2 + 300(9.375)
h(9.375) = 300 ft
Therefore, the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot).
The complete question is :
flight of a rocket the altitude in feet attained by a model rocket t time seconds into flight is given by the function h(t). find the maximum altitude (in ft) attained by the rocket. (round your answer to the nearest foot.) h(t)= -16t2 + 300t
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Multiple choice. Answer
The function g(x) = (x - 5)² has a translation of 5 units to the right.
What are some rules for the transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over x-axis, (-x, y).
-f(x) = Reflection over y-axis, (x, -y).
The parent function is a quadratic f(x) = x².
Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.
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The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month). Water costs 0.20 dollars per liter. How much money did Trevor's family spend, in total, on shower water in the past month?
The money Trevor's family spend, in total, on shower water in the past month is $14.4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms.
In the past month, each person showered for an average of 480 minutes
an average 72 liters of shower water (over the entire month)
The cost of water per litre is 0.20 dollars.
We need to find the money Trevor's family spend, in total, on shower water in the past month
Cost of water used per minute = Water used by each person per month / Time each person spent bathing × Cost of water per liter
= 72 / 480 × 0.20
= 0.15 × 0.20
= $0.03.
Now 0.03×480=14.4.
Hence, 14.4 is the money Trevor's family spend, in total, on shower water in the past month.
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Which statement can you conclude is true from
the given information?
Given: AB is the perpendicular bisector of IK.
( please help me , answers my questions )
As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?
A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?
A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G) i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f) i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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A) Q''(−5, 6), R''(−2, 1), S''(1, 5)
B) Q''(7, 11), R''(10, 16), S''(13, 12)
C) Q''(−5, 2), R''(−2, 7), S''(1, 3)
D) Q''(13, 2), R''(10, 7), S''(7, 3)
The correct answer is C.
In 2008, Yolanda paid $3,875 in Social Security tax. If the Social Security tax rate was 6.2% to the maximum income of $94,200 that year, what was Yolanda's taxable income
The Yolanda's taxable income is $62,500.
What is income tax?
An income tax is a charge levied against people or organizations in relation to the income or profits they make. In most cases, income tax is calculated as the sum of the tax rate and the amount of taxable income. The type of taxpayer and the type of income are two factors that can affect the tax rate.
Given:
In 2008, Yolanda paid $3,875 in Social Security tax.
The Social Security tax rate was 6.2% to the maximum income of $94,200 that year.
Lets assume Yolanda´s income be `x`.
Now, calculating the taxable income of Yolanda
6.2% x (x) = 3875
[tex]\frac{6.2}{100} (x) = 3875\\x = 3875(\frac{100}{6.2}) \\x = 62500[/tex]
Hence, the Yolanda's taxable income is $62,500.
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what is the z-score of a value 20 from a binomial distribution with 50 trials and probability 0.76 of success? round your answer to three decimal places. incorrect answer:
z-score of a value is -5.96
What is z-score in binomial distribution?
The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.
What is Probability?
The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.
Given,
A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.
We must ascertain the z-score (Z) of the value 20 = that this random variable X has chosen.
Now, for a random variable, say X, its z-score (Z) is defined as ,
Z = (X - mean of X)/ Standard deviation of X
A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]
The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933 while the mean of X is given as 50*0.76 = 38.
Therefore, the required z-score (Z) for X = 20, is given as,
Z = 20-38/3.0199933
Z= -5.9602781238
Z= -5.96 that is the necessary z-score.
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There are 24 men and 25 women running a race. What is the ratio of the number of female runners to the total number of runners?
Answer:
5/9 In fraction form. In decimal form 0.51 and in percentage form %51
Step-by-step explanation:
To find the ratio of the number of female runners to the total number of runners, we can divide the number of female runners by the total number of runners and express the result as a fraction. There are 25 female runners, and there are a total of 24 men + 25 women = 49 runners. Therefore, the ratio of the number of female runners to the total number of runners is 25/49. This fraction can be reduced to 5/9.
Sin 30° x tan 60° in simplest form
The simplest form of Sin 30° x tan 60° is √3/2 or sin 60° or cos 30°.
What are trigonometry ratios?
Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).
Given that the trigonometry function is
sin 30° x tan 60°
Putting sin 30° = 1/2 and tan 60° = √3
= (1/2) ×√3
= (1/2) ×(√3/1)
Now multiply the denominators and numerators:
= √3/2
Putting √3/2 = sin 60°
= sin 60°
Again sin 60° = cos 30°
= cos 30°
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fast as you can. point slope form. algebra 1)
Answer: Y=mx+b
Step-by-step explanation:
Which of the following can be represented by the equation 3x = 24?(1 point)
Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
A survey was conducted to determine the favorite subject of seventh grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?
Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?
The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?
Answer:
The last answer is correct
Step-by-step explanation:
3x = 24 Divide both sides by 3
x = 8
A pair of shoes cost $8
Katrin estimated that she sold 40 sandwiches at her food truck during lunch. Later, a count showed that she actually sold 44. Find Katrin's percent error to the nearest tenth.
Answer:
10%
Step-by-step explanation:
percent error: p
44 - 40 = 4
4/40 × 100 = p
p = 0.1 × 100
p = 10%
Percent error is 10%
If a plane can travel 480 miles per hour with the wind and 380 miles per hours against the wind, find the speed of the wind and the speed of the plane in still air
Answer:
Step-by-step explanation:
I am not super sure about this one
Answer it and explain how you got the answer
a. Using the graph, the estimated solution is: (-2, -0.6).
b. Solving algebraically, the exact solution is: (-2, -4/6).
How to Find the Solution of a System of Equations?The solution 0f a system of equations is that point of intersection where the lines of the two equations meet when they are plotted on a graph.
a. Given the graph of the equations, 2x - 3y = -2 and x + 1.5y = -3, the estimated solution, which is the point of the intersection of both lines can be, (-2, -0.5)
b. To get the exact solution, we would solve algebraically as shown below:
2x - 3y = -2 --> eqn. 1
x + 1.5y = -3 --> eqn. 2
Rewrite eqn. 2:
x = -3 - 1.5y --> eqn. 3
Substitute the value of x into eqn. 1:
2(-3 - 1.5y) - 3y = -2
-6 - 3y - 3y = -2
-6 - 6y = -2
-6y = -2 + 6
-6y = 4
y = 4/-6
y = -4/6
Substitute the value of y into eqn. 3:
x = -3 - 1.5(-4/6)
x = -3 + 1
x = -2.
The exact solution is (-2, -4/6).
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y= 1/2x + 1
y=-x + 7
Answer: point form: (4,3) equation form: x=4 y=3
Step-by-step explanation:
Enter the measurement of the vehicle part.
Answer:
2 1/4
Step-by-step explanation:
I know bc its basic math
Please help quickly 15 points and brainlyest if you get the questions right!
Answer:
1: B
2: A
3: D
4: A
5: A, B
Step-by-step explanation:
1: 6/5 is 1.2 2/10 is 1/5
2: 6/14= 3/7 or 6/14
3: 3/12 is 1/4 or 3/12
4: 28/13 is 2 2/13
5: 35/6 which is also 2 3/16
#/# means divide so 35/6 is 35 divided by 6
what does a z-score tell us about an individual observation in a data set? it is the number of standard deviations an observation is away from the mean. the midpoint of the sorted sample data set the sum of all data values divided by the number of data items. the average. the most frequently occurring data value in the set. none of the above
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.
A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.
The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.
Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.
Therefore,
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
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rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?
a. 2w^2+5W,where w is the width
b. 2w^2+5,where w is the width
c. 2w^2,where w is the width
d. 10w^2,where w is the width
The carbinet has rectangular floor plan where the length is equal to 5 feet more than twice the width. The the expression that represents the area in square feet is Option B 2w²+5. ∧where w is the width
How to calculate Area of rectangle?The area of the rectangle is the floor space the rectangle can occupy at a given time.
The given parameters are
L= 2w+5
The width = w
Then area is given by the formula
A=L*W
A=2w*w+5
Simplify the expression you have
A=2w²+5 where w is the width
Therefore the area is b. 2w²+5, where w is the width
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what is the probability that you will draw 4 kings when you draw 4 cards from a standard 52-card deck?
The probability that we will draw 4 kings from the 52-card deck be 1/270725.
Given, we draw 4 cards from a standard 52-card deck
we have to find the probability that we draw 4 kings
As, we know that the deck of cards contain 4 kings of two red and two black.
we have to choose 4 kings from 4 kings in the deck
Number of ways to choose 4 kings from the deck of cards = C(4 , 4)
Now, total number of ways in which 4 cards can be chosen be,
C(52 , 4)
So, the probability of drawing 4 kings from the deck of cards be,
P(E) = C(4 , 4)/C(52 , 4)
P(E) = 4×3×2 / 52×51×50×49
P(E) = 1 / 13×17×25×49
P(E) = 1/270725
Hence, the required probability be 1/270725
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If you roll a fair die, what is the probability you will roll a 5 or a number less than 3?
Answer:
1/2
Step-by-step explanation:
Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.
Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.
Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6
3/6=1/2
A music store marks up the instruments it sells by 50%. If the mark up price on the trumpet was $120, what was the ORIGINAL PRICE of the instrument?
The original price of the instrument is $60.
Discount Price:
50% of 120 = 50/100 * 120
= 0.5 * 120
= 60
Original Price = Sale Price - Discount Price
= 120 - 60
= 60
Therefore, the original price of the instrument is $60.
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PLEASE HELP!!!!
Write the quadratic equation whose graph has x-intercepts of -11 and 3 and passes through the point (1, 192)
A: y=8x^2+64x−264
B: y=8x^2−64x−264
C: y=−8x^2+64x+264
D: y=−8x^2−64x+264
The quadratic equation with the given x-intercepts and that passes through the point (1, 192) is the one in option D.
y = -8x^2 -64x + 264
What is the quadratic equation?If a quadratic equation has x-intercepts x₁ and x₂ and a leading coefficient a, we can write the quadratic equation as:
y = a*(x - x₁)*(x - x₂)
Here we know that the x-intercepts are -11 and 3, replacing that in the equation above we will get:
y = a*(x + 11)*(x - 3)
We also know that the line passes through the point (1, 192), replacing the values in the quadratic equation we will get:
192 = a*(1 + 11)*(1 - 3)
192 = a*12*-2
192 = -24*a
192/-24 = a
-8 = a
So the quadratic equation is:
y = -8*(x + 11)*(x - 3)
Expanding this, we will get:
y = -8x^2 -64x + 264
So the correct option is D.
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What does y equal, in this picture with 30 60 90 triangles?
The value of y= 5.49≈ 5.5cm
What is 30-60-90 traingle?
The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.
By 30-60-90 triangle rule,
Side across 60° angle = x
Hypotenuse side = 2x= 15
Side across 30° angle = x√3
By solving,
2x= 15
x= 7.5cm
So side across 60° angle= 7.5 cm
Side across 30° angle = 7.5×√3
= 7.5× 1.732= 12.99≈ 13cm
As the figure given us square so,
13= 7.5+y
y= 13-7.5
y= 5.5 cm
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Graph the inequality on the axes below
x+ 5y <-30
The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).
What is an inequality?Inequality is defined as a relationship between two expressions or values that are not equal to each other.In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).Here given the inequality.
x + 5y ≤ 30
To find the x-intercepts.
We have to substitute 0 for y and solve x to determine the x-intercepts.
x + 5 × 0 = 30
By solving the equation.
x = 30
( 30, 0 ) is the x-intercepts.
To find the y-intercepts.
By substituting 0 for x and solving y will get the y-intercept(s).
0 + 5y = 30
5y =30
y = 30/5
y = 6
In the point form, y-intercept.
Y-intercept(s): ( 0, 6 )
(30, 0) is the x-intercept.
Y-intercepts at : ( 0, 6 ).
The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).
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Find the circumference of a circle with an area of 676πsquare millimeters. Leave your answer in terms of pi,
Answer:
Below
Step-by-step explanation:
Area = pi r^2
r = sqrt ( area/pi) = sqrt( 676 ) = 26
Circumference = pi d = 2 pi r = 2 pi (26) = 163.4 mm
One angle measures 170°, and another angle measures (6k 44)°. if the angles are vertical angles, determine the value of k. k = 12 k = 20 k = 21 k = 126
Answer: the answer is 21
Step-by-step explanation:
If one angle measures 170°, and another angle measures (6k + 44)° and both are vertical angles that means the second angle should be the same as the first angle.
Vertical angles are congruent meaning they have an equal measure.
Now we have to find k
(6k + 44) = 170
subtract 44 - 44 and 170 - 44
(6k) = 126
divide 6 by 6, that leaves with just k on the left.
126 divided by 6 equals to 21
k = 21
Hope this helps!
How can we use the formula M= 58h + 135 to determine the mile marker that Sam passed at hour 6
Sam passed the marker of 483 miles, in 6 hours.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135
Simplifying the above expression gives the mile marker
M = 483 miles
Thus, the required miles are 483.
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If M is a centroid of triangle WOR and YR = 11, what is the length of WR?
Answer:
22
Step-by-step explanation:
Y is midpoint of WR.
Hence,
YR = 1÷2 of WR ( Half of WR )
So,
WR = 2YR
= 2×11
= 22
the table shows the number of stickers three friends have, Hannah has fewer stickers than Marco but more stickers than Addison. how many stickers could Hannah have?
Solve the inequality, show all of your work: -5x + 2 > 37
Answer:
[tex]x < -7[/tex]
Step-by-step explanation:
First subtract 2 from both sides.
[tex]-5x+2-2 > 37-2[/tex]
[tex]-5x > 35[/tex]
Then divide both sides by -5.
[tex]\frac{-5x}{-5} > \frac{35}{-5}[/tex]
For x < - 7, the inequality {- 5x + 2 > 37} is satisfied.
What are inequalities?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.It is used most often to compare two numbers on the number line by their sizeGiven is the inequality as follows -
- 5x + 2 > 37
The given inequality is -
- 5x + 2 > 37
- 5x + 2 > 37
- 5x + 2 - 2 > 37 - 2
- 5x > 35
x < - 7
Therefore, for x < - 7, the inequality {- 5x + 2 > 37} is satisfied.
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