Answer:
A) 8 feet.
B) 72 feet
Step-by-step explanation:
We have the function [tex]f(x)=-16x^2+64x+8[/tex] which gives the height of the rocket (in feet) as a function of the rocket's horizontal distance.
Part A)
We want to find the initial height of the rocket when it was shot.
At the initial height, the rocket has not moved anywhere. So, the horizontal distance will be 0.
Therefore, to find the initial height, we will substitute 0 into our function. This yields:
[tex]f(0)=-16(0)^2+64(0)+8[/tex]
Evaluate:
[tex]f(0)=8[/tex]
Therefore, the initial height was 8 feet.
Part B)
Notice that our function is a quadratic.
Therefore, the maximum height will be given by the vertex of our quadratic.
To find the vertex, we use:
[tex](-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]
Let's label our coefficients. We have [tex]-16x^2+64x+8[/tex]
Therefore, a=-16, b=64, and c=8.
Substitute them into the vertex formula to find the x-coordinate:
[tex]x=-\frac{64}{2(-16)}\\\Rightarrow x=64/32=2[/tex]
Now, to find the maximum height, substitute 2 back into our function f(x):
[tex]f(2)=-16(2)^2+64(2)+8[/tex]
Evaluate:
[tex]f(2)=-16(4)+64(2)+8\\\Rightarrow f(2)=-64+128+8\\\Rightarrow f(2)=72\text{ feet}[/tex]
Therefore, the rocket reaches a maximum height of 72 feet.
Given f(x) = 5x + 1, find f(-3).
I need help ASAP
Answer:
take a look ...........
HURRY whats the rate of change
Answer:
G. -9/2 o -4.5
Step-by-step explanation:
Answer:
G. -9/2
Step-by-step explanation:
this is the rate of change
plz help im having a very hard time answering these questions
i will mark u as brainliest
STEP BY STEP EXPLANATION:
drops
If f(x)=x^2 and g(x) =3x-1 find [g • f](x)
Answer:
3x²-1
Step-by-step explanation:
f(x) = x²
g(x) = 3x-1
[g·f](x)
g(f(x))
3(x²)-1
Steven put together 2,494 pieces of a puzzle. About how many pieces did he put together?
Answer:
2,494
Step-by-step explanation:
if he put 2,494pieces together you repeated the same question
One of the dog treats in Shelley’s shop is 8 inches long and 3.2 inches wide. She wants to make a miniature version that has proportional dimensions. If the miniature treat will be 3 inches long, how wide should it be?
Answer:
1.2in
Step-by-step explanation:
Answer:
(1) 1.2 inches
PLEASE HELP ME IM BEGGING YOU!!!
FIND THE VALUE OF X
84 I'm sure it's that I did it before
IMPLAYER
Every day after ser daily walk, Dena drinks 1.06 liters of water. Which decimal is equivalent to 1.06?
A 1.6
O
B. 1.600
C. 1.060
D. 1.006
Answer:
C. 1.060
Explanation:
r Which decimal is equivalent to 1.06? Well, if you look at it, c. 1.060 is just 1.06 with a zero added at the end... And we all know zeros have no value. So you can technically just take off the zero at the end and have 1.06. But this is a multiple-choice so you don't get to choose whether or not to take the zero off. So yeah, the answer is c.
Please mark brainliest!
how to factor g2 − 32g + 256
Answer:
Using the snowflake method, you have to find the factors of 256 that add up to get 32.
The result will look like this:
(g-16)(g-16)
Answer:
[tex](g-16)^2[/tex]
Step-by-step explanation:
[tex]g^2-32g + 256[/tex]
To factor it you should remember that
[tex](a-b)^2 = a^2 -2ab+b^2[/tex]
It is easy to seee that
[tex]32 = 2 \cdot 16[/tex]
and
[tex]256 = 16^2[/tex]
Therefore
[tex]g^2-32g + 256 = g^2 - (2\cdot 16)g+ 16^2 = (g-16)^2[/tex]
The equation of a circle is (x−2)2+(y+6)2=100. Find the equation of a circle that is externally tangent to the given circle and has a center at (18, −6).
Answer:
(x-18)^2+(y+6)^=36
Step-by-step explanation:
circle basic equation is (x-h)^2+(y-k)^2=r^2
center is (18,-6) it is also externally tangent
so
(x-18)^2+(y+6)^2=36 answer
The equation of a circle that is externally tangent to the given circle and has a center at (18, −6) is [tex](x-18)^2+(y+6)^=36[/tex]
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length. Let the center of the considered circle be at (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Given that the circle basic equation is [tex](x-2)^2+(y+6)^2=100[/tex]
The center is (18,-6) it is also externally tangent;
Therefore,
[tex](x-18)^2+(y+6)^2=36[/tex]
Therefore, the equation of a circle that is externally tangent to the circle is; [tex](x-18)^2+(y+6)^2=36[/tex]
Learn more about equation of a circle here:
https://brainly.com/question/10165274
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What is the interquartile range (IQR) of the salaries?
25
35
70
100
Answer:
First you order the data from least to greatest
then find the mean
next you Calculate the median of both the lower and upper half of the data
The IQR is the difference between the upper and lower medians.
Step-by-step explanation:
In order to compare the durability of four different brands of golf balls (ALPHA, BEST, CENTURY, and DIVOT), the National Golf Association randomly selects five balls of each brand and places each ball into a machine that exerts the force produced by a 250-yard drive. The number of simulated drives needed to crack or chip each ball is recorded. The results are given in the following table.
Alpha Best Century Divot
281 270 218 364
220 334 244 302
274 307 225 325
242 290 273 337
251 331 249 355
Provide the EXCEL printout of ONEWAY ANOVA using either DATA ANALYSIS or PTSTAT2 to determine whether the mean number of stimulated drives differs by brand of golf ball.
Use the ANOVA printout to write-up the six step hypothesis testing procedure for determining whether the average number of simulated drives differs by brand of golf ball. What is the p-value for this problem and what does it mean? Assume alpha =.05.
Answer:
As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.
Step-by-step explanation:
Excel output print out
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Alpha 5 1268 253.6 609.3
Best 5 1532 306.4 740.3
Century 5 1209 241.8 469.7
Divot 5 1583 316.6 1235.3
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 20960.4 3 6986.8 9.149217573 0.000925804 3.238871517
Within Groups 12218.4 16 763.65
Total 33178.8 19
The six steps of hypothesis are
1. Null hypothesis: The average number of simulated drives are same by brand of golf ball
Alternative hypothesis: The average number of simulated drives differs by brand of golf ball
2. Significance level: α=0.05
3. Test statistic: F-ratio for one way anova
4. Computations
F=9.149
5. Critical region: F>3.239
6. Conclusion:
As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.
Alice was rock climbing. She climbed to a height of 22 feet. Next, she descended 8 feet. Then, she ascended another 34 feet. What was
Alice's elevation?
Answer:
48 brainlest plz
Step-by-step explanation:
22-8=14
14+34=48
Eight more than.twice an number is four less than the same number
Answer:
2x+8=x-4
Step-by-step explanation:
I think that's right, let me know if it's wrong and I'll delete
The body mass index (BMI) of a person is the person’s weight divided by the square of his or her height. It is an indirect measure of the person’s body fat and an indicator of obesity. Results from surveys conducted by the Centers for Disease Control and Prevention (CDC) showed that the estimated mean BMI for US adults increased from 25.0 in the 1960–1962 period to 28.1 in the 1999–2002 period.
Suppose you are a health researcher. You conduct a hypothesis test to determine whether the mean BMI of US adults in the current year is lower than the mean BMI of US adults in 2000. Assume that the mean BMI of US adults in 2000 was 28.1 (the population mean). You obtain a sample of BMI measurements of 1,034 US adults, which yields a sample mean of M = 28.9. Let μ denote the mean BMI of US adults in the current year.
Required:
Formulate your null and alternative hypotheses by selecting the appropriate values in the blue dropdown menus that follow.
Answer:
The null hypothesis is [tex]H_o : \mu = 28.1[/tex]
The alternative hypothesis is [tex]H_a : \mu < 28.1[/tex]
Step-by-step explanation:
From the question we are told that
The population mean at 1960 - 1962 is [tex]\mu_1 = 25.0[/tex]
The population mean at 1999- 2002 is [tex]\mu_2 = 28.1[/tex]
The sample size is n= 1034
The sample mean is [tex]M = 28.9[/tex]
The null hypothesis is [tex]H_o : \mu = 28.1[/tex]
The alternative hypothesis is [tex]H_a : \mu < 28.1[/tex]
help with math, please
will give 100 points
Answer: y=x10
Step-by-step explanation:
What is the slopeWhat is the slope of this
linear equation:
2x+3y= -4x+9 of this linear equation: 2x+3y= -4x+9
Answer:
Slope = -2
Step-by-step explanation:
Equation in slope intercept form:
y = -2x + 3
Meaning slope equals -2
−3.5=x4 please help me
please help!! I'm really confused
Answer:
Point a is correct.
Step-by-step explanation:
hope I helped.
3. At a road work site, 20 cones are placed along 50 feet of road. How many cones are placed
along 35 feet of road? *
Answer:
14 cones
Step-by-step explanation:
20/50=0.4
0.4 times 35=14
State the domain of the relation (1,2,3,3,4,5) (-3,-1,1,2,3)
Nicole used 3/8 of her ribbon to wrap a present. If she used 6 feet of ribbon for the present, how much ribbon did Nicole have at first?
Answer:
She had 16 feet of ribbon
Step-by-step explanation:
Answer:
16 ft of ribon
Step-by-step explanation:
divide 6 by 3 and get 2. there is 2 ft for every 8th of the ribbon so 2×8=16
hope it helped
There are 20 students in a class and 70% of these students passed their Biology test.
What number of these students passed their test? Round your answer to the nearest whole
number if necessary.
Answer:
The answer is 14 students.
Step-by-step explanation:
70% of 20 = 14
There are 8 dinner rolls in a package.
How many packages will be needed to feed 100 people if each person has 2 dinner rolls? Enter the correct answer to complete the statement.
They will need
packages.
Answer: 25 packages
Step-by-step explanation: 100x2=200 / 200/8=25
Answer:
100x2 = 200 dinner rolls
200 ÷ 8 = 25 packages
14 is no less than 8 times a number x plus 6.
An inequality is ?
Answer:
The inequality is 14 ≤ 8x + 6
Please help (click picture)
Answer:check photo
Step-by-step explanation:
Please help, I’ve been stuck
Somebody please answer this question I’m begging you
Answer: The answer is A, the y value increases by 1.5 as the x value increases by 1. Therefore A does not describe the graph.
Alex needs to bisect ∠ABC using a compass and straightedge. He starts by performing the following steps. Step 1: Place the compass on vertex B of the angle. Step 2: Draw an arc that intersects both sides of the angle. Step 3: Label these intersections as point D and point E . Step 4: Place the compass at point D and draw an arc in the interior of the angle. What are the next steps Alex should take in his construction?
Answer:
Step 5: Without changing the length of the compass place it on point E and draw an arc in the interior of the angle.
Step 6: Draw a straight line with the straight edge that goes from the vertex and thru the intersection of both arcs.
Step-by-step explanation:
To bisect and angle is to split it prefectly in half, making for example a 90º angle into two 45º angles, in order to do this you will just need to use your compass and draw an arc that will pass over both sides of the angle, after that you put it in the intersections of the arc and the sides and just draw arcs that fit inside the angle from there where both arcs created from the intersections of the precious arc meet that's the middle of the angle, so now you just draw a straight line from the vertex to the intersection of both arcs and you just have bisected an angle.
insert two arithmetic means between 15 and 36
Answer: a_1 = 15
a_4 = 36
a_n = a_1 + (n - 1)d
36 = 15 + (4 - 1)d
21 = 3d
7 = d
15, 22, 29, 36