Answer:
a. 22.3°
b. 2940.16 ft/s
Step-by-step explanation:
Here is the complete question
A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at the relationship cot theta = 2x/2y + gt^2 where theta is the angle of elevation of the launcher and g is the acceleration due to gravity (32.2 feet/second^2). An artillery man is firing at an enemy barker located 2275 feet up the side of a hill that is 6325 feet away. He fires a round, and exactly 2.84 seconds later he scores a direct hit.
a. What angle of elevation did he use? theta = degree (Do not round until the final answer. Then round to one decimal place as needed.)
b. f the angle of elevation is also given by sec theta = v_0 t/x, where v_0 is the velocity of the weapon, find the muzzle velocity of the artillery piece he used. v_0 = feet/second (Round to two decimal places as needed.)
Solution
(a) What angle of elevation did he use?
Given that cosθ = 2x/(2y + gt²) where x = horizontal distance of projectile = 6175 feet away,y = vertical distance of projectile = 2450 feet up, g = acceleration due to gravity = 32 ft/s² and t = time of hit = 2.27 s
So, cosθ = 2x/(2y + gt²)
cotθ = 2 × 6175 ft/(2 × 2450 ft + 32 ft/s² × (2.27 s)²)
cotθ = 12350 ft/(4900 ft + 32 ft/s² × 5.1529 s²)
cotθ = 12350 ft/(4900 ft + 164.8928 ft)
cotθ = 12350 ft/(5064.8928 ft)
1/tanθ = 2.4384
tanθ = 1/2.4384
tanθ = 0.4101
θ = tan⁻¹(0.4101)
θ = 22.3°
(b) If the angle of elevation is also given by sec θ = υ0t/x. where υ0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
Making u0 subject of the formula, we have
u0 = xsecθ/t
u0 = x/tcosθ
since x = 6175ft, t = 2.27 s and θ = 22.3°, then
u0 = x/tcosθ
u0 = 6175 ft/(2.27 s × cos22.3°)
u0 = 6175 ft/(2.27 s × 0.9252)
u0 = 6175 ft/(2.1 s)
u0 = 2940.16 ft/s
vTo estimate the parameter stated in question 2, the following was done. A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8. An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6. If appropriate, use this information to calculate and interpret a 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.
Answer:
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8.
This means that:
[tex]\mu_A = 85, s_A = \frac{9.8}{\sqrt{22}} = 2.09[/tex]
An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6.
This means that:
[tex]\mu_N = 77, s_N = \frac{10.6}{\sqrt{47}} = 1.55[/tex]
Distribution of the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.
Mean:
[tex]\mu = \mu_A - \mu_N = 85 - 77 = 8[/tex]
Standard deviation:
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{2.09^2 + 1.55^2} = 2.6[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
So
[tex]M = 1.645*2.6 = 4.3[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 4.3 = 3.7
The upper end of the interval is the sample mean added to M. So it is 8 + 4.3 = 12.3
The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).
Can someone higher please help ?
.....................................................................................
Answer: -0.833 (repeating decimal)
Step-by-step explanation: fg(x) means plug the g(x) equation into f(x), and for gf(x) it’s vice versa:
Fg(x) = 3x^2 - 1 + 2
Gf(x) = 3(x + 2)^2 - 1
First, we should simplify gf(x) to eliminate the (x + 2)^2:
3(x^2 + 4x + 4) - 1
3x^2 + 12x + 12 - 1
3x^2 + 12x + 11
Second, simplify fg(x) by solving -1 + 2: 1
Now, we can set the two equations equal to each other and solve:
3x^2 + 1 = 3x^2 + 12x + 11 (subtract 3x^2 from each other and 1 from 11)
-10 = 12x (Divide)
-0.8333... = x
To make sure this answer is correct, plug -0.833 into the original equations and set them equal to each other:
3(-0.833)^2 + 1 = 3(-0.833)^2 + 12(-0.833] + 11
3.083 = 3.083
tam
If ABCD is dilated by a factor of 2, the
coordinate of A' would be:
5
4
3
С
2
B
1
-8 -7 -6
-5
-3-2
-10
1
2
3
5
6
7
8
9 10
А
-2
D
-3
A' = ([?], [D
Answer:
-6,-2 is the answer!!
Step-by-step explanation:
The coordinate of A' would be (-6, -2)
Dilation of figureDilation is a transformation technique that changes the size of an object by a scale factor "k"
From the diagram shown, the measure of the coordinate point is given as (-3, -1).
If the coordinate A is dilated by a factor of 2, the resulting coordinate A' will be given as:
A' = (2(-3), 2(-1)) = (-6, -2)
Hence the coordinate of A' would be (-6, -2)
Learn more on dilation here: https://brainly.com/question/3457976
Can someone solve these for me?
Answer:
In order of pictures,
Picture #1: 230
Picture #2: 140
Picture #3: 9.9
Picture #4: 13.5
Picture #5: 7.07
Step-by-step explanation:
I am not entirely sure that 3 - 5 are correct, but I know that 1 and 2 are correct. I am sorry if they are incorrect.
Hope that this helps!
A box contains 4 yellow markers, 3 blue markers, 6 black markers and 2 red markers. Suppose a marker is chosen randomly, and then returned to the box.
Determine the probability of selecting a yellow marker, then a red marker.
Answer:
4+3+6+2 = 15
Step-by-step explanation:
selecting a yellow marker 4/15
selecting a red marker 2/15
if a1= 7 and r=3, find a4
Answer:
a4 = 189
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient r between consecutive terms is always the same.
The nth term of the sequence is given by:
[tex]a_n = a_1*r^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this question:
[tex]a_1 = 7, r = 3[/tex]
The fourth term is:
[tex]a_4 = 7*3^3 = 189[/tex]
So
a4 = 189
1/10 *as a fraction* divided by 5
Please help! Fast!!
Answer:
1/50
Step-by-step explanation:
1/10÷5/1=
1/10•1/5=
1/50
if a line passing through (4,-p) and (-2,6)is parallel to 2y+3x= -3, find p.
Simplify (-32) divided by (-4)
Answer:
[tex] \frac{8}{1} [/tex]
Step-by-step explanation:
[tex] \frac{ - 32}{ - 4} [/tex]
Reduce factor by 4
[tex] \frac{ - 8}{ - 1} [/tex]
A negative divided by a negative equal positve so
[tex] \frac{8}{1} [/tex]
the simplest form of 32/4 is 8/1
find the GCD ( or HCF) of numerator and denominator GCD of 32 4 is 4
divide both the numerator and denominator GCD
32/4 ÷ 4/4
reduce fraction: 8/1
therefore, 32/4 simplify to lowest terms is 8/1.
Use the Law of Cosines to find the measure of ∠F. Round to the nearest degree.
f = 5, g = 6, h = 7
Use: f² = g² + h² – 2gh cos F
Answer:
Solution given.
f = 5, g = 6, h = 7
<F=?
we have;
f² = g² + h² – 2gh cos F
5²-6²-7²=-2×6×7 cos F
-60/-84=cos F
F=cos-¹(5/7)=44.41°
<F=44.4° is a required answer
Which of these tables represents a function?
Table A
Table B
Table C
Table D
Determine whether each ordered pair is a solution of the inequality-3x-4y<6
Answer:
it's (6,0) I can't explain though
Simplify
1/6 / 1 3/8
Answer:
1/6 = 1/6 (already simplified) 1 3/8 = 11/8
Step-by-step explanation:
What is the end behavior of this radical? f(x) = 4 square root x - 6
Answer:
I think you can answer it with a chart, I guess, of course I'm not sure♀️
5 times the sum of 24 and 7
Answer:
Your answer should be 155!
Step-by-step explanation:
Sum means to add, so 24 + 7 = 31
31 x 5 = 155
I hope this helps!
A summation, also called a sum, is the result of arithmetically adding numbers or quantities. 155 is the answer for 5 times the sum of 24 and 7.
What is Sum?A summation, also called a sum, is the result of arithmetically adding numbers or quantities.
Given,
5 times the sum of 24 and 7
Sum is nothing but addition.
When we see the word sum it means we are adding some value with other factor. In the given problem 24 and 7 are added.
Times means multiplication.
We have to convert 5 times the sum of 24 and 7 to expression.
When we see times, it means product or we are multiplying a number with the other number. Here with 5 we are multiplying the sum of 24 and 7.
5×(24+7)
Firstly we calculate value in parenthesis.
twenty four plus seven is thirty one.
5×31
The product of 5 and 31 is 155.
155
Hence 155 is the answer for 5 times the sum of 24 and 7.
To learn more on Sum click:
https://brainly.com/question/13013054
#SPJ2
The number of members in a labor union is 240, and the number increases by 5% each year. Find the number of members after 4 years.
Answer: 292
Step-by-step explanation:
Given
There are 240 members in a labor union
The number increases by 5% each year
After 1 year it is
[tex]\Rightarrow 240+5\%\times 240\\\Rightarrow 240(1+0.05)[/tex]
After 2 years
[tex]\Rightarrow 240(1+0.05)+5\%\times 240(1+0.05)\\\Rightarrow 240(1+0.05)(1+0.05)=240(1+0.05)^2[/tex]
Similarly, after 4 years
[tex]\Rightarrow 240(1+0.05)^4\\\Rightarrow 291.72\approx 292[/tex]
Help me please? I’ll give out brainly. No links.
Answer:
A = 8 unites
Step-by-step explanation:
8 - 2 = 6
the y-intercept stays the same
only x-intercept changes
Answer:sorrY mAaM cAnt heLp yOu
Step-by-step explanation:
Work out the mean for the data set below: 5, 6 Give your answer as a decimal.
Answer:
5.5
Step-by-step explanation:
5 + 6 =
11 / 2 =
5.5
Choose the Inequality that matches the graph below.
Answer:
The answer would be A
Step-by-step explanation:
Because the circle is an open circle, also its point towards the positive so that means A is the correct answer
56,252 rounded to the nearst ten thousandths
Answer:
60,000
Step-by-step explanation:
Answer:
60,000
Step-by-step explanation:
Jill Kingman pays a $419.00 premium annually. This represents 35% of the total premium. The rest of the premium is paid by her employer.
Use a thousands comma where applicable.
1. the company's percentage
%
2. the total premium $
3. the company's payment $
Calculate the missing values.
Jill Kingman pays a $419.00 premium annually. This represents 35% of the total premium. The rest of the premium is paid by her employer.
Use a thousands comma where applicable.
1. 100 (100% of cost) - 35 = 65% company percent
2. 419.00 ÷ .35 (or, 35%, but use the decimal) = 1197 total premium
3. 0.65 × 1197 = 778.05 company payment
I tried to make it so you could see where the numbers came from, by making the ones bold, others, italics, and other combinations. I hope you understand what I did. I tried to explain how the guy above did it. He did well, so brainliest goes to him.
observa con atencion los siguientes desarrollos planos y encierra con cual de ellos se puede armar cada cuerpo uno de ellos tiene dos respuestas
Answer:
Can you give it in a english
Step-by-step explanation:
This dot plot is not symmetric, and the data set has two
extreme values.
.
2
3
8
What is the best measure of center for this dot plot?
O A. The mean absolute deviation (MAD)
B. The interquartile range (IQR)
C. The median
D. The mean
Answer:
C: The median
Step-by-step explanation:
HELP! PLEASEEEEE
IMAGE BELOW!
Answer:
Quadrant I and Quadrant II
Step-by-step explanation:
Quadrant I has both positive x and y coordinates,Quadrant II has a negative x coordinate but the y coordinate is positive.
jane bought 5 3/5 boxes of raspberries and 2 1/4 boxes of strawberries. How much more boxes of raspberries did jane buy?
Answer: 3 7/20
Step-by-step explanation:
5 3/5 - 2 1/4
Find GCD.
5 12/20 - 2 5/20
3 7/20 more boxes of raspberries than strawberries
What is the line segment from the center of the circle to any point on the circle
please help me Answer this question
Step-by-step explanation:
the circle to any point on the circle
Answer:
Radius
.....................
which table represents a linear function? HELP FAST PLEASE
Answer:
the bottom left
Step-by-step explanation:
A linear function will have a constant slope so the bottom left graph is the only one with a constant slope. The y-values are all increasing by 2.
An equation of the line through the points (-2.5) and (3, -4) is:
In ΔMNO, the measure of ∠O=90°, OM = 69 feet, and NO = 16 feet. Find the measure of ∠N to the nearest tenth of a degree.
9514 1404 393
Answer:
76.9°
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
tan(N) = OM/ON
N = arctan(OM/ON) = arctan(69/16)
N ≈ 76.9°
answer 4 some free pointz
Answer:
Step-by-step explanation: