Answers
Answer:
(1)
[tex]a = \frac{3\sqrt 3}{2}[/tex]
[tex]b = \frac{3}{2}[/tex]
(2)
[tex]a = \sqrt 6[/tex]
[tex]b = \sqrt 2[/tex]
Step-by-step explanation:
Solving (1):
Considering
[tex]\theta = 60^o[/tex]
We have:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60^o) = \frac{a}{3}[/tex]
Solve for a
[tex]a = 3 * \sin(60^o)[/tex]
[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]
So:
[tex]a = 3 * \frac{\sqrt 3}{2}[/tex]
[tex]a = \frac{3\sqrt 3}{2}[/tex]
To solve for b, we make use of Pythagoras theorem
[tex]3^2 = a^2 + b^2[/tex]
This gives
[tex]3^2 = (\frac{3\sqrt 3}{2})^2 + b^2[/tex]
[tex]9 = \frac{9*3}{4} + b^2[/tex]
[tex]9 = \frac{27}{4} + b^2[/tex]
Collect like terms
[tex]b^2 = 9 - \frac{27}{4}[/tex]
Take LCM and solve
[tex]b^2 = \frac{36 - 27}{4}[/tex]
[tex]b^2 = \frac{9}{4}[/tex]
Take square roots
[tex]b = \frac{3}{2}[/tex]
Solving (2):
Considering
[tex]\theta = 60^o[/tex]
We have:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60^o) = \frac{a}{2\sqrt 2}[/tex]
Solve for a
[tex]a = 2\sqrt 2 * \sin(60^o)[/tex]
[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]
So:
[tex]a = 2\sqrt 2 * \frac{\sqrt 3}{2}[/tex]
[tex]a = \sqrt 2 * \sqrt 3[/tex]
[tex]a = \sqrt 6[/tex]
To solve for b, we make use of Pythagoras theorem
[tex](2\sqrt 2)^2 = a^2 + b^2[/tex]
This gives
[tex](2\sqrt 2)^2 = (\sqrt 6)^2 + b^2[/tex]
[tex]8 = 6 + b^2[/tex]
Collect like terms
[tex]b^2 = 8 - 6[/tex]
[tex]b^2 = 2[/tex]
Take square roots
[tex]b = \sqrt 2[/tex]
Related Questions
The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 16 and 4, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a bell-shaped distribution. Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the distribution.
A) between 12 and 20 hours per week
B) between 8 and 24 hours per weelk
C) between4 and 28 hours per week
D) less than 12 and more than 20 hours per week
Answers
Answer:
B) between 8 and 24 hours per week
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 16, standard deviation of 4.
Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the distribution.
Within 2 standard deviations of the mean, so:
16 - 4*2 = 16 - 8 = 8 hours per week.
16 + 4*2 = 16 + 8 = 24 hours per week.
This means that the correcgt answer is given by option B.
What is the sales tax for a purchase of $20 if the tax rate is 10 percent?
Answers
Answer:
2
Step-by-step explanation:
If you multiply it by 0.10 that is 10 percent and you get 22 which is 2 more than 20
Answer:
Before Tax Price: $20.00
Sale Tax: 10.00% or $2.00
After Tax Price: $22.00
Step-by-step explanation:
The product of the square of a number and 8. Let the unknown number equal five. plz i need the answer
Answers
Answer:
200
Step-by-step explanation:
If you multiply 8 by the number 5's square, 25, you get 200
Right Triangles
Solve the right triangle shown in the figure
BC = 2.7cm, AC = 1.1cm, ∠C = 90°
a. ∠A = 68°, ∠B = 22°. AB = 2.9cm
b. ∠A = 22°, ∠B = 68°, AB = 2.9cm
c. ∠A = 63°, ∠B = 27°, AB = 2.9cm
d. ∠A = 24°, ∠B = 66°, AB 3.8cm
Please select the best answer from choices provided
Answers
Answer:
A. ∠A = 68°, ∠B = 22°, AB = 2.9cm
Step-by-step explanation:
I calculated it logically
1. Sandra is trying to determine the height of a light pole at the corner of the block on
which she lives. The shadow cast by the light pole is 5 feet.
If the angle of elevation from the sidewalk to the top of the light pole is represented
as e, which equation could be used to find the height of the light pole?
Answers
Answer:
h = 5(tane)
Step-by-step explanation:
The diagrammatic representation of the question given is attached below ;
The height of the light pole, h = opposite side
Adjacent side = 5 feets
Angle of elevation = e
Using trigonometry ;
Tan e = opposite / Adjacent
Tan e = h / 5
Making h the subject ;
h = 5(tane)
2.
Which choice shows temperatures in order from coldest to
warmest?
F 17°, 0°, -13.5°, -3.2°
G -3.2°, -13.5°, 0°, 17°
H -13.5°, -3.2°, 0°, 17°
1 -13.5°, 0°, -3.2°, 17°
Answers
Answer:
H
Step-by-step explanation:
When the absolute value is bigger with a (-) negative sign, it means that it is the smallest. Since -13.5 has the greatest absolute value with a negative sign, then -3.2 is smaller than 0, the answer is H.
Answer:
H -13.5°, -3.2°, 0°, 17°
Step-by-step explanation:
These are not the answers!!
F 17°, 0°, -13.5°, -3.2°
G -3.2°, -13.5°, 0°, 17°
1 -13.5°, 0°, -3.2°, 17°
Pls help
Zzzzzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
d po yung answer
Step-by-step explanation:
sana makatulong
g The least-squares regression line of the number of visitors, y, at a national park and the temperature, x, is modeled by the equation . What is the predicted number of visitors when the temperature is 78o? 10.3 visitors 85.2 visitors 95.5 visitors 888.6 visitors 6,655.9 visitors
Answers
Answer: D) 888.6
Step-by-step explanation:
The expression which would help arrive at the required answer is y = 78b + c.
The least regression equation is the equation of best fit obtained from a linear regression graph.
The linear regression equation is expressed in the form :
y = bx + c ; where ;
y = Predicted variable
x = predictor variable
c = intercept
b = slope
The least regression equation is not given in the question above.
However, we could give the equation in the linear regression format :
y = number of visitors
y = number of visitors x = temperature = 78°
Hence, the equation becomes :
y = b(78) + c
y = 78b + c
Inputting the values of b and c in the equation will give the required answer.
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18
The measures tanker are shown
12 inches
10 inches
8 inches
Enter the come of the coolerin cubie inches
Answers
Answer:
78
Step-by-step explanation:
simplify 1/3 : 2.5 : 3 3/4
Answers
Answer:
1/3x3 3/4 /2.5 = 0.3
A patient has been instructed to drink a gallon of water each day. How many cups does the patient
need to drink?
Thank
Answers
Answer:
16 cups a day
Step-by-step explanation:
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 30 feet more than the length of the shortest side. Find
the dimensions if the perimeter is 198 feet.
What is the length of the shortest side?
The length of the shortest side is
Answers
Answer:
The three sides are 36 f t , 72 f t and 59 f t .
Step-by-step explanation:
Let the length of the shortest side of the triangular flower bed be x feet.
Then the length of the second side is 2x and
the length of the third side is x + 23
The given perimeter is 167 f t hence:
x+2x+x+23=167
4x+23=167
4x=167-23
4 x = 144
x = 144 /4 = 36
2 x = 2 ⋅ 36 = 72
x +23 = 36 + 23 = 59
The length of the three sides of the triangular flower bed are 36 f t , 72 f t and 59 f t .
Jonah wants to make a one-sample
z
zz interval using
99
%
99%99, percent confidence to estimate what proportion of silicon wafers at his factory are defective. He wants the margin of error to be no more than
3
%
3%3, percent. A previous study suggests that about
6
%
6%6, percent of these wafers are defective.
If we assume
p
^
=
0.06
p
^
=0.06p, with, hat, on top, equals, 0, point, 06, what is the smallest sample size required to obtain the desired margin of error?
Answers
Answer:
416
Step-by-step explanation:
Kahn Academy
What is the midpoint of the line with endpoints (3,-2) and (-3,6)
Answers
(0, 2)
Step-by-step explanation:
The coordinates of the midpoint of a line segment is given by
[(x2 + x1)/2 , (y2 + y1)/2]
Let P1 = (3, -2) and P2 = (-3, 6)
x-coordinate:
(1/2)(x2 + x1) = (1/2)[(-3) + 3] = 0
y-coordinate:
(1/2)(y2 + y1) = (1/2)[6 + (-2)] = 2
Therefore, the coordinates of the midpoint whose endpoints are (3, -2) and (-3, 6) are
(0, 2)
PLEASE HELP MEEEEEE!!!
Answers
Answer:
100
Step-by-step explanation:
A town is trying to determine if a new recycelin incentive would increase the number of people thatseperate their garbage from recycable iems. to make this determination a simple random sample of 10 streets and the number of people that recycle on these streets is countedonce before and once after the recycling incentive has been intitated. the date shows a mean difference of3.78 and a standard deviation of 1.33.
Required:
Determie if the recycling incentive was effectiive with a 5% significnc level.
Answers
Answer:
The recycling incentive was effective at 5% significance level.
Step-by-step explanation:
The null and alternative hypothesis are
H0 u1≤ u2 against the claim Ha: u1> u2
or
H0 ud=0 against the claim Ha: ud > 0
The significance level is ∝=0.05
Data given
d`= 3.78
sd= 1.33
n= 10
The test statistic is
t= d`/ sd/ √n
t= 3.78/1.33/√10
t= 9.3889
The critical region for ∝=0.05 and df.= (n-1)= 9 is t> 1.833
Since the calculated value of t lies in the critical region it is concluded that new recycling incentive would increase the number of people that seperate their garbage from recyclable items.
H0 is rejected and Ha is accepted.
What is the exponential regression equation for the data set?
yˆ=1.08⋅32.11x
yˆ=(1.08⋅32.11)x
yˆ=32.11⋅0.08x
yˆ=32.11⋅1.08x
Answers
Answer:
yˆ=32.11⋅1.08x
Step-by-step explanation:
just took the test
Option: A is the correct answer.
The quadratic regression equation for the data set is:
A. y = 0.056x²+1.278x-0.886
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
We are given a set of data value as:
x y
3 3.45
5 6.9
6 8.79
8 12.91
10 17.48
12 22.49
15 30.85
On plotting these points on a scatter plot we see that the line that best fits these data points is a parabola i.e. the equation is a equation of a quadratic function.
The equation of the line of best fit is:
y = 0.056x²+1.278x-0.886
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Zach has $50 to spend on a sweater. Let c represent the cost of the sweater. He has a coupon for 5% off. The expression 50 -(c -0.05c)
represents how much money Zach has left after buying the sweater and using his coupon.
Choose two expressions that also represent how much money Zach has left.
A. 0.950
B. 50 -0.05c
C. 50 -0.950
D. 50-C-0.050
E. 50-C+0.050
Answers
Answer:
B and D
Step-by-step explanation:
I will be giving brainliest whoever answers these
Answers
Answer:
3, 5, 1, -1, 5, -1, -1, 5
Step-by-step explanation:
Because it is I am tired sorry
40 PTS ! The length of the rectangle is 2 ft more than its width. The area of the rectangle is 80 square feet. Find the width of the rectangle.
Answers
Answer:
The length of a rectangle is 2 feet more than it's width. How do you find the dimensions of the rectangle if its area is 63 square feet?
Step-by-step explanation:
x(x+2) = 63
x^2 + 2x = 63
x^2 + 2x - 63 = 0
Quadratic formula with numbers plugged in: (-2 +or- sqrt(4 - 4* 1 * -63))/2 becomes
-2 +or- sqrt(256)/2 so (-2 +or- 16)/2 therefore -18/2 or 14/2. Discard negative result.
x = 7. 63/7=9. Sides are 7ft and 9ft.
Answer:
8 ftStep-by-step explanation:
Given
The length l = w + 2The area lw = 80Substitute l and solve the following for w:
w(w + 2) = 80w² + 2w = 81w² + 2w + 1 = 81(w + 1)² = 9²w + 1 = 9w = 8The width is 8 ft
Jake throws a dart that hits the square shown below:
A square is drawn. A circle of radius 8 units touches the sides of the square.
What is the probability that the dart hits a point in the circle?
(1) 16%
(2) 21.5%
(3) 64%
(4) 78.5%
Answers
Solve for p.
p + 36 = 73
p =
Answers
Answer:
p=37
Step-by-step explanation:
to get p by its self, you would do:
p+36=73
-36=-36
p=37
Answer:
37
Step-by-step explanation:
Order from greatest to least: 12, -4,8, -3, 0.
Answers
Answer:
-4,-3,0,8,12 its backwards my bad
Step-by-step explanation:
because it is
Answer:
12, 8, 0, -3, -4
hope it helps
Which expression is equivalent to -51 - (-60)?
Choose 1 answer:
А
-60 +(-51)
В.
-51 +60
51 - 60
60 + 51
2 of 4
Answers
Examine the system of equations.
5x + 6y = 32
5x – 6y = 8
Which variable or variables will be eliminated when you add the system of equations?
Which equation results from adding the system of equations?
Answers
9514 1404 393
Answer:
y is eliminated10x = 40Step-by-step explanation:
The coefficients of y are opposites. Adding opposites results in a sum of 0. The y-term will be eliminated by adding the equations.
The result of that addition is ...
(5x +6y) +(5x -6y) = (32) +(8)
10x = 40
The Sine Function
A sine curve is periodic. What does this mean?
a. the curve goes through one cycle and starts over
b. there is no pattern
c. the amplitude stays the same
d. one period equals 180 degrees
Please select the best answer from choices provided
Answers
Answer:
A. The curve goes through one cycle and starts over
Step-by-step explanation:
I calculated it logically
helppppppppppppppppp
Answers
Answer:
6.4
Step-by-step explanation:
The Pythagorean Theorem says that in a right triangle,
[tex](\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2[/tex].
In this problem,
[tex]a^2+b^2=c^2\\\\4^2+5^2=c^2\\\\16+25=c^2\\\\41=c^2\\\\c=\sqrt{41} \approx 6.4[/tex]
Two trucks started toward each other at the same time from towns 500 lm scart One truck traveled at a rate of 65 km per hour wrile the other traveled at 50 km per hour. After how many hours did they meet?
If represents the number of hours, which of the following equations could be used to solve the problem?
65x=60x
65x -60x=500
65x+60x=500
Answers
Answer:
65x + 60x = 500
add 65x and 60x
this will equal 125x
divide 500 by 125
this will give you x = 4
which gives you the answer that the trucks will meet in 4 hours
please mark as brainliest
hope this helps : )
Step-by-step explanation:
Neesha uploaded a funny video of her dog onto a website. The relationship between the elapsed
time, d, in days, since the video was first uploaded, and the total number of views V (d), that the
video received is modeled by the function V (d) = 31.5d.
How many views will the video receive after 5 days? Round your answer to the nearest whole
number.
Answers
Answer:
the answer is 2
Step-by-step explanation:
TULI
Spinner A
Spinner
025
05
Tim has two spinners, spinner A and Spinner B.
Each spinner can only land on red or bloe.
The probability that spinner A will land on red is 0.5
The probability that spinner will land on red is 0.6
The tree diagram shows this information
Tim spins spinner A once and he
spins spinner Bonce
He does this a number of times.
The number of times both spinners 0.5
land on red is 84.
Work out an estimate for the
number of times both spinners land on blue.
red
05
blu
blue
Answers
So we would expect both spinners to land on blue once, approximately.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. The closer the probability is to 1, the more likely the event is to occur, while the closer it is to 0, the less likely it is to occur.
Here,
To solve this problem, we can use the multiplication rule of probability, which states that the probability of two independent events A and B occurring together is equal to the product of their individual probabilities:
P(A and B) = P(A) × P(B)
In this case, we want to find the number of times both spinners land on blue, which is equivalent to the probability that spinner A lands on blue (0.5) multiplied by the probability that spinner B lands on blue (0.4), because the events are assumed to be independent. Therefore:
P(both blue) = P(A blue) × P(B blue) = 0.5 × 0.4 = 0.2
This means that the probability of both spinners landing on blue is 0.2, or 20%.
To estimate the number of times both spinners land on blue out of a certain number of trials, we can use the expected value of a binomial distribution, which is given by:
E(X) = n × p
where X is the random variable representing the number of successes (in this case, both spinners landing on blue), n is the number of trials, and p is the probability of success (0.2 in this case).
We are given that the number of times both spinners land on red is 84, which is equivalent to the number of trials minus the number of times both spinners land on blue. Let's denote the number of trials as n. Then we have:
n - 84 = number of times both spinners land on blue
Substituting the values we have found, we get:
n - 84 = 0.2n
Simplifying and solving for n, we get:
0.8n = 84
n = 105
Therefore, the estimated number of times both spinners land on blue out of 105 trials is: number of times both spinners land on blue
= 0.2 × 105 - 84 ≈ 1
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