Answer:
left: 123.607 lbright: 380.423 lbStep-by-step explanation:
By balancing horizontal and vertical forces, we find the cable tensions to be ...
Ta = W·sin(b)/sin(a+b) . . . . . where W is the weight being held
Tb = W·sin(a)/sin(a+b)
Where Ta is the tension in the cable that makes an angle of 'a' with respect to the vertical, and Tb is the tension in the cable that makes an angle of 'b' with respect to the vertical.
__
The given angles are with respect to the ceiling, so the angles with respect to the vertical will be their compmements.
left cable (a)angle 'a' is 90° -18° = 72°
angle 'b' is 90° -72° = 18°
a+b = 72° +18° = 90°
Ta = (400 lb)sin(18°)/sin(90°) = 123.607 lb
right cable (b)Tb = (400 lb)sin(72°)/sin(90°) = 380.423 lb
_____
Additional comment
The nice expressions for cable tension come from the balance of forces.
vertical: Ta·cos(a) +Tb·cos(b) = W
horizontal: Ta·sin(a) = Tb·sin(b)
Solving the horizontal equation for Ta, we get ...
Ta = Tb·sin(b)/sin(a)
Substituting into the vertical equaiton gives ...
Tb·sin(b)cos(a)/sin(a) +Tb·cos(b) = W
Multiplying by sin(a) gives ...
Tb(sin(b)cos(a) +sin(a)cos(b)) = W·sin(a)
Using the trig identity for the sine of the sum of angles, we can rewrite this in the form shown above:
Tb = W·sin(a)/sin(a+b)
The problem is symmetrical with respect to 'a' and 'b', so the other tension is found by interchanging 'a' and 'b' in the equation:
Ta = W·sin(b)/sin(a+b)
Test the claim that LeBron James and Steph Curry average the same amount of points per game, on average.
Be sure to include the claim, critical values, test statistic and the conclusion.
For 70 games Lebron James averaged 30.1 points with a standard deviation of 9.112
For 70 games Steph Curry averaged 25.5 points with a standard deviation of 12.602
When the variances are known and the sample size is high, a z-test is used to assess if two population means vary. The mean of the two players is not the same.
What is a Z-test?When the variances are known and the sample size is high, a z-test is used to assess if two population means vary.
In order to execute an appropriate z-test, the test statistic is expected to have a normal distribution, and nuisance factors such as standard deviation should be known.
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ H_a: \mu_1 & \ne & \mu_2 \end{array}[/tex]
This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations, will be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is [tex]z_c = 1.96[/tex]
The rejection region for this two-tailed test is R={z:∣z∣>1.96}
(3) Test Statistics
The z-statistic is computed as follows:
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
(4.) The decision about the null hypothesis
Since it is observed that |z| = 2.475 > z_c = 1.96, it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value is p = 0.0133p=0.0133, and since p = 0.0133 < 0.05p=0.0133<0.05, it is concluded that the null hypothesis is rejected.
(5.) As it is concluded that the null hypothesis H₀ is rejected. Therefore, there is enough evidence to claim that the population mean μ1 is different than μ2.
Hence, the mean of the two players is not the same.
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The area of a rectangular patio is 24 3/8
square meters. The width of the patio is 3 3/4
meters. What is the length? Enter your answer as a mixed number in simplest form.
The length of the patio is ___ meters.
Answer:
6 1/2
Step-by-step explanation:
Use the area formula: A=LengthxWidth
Plug in what we know: 24 3/8= 3 3/4x Width
We need to isolate the width; get it by itself.
Do this by (24 3/8)/(3 3/4). The best way is to enter this into a calculator.
Your answer is 6 1/2
What is the surface area?
2 ft
5 ft
3 ft
square feet
Submit
I am playing a number game, there are 2 tiles for each number from 0 thru 9. One tile is chosen at random, can you list the possible outcomes ?
Answer:
If each tile has a number from 0 thru 9 then the possible outcomes for each tile are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
What negative impact can interdependence have on a country?
A. Threat to political interference
B. Threat to security
C. Threat to industrialization
D. Increased progress and industrialization
Given sides a-10, b=5 and angle ZA-100°. Find the corresponding value for ZB. Options: A 60° B 5° D -29.5° C 29.5°
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The measure of the ∠B=29.5°.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given that sides a=10, b=5 and the measure of the ∠A=100°. Therefore, the using the sine law,
[tex]\rm \dfrac{Sin\ A}{a} = \dfrac{Sin\ B}{b}[/tex]
[tex]\rm \dfrac{Sin\ 100^o}{10} = \dfrac{Sin\ B}{5}\\\\\rm \dfrac{(Sin\ 100^o) \times 5}{10} = Sin\ B\\\\Sin\ B = 0.04924\\\\\angle B = 29.498^o \approx 29.5^o[/tex]
Hence, the measure of the ∠B=29.5°.
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find KM ( SHOW YOUR WORK )
A property's value is $400,000 and its land value is $75,000. Assuming a depreciation term of 39 years, what is the amount of annual depreciation?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &75000\\ P=\textit{initial amount}\dotfill &400000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &39\\ \end{cases} \\\\\\ 75000=400000(1 - \frac{r}{100})^{39}\implies \cfrac{75000}{400000}=\left( \cfrac{100-r}{100} \right)^{39}[/tex]
[tex]\cfrac{3}{16}=\left( \cfrac{100-r}{100} \right)^{39}\implies \sqrt[39]{\cfrac{3}{16}}=\cfrac{100-r}{100}\implies 100\sqrt[39]{\cfrac{3}{16}}=100-r \\\\\\ r=100-100\sqrt[39]{\cfrac{3}{16}}\implies r\approx 4.2[/tex]
Suppose you draw a card from a well-shuffled deck of 52 cardsWhat is the probability of drawing a 2 or a queen?
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:Probability is finding the chance that some specific outcome will occur. In this case, we are looking for the probability of one of two outcomes.
Equally Likely Outcomes
When drawing a card from a well-shuffled deck, all outcomes (cards) are equally likely to be drawn. Each card was a 1/52 probability of occurring.
Probability of Two Outcomes
In a deck of cards, there are 4 cards of each number. This means that the probability of drawing a 2 is 4/52, the same for a queen.
So, to find the probability of one of the two desired outcomes is equal to adding the probabilities together.
[tex]\frac{4}{52} +\frac{4}{52} =\frac{8}{52}[/tex]This fraction can then be simplified further:
[tex]\frac{2}{13}[/tex]Graph the function with the following domain and range domain 0,1,2,3 and range -3,0,5
Answer:
hope this is what you ask for and i hope it helps
Step-by-step explanation:
Need to show work for limits
Answer:
[tex]\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3) = \infty[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3)[/tex]
Step 2: Evaluate
[Limit] Apply Limit Rule [Variable Direct Substitution]:Recall that x⁵ is a "faster" function than x³. Also recall that we have 2 negatives, which would turn positive. Therefore, we can ignore the 2nd part of the limit and focus on the first:
[tex]\displaystyle \begin{aligned}\lim_{x \to -\infty} (-7x^5 + x^3) & = -7(- \infty)^5 + (- \infty)^3 \\& = -7(- \infty)^5 \\& = -7(- \infty) \\& = 7(\infty) \\& = \boxed{\infty} \\\end{aligned}[/tex]
∴ we have found the limit to equal infinity.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
i would like the answer to 1/4 minus 1/3 is it 12
Answer:
-1/12
Step-by-step explanation:
1/4 - 1/3 = 3/12 - 4/12 = - 1/12
What is the area, in square centimeters, of the parallelogram?
(20 points)
Answer:
30
Step-by-step explanation:
10 x 3 = 30
Answer:
30 centimeters squared
Step-by-step explanation:
The area of a parallelogram can be found by using the formula base x height. The base of this parallelogram is 10, and the height is 3. Therefore the area is 30 square centimeters.
The fox observed that the tortoise plodded along at a rate of 20 meters per minute throughout the 1000-meter race.
1. Complete the table below indicating the distance traveled by the tortoise in the time elapsed.
The values that are required to complete the table above indicating the distance traveled by the tortoise in the time elapsed are calculated below.
How to calculate the distance traveled?Mathematically, the distance traveled by the tortoise would be calculated by using this formula:
Distance = speed (rate) × time
When time = 1 min, we have:
D₁ = 20 × 1
D₁ = 20 meters.
When time = 2 min, we have:
D₂ = 20 × 2
D₂ = 40 meters.
When time = 3 min, we have:
D₃ = 20 × 3
D₃ = 60 meters.
When time = 4 min, we have:
D₄ = 20 × 4
D₄ = 80 meters.
When time = 5 min, we have:
D₅ = 20 × 5
D₅ = 100 meters.
When time = 6 min, we have:
D₆ = 20 × 6
D₆ = 120 meters.
When time = 7 min, we have:
D₇ = 20 × 7
D₇ = 140 meters.
When time = 10 min, we have:
D₁₀ = 20 × 10
D₁₀ = 200 meters.
When time = 15 min, we have:
D₁₅ = 20 × 15
D₁₅ = 300 meters.
When time = 20 min, we have:
D₂₀ = 20 × 20
D₂₀ = 400 meters.
When time = 25 min, we have:
D₂₅ = 20 × 25
D₂₅ = 500 meters.
When time = 30 min, we have:
D₃₀ = 20 × 30
D₃₀ = 600 meters.
When time = 35 min, we have:
D₃₅ = 20 × 35
D₃₅ = 700 meters.
When time = 40 min, we have:
D₄₀ = 20 × 40
D₄₀ = 800 meters.
When time = 50 min, we have:
D₅₀ = 20 × 50
D₅₀ = 1,000 meters.
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Wen painted 3/10 of her living room yesterday and 4/10 to today. What fraction of the room has she painted so far?
Answer:
7
Step-by-step explanation:
3/10+4/10 =7/10
Answer:
7/10, or 70%
Step-by-step explanation:
You just add the fractions together and get 7/10. You could also find a common denominator and the add them together. You would do, 9/30+ 12/30= 21/30, or 7/10.
Use 2-3 sentences to explain, in your own words, the difference between an angle of elevation and an angle of depression. Use geometry vocabulary.
Giving brainliest :D (show steps in a simple way ty!)
Answer:
5xsquared+x+5
Step-by-step explanation:
first combine x squared with 4x squared and you will get 5xsquared.
next combine 6x and -5x and you will get 1x or just simply x. Finally combine 3 and 2 (3+2) = 5.
Find the area of the triangle.
Answer:
40m^2 :)
Step-by-step explanation:
Area of a triange = (h·b)/2
Now lets solve :)
4 + 6 = 10
(8·10)/2
80/2
40
Have an amazing day!!
Please rate and mark brainliest!!
Find center and radius of this circle:
[tex](x-2)^2+(x+12)^2=81[/tex]
Answer:
center: (2,-12)
radius: 9
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex]h=2\\k=-12\\r=9[/tex]
get r by getting square root of 81
center = (h,k)
Answer:
center: (2,-12)
radius: 9
Step-by-step explanation:
(x-h)^2+(y-k)^2=r^2
h=2
k=-12
r=9
It is estimated that 0.54 percent of the callers to the Customer Service department of Dell Inc. will receive a busy signal. What is the probability that of today's 1,300 callers at least 5 received a busy signal?
Using the binomial distribution, it is found that there is a 0.8295 = 82.95% probability that at least 5 received a busy signal.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
0.54% of the calls receive a busy signal, hence p = 0.0054.A sample of 1300 callers is taken, hence n = 1300.The probability that at least 5 received a busy signal is given by:
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{1300,0}.(0.0054)^{0}.(0.9946)^{1300} = 0.0009[/tex]
[tex]P(X = 1) = C_{1300,1}.(0.0054)^{1}.(0.9946)^{1299} = 0.0062[/tex]
[tex]P(X = 2) = C_{1300,2}.(0.0054)^{2}.(0.9946)^{1298} = 0.0218[/tex]
[tex]P(X = 3) = C_{1300,3}.(0.0054)^{3}.(0.9946)^{1297} = 0.0513[/tex]
[tex]P(X = 4) = C_{1300,4}.(0.0054)^{4}.(0.9946)^{1296} = 0.0903[/tex]
Then:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0009 + 0.0062 + 0.0218 + 0.0513 + 0.0903 = 0.1705.
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.1705 = 0.8295[/tex]
0.8295 = 82.95% probability that at least 5 received a busy signal.
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I need help with my geometry homework.
Step-by-step explanation:
5x + 80 = 180
x = 20
2x = 40
3x=60
7x=140
what is 9x-2=(3x+9) + (5x) ?
A fictional country has a population of 5 million people and a net immigration rate of 1 person per 1000 people. The population is increasing only due to migration and not biological replacement. How long will it take the country’s population to double?
Group of answer choices
300 years
1,000 years
5,000 years
700 years
Answer:
1,000
Step-by-step explanation:
just took the quiz
the hooded men rushed out of town at 100 miles per hour one hour later the masked men left town in pursuit at 125 mph how many hours did it take the masked men to catch up to the hooded men
Answer:
It took 12.5 hours to catch up with the men
Question:
the hooded men rushed out of town at 100 miles per hour one hour later the masked men left town in pursuit at 125 mph how many hours did it take the masked men to catch up to the hooded men
Answer:
12.5
Step-by-step explanation:
This doesn't say it in the question but the hooded man drove 125 miles,
his speed was 100 mph.
The masked man drove also drove 125 miles but he drove at 125 mph.
Ok sorry lets make this simpler.
divide 1250 by 100 and your answer is:
12.5
So, it took the masked man 12.5 hours to catch up with the hooded man.
To be able to buy a new computer, Yoko decides to save for 5 years. She opens a savings account with $400. The account pays simple interest at an annual rate of 2%. She doesn't make any more deposits.
(a) How much total interest will Yoko earn?
(b) What will the total amount in the account be (including interest)?
Answer:
A) $40 total interest
B) $440
I NEED HEEEEELP WITH THIS QUESTIOOOON, maybe for some people it is very easy but not for me
Answer:
the 1.5 goes between -1 and 0 and -3/2 too and -4/3 between the-2 and the 3/2 between the 0 and 1
Step-by-step explanation:
what is the volume of this prism ?
Answer:
576cm³
Step-by-step explanation:
8×6=48
48×12=576
The volume of a rectangular prism is
300 in. If the length is 10in, the width
is 2 in, what is the height?
Answer:
The Height is 15in
Step-by-step explanation:
V=L.W.H
300=10x2xH
300=20xH
300/20=H
H=15in
The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?
A. H0: p ≥ 0.10 and H1: p < 0.10
B. H0: p ≤ 0.10 and H1: p > 0.10
C. H0: p > 0.10 and H1: p ≤ 0.10
D. H0: p = 0.10 and H1: p ≠ 0.10
The appropriate null and alternate hypotheses are (d) H0: p = 0.10 and H1: p ≠ 0.10
How to determine the hypotheses?From the question, we understand that:
The proportion of reports that have their cars stolen is given as 10%
Null hypothesis is represented with the equality sign.
So, the null hypothesis is H0: p = 0.10
The alternate hypothesis is represented with the unequal sign.
So, the alternate hypothesis is H1: p ≠0.10
Hence, the appropriate hypotheses are (d) H0: p = 0.10 and H1: p ≠ 0.10
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The price of an item has been reduced by $3.49. The new sale price is $31.38. What was the original price?
Add the amount it was reduced to the new price:
3.49 + 31.38 = 34.87
Original price = $34.87
Answer:
When finding the unknown original price, add the sale reduction to the new sale price to get the old sale price.
[tex]3.49 + 31.38 = 34.87[/tex]
Therefore, the original sales price was 34.87