Answer:
[tex]x=\frac{\pi }{6} ,\frac{7\pi }{6}[/tex]
Step-by-step explanation:
[tex]3*cot^2x-1=0\\\\3*cot^2x=1\\\\cot^2x=\frac{1}{3} \\\\cot(x)=\sqrt{\frac{1}{3} } \\\\cot(x)=\frac{1}{\sqrt{3} } \\\\\frac{1}{tan(x)}=\frac{1}{\sqrt{3} } \\\\tan(x)=\sqrt{3} \\[/tex]
x=tan^-1([tex]\sqrt{3}[/tex])
It has to be in Quadrant 1 [tex]\frac{+}{+} =+[/tex] or 3 [tex]\frac{-}{-}=+[/tex] for positive.
[tex]x=\frac{\pi }{6} ,\frac{7\pi }{6}[/tex]
Unless that incorrect due to tan(x) range is [tex]-\frac{\pi }{2} \leq x\leq \frac{\pi }{2}[/tex]. Then the only answer is [tex]x=\frac{\pi }{6}[/tex]
Can someone please go into detail on how they simplified this expression? Thanks!
: 4a - (4a-3)=4a 1(4a 3) Identity property
4a -4a + 3 Distributive property
0 -3 Combine like terms.
3 simplify
I really don't get how they got plus 3
Thanks again!
Answer:
Step-by-step explanation:
4a - (4a-3)
= 4a -1(4a - 3)
= 4a - 4a + 3 <--- Distributing the -1 over the parenthes
= 3 <---- ( as 4a - 4a = 0)
Helpppppp pleaseeeee ):
Answer:
Smily face=5 lightning=8
Step-by-step explanation:
5+5=10 8x3=24 24+10=34
8x5=40 5x8=40
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.
NO LINKS!! Please help me with this problem
FGHIJ ≅ STUQR
Solve for HI
[tex]\sf \dfrac{HI}{GH} = \dfrac{UQ}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{HI}{56} = \dfrac{25}{35}[/tex]
[tex]\rightarrow \sf HI = 40[/tex]
Solve for QR
[tex]\sf \dfrac{IJ}{GH} = \dfrac{QR}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{72}{56} = \dfrac{QR}{35}[/tex]
[tex]\rightarrow \sf QR = 45[/tex]
Solve for ST
[tex]\sf \dfrac{FG}{GH} = \dfrac{ST}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{48}{56} = \dfrac{ST}{35}[/tex]
[tex]\rightarrow \sf ST =30[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{GH}{HI}=\dfrac{UT}{UQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{HI}=\dfrac{35}{25}=\dfrac{7}{5}[/tex]
[tex]\\ \rm\Rrightarrow HI=56(5)/7=8(5)=40[/tex]
#QR
[tex]\\ \rm\Rrightarrow \dfrac{GH}{JI}=\dfrac{UT}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{72}=\dfrac{35}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{7}{9}=\dfrac{35}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow RQ=35(9)/7=5(9)=45[/tex]
#ST
[tex]\\ \rm\Rrightarrow \dfrac{GH}{FG}=\dfrac{UT}{ST}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{48}=\dfrac{7}{6}=\dfrac{35}{ST}[/tex]
[tex]\\ \rm\Rrightarrow ST=6(35)/7=6(5)=30[/tex]
what is the volume of this prism ?
Answer:
576cm³
Step-by-step explanation:
8×6=48
48×12=576
Find all solutions in the interval [0,2π)
Answer:
Its B
Step-by-step explanation:
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
a sphere is inscribed in a cube with a volume of 125 cubic inches what is the volume of the sphere
Answer:
using [tex]\pi[/tex]: 65.45 in³ (nearest hundredth)
using [tex]\pi =3.14[/tex]: 65.42 in³ (nearest hundredth)
Step-by-step explanation:
The radius of the sphere is half the side length of the cube (see attached diagram). Therefore, the side length of the cube = 2r
Given:
volume of the cube = 125 in³side length of cube = 2r[tex]\textsf{Volume of a cube}=x^3\quad \textsf{(where}\:x\:\textsf{is the side length)}[/tex]
[tex]\implies 125=(2r)^3[/tex]
[tex]\implies \sqrt[3]{125}=2r[/tex]
[tex]\implies 5=2r[/tex]
[tex]\implies r=\dfrac52[/tex]
Substitute the found value of r into the volume of a sphere equation:
[tex]\begin{aligned}\textsf{Volume of a sphere} & =\dfrac43 \pi r^3\\\\ & =\dfrac43 \pi \left(\dfrac52\right)^3\\\\ & =\dfrac43 \pi \left(\dfrac{125}{8}\right)\\\\ & =\dfrac{500}{24} \pi\\\\ & =\dfrac{125}{6} \pi\\\\ & =65.45\:\sf in^3\:(nearest\:hundredth) \end{aligned}[/tex]
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.
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]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
A triangle has perimeter 38 cm.
Two sides of the shapes are put
together to make a pentagon
A square has perimeter 48 cm.
What is the perimeter
of the pentagon?
cm
Answer:
62cm
Step-by-step explanation:
You were told the perimeter of the triangle is 38
but two sides are added to make a Pentagon. and that Pentagon is made up of a triangle and a square.
so if we find the side of the square, we can equally get the other two sides of the triangle.
hint: (because it's a square, we would be getting an isosceles triangle, meaning two sides are equal)
because one side of the pentagon added to the other two sides of the triangles gives us the perimeter of the triangle.
we first find the sides of the square with all sides equal by diving by 2
[tex] \frac{48}{2} = 12[/tex]
the sides of the square making the perimeter of the square 12cm.
now we subtract 12 from the perimeter of the triangle 38
[tex]38 - 12 = 26[/tex]
now that we have gotten one side we can get the other two by dividing the result by 2
[tex] \frac{26}{2} = 13[/tex]
so the other two sides of the triangle are 13cm.
now since we have the sides of the square and the triangle, we can find the perimeter of the pentagon by adding.
all the sides of the triangle without the base which is also the top of the square.
so instead of adding 4 times of 12, we add 3 times of 12 and 2 times of 13.
3(12)+2(13) = 62
or
12 + 12 + 12 + 13 + 13 = 62cm
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.
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
What is the surface area?
2 ft
5 ft
3 ft
square feet
Submit
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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I need help with my geometry homework.
Step-by-step explanation:
5x + 80 = 180
x = 20
2x = 40
3x=60
7x=140
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!!
what is 9x-2=(3x+9) + (5x) ?
find KM ( SHOW YOUR WORK )
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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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.
4th question!!! Can anyone help me ?
Answer:
₹528Step-by-step explanation:
Length of Fence
Circumference = 2πr or πdπd22/7 x 21 m22 x 3 m66 m2 rounds = 66 x 2 = 132 mCost
₹4 x 132₹528The 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
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
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]
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:
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:
Jennifer jones has an idea. Join the bbq parties together . She thinks they can rope off more total area if the tie two ropes together to make one giant bbq than the families could have separately. Is this true?
Jennifer idea of roping off more total area if the tie two ropes together to make one giant BBQ is a true statement.
What is total surface area?The total surface area is known to be the addition of all the sum of any given area of surfaces of a solid together.
Conclusively, Note that by joining together the 2 parties, one can cut off some activities that will be be doubled if it were two separate event and as such, the use of space is been maximize and then the area of the space they will use for the event will be reduced.
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