Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.Given right triangle GYK, what is the value of tan(G)?
Answers
Answer:
Sqrt 3
Step-by-step explanation:
The value of tan(G) is √3
What is right triangle?
Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.
In ΔGYK
∠GYK = 90°
∠KGY = 60°
∠GYK = 30°
side GK = 27
Let side KY = x
tan(Y) = tan30° = GK/KY
1/√3 = 27/x
x = 27√3
So side KY = 27√3
tan(G) = KY/KG
tan(G) = 27√3/27
tan(G) = √3
Hence, the value of tan(G) is √3
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Related Questions
{3, 6, 9, 12, 15} {1, 6, 12, 18, 24}Which of the following shows the intersection of the sets?
Answers
Answer:
{ 6,12}
Step-by-step explanation:
The intersection is what the two sets have in common
{3, 6, 9, 12, 15}∩ {1, 6, 12, 18, 24}
= { 6,12}
find an angle between 0 and 2π that is coterminal with -3π /10
Answers
Answer:
17π/10
Step-by-step explanation:
To find a co-terminal angle in a specific range, add or subtract multiples of 2π until you have an angle in the desired range. Here, you can add 2π.
-3π/10 +20π/10 = 17π/10 . . . . angle co-terminal with -3π/10
A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 1515 years with a variance of 2525. If the claim is true, in a sample of 4141 wall clocks, what is the probability that the mean clock life would differ from the population mean by more than 0.40.4 years
Answers
Answer:
The correct answer will be "0.3043".
Step-by-step explanation:
The given values are:
[tex]\mu = 15[/tex]
[tex]n=41[/tex]
[tex]\sigma^2=25[/tex]
then,
[tex]\sigma=5[/tex]
If researchers know representative sample n > 30 and default deviation those who use z-test
∴ [tex]P(x>15.4)[/tex]
⇒ [tex]1-P(x<15.4)[/tex]
⇒ [tex]1-P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } } <\frac{15.4-15}{\frac{5}{\sqrt{41} } } )[/tex]
⇒ [tex]1-P(Z<0.51225)[/tex]
⇒ [tex]1-0.695762[/tex]
⇒ [tex]0.3043[/tex]
a patient is taking 65 grams of medicine if it is increased by 20% how many grams are they taking
Answers
Answer:
78 grams
Step-by-step explanation:
20% is 1/5
1/5 of 65 is 13
65 + 13 = 78
brainliest?
I need help on this question
Answers
Answer:
Step-by-step explanation:
First off, you need to add up AB and BC. You would get the equation:
2(3x-4)=62, since there are two segments. Solve it/simplfy.
6x-8=62 => 6x=70 => x= 11.66666(forever)
Since you alreday solved one, you easily know the answer is c.
please help hurryyyyyyy
Answers
Answer:
Hey there!
40 is 25% of 120.
We can see that 30 is 25% of 120, because 0.25(120)=30.
Hope this helps :)
Answer:
30 is 25% of 120
Step-by-step explanation:
What is 25% of 120
Is means equals and of means multiply
What = 25% * 120
What = .25 * 120
What =30
30 is 25% of 120
help :(( i am very confused and if the screenshot says 25 just know its 26 not 25
Answers
Answer:
9/26
Step-by-step explanation:
Answer:
Step-by-step explanation:
25-3 =22 have a cat or a dog
15 +16 =31 students are in the class if every person has either a cat or a dog
But we have 22
so 31 - 22 = 9 have both cat and dog
the probability is 9/25
In a circle of radius 5 miles, the length of the arc that subtends a central angle of 4 radians is how many miles?
Answers
Answer:
The length of the arc is 20 miles.
Step-by-step explanation:
We know that an arc formed by an angle of 1 radian in a circle of radius of 1 mile will have a length of 1 mile.
If the radius is 5 miles, an arc of 1 radian will have a length of 5 miles.
Then, if the angle is 4 radians, and the radius is 5 miles, we will have an arc length of:
[tex]\text{arc length}=\text {angle} \cdot \text {radius}=4\cdot 5 =20\;\text{miles}[/tex]
need help asap! what is the value of x given that figure MNOP is a trapezoid with median QR
Answers
Answer:
x = 8
Step-by-step explanation:
To find the possible value of x in the given trapezoid MNOP with median QR, recall that one of the properties of a trapezoid is that the median length = ½ of the sum of the length of the parallel bases
Thus, ½ of [x + (3x + 8)] = 20
Let's find x
½*[x + (3x + 8)] = 20
½*[x + 3x + 8)] = 20
½*[4x +8] = 20
Multiply both sides by 2
4x + 8 = 20*2
4x + 8 = 40
Subtract 8 from both sides
4x = 40 - 8
4x = 32
Divide both sides by 4
x = 32/4
x = 8
Answer:
I think its 8 ♂️
Step-by-step explanation:
The table shows claims and their probabilities for an insurance company.
O A. (a)
O B. (a)
Amount of Claim
$0
$50,000
$100,000
$150,000
$200,000
$250,000
Probability
0.60
0.25
0.09
0.04
0.01
0.01
O c. (a) $
OD. (a) $
(a) Calculate the expected value.
(b) How much should the company charge as an average premium so that it breaks even on its claim
costs?
(c) How much should the company charge to make a profit of $60 per policy?
Answers
Answer:
a) Expected Value of Claims = $32,000
b) Average premium per claim, in order to break-even on claim costs
= $5,333.33
c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:
= $5,393.33 per policy
Step-by-step explanation:
a) Data and Calculations:
Amount of Claim Probability Expected Value
$0 0.60 $0
$50,000 0.25 $12,500
$100,000 0.09 9,000
$150,000 0.04 6,000
$200,000 0.01 2,000
$250,000 0.01 2,500
Expected Cost of claims = $32,000
b) Average premium per claim, in order to break-even on claim costs
= Total Claim cost divided by number of policies
= $32,000/6 = $5,333.33
c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:
Total Claim cost + Total profit / 6 or Average Premium plus Profit per policy =
= ($32,000 + $360)/6 or $5,333.33 + $60
= $32,360/6 or $5,393.33
= $5,393.33
The total expected value is $32000, the average premium so that it breaks even on its claim costs are $5333.33 and the company charge to make a profit of $60 per policy is $5393.33.
Given :
The table shows claims and their probabilities for an insurance company.
Amount of Claim Probability Expected Value
$0 0.60 0
$50000 0.25 $12500
$100000 0.09 $9000
$150000 0.04 $6000
$200000 0.01 $2000
$250000 0.01 $2500
A) So, the total expected value is = 12500 + 9000 + 6000 + 2000 + 2500
= $32000
B) The average premium is given by:
[tex]=\dfrac{32000}{6}[/tex]
= $5333.33
C) The company charge to make a profit of $60 per policy is:
[tex]= \dfrac{32000+360}{6}[/tex]
[tex]=\dfrac{32360}{6}[/tex]
= $5393.33
For more information, refer to the link given below:
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Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309. Adam reads that the average speed that cars drive on the highway is 65 mph. The t-test statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place.
Answers
Answer:
We accept null hypothesis
Step-by-step explanation:
We assume a normal distribution
The population mean μ₀ = 65 mph
Sample mean μ = 63,2 mph ( calculated from data )
Sample standard deviation σ = 7,309
Sample size n = 8
Degree of freedom is n - 1 8 - 1 = 7
As n < 30 we have to use the t-student test
We will do our test with a confidence interval of 95 % that means α = 5 %
or α = 0,05 and as we are going through a two-tail test α/2 = 0,025
Test Hypothesis:
Null Hypothesis: H₀ μ = μ₀
Alternate Hypothesis Hₐ μ ≠ μ₀
From t-student table for the degree of freedom 7, α/2 = 0,025 two-tail test we find tc
tc = 2,365
And calculate ts as
ts = ( μ - μ₀ ) / σ /√n
ts = ( 63,2 - 65 ) / 7,309/ √8
ts = - 1,8 *2,828/ 7,309
ts = - 5,091 /7,309
ts = - 06965
Now we compare ts and tc
tc = 2,365 or tc = - 2,365 ( by simmetry) tc = -2,37
and ts = -0,06965 ts = - 0,07
As |ts| < |tc|
ts is in the acceptance zone so we accept null hypothesis
Answer:
-0.70
Step-by-step explanation:
For the tabulated value the mean is calculated as:
Mean = (60.5 + 63.2 + 54.7 + 51.6 + 72.3 + 70.7 + 67.2 + 65.4)/8
= 505.6/8
Mean \bar{x}= 63.2
and population mean as assumption u= 65
and given that the sample standard deviation is: s= 7.309
The test statistic is calculated as:
Ζ = Τ –μ 63.2 - 65 = -0.696 -0.70 S
Hence the T statistic would be -0.70
here is a question for all :)
Answers
Answer:
The circle on the far left is the sum of 4x + 3y and 2x - y so the answer is 4x + 3y + 2x - y = 6x + 2y. The circle on the far left is the sum of x + 4y and something. To find that "something" we can do 4x + 5y - (x + 4y) = 3x + y which is the value of the bottom right rectangle. This means that the value of the bottom circle is 2x - y + 3x + y = 5x.
Answer:
Step-by-step explanation:
left circle=4x+3y+2x-y=6x+2y
right bottom rectangle=4x+5y-(x+4y)=4x+5y-x-4y=3x+y
Bottom circle=2x-y+3x+y=5x
Which property is displayed in the example below: 4(x + 3) = 4x + 12
Answers
Answer:
This equation displays the distributive property which states that a(b + c) = a(b) + a(c).
Answer:
Distributive property
Step-by-step explanation:
4(x+3)=4x+12
This example shows distributive property because 4 is distributed (multiplied) to x +3. When 4 is distributed, it will equal 4x+12!!
Hope it helps!!!!
A taxi company charges $2.25 per ride plus $0.30 per mile. Enter a linear model represents the cost, C, as a function of d, the number of miles of the ride.
Answers
Answer:
C(d) = d(2.25) + m(0.3)
Step-by-step explanation:
A taxi company charges $2.25 per ride plus $0.30 per mile.
Let d represent number of rides..
Let m represent number of Miles...
Then let C represent the total cost for each ride at a specific number of Miles.
The linear model representing the cost as a function of d the total ride
C(d) = d(2.25) + m(0.3)
The values stand independently because the customer can choose a different right and a different mile.
what is 3 x 3 1/4 x 3 3/4
Answers
Answer:36.5625
Step-by-step explanation:
Hope this helped!
<!> Brainliest is appreciated! <!>
Find the total area of the prism.
Answers
Answer:
864
Step-by-step explanation:
AT= 2Area base+ph
AT= 2(12*12) +(12*4)12
AT=2 (144)+576
AT= 288+576
AT=864"
Not sure how to graph this
Answers
Answer:
y=2x+6
Step-by-step explanation:
The slope is 2x and the y-intercept is 6. It is shown how to graph it in the attachment.
The domain and range of H
Answers
R: {-4,0,1,2}
Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant.
Answers
Find the intercepts for both planes.
Plane 1, x + y + 2z = 2:
[tex]y=z=0\implies x=2\implies (2,0,0)[/tex]
[tex]x=z=0\implies y=2\implies(0,2,0)[/tex]
[tex]x=y=0\implies 2z=2\implies z=1\implies(0,0,1)[/tex]
Plane 2, 4x + 4y + z = 8:
[tex]y=z=0\implies4x=8\implies x=2\implies(2,0,0)[/tex]
[tex]x=z=0\implies4y=8\impliesy=2\implies(0,2,0)[/tex]
[tex]x=y=0\implies z=8\implies(0,0,8)[/tex]
Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.
Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.
So the volume of the region is
[tex]\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx[/tex]
[tex]=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx[/tex]
[tex]=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}[/tex]
Find the length of KC
Answers
Answer:
54
give me brainliest please please please and follow my page
Step-by-step explanation:
To find length of KC...we need to find the length of HM and MU first ...
so....HM= 96- 78 = 14
JU = 96 + HM = 96 + 14 = 110
....
KU = 110 - JK = 110 - 82 = 28
....
UN = 105+ 82 -( 96 + 14 )
187 - 110
= 77
UC = 77 - 51 = 26
KC = UC + KU = 26 + 28 = 54
The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.
How do you compute the length of [tex]\overline{KC}[/tex]?To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.
[tex]\overline{HM}[/tex] = 96 - 78
[tex]\overline{HM}[/tex] = 14
[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]
= 96 + 14
[tex]\overline{JU}[/tex]= 110
[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]
= 110 - 82
[tex]\overline{KU}[/tex]= 28
[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )
=187 - 110
[tex]\overline{UN}[/tex]= 77
[tex]\overline{UC}[/tex] = 77 - 51
[tex]\overline{UC}[/tex]= 26
Thus,
[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]
[tex]\overline{KC}[/tex]= 26 + 28
[tex]\overline{KC}[/tex]= 54
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The Demon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three other were sprayed with Action. When the grape ripened, 400 of the vines treated with Pernod 5 and 400 of the vines treated with Action were checked for infestation. The number of infested vines treated with Pernod 5 and Action are 24 and 40 respectively.
At 0.05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?
Answers
Answer:
At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
Then, the null and alternative hypothesis are:
H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0
The significance level is 0.05.
The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.
[tex]p_1=X_1/n_1=24/400=0.06[/tex]
The sample 2, of size n2=400 has a proportion of p2=0.1.
[tex]p_2=X_2/n_2=40/400=0.1[/tex]
The difference between proportions is (p1-p2)=-0.04.
[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]
As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.
For each ordered pair, determine whether it is a solution to the system of equations. y=6x-7 9x-2y=8
Answers
Answer:
x = 2, y = 5
Step-by-step explanation:
Hello,
y=6x-7
9x-2y=8
can be written as
(1) 6x - y = 7
(2) 9x -2y = 8
(2)-2*(1) gives
9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6
<=> -3x=-6
<=> x = 6/3=2
and we replace it in (1)
y = 6*2-7=12-7=5
hope this helps
This is not an incomplete question, it has come from a very reliable source, please dont delete. If 60% of the students in Mr. Bobby's class are bio majors, which of the following could be the total number of students in his class? 28 32 35 39 PLZHELPTHANKS
Answers
Answer:
35 students
Step-by-step explanation:
Take the number of students in the class and multiply by 60% and see if you get an integer number
28 * .60 =16.8 not an integer
32 * .6 =19.2
35 * .6 =21 yes
39*.6 =23.4
find the area of the shaded region. 27.8 in and 150 degrees
Answers
Answer: 57769.8 in²
Let A be the area of the shaded region
We have a relation that can help us calculate its area
A= 0.5*(θ-sin(θ))*r² where r is the radius and θ the angle
A= 0.5*(150-sin(150°))* 27.8² =57769.79≈57769.8 in²
Answer:
818.4
Step-by-step explanation:
You want to put a 2 inch thick layer of topsoil for a new 14 ft by 26 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answers
Answer:
2 1/4
Step-by-step explanation:
The volume of soil needed is ...
(14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³
The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.
You need to order 2 1/4 cubic yards.
___
There are 3 ft or 36 inches to a yard.
Answer pls ASAP thanks for answering if it is answered
Answers
Answer:
The trransformation was a reflection.
Which polynomial equation of least degree has -2, -2, 3, and 3 as four of its roots? (x + 2)(x - 3) = 0 (x - 2)-2(x + 3)3 = 0 (x-2 + 2)(x2- 3) = 0 (x + 2)2(x - 3)2 = 0
Answers
Answer:
(x + 2)²(x - 3)² = 0
Step-by-step explanation:
Since we have a degree of 2 and double of the same roots, we know that each root would have a multiplicity of 2. Therefore, our answer is(x + 2)²(x - 3)² = 0
Hi, what trigonometry is?
Answers
Trigonometry is the study of the properties of triangles and trigonometric functions and of their applications.
I'm not sure how you'd want me to answer your question though, but stay safe!!
- eli <3
in QRS, m Q = 70°, m R = 44", and m S = 66º. Which side of QRS is the shortest?
Answers
Answer:
QS
Step-by-step explanation:
The side opposite to the smallest angle must be the shortest side. The smallest angle is ∠R so the opposite side is QS.
Answer:
Hey there!
Smaller angles are opposite smaller sides, so the side opposite to angle R would be the shortest. (Or side SQ)
Hope this helps :)
What are the composite factor of 20
Answers
Answer:
4×4+4Step-by-step explanation:
hope its helpful
Answer:
4, 10, and 20.
Step-by-step explanation:
20 is a composite number because it has more than 2 factors.
The factors of 20 are 1, 2, 4, 5, 10, and 20.
1 is neither prime nor composite.
2, 5 are prime numbers because they only have 2 factors.
4, 10, 20 are composite numbers because they have more than 2 factors.