Answer:
Cos A=5/13
we have
Cos² A=[tex] 1-Sin ²A[/tex]
25/169=1-Sin²A
sin²A=1-25/169
sin²A=144/169
Sin A=[tex] \sqrt{144/169}=12/13[/tex]
again
Tan B=4/3
P/b=4/3
p=4
b=3
h=[tex]\sqrt{3²+4²}=5[/tex]
Now
Sin B=p/h=4/5
in IV quadrant sin angle is negative so
Sin B=-4/5
CosB=b/h=3/5
Now
Sin(A+B):sinAcosB+CosAsinB
now
substitute value
Sin(A+B):12/13*3/5+5/13*(-4/5)=36/65-4/13
=16/65 is a required answer
Find the area of the shape. Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal.
Answer:
314
Step-by-step explanation:
First, find the diameter which is 10 and square it. Then, multiply by pi or 3.14 to get 314.
(IF THIS HELPED PLEASE GIVE BRAINLIEST!)
What is the area? PLEASE HELP
Answer:
14mm×20mm=280mm²
14mm×12mm/2=84mm²
3.14×10²mm=314mm²
280m²+84mm²+314mm²=678mm²
Answer:
521mm^2
Step-by-step explanation:
First, separate the shapes.
-Half circle= diameter of 20, radius 10
-Rectangle= 14x20
-Triangle= (32-20)x14= 12x14
Then, calculate
Circle equation= (pi)r^2= (pi)(10)^2= 314.16 -> divide by 2 for half circle= 157.1
Rectangle= 14x20=280
Triangle= (12x14)=168 -> Divide by two because it's a triangle= 84
Add 157 + 280 + 84 and you get 521
Arrivals of cars at a gas station follow a Poisson distribution. During a given 5-minute period, one car arrived at the station. Find the probability that it arrived during the last 30 seconds of the 5-minute period g.
Answer:
0.9 = 90% probability that it arrived during the last 30 seconds of the 5-minute period.
Step-by-step explanation:
The car is equally as likely to arrive during each second of the interval, which means that the uniform distribution is used to solve this question.
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distribution has two bounds, a and b, and the probability of finding a value higher than x is given by:
[tex]P(X \geq x) = \frac{b - x}{b - a}[/tex]
5-minute period
This means that [tex]a = 0, b = 5*60 = 300[/tex]
Find the probability that it arrived during the last 30 seconds of the 5-minute period.
300 - 30 = 270. So
[tex]P(X \geq 270) = \frac{300 - 270}{300 - 0} = 0.9[/tex]
0.9 = 90% probability that it arrived during the last 30 seconds of the 5-minute period.
2/5 of a number is 2/5 greater than 1/3 of a number? What is the number?
Answer:
5
Step-by-step explanation:
Will someone help with this???? ALG 2
Answer:
The answer is D
Step-by-step explanation:
The two solutions are (-2,0) (this is the solution that is on the x axis to the left).
And
(0,2)
Remember the notation is alphabetical. The x value is stated on the left. Then comes a comma, and the y value is on the right of the comma.
A school spent $780,000 in one year to pay all of its teachers and administrators. The school has a total of twenty-four teachers and administrators combined. If teachers make $35,000 per year and administrators make $40,000 per year, how many teachers and how many administrators does the school have?
Answer: Impossible
Step-by-step explanation: Even if 24 people were on the teacher salary, 780,000 still couldn't cover them all.
Subtract the sum of 13 and 6 from 40. *
Currently, there are 1,460 wolves in Scataway National Park. If the population of wolves is growing at a rate of 6% every year,
which function represents the number of wolves in Scataway National Park in tyears?
OA W0 = 1,460(1.06)
B. WO = 1,460(0.94)
OC M6 = 1,460(0.06)
OD. WO = (1,460)(1.06)
Answer:
[tex]P(t) = 1460(1.06)^t[/tex]
Step-by-step explanation:
Exponential equation for population growth:
The exponential equation for a population after t years is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
Currently, there are 1,460 wolves in Scataway National Park.
This means that [tex]P(0) = 1460[/tex]
Growing at a rate of 6% every year:
This means that [tex]r = 0.06[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 1460(1+0.06)^t[/tex]
[tex]P(t) = 1460(1.06)^t[/tex]
Answer:
Step-by-step explanation:
Which of the following ordered pairs are solutions to the system of equations below?
(3x + 5y = 14
y = 1/2x + 5)
O (2.4)
0 (-2,4)
O (2,6)
O (-2,6)
Answer:
(- 2, 4 )
Step-by-step explanation:
Given the 2 equations
3x + 5y = 14 → (1)
y = [tex]\frac{1}{2}[/tex] x + 5 → (2)
Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)
3x + 5([tex]\frac{1}{2}[/tex] x + 5) = 14
3x + [tex]\frac{5}{2}[/tex] x + 25 = 14
[tex]\frac{11}{2}[/tex] x + 25 = 14 ( subtract 25 from both sides )
[tex]\frac{11}{2}[/tex] x = - 11 ( multiply both sides by 2 )
11x = - 22 ( divide both sides by 11 )
x = - 2
Substitute x = - 2 into (2) for corresponding value of y
y = [tex]\frac{1}{2}[/tex] × - 2 + 5 = - 1 + 5 = 4
solution is (- 2, 4 )
Tell whether one figure is a reflection of the other figure
yes or no
Answer:
No
Step-by-step explanation:
There are 120 children of whom
9/7are boys. How many are boys?
NO LINKS. Find the segment length indicated. Assume that lines which appear to be tangent are tangent. PLEASE SHOW WORK!!
Answer:
? = 9.2
Step-by-step explanation:
The angle between a tangent and radius at the point of contact is 90°
Then the triangle shown is right with legs ? , 6.9 and hypotenuse = (6.9 + 4.2) = 11.5
Using Pythagoras' identity in the right triangle
?² + 6.9² = 11.5²
?² + 47.61 = 132.25 ( subtract 47.61 from both sides )
?² = 84.64 ( take the square root of both sides )
? = [tex]\sqrt{84.64}[/tex] = 9.2
Answer:
Solution given:
BC=BD=6.9 units
AD=4.6units
Now
AB=4.6+6.9=11.5units.
we have
<C=90°[the line from the tangent is perpendicular to the radius of circle]
we know that ∆ABC is a right angled triangle.
hypotenuse [h]=AB=11.5units
base[b]=BC=6.9 units
perpendicular [p]=x units
By using Pythagoras law
h²=p² +b²
11.5²=x²+6.9²
x²=11.5²-6.9²
x²=84.64
x=[tex] \sqrt{86.64} [/tex]=9.2
Sothe segment length indicated is 9.2 units.
How many American adults must be interviewed to estimate the proportion of all American adults who actively try to avoid drinking regular soda or pop within 0.01 margin of error with 95% confidence using the large-sample confidence interval
Answer:
9604 American adults must be interviewed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How many adults must be interviewed for the margin of error to be 0.01?
This is n, which is found for M = 0.01.
We have no estimate for the proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample size will be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.01 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.01})^2[/tex]
[tex]n = 9604[/tex]
9604 American adults must be interviewed.
A professor pays 25 cents for each blackboard error made in lecture to the student who pointsout the error. In a career ofnyears filled with blackboard errors, the total amount in dollarspaid can be approximated by a Gaussian random variableYnwith expected value 40nandand variance 100n. What is the probability that 20exceeds 1000
Answer:
The correct answer is "0.0000039110".
Step-by-step explanation:
The given values are:
[tex]Y_n\rightarrow N(\mu, \sigma^2)[/tex]
[tex]\mu = 40n[/tex]
[tex]\sigma^2=100n[/tex]
[tex]n=20[/tex]
then,
The required probability will be:
= [tex]P(Y_{20}>1000)[/tex]
= [tex]P(\frac{Y_{20}-\mu}{\sigma} >\frac{1000-40\times 20}{\sqrt{100\times 20} } )[/tex]
= [tex]P(Z>\frac{1000-800}{44.7214} )[/tex]
= [tex]P(Z>\frac{200}{44.7214} )[/tex]
= [tex]P(Z>4.47)[/tex]
By using the table, we get
= [tex]0.0000039110[/tex]
Can someone please help?
9514 1404 393
Answer:
x > 3 : bothx < 3 : g onlyx = 3 : f onlyx ≠ 3 : g onlyStep-by-step explanation:
The attached number lines show the domains of each function.
x > 3 — both number lines are included
x < 3 — only the g(x) domain is included
x = 3 — only the f(x) domain is included
x ≠ 3 — only the g(x) domain is included in the entire region
giving branliest for correct person.. incorrect doesnt get points or branliest..
Answer:
A
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
Need help due in 10!
Answer:
1. (28-2)x
2.(12+6)x
3.(15+1)x
Step-by-step explanation:
based on the information in the diagram?
Answer:
We can not use ASA property of congruence.
Step-by-step explanation:
In ΔHML and ΔHMK,
HL ≅ HK [Given]
LM ≅ KM [Given]
HM ≅ HM [Reflexive property]
m∠L ≅ m∠K [Given]
ASA property of congruence,
Angle-Side-Angle property of congruence.
False
SSS property of congruence,
Side-Side-Side property of congruence,
True
SAS property of congruence,
Side-Included Angle-Side property of congruence,
True.
Therefore, we can not use ASA property of congruence.
A sphere is cut into 8 congruent pieces. The radius of the
sphere is 8 centimeters. One piece is shown in the diagram,
What is the surface area of one piece of the sphere, as
shown in the diagram? Express the answer in terms .
Step-by-step explanation:
i hope this will help you!
Let Y1 denote the weight of a bulk item stocked by a supplier, with a uniform distribution over the interval (0, 1). The random variable Y2 denotes the weight of the item sold and is assumed to have a uniform distribution over the interval (0, y1), where y1 is a specific value of Y1. If the supplier stocked 5 6 ton, what amount in tons could be expected to be sold during the week
Answer:
5/12 ton
Step-by-step explanation:
Y1 ( uniform random variable ) : ( 0, 1 )
Y2 ( uniform distribution ) ; ( 0, y1 )
supplier stocked ; 5/6 ton
Determine the amount of tons expected to be sold
F ( y2 | y1 ) = 1 / y1
E ( y2 | y1 = 5/6 )
The number of tons expected to be sold = 5/12 ton
attached below is the detailed solution
find x and y. give answer in insimplified radical form, not decimal.
Finding x,
We will use Pythagoras theorem to determine the value of x:
[tex]9^{2} = {8}^{2} + {x}^{2} \\ 81 = 64 + {x}^{2} \\ 81 - 64 = {x}^{2} \\ {x}^{2} = 17 \\ x = \sqrt{17} [/tex]
Finding y,
We have to determine the angle, at the bottom left of the bigger triangle.
Using sine rule,
[tex] \frac{9}{sin(90)} = \frac{8}{sin(z)} \\ sin(z) = 0.8889 \\ z = {sin}^{ - 1} (0.8889) \\ z = 62.73[/tex]
To find the angle on the smaller triangle,
[tex]a = 90 - 62.73 \\ a = 27.27[/tex]
Finding the missing length of y,
[tex] \frac{ \sqrt{17} }{sin(62.73)} = \frac{m}{sin(27.27)} \\ m = 2[/tex]
So y = 2 + 8, y = 10
Alonzo deposits 300 into an account that pays simple interest at a rate of 4% per year . How much interest will he be paid in the first 4 years
Answer:
1200 was is interested in the first 4years
If X = 14 units and h = 7 units, then what is the area of the triangle shown above?
A. 196 square units
B. 98 square units
C. 24.5 square units
D. 49 square units
Please help me
Answer:
B
Step-by-step explanation:
Answer:
B is the answer 98 square units
Someone help me out my grads are bad
Answer:
19 in^2
Step-by-step explanation:
3in * 5in = 15in^2
2in * 2in = 4in^2
15in^2 + 4in^2 = 19in^2
Feel free to mark it as brainliest :D
Answer: 19
Step-by-step explanation:
Area of the square + Area of the Triangle
good luck my boi
What is Mary's location if she travels 3 units left and 4 units up from (5, 0)?
A - (2, 5)
B - (8, 6)
C - (2, 4)
D - (8, 5)
Answer:
here is the right answer
C- (2,4)
what is 125%of$500.00
Answer:
125 percent
Step-by-step explanation:
25 percent *500.00 =
(25:100)*500.00 =
(25*500.00):100 =
12500:100 = 125
Now we have: 25 percent of 500.00 = 125
Question: What is 25 percent of 500.00?
Percentage solution with steps:
Step 1: Our output value is 500.00.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$500.00=100\%$.
Step 4: Similarly, $x=25\%$.
Step 5: This results in a pair of simple equations:
$500.00=100\%(1)$.
$x=25\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{500.00}{x}=\frac{100\%}{25\%}$
Step 7: Again, the reciprocal of both sides gives
{x}/{500.00}={25}/{100}$
$Rightarrow x=125$
Therefore, $25\%$ of $500.00$ is $125$
Suppose y varies directly with x. When
x is 4, y is 10. Write the equation that
relates x and y
Answer: y = (5/2)x
Step-by-step explanation:
y varies directly with x implies that y∝x
To turn y∝x to a full equation, introduce a constant k to the right hand side.
Therefore, y = kx
Given that x is 4 and y is 10, substitute x and y in the equation above.
Then, 10 = 4k
4k = 10
k = 10/4
k = 5/2
Since k = 5/2, then the equation y = kx becomes,
y = (5/2)x
Find each angle measure.
Figures are not drawn.!!
Answer: See explanation
Step-by-step explanation:
1 . 61
2 124
3 27
4 29
Convert 600 bags of cement to tons
Answer:
the 600 bags of cement would weigh 25.5826 tonnes
Answer:
600-90 lb bags of cement weigh 27 tons
Step-by-step explanation:
You don't say how much each bag weighs. Let's suppose that that weight is 90 lb.
Then:
90 lb 1 ton
----------- * -------------- = 9/200 ton/bag
1 bag 2000 lb
Now multiply this by 600 bags:
9 tons 600 bags
--------------- * ------------------ = 27 tons
200 bags 1
600-90 lb bags of cement weigh 27 tons
1 4/5 is an example of a (n)
Answer:
Mixed Fraction
Step-by-step explanation:
A mixed fraction is a fraction with a whole number attached to it like 5 1/5 or 3 1/2
[tex]1\frac{4}{5}[/tex] is an example of a mixed fraction.
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers.
A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.
Properties of Mixed Numbers :
1. It is partly a whole number.
2. It is partly a fraction.
[tex]1\frac{4}{5}[/tex] is an example of a mixed fraction.
In [tex]1\frac{4}{5}[/tex] , 2 is the quotient, 4 is the remainder.
Find out more information about mixed fraction here
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