To find the distance AB across a river, a distance BC of 415 m is laid off on one side of the river. It is found that B = 112.2° and C = 18.3°. Find AB.
Answers
Answer:
AB or the distance across the river is about 171.36 meters.
Step-by-step explanation:
Please refer to the diagram below (not to scale). The area between the two blue lines is the river.
To find AB, we can use the Law of Sines. Recall that:
[tex]\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}[/tex]
BC (or a) is opposite to ∠A and AB (or c) is opposite to ∠C. Thus, we will substitute in these values.
First, find ∠A. The interior angles of a triangle must total 180°. Thus:
[tex]m\angle A + m\angle B + m\angle C = 180^\circ[/tex]
Substitute:
[tex]\displaystyle m\angle A + (112.2^\circ) +(18.3^\circ) = 180^\circ[/tex]
Solve for ∠A:
[tex]m\angle A = 49.5^\circ[/tex]
Substitute BC for a, AB for c, 49.5° for A and 18.3° for C into the Law of Sines. Thus:
[tex]\displaystyle \frac{\sin 49.5^\circ}{BC} = \frac{\sin 18.3^\circ}{AB}[/tex]
Since BC = 415 m:
[tex]\displaystyle \frac{\sin 49.5^\circ}{415} = \frac{\sin 18.3^\circ}{AB}[/tex]
Solve for AB. Cross-multiply:
[tex]\displaystyle AB \sin 49.5^\circ = 415\sin 18.3^\circ[/tex]
And divide:
[tex]\displaystyle AB = \frac{415\sin 18.3^\circ}{\sin 49.5^\circ}[/tex]
Use a calculator. Hence:
[tex]AB = 171.3648...\approx 171.36\text{ m}[/tex]
AB or the distance across the river is about 171.36 meters.
Related Questions
Which of these statements is NOT true regarding a randomized block design experiment?
a.)
This design has an advantage of controlling for variables that might confound the response.
b.)
The elements are randomly allocated to treatment and control groups.
c.)
The sample is divided into participants or subjects and then grouped by a variable of interest.
d.)
Elements are randomly selected from equal-sized blocks of the total population.
Answers
The correct answer is D. Elements are randomly selected from equal-sized blocks of the total population is NOT true regarding a randomized block design experiment
From the question we are told that one statement is NOT true regarding a randomized block design experiment.
Where
A) This design has an advantage of controlling for variables that might confound the response is TRUEB)The elements are randomly allocated to treatment and control groups is TRUEC)The sample is divided into participants or subjects and then grouped by a variable of interest is TRUED) Elements are randomly selected from equal-sized blocks of the total population is Not True
In conclusion
The all other Options are true except option D which states that Elements are randomly selected from equal-sized blocks of the total population.
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1. Find the HCF of the following numbers by prime factorisation and continued division method10,35,40
Answers
Answer:
Step-by-step explanation:
10 = 2*5
35 = 5*7
40 = 2*2*2*5
The number 5 is common to all three factorisations
So the HCF = 5.
Continued division:
10 and 35:
10) 35(3
30
5)10(2
10
0
- so the HCF of 10 and 35 is 5.
10 and 40:
10)40( 4
40
0
So the HCF of 10 and 40 is 10
We found HCF of 10 and 35 is 5 so:
HCF of 10, 35 and 40 is HCF of 5 and 10 which is 5.
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answers
Answer:
Step-by-step explanation:
Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods
1/PV (FV) = (PV(1 + r^n)1/PV divide by PV
ln(FV/PV) = ln(1 + r^n) convert to natural log function
ln(FV/PV) = n[ln(1 + r)] by simplifying
n = ln(FV/PV) / ln(1 + r) solve for n
n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually
n = 9
n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly
n = 104 months or 8.69 years
n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily
n = 3163 days or 8.67 years
Alternatively
A = P e ^(rt)
Given that r = 8%
= 8/100
= 0.08
2 = e^(0.08t)
ln(2)/0.08 = t
0.6931/0.08 = t
t= 8.664yrs
t = 8.67yrs
Which ever approach you choose to use,you will still arrive at the same answer.
Assume a random sample of size n is from a normal population. Assume a single sample t test is used to for hypothesis testing. The null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. If the sample size is decreased, and the Type I error rate is unchanged, then the Type II error rate will increase.a. Trueb. False
Answers
Answer:
true
Step-by-step explanation:
type 1 and type 2 are not independent of each other - as one increases, the other decreases
A type of related samples design in which participants are observed more than once is called a
A. repeated measures design
B. matched pairs design
C. matched samples design
D. both matched pairs design and matched samples design
Answers
Answer:
Option A (repeated measures design) is the correct option.
Step-by-step explanation:
Researchers as well as statisticians vary in terms of methods used mostly for repetitive measurements. Besides illustration, repeated models of measurements are however recognized as repeated analyzes of variance measurements, standardized considerations of measurements, or layouts of objects throughout them.The other three options are not related to the given instance. So that alternative A would be the correct choice.
James has a total of 66 dollars in his piggy bank. He only has one dollar bills and two dollar bills in his piggy bank. If there are a total of 49 bills in James's piggy bank, how many one dollar bills does he have?
Answers
Answer:
32 one-dollar bills.
Step-by-step explanation:
Let x represent one-dollar bills and y represent two-dollar bills.
He has a total of 49 bills. Therefore:
[tex]x+y=49[/tex]
The total amount of money James has is 66. x is worth one dollar, while y is worth two dollars. Therefore:
[tex]1x+2y=66\\x+2y=66[/tex]
We have a system of equations. Solve by substitution:
[tex]x+2y=66\\x+y=49\\x=49-y\\(49-y)+2y=66\\y=17\\x=49-17=32[/tex]
Therefore, James has 32 one-dollar bills and 17 two-dollar bills.
Checking:
[tex]32(1)+17(2)\stackrel{?}{=}66\\32(1)+17(2)\stackrel{\checkmark}{=}66\\\\32+17\stackrel{?}{=}49\\49\stackrel{\checkmark}{=}49[/tex]
Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131
Is there evidence to doubt the color distribution claimed by the website? Use =0.05
Answers
Answer:
Calculated χ² = 13.425
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
Step-by-step explanation:
Color Blue Orange Green Red Yellow Brown
Frequency 30 48 55 66 70 131
Expected 40 40 40 80 80 120
H0: The bag of plain M&Ms is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown
Ha: The color distribution is not equal to the distribution stated in the null hypothesis.
Calculate chi square
χ² = (30-40)² /40 + (48-40)²/40 + (55-40)²/40 + (66-80)²/80 + (70-80)²/80 + (131-120)²/120
χ² = 2.5 + 1.6 + 5.625 + 2.45 + 1.25= 13.425
The critical region for χ² for 5 degrees of freedom with ∝= 0.05 is
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
A right triangle has the following vertices Find the area of the triangle
(7,-3) (4,-3) (4,9)
20 pnts
Answers
Answer:
Area = 18 square units
Step-by-step explanation:
To find the area of the triangle, let's go through the following steps:
(i) Let the vertices be;
A = (7, -3)
B = (4, -3)
C = (4, 9)
(ii) The sides of the triangle are therefore,
AB, BC and CA
(iii) Using the distance formula, calculate the lengths of AB, BC and CA
[tex]AB = \sqrt{(7-4)^2 + ( -3 - (-3))^2}[/tex]
[tex]AB = \sqrt{3^2 + (0)^2}\\[/tex]
[tex]AB = \sqrt{9}[/tex]
[tex]AB = 3[/tex]
[tex]BC = \sqrt{(4-4)^2 + ( -3 - 9)^2}[/tex]
[tex]BC = \sqrt{0^2 + (-12)^2}[/tex]
[tex]BC = \sqrt{144}[/tex]
[tex]BC = 12[/tex]
[tex]CA = \sqrt{(4-7)^2 + ( 9 - (-3))^2}[/tex]
[tex]CA = \sqrt{(-3)^2 + (12)^2}[/tex]
[tex]CA = \sqrt{9 + 144}[/tex]
[tex]CA = \sqrt{153}[/tex]
[tex]CA = 12.4[/tex]
(iv) Now that we have all the sides, let's calculate the area of the triangle using the Heron's formula.
Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where;
p = [tex]\frac{a + b + c}{2}[/tex]
a, b and c are the sides of the triangle.
In our case,
let
a = AB = 3
b = BC = 12
c = CA = 12.4
∴ p = [tex]\frac{3 + 12 + 12.4}{2}[/tex]
p = 13.7
Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]
Area = [tex]\sqrt{13.7(13.7-3)(13.7-12)(13.7-12.4)}[/tex]
Area = [tex]\sqrt{13.7(10.7)(1.7)(1.3)}[/tex]
Area = [tex]\sqrt{323.9639}[/tex]
Area = 17.999
Area = 18 square units
OR
To get the area of the triangle, we can use a much simpler approach.
Since the triangle is a right triangle,
(i) the hypotenuse, which is the longest side is CA = 12.4
(ii) the other two sides are AB and BC. These two sides will form the right angle.
Therefore, we can use the relation:
Area = [tex]\frac{1}{2}[/tex] x base x height
Where;
the base or height can either be AB or BC
Area = [tex]\frac{1}{2}[/tex] x 3 x 12
Area = 18 square units
PS: In a right triangle, the other two sides apart from the hypotenuse form the right angle.
Pls help need this done hurry
Answers
Answer:
Shade 23 boxes
Step-by-step explanation:
This is the first two rows fully (all 10 boxes) and then three more from the third row.
xxxxxxxxxx
xxxxxxxxxx
xxx . . . . . . .
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A concern of Major League Baseball is that games last too long. Some executives in the league's headquarters believe that the mean length of games this past year exceeded 3 hours (180 minutes). To test this, the league selected a random sample of 80 games and found the following results: = 193 minutes and s = 16 minutes.
Based on these results, if the null hypothesis is tested using an alpha level equal to 0.10, which of the following is true?
a. The null hypothesis should be rejected if xbar > 182.31.
b. The test statistic is t = 1.2924.
c. Based on the sample data, the null hypothesis cannot be rejected.
d. It is possible that when the hypothesis test is completed, a Type II statistical error has been made.
Answers
Answer:
it is possible that when the hypothesis test is completed,a type ll statistical error has been made
Type an equation for the
following pattern.
X
Y
1
5
N
2
3
-1
y=[? ]x+[ ]
4
Answers
Answer:
Does the answer help you?
please mark this question as brainliest answer.Cause it take a few mins to solve your question.Tq
Does the equation, x + y = 6 show direct variation?
Answers
Answer:
Yeah, x varies directly with (6 - y)
Step-by-step explanation:
[tex]x = 6 - y \\ x = k(6 - y) \\ x \: \alpha \: (6 - y)[/tex]
Solve for x² in x²-3x+2=0
Answers
[tex]x^2-3x+2=0\\x^2-x-2x+2=0\\x(x-1)-2(x-1)=0\\(x-2)(x-1)=0\\x=2 \vee x=1\\\\x^2=4 \vee x^2=1[/tex]
Answer:
Step-by-step explanation:
First we try to factor x²-3x+2.
We have to look for two numbers that multiply to 2 and add -3.
The two numbers are -1 and -2.
(x-1)(x-2) = 0
x-1 = 0 -> x = 1
x-2 = -> x = 2
Now we find x^2.
(1)^2 = 1
(2)^2 =4
For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is
Answers
Answer:
1.16
Step-by-step explanation:
Given that;
For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.
This implies that:
P(0<Z<z) = 0.3770
P(Z < z)-P(Z < 0) = 0.3770
P(Z < z) = 0.3770 + P(Z < 0)
From the standard normal tables , P(Z < 0) =0.5
P(Z < z) = 0.3770 + 0.5
P(Z < z) = 0.877
SO to determine the value of z for which it is equal to 0.877, we look at the
table of standard normal distribution and locate the probability value of 0.8770. we advance to the left until the first column is reached, we see that the value was 1.1. similarly, we did the same in the upward direction until the top row is reached, the value was 0.06. The intersection of the row and column values gives the area to the two tail of z. (i.e 1.1 + 0.06 =1.16)
therefore, P(Z ≤ 1.16 ) = 0.877
What is the solution to this ?
Answers
Answer:
[tex]\boxed{\sf C. \ x\geq -4}[/tex]
Step-by-step explanation:
[tex]-8x+4\leq 36[/tex]
[tex]\sf Subtract \ 4 \ from \ both \ sides.[/tex]
[tex]-8x+4-4 \leq 36-4[/tex]
[tex]-8x\leq 32[/tex]
[tex]\sf Divide \ both \ sides \ by \ -8.[/tex]
[tex]\frac{-8x}{-8} \leq \frac{32}{-8}[/tex]
[tex]x\geq -4[/tex]
While organizing the magazines at the doctor's office, Camille put 12 magazines in the first pile, 15 magazines in the second pile, 18 magazines in the third pile, 21 magazines in the fourth pile, and 24 magazines in the fifth pile. If this pattern continues, how many magazines will Camille put in the sixth pile?
Answers
Answer:
27
Step-by-step explanation:
since you are adding 3 to the pile each time, on the 6th pile you would have 27 because 24 + 3 = 27
Which is the best definition of mathematical proof? a/A sequence of statements that demonstrates the truth of an assertion. b/Statements that show the assertion is false using a counterexample. c/A paragraph that always has three parts and shows that an assertion is true. d/Statements in any order that show that an assertion is true.
Answers
Answer:
A. A sequence of statements that demonstrates the truth of an assertion.
Step-by-step explanation:
Mathematical proofs are a series of statements in order that help prove that something is true.
Proofs do not prove that something is false, they are not always 3 parts, and they are not in any order, because they have to be in an organized sequence.
So, A is correct.
Answer:
A sequence of statements that demonstrates the truth of an assertion.
Step-by-step explanation:
Solve for x: 3(x + 1)= -2(x - 1) + 6.
Answers
Answer:
x=1
Step-by-step explanation:
3(x + 1)= -2(x - 1) + 6.
Distribute
3x+3 = -2x+2+6
Combine like terms
3x+3 = -2x+8
Add 2x to each side
3x+3+2x = 8
5x+3 = 8
Subtract 3 from each side
5x =5
Divide by 5
x =1
HELPPP ASPPP PLZZ Select the correct answer
Answers
Answer: Choice C
[tex]\frac{2x+3}{x+2}[/tex]
===============================================
Work Shown:
[tex]h(x) = f(x) \div g(x)\\\\h(x) = \frac{f(x)}{g(x)}\\\\h(x) = \frac{2x^2-x-6}{x^2-4}\\\\h(x) = \frac{(x-2)(2x+3)}{(x-2)(x+2)}\\\\h(x) = \frac{2x+3}{x+2}\\\\[/tex]
Optional Extra Info:
Keep in mind that [tex]x \ne 2[/tex] and [tex]x \ne -2[/tex] to avoid division by zero errors. We can plug in x = 2 just fine into the simplified version of h(x), but we always need to go back to the original.
Let R be a system consisting of rational expressions. Which operations are closed for R?
Answers
Answer:
D
Step-by-step explanation:A set is said to be closed under an operation when the application of the operation between any two elements of the set leads to an element that belongs to the same set. If a set is closed under an operation, it is said to have the closure property of that operation. When we combine two rational expressions by adding, subtracting, multiplying, or dividing, we get a rational expression. This pattern indicates that rational expressions are closed for all four operations.
A jar of honey is $2.40. How much do 4 jars of honey cost
Answers
Answer:
It would cost you 9.6 dollar .
I hope it is helpful mark me as brainlest and follow me for more good answer plz♥️♥️
Proof:
what is an example of a quintic bionomial?
Answers
quantic means with the degree of 5 and binomial means two terms.
Using the insurance company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period. Round your answer to four decimal places.
Answers
Answer: 19.2222
Step-by-step explanation:
given data;
no of tornadoes = 2,1,0 because it’s fewer than 3.
period = 14 years
probability of a tornado in a calendar year = 0.12
solution:
probability of exactly 2 tornadoes
= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )
= 0.0144 * 0.2451 * 1092
= 3.8541
probability of exac one tornado
= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )
= 0.12 * 0.2157 * 182
= 12.7109
probability of exactly 0 tornado
= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )
= 1 * 0.1898 * 14
= 2.6572
probability if fewer than 3 tornadoes
= 3.8541 + 12.7109 +2.6572
= 19.2222
If you roll 2 dice, what is the probability the sum is a 4, 7 or 10?
Answers
Answer:
4=3
7=6
10=3
Step-by-step explanation:
P4= (3,1), (1,3), (2,2)
P7= (6,1), (4,3), (5,2), (3,4), (2,5), (1,6)
P10= (5,5), ( 6,4), (4,6)
Help me please please please please
Answers
Answer:
1.
d. (-14) + (-8)
2.
a. (-14) + 8
Step-by-step explanation:
(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.
(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.
Answer:
1. D
2. A
Step-by-step explanation:
1. It asks you what expression has the same value as (-14)-8. All you need to do is find other equations that have the same value as that. So the equation is -14-8. IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5. If it's both negative: -(-5), it will be +5. If it is both positive: +(+5), it is going to be +5.
IMPORTANT!
- and + = -
- and - = +
+ and + = +
What we are looking for: -14-8
So choice A is (-14)+8 which is simplified to -14+8. So, this one isn't right.
Choice B: 14-(-8)= 14+8. So, it's incorrect.
Choice C: 14+(-8)= 14-8. Again, it's not -14-8 so it's not right.
Choice D: (-14)+(-8)= -14-8. This equation matches the one we are looking for! So it's correct!
2. Same thing as number 1. Let's simplify the equation it wants us to find first.
(-14)-(-8)= -14+8
So -14+8 is what we are looking for.
Choice A: (-14)+8= -14+8. It matches! So it is correct. Let's look at the other options anyway.
Choice B: 14-(-8)= 14+8. Nope. Not right.
Choice C: 14+(-8)= 14-8 because - always beats +. So, this one is also incorrect.
Choice D: (-14)+(-8)= -14-8. Oops, this is also wrong. So choice A is the right answer.
Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:
(When there is a number outside and inside a parentheses, multiply them.)
2(5)=10, CORRECT! 2+(5) is not 2 times 5. It's whatever is closest to the parentheses, in this case being the positive sign. So + and 5 is just 5!
IMPORTANT!
-2(-5)= - and - is positive, so positive (2 times 5). Positive 10.
-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.
+2(+5)= + and + is positive, so positive (2 times 5). Positive 10.
$88 tickets to the San Francisco 49ers game are offered at a 15%
discount. What is the sale price?
Answers
Answer:
74.80
Step-by-step explanation:
First find the discount
88 * 15%
88*.15
13.2
Subtract the discount from the original price
88-13.2
74.80
If the occurrence of one event does not influence the outcome of another event, then two events are:
A. conditional
B. disjoint
C. independent
D. interdependent
Answers
Answer:
C. Independent
Step-by-step explanation:
Independent events are events that have no impact on each other.
So, if the occurrence of an event doesn't influence the outcome of another, this means that they are independent because they do not impact each other.
This must mean C is correct because the two events have to be independent.
STUCK Basic geometry A for senior year school
Answers
Answer:
(C) A reflection across a horizontal line and a horizontal translation
Step-by-step explanation:
We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.
Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.
Hope this helped!
A survey of 500 randomly selected adults found that 57% say that they would take a ride in a fully self-driving car. The 95% confidence interval for the true proportion of all adults who would take a ride in a full self-driving car is found to be (0.5266, 0.6134). Can we conclude that the majority of all adults would take a ride in a fully self-driving car?
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
No; The data does not include all adults, so we cannot make a conclusion about the population.
No; The confidence interval limits are not large enough to determine that a majority rely only on cellular phones. The proportion would need to be much greater than 50%, and the one above is only slightly larger.
Yes; Since the proportion of adults who said yes is 57%, and this is higher than 50%, we can conclude that a majority would take a ride in a fully self-driving car.
Answers
Answer:
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The sample proportion is [tex]\r p = 0.57[/tex]
The 95% confidence interval is (0.5266, 0.6134)
Looking at the 95% confidence level interval we see that the sample proportion is within the interval and given that the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
If you have 2 distinct black playing cards and 2 distinct red playing cards, how many ways can you arrange the four cards given that the red cards can never be next to each other
Answers
Answer:
I'm not 100% on the interoperation of this question...
are the two red cars out of a 52 card deck and you can try all the combinations of two red and black cards ????
for this answer i will assume that you have 4 coins two nickels and 2 quarters
and the question is " how many ways can you arrange the four coins given that the nickels can not be next to the quarters"
in that case I think the answer is 8
Step-by-step explanation:
1- N1 Q1 N2 Q2
2- N1 Q2 N2 Q1
3- N2 Q1 N1 Q2
4- N2 Q2 N1 Q1
5- Q1 N2 Q2 N1
6- Q2 N2 Q1 N1
7- Q1 N1 Q2 N2
8- Q2 N1 Q1 N2
[tex]2\cdot \left(\left(2\:choose\:1\right)\:\cdot \:\left(2\:choose\:1\right)\right)[/tex]