Answers
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.
tan(54) = 16/BC
BC = 16/tan(54)
BC = 11.62 units
Hope this helps!
Related Questions
C 89. What is the power of 5, so that 1 its value become ? (५ को घाताङ्क 25 कति हुदा त्यसको मान 25 हुन्छ ?) .7
Answers
C 89. What is the power of 5, so that 1 its value become ?
The power is 0. because if 0 is tge powwe of any variable or letters the value becomes 1.
Suppose a deck of cards contains 13 cards:
5 green cards numbered 1-5, 4 red cards numbered 1-4, and 4 blue cards numbered 1-4.
For 3.1-3.3, 5 draws are made without replacement. X is the number of green cards drawn and Y is the number of red cards drawn. Z is the sum of the numbers on the tickets.
G1 = first card is green
G2 = second card is green
Enter the probability as a fraction.
P(at least one green) = ______.
Answers
Answer:
[tex]P(G_1) = \frac{5}{13}[/tex]
[tex]P(G_2) = \frac{1}{3}[/tex]
[tex]P(X \ge 1) = \frac{25}{39}[/tex]
Step-by-step explanation:
Given
[tex]G = 5[/tex]
[tex]R = 4[/tex]
[tex]B = 4[/tex]
[tex]n = 13[/tex]
Solving (a): [tex]P(G_1)[/tex]
This is calculated as:
[tex]P(G_1) = \frac{G}{n}[/tex]
[tex]P(G_1) = \frac{5}{13}[/tex]
Solving (b): [tex]P(G_2)[/tex]
This is calculated as:
[tex]P(G_2) = \frac{G - 1}{n - 1}[/tex] -- this is so because the selection is without replacement
[tex]P(G_2) = \frac{5 - 1}{13 - 1}[/tex]
[tex]P(G_2) = \frac{4}{12}[/tex]
[tex]P(G_2) = \frac{1}{3}[/tex]
Solving (c): [tex]P(X \ge 1)[/tex]
Using the complement rule, we have:
[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]
To calculate [tex]P(X = 0)[/tex], we have:
[tex]G = 5[/tex] --- Green
[tex]G' = 8[/tex] ---- Not green
The probability that both selections are not green is:
[tex]P(X = 0) = P(G'_1) * P(G'_2)[/tex]
So, we have:
[tex]P(X = 0) = \frac{G'}{n} * \frac{G'-1}{n-1}[/tex]
[tex]P(X = 0) = \frac{8}{13} * \frac{8-1}{13-1}[/tex]
[tex]P(X = 0) = \frac{8}{13} * \frac{7}{12}[/tex]
Simplify
[tex]P(X = 0) = \frac{2}{13} * \frac{7}{3}[/tex]
[tex]P(X = 0) = \frac{14}{39}[/tex]
Recall that:
[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]
[tex]P(X \ge 1) = 1 - \frac{14}{39}[/tex]
Take LCM
[tex]P(X \ge 1) = \frac{39 -14}{39}[/tex]
[tex]P(X \ge 1) = \frac{25}{39}[/tex]
Use the equation d=z–9 to find the value of d when z=10.
d=
Answers
Step-by-step explanation:
d = z - 9
d = 10 - 9 ----> substitute
d = 1
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2
= 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance σ2 = 83.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Use the traditional method. Assume that a simple random sample is selected from a normally distributed population.
a. Check requirements.
b. Establish H0 and H1 and note the level of significance.
c. Find the sample test statistic.
d. Find Critical Value.
e. Conclude the test and interpret results.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
For a given function ƒ(x) = x2 – x + 1, the operation –ƒ(x) = –(x2 – x + 1) will result in a
A) reflection across the x-axis.
B) horizontal shrink.
C) reflection across the y-axis.
D) vertical shrink.
Answers
Given:
The function is:
[tex]f(x)=x^2-x+1[/tex]
To find:
The result of the operation [tex]-f(x)=-(x^2-x+1)[/tex].
Solution:
If [tex]g(x)=-f(x)[/tex], then the graph of f(x) is reflected across the x-axis to get the graph of g(x).
We have,
[tex]f(x)=x^2-x+1[/tex]
The given operation is:
[tex]-f(x)=-(x^2-x+1)[/tex]
So, it will result in a reflection across the x-axis.
Therefore, the correct option is A.
Answer:
A) reflection across the x-axis.
Step-by-step explanation: I took the test
a person who take 40 paces to cover 20m finds that a square field has a side that is 520 paces long .calculate the length of the side and the area of the field
Answers
The area of the square field is 67600 m² and the side is 260 m long.
What is square?A quadrilateral with all sides equal and all angles are right angles.
Given that, a person takes 40 paces to cover 20 m of a square field according to him the field has a side that is 520 paces long, we need to find the measure of the side and the area,
Since,
40 paces = 20 m
1 pace = 1/2 m
Therefore,
520 paces = 0.5 x 520 m
= 260 m
Therefore, the square field is 260 m long,
Area of the square field = side² = 260²
= 67600 m²
Hence, the area of the square field is 67600 m² and the side is 260 m long.
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A large cable company reports that 42% of its customers subscribe to its Internet service, 32% subscribe to its phone service and 23% subscribe to both its Internet service and phone service.
a) What is the probability that a randomly selected customer subscribes to the Internet service or the phone service?
b) What percent of customers subscribe to neither the Internet service nor the phone service?
Answers
9514 1404 393
Answer:
a) 51%
b) 49%
Step-by-step explanation:
a) P(A∪B) = P(A) +P(B) - P(A∩B)
P(A∪B) = 42% +32% -23% = 74% -23% = 51%
51% subscribe to one or the other.
__
b) P(¬A∩¬B) = P(¬(A∪B)) = 1 -P(A∪B) = 1 -51% = 49%
49% of customers subscribe to neither service.
muscle max gym charges a $30 fee to join plus $2 each day that you go workout. Capital cross-fit charges $10 to join and $4 each day you use the gym. After how many days of workouts would the two gyms have cost you the same amount of money?
Answers
Set up equations for each gym.
multiply daily cost by number of days(x) and add the fee:
Muscle max: 2x + 30
Capital: 4x + 10
Now set them
Equal to each other and solve for x:
2x + 30 = 4x + 10
Subtract 2x from both sides :
30 = 2x + 10
Subtract 10 from both sides :
20 = 2x
Divide both sides by 2:
X = 10
It will take 10 days
Cual es el capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de 1140
Answers
Answer:
El capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de $1140 es $3,600.
Step-by-step explanation:
Para determinar cuál es el capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de $1140 se debe realizar el siguiente cálculo:
6 / 2 = 3
10/60 = 0.16666
10 x 3.1666 = 31.666
31.666 = 1140
100 = x
100 x 1140 / 31.666 = X
114,000 / 31.666 = X
3,600 = X
Por lo tanto, el capital que prestado al 10% bimestral durante 6 meses y 10 días produce un interés de $1140 es $3,600.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 21 bag sample had a mean of 401 grams with a standard deviation of 26. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answers
Answer:
The decision rule is to Reject H0 if Z ≤ -1.282
Step-by-step explanation:
We are given;
Population mean; μ = 409 g
Sample mean; x¯ = 401 g
Sample size; n = 21
Standard deviation; s = 26
Let's define the hypotheses;
Null hypothesis; H0: μ = 409 g
Alternative hypothesis; Ha : μ ≠ 409 g
Formula for test statistic is;
z = (x¯ - μ)/(s/√n)
z = (401 - 409)/(26/√21)
z = -1.410
z-value is negative and thus this is a lower tail test.
At significance level of 0.1, the critical value is -1.282.
Thus, the decision rule is;
Reject H0 if Z ≤ -1.282
I NEED HELP ON MATH PLS
Answers
Answer:
5/2 or 2½ or 2.5
Step-by-step explanation:
20/8 = 2.5
10/4 = 2.5
What is the approximate value of log b to the nearest hundredth? 0.93 1.23 9.16 65.53
Answers
Answer:
1.23
Step-by-step explanation:
A population of bacteria contains 80 bacteria in generation 1 and triples in
population every generation. This sequence represents the number of
bacteria for the first few generations:
80, 240, 720, ...
What is the explicit formula for the number of bacteria in generation n?
A. a(n) = 80 + (n - 1)3
B. a(n) = 3.801-1
C. a(n) = 3 + (n-1)80
D. a(n) = 80.30-1
Answers
Answer:
A
Step-by-step explanation:
Answer:a(n)=80•3n-1
Step-by-step explanation:
On a map, the scale shown is 1 inch : 5 miles. If an island is 2.5 squire inches on the map, what is the actual area of the island? The actual island's area is square miles.
Answers
Answer:
62.5 square miles
Step-by-step explanation:
if the scale is 1 in. = 5 mi, then 1 square in. = 25 square miles
so if 1 in^2 = 25 mi^2
then you make a proportion
25/1 = x/2.5
(the square inches on the bottom and the square miles on top)
solving for x gives you
x=62.5 square miles
Find the missing side length in the image below
Answers
Suppose the distributor charges the artist a $40.00 cost for distribution, and the streaming services pays $4.00 per unit. (Note: One unit = one thousand streams)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Formula: y = 40x + 4 (Graph Attached)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
After how many streams will you pay for the distributor charges? (Hint: this is where the line crosses the x-axis, round to the nearest thousand)
Answers
Answer:
356 streams
Step-by-step explanation:
From the graph, you will see that the line cross the x-axis at x = 8.8
Substitute into the expression y = 40x + 4
y = 40(8.8)+4
y = 352 + 4
y = 356
Hence the distributor charges will be paid for after 356 streams
I want to know how to solve this equation
Answers
Answer:
B
Step-by-step explanation:
5³.5^×
simply means
5³×5^×
using indices rule,
multiplication is addition
5 is common
so 5(³+×)
hence 5^3+×
simplify 7-(3n+6)+10n
Answers
Answer:
1 + 7n
Step-by-step explanation:
7-(3n+6)+10n
7 - 3n - 6 + 10 n
1 - 7n
Answered by Gauthmath
If 25 burgers feed 15 kids how many burgers would feed 55 kids
Answers
Answer:
1375
Step-by-step explanation:
One angle of an isosceles triangle is 16 what are the other 2 angles
Answers
Answer:
other two angle will be
82
as 82+82+16 = 180'
Christian randomly selects students from his grade to rate a math test as easy, moderate, or difficult. Of the students he surveyed, 13 said the test was easy, 11 rated it as moderate, and 3 found it difficult. Assuming that all students took the same test, how many of the 162 total students in Christian’s grade would probably rate the test something other than easy?
A.
27
B.
78
C.
84
D.
126
Answers
Answer:
C.
84
Step-by-step explanation:
This question is solved using proportions.
From the sample:
11 + 3 = 14 out of 13 + 11 + 3 = 27 would rate the test something other than easy.
Out of 162:
Applying the rule of three:
14 - 27
x - 162
Applying cross multiplication:
[tex]27x = 14*162[/tex]
[tex]x = \frac{14*162}{27}[/tex]
[tex]x = 84[/tex]
Thus the correct answer is given by option C.
Answer:
I hope this helps
Step-by-step explanation:
Please help !!! Plzzzz
Answers
Explanation:
Because we have a midsegment, this means that it is half as long as the side it's parallel to. You can think of "mid" as "middle" and that could lead to "halfway" to remember to take half.
So z = 14/2 = 7
6. 5x = -25
a. X= 5
b. X=-5
c. x=2
Answers
Answer:
x = -5
Step-by-step explanation:
5x = -25
Divide each side by 5
5x/5 = -25/5
x = -5
Answer:
[tex]Option\ B,\ x = -5[/tex]
Step-by-step explanation:
Step 1: Divide both sides by 5
[tex]5x = -25[/tex]
[tex]5x / 5 = -25 / 5[/tex]
[tex]x = -25/5[/tex]
[tex]x = -5[/tex]
Answer: [tex]Option\ B,\ x = -5[/tex]
There are five cities in a network. The cost of building a road directly between i and j is the entry ai,j in the matrix below. An infinite entry indicates that there is a mountain in the way and the road cannot be built. Determine the least cost of making all the cities reachable from each other.
0 3 5 11 9
3 0 3 9 8
5 3 0 [infinity] 10
11 9 [infinity] 0 7
9 9 10 7 0
Answers
Solution :
Given :
There are five cities in a network and the cost of [tex]\text{building}[/tex] a road directly between [tex]i[/tex] and [tex]j[/tex] is the entry [tex]a_{i,j}[/tex]
[tex]a_{i,j}[/tex] refers to the matrix.
Road cannot be built because there is a mountain.
The given matrix :
[tex]\begin{bmatrix}0 & 3 & 5 & 11 & 9\\ 3 & 0 & 3 & 9 & 8\\ 5 & 3 & 0 & \infty & 10\\ 11 & 9 & \infty & 0 & 7\\ 9 & 8 & 10 & 7 & 0\end{bmatrix}[/tex]
The matrix on the left above corresponds to the weighted graph on the right.
Using the [tex]\text{Kruskal's algorithm}[/tex] we can select the cheapest edge that is not creating a cycle.
Starting with 2 edges of weight 3 and the edge of weight 5 is forbidden but the edge is 7 is available.
The edge of the weight 8 completes a minimum spanning tree and total weight 21.
If the edge of weight 8 had weight 10 then either of the edges of weight 9 could be chosen the complete the tree and in this case there could be 2 spanning trees with minimum value.
perimeter of a circle 8 centimeter wide
Answers
Answer:
25.13 cm
Step-by-step explanation:
Perimeter ( circumference ) of a circle = 2πr
Given,
The circle is 8 cm wide
which means,
The diameter (d) of the circle is 8 cm.
Radius (r) of the circle = d/2
= 8/2
= 4
Radius = 4 cm
Putting the value in the formula;
2πr
= 2 (22/7) (4)
= 25.13 cm (approx)
The pie chart shows the favorite type of book of the more than 50,000 high school students. About what percent of favorite type of book is drama? About what percent is mystery?
Complete the statements based on the information.
About
% of high school students chose dramas as their favorite type of book.
About
% of high school student chose mysteries as their favorite type of book.
Ans:
50%
25%
Answers
About 50% of high school student chose dramas as their favorite type of book.
About 25% of high school student chose mysteries as their favorite type of book.
Thus, 50% of high school students chose dramas as their favorite type of book and 25% of high school students chose mysteries as their favorite type of book.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
The pie chart shows the favorite type of book of more than 50,000 high school students.
As we know,
A circular statistical visual with slices illustrating a normal probability plot is named a pie chart. Each slice's arc length in a pie chart matches to the quantity it displays.
Thus, 50% of high school students chose dramas as their favorite type of book and 25% of high school students chose mysteries as their favorite type of book.
Learn more about the percentage here:
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7. A machine produces memory sticks of varying lengths, distributed uniformly between 3mm and 13 mm. Memory sticks longer than 10 mm do not meet the design criteria and must be scrapped. Calculate the proportion of memory sticks that will be scrapped, which is the probability that memory stickers longer than 10 mm will be scrapped.
Answers
Answer:
The proportion of memory sticks that will be scrapped is 0.3 = 30%.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Distributed uniformly between 3mm and 13 mm.
This means that [tex]a = 3, b = 13[/tex]
Calculate the proportion of memory sticks that will be scrapped:
[tex]P(X > 10) = \frac{13 - 10}{13 - 3} = \frac{3}{10} = 0.3[/tex]
The proportion of memory sticks that will be scrapped is 0.3 = 30%.
Please help explanation if possible
Answers
Answer:
Step-by-step explanation:
so d = 2r which means r = 5cm.
A = πr^2 = π(5)^2 = 25π = (25)(3.14) = 78.5 cm^2.
So input 78.5
Answer:
see below
Step-by-step explanation:
so d = 2r which means r = 5cm.
A = πr^2 = π(5)^2 = 25π = (25)(3.14) = 78.5 cm^2.
So input 78.5
HOPE IT HELPS YOU
Find y on this triangle
Answers
Answer:
5√3 / 2
Step-by-step explanation:
tan 30 = ( 5 / 2 ) / y
1 / √3 = 5 / 2y
2y = 5√3
y = 5√3 / 2
1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.
2. You are given the 3rd and 5th term of an geometric sequence. Describe how to determine the 10th term without finding the general term.
Answers
Step-by-step explanation:
1. In an arithmetic sequence, the general term can be written as
xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.
Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =
x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get
x₅-x₃ = 2d
divide by 2 to isolate d
(x₅-x₃)/2 = d
This lets us solve for d. Given d, we can say that
x₃ = y+d(2)
subtract 2*d from both sides to isolate the y
x₃ -2*d = y
Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of
xₙ = y + d(a-1)
2.
Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is
x₃* r * r
= x₃*r² = x₅
divide both sides by x₃ to isolate the r²
x₅/x₃ = r²
square root both sides
√(x₅/x₃) = ±r
One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.
Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence
