Answers
Answer:
The answer is option AStep-by-step explanation:
To find the length of BC we use tan
tan ∅ = opposite / adjacent
From the question
AC is the opposite
BC is the adjacent
So we have
tan 61 = AC / BC
tan 61 = 47/BC
BC = 47/tan 61
BC = 26.05Hope this helps you
Related Questions
In 2010 polls indicated that 75% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2010?
We test the hypothesis that the percentage supporting mandatory testing is less than 75% this year The p-value is 0.013
Which of the following interpretation of this p-value is valid?
A. The probability that Americans have changed their opinion on this issue since 2010 is 0.013.
B. There is a 1.3% chance that the null hypothesis is true.
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Answers
Answer:
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 1000 Americans is under test. It is the result of the poll that 75% still favor mandatory testing.
24=3(n-5) solve for n
Answers
Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
Answer:
[tex]\boxed{\sf n=13}[/tex]
Step-by-step explanation:
[tex]\sf 24=3(n-5)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]\sf 24=3n-15[/tex]
[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]
[tex]\sf 24+15=3n-15+15[/tex]
[tex]\sf 39=3n[/tex]
[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]
[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]
[tex]\sf 13=n[/tex]
Given p(x) = x4 + x3 - 13x2 - 25x - 12
1. What is the remainder when p(x) is divided by X - 4?
2. Describe the relationship between the linear expression and the polynomial?
How do we describe the relationship?
Answers
When a number is divided by a number it results in a quotient and a remainder
E.g. 9 / 4 = 2 remainder 1
9 is the dividend
4 is the divisor
2 is the quotient
1 is the remainder
Same way when a polynomial is divided by a linear expression
E.g.
Ax^2 + bx + c / (x-b) = (x+a) + r
Which can be rearranged to
ax^2 + bx + c = (x+a)(x-b) + r
When x = - a or b, only the remainder is left since either (x+a)(x-b) is 0.
If x = - a or b is substituted into the polynomial and the value is 0 then there is no remainder,
This would suggest (x+a) or (x-b) are factors of the polynomial.
Now apply this logic to these questions
1. Let’s assume (x-4) is a factor, this would mean that when x=4 is substituted into the polynomial the answer would be 0.
This is the case, therefore the remainder is 0.
2. Having seen the logic above (applied using the remainder and factor theorem) the linear expression is a factor of the polynomial.
simplify (3+3 / x(x+1) )(x-3 / x(x-1) )
Answers
Answer:
I think it is [tex]\frac{6x-18}{x^{4} }[/tex]
Step-by-step explanation:
Find the smallest positive integer that is greater than $1$ and relatively prime to the product of the first 20 positive integers. Reminder: two numbers are relatively prime if their greatest common divisor is 1.
Answers
Answer:
23
Step-by-step explanation:
since the number is relatively prime to the product of the first 20 positive numbers
It number must not have factor of (1-20)
Therefore the smallest possible number is the next prime after 20
Answer is 23
The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).
Hence, The smallest possible number is the next prime after 20 is, 23
Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
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The area of a square is 64n36. What is the length of one side of the square?
Answers
Answer:
8n6
step by step explanation.
An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?
Answers
Answer
[tex]P= 0.144[/tex] ways
the coin can land tails either exactly 8 times or exactly 5 times in
[tex]0.144[/tex] ways
Step by step explanation:
THis is a binomial distribution
Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.
P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹
p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³
p=(9)+p(3)
p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴
P= (0.5)¹⁴ [C(14,9) + C(14,3)]
P= (0.5)¹⁴ [2002 * 364]
P= 1/16384 * (2002 +364)
P= 91091/2048
P= 0.144
Hence,the coin can land tails either exactly 8 times or exactly 5 times in
[tex] 0.144[/tex] ways
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)
Answers
Answer:
b. [tex]g(x)=f(x)-5[/tex]
Step-by-step explanation:
You have that the function f(x) has its y-intercept for y=3.
Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.
In this case you have that f(x) has been translated vertically downward.
The general way to translate a function vertically in the coordinate system is:
[tex]g(x)=f(x)+a[/tex] (1)
being a positive or negative.
if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:
a = -2 -3 = -5
Then, the answer is:
b. [tex]g(x)=f(x)-5[/tex]
Answer: g(x) = f(x) - 5
Step-by-step explanation:
just took this
6th grade math , help me please :)
Answers
Answer:
A. Eric rode 2 more miles per week than Kim rode
Step-by-step explanation:
Number of miles Kim rode bicycle in 9 weeks = 135 miles
Let x be the number of miles per week.
135miles => 9 weeks
x miles => 1 week
[tex] x = \frac{135}{9} [/tex]
[tex] x = 15 [/tex]
Kim rode the bicycle 15 miles per week
Number of miles Eric rode bicycle in 6 weeks = 102 miles
Let x be the number of miles per week Eric rides the bicycle.
102 miles => 6 weeks
x miles => 1 week
[tex] x = \frac{102}{6} [/tex]
[tex] x = 17 [/tex]
Kim rode the bicycle 17 miles per week
Comparing the number of miles per week they rode, we would conclude that: "Eric rode 2 more miles per week than Kim rode".
Two jokers are added to a $52$ card deck and the entire stack of $54$ cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answers
Answer:
52/3.
Step-by-step explanation:
There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.
Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:
For jokers: JJ---... there are 0 cards between. This will be the case also for ...
-JJ---...
--JJ---...
and so on, down to ...
...---JJ
The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.
__
For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.
__
Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...
[tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]
5/12 +( 5/12 + 3/4 ) =
Answers
Answer:
Proper: 15/4
Improper: 3 3/4
Step-by-step explanation:
Well to solve the following question,
5/12 + (5/12 + 3/4)
We solve the part in the parenthesis first,
5/12 + 3/4 = 14/4
Simplified -> 7/2
5/12 + 7/2
= 45/12
Simplified -> 15/4
Thus,
the answer is 15/4 or 3 3/4.
Hope this helps :)
Answer:
19/12= [tex]1 \frac{7}{12}[/tex]Step-by-step explanation:
[tex]\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\\\\=\frac{5}{12}+\frac{5}{12}+\frac{3}{4}\\\\\mathrm{Add\:similar\:elements:}\:\frac{5}{12}+\frac{5}{12}=2\times \frac{5}{12}\\=2\times \frac{5}{12}+\frac{3}{4}\\\\=\frac{5\times \:2}{12}\\\\=\frac{10}{12}\\\\=\frac{10}{12}\\\\=\frac{5}{6}+\frac{3}{4}\\L.C.M =12\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{5}{6}=\frac{5\cdot \:2}{6\times \:2}=\frac{10}{12}\\\\\frac{3}{4}=\frac{3\times \:3}{4\times \:3}=\frac{9}{12}\\[/tex]
[tex]\\=\frac{10}{12}+\frac{9}{12}\\\mathrm{Since\:the\:denominators\:are\:equal\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{10+9}{12}\\\\=\frac{19}{12}[/tex]
10=12-x what would match this equation
Answers
Answer:
x=2
Step-by-step explanation:
12-10=2
Answer:
x=2
Step-by-step explanation:
10=12-x
Subtract 12 from each side
10-12 = 12-12-x
-2 =-x
Multiply by -1
2 = x
Rachel's waist circumference is 37 inches and her hip circumference is 39 inches. Based on this information, what does her waist-to-hip ratio tell you?
Answers
Answer:
[tex]n = 0.949[/tex]. The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
Step-by-step explanation:
The waist-to-hip ratio of Rachel is:
[tex]n = \frac{37\,in}{39\,in}[/tex]
[tex]n = \frac{37}{39}[/tex]
[tex]n = 0.949[/tex]
The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
The length of her waist circumference is 94.9% the length of her hip circumference.
From the information given, Rachel's waist circumference is 37 inches and her hip circumference is 39 inches.
Therefore, her waist to hip ratio will be calculated thus:
n = 37/39
n = 0.949
This implies that the length of her waist circumference is 94.9% the length of her hip circumference.
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a warehouse had 3 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. all the shelves are full how many boxes are on the shelves all together?
Answers
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I think. I just multiplies the 3 numbers. Hope this helps (:
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I just multiplies the 3 numbers.
HELP! WILL GIVE BRAINLIEST!
Answers
Answer:
Her eye discourses; I will answer it.
I am too bold; ’tis not to me she speaks:
Two of the fairest stars in all the heaven,
Having some business, do entreat her eyes
To twinkle in their spheres till they return.
Step-by-step explanation:
A researcher studying public opinion of proposed Social Security changes and asks a random sample of adult Americans whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many adult Americans does the researcher need to sample in the following cases
(a) if 37% of all adult Americans support the changes?
(b) 25% of all adults Americans support the changes?
Answers
Complete question is;
A researcher studying public opinion of proposed Social Security changes and asks a random sample of 30 adult Americans whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many adult Americans does the researcher need to sample in the following cases
(a) if 37% of all adult Americans support the changes?
(b) 25% of all adults Americans support the changes?
Answer:
A) 13 adults
B) 23 adults
Step-by-step explanation:
A) We are given;
p = 37% = 0.37
Since we are told that this is an approximately normal distribution, we will use the formula;
np(1 - p) ≥ 10
Thus;
0.37n(1 - 0.37) ≥ 10
n ≥ 10/(0.63 × 0.37)
n ≥ 42.9
We need a whole number, thus n = 43
From the question, we have already 30 adults , so the required number of adults are; 43 - 30 = 13 adults
B) We are given;
p = 25% = 0.25
Since we are told that this is an approximately normal distribution, we will use the formula;
np(1 - p) ≥ 10
Thus;
0.25n(1 - 0.25) ≥ 10
n ≥ 10/(0.75 × 0.25)
n ≥ 53.33
n ≈ 53
From the question, we have already 30 adults , so the required number of adults are; 53 - 30 = 23 adults
Given that 243√3 =3^a, find the value of a
Answers
Answer:
a=11/5 OR 5.5
Step-by-step explanation:
A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.
Answers
Answer:
95% confidensce interval of the mean (two-tail) = [132.2, 139.2]
Step-by-step explanation:
Given:
N = size of sample = 61
m = sample mean = 135.7
s = sample standard deviation 13.7
Need 95% confidence interval
Solution.
alpha (95% confidence interval) = 0.05
(1-alpha/2) = 0.975 [two sided]
Equation for confidence interval of the mean
= m +/- t(1-alpha/2,N-1) * s / sqrt(N)
= 135.7 +/- 2.0003 * 13.7 / sqrt(60)
= [132.16, 139.24]
A 12 inch ruler is closest in length to which of the following metric units of measure 30cm 30000 mm 0.030 km or 30 m
Answers
Answer:
30 cm
Step-by-step explanation:
1 inch is 2.54 centimeters, and 2.54 times 12 is 30.48, which would be the closest.
The following metric units of measure is 30 cm
The correct option is (A)
What is measurement?Measurement” is the act of determining a target's size, length, weight, capacity, or other aspect.
How do you calculate unit conversion?Step 1: Write the conversion as a fraction.
Step 2: Multiply or divide, as required.
Step 3: Cancel the units (same units from top and bottom)
Step 4: Write the simplified answer with its correct unit.
Now, as we know that
1 inch = 2.54 cm
So, we can write
12 inch = 2.54 * 12
12 inch= 30.48 cm
Hence, the closest unit is 30 cm in the given metric system.
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A bicycle tire has a radius of 5 inches. To the nearest inch, how far does the tire travel when it makes 8 revolutions?
Answers
Answer:
251 inches
Step-by-step explanation:
c = 2πr
c = 2(3.14)(5) = 31.4
31.4 x 8 rev. = 251 inches
A certain article indicates that in a sample of 1,000 dog owners, 680 said that they take more pictures of their dog than of their significant others or friends, and 490 said that they are more likely to complain to their dog than to a friend. Suppose that it is reasonable to consider this sample as representative of the population of dog owners.
(a) Construct a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends. (Use a table or technology. Round your answers to three decimal places.)
(______),(_________)
(b) Construct a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend. (Use a table or technology. Round your answers to three decimal places.)
(_______),(_______)
Answers
Answer: a) a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).
b) a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).
Step-by-step explanation:
Confidence interval for a population proportion is given by:-
[tex]\hat{p}\pm z(\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]
, where [tex]\hat{p}[/tex] = sample proportion , n= sample size, z= critical z-value.
As per given,
a) n=1000
Sample proportion of dog owners say they take more pictures of their dog than of their significant others or friends =[tex]\hat{p}=\dfrac{680}{1000}=0.68[/tex]
critical value for 90% confidence = 1.645 [By table]
A 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends.
[tex]0.68\pm (1.645)\sqrt{\dfrac{0.68(1-0.68)}{1000}}\\\\\approx0.68\pm0.024=(0.68-0.024,0.68+0.024)=(0.656,0.704)[/tex]
Hence, a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).
b) Sample proportion of dog owners say they are more likely to complain to their dog than to a friend =[tex]\hat{p}=\dfrac{490}{1000}=0.49[/tex]
critical value for 95% confidence = 1.96 [By table]
A 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend:
[tex]0.49\pm (1.96)\sqrt{\dfrac{0.49(1-0.49)}{1000}}\\\\\approx0.49\pm0.031=(0.49-0.031,0.49+0.031)=(0.459,0.521)[/tex]
Hence, a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).
When a button is pressed, a computer program outputs a random even number greater than 0 less than 8. You press the button 4 times.
Can some help me with this?
Answers
Answer:
Well all even numbers between 0 and 8 are,
2, 4, 6, 8
Meaning if the button is pressed 4 times 2, 4, 6, or 8 will be outputted.
When press button 4 times. Then output of the program will be, [tex](2,4,6,2)[/tex]
Even number:Any number that can be exactly divided by 2 is called as an even number.
Given that, When a button is pressed, a computer program outputs a random even number greater than 0 less than 8.
Even numbers greater than 0 less than 8 are,
[tex]=2,4,6[/tex]
When press button 4 times. Then output of the program will be,
[tex]=(2,4,6,2)[/tex]
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Which inequality has a dashed boundary line when graphed? A y>=3/5x+1 B y>= -1/3x+1 C y>3x+1
Answers
Answer: C y>3x+1
Step-by-step explanation:
When we graph an inequality with strictly greater of less than sign ('<' or '>'), then the graph has a dashed boundary line .Further it indicates that it does not include the points on the line.From all the given options , only C contains inequality with '>' sign .
Hence, y>3x+1 is the inequality has a dashed boundary line when graphed.
hence, the correct option is C.
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
Answers
Answer:
[tex]B'(x,y) = (0,-2)[/tex]
Step-by-step explanation:
Given
The attached grid
Translation rule: [tex](x,y) = (x + 5, y - 2)[/tex]
Required
Determine the coordinates of B'
First, we have to write out the coordinates of B
[tex]B(x,y) = (-5,0)[/tex]
Next is to apply the translation rule [tex](x,y) = (x + 5, y - 2)[/tex]
[tex]B(x,y) = (-5,0)[/tex] becomes
[tex]B'(x,y) = B(x+5,y-2)[/tex]
Substitute -5 for x and 0 for y
[tex]B'(x,y) = (-5+5,0-2)[/tex]
[tex]B'(x,y) = (0,-2)[/tex]
find the values of x and y that make k ll j and m ll n
Answers
Answer:
x = 80
y = 130
Step-by-step explanation:
The 2 angles are supplementary. so, x-30 + x+50 = 180.
We solve and get 2x = 180-20
x = 80
y = x+50, because of parallel rules.
y = 130
Answer:
x = 80
y = 130
Step-by-step explanation:edge 2020
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answers
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
PLEASE HELP I WILL GIVE BRAINLIEST TO CORRECT ANSWER
A greengrocer has 38 lb of carrots when he opens on Monday morning. During the day
he gets a delivery of 60lb of carrots and sells 29 lb of the carrots. How many pounds of
carrots are left when he closes on Monday evening?
Answers
Answer:
9 is the answer
Step-by-step explanation:
got a delivery of 60ib...but dont have enough .thats why he or she sells 29..totally he or she have 38ib of carrots ...so when we subtract 38_29
its =9
Find the measure of the indicated angle to the nearest degree. Thanks.
Answers
Answer:
θ ≈ 40°
Step-by-step explanation:
Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
In the picture attached,
Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.
tanθ = [tex]\frac{19}{23}[/tex]
θ = [tex]\text{tan}^{-1}(\frac{19}{23})[/tex]
θ = 39.56
θ ≈ 40°
Hong buys a bag of 11 tangerines for $2.86.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Answers
Answer:
$0.26
Step-by-step explanation:
To find the unit price, divide the cost by the amount you have.
$2.86/11 = $0.26
The unit price is $0.26.
Hi any help is appreciated. Just wanna graduate:))
Answers
Answer: C
Step-by-step explanation:
h · k(x) = 2(3x - 5)(-2x + 1)
= (6x - 10)(-2x + 1)
= -12x² + 6x + 20x - 10
= -12x² + 26x - 10
Answer:
C
Step-by-step explanation:
h(x) × k(x)
= 2(3x - 5)(- 2x + 1) ← expand factors using FOIL
= 2(- 6x² + 3x + 10x - 5)
= 2(- 6x² + 13x - 5) ← distribute parenthesis by 2
= - 12x² + 26x - 10 → C