Answer:
estimated error=±0.725
Step-by-step explanation:
Side of the triangle= 12cm
Opposite of triangle x= 30
h= hypotenose side
Error= =±1
From trigonometry
Sin(x)=opposite/hypotenose
hypotenose=opposite/sin(x)
h=12/sin(x)
h=12Csc(x)
dh=-12Csc(x)Cot(x) dx...............eqn(1)
dx is the possible error in angle measurements
So we need to convert to radius
dx=±1°× (π/180)
=±1°(π/180)
Substitute x and dx into equation (1)
dh= - 12Csc30°Cot30°×[±(π/180)]
= -12(2)(√3)(±(π/180)
==±0.725
Therefore, estimated error=±0.725
When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense anymore.
a. True
b. False
Answer: b. False
Step-by-step explanation:
A dummy variable is a numerical variable used in regression analysis to represent values for categorical data by using value 0 (shows absence of particular category) or 1 (shows presence of particular category) .We cannot use categorical data to evaluate the slope coefficient (numerical value) until we convert them into dummies.Hence, the given statement is absolutely false.
6. If x + 2 is the only factor of the polynomial P(x),then P(2) is:
Options:
A. Cannot be determined
B. Not Zero
C. R(2)
D. Zero
Answer:
P(x) = x + 2p(2) = 2 + 2 p(2) = 4So option B is the answer.
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) is Not Zero. Therefore, the option B is the correct answer.
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
Given information;
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) :
P(x) = x + 2
p(2) = 2 + 2
p(2) = 4
The P(2) is Not Zero.
Therefore, the option B is the correct answer.
Learn more about standard form of a polynomial here:
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Please answer this correctly without making mistakes
Answer:
7/10 mi
Step-by-step explanation:
The total distance is 3 miles = 30/10 miles.
The other distances added gives 7/10+7/10+9/10 = 23/10
Therefore the last hop from Kingwood to Silvergrove is 30/10 - 23/10 = 7/10
Here is some information about the goals scored in some hockey games. Each game has four quarters. Please give the answer asap with full explanation and working out.
Answer:
8 home games and 10 away games
Step-by-step explanation:
Total home goals
= 8+5+9+8
= 30
Number of home games
= 30/3.75
= 8
Total away game goals
= 7+8+4+5
= 24
Number of away games
= 24/2.4
= 10
Answer:
i think it is 8 home and 10 away matches
Step-by-step explanation:
whats is 5% in words?
Here are a few ways 5% could be written in words:
-five percent
-five thousandths (0.05)
Hope this helps! :)
Answer:
0.05
Step-by-step explanation:
Assuming you mean as a decimal...
5/100 = 0.05
ALTERNATIVELY
5% = Five Percent
0.05 = Five Thousandths, Zero Point Zero Five
Question: Complete the point-slope equation of the line through (1,3)and (5,1). Use exact numbers. Equation: y-3=(Answer ?)
Answer:
y - 3 = -1/2(x - 1)
Step-by-step explanation:
Hey there!
Well point slope form is,
[tex]y - y_{1} = m(x - x_{1})[/tex]
We can use the point (1,3)
y - 3 = m(x - 1)
Now we need to find slope with the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex], we’ll use the points (1,3) and (5,1).
[tex]\frac{1-3}{5-1}[/tex]
-2/4
Slope or m = -1/2
y - 3 = -1/2(x - 1)
Hope this helps :)
if 80% of 2 is 200.what is 70% of 27
Answer:
18.90
Hope i got it right
pls help:Find all the missing elements:
Answer:
B = 48.7° , C = 61.3° , b = 12Step-by-step explanation:
In order to find B we must first angle C
To find angle C we use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]
From the question
a = 15
A = 70°
c = 14
So we have
[tex] \frac{15}{ \sin(70) } = \frac{14}{ \sin(C) } [/tex]
[tex] \sin(C) = \frac{14 \sin(7 0 ) }{15} [/tex]
[tex]C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} ) [/tex]
C = 61.288
C = 61.3° to the nearest tenthSince we've found C we can use it to find B.
Angles in a triangle add up to 180°
To find B add A and C and subtract it from 180°
That's
A + B + C = 180
B = 180 - A - C
B = 180 - 70 - 61.3
B = 48.7° to the nearest tenthTo find b we can use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) } [/tex]
[tex] \frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) } [/tex]
[tex] |b| = \frac{15 \sin(48.7) }{ \sin(70) } [/tex]
b = 11.9921
b = 12.0 to the nearest tenthHope this helps you
How many variables terms are in the expression 3xcube y+5xsquare+y+9
Answer: Please Give Me Brainliest, Thank You!
2
Step-by-step explanation:
There are two variables here, X and Y
How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 147 153 170 172 185 181 182 185 181 170 181 167 153 145
Answer:
Mean: 169.4
Median: 171
Mode: 181
Step-by-step explanation:
I first sorted the numbers by value, least to greatest.
145 147 153 153 167 170 170 172 181 181 181 182 185 185
We can see that 181 occurs the most, 3 times, so it's the mode.
The median of this set will be the middle number(s).
When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.
We can add all the numbers and divide by 14 to get the mean.
[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]
Hope this helped!
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55, then P( A| B) is:_________.
a. .19
b. 1.57
c. .64
d. .91
Answer:
P( A| B)= 0.35. None of the options are correctStep-by-step explanation:
Two events A and B are said to be independent if the occurrence of one of the events does not affect the other occurring. For example, the event of tossing two coins is an independent event since they occur simultaneously. Two events are therefore independent if the following are true.
P(A|B) = P(A)
P(B|A) = P(B)
P(A and B) = P(A)P(B)
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55,
then P( A| B) is a probability of A occurring provided that B has occurred. This is known as conditional probability for an independent event.
From the condition above for independent events, P(A|B) = P(A) and since P(A) = 0.35, hence P(A|B) =0.35
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time it takes to produce the product using the new machine is significantly less than the production time using the old machine. To test the claim, independent random samples were taken from both machines. You are given the following results.
New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain.
Answer:
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
Step-by-step explanation:
We must evaluate the differences of the means of the two machines, to do so, we will assume a CI of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).
New machine
Sample mean x₁ = 25
Sample variance s₁ = 27
Sample size n₁ = 45
Old machine
Sample mean x₂ = 23
Sample variance s₂ = 7,56
Sample size n₂ = 36
Test Hypothesis:
Null hypothesis H₀ x₂ - x₁ = d = 0
Alternative hypothesis Hₐ x₂ - x₁ < 0
CI = 90 % ⇒ α = 10 % α = 0,1 z(c) = - 1,28
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √s₁² / n₁ + s₂² / n₂
s₁ = 27 ⇒ s₁² = 729
n₁ = 45 ⇒ s₁² / n₁ = 16,2
s₂ = 7,56 ⇒ s₂² = 57,15
n₂ = 36 ⇒ s₂² / n₂ = 1,5876
√s₁² / n₁ + s₂² / n₂ = √ 16,2 + 1.5876 = 4,2175
z(s) = (23 - 25 )/4,2175
z(s) = - 0,4742
Comparing z(s) and z(c)
|z(s)| < | z(c)|
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean
Select the correct answer from each drop-down menu.
A cross section is the intersection of a
Solid or point and a plane or plane. Helpp
Answer:
solid, plane
Step-by-step explanation:
A cross section is the intersection of a solid and a plane.
Answer:
A cross section is the intersection of a solid and a plane.
Step-by-step explanation:
Got this right on plato, hope it helps :P
If two events are mutually exclusive, can they occur concurrently? Explain. Yes. By definition, mutually exclusive events can occur together. No. By definition, mutually exclusive events cannot occur together. No. Two events will never occur concurrently. Yes. Any two events can occur concurrently.
Answer:
No. By definition, mutually exclusive events cannot occur together.
Step-by-step explanation:
If two events are mutually exclusive, can they not occur concurrently because by definition, mutually exclusive events cannot occur together or at the same time. This ultimately implies that the events or outcome of the sampling is disjointed.
Mathematically, if two events A and B are mutually exclusive;
[tex]P(AnB) = 0[/tex]
From the above expression, we can deduce that the probability of the two (2) events occurring or having an intersection is zero (0).
[tex]P(A or B) = P(A) + P(B)[/tex]
From the above expression, we can deduce that the probability of either of the two (2) events occuring is the sum of the probability of each occurrence.
For example, when a fair die is tossed once, the outcomes are mutually exclusive.
P(d) = 1, 2, 3, 4, 5 and 6.
Other examples include;
1. Tossing a coin once, you'll either get a head or a tail but not a head and a tail at the same time.
2. In cards, both a king and an ace or a king and a queen are mutually exclusive because you can't have both occurring at the same time.
The probability that a company will launch the product A and B are 0.45 and 0.60 respectively, in main while, probability that both products launched, is 0.35. what is the probability that Neither will of these products launch ? At least one product will be launched ?
Answer:
a) what is the probability that Neither will of these products launch ?
= 0.30
b) At least one product will be launched ?
= 0.70
Step-by-step explanation:
From the above question, we have the following information:
P(A) = 0.45
P(B) = 0.60
P(A ∩ B) = P(A and B) launching = 0.35
Step 1
We find the Probability that A or B will launch
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
a) what is the probability that Neither will of these products launch ?
1 - Probability ( A or B will launch)
= 1 - 0.70
= 0.30
b)At least one product will be launched?
This is equivalent to the probability that A or B will be launched
P (A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 + 0.45 - 0.35
= 1.05 - 0.35
= 0.70
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
Find a polar equation r for the conic with its focus at the pole and the given eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form.)
Conic: Parabola Eccentricity: e = 1 Directrix: y = 4
Answer:
The equation is [tex]r = \frac{4 }{ 1 + cos (\theta )}[/tex]
Step-by-step explanation:
From the equation we are told that
The Eccentricity: e = 1
The Directrix is y = 4
Generally the polar equation for e = 1 and y = + c is mathematically represented as
[tex]r = \frac{e * c }{ 1 + ecos (\theta )}[/tex]
So
[tex]r = \frac{1 * 4 }{ 1 + 1 * cos (\theta )}[/tex]
[tex]r = \frac{4 }{ 1 + cos (\theta )}[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.
V6 18
311
123 45
6
7
8
+
x
Question: Perform the following computation with radicals. Simplify the answer. √6 • √8
Answer:
[tex] 4\sqrt{3} [/tex]
Step-by-step explanation:
Given, √6 • √8, to perform the computation, we would simply evaluate the radicals and try as much as possible to leave the answer in the simplest form in radicals.
Thus,
[tex] \sqrt{6}*\sqrt{8} = \sqrt{6*8} [/tex]
[tex] = \sqrt{48} [/tex]
[tex] = \sqrt{16*3} = \sqrt{16}*\sqrt{3}[/tex]
[tex] = 4\sqrt{3} [/tex]
The grade appeal process at a university requires that a jury be structured by selecting individuals randomly from a pool of students and faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of students and faculty
Correct question is ;
The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of nine students and eleven faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of six students and two faculty?
Answer:
A) 7.144 × 10^(-5)
B) 0.00131
C) 0.0367
Step-by-step explanation:
We are given;
Number of students = 9
Number of faculty members = 11
A) Now, the number of ways we can select eight students from 9 =
C(9, 8) = 9!/(8! × 1!) = 9
Also, number of ways of selecting 8 individuals out of the total of 20 = C(20,8) = 20!/(8! × 12!) = 125970
Thus, probability of selecting a jury of all students = 9/125970 = 7.144 × 10^(-5)
B) P(selecting a jury of all faculty) = (number of ways to choose 8 faculty out of 11 faculty)/(Total number of ways to choose 8 individuals out of 20 individuals) = [C(11,8)]/[C(20,8)] = (11!/(8! × 3!))/125970 = 0.00131
C) P(selecting a jury of six students and two faculty) = ((number of ways to choose 6 students out of 9 students) × (number of ways to choose 2 faculty out of 11 faculty))/(Total number of ways to choose 8 individuals out of 20 individuals) = [(C(9,6) × C(11,2)]/125970
This gives;
(84 × 55)/125970 = 0.0367
What is the approximate diameter of a sphere whose surface area is 83.96 square inches? Use π = 3.14.
Answer:
5.17
Step-by-step explanation:
The surface area of a sphere is 4[tex]\pi[/tex]r².
83.96=4[tex]\pi[/tex]r²
Divide by 4
20.99=3.14r²
divide by 3.14
6.6847=r²
take the square root
2.585=r
mulitply by 2 (diameter is twice the radius)
5.17
The diameter of the sphere is 5.17 inches.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called as the surface area.
The surface area of a sphere is 4πr².
83.96=4πr²
Divide by 4
20.99=3.14r²
Divide by 3.14
6.6847=r²
Take the square root.
2.585=r
Multiply by 2 (diameter is twice the radius).
r= 2 x 2.585
r = 5.17 inches
Therefore, the diameter of the sphere is 5.17 inches.
To know more about a surface area follow
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What is the sum of the complex numbers −9−i−9−i and −5−i−5−i?
Answer:
The sum of the complex numbers will be - 28 - 4i
Step-by-step explanation:
We have the sum −9−i−9−i + −5−i−5−i. Let's group like elements and simplify this expression,
−9−i−9−i + −5−i−5−i ( Group like terms )
- i - i - i - i - 9 - 9 - 5 - 5 ( Add like terms )
- i - i - i - i = - 4i, - 9 - 9 = - 18, and - 5 - 5 = - 10
- 18 - 10 = - 28 ( Substitute )
Solution : - 28 - 4i
Find the distance between points P(5, 1) and Q(3, 4) to the nearest tenth.
3.6
5
9.4
13
Answer:
≈ 3.6
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)
d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]
= [tex]\sqrt{(-2)^2+3^2}[/tex]
= [tex]\sqrt{4+9}[/tex]
= [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )
Answer:
3.6
Step-by-step explanation:
Look above bru
What is the value of the product (3 – 2i)(3 + 2i)?
Answer:
13
Step-by-step explanation:
(3 - 2i)(3 + 2i)
Expand
(9 + 6i - 6i - 4i^2)
Add
(9 - 4i^2)
Convert i^2
i^2 = ([tex]\sqrt{-1}[/tex])^2 = -1
(9 - 4(-1))
Add
(9 + 4)
= 13
Answer:
13.
Step-by-step explanation:
(3 - 2i)(3 + 2i)
= (3 * 3) + (-2i * 3) + (2i * 3) + (-2i * 2i)
= 9 - 6i + 6i - 4[tex]\sqrt{-1} ^{2}[/tex]
= 9 - 4(-1)
= 9 + 4
= 13
Hope this helps!
Select the best with the least expensive corn per ounce The choices are in the image
Answer:
B
Step-by-step explanation:
Option A:
1.50÷18≈0.0833
3.00÷36≈0.0833
4.50÷54≈0.0833
Option B:
0.75÷15=0.05
Option C:
2.20÷15=0.146
Algebra Review
Write an algebraic expression for each verbal expression.
1. the sum of one-third of a number and 27
2. the product of a number squared and 4
3. Write a verbal expression for 5n^3 +9.
Answer:
Step-by-step explanation:
1. The sum of one-third of a number and 27
= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]
2. The product of a number squared and 4
[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]
3.Write a verbal expression for 5n^3 +9.
The sum of the product and of 5 and a cubed number and 9
y - 4= -2(x + 3)
Complete the missing value in
the solution to the equation.
(-3, _ )
Answer:
4
Step-by-step explanation:
i distributed the -2 to what's in the parentheses. that equal 0. I then moved the 4 to the zero so that it becomes positive. I just assumed that you were ask for Y
Step-by-step explanation:
y-4=-2(x+3)....eq(1)
y- 4= -2x-6
y=-2x-2...eq(2)
subtituting equation 2 in equation 1
(-2x-2)-4=-2x-6
-2x-6=-2x-6
=0
In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. Group of answer choices may have different df values but they all have the same denominator all have the same df values and they all have the same denominator may have different df values and may have different denominators all have the same df values but they may have different denominators
Answer:
may have different df values but they all have the same denominator
Step-by-step explanation:
In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. may have different df values but they all have the same denominator
In two--factor analysis of variance, the estimates of the variance can be obtained by partitioning the total sum of squares into three components corresponding to the three possible sources of variation , viz; Between Rows, Between Columns, and Within Samples or error.
As the number of rows and columns may differ the degrees of freedom differ with them.
In other words
Total df= Rows df + Columns df + Error df
Since the variance is identically the same for each row of the c values and variance is the same for each observation in the jth column of r values the sum of squares becomes an identity.
Therefore it may have different df values but they all have the same denominator.
(3) In a group of 60 seldiers have enough food for
20 days - How many soldiers should leave the group
so that the food is enough for 100 days ? Find it.
Answer:
48 soldiers
Step-by-step explanation:
60 soldiers 20 days
x soldiers 100 days
60 x 20 = 1200 = 100x
Therefore x = 1200/100 = 12
60 - 12 = 48
Hope that helped!!! k
Answer:
30 Soldiers
Step-by-step explanation:
Given:
1) No of soldiers=60
No of days=20
2) No of days=100
No of soldiers=?
No of soldiers to leave=?
Solution:
Let us use the cross multiplication method.
Let x be the no of soldiers.
No of days No of soldiers
1) 20 60
2) 100 x
by cross multiplying,
20x=100 x 60
20x=600
x=600/20
x=30 soldiers
Therefore, No of soldiers to leave =60-30=30 soldiers
2. Find the value of the expression 21 – 2a if a = 3.
O A. 15
O B. 57
O C. 27
O D. 16
Answer:
A
Step-by-step explanation:
we just substitute the value of "a" given in the above expression we get
21-2(3)
21-6=15
Answer:
a. 15
Explanation:
Step 1 - Input the value of 'a' in the expression.
21 - 2a
21 - 2(3)
Step 2 - Multiply two and three
21 - 2(3)
21 - 6
Step 3 - Subtract six from twenty one
21 - 6
15
Therefore, the value of the expression 21 - 2a if a = 3 is a. 15.
A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate. Suppose it is known that heart rate (in beats per minute) is normally distributed with an average of 70 bpm for adults. A random sample of 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption, with a standard deviation of 7 bpm. In order to test belief at the 10% significance level, determine P-value for the test.
Answer:
Step-by-step explanation:
Given that:
mean μ = 70
sample size = 25
sample mean = 73
standard deviation = 7
level of significance = 0.10
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o : \mu = 70} \\ \\ \mathtt{H_1 : \mu > 70 }[/tex]
The z score for this statistics can be calculated by using the formula:
[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{73- 70}{\dfrac{7}{\sqrt{25}}}[/tex]
[tex]z = \dfrac{3}{\dfrac{7}{5}}[/tex]
[tex]z = \dfrac{3 \times 5}{{7}{}}[/tex]
z = 2.143
At level of significance of 0.10
degree of freedom = n -1
degree of freedom = 25 - 1
degree of freedom = 24
The p - value from the z score at level of significance of 0.10 and degree of freedom of 24 is:
P - value = 1 - (Z < 2.143)
P - value = 1 - 0.9839
P - value = 0.0161
Decision Rule: since P value is lesser than the level of significance, we reject the null hypothesis.
Conclusion: We conclude that energy drink consumption increases heart rate.
