Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle. If (3x+3) (5x-9)
Answer:
39 degrees and 51 degrees respectively.
Step-by-step explanation:
Two angles are complementary if their sum adds up to 90 degrees.
Given the pair of complementary angles formed by the three support beams:
3x+3 and 5x-9
Then:
3x+3+5x-9=90 degrees
Collect like terms
3x+5x=90+9-3
8x=96
Divide both sides by 8
x=12
Therefore, the measure of each angle is:
[tex](3x+3)=3(12)+3=36+3=39^\circ\\(5x-9)=5(12)-9=60-9=51^\circ[/tex]
The measure of each angle is 39 degrees and 51 degrees respectively.
Answer:
39 and 51 degrees
Step-by-step explanation:
Please answer this correctly
Answer:
# of plants # of gardens
10-14 2
15-19 2
20-24 5
25-29 3
30-34 3
35-39 5
40-44 4
Step-by-step explanation:
10-14: 10, 12 (2 numbers)
15-19: 18, 19 (2 numbers)
20-24: 20, 22, 23, 24, 24 (5 numbers)
25-29: 25, 27, 38 (3 numbers)
30-34: 31, 33, 33 (3 numbers)
35-39: 36, 36, 36, 37, 38 (5 numbers)
40-44: 40, 44, 44, 44 (4 numbers)
Answer:
10-14 ⇒ 2
15-19 ⇒ 2
20-24 ⇒ 5
25-29 ⇒ 3
30-34 ⇒ 3
35-39 ⇒ 5
40-44 ⇒ 4
The sum of the ages of ahsan and his mother is 61 years.The difference in their ages is 29 years.By forming a pair of simultaneous linear equations,find (i)ahsan's present age (ii)the age of ahsan's mother when ahsan is 21 years old
Answer:
a. 16 years
b. 50 years
Step-by-step explanation:
Let us assume the age of Ahsan be X
And, the age of his mother be Y
It is mentioned in the question that the sum of the both ages to be 61 years and their difference is 29 years
So now the equation is as follows
X + Y = 61 .............................. (1)
-X + Y = 29 .............................. (2)
Now solve this
We get
2Y = 90
Y = 45 = Ahsan mother age age
Now put the value of Y in any of the above equation
So X would be
X = 61 - 45
= 16 i.e ahsan age
The mother age is
= 45 years + 5 years
= 50 years
The 5 years come from
= 21 years - 16 years
= 5 years
Discuss what some of those rules are, and how they get applied in your analysis. If an engineering challenge includes "more than one reasonable estimator," (Devore, p. 249, Example 6.1 in Section 6.1) how do engineers know which to pick, and what issues arise statistically and in engineering management when making those choices?
Answer:
The engineer must verify and verify through a statistical inference that estimates and possible parameters may emerge, as well as determine what hypothesis tests should be performed to draw the most accurate conclusion.
Step-by-step explanation:
The engineer must assume that there may be more than one reasonable estimator for a different event or experiment; Something that could help you would be to perform an estimation of parameters, in that estimation it is required to know the properties of the estimators; that is to say that the closer the value of an estimator is to the real value of the parameter, it could be said that it is the most efficient or exact extimator.
The average American generates 4.4 lbs of trash every day. We circulated fliers that listed tips on how to reduce wastefulness in three separate neighborhoods. For the next week, we measured the amount of trash each person produced each day in those neighborhoods. There were 625 people total in our study. The mean trash per person was 4.3 lbs with a standard deviation of 1
Determine your sample's score on the comparison distribution.
a) -2
b) -1
c) -1.5
d) -2.5
Answer:
[tex]z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z=\frac{4.3 -4.4}{\frac{1}{\sqrt{625}}}= -2.5[/tex]
And the best option would be:
d) -2.5
Step-by-step explanation:
For this problem we know that the true mean of trash every day is:
[tex]\mu =4.4[/tex]
And from the info given we also know that:
[tex]\bar X=4.3[/tex] represent the sample mean
[tex]n=625[/tex] sample size selected
[tex]\sigma = 1[/tex] the population standard deviation assumed
If we want to find the z score for the person we can use the following formula:
[tex]z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z=\frac{4.3 -4.4}{\frac{1}{\sqrt{625}}}= -2.5[/tex]
And the best option would be:
d) -2.5
Please answer this correctly
Answer:
First box is 4This is because 2 is the stem and the leaves are 1, 2, 4, and 5
so the numbers are 21, 22, 24, and, 25
Second box is 3This is because 2 is the stem for the leaves 6 and 7
3 is the stem for the leaf 0
So the numbers are 26, 27, and 30
Hope this helped
Answer:
As you know about the stem and leaf plot
1 |7 7 7 8 => 17, 17, 17, 18
2|1 2 4 5 6 7 => 21, 22, 24, 25, 26, 27
3|0 2 5 5 6 7 7 8 9 => 30, 32, 35, 35, 36, 37, 37, 38, 39
4|1 2 => 41, 42
Now we count to complete the table:
16-20 | 4 {17, 17, 17, 18}
21-25 | 4 {21, 22, 24, 25}
26-30 | 3 {26, 27, 30}
31-35 | 3 {32, 35, 35}
36-40 | 5 {36, 37, 37, 38, 39}
41-45 | 2 {41, 42}
Hope this helps!
Once a fire is reported to a fire insurance company, the company makes an initial estimate, X, of the amount it will pay to the claimant for the fire loss. When the claim is finally settled, the company pays an amount, Y, to the claimant. The comapny has determined that X and Y have the joint density functionf(x,y) = Given that the initial claim estiamted by the comapny is 2, determine the probability that the final settlement amount is between 1 and 3.
Answer:
The probability that the final settlement amount is between 1 and 3 given that the initial claim is 2 = (2/9) = 0.2222
Step-by-step explanation:
The complete question is presented in the attached image to this solution
The joint probability distribution is given as
f(x, y) = {2/[x²(x - 1)} × y^-[(2x-1)/(x-1)] for x>1 And y>1
Given that the initial claim estiamted by the comapny is 2, determine the probability that the final settlement amount is between 1 and 3.
That is, x = 2, and y ranges from 1 to 3
Inserting x = 2 into the expression, we obtain
f(y) = (1/2) × y⁻³ = (y⁻³/2)
The required probability would then be
P(1 < y ≤ 3) = ∫³₁ f(y) dy
= ∫³₁ (y⁻³/2) dy
= [y⁻²/-4]³₁
= [3⁻²/-4] - [1⁻²/-4]
= (-1/36) - (-1/4)
= (1/4) - (1/36)
= (8/36)
= (2/9) = 0.2222
Hope this Helps!!!
At a cell phone assembly plant, 75% of the cell phone keypads pass inspection. A random sample of 110 keypads is analyzed. Find the probability that more than 78% of the sample keypads pass inspection. Use at least five decimal places for the denominator.
Answer:
23.27%
Step-by-step explanation:
From the statement we know that random sample n is 110 and that p is 75% and x the percentage to evaluate is 78%
We have that the probability would be equal:
P (x > 0.78) = [tex]P(z <\frac{x-p}{\sqrt{\frac{p*(1-p)}{n} }})[/tex]
Replacing we have:
[tex]P(z <\frac{0.78-0.75}{\sqrt{\frac{0.75*(1-0.75)}{110} }})[/tex]
P ( z < 0.73) = 1 - P ( z => 0.73)
= 1 - 0.7673
= 0.2327
Therefore the probability is 23.27%
write 2^((5)/(2)) in surd form
Answer:
[tex]\sqrt{2^5}[/tex]
Step-by-step explanation:
The applicable rule of exponents is ...
[tex]\displaystyle a^{b/c}=\sqrt[c]{a^b}[/tex]
So, ...
[tex]2^{5/2}=\boxed{\sqrt{2^5}}[/tex]
_____
This can be simplified to ...
[tex]\sqrt{32}=4\sqrt{2}[/tex]
Find the distance from point B to point C.
Enter as a decimal rounded to the nearest tenth.
66°
5 mi
B
BC = [?] mi
Answer:
BC = 11.2 mi.
Step-by-step explanation:
Tan 66 = [tex]\frac{opposite }{adjacent}[/tex]
2.246 = [tex]\frac{BC}{5}[/tex]
=> BC = 5 × 2.246
=> BC = 11.2 mi.
Factor 5x4 - 30x2 - 135.
Answer:
20 - 60 - 135
95
Step-by-step explanation:
All you have to do is add/subtract the factors together
Answer:
5(x - 3)(x + 3)(x^2 + 3)
Step-by-step explanation:
First take out the GCF of the 3 numbers (5):-
= 5(x^4 - 6x^2 - 27)
= 5(x^2 - 9)(x^2 + 3)
= 5(x - 3)(x + 3)(x^2 + 3).
The mail arrival time to a department has a uniform distribution over 5 to 45 minutes. What is the probability that the mail arrival time is more than 25 minutes on a given day? Answer: (Round to 2 decimal places.)
Answer:
0.5
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X higher than x is given by the following formula.
[tex]P(X > x) = \frac{b - x}{b-a}[/tex]
The mail arrival time to a department has a uniform distribution over 5 to 45 minutes.
This means that [tex]a = 5, b = 45[/tex].
What is the probability that the mail arrival time is more than 25 minutes on a given day?
[tex]P(X > 25) = \frac{45 - 25}{45 - 5} = 0.5[/tex]
So the probability that the mail arrival time is more than 25 minutes on a given day is 0.5.
A television network, Network A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m. slot, Network A has selected its top show. If its rival network, Network B, schedules its top show during the same time slot, Network A estimates that it will get 1.1 million viewers. However, if Network B schedules a different show during that time slot, Network A estimates that it will get 1.9 million viewers. Network A believes that the probability that Network B will air their top show is 0.7 and the probability that Network B will air another show is 0.3. Determine the expected number of viewers for Network A's top show.
Answer:
1,280,000 (1.28 million.)
Step-by-step explanation:
If Network B schedules its top show (with a probability of 0.7), Network A will get 1.1 million viewers.
If Network B schedules a different show during that time slot, (with a probability of 0.3), Network A will get 1.9 million viewers.
Therefore, the probability distribution table of number of viewers of Network A is:
[tex]\left|\begin{array}{c|c|c}$Number of Viewers, x&1.1$ million&$1.7 million\\P(x)&0.7&0.3\end{array}\right|[/tex]
Therefore, the expected number of viewers for Network A's top show
= (1100000 X 0.7) + (1700000 X 0.3)
=1,280,000
The expected number of viewers for Network A's top show is 1.28 million.
Please please help me on this one!
Answer:
3422 x232
Step-by-step explanation:
A sample of 1300 computer chips revealed that 58% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 61% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
There is enough evidence to support the claim that that the actual percentage that do not fail is different from the stated percentage (61%).
Test statistic z = -2.19.
P-value = 0.03.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that that the actual percentage that do not fail is different from the stated percentage (61%).
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.61\\\\H_a:\pi\neq 0.61[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=1300.
The sample proportion is p=0.58.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.61*0.39}{1300}}\\\\\\ \sigma_p=\sqrt{0.000183}=0.014[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.58-0.61+0.5/1300}{0.014}=\dfrac{-0.03}{0.014}=-2.189[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z<-2.189)=0.03[/tex]
As the P-value (0.03) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that that the actual percentage that do not fail is different from the stated percentage (61%).
Question 1 of 10
2 Points
The standard form of the equation of a parabola is y = 7x2 + 14x + 4.
What is the vertex form of the equation?
A. y = 7(x + 1)2-3
B. y= 7(x + 2)2-3
c. y= 7(x + 1)2 + 3
D. y= 7(x + 2)2 + 3
SUBMIT
Answer:
A. y = 7(x + 1)²-3
Step-by-step explanation:
Parabola:
[tex]y = 7x^{2} + 14x + 4[/tex]
[tex]y = 7(x^{2} + 2x) + 4[/tex]
Putting into vertex form, remember that:
[tex](x + a)^{2} = x^{2} + 2ax + a^{2}[/tex]
In this question:
[tex]x^{2} + 2x[/tex], to put into this format:
[tex]x^{2} + 2x + 1 = (x + 1)^{2}[/tex]
We add one inside the parenthesis to do this. The parenthesis is multiplied by 7, so for the equivalent, we also have to subtract 7. Then
Vertex form:
[tex]y = 7(x^{2} + 2x + 1) + 4 - 7[/tex]
[tex]y = 7(x + 1)^{2} - 3[/tex]
So the correct answer is:
A. y = 7(x + 1)²-3
I sell hot dogs at a football game. I can make a hot dog for $0.65 and sell it for $1.00. If i sell 50 hot dogs, what is my profit? show your work
Answer:
17.50
Step-by-step explanation:
The profit on one hotdog is
1 - .65 = .35
Multiply by the number of hotdogs sold
.35 * 50 =17.50
Information about five planets is shown in the table below.
Planet Diameter (km) Mass (kg)
Mercury 4.88 x 10 3.3 x 1023
Jupiter 1.43 x 10 1.898 x 1027
Earth
1.28 104 5.97 x 1024
Mars
6.78 x 103 6.42 x 1023
Saturn
1.21 10% 5.68 x 1026
a) Write down the name of the planet with the greatest mass.
b) Work out the radius of Mercury giving your answer as an ordinary number.
c) Work out the difference between the masses of Jupiter and Saturn.
Give your answer in standard form.
Answer:
(a)Jupiter
(b)24.4 km
(c)[tex]1.33 \times 10^{27}$ kg[/tex]
Step-by-step explanation:
Part A
The planet with the greatest ma.ss is Jupiter.
It has a ma.ss of [tex]1.898 X 10^{27}$ kg[/tex]
Part B
The diameter of Mercury = 4.88 X 10
Radius = Diameter/2
Therefore:
Radius of Mercury
[tex]=\dfrac{4.88 X 10}{2}\\ =2.44 X 10\\=24.4$ km[/tex]
Part C
[tex]M$a.ss of Saturn = 5.68 X 10^{26}\\$Mass of Jupiter = 1.898 X 10^{27}\\$Difference in their ma.ss =(1.898 X 10^{27})-(5.68 X 10^{26})\\=1.33 \times 10^{27}$ kg[/tex]
Jack knows the surface area of a cylinder and its radius. He wants to find the cylinder's helght. He needs to rewrite the formula A = 2#r(+h)
to find the cylinder's height (h) In terms of the cylinder's surface area (A) and its radius (7). Which is the correct formula?
Answer:
h= pi(r)2/A or h= 3.14 times 7 times 2 divided by A
Step-by-step explanation:
u need to do the opposite of multiplication which is division to find the height
hope this helps
correct me if this is wrong
find the equation of the line that is perpendicular to y= -1/5x-3 and contains the point (1,2) answer all boxes please
Answer:
Y = 5x -3
Step-by-step explanation:
Let's look for the gradient to solve this question for.
We are given y= -1/5x-3
Any line perpendicular to the above line will have a graient of m'.
Where mm'= -1
m = -1/5 from the line equation
So
mm'= -1
-1/5m'= -1
m' =5
For the equation of point (1,2)
(Y-y1)/(x-x1) = m'
(Y-2)/(x-1)= 5
Y-2= 5x -5
Y = 5x -3
Which expression shows that the quotient {Read Attachment for full question}
Answer:
option 2
Step-by-step explanation:
2 / (3x - 1) ÷ 6 / (6x - 1)
= 2 / (3x - 1) * (6x - 1) / 6
= 1 / (3x - 1) * (6x - 1) / 3
= 6x - 1 / 9x - 3
How many edges and vertices does a prism with 100 sided end faced have ? Please answer as quickly as possible ≈[infinity]
Answer:
We have 300 edges and 200 vertices
Step-by-step explanation:
A prism is basically a 2D shape which extends into three dimensions. Thus, it has two end faces, and one face for each side on the original shape.
In addition to the two 100-sided polygons at top and bottom, the prism will also have 100 rectangular faces.
We will solve this by Euler’s formula which ks:
V - E + F = 2
where;
V is the number of vertices (corners),
E is the number of edges
F is the number of faces (of any polyhedron).
Number of vertices is 100 surrounding the top while it's 100 at the bottom. So total V = 100 + 100 = 200 .
The number of edges is 100 at the top, and 100 at the bottom. Also an additional 100 separating the hundred vertical faces.
Total number of edges is;
E = 100 + 100 + 100 = 300.
Thus, we have 300 edges and 200 vertices
(a) Explain what is wrong with the following ‘proof’:Statement:IfRis symmetric and transitive, thenRis reflexive."Proof":SupposeRis symmetric and transitive. Symmetric means thatx R yimpliesy R x. We apply transitivity tox R yandy R xto givex R x. Therefore,Ris reflexive.(b) Give an example of a relation on a set that is both symmetric and tran-sitive, but not reflexive
Answer:
Step-by-step explanation:
Recall that, in this case, the subset of X for which R is defined is called the domain of R. The mistake occurs when we assume that the domain R is the whole set X, but it could happen that R is not defined for some elements of X.
Recall the following example:
X = {2,4,6}.
We can define R as follows {(2,2), (4,4), (2,4), (4,2)}. We can easily check that this is a transitive and symmetric relation, but since we don't have the element (6,6) it fails to be reflexive.
Can advise on the solution?
Answer:
340
Step-by-step explanation:
If x is the amount of pages in the book we can write:
1/4x + 5 + 3/5(x - (1/4x + 5)) + 10 + 12 + 24 = x
1/4x + 51 + 3/5(3/4x - 5) = x
1/4x + 51 + 9/20x - 3 = x
7/10x + 48 = x
3/10x = 48
x = 160
Write the number six hundred and forty-
nine thousand and six in figures
Answer:
649,006
Step-by-step explanation:
Six hundred and forty nine thousand= 649,000
and six so we have
649006
THE ANSWER IS 649,006 HOPE IT HELPS
Suppose we want to study the weekly rate of alcohol drinking among USF undergraduate students. Which of the following would be the LEAST preferred method of randomly selecting participants?
A. Selecting a random sample of students from each residence hall
B. Selecting a random sample of students from the list of all undergraduate students from the university's registrar office
C. Selecting a random sample of students who have used the university health services in the past month
D. Selecting a random sample of students from each college
Answer:
Option D
Step-by-step explanation:
I think the least preferred method the researcher would like is to select a random sample of students from each college. This means the researcher would have to go to every college and randomly selects participants which is very exhausting. Thus, this would be the least prefer method over the others...
What is the quoteint of 2/3 in 2/9
State whether the decay is linear or exponential, and answer the associated question. The value of a car is decreasing by 9% per year. If the car is worth $11 comma 000 today, what will it be worth in two years? g
Answer:
ExponentialA(2)=$9109.10Step-by-step explanation:
Since the value of the car decreases by a common factor each year, the decay is exponential.
An exponential decay function is of the form
[tex]A(t)=A_0(1-r)^t$ where:\\Initial Value, A_0=\$11,000\\$Decay Factor, r=9%=0.09[/tex]
Therefore, the function modeling the car's decay is:
[tex]A(t)=11000(1-0.09)^t[/tex]
We want to determine the car's value in two years.
When t=2
[tex]A(2)=11000(1-0.09)^2\\A(2)=\$9109.10[/tex]
The value of the car in 2 years will be A(t)=$9109.10
Final value of the car after 2 years will be $9109.10
Value of the car decay by 9%.
Since, 9% is a common factor by which the value of car is decreasing,
Therefore, decay will be exponential.
Expression for the exponential decay is given by,
[tex]P=P_0(1-\frac{r}{100} )^t[/tex]
Here, [tex]P=[/tex] Final price
[tex]P_0=[/tex] Initial price
[tex]r=[/tex] Rate of decay
[tex]t=[/tex] time
If initial price of the car [tex]P_0=11000[/tex], rate of decay [tex]r=0.09[/tex] and [tex]t=[/tex] Number of years
By substituting the values in the expression,
P = [tex]11000(1-0.09)^2[/tex]
= 11000(0.91)²
= $9109.10
Therefore, final value of the car after 2 years will be $9109.10
Learn more,
https://brainly.com/question/24515212
Which is the better buy?. Store A $180 at 1/3 off Or Store B $110 at 10% off (SHOW YOUR WORK)
Answer:
not 100% sure but my answer is 110
Step-by-step explanation:
It is More Affordable and is the better Buy From All the other choices.
If f(x) = x^2 is reflected over the x-axis and the shifted 4 units down, what is the equation of the new function, g(x)?
Answer:
g(x) = -x² - 4
Step-by-step explanation:
In this case, we are only changing a (reflection and vertical shrink/stretch) and k (vertical movement)
k = -4 because we are moving 4 units down
a = -1 because we are just reflecting over the x-axis