Answer:
495°
Step-by-step explanation:
To find a coterminal angle, simply add 360° to the given angle.
Answer:
The answer to this quesiton is C. 495
But the answers to the whole test are
1. A) Quadrant 1
2. B) –270° and 90°
3. D) 126° + (720n)°, for any integer n
4. A) –90° and 630°
5. A) (the first graph)
6. D) n = 6
7. C) x = y + 360 n, for any positive integer n
8. B) 10°
9. C) (the third graph)
10. C) 495°
Step-by-step explanation:
Just took it. Edg 2021. Hope this helps :) (smiley's name is George, George says hi)
What is the slope of the line that contains the points (7,-1)and(6,-4)
Answer:
3Solution,
Let the points be A and B
A(7,-1)--->( X1,y1)
B(6,-4)---->(x2,y2)
Now,
[tex] slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: = \frac{ - 4 - ( - 1)}{6 - 7} \\ \: \: \: \: \: \: = \frac{ - 4 + 1}{ - 1} \\ \: \: \: \: \: = \frac{ - 3}{ - 1} \\ \: \: \: \: = 3[/tex]
Hope this helps..
Good luck on your assignment..
Answer:
-1/3 (given that the first co-ordinate is the initial point)
Step-by-step explanation:
slope of a line is basically the change in y divided by the change in x.
we have the 2 co-ordinates (7,-1) , (6,-4)
lets find the change in x = 7 - 6 (the difference of the x - values of both the coordinates)
change in y = -1 - (-4)
change in x = -1
change in y = 3
now, slope is change in y / change in x
slope = -1/3
Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classnate?
Step-by-step explanation:
If all three sides have the same length then it's an equilateral triangle, if two sides are congruent then it's an isosceles triangle, and if there are no sides that have the same length then it's a scalene triangle.
Answer:
Sample Response: First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse.
Step-by-step explanation:
booyah
6th grade math :) help me please!
Answer:
b) 7r +r +2d) 3u +1 +7yStep-by-step explanation:
Identify the variable in each term. If two or more terms have the same variable, they are "like" terms.*
1) Like terms are found in selection b. They are 7r and r.
__
2) The variables in selection d are u and y, not the same. Only unlike terms are found in selection d. (Selection b has variables x, b, x. The x-terms are like terms and can be combined.)
_____
* Strictly speaking, it is the constellation of variables you want to match. For example, terms 3xy, 4xy², and -5x²y all have variables x and y, but the powers of those variables don't match from term to term. For terms to be "like", the variables and their powers need to match.
Tension needs to eat at least an extra 1,000 calories a day to prepare for running a marathon. He has only $25 to spend on the extra food he needs and will spend it on $0.75 donuts that have 360 calories each and $2 energy drinks that have 110 calories. This results in the following system of equations:
0.75d+2e≤25
360d+110e≥1,000
where d is donuts and e is energy drinks. Can Tension buy 8 donuts and 4 energy drinks?
Select the correct answer below:
Yes or No
Answer:
Yes, he can buy 8 donuts and 4 energy drinks.
Step-by-step explanation:
If Tension is able to buy 8 donuts and 4 energy drinks, then both inequalities would be valid when we use these numbers as inputs. Let's check each expression at a time:
[tex]0.75*d + 2*e \leq 25\\0.75*8 + 2*4 \leq 25\\6 + 8 \leq 25\\14 \leq 25[/tex]
The first one is valid, since 14 is less than 25. Let's check the second one.
[tex]360*d + 110*e \geq 1000\\360*8 + 110*4 \geq 1000\\2880 + 440 \geq 1000\\3320 \geq 1000[/tex]
The second one is also valid.
Since both expressions are valid, Tension can buy 8 donuts and 4 energy drinks and achieve his goal of having a caloric surplus of at least 1000 cal.
Which set of numbers can represent the lengths of the sides of a triangle? A. {1,2,3} B. {3,5,7} C. {3,9,14} D. {4,4,8}
The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.
What is a triangle?Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.
That is to say, 3+5 = 8 is greater than the third side which is 7.
Therefore, the set of numbers the would represent a triangle are 3,5,7.
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Suppose that c (x )equals 5 x cubed minus 40 x squared plus 21 comma 000 x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.
Answer
X= 64.8 gives the minimum average cost
Explanation:
The question can be interpreted as
C(x)= 5x^3 -40^2 + 21000x
To find the minimum total cost, we will need to find the minimum of
this function, then Analyze the derivatives.
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
The coordinates of the point that is a reflection of Y(-4, -2) across the x-axis are ( , ). The coordinates of the point that is a reflection of Y across the y-axis are ( , ).
Answer:
Reflection across the x-axis: (-4,2)
Reflection across the y-axis: (4,-2)
Step-by-step explanation:
Going based off of what I see, a reflection across the x axis changes "y" & the same rule applies to the y axis.
It should be an L shape.
15% as a fraction in its lowest terms is:
-3/20
-5/100
-1/15
-3/100
Answer:
3/20
Step-by-step explanation:
15%
15/100
/5 /5
3/20
To investigate whether or not people tend to marry spouses of similar ages or whether husbands tend to be older than their wives, a student gathered age data from a sample of 24 couples, taken from marriage licenses filed in Cumberland County, PA, in June and July 1993.
Diff(H-W)
1
-4
-4
18
2
2
1
1
2
1
0
4
2
-5
7
6
7
2
4
1
-6
1
2
-7
1
16
3
13
2
-1
-1
10
-1
1
0
-4
1
8
-1
-7
1
4
5
3
9
-5
3
-7
2
1
2
-4
0
12
4
13
-1
3
5
3
-2
2
0
2
0
2
13
-1
1
1
2
-3
6
1
1
-5
2
7
-2
-7
-1
1
9
1
-2
-1
3
5
-5
8
1
1
0
2
-2
-7
1
5
7
15
1) Define, in words.
A. The total difference in husband and wife marriage ages in Cumberland County; μd.
B. Average age of men and average age of women; μm and μw.
C. The average difference in husband and wife marriage ages in Cumberland County; μd.
2) Select the appropriate null and alternative hypotheses in the context of the study.
A. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is not 0.
B. Null: The average difference in marriage ages in Cumberland County is not 0. Alt: The average difference in marriage ages is 0.
C. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is less than 0.
D. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is greater than 0.
3) Select the appropriate null and alternative hypotheses in the context of the study depicted using symbols
A. Null: μd = 0, Alt: μd > 0
B. Null: μd = 0, Alt: μd ≠ 0
C. Null: μd > 0, Alt: μd = 0
D. Null: μd = 0, Alt: μd < 0
4) For the 24 couples, the husbands are, on average, 1.875 years older than their wives (SD = 4.812). Use these statistics and the Theory-Based Inference applet to conduct a test of significance and report the resulting p-value to four decimal places.
5) Based on the p-value, do you have strong evidence that, on average, husbands are older than their wives in Cumberland County?
Answer:
See explanation below
Explanation:
1) Option C is correct.
The average difference in husband and wife marriage ages in Cumberland County; μd
2) Option D is correct.
Null: The average difference in marriage ages in Cumberland County is 0.
Alt: The average difference in marriage ages is greater than 0.
3) Option A is correct
Null: μd = 0
Alt: μd > 0
4) Given:
n = 24
d' = 1.875
Sd = 4.812
Find test statistic:
[tex] t = \frac{d'}{Sd/\sqrt{n}} [/tex]
[tex] = \frac{1.875}{4.812/\sqrt{24}} [/tex]
[tex] t = 1.909 [/tex]
Degree of freedom, df = n - 1 = 24 - 1 = 23
Pvalue [tex] = (t_2_3 > 1.909) = 0.0344 [/tex]
Pvalue = 0.0344
Significance level = 0.05
5) Since p value is less than significance level, reject null hypothesis H0
Hence, there is strong evidence that, on average, husbands are older than their wives in Cumberland County
Answer:
CDA
Step-by-step explanation:
Dude trust me...
objective: Solve applications involving problem-s...
1 of 21 (0
1.1.A-4
Cookies are sold singly or in packages of 8 or 24. With this packaging, how many
ways can you buy 48 cookies?
Step-by-step explanation:
With the packaging of 8
48 cookies = 48 ÷ 8 = 6 boxes
With the packaging of 24
48 cookies = 48 ÷ 24 = 2 boxes
Right Angle Trigonometry
Applicatio
5 of 10
Round your answer to one decimal place.
Type in your response.
The angle between the string attached to a flying kite
and the ground is 60°
How far above the ground, in feet, is the kite if 220 ft
of string have been let out?
TT
Clear
Done
BA
220
760°
A
с
Menu
Answer:
Step-by-step explanation:
BC/220=sin 60
BC=220 sin 60=220×√3/2=110√3≈190.5 ft
Answer:
190.5 ft
Step-by-step explanation:
For the 60-deg angle, BC is the opposite leg. AB is the hypotenuse.
The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.
[tex] \sin A = \dfrac{opp}{hyp} [/tex]
[tex] \sin 60^\circ = \dfrac{BC}{220} [/tex]
[tex] BC = 220 \sin 60^\circ [/tex]
[tex] BC = 190.5 [/tex]
Which expressions are equivalent to 7x – 14? Check all that apply. 14 – 7x x – 2 –(14 – 7x) 7(x – 2) 3x – 14 + 4x 2x – 10 + 5x + 4
Answer:
-(14 - 7x)
7(x - 2)
3x - 14 + 4x
Step-by-step explanation:
The expressions have to equal 7x - 14.
-(14 - 7x)
-14 + 7x
7(x - 2)
7x - 14
3x - 14 + 4x
7x - 14
The equivalent expression for the given expression 7x - 14 will be 7(x – 2) and 3x – 14 + 4x.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 7x – 14. The equivalent expression to 7x - 14 will be,
E = 7(x – 2)
E = 7x - 14
E = 3x - 14 + 4x
E = 3x+ 4x - 14
E = 7x - 14
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Logs are stacked in a pile. The bottom row has 50 logs and next to bottom row has 49 logs. Each row has one less log than the row below it. How many logs will be there in 5th row? Use the recursive formula.
Answer:
46 logs on the 5th row.
Step-by-step explanation:
Number of logs on the nth row is
n = 50 - (n-1)
n = 51 - n (so on the first row we have 51 - 1 = 50 logs).
So on the 5th row we have 51 - 5 = 46 logs.
The given relation is an arithmetic progression, which can be solved using the recursive formula: aₙ = aₙ₋₁ + d.
The 5th row has 46 logs.
What is an arithmetic progression?An arithmetic progression is a special series in which every number is the sum of a fixed number, called the constant difference, and the first term.
The first term of the arithmetic progression is taken as a₁.
The constant difference is taken as d.
The n-th term of an arithmetic progression is found using the explicit formula:
aₙ = a₁ + (n - 1)d.
The recursive formula of an arithmetic progression is:
aₙ = aₙ₋₁ + d.
How to solve the question?In the question, we are informed that logs are stacked in a pile. The bottom row has 50 logs and the next bottom row has 49 logs. Each row has one less log than the row below it.
The number of rows represents an arithmetic progression, with the first term being the row in the bottom row having 50 logs, that is, a₁ = 50, and the constant difference, d = -1.
We are instructed to use the recursive formula. We know the recursive formula of an arithmetic progression is, aₙ = aₙ₋₁ + d.
a₁ = 50.
a₂ = a₁ + d = 50 + (-1) = 49.
a₃ = a₂ + d = 49 + (-1) = 48.
a₄ = a₃ + d = 48 + (-1) = 47.
a₅ = a₄ + d = 47 + (-1) = 46.
Hence, the 5th row will have 46 logs.
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Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 6 p plus 3 x plus 2 pxequals69. Suppose also that p and x are both functions of time, measured in days. Find the rate at which x is changing when xequals3, pequals5, and StartFraction dp Over dt EndFraction equals1.5.
Answer:
[tex]\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]
Step-by-step explanation:
The price p, in dollars, and the number of sales, x, of a certain item follow the equation: 6p+3x+2px=69
Taking the derivative of the equation with respect to time, we obtain:
[tex]6\dfrac{dp}{dt} +3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}+2x\dfrac{dp}{dt}=0\\$Rearranging$\\6\dfrac{dp}{dt}+2x\dfrac{dp}{dt}+3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}=0\\\\(6+2x)\dfrac{dp}{dt}+(3+2p)\dfrac{dx}{dt}=0[/tex]
When x=3, p=5 and [tex]\dfrac{dp}{dt}=1.5[/tex]
[tex](6+2(3))(1.5)+(3+2(5))\dfrac{dx}{dt}=0\\(6+6)(1.5)+(3+10)\dfrac{dx}{dt}=0\\18+13\dfrac{dx}{dt}=0\\13\dfrac{dx}{dt}=-18\\\dfrac{dx}{dt}=-\dfrac{18}{13}\\\\\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]
The number of sales, x is decreasing at a rate of 1.3846 sales per day.
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 27 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
Answer:
The probability is 12.66%.
This is a low probability, so it is unlikely for such a combined sample to test positive.
Step-by-step explanation:
If the probability of being infected is 0.005, the probability of not being infected is 0.995.
Then, to find the probability of at least one of the 27 people being infected P(A), we can find the complementary case: all people are not infected: P(A').
[tex]P(A') = 0.995^{27}[/tex]
[tex]P(A') = 0.8734[/tex]
Then we can find P(A) using:
[tex]P(A) + P(A') = 1[/tex]
[tex]P(A) = 1 - 0.8734[/tex]
[tex]P(A) = 0.1266 = 12.66\%[/tex]
This is a low probability, so it is unlikely for such a combined sample to test positive.
The perimeter of a triangle is 82 feet. One side of the triangle is 2 times the second side. The third side is 2 feet longer than the second side. Find the length of each side.
Answer:
Side 1: 40 feet
Side 2: 20 feet
Side 3: 22 feet
Step-by-step explanation:
Side 1 is twice the length of side 2 and side 2 is 20 feet, which means side 1 is 40 feet. Side 3 is the the length of the second side plus 2, which means it has a length of 22 feet.
The heights of American men are normally distributed. If a random sample of American men is taken and the confidence interval is (65.3,73.7), what is the sample mean x¯? Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.
Answer:
69.5Step-by-step explanation:
Given the confidence interval of the heights of american heights given as (65.3,73.7);
Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7
Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]
[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]
Hence, the sample mean is 69.5
Data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20-year-olds consumed alcoholic beverages in 2008.
(a) Suppose a random sample of the ten 18-20-year-olds is taken. Is the use of the binomial distribution appropriate for calculating the probability that exactly six consumed alcoholic beverages?
i. No, this follows the bimodal distribution.
ii. Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.
iii. No, the trials are not independent.
iv. No, the normal distribution should be used.
(b) Calculate the probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink.
(c) What is the probability that exactly four out of the ten 18-20-year-olds have not consumed an alcoholic beverage?
(d) What is the probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages?
Answer:
(a) Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.
(b) The probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is 0.203.
(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is 0.203.
(d) The probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is 0.167.
Step-by-step explanation:
We are given that data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20-year-olds consumed alcoholic beverages in 2008.
(a) The conditions required for any variable to be considered as a random variable is given by;
The experiment consists of identical trials.Each trial must have only two possibilities: success or failure.The trials must be independent of each other.So, in our question; all these conditions are satisfied which means the use of the binomial distribution is appropriate for calculating the probability that exactly six consumed alcoholic beverages.
Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.
(b) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 10 people
r = number of success = exactly 6
p = probability of success which in our question is % 18-20
year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.
So, X ~ Binom(n = 10, p = 0.697)
Now, the probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is given by = P(X = 6)
P(X = 3) = [tex]\binom{10}{6}\times 0.697^{6} \times (1-0.697)^{10-6}[/tex]
= [tex]210\times 0.697^{6} \times 0.303^{4}[/tex]
= 0.203
(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is given by = P(X = 4)
Here p = 1 - 0.697 = 0.303 because here our success is that people who have not consumed an alcoholic drink.
P(X = 4) = [tex]\binom{10}{4}\times 0.303^{4} \times (1-0.303)^{10-4}[/tex]
= [tex]210\times 0.303^{4} \times 0.697^{6}[/tex]
= 0.203
(d) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 5 people
r = number of success = at most 2
p = probability of success which in our question is % 18-20
year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.
So, X ~ Binom(n = 5, p = 0.697)
Now, the probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 3)
= [tex]\binom{5}{0}\times 0.697^{0} \times (1-0.697)^{5-0}+\binom{5}{1}\times 0.697^{1} \times (1-0.697)^{5-1}+\binom{5}{2}\times 0.697^{2} \times (1-0.697)^{5-2}[/tex]
= [tex]1\times 1\times 0.303^{5}+5 \times 0.697^{1} \times 0.303^{4}+10\times 0.697^{2} \times 0.303^{3}[/tex]
= 0.167
4. In ABC, AB = 8,BC = 10, and AC = 7
Order the angles of the triangle from smallest to largest.
a.
b.
C.
d.
Answer:
B, C, A
Step-by-step explanation:
If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.
Draw the triangle.
AC (7) is opposite from B
AB (8) is opposite from C
BC (10) is opposite from A
From smallest to largest: 7>8>10
7, 8, 10
or
B, C, A
A rectangle has a length of x and a width of 5x^3+4-x^2. What is the polynomial that models the perimeter of the rectangle
Answer:
[tex] L= x[/tex]
And the width for this case is:
[tex] W= 5x^3 +4 -x^2[/tex]
And we know that the perimeter is given by:
[tex] P= 2L +2W[/tex]
And replacing we got:
[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]
And symplifying we got:
[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]
Step-by-step explanation:
For this problem we know that the lenght of the rectangle is given by:
[tex] L= x[/tex]
And the width for this case is:
[tex] W= 5x^3 +4 -x^2[/tex]
And we know that the perimeter is given by:
[tex] P= 2L +2W[/tex]
And replacing we got:
[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]
And symplifying we got:
[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]
Find the indicated conditional probability
using the following two-way table:
P( Drive to school | Sophomore ) = [?]
Round to the nearest hundredth.
Answer:
0.07
Step-by-step explanation:
The number of sophmores is 2+25+3 = 30.
Of these sophmores, 2 drive to school.
So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.
Answer:
[tex]\large \boxed{0.07}[/tex]
Step-by-step explanation:
The usual question is, "What is the probability of A, given B?"
They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"
We must first complete your frequency table by calculating the totals for each row and column.
The table shows that there are 30 students, two of whom drive to school.
[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]
Which of the following graphs is described by the function given below?
y = 2x^2 + 8x + 3
Answer:
Option A
Step-by-step explanation:
Equation of the given quadratic function is,
y = 2x² + 8x + 3
y = 2(x² + 4x) + 3
= 2(x² + 4x + 4 - 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5
By comparing this equation with the equation of a quadratic function in vertex form,
y = a(x - h)² + k
Here (h, k) is the vertex of the parabola
Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)
Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.
Option (A). Graph A will be the answer.
how many types of progression in mathematics?
whats 1 and 1/2 + 2 and 3/10
Answer:
[tex]3\frac{4}{5}[/tex]
Step-by-step explanation:
You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.
10/10-->1
1/2--> 5/10
2--> 20/10
3/10, the denominator is already 10, so don't need to change.
10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]
Answer:
3 4/5
Step-by-step explanation:
hopefully this helped :3
Questions 16-17. Suppose a tortoise is 1000 feet from the ocean. Each day the tortoise travels three-fifths of the remaining distance to the ocean. Use this information to: Construct a model that represents the remaining distance that the tortoise must travel to reach the ocean.
Answer:
r(n) = 1000·(2/5)^n
Step-by-step explanation:
Since the tortoise travels 3/5 the remaining distance, the remaining distance at the end of the day is 2/5 of what it was at the beginning of the day. So, the function can be modeled by an exponential with a "growth" factor of 2/5:
r(n) = 1000·(2/5)^n
where r(n) is the number of remaining feet after n days of travel.
A survey was conducted that asked 1003 people how many books they had read in the past year. Results indicated that x= 14.8 Books & S= 16.6 books. construct a 95% confidence interval for the mean number of books read. Interpret the interval.
construct a 95% confidence interval for the mean number of books people read and interpret the results. Select the correct choice below and fill in the answer boxes to complete your choice.
a) if repeater samples are taken, 95% of them will have a sample mean between _______and __________.
b) there is a 95% chance that the true me number of books read is between ________ and ________.c) there is 95% confidence that the population mean number of books read is between __________ and _____.
Answer:
c) there is 95% confidence that the population mean number of books read is between 13.77 and 15.83.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=14.8.
The sample size is N=1003.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{16.6}{\sqrt{1003}}=\dfrac{16.6}{31.67}=0.524[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=1003-1=1002[/tex]
The t-value for a 95% confidence interval and 1002 degrees of freedom is t=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.96 \cdot 0.524=1.03[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 14.8-1.03=13.77\\\\UL=M+t \cdot s_M = 14.8+1.03=15.83[/tex]
The 95% confidence interval for the mean number of books read is (13.77, 15.83).
This indicates that there is 95% confidence that the true mean is within 13.77 and 15.83. Also, that if we take multiples samples, it is expected that 95% of the sample means will fall within this interval.
A poll agency reports that 75% of teenagers aged 12-17 own smartphones. A random sample of 234 teenagers is drawn. Round your answers to four decimal places as needed. Part 1. Find the mean . Part 2. out of 6 Find the standard deviation
Answer:
If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:
[tex] X \sim Binom(n=234, p=0.75)[/tex]
And the mean for this case would be:
[tex] E(X) =np = 234*0.75= 175.5[/tex]
And the standard deviation would be given by:
[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]
Step-by-step explanation:
If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:
[tex] X \sim Binom(n=234, p=0.75)[/tex]
And the mean for this case would be:
[tex] E(X) =np = 234*0.75= 175.5[/tex]
And the standard deviation would be given by:
[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]
We can show that ∆ABC is congruent to ∆A′B′C′ by a translation of
CHECK THE ATTACHMENT FOR COMPLETE QUESTION
Answer:
We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 unit(s) Left and a Reflection across the x axis.
Step-by-step explanation:
We were given triangles ABC and A'B'C' of which were told are congruents,
Now we can provide the coordinates of A and A' from the given triangles ΔABC and ΔA'B'C' ,if we choose a point of A from ΔABC and A' from ΔA'B'C' we have these coordinates;
A as (8,8) and A' (6,-8) from the two triangles.
If we shift A to A' , we have (8_6) = 2 unit for that of x- axis
If we try the shift on the y-coordinates we will see that there is no translation.
Hence, the only translation that take place is of 2 units left.
It can also be deducted that there is a reflection
by x-axis to form A'B'C' by the ΔABC.
BEST OF LUCK
Factor the trinomial!! PLEASE HELP and if possible please explain how to do this!!
Answer:
d. a = 39
Step-by-step explanation:
Question:
for which value of "a" will the trinomial be factorizable.
x^2+ax-40
For the expression to have integer factors, a = sum of the pairs of factors of -40.
-40 has following pairs of factors
{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }
meaning that the possible values of a are
+/- 39, +/- 18, +/- 6, +/- 3
out of which only +39 appears on answer d. a=39
A trailer in the shape of a rectangular prism has a volume of 3,816 cubic feet. The length of the trailer is 11 feet less than 8 times the width w, and the height is 1 foot more than the width. Please help right away! Thank you so much!
Answer:
Width = 8 ft
Length = 53 ft
Height = 9 ft
Step-by-step explanation:
Let width be x
Length will be 8x-11
Height will be x + 1
Volume = width x height x length
=
x * (8x-11) * (x+1) = 3816
(8x^2 - 11x) * (x+1) = 3816
8x^3 + 8x^2 - 11x^2 - 11x = 3816
8x^3 -3x^2 - 11x = 3816
8x^3+64x^2-61x^2-488x +477x-3816= 0
8x^2 (x-8)+61x(x-8)+488(x-8)
(x-8)(8x^2 + 61x + 477) = 0
x-8
8x^2 + 61x + 477 = 0
Solve the equations:
x = 8
Length = 8x -11 = 64-11 = 53
Height = 8+1 = 9
Answer:
8w^3-3w^2-11w=3816
Step-by-step explanation:
Find the equation, in terms of w, that could be used to find the dimensions of the trailer in feet. Your answer should be in the form of a polynomial equals a constant.