Answer:
a) variable = X
N = 15
Mean = 50.0933
SE Mean = 1.58
StDev = 6.11
Variance = 37.3321
Sum = 751.40
b) 95% Confidence interval = (46.997, 53.190) = (47.00, 53.19)
Step-by-step explanation:
variable = X
N = ?
Mean = ?
SE Mean = 1.58
StDev = 6.11
Variance = ?
Sum = 751.40
To fill in the missing quantities, we need to use some of their formulas.
For N, the number of variables
SE = Standard Error of the mean = σₓ = (σ/√N)
σₓ = Standard Error of the mean = 1.58
σ = standard deviation of the sample = 6.11
N = sample size = ?
1.58 = (6.11/√N)
√N = (6.11/1.58) = 3.8671
N = 3.8671² = 14.954374299 = 15 to the nearest whole number.
For the Mean
Mean = (Sum of variables)/(Number of variables)
Mean = ?
Sum of variables = 751.40
Number of variables = N = 15
Mean = (751.40/15) = 50.0933333333 = 50.093
For Variance
Variance = (Standard deviation)² = (6.11)² = 37.3321
b) To compute the confidence interval.
idence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 50.0933
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample size is large enough for the sample properties to approximate the population properties.
To find the critical value from the z-tables,
z at 95% confidence level = 1.960 (from the z-distribution tables)
Standard error of the mean = σₓ = (σ/√N)
Already calculated to be 1.58
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 50.0933 ± (1.960 × 1.58)
CI = 50.0933 ± 3.0968
95% CI = (46.9965, 53.1901)
95% Confidence interval = (46.997, 53.190) = (47.00, 53.19)
Hope this Helps!!!
If 2x+9<32 then x could be
Answer:
x < 11.5
Step-by-step explanation:
2x + 9 < 32
(2x + 9) - 9 < 32 - 9
2x < 23
2x/2 < 23/2
x < 11.5
Answer:
x < 11 1/2
Step-by-step explanation:
2x+9<32
Subtract 9 from each side
2x+9-9 < 32-9
2x<23
Divide by 2
2x/2 <23/2
x < 11 1/2
X is any number less than 11 1/2
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]
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 58.2 σ=58.2. You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.
Answer:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
Step-by-step explanation:
Let's define some notation
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=58.2[/tex] represent the population standard deviation
n represent the sample size
[tex] ME =1[/tex] represent the margin of error desire
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
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
Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?
Got the explanation from classmates
N=??? I/Y=5 PV=1000000 PMT=-65000 FV=0
It will last 27 years.
Answer:
27 years
Step-by-step explanation:
The formula for the number of payments can be used:
N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03
There will be a couple thousand dollars left after the 27th payment.
The winnings will last 27 years.
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
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.
Betty has several of the standard six-sided dice that are common in many board games. If Betty rolls one of these dice, what is the probability that: She rolls a three. (enter the answer as a percent rounded to the nearest tenth as needed)
Answer:
16.7%
Step-by-step explanation:
Each of the six faces of a six-faced die shows one of the numbers: 1, 2, 3, 4, 5, 6.
A roll of a die is equally likely to land on any face, so the total number of possible outputs is 6, corresponding to the number of faces on the die.
The desired outcome here is 3, meaning the face that shows the number 3. Only one face has the number 3, so the number of desired outcomes is 1.
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(3) = 1/6 = 0.16666... = 16.7%
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.
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]
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 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.
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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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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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
find the LCM and solve, it's very very urgent.
Answers:
1. 10502. 12003. 12004. 33605. 10806. 480please see the attached picture for full solution..
Hope it helps....
Good luck on your assignment...
The area of a rectangular horse pasture is 268,500 square yards. The length of the pasture is 5 yards less than three times the width. What is the width of the pasture in yards? Do not include units in your answer. Please help right away! Thank you very much!
Answer: width = 300
Step-by-step explanation:
Area (A) = Length (L) x width (w)
Given: A = 268,500
L = 3w - 5
w = w
268,500 = (3w - 5) x (w)
268,500 = 3w² - 5w
0 = 3w² - 5w - 268,500
0 = (3w + 895) (w - 300)
0 = 3w + 895 0 = w - 300
-985/3 = w 300 = w
Since width cannot be negative, disregard w = -985/3
So the only valid answer is: w = 300
how many types of progression in mathematics?
Find the area of this parallelogram.
6 cm
11 cm
Step-by-step explanation:
given,
base( b) = 6cm
height (h)= 11cm
now, area of parallelogram (a)= b×h
or, a = 6cm ×11cm
therefore the area of parallelogram (p) is 66cm^2.
hope it helps...
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
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.
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
Among all pairs of numbers whose sum is 6, find a pair whose product is as large as possible. What is the maximum product? The pair of numbers whose sum is 6 and whose product is as large as possible is
Answer:
The pair of numbers is (3,3) while the maximum product is 9
Step-by-step explanation:
The pairs of numbers whose sum is 6 starting from zero is ;
0,6
1,5
2,4
3,3
Kindly note 2,4 is same as 4,2 , so there is no need for repetition
So the maximum product is 3 * 3 = 9 and the pair is 3,3
The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.
Calculation of the pair of the numbers:Since the sum of the pairs is 6
So, here are the following probabilities
0,6
1,5
2,4
3,3
Now if we multiply 3 and 3 so it comes 9 also it should be large
Therefore, The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.
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PLEASE HELP ME!!!!!! Consider what would happen if you were to slice a face at a vertex (cut a corner) of a particular polyhedron. You would see a new polygonal face where the old vertex used to be. What type of polygon would a slice of a cube at a vertex create? Explain how you know.
Answer:
See below.
Step-by-step explanation:
There are 3 edges and 3 faces projecting out from a vertex of a cube.
So the polygon produced would be a triangle.
Answer:
A triangle.
Step-by-step explanation:
As shown above, the plane which slices a corner intersects the polyhedron in [tex] n [/tex] faces which depend on the particular polyhedron.
Here it is a cube, and it intersects three faces. Since the intersection of two planes is a line and there are three planes to intersect with, there are three sides of the polygon.
Hence the polygon is a triangle.
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
Reese needs to understand the integer laws to complete his homework. As he recites his rules, he is overheard saying "a positive plus a positive is positive, a negative plus a negative is negative, and a positive plus a negative is a negative". Is he right? Explain why or why not?
Answer:
No
Step-by-step explanation:
Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.
To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.
To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.
Perform the operation 3/a^2+2/ab^2
Answer:
Step-by-step explanation:
Least common denominator = a²b²
[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]
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
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]
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