Answer:
Calculated |t |= 7.72 > 2.1314 at 0.05 level of significance
Null hypothesis is rejected
The night shift-workers show more variability in their output levels are greater than day workers
Step-by-step explanation:
Step(i):-
Given first sample size n₁ = 9
Given mean of the first sample x₁⁻ = 520
Given sample variance of the first sample'S²₁' = = 38
Standard deviation of the first sample 'S₁' = √38 =6.16
Given second sample size n₂ = 8
Given mean of the second sample x₂⁻ = 540
Given sample variance of the second sample ( 'S²₂' = 20
Standard deviation of the second sample 'S₂' = √20 = 4.4712
Step(ii):-
Null hypothesis :H₀: σ²₁ =σ²₂
Alternative Hypothesis:H₁: σ²₁ > σ²₂
Test statistic
[tex]t = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S^2_{1} }{n_{1} }+\frac{S^2_{2} }{n_{2} } } }[/tex]
[tex]t = \frac{520 - 540 }{\sqrt{\frac{38 }{9 }+\frac{20 }{8 } } }[/tex]
t = - 7.72
|t| = |- 7.72| = 7.72
Degrees of freedom
ν = n₁ + n₂ -2 = 9 +8 -2 = 15
t₀.₀₅ = 2.1314
Final answer:-
Calculated |t |= 7.72 > 2.1314 at 0.05 level of significance
Null hypothesis is rejected
The night shift-workers show more variability in their output levels are greater than day workers
(d) A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 100ml of coffee. The machine actually dispenses a mean amount of 105ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispenses into each cup is normally distributed, find the standard deviation of the amount of coffee dispensed per cup in ml.
Answer:
The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Step-by-step explanation:
Let the random variable X denote the amount of coffee dispensed by the machine.
It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.
It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.
And 10% of the cups contain less than the amount stated on the sign.
To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of z for the above probability is, z = -1.28.
*Use a z-table
Compute the value of standard deviation as follows:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]-1.28=\frac{100-105}{\sigma}[/tex]
[tex]\sigma=\frac{-5}{-1.28}[/tex]
[tex]=3.90625\\\\\approx 3.91[/tex]
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
What values of a, b, and c would you use in the quadratic formula for the following equation? 6x^2+5x-4=0
Find the center (h,k) and radius r of the circle. Graph the equation. x^2 + y^2 - 2x - 10y + 1 = 0
Answer:
Center: (1, 5)
Radius: r = 5
Step-by-step explanation:
Step 1: Rewrite equation
x² - 2x + y² - 10y = -1
Step 2: Complete the Square (x2)
x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25
(x - 1)² + (y - 5)² = 25
Step 3: Find answers
Center = (h, k)
(1, 5) as Center
Radius = r
r² = 25
r = 5
Answer: Center = (1, 5)
Radius = 5
Step-by-step explanation:
The standard form for a circle is: (x - h)² + (y - k)² = r² where
Center = (h, k)Radius = rFirst, group the x's and group the y's in order to complete the square.
x² - 2x + y² - 10y = -1
↓ ↓
(-2/2)²=1 (-10/2)²=25
Add those values to BOTH sides:
x² - 2x + 1 + y² - 10y + 25 = -1 + 1 + 25
Rewrite the left side as perfect squares and simplify the right side.
(x - 1)² + (y - 5)² = 25
We end up with (h, k) = (1, 5) this is the center
and r² = 25 --> r = 5 this is the radius
To graph the circle, place an x at the center (1, 5). Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.
Can some help me if your good at maths
Answer:
36=2×3×3×3
36=2×3³Answer
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
Step-by-step explanation:
First write the prime factors of 36 that you can see here
[tex]2 \: \: \: 2 \: \: \: 3 \: \: \: 3[/tex]
Now write 36 as a product of its prime factors.
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
I earn $20.00 in 4 hours. At this rate, how much will i earn in 28 hours (show your work)
Answer:
140$
Step-by-step explanation:
4 hours = 20
28 hours divided by 4 is 7
7 x 20 = 140
Find the area of a circle with a circumference of 6.28 units
Answer:
The answer would be 3.14
Step-by-step explanation:
6.28
2 π
≈ 6.28
2 ⋅ 3.14 = 1
Areaπ r 2 ≈ 3.14 ⋅ 1 2 =
3.14
Hope that was helpful.Thank you!!!
Answer:
Step-by-step explanation:
Circumference = 6.28 units
2πr = 6.28
2*3.14 *r = 6.28
[tex]r=\frac{6.28}{2*3.14}\\\\[/tex]
r = 1 unit
Area =πr²
= 3.14 * 1 * 1
= 3.14 square units
What is the value of g(9)?
Plz answer ASAP with work ty!
Answer: [tex]8\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\frac{2^4\sqrt{3}}{\sqrt{2}}[/tex]
[tex]2^{\frac{7}{2}}\sqrt{3}[/tex]
[tex]2^{\frac{7}{2}}=2^{3+\frac{1}{2}}[/tex]
[tex]2^3\cdot \:2^{\frac{1}{2}}[/tex]=
[tex]2^3\sqrt{2}[/tex]
= [tex]2^3\sqrt{2}\sqrt{3}[/tex]=
[tex]2^3\sqrt{2\cdot \:3}[/tex]
=[tex]2^3\sqrt{6}[/tex]
[tex]2^3=8[/tex]
Answer- [tex]8\sqrt{6}[/tex]
In a bag there are 2 red, 3 yellow, 4 green, and 6 blue marbles.
What is the probability of P (yellow or green)?
Answer:
7/15
Step-by-step explanation:
There are 15 marbles total. -->
3 of them are yellow => 4 of them are green
3 + 4 = 7
7/15
Hope This Helps!
Answer: 7/15=46%
Step-by-step explanation:
There is in total of 15 marbles
but 3 of them are yellow and 4 are green.
4+3=7
7/15=0.466...
7/15≈0.46
0.46=46%
Evaluate the expression (1/5) to the 3rd power
Answer:
1/125
Step-by-step explanation:
(1/5) ^3
1/5 *1/5 *1/5
1/125
The formula for the area of a parallelogram is A = bh,
where b is the base and h is the height.
(x-4) cm
(2x2 + 2x-6) cm
(Not drawn to scale)
Answer:
B) 2x³ – 6x² – 14x + 24 square centimetersStep-by-step explanation:
The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.
"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"
Area of a parallelogram = Base * Height.
Given the height of the parallelogram = (x-4)cm
Base = (2x² + 2x-6) cm
Area of the parallelogram = (x-4)cm * (2x² + 2x-6) cm
Area of the parallelogram = (x-4)(2x²+2x-6)
Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24
= 2x³+2x²-8x²-6x-8x+24
= (2x³-6x²-14x+24)cm²
Some equilateral triangles are not isosceles.
O A. True
O
B. False
Answer: B. false
Step-by-step explanation:
An equilateral triangle has 3 equal sides
Isosceles triangle has two equal sides.
Which means that equilateral triangles cannot become isosceles.
Answer:
False
Step-by-step explanation:
An equilateral triangle has all three sides equal
An isosceles triangle has at least 2 sides equal
An equilateral triangle is a special isosceles triangle
Find the sum of the first 100 terms of the arithmetic sequence with the first term 2 and the common difference 5. plz only answer if you actually have read the question and know the answer.
Answer:
25,200
Step-by-step explanation:
To find the sum of an arithmetic series, one can use the formula for an arithmetic series: n×[tex]\frac{(term 1)+(final term)}{2}[/tex]=the sum of the series.
To find the final term we need to use the rule: the first term is 2, so you will have to add on two at the end, and then each term is 5 larger than the last, so if you want to quickly calculate the 100th term you can multiply (which is basically just fast addition). The formula for the 100th term is 5(100)+2=502.
Now you have all of the necessary parts for the sum of the series formula: n=100, first term=2, final term=502.
100×[tex]\frac{2+502}{2}[/tex]=100×[tex]\frac{504}{2}[/tex]=100×252=25,200.
Answer:
24950
Step-by-step explanation:
100th term is 497 and we then use the gause method which is (1+497)*497/2
A simulated exercise gave n = 20 observations on escape time (sec) for oil workers, from which the sample mean and sample standard deviation are 370.42 and 25.74, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 min. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using a significance level of .05. (Give t to 2 decimal places and the p-value to 3 decimal places.)t =P-value =ConclusionReject the null hypothesis, there is significant evidence that true average escape time exceeds 6 min. Reject the null hypothesis, there is not significant evidence that true average escape time exceeds 6 min. Fail to reject the null hypothesis, there is not significant evidence that true average escape time exceeds 6 min. Fail to reject the null hypothesis, there is significant evidence that true average escape time exceeds 6 min.
Answer:
Reject the null hypothesis, there is significant evidence that true average escape time exceeds 6 min.
Step-by-step explanation:
In this case we need to test whether the data contradict the prior belief that the true average escape time for oil workers would be at most 6 min or 360 seconds.
The information provided is:
[tex]n=20\\\bar x=370.42\\s=25.74\\\alpha =0.05[/tex]
The hypothesis for the test can be defined as follows:
H₀: The true average escape time for oil workers is more than 360 seconds, i.e. μ > 360.
Hₐ: The true average escape time for oil workers is at most 360 seconds, i.e. μ ≤ 360.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{\s/\sqrt{n}}=\frac{370.42-360}{25.74/\sqrt{20}}=1.81[/tex]
Thus, the test statistic value is 1.81.
Compute the p-value of the test as follows:
[tex]\text{p-value}=P(t_{n-1}<t)[/tex]
[tex]=P(t_{20-1}<1.81)\\\\=P(t_{19}<1.81)\\\\=0.044[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.044.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.044 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that the true average escape time would be at most 6 min.
1. In a basket, there are white and red balls. What is the smallest number of balls you need to take out of the basket so that there are definitely two balls of the same color among them?
2. A drawer contains 10 pairs of socks. Each pair is either black or white. What is the minimum number of socks that must be drawn, at random, from the drawer to ensure that you have 3 pairs of all the same color socks? 3. A bowl contains 5 red balls and 5 white balls. Dorothy selects balls at random without looking at them. How many balls must she select to be sure she has at least two red balls?
Answer:
377Step-by-step explanation:
1. In 2 draws, you can get one of each, so a minimum of 3 draws will guarantee at least 2 of one color.
__
2. A minimum of 3 socks must be drawn to ensure one pair. A minimum of 2 must be drawn to ensure an additional pair. For three pairs, 7 socks must be drawn.
__
3. The first 5 balls drawn could be white, so an additional 2 must be drawn to ensure 2 red balls. To be sure of 2 red balls, 7 balls must be drawn.
Pls answer either of these questions with step by step explanation
Answer:
C and B
Step-by-step explanation:
31. Thrice means 3 times as much. Let's call Rahul and Shivam's present ages r and s respectively. We can write:
r = 3s
r + 8 = 1 + (s + 8) * 2
Simplifying the second equation gives us r + 8 = 2s + 17. When we substitute r = 3s into the second equation we get 3s + 8 = 2s + 17 which gives us s = 9. This means r = 9 * 3 = 27 so Rahul's age 8 years before the present is 27 - 8 = 19.
32. Let's call Ravi and Kishan's ages r and k. We can write:
r + k = 69
r - 8 = 2(k - 8) - 4
Rewriting the first equation gives us r = -k + 69 and when we substitute this into the second equation we get -k + 69 - 8 = 2k - 16 - 4. Solving for k we get k = 27 which means r = 42. 42 - 27 = 15.
what is the volume of a cone with the given dimensions. radius=4 cm; height= 10 cm
Answer:
[tex] 167.47 \: {cm}^{3} [/tex]
Step-by-step explanation:
[tex]V_{cone} = \frac{1}{ 3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \pi \times {4}^{2} \times 10 \\ \\ = \frac{1}{ 3} \times 3.14 \times 16 \times 10 \\ \\ = \frac{1}{ 3} \times \: 502.4 \\ \\ = 167.466667 \\ \\ = 167.47 \: {cm}^{3} [/tex]
Find the volume of the following solid figure. Use = 3.14.
V = 4/313. A sphere has a radius of 3.5 inches.
Answer:
V = 51.3 in.³
Step-by-step explanation:
Volume of Sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r = 3.5
So,
V = [tex]\frac{4}{3} (3.14)(3.5)^3[/tex]
V = [tex]\frac{4}{3} (3.14)(12.25)[/tex]
V = [tex]\frac{153.9}{3}[/tex]
V = 51.3 in.³
(m-3)/(7)=(m)/(m+8) Solve the proportion.
Answer: m=6, m=-4
Step-by-step explanation:
To solve this proportion, we have to cross multiply.
[tex]\frac{m-3}{7} =\frac{m}{m+8}[/tex]
[tex](m-3)(m+8)=7m[/tex]
Now that we have cross multiplied, we actually need to FOIL the left side to expand the equation.
[tex]m^2+8m-3m-24=7m[/tex]
Combine like terms.
[tex]m^2+5m-24=7m[/tex]
We can move all terms to one side and then solve for m.
[tex]m^2-2m-24=0[/tex]
We can actually factor this to:
[tex](m-6)(m+4)=0[/tex]
We set each factor equal to 0 to find m.
m-6=0
m=6
m+4=0
m=-4
A tooth-whitening gel is to be tested for effectiveness. A group of 85 adults have volunteered to participate in the study. Of these, 43 are to be given a gel that contains the tooth-whitening chemicals. The remaining 42 are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals. A standard method will be used to evaluate the whiteness of teeth for all participants. Then the results for the two groups will be compared. 1. After the treatment period, compare the whiteness of the 43 treated adults. 2. A placebo is not being used. 3. After the treatment period, compare the whiteness of the two groups. 4. Randomly select 85 adults to be given the treatment gel. 5. The remaining 42 adults receive the placebo gel. 6. Randomly select 43 adults to be given the treatment gel.
Answer:
(a) 3, 5 and 6
Step-by-step explanation:
In the experiment, 43 are to be given a gel that contains the tooth-whitening chemicals while the remaining 42 are to be given a placebo. Therefore, a placebo is used.
The 43 that will receive the gel are to be selected randomly.
After the experiment, the whiteness of the two groups will be compared to see the effect of the gel.
Therefore for the experiment to be completely random, 3, 5, and 6 apply.
(b)
For the experiment to be double-blind, the researchers who will evaluate the whiteness and interact with the subjects, and the subjects would not know which subjects received either the whitening gel or the placebo.
The table shows the battery lives, in hours, of ten Brand A batteries and ten Brand B batteries.
Battery Life (hours)
Brand A
Brand B
22.5 17.0 21.0 23.0 22.0 18.5 22.5 20.0 19.0
20.0 19.5 20.5 16.5 14.0 17.0 11.0 19.5 21.0
23.0
12.0
Which would be the best measure of variability to use to compare the data?
Only Brand A data is symmetric, so standard deviation is the best measure to compare variability.
Only Brand B data is symmetric, so the median is the best measure to compare variability.
Both distributions are symmetric, so the mean is the best measure to compare variability.
Both distributions are skewed left, so the interquartile range is the best measure to compare variability
Answer:
D. Both distributions are skewed left, so the interquartile range is the best measure to compare variability.
Step-by-step explanation:
Plotting the data roughly shows that the data is skewed to the left. In other words, data is skewed negatively and that the long tail will be on the negative side of the peak.
In such a scenario, interquartile range is normally the best measure to compare variations of data.
Therefore, the last option is the best for the data provided.
please mark me brainliest :)
the sum of 60 and 30 is divided by 10 and the difference of quotient and 3 is divided by 2
Answer:
Final result is 3.
Step-by-step explanation:
Quotient = (60 + 30) / 10
= 90/10
= 9.
Difference of quotient and 3
= 9 - 3
= 6
6 / 2 = 3.
The sum of 60 and 30 is divided by 10 and the difference of the quotient and 3 divided by 2 is 3
The process for finding the above value to the word problem question is as follows;
The sum of 60 and 30 is 60 + 30 = 90
The above sum of 60 and 30 divided by 10 is 90 divided by 10, which is given as follows;
[tex]\mathbf{\dfrac{60 + 30}{10} = \dfrac{90}{10} = 9 =} \mathbf{ \ The \ quotient}[/tex]
The quotient = 9
The difference of the quotient and 3 divided by 2 is (quotient - 3)/2, which is found as follows;
(quotient - 3)/2 = [tex]\mathbf{\dfrac{9 - 3}{2} = 3}[/tex]
Therefore, the sum of 60 and 30 is divided by 10 and the difference of the quotient and 3 divided by 2 = 3
Learn more about word problem here;
https://brainly.com/question/20521181
American adults are watching significantly less television than they did in previous decades. In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day. 1. Find the probability that an average American adult watches more than 309 minutes of television per day. Answer in three decimal places. 2. Find the probability that an average American adult watches more than 2,250 minutes of television per week. Answer in three decimal places.
Answer:
1. 0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.
2. 0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the normal distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.
Normal distribution:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]
In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day.
This means that [tex]\lambda = 320n[/tex], in which n is the number of days.
1. Find the probability that an average American adult watches more than 309 minutes of television per day.
One day, so [tex]\mu = 320, \sigma = \sqrt{320} = 17.89[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 309. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{309 - 320}{17.89}[/tex]
[tex]Z = 0.61[/tex]
[tex]Z = 0.61[/tex] has a pvalue of 0.729
1 - 0.729 = 0.271
0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.
2. Find the probability that an average American adult watches more than 2,250 minutes of television per week.
[tex]\mu = 320*7 = 2240, \sigma = \sqrt{2240} = 47.33[/tex]
This is 1 subtracted by the pvalue of Z when X = 2250. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2250 - 2240}{47.33}[/tex]
[tex]Z = 0.21[/tex]
[tex]Z = 0.21[/tex] has a pvalue of 0.583
1 - 0.583 = 0.417
0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.
a circle has a radius of 2 meters. find the exact circumference of this circle in terms of pi
Answer:
See below.
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex]
We know that the radius is 2 meters, so:
[tex]2(2) \pi[/tex]
[tex]4\pi[/tex] meters.
What is the product of 2x + y and 5x - y + 3?
22+
py +
be +
y24
Y
Answer:
10x² + 3xy + 6x + 3y - y²
Step-by-step explanation:
Step 1: Distribute
10x² - 2xy + 6x + 5xy - y² + 3y
Step 2: Combine like terms
10x² + 3xy + 6x + 3y - y²
And we have our final answer!
The television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast. Find the probability that none of the households are tuned to 50 Minutes.
Answer:
The probability that none of the households are tuned to 50 Minutes is 0.04398.
Step-by-step explanation:
We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.
A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.
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 = 0,1,2,3,.........[/tex]
where, n = number of samples (trials) taken = 14 households
r = number of success = none of the households are tuned to 50 min
p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%
Let X = Number of households that are tuned to 50 Minutes
So, X ~ Binom(n = 14, p = 0.20)
Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)
P(X = 0) = [tex]\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}[/tex]
= [tex]1 \times 1 \times 0.80^{14}[/tex]
= 0.04398
Mary is selling chocolate bars to raise money. She earns $3 for each solid milk chocolate bar sold and $4 for each caramel-filled bar sold. If m represents the number of milk chocolate bars sold, and c represents the number of caramel bars sold, which of the following expressions represents the amount of money that Mary has raised? Question 6 options: A) 3m – 4c B) m∕3 + i∕4 C) 12mc D) 3m + 4c
Answer:
3m + 4c
Step-by-step explanation:
Whenever a word problem says the word earn that means the slope, also known as the rate of change, will be positive. Knowing this you can determine that both the caramel and milk chocolate slopes will be positive. After figuring all that out the only thing left to do is to make the equation. You know you have two slopes, and each slope needs a variable, so you will have to look back at the question. It is given that m represents the milk chocolate and c represents the caramel. Now all you have to do is make the slope the coefficient to the corresponding variable. The milk chocolates are 3 dollars, so the 3 goes in front of the m and the caramel chocolates are 4 dollars, so teh 4 goes in front of the 4. Since both slopes are positive no negatives or minus signs will be used in the equation. Knowing all this information you can now create the expression 3m + 4c.
Answer:
D
Step-by-step explanation:
3m + 4c
A fort had enough food for 80 soldiers for 60 days .How long would the food last if 20 more soliders join after 15 days ?
Answer:
The food would last 51 days
Step-by-step explanation:
After 15 days are over, you could say that the 16th day would be as follows -
80 soldiers, food finished in 60 - 15 = 45 days.
If 20 more soldiers arrive, there would be a total of 100 soldiers, so if 80 soldiers can finish their food in 45 days - 1 soldier can finish = 45 * 80. Respectively, 100 soldiers can consume their food in ( 45 * 80 ) / 100 = 36 days.
As 15 days are already over, adding 36 more days = 51 days
The food would last 51 days if 20 more soldiers join after 15 days
There are several possible ways to answer this question, but I hope that explanation helps!
Answer:
A total of 51 days, or 36 days after the extra soldiers join in.
Step-by-step explanation:
Let's say a soldier eats 1 portion of food in 1 days. That portion may be divided into breakfast, lunch , and dinner, but it is still accounted as 1 portion per soldier per day.
There are 80 soldiers and enough food for 60 days.
The number of portions is
60 * 80 = 4800
The fort started with 4800 portions.
80 soldiers ate their portions for 15 days.
80 * 15 = 1200
After 15 days, they have
4800 - 1200 = 3600 portions left.
After 15 days, 20 more soldiers joined in.
Now there are 80 + 20 = 100 soldiers.
There are 3600 portions left for 100 soldiers.
3600/100 = 36
The food would last 36 days after the 15 days, or a total of 51 days.
128 to 1 significant number
Answer:
The answer is 100.
Step-by-step explanation:
The original figure has 3 significant figures
Rounded to 1 significant figure is 100
Birth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights between 125 oz and 140 oz is:
Answer:
The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 110, \sigma = 0.15[/tex]
The proportion of infants with birth weights between 125 oz and 140 oz is
This is the pvalue of Z when X = 140 subtracted by the pvalue of Z when X = 125. So
X = 140
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 110}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 125
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 110}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.9772 - 0.8413 = 0.1359
The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.