Hello!
Answer:[tex]\boxed{ \bf Each~side~is~4~in~long.}[/tex]
Explanation:We know that the formula for volume of a cube is:
V = a³
64 = a³
To find the side length, all we have to do is find the cube root of both sides.
[tex]\sqrt{64} = \sqrt{a^3}[/tex]
4 = a
Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let p(x) represent Primo Pizza's profit (in dollars) x days after June 1. Let s(x) represent Pizza Supreme's profit (in dollars) x days after June 1.
c. Suppose Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.
i) Write a function formula for p using the function s
. p(x)=
ii) Write a function formula for s using the function p
s(x)=
.
Answer:
a)
i) p(x) = 1.4 s(x)
ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4
b)
i) p(x) = [s(x) + 200]
ii) s(x) = [p(x) - 200]
c)
i) p(x) = s(x+4)
ii) s(x) = p(x-4)
Step-by-step explanation:
Complete Question
Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let p(x) represent Primo Pizza's profit (in dollars) x days after June 1. Let s(x) represent Pizza Supreme's profit (in dollars) x days after June 1.
a) Suppose Primo Pizza's profit each day is 1.4 times as large as the profit of Pizza Supreme
i. Write a function formula for p using the function s.
ii. Write a function formula for s using the function p.
b) Suppose Primo Pizza's profit each day is $200 more than the profit of Pizza Supreme.
i) Write a function formula for p using the function s.
ii) Write a function formula for s using the function p.
c) Suppose Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.
i) Write a function formula for p using the function s.
ii) Write a function formula for s using the function p.
The profits per day for Primo Pizza, x days after June 1 = p(x)
The profits per day for Supreme Pizza, x days after June 1 = s(x)
a) Primo Pizza's profits per day is 1.4 times that of Supreme Pizza's per day.
Primo Pizza's profits per day, x days after June 1 = p(x)
Supreme Pizza's profit per day, x days after June 1 = s(x)
i) p(x) = 1.4 s(x)
ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4
b) Primo Pizza profits per day is $200 more than that of Supreme Pizza
Primo Pizza's profits per day, x days after June 1 = p(x)
Supreme Pizza's profit per day, x days after June 1 = s(x)
i) p(x) = [s(x) + 200]
ii) s(x) = [p(x) - 200]
c) Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.
Primo Pizza's profits per day, x days after June 1 = p(x)
Supreme Pizza's profit per day, x days after June 1 = s(x)
Supreme Pizza's profit per day, 4 days later = s(x+4)
So,
i) p(x) = s(x+4)
ii) This means that Supreme Pizza's profit per day is the same as Primo Pizza's profit per day four days ago.
Primo Pizza's profit per day four days ago = p(x-4)
So,
s(x) = p(x-4)
Hope this Helps!!!
Primo Pizza's profit function p(x) is related to Pizza Supreme's profit function s(x) such that p(x) = s(x + 4). Similarly, s(x) = p(x - 4). These functions express the profits in terms of each other with a 4-day shift in time.
Explanation:Given that Primo Pizza's profit p(x) on a given day is the same as Pizza Supreme's profit s(x) 4 days later, we can write the following relationships between the two functions:
p(x) = s(x + 4)
s(x) = p(x - 4)
This implies that to find Primo Pizza's profit on the x-th day, we need to find out what Pizza Supreme's profit was on the (x + 4)-th day. Conversely, to compute Pizza Supreme's profit on the x-th day, we need to find Primo Pizza's profit 4 days earlier, on the (x - 4)-th day.
A sample of 90 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.284 and the equation of the regression line is ModifyingAbove y with caret equals 18.4 plus 0.930 x, where x represents height. The mean of the 90 heights is 63.4 in and the mean of the 90 pulse rates is 77.9 beats per minute. Find the best predicted pulse rate of a woman who is 66 in tall. Use a significance level of alpha equals 0.01.
The best-predicted pulse rate for a woman who is 66 inches tall, using the given regression equation 18.4 + 0.930x, is approximately 79.78 beats per minute.
To predict the pulse rate of a woman who is 66 inches tall using the given regression equation, we plug in the height (x = 66) into the equation:
ModifyingAbove y with caret = 18.4 + 0.930x
Substituting x = 66:
ModifyingAbove y with caret = 18.4 + 0.930(66)
Perform the calculation:
ModifyingAbove y with caret = 18.4 + 61.38
ModifyingAbove y with caret = 79.78
Therefore, the best-predicted pulse rate for a woman who is 66 inches tall is approximately 79.78 beats per minute. This prediction assumes that the relationship between height and pulse rate holds for this particular height value.
The number of women graduating from 4-yr colleges in a particular country grew from 1930, when 48,833 women earned a bachelor's degree, to 2004, when approximately 870,000 women received such a degree. Find an exponential function that fits the data, and the exponential growth rate.
Answer:
[tex]A(t) = 48833e^{0.0389t}[/tex]
The exponential growth rate is r = 0.0389
Step-by-step explanation:
An exponential function for the number of women graduating from 4-yr colleges in t years after 1930 can be given by the following equation:
[tex]A(t) = A(0)e^{rt}[/tex]
In which A(0) is the initial amount, and r is the exponential growth rate, as a decimal.
1930, when 48,833 women earned a bachelor's degree
This means that [tex]A(0) = 48833[/tex]
2004, when approximately 870,000
2004 is 74 years after 1930, which means that [tex]A(74) = 870000[/tex]
Applying to the equation:
[tex]A(t) = A(0)e^{rt}[/tex]
[tex]870000 = 48833e^{74r}[/tex]
[tex]e^{74r} = \frac{870000}{48833}[/tex]
[tex]\ln{e^{74r}} = \ln{\frac{870000}{48833}}[/tex]
[tex]74r = \ln{\frac{870000}{48833}}[/tex]
[tex]r = \frac{\ln{\frac{870000}{48833}}}{74}[/tex]
[tex]r = 0.0389[/tex]
So
[tex]A(t) = A(0)e^{rt}[/tex]
[tex]A(t) = 48833e^{0.0389t}[/tex]
To find an exponential function that fits the given data, determine the values of the base and the exponent. The exponential function that fits the data is y = 2.311 * 1.049^x. The exponential growth rate is approximately 1.049.
Explanation:To find an exponential function that fits the data, we need to determine the values of the base and the exponent. Let's let the year be the input, x, and the number of women graduating be the output, y. The general form of an exponential function is y = ab^x, where a is the initial value and b is the growth rate. Substituting the given data, we have the equation:
48,833 = a * b1930
870,000 = a * b2004
By dividing the second equation by the first equation, we can eliminate a:
870,000 / 48,833 = (a * b2004) / (a * b1930)
17.821 = b2004-1930
17.821 = b74
Taking the log base b of both sides, we get:
logb 17.821 = 74
Solving for b using logarithmic properties, we find:
b = 17.8211/74
b ≈ 1.049
Now that we have the value of b, we can substitute it into one of the original equations to find a:
48,833 = a * 1.0491930
Solving for a, we get:
a ≈ 2.311
Therefore, the exponential function that fits the data is y = 2.311 * 1.049x. The exponential growth rate is approximately 1.049.
Learn more about Exponential function here:https://brainly.com/question/37289664
#SPJ3
An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line at their site. A consumer group is suspicious of the claim and thinks that the proportion is lower than 60%. A random sample of 80 graduate students show that only 44 students have ever done so. Is there enough evidence to show that the true proportion is lower than 60%? Assume that significance level of 0.05. Use the hypothesis testing template provided.'
Answer:
We accept H₀ we don´t have enough evidence to conclude that a consumer group position is correct
Step-by-step explanation:
We have a case of test of proportion, as a consumer group is suspicious of the claim and think the proportion is lower we must develop a one tail test (left tail) Then
1.- Test hypothesis:
Null hypothesis H₀ P = P₀
Alternative hypothesis Hₐ P < P₀
2.- At significance level of α = 0,05 Critical value
z(c) = -1,64
3.-We compute z(s) value as:
z(s) = ( P - P₀ )/ √P*Q/n where P = 44/80 P = 0,55 and Q = 0,45
P₀ = 0,6 and n = 80
Plugging all these values in the equation we get:
z(s) = ( 0,55 - 0,6 ) / √(0,2475/80)
z(s) = - 0,05/ √0,0031
z(s) = - 0,05/0,056
z(s) = - 0,8928
4.-We compare z(s) and z(c)
z(s) > z(c) -0,8928 on the left side it means that z(s) is in the acceptance region so we accept H₀
4)
I
You deposit $2500 in an account that pays 6 percent annual interest. Find the balance after 3
years if the interest is compounded with the given frequency.
Answer:
$2,977.54
Step-by-step explanation:
You are going to use the compound interest formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate
n = number of times compounded annually
t = time
First, change 6% into the decimal form:
6% -> [tex]\frac{6}{100}[/tex] -> 0.06
Next, lets plug in the values:
[tex]A=2,500(1+\frac{0.06}{1} )^{3(1)}[/tex]
[tex]A=2,977.54[/tex]
Your answer will be $2,977.54
In the data set below, what are the lower quartile, the median, and the upper quartile?
2,2,2,4,5,6
Lower Quartile: 2
Upper Quartile: 5.25
Median: 3
Final answer:
In the given data set 2, 2, 2, 4, 5, 6, the lower quartile is 2, the median is 3, and the upper quartile is 5.
Explanation:
To find the lower quartile, median, and upper quartile of the given data set 2, 2, 2, 4, 5, 6, we first need to organize it in ascending order, which is already done. Next, we compute the median, which is the middle value when the data set is listed in order. Since there are six numbers, the median will be the average of the third and fourth numbers, (2+4)/2, which is 3.
To find the first quartile (Q1) or lower quartile, we take the median of the lower half of the data set, not including the median. This would be the median of the first three numbers: 2, 2, and 2, which is simply 2. To find the third quartile (Q3) or upper quartile, we look at the upper half of the data set, again not including the median. The median of the last three numbers 4, 5, and 6 is 5.
Therefore, the lower quartile is 2, the median is 3, and the upper quartile is 5.
What is the approximate circumference of the circle shown below
Answer:
147.58 cm
Step-by-step explanation:
Circumference is represented by 2πr.
R is 23.5, and I'll approximate π to 3.14, as is common.
This creates 2 • 3.14 • 23.5
Simplify to: 147.58, which is your circumference
Answer:
148
Step-by-step explanation:
To find the circumference, use 2r*3.14 for a approximate answer. in this case, 23.5*2=47.
47*3.14=147.58.
Rounded to the nearest whole number, the answer is 148.
FInd the measure of RST.
A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds that 77% of them received a passing grade. Create a 99% confidence interval for the population proportion of passing test scores. Enter the lower and upper bounds for the interval in the following boxes, respectively. You may answer using decimals rounded to four places or a percentage rounded to two. Make sure to use a percent sign if you answer using a percentage.
Answer:
99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].
Step-by-step explanation:
We are given that a high school principal wishes to estimate how well his students are doing in math.
Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.
Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of students received a passing grade = 77%
n = sample of tests = 40
p = population proportion
Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.
So, 99% confidence interval for the population proportion, p is ;
P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%
level of significance are -2.5758 & 2.5758}
P(-2.5758 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.5758) = 0.99
P( [tex]-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
P( [tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
99% confidence interval for p = [[tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }[/tex] , [tex]0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }[/tex] ]
= [0.5986 , 0.9414]
Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].
Lower bound of interval = 0.5986
Upper bound of interval = 0.9414
Which is the graph of a logarithmic function?
On a coordinate plane, a parabola is shown.
On a coordinate plane, a function is shown. It approaches the x-axis in quadrant 2 and then increases into quadrant 1. It goes through (0, 1) and (1, 2).
On a coordinate plane, a function is shown. It approaches the y-axis in quadrant 4 and approaches y = 2 in quadrant 1. It goes through (1, 0) and (3, 1).
On a coordinate plane, a hyperbola is shown.
Answer:
the third one
Step-by-step explanation:
you can cross out parabola and hyperbola. the second graph is an exponential function because exponential functions go through (0,1), While logarithmic functions go through (1,0).
Answer:
Option 3
Step-by-step explanation:
Edge 2021
7. (Sec. 7.2) In a survey of 2004 American adults, 501 of them said that they believed in astrology. (a) Calculate and interpret a confidence interval at the 95% confidence level for the proportion of all adult American adults who believe in astrology. (b) Calculate and interpret a 95% lower confidence bound for the proportion of all adult American adults who believe in astrology.
Find the given attachments for complete answer
Answer:
The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).
This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.
Step-by-step explanation:
We have to construct a 95% confidence interval for the proportion.
The sample proportion is p=0.25.
[tex]p=X/n=501/2004=0.25[/tex]
The standard deviation can be calculated as:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.25*0.75}{2004}}=\sqrt{ 0.000094 }=0.01[/tex]
For a 95% confidence interval, the critical value of z is z=1.96.
The margin of error can be calculated as:
[tex]E=z\cdot \sigma_p=1.96*0.01=0.0196[/tex]
Then, the lower and upper bounds of the confidence interval can be calculated as:
[tex]LL=p-E=0.25-0.0196=0.2304\approx0.23\\\\UL=p+E=0.25+0.0196=0.2696\approx 0.27[/tex]
The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).
This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.
Hey, I need help! 2+2+=?
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
1. The flag-down fare of a taxi is $3.
a. Given that the passenger is charged $0.50 for each kilometer the taxi travels, find the amount of money the passenger has to pay if the taxi covers a distance of
(i) 3 km
(ii) 6 km
(iii) 10 km
b. Given that $y represents the amount of money a passenger has to pay if the taxi travels x km, copy and complete the table.
x 3 6 10
y
Answer:
3 x 0.50=1.5
6 x 0.50=3
10 x 0.50=5
Step-by-step explanation:
x 3, 6, 10
y 1.5, 3, 5
The charges are
For 3 Km the charges would be is $1.5
For 6 Km the charges would be is $3
For 10 Km the charges would be is $5
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The passenger is charged $0.50 for each kilometer
For 3 Km the charges would be
=3 x 0.50
= $1.5
For 6 Km the charges would be
= 6 x 0.50
=$3
For 10 Km the charges would be
= 10 x 0.50
=$5
The complete Table is
x 3, 6, 10
y 1.5, 3, 5
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
I need help with part b. I feel like there’s a catch, I want to do the first derivative test, however, I feel like there is a better way.
Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:
[tex]P_5(x)=g(-1)+g'(-1)\,(x+1)+g"(-1)\, \frac{(x+1)^2}{2!} +g^{(3)}(-1)\, \frac{(x+1)^3}{3!} + g^{(4)}(-1)\, \frac{(x+1)^4}{4!} +g^{(5)}(-1)\, \frac{(x+1)^5}{5!}[/tex]
and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders: [tex]g'(-1)\,(1)[/tex] since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: [tex]g'(-1)= 7[/tex] as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1
At the Canada Open Tennis Championship, a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 99 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph.
If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves.
a) 54 mph to 144 mph
b) 39 mph to 159 mph
c) 144 mph to 189 mph
d) 69 mph to 129 mph
Answer:
a) 54 mph to 144 mph
Step-by-step explanation:
We don't know the shape of the distribution, so we use Chebyshev's Theorem to solve this question. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
At least eight-ninths of the player's serves.
8/9 is approximately 89%
So
Mean: 99, standard deviation: 15
99 - 3*15 = 54
99 + 3*15 = 144
So the correct answer is:
a) 54 mph to 144 mph
Find the area under the standard normal curve between z = - 1.5 and z = 2.5
Answer:
Step-by-step explanation:
Z=-1.5
-1.5=2.5
Final answer:
To find the area under the standard normal curve between z = -1.5 and z = 2.5, subtract the area to the left of z = -1.5 from the area to the left of z = 2.5 to be 0.927.
Explanation:
To find the area under the standard normal curve between z = -1.5 and z = 2.5, we can subtract the area to the left of z = -1.5 from the area to the left of z = 2.5.
Using the z-table, we can find that the area to the left of z = -1.5 is approximately 0.0668 and the area to the left of z = 2.5 is approximately 0.9938.
Therefore, the area between z = -1.5 and z = 2.5 is approximately 0.9938 - 0.0668 = 0.927.
Ron wants to calculate the sales tax on two items. He is purchasing a helmet for $42 and gloves for $5.65. Sales tax is 7%. Which expression shows how Ron should calculate his total sales tax?
A
$42 + $5.65 x 7
B
$42 + $5.65 x 0.7
C
($42 + $5.65) x 0.7
D
($42 + $5.65) x 0.07
which point represent on the number line -3/2
Answer:
Half way in between negative 1 and negative 2.
Step-by-step explanation:
Explaining What Causes Seasons
Which factors cause Earth to experience seasons? Check all that apply.
the speed of Earth’s rotation
the tilt of Earth’s axis
the directness of the Sun’s rays
the distance from the Sun
the distance from the equator
the altitude of an area
Answer:
The factors that cause Earth to experience seasons are:
1. the tilt of Earth’s axis
2. the directness of the Sun’s rays
The factors that cause Earth to experience seasons are:
1. the tilt of Earth’s axis
2. the directness of the Sun’s rays
Factors that result in the earth experiencing the seasons should be:The reason why the Earth contains various seasons because it deals with the variation of the sun's rays angles and the earth titles to the 23.5 degrees on its axis. Also along with the earth rotation, the earth orbits should be around to the sun because of which various parts should be exposed to the different amount of lights
Therefore, the above two points should be considered.
Learn more about earth here: https://brainly.com/question/442818
Please help numbers 2-20 evens only
Answer:
clearing picture
Step-by-step explanation:
What shapes have 2 abtuse angles
Answer:
a parallelogram, trapezium and rhombus
Step-by-step explanation:
Mike weights 200 pounds and plans to lose 1.5 pounds a week, Jeff weights 180 pounds and plans to lose 0.5 pounds a week. When will mike and Jeff weigh the same
The thumb length of fully grown females of a certain type of frog is normally distributed with a mean of 8.59 mm and a standard deviation of 0.63 mm. Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
Answer:
21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 problem, we have that:
[tex]\mu = 8.59, \sigma = 0.63[/tex]
Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
This is 1 subtracted by the pvalue of Z when X = 9.08. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.08 - 8.59}{0.63}[/tex]
[tex]Z = 0.78[/tex]
[tex]Z = 0.78[/tex] has a pvalue of 0.7823
1 - 0.7823 = 0.2177
21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
In ΔWXY, the measure of ∠Y=90°, XW = 25, YX = 24, and WY = 7. What is the value of the cosine of ∠W to the nearest hundredth?
Answer:
7/25
Step-by-step explanation:
Just did on delta math
Use mental math to find the sum of 43 and 57
Answer:
100
Step-by-step explanation:
43+57=100
I added 3+7=10
Then 40+50=90 and added them
90+10=100
Answer: 100
Step-by-step explanation:
You know that 3+7=10
You know that 40+50=90
90+10=100
Now suppose that out of the 10 dishes that the restaurant offers, only 3 of them are vegetarian. If Fiona must select a vegetarian option on Friday, how many ways are there for her to select her lunches?
Answer:
The number of ways she can select her lunches N ;
N = 10×10×10×10×3 = 30000 ways
Step-by-step explanation:
Number of week days = 5
Total number of dishes = 10
Number of vegetarian dishes = 3
Note; on other week days apart from Friday she can select any lunch she want vegetarian or not...
Therefore, on Monday to Thursday she has ten choices per day, and on Friday she has 3 choices
The number of ways she can select her lunches N ;
N = 10×10×10×10×3 = 30000 ways
find the area of the polygons 5 cm 5 cm 8 cm square centimeters
Answer:
Answer: 600
Step-by-step explanation:
5x5=25
3x8=24
25x24=600
A wildlife sanctuary has two elephants. One has a weight of 11,028 pounds and the other has a weight of 5 1/2 tons. A platform can hold 22,000 pounds. Can the platform hold both elephants
Answer:
The platform cannot hold both elephants.
Step-by-step explanation:
This problem is solved by conversion of units.
Elephant A weighs 11,028 pounds
Elephant B weighs 5 1/2 = 5.5 tons
The platform can hold 22,000 pounds
To see if the platform holds both elephants, the first step is converting the weigth of Elephant B to pounds.
Each ton has 2000 pounds.
So 5.5 tons have 5.5*2000 = 11000 pounds.
So Elephant B weighs 11000 pounds
Combined weights of Elephants A and B
11,028 + 11,000 = 22,028 > 22,000
The platform cannot hold both elephants.
A bottler of drinking water fills plastic bottles with a mean volume of 1,000 milliliters (mL) and standard deviation The fill volumes are normally distributed. What proportion of bottles have volumes greater than
Answer:
84.13% of bottles will have volume greater than 994 mL
Step-by-step explanation:
Mean volume = u = 1000
Standard deviation = [tex]\sigma[/tex] = 6
We need to find the proportion of bottles with volume greater than 994. So our test value is 994. i.e.
x = 994
Since the data is normally distributed we will use the concept of z-score to find the required proportion. First we convert 994 to its equivalent z-score, then using the z-table we will find the corresponding value of proportion. The formula to calculate the z score is:
[tex]z=\frac{x-u}{\sigma}[/tex]
Substituting the values, we get:
[tex]z=\frac{994-1000}{6}=-1[/tex]
This means 994 is equivalent to a z score of -1. Now we will find the proportion of z values which are greater than -1 from the z table.
i.e. P(z > -1)
From the z-table this value comes out to be:
P(z >- 1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
Since, 994 is equivalent to a z score of -1, we can write that proportion of values which will be greater than 994 would be:
P( X > 994 ) = P( z > -1 ) = 0.8413 = 84.13%
To find the proportion of bottles with more than 994 mL, calculate the z-score and use a z-table. Approximately 93.32% of bottles are filled with more than 994 mL.
Explanation:To determine the proportion of bottles with volumes greater than 994 mL, we need to use the properties of the standard normal distribution. The mean volume of a bottle is given as 1000 mL with a standard deviation of 4 mL. We first calculate the z-score for 994 mL, which is the number of standard deviations 994 mL is from the mean.
Z = (X - μ) / σ = (994 mL - 1000 mL) / 4 mL = -1.5
Using a z-table or standard normal distribution calculator, we can find the proportion of the area to the right of z = -1.5, which represents the proportion of bottles filled with more than 994 mL. The area to the right of z = -1.5 is approximately 0.9332. Therefore, about 93.32% of the bottles are expected to have volumes greater than 994 mL.
A glider begins its flight 3/4 mile above the ground. After 45 minutes, it is 3/10 mile above the ground. Find the change in height of the glider. If it continues to descend at this rate, how long does the entire descent last?
Answer:
1 hour 15 Minutes
Step-by-step explanation:
The glider begins its flight [tex]\dfrac{3}{4}[/tex] mile above the ground.
Distance above the ground after 45 minutes =[tex]\frac{3}{10} \:mile[/tex]
Change in height of the glider
[tex]=\frac{3}{4}-\frac{3}{10} \\\\=\frac{15-6}{20}\\\\=\frac{9}{20} miles[/tex]
Next, we determine how long the entire descent last.
Expressing the distance moved as a ratio of time taken
[tex]\frac{9}{20} \:miles : 45 \:minutes\\\\\frac{3}{10}\:miles:x \:minutes\\\\x=45X\frac{3}{10}\div\frac{9}{20} =30 Minutes[/tex]
Therefore: Total Time taken =45+30=75 Minutes
=1 hour 15 Minutes