Answer: 4 outcomes
Step-by-step explanation:
For two number cubes, the total possible outcomes are:
6 events for the first and 6 events for the second, then the total number of combinations is 6*6 = 36
If the dice are different, the possible outcomes are:
Dice 1 = 3, Dice 2 = 2
Dice 1 = 2, Dice 2 = 3
Dice 1 = 4, Dice 2 = 1
Dice 1 = 1, Dice 2 = 4
Then we have 4 outcomes in the collection for event E.
Answer:
4
Step-by-step explanation:
I did it on college board
Each day, a factory produces a total of 280 containers of ice cream. The flavors are vanilla, chocolate, and strawberry. Each day, the factory produces twice as much chocolate ice cream as strawberry ice cream and 20 more containers of vanilla ice cream than strawberry ice cream.What is the correct equation, and what is the correct solution, for this situation, where s represents the number of containers of strawberry ice cream produced per day
Answer:
The correct equation in terms of s is: 4s=260
The number of strawberry ice cream produced per day, s=65.The number of chocolate ice cream produced per day ,c=130. The number of vanilla ice cream produced per day ,v=85.Step-by-step explanation:
Let the number of containers of strawberry ice cream produced per day=s
Let the number of containers of vanilla ice cream produced per day=v
Let the number of containers of chocolate ice cream produced per day=c
Total Number of Ice Cream Containers=280
s+v+c=280Given:
The factory produces twice as much chocolate ice cream as strawberry ice cream. This is written as:
c=2sThe factory produces 20 more containers of vanilla ice cream than strawberry ice cream. This is written as:
v=s+20Therefore substituting c=2s and v=s+20 into the first equation: s+v+c=280
s+s+20+2s=280
4s=280-20
4s=260
Divide both sides by 4
s=65
The number of strawberry ice cream produced per day is 65.
The number of chocolate ice cream produced per day =2s=2(65)=130.
The number of vanilla ice cream produced per day =s+20=65+20=85.
Final answer:
The number of containers of strawberry ice cream produced per day is 65.
Explanation:
The question is asking us to find the correct equation and solution for the number of containers of strawberry ice cream produced per day by a factory, while taking into account that chocolate is produced at twice the rate and vanilla at 20 more containers than strawberry.
Given the total production is 280 containers, the equation can be set up as follows:
s + 2s + (s + 20) = 280,
where s represents the number of strawberry ice cream containers produced per day.
Step-by-step, we can solve this equation:
Add up the s terms: s + 2s + s = 4s.Substitute the sum into the original equation: 4s + 20 = 280.Subtract 20 from both sides: 4s = 260.Divide both sides by 4: s = 65.Therefore, the factory produces 65 containers of strawberry ice cream per day.
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. If students have only 90 minutes to complete the exam, what percentage of the class will not finish the exam in time?
Answer:
Hence total of 10 students are not able to complete the exam.
Step-by-step explanation:
Given:
Mean for completing exam =80 min
standard deviation =10 min.
To find:
how much student will not complete the exam?
Solution:
using the Z-table score we can calculate the required probability.
Z=(Required time -mean)/standard deviation.
A standard on an avg class contains:
60 students.
consider for 70 mins and then 90 mins (generally calculate ± standard deviation of mean)(80-10 and 80+10).
1)70 min
Z=(70-80)/10
Z=-1
Now corresponding p will be
P(z=-1)
=0.1587
therefore
Now for required 90 min will be
Z=(90-80)/10
=10/10
z=1
So corresponding value of p is
P(z<1)=0.8413
this means 0.8413 of 60 students are able to complete the exam.
0.8413*60
=50.47
which approximate 50 students,
total number =60
and total number student will able to complete =50
Total number of student will not complete =60-50
=10.
About 15.87% of college students are expected not to finish the final examination within the 90-minute time limit, based on the properties of the normal distribution with a mean of 80 minutes and a standard deviation of 10 minutes.
Explanation:The student's question involves using the properties of the normal distribution to determine the percentage of students who will not finish a final examination in the given time frame.
To compute this, we need to calculate the z-score that corresponds to the 90-minute time limit. The z-score formula is:
Z = (X - μ) / σ
where X is the value of interest, μ (mu) is the mean, and σ (sigma) is the standard deviation. Plugging in the numbers:
Z = (90 - 80) / 10 = 1
A z-score of 1 corresponds to a percentile of approximately 84.13%, meaning about 84.13% of students will finish within 90 minutes. To find the percentage that will not finish in time, we subtract this from 100%:
100% - 84.13% = 15.87%
Therefore, approximately 15.87% of the class will not finish the exam in time.
Emma tiled a rectangle and then sketched her work. Write a multiplication equation to find the area of Emma's rectangle?
I was wondering if I was correct (my work) -
A = l x w
A = 3 1/2 units x 2 units
A = 7 units
Answer:
[tex]A=7 \: Square\: Units[/tex]
Step-by-step explanation:
From your work here, if the diagram corresponds with what was tiled, then:
Length of the Rectangle=[tex]3\frac{1}{2} \:Units[/tex]
Width of the Rectangle =2 Units
We know that:
Area of a Rectangle = Length X Width
[tex]=3\frac{1}{2} X 2\\A=7 \: Square\: Units[/tex]
The only thing wrong is the unit of the area given. The unit of area is supposed to be in Square Units.
log base 8 of 8 ^x+1
Answer:
[tex]x + 1[/tex]
Step-by-step explanation:
log(x) is the inverse function of an exponent. "log base 8 of xyz" means "what number do I have to raise 8 to, to get xyz". In this case, it means, "what number do I have to raise 8 to, to get x + 1". That's simple, it's just x + 1!
At a point on the ground 46 feet from the foot of a tree, the angle of elevation to the top of the tree is 68°. What is the height of the tree?
Final answer:
The height of the tree is approximately 113.85 feet, which is determined by using the tangent of the given angle of elevation (68°) and the distance from the tree (46 feet) in a trigonometric calculation.
Explanation:
To find the height of the tree, we can use trigonometry. The student is 46 feet from the tree, and the angle of elevation to the top of the tree is 68°. The height of the tree can be found using the tangent function in a right triangle, where the opposite side is the tree height (h), and the adjacent side is the distance from the tree (46 feet). The tangent of the angle of elevation (θ) is the ratio of the opposite side to the adjacent side.
So, tan(68°) = h / 46 feet. To find the height (h), multiply both sides by 46 feet:
h = 46 feet × tan(68°)
We can use a calculator to find that tan(68°) is approximately 2.475. Now, multiply 46 feet by this tangent value to get the height:
h = 46 feet × 2.475h = 113.85 feet (rounded to two decimal places)
Therefore, the height of the tree is approximately 113.85 feet.
According to the manufacturer of a backup UPS device, the normal output voltage is 120 volts. The sample of 40 measured voltage amounts from a unit have a mean of 123.59 volts and a standard deviation of 0.31 volts. Use a 0.05 significance level to test the claim that the sample is from a population with a mean equal to 120 volts.
Answer:
z = 1.83<1.96
null hypothesis is accepted
The sample is came from a population mean
Step-by-step explanation:
Step :-1
The sample of 40 measured voltage amounts from a unit have a mean of 123.59 volts and a standard deviation of 0.31 volts
given sample size n =40
mean of the sample ×⁻ = 123.59 volts
standard deviation of sample σ = 0.31 volts
Step2:-
Null hypothesis :-
the sample is from a population with a mean equal to 120 volts.
H₀ : μ =120
Alternative hypothesis:-
H₁ : μ ≠120
level of significance:- α =0.05
Step 3:-
The test statistic
[tex]z = \frac{x_{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
substitute values and simplification
[tex]z = \frac{123.59-120}{\frac{0.31}{\sqrt{40} } }[/tex]
on simplification we get the calculated value
z = 1.83
The tabulated value z =1.96 at 0.05 % level of significance
Conclusion:-
Calculated Z < The tabulated value z =1.96 at 0.05 % level of significance
so the null hypothesis is accepted
The sample is came from a population mean
Answer: REJECT the null hypothesis; there IS sufficient evidence to warrant a rejection of the claim that the mean voltage is 120 volts.
t-calculated = 73.242
t-critical = 2.023
In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?
Quadratic formula: x =
x = 5
x = 5
x = 5
x = 5
Answer:
Step-by-step explanation:
quadratic equation: ax² + bx + c =0
x' = [-b+√(b²-4ac)]/2a and x" = [-b-√(b²-4ac)]/2a
6 = x² – 10x ; x² - 10x -6 =0
(a=1, b= - 10 and c = - 6
x' = [10+√(10²+4(1)(-6)]/2(1) and x" = [10-√(10²+4(1)(-6)]/2(1)
x' =5+√31 and x' = 5-√31
The divisor of 0.004 is almost zero. What does this tell you about the quotient?
Answer:
Its magnitude will be larger than 0.004.
Step-by-step explanation:
When a divisor is less than 1, the quotient will be greater than the dividend.
When the divisor is "almost zero", the quotient will be much greater than the dividend. Here, the dividend may be considered to be "almost zero", so we cannot say anything about the actual quotient except to say its magnitude will be greater than the dividend.
_____
The dividend is positive, so the quotient will have the same sign as the divisor. (Negative divisors can be "almost zero," too.)
-1.9+4+(-1.6) simplify the expression
Answer:
.5
Step-by-step explanation:
-1.9+4=2.1
2.1+(-1.6)=.5
For the example below, prorate the given expenses to find the monthly cost.
Sara pays $4000 for tuition and fees for each of the two semesters, plus an additional $240 for textbooks each semester.
The prorated monthly cost for tuition and fees and textbooks is $___
(Round to the nearest dollar as needed.)
Answer:
The prorated monthly cost for tuition and fees and textbooks is $707
Step-by-step explanation:
Each semester costs $4000 + $240 = $4240.
A year has 12 months. A semester is 6 months. 12/6 = 2. So an year has two semesters.
The yearly cost is 2*$4240 = $8480
Monthly cost
12 months cost $8480
$8480/12 = $706.67
So the answer is:
Rounded to the nearest dollar
The prorated monthly cost for tuition and fees and textbooks is $707
The prorated monthly cost for tuition and fees and textbooks is $707
How to solve equationFees for each semester = $4000Cost of textbook per semester = $240Total cost per semester = Fees for each semester + Cost of textbook per semester
= $4000 + $240
= $4,240
Total cost for two semesters = 2 × Total cost per semester= 2 × $4,240
= $8480
Prorated monthly cost for tuition and fees and textbooks = Total cost for two semesters / 12= $8480 / 12
= $706.666666666666
Approximately,
$707
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Which is a correct first step for solving this equation?
2 + 7 = 2x + 5 – 4x
Step-by-step explanation:
Bringing like terms on one side
2 + 7 - 5 = 2x - 4x
9 - 5 = - 2x
4 = - 2x
4/ - 2 = x
- 2 = x
What’s .24 in two equivalent forms
.24 is equivalent to
24%
24/100
6/25
12/50, and more!
Hope this helped
WILL GIVE BRAINLIEST
The measurement of a side of a square is found to be 10 centimeters, with a possible error of 0.07 centimeter. (a) Approximate the percent error in computing the area of the square. % (b) Estimate the maximum allowable percent error in measuring the side if the error in computing the area cannot exceed 2.7%. %
Answer:
a) [tex]\delta = 1.4\,\%[/tex], b) [tex]\delta_{max} = 1.35\,\%[/tex]
Step-by-step explanation:
a) The area formula for a square is:
[tex]A =l^{2}[/tex]
The total differential for the area is:
[tex]\Delta A = \frac{\partial A}{\partial l}\cdot \Delta l[/tex]
[tex]\Delta A = 2\cdot l \cdot \Delta l[/tex]
The absolute error for the area of the square is:
[tex]\Delta A = 2\cdot (10\,cm)\cdot (0.07\,cm)[/tex]
[tex]\Delta A = 1.4\,cm^{2}[/tex]
Thus, the relative error is:
[tex]\delta = \frac{\Delta A}{A}\times 100\,\%[/tex]
[tex]\delta = \frac{1.4\,cm^{2}}{100\,cm^{2}} \times 100\,\%[/tex]
[tex]\delta = 1.4\,\%[/tex]
b) The maximum allowable absolute error for the area of the square is:
[tex]\Delta A_{max} = \left(\frac{\delta}{100} \right)\cdot A[/tex]
[tex]\Delta A_{max} = \left(\frac{2.7}{100} \right)\cdot (100\,cm^{2})[/tex]
[tex]\Delta A_{max} = 2.7\,cm^{2}[/tex]
The maximum allowable absolute error for the length of a side of the square is:
[tex]\Delta l_{max}= \frac{\Delta A_{max}}{2\cdot l}[/tex]
[tex]\Delta l_{max} = \frac{2.7\,cm^{2}}{2\cdot (10\,cm)}[/tex]
[tex]\Delta l_{max} = 0.135\,cm[/tex]
Lastly, the maximum allowable relative error is:
[tex]\delta_{max} = \frac{\Delta l_{max}}{l}\times 100\,\%[/tex]
[tex]\delta_{max} = \frac{0.135\,cm}{10\,cm} \times 100\,\%[/tex]
[tex]\delta_{max} = 1.35\,\%[/tex]
Check all that apply?
Answer:
–11 and 2
Step-by-step explanation:
observe
x² + 9x – 22 = 0
(x + 11)(x – 2) = 0
x = –11 or x = 2
In how many ways can Susan arrange 7 books into 5 slots on her bookshelf?
Answer:
2520Step-by-step explanation:
This is permutation question
The formula for it:
N = b!/(b-s)!, where N- number of ways, b- number of books, s- number of slotsFinding the answer:
N = 7!/(7-5)! = 7!/2! = 7*6*5*4*3 = 2520Consider the following function. f(x) = 1/x, a = 1, n = 2, 0.6 ≤ x ≤ 1.4 (a) Approximate f by a Taylor polynomial with degree n at the number a. T2(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R2(x)| ≤ 7.71604938 Incorrect: Your answer is incorrect. (c) Check your result in part (b) by graphing |Rn(x)|.
The Taylor polynomial approximation to f(x) = 1/x up to degree 2 about x=a was calculated. It was mentioned that Taylor's inequality could be used to estimate the accuracy of this approximation. However, due to the lack of necessary information, an exact error bound or graphical check couldn't be determined.
Explanation:To begin the solution, we'll need to find the first couple of derivatives for the function f(x) = 1/x. The first derivative is f'(x) = -1/x² and the second derivative is f''(x) = 2/x³. These derivatives will be used to form the Taylor series approximation.
The Taylor series polynomial of degree 2 is given by the formula T₂(x) = f(a) + f'(a)*(x-a) + f''(a)*(x-a)²/2!, where a is the point we are approximating about and n is the degree of the Taylor polynomial. Substituting the given values, we get: T₂(x) = 1/1 - 1/1² * (x-1) + 2/1³ * (x-1)²/2!.
To estimate the accuracy of this approximation, we use Taylor's Inequality which provides an upper bound for the absolute error. The remainder term in Taylor's series is given by |R₂(x)| ≤ M * |x - a|³ / (3!*n), where M is the maximum value of the absolute third derivative on the interval [a, x]. After applying Taylor's inequality, we can get an accuracy estimate but unfortunately, the information provided doesn't give enough specifics for an exact calculation.
Finally, to verify the result graphically, you would plot |R₂(x)|, but without the explicit remainder term, this cannot be done.
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Let V be the set of functions f:R→R. For any two functions f,g in V, define the sum f+g to be the function given by (f+g)(x)=f(x)+g(x) for all real numbers x. For any real number c and any function f in V, define scalar multiplication cf by (cf)(x)=cf(x) for all real numbers x.
Answer:
To check that V is a vector space it suffice to show
1. Associativity of vector addition.
2. Additive identity
3. Existence of additive identity
4. Associativity of scalar multiplication
5. Distributivity of scalar sums
6. Distributivity of vector sums
7. Existence of scalar multiplication identity.
Step-by-step explanation:
To see that V is a vector space we have to see that.
1. Associativity of vector addition.
This property is inherited from associativity of the sum on the real numbers.
2. Additive identity.
The additive identity in this case, would be the null function f(x)=0 . for every real x. It is inherited from the real numbers that the null function will be the additive identity.
3. Existence of additive inverse for any function f(x).
For any function f(x), the function -f(x) will be the additive inverse. It is in inherited from the real numbers that f(x)-f(x) = 0.
4. Associativity of scalar multiplication.
Associativity of scalar multiplication is inherited from associativity of the real numbers
5. Distributivity of scalar sums:
Given any two scalars r,s and a function f, it will be inherited from the distributivity of the real numbers that
(r+s)f(x) = rf(x) + sf(x)
Therefore, distributivity of scalar sums is valid.
5. Distributivity of vector sums:
Given scalars r and two functions f,g, it will be inherited from the distributivity of the real numbers that
r (f(x)+g(x)) = r f(x) + r g(x)
Therefore, distributivity of vector sums is valid.
6. Scalar multiplication identity.
The scalar 1 is the scalar multiplication identity.
10 x .89 +7.2
please and thank you
Answer:
16.1 my friend
Step-by-step explanation:
Answer:
16.1
Step-by-step explanation:
Remember to always follow PEMDAS. In this case, we need to multiply before we divide.
10 x .89 + 7.2
8.9 + 7.2 = 16.1
The answer is 16.1
A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 50 months and a standard deviation of 9 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)
Answer:
A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 50 months and a standard deviation of 9 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries?
The company should guarantee the batteries for 38 months.
Step-by-step explanation:
Using standard normal table,
P(Z < z) = 10%
=(Z < z) = 0.10
= P(Z <- 1.28 ) = 0.10
z = -1.28
Using z-score formula
x = zσ + μ
x = -1.28 *9+50
x = 38
Therefore, the company should guarantee the batteries for 38 months.
Answer:
The company should guarantee the batteries (to the nearest month) for 38 months.
Step-by-step explanation:
We have here a normally distributed data. The random variable is the average life of the batteries.
From question, we can say that this random variable has a population mean of 50 months and population standard deviation of 9 months. We can express this mathematically as follows:
[tex] \\ \mu = 50[/tex] months.
[tex] \\ \sigma = 9[/tex] months.
The distribution of the random variable (the average life of the batteries) is the normal distribution, and it is determined by two parameters, namely, the mean [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex], as we already know.
For the statement: "The company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy", we can say that it means that we have determine, first, how many months last less of 10% of the batteries that its average life follows a normal distribution or are normally distributed?
To find this probability, we can use the standard normal distribution, which has some advantages: one of the most important is that we can obtain the probability of any normally distributed data using standardized values given by a z-score, since this distribution (the normal standard) has a mean that equals 0 and standard distribution of 1.
Well, the z-score is given by the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where, x is a raw score coming from a normally distributed data. This is the value that we have to transform into a z-score, that is, in a standardized value.
However, from the question, we want to know what value of z represents a cumulative probability of 10% in the cumulative standard normal distribution. We can find it using the standard normal table, available in Statistics books or on the Internet (of course, we can use also Statistics packages or even spreadsheets to find it).
Then, the value of z is, approximately, -1.28, using a cumulative standard normal table for negative values for z. If the cumulative standard normal only has positive values for z, we can obtain it, using the following:
[tex] \\ P(z<-a) = 1 - P(z<a) =P(z>a)[/tex]
That is, P(z<-1.28) = P(z>1.28). The probability for P(z<1.28) is approximately, 90%.
Therefore, using the formula [1]:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ -1.28 = \frac{x - 50}{9}[/tex]
[tex] \\ -1.28 * 9 = x - 50[/tex]
[tex] \\ -11.52 = x - 50[/tex]
[tex] \\ -11.52 + 50 = x[/tex]
[tex] \\ 38.48 = x[/tex]
[tex] \\ x = 38.48[/tex] months.
That is, less than 10% of the batteries have a average life of 38.48 months. Thus, the company should guarantee the batteries (to the nearest month) for 38 months.
What ordered pair corresponds to the vertex of the function
Answer:A+b
by-step explanation:
Answer:
you have the correct answer!
Step-by-step explanation:
A sample of 56 fish (Mogul liza species) were tested for zinc concentration (Environmental Monitoring and Assessment, 1993). The interval from 8.8 mg/g to 9.5 mg/g is the 95% confidence interval for the population mean zinc concentration. (The sample mean was 9.15.) Which following statements is the best interpretation for the meaning of this confidence interval? The probability that this confidence interval (8.8, 9.5) contains the true population mean is 0.95. In repeated sampling from this fish population, about 95% of the confidence intervals calculated from these samples will contain 9.15. We can be 95% sure that the true population mean zinc concentration is between 8.8 mg/g and 9.5 mg/g. The probability that this confidence interval (8.8, 9.5) contains the sample mean is 0.95. In repeated sampling from this fish population, about 95% of the confidence intervals calculated will contain 95% of the zinc concentrations of the fish. We can be sure that 95% of all Mogul liza species will have zinc concentrations between 8.8 mg/g and 9.5 mg/g.
Answer:
We can be 95% sure that the true population mean zinc concentration is between 8.8 mg/g and 9.5 mg/g.
Step-by-step explanation:
Given that
N = Sample = 56
Confidence Interval = 95%
Mean Interval = 8.8 mg/g to 9.5 mg/g
UB = Upper Bound = 9.5mg/g
LB = Lower Bound = 8.8mg/g
The sample mean was 9.15mg/g
The sample mean is gotten from ½(UB + LB)
Sample Mean = ½(8.8 + 9.5)
Sample Mean = ½ * 18.3
Sample Mean = 9.15mg/g
From the definition of confidence Interval;
"Confidence Interval is a range of values so defined that there is a specified probability that the value of a parameter lies within it"
This means that the best interpretation of the data given is "the mean value of the 56 sample of fishes is between 8.8mg/g and 9.5mg/g;"
With 8.8mg/g as the lower bound and 9.9mg/g as the upper bound.
Analyze the diagram below and complete the instructions that follow.
and are similar. Find the value of x.
A.
5
B.
15
C.
60
D.
240
Please select the best answer from the choices provided
A
B
C
D
The mean crying time of infants during naptime at a local preschool is 12 mins. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8 ± 4.6 (M ± SD) minutes. Test whether this new naptime routine reduced crying time at a 0.05 level of significance.A) The new naptime routine significantly reduced crying time, t(24) = ?4.35, p <0.05.B) The new naptime routine did not reduce crying time, t(24) = ?4.35, p < 0.05.C) The new naptime routine did not reduce crying time, t(24) = 0.92, p > 0.05.D) The new naptime routine significantly reduce crying time, t(24) = 0.92, p < 0.05.
Answer:
Step-by-step explanatio n: ummmoirnd iehcn
Many urban zoos are looking at ways to effectively handle animal waste. One zoo has installed a facility that will transform animal waste into electricity. To estimate how many pounds of waste they may have to fuel the new facility they began keeping meticulous records. They discovered that the amount of animal waste they were disposing of daily is approximately Normal with a mean of 348.5 pounds and a standard deviation of 38.2 pounds. Amounts over 350 pounds would generate enough electricity to cover what is needed to for the entire aquarium that day. Approximately what proportion of the days can the zoo expect to obtain enough waste to cover what is needed to run the entire aquarium for the day (A) 0.484 (B) 0.499 (C) 0.516 (D) 0.680 (E) 0.950
Answer:
Option A: 0.484Explanation:
The amount of animal waste one zoo is diposing daily is approximately normal with:
mean, μ = 348.5 lbsstandard deivation, σ = 38.2 lbsThe proportion of waste over 350 lbs may be found using the table for the area under the curve for the cumulative normal standard probability.
First, find the z-score for 350 lbs:
[tex]z-score=\dfrac{X-\mu}{\sigma}[/tex]
[tex]z-score=\dfrac{350lbs-348.5lbs}{38.2lbs}\approx0.04[/tex]
There are tables for the cumulative areas (probabilities) to the left and for the cumulative areas to the right of the z-score.
You want the proportion of the days when the z-score is more than 0.04; then, you can use the table for the values to the rigth of z = 0.04.
From such table, the area or probability is 0.4840.
The attached image shows a portion of the table with that value: it is the cell highlighted in yellow.
Hence, the answer is the option (A) 0.484.
By calculating the z-score for 350 pounds of waste and consulting the standard normal distribution, the proportion of days the zoo can expect to have enough animal waste to power the entire aquarium is approximately 0.484.
To determine the proportion of days the zoo can expect to generate enough animal waste to run the entire aquarium, we can use z-scores in a normal distribution. Given the mean (μ = 348.5) and standard deviation (σ = 38.2), we want to find the proportion of the data that is above 350 pounds.
First, we calculate the z-score for 350 pounds:
z = (X - μ) / σ = (350 - 348.5) / 38.2 ≈ 0.04
Now we need to find the probability that the z-score is greater than 0.04. Consulting a standard normal distribution table or using a calculator, this gives us a probability of approximately 0.484.
Therefore, the proportion of the days the zoo can expect to obtain enough waste to cover the energy demands for the entire aquarium is 0.484.
$1500 is invested at a rate of 3% compounded monthly. Write a compound interest function to model this situation. Then find the
balance after 5 years.
Answer:
Equation: [tex]F=1500(1.0025)^{12t}[/tex]
The balance after 5 years is: $1742.43
Step-by-step explanation:
This is a compound growth problem . THe formula is:
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]
Where
F is future amount
P is present amount
r is rate of interest, annually
n is the number of compounding per year
t is the time in years
Given:
P = 1500
r = 0.03
n = 12 (compounded monthly means 12 times a year)
The compound interest formula modelled by the variables is:
[tex]F=1500(1+\frac{0.03}{12})^{12t}\\F=1500(1.0025)^{12t}[/tex]
Now, we want balance after 5 years, so t = 5, substituting, we get:
[tex]F=1500(1.0025)^{12t}\\F=1500(1.0025)^{12*5}\\F=1500(1.0025)^{60}\\F=1742.43[/tex]
The balance after 5 years is: $1742.43
Mollie is training for a race. She will swim, bike and run during the race. One week, she swims 1 2/4 miles and bikes 22 3/4 miles. She also runs during rhe week. The total distance she swims, bikes, and runs during the week is 30 2/4 miles. How far does she run during the week?
100 POINTS!!!!! HELP ME PLEASE DONT HAVE A LOT OF TIME!!!!! HELP!!!!!
The school wants to order a new counter top for the teacher’s lounge. The shape of the counter top that they are replacing is shown below.
A countertop can be broken into 2 rectangles. 1 rectangle has a base of 70 inches and height of 20 inches. The other rectangle has a base of 20 inches and height of 30 inches.
If the new countertop costs $0.75 per square inch, what is the price of the replacement countertop?
$1,500
$1,800
$2,000
$2,400
Answer:
A. $1500
Step-by-step explanation:
We need to find the countertop area, so let's calculate the areas of the rectangles that the problem broke the countertop into:
1. "1 rectangle has a base of 70 inches and height of 20 inches"
The area of a rectangle is denoted by: A = bh, where b is the base and h is the height. Here, b = 70 and h = 20, so the area is: A = 70 * 20 = 1400 inches squared
2. "The other rectangle has a base of 20 inches and height of 30 inches"
Again, use A = bh: b = 20 and h = 30, so A = 20 * 30 = 600 inches squared
Add up these two areas: 1400 + 600 = 2000 inches squared.
The problem says that the cost is $0.75 per square inch, so multiply this by 2000 to get the total cost of 2000 square inches:
2000 * 0.75 = $1500
Thus, the answer is A.
Hope this helps!
Answer:
$1500
Step-by-step explanation:
You can divide this figure into 2 rectangle with dimensions:
1) 70 × 20
2) 20 × (50-20: 20 × 30
Area:
(70×20) + (20×30)
1400 + 600
2000 in²
Cost per in²: 0.75
2000in² cost:
2000 × 0.75
$1500
Kelsey’s bank changed her $17.50
Identify the range of the function shown in the graph.
NEED HELP ASAP!!!!
Answer:
B - -5 < y < 5
Step-by-step explanation:
Range is highest and lowest y value the graph goes to.
You can see on the graph that it does not pass 5 and -5