Answer:
42 inches
Step-by-step explanation:
1 ft = 12 inch
Answer:
42 inches.
Step-by-step explanation:
Unit of measurement:
1 foot = 12 inches.
3 ft x 12 inches = 36 inches.
1/2 foot x 12 inches = 12/2 = 6 inches.
36 inches + 6 inches = 42 inches
42 inches is your answer.
~
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.
(a)
[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]
[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]
[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]
(b)
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]
The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is not information about the proportion of students who might choose the option. What size sample should the department head take if he wants to be 95% confident that the estimate is within 0.10 of the true proportion
Answer:
96
Step-by-step explanation:
From the given information:
At 95% Confidence interval level,Level of significance [tex]\alpha[/tex] 0.05, the value of Z from the standard normal tables = 1.96
Margin of Error = 0.10
Let assume that the estimated proportion = 0.5
therefore; the sample size n can be determined by using the formula: [tex]n =(\dfrac{Z}{E})^2 \times p\times (1-p)[/tex]
[tex]n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)[/tex]
[tex]n =(19.6)^2 \times 0.5\times (0.5)[/tex]
n = 96.04
n [tex]\approx[/tex] 96
Given a dataset with the following properties:
mean = 50
median = 40
standard deviation = 5
What is the shape of the distribution?
Answer:
The distribution is positively skewed.
Step-by-step explanation:
A measure of skewness is defined in such a way that the measure should always be zero when the distribution is symmetric and measure should be a pure number i.e independent of origin and units of measurement.
The shape of the distribution can be found by finding the coefficient of skewness.
The coefficient of skewness can be found by
Sk= 3(Mean-Median)/ Standard Deviation
Sk= 3( 50-40)5= 30/5=6
The shape will be positively skewed.
In a positively skewed distribution the mean > median > mode. It has a long right tail.
Using the skewness formula, it is found that the distribution is right-skewed.
------------------
The skewness of a data-set with mean M, median [tex]M_e[/tex] and standard deviation s is given by:[tex]S = \frac{3(M - M_e)}{s}[/tex]
If |S| < 0.5, the distribution is said to be symmetric.If S <-0.5, the distribution is left-skewed.If S > 0.5, the distribution is right-skewed.------------------
Mean of 50, thus, [tex]M = 50[/tex]Median of 40, thus [tex]M_e = 40[/tex]Standard deviation of 5, thus, [tex]s = 5[/tex]The coefficient is:
[tex]S = \frac{3(M - M_e)}{s} = \frac{3(50 - 40)}{5} = \frac{30}{5} = 6[/tex]
Thus, the distribution is right-skewed.
A similar problem is given at https://brainly.com/question/24415645
Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131
Is there evidence to doubt the color distribution claimed by the website? Use =0.05
Answer:
Calculated χ² = 13.425
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
Step-by-step explanation:
Color Blue Orange Green Red Yellow Brown
Frequency 30 48 55 66 70 131
Expected 40 40 40 80 80 120
H0: The bag of plain M&Ms is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown
Ha: The color distribution is not equal to the distribution stated in the null hypothesis.
Calculate chi square
χ² = (30-40)² /40 + (48-40)²/40 + (55-40)²/40 + (66-80)²/80 + (70-80)²/80 + (131-120)²/120
χ² = 2.5 + 1.6 + 5.625 + 2.45 + 1.25= 13.425
The critical region for χ² for 5 degrees of freedom with ∝= 0.05 is
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Social Activity Education Above Average Average Below Average College 30 20 10 High School 20 40 90 Grade School 10 50 130 Using 0.05 as the significance level, what is the critical value for the test statistic
Answer:
9.488
Step-by-step explanation:
The critical value is found by first assessing which statistical test should be used.
We are interested in investigating relationship between social activity and education so chi-square test would be appropriate.
We have 3 rows and 3 columns. The degree of freedom for chi-square critical value is (r-1)(c-1)=(3-1)(3-1)=2*2=4
Chi-square critical value(0.05,4)= 9.488
Cancel the common factor of the numerator and the denominator and write specified expression
Step-by-step explanation:
Hello,
I hope you mean to cancel the common factor that exists in numerator and denominator,right.
so, Let's look for the common factor,
here, the expression is,
=4(x-2)/ (x+5)(x-2)
so, here we find the common factor is (x-2)
now, we have to cancel it. And after cancelling we get,
=4/(x+5)
Note:{ we cancel the common factor if the common factors are in multiply form.}
Hope it helps
Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ(x) = 2x2 + 4x – 16 C ƒ(x) = x2 – 2x – 8 D ƒ(x) = 2x2 – 4x – 16
Answer:
D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]
Step-by-step explanation:
Any parabola is modelled by a second-order polynomial, whose standard form is:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.
In addition, a system of three linear equations is constructed by using all known inputs:
(-2, 0)
[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)
(4, 0)
[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)
(0,-16)
[tex]c = -16[/tex] (Eq. 3)
Then,
[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)
[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)
(Eq. 3 in Eqs. 1 - 2)
[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)
[tex]a = 4 + 0.5\cdot b[/tex]
Then,
[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)
[tex]64 + 12\cdot b = 16[/tex]
[tex]12\cdot b = -48[/tex]
[tex]b = -4[/tex]
The remaining coeffcient is:
[tex]a = 4 + 0.5\cdot b[/tex]
[tex]a = 4 + 0.5\cdot (-4)[/tex]
[tex]a = 2[/tex]
The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.
Answer:
D ƒ(x) = 2x2 – 4x – 16
Step-by-step explanation:
Sherina wrote and solved the equation. x minus 56 = 230. x minus 56 minus 56 = 230 minus 56. x = 174. What was Sherina’s error?
Answer:
subtracting 56 instead of adding (or adding wrong)
Step-by-step explanation:
She wrote ...
x - 56 = 230
x - 56 - 56 = 230 -56 . . . . correct application of the addition property*
x = 230 -56 . . . . . . . . . . . . incorrect simplification
Correctly done, the third line would be ...
x -112 = 174
This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...
x - 56 + 56 = 230 + 56 . . . using the addition property of equality
x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides
__
There were two errors:
1) incorrect strategy --- subtracting 56 instead of adding
2) incorrect simplification --- simplifying -56 -56 to zero instead of -112
We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.
_____
* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.
Answer:
D: Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
I got a 100% on my test.
I hope this helps.
A local mattress manufacturer wants to know if its manufacturing process is in or out of control and has hired you, a statistics expert in the field, to analyze its process. Specifically, the business has run 20 random samples of size 5 over the past month and has determined the mean of each sample.
a. Determine the estimate of the mean when the process is in control.
b. Assuming the process standard deviation is .50 and the mean of the process is the estimate calculated in part a, determine the Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process.
c. Explain the results to the vice-president of the mattress manufacturer focusing on whether, based on the results, the process is in or out of control.
Sample no. Mean of Sample
1 95.72
2 95.44
3 95.40
4 95.50
5 95.56
6 95.72
7 95.60
8 95.24
9 95.46
10 95.44
11 95.80
12 95.20
13 94.82
14 95.78
15 95.18
16 95.32
17 95.08
18 95.22
19 95.04
20 95.
Answer:
Answer to question a = 95.4
Answer to question b = UCL = 96.07
LCL = 94.73
Answer to question c = Process is still in control
Step-by-step explanation:
a. The computation of estimate mean is as shown below:-
= 95.4
b. The computation of Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process is shown below:-
= 95.4 + 0.67082
= 96.07
= 95.4 - 0.67082
= 94.73
c. The explanation is shown below:-
From the above calculation we can see that the sample lies between LCL AND UCL that is (94.73 ,96.07) ,
The Process is still in control
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?
iv. Describe how you would guide a JHS student to find the bearing and distance of
Musah’s final point from the centre.
Answer:
ii. 75 steps
iii. 75 steps
iv. 106 steps, and [tex]315^{0}[/tex]
Step-by-step explanation:
Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.
ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;
bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]
To determine distance AB,
[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex] + [tex]/25/^{2}[/tex]
= 25000 + 625
= 3125
AB = [tex]\sqrt{3125}[/tex]
= 55.90
AB ≅ 56 steps
Thus, AC = 50 steps + 56 steps
= 106 steps
From ΔACD,
Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]
⇒ x = 106 × Sin [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance west from centre to final point is 75 steps
iii. From the secon attachment, Musah's distance north, y, can be determined by;
Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]
⇒ y = 106 × Cos [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance north from centre to final point is 75 steps.
iv. Musah's distance from centre to final point is AC = AB + BC
= 50 steps + 56 steps
= 106 steps
From ΔACD,
Tan θ = [tex]\frac{75}{75}[/tex]
= 1.0
θ = [tex]Tan^{-1}[/tex] 1.0
= [tex]45^{0}[/tex]
Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]
= [tex]315^{0}[/tex]
Factor 13ab3 + 39a2b5.
[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]
Brazil number one.
Answer:
there's no answer for that equation
[tex]f(x) = sqr root x+3 ; g(x) = 8x - 7[/tex]
Find (f(g(x))
[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]
Can someone do this assuming that it is infinite and as well as assuming it's not infinite? Thanks!
Answer:
see below
Step-by-step explanation:
4,7,12,19
We are adding 3,5,7,9..... each time
The sequence is not arithmetic because we are not adding a constant. It is not geometric since we are not multiplying by a constant term each time
There is no common difference or common ratio.
The explicit formula is
an =n^2 +3
The recursive formula is
(n+1)^2 +3 - (n^2 +3)
n^2 +2n+1+3 - ( n^2+3)
2n+1
a sub(n+1) = a sub( n) + 2n+1
The 10th term
an = n^2 +3
Let n=10
an = 10^2+3
= 100+3
= 103
summation
see image
since the numbers are increasing and greater than 1 the sum does not exist
The expression −50x+100 represents the balance, in dollars, of a bank account after x months. What is the rate of change, in dollars per month, of the bank account balance?
Answer:
-50
Step-by-step explanation:
Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)
-50(0)+100 (0,100) Y₂-Y₁/X₂-X₁ 50-100/1-0
Rate of change per month = -$50
what should be added to 66.778 get 78.2
Answer:
11.422
Step-by-step explanation:
[tex]78.2 - 66.778 \\ = 11.422[/tex]
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.) ∫4x2 lnx dx ; u= lnx , dv=4x 2dx
Take
[tex]u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x[/tex]
[tex]\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3[/tex]
Then
[tex]\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C[/tex]
[tex]=\boxed{\dfrac49x^3(3\ln x-1)+C}[/tex]
The required integration is,
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C
The given integral is,
∫4x² lnx dx
Using integration by parts, choose u and dv.
In this case, we choose u = lnx and dv = 4x²dx.
Using the formula for integration by parts, we have:
∫ u dv = uv - ∫ v du
Substituting the values of u and dv, we get:
∫4x² lnx dx = (lnx) (∫ 4x² dx) - ∫ [(d/dx)lnx] (∫4x² dx) dx
Simplifying the first term using the power rule of integration, we get:
∫ 4x² dx = (4/3)x³ + C₁
For the second term, we need to evaluate (d/dx)lnx,
Which is simply 1/x. Substituting this value, we get:
∫ [(d/dx)lnx] (∫4x² dx) dx = ∫ [(1/x) ((4/3)x³ + C₁)] dx
Simplifying this expression, we get:
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - ∫ [(4/3)x³/x] dx
Using the power rule of integration again, we get:
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C
Where C is the constant of integration.
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Given: x - 5 > -2. Choose the solution set.
Answer: x>3
Step-by-step explanation:
x-5>2
x>+5-2
x>3
The ages of some lectures are 42,54,50,54,50,42,46,46,48 and 48.Calculate the:
(a)Mean Age.
(b)Standard deviation.
Answer:
The mean age is 48
The standard deviation is 4
Step-by-step explanation:
The answer is, (a) mean age is 48.
(b) standard deviation is 4.
What is a mean age?Average age of the population calculated as the arithmetic mean.Another parameter determining the average age of the population is the median age.What does standard deviation of age mean?In general, the standard deviation tells us how far from the average the rest of the numbers tend to be, and it will have the same units as the numbers themselves. If, for example, the group {0, 6, 8, 14} is the ages of a group of four brothers in years, the average is 7 years and the standard deviation is 5 years.How do you find the mean age?To find the mean add all the ages together and divide by the total number of children.
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Karl needs a total of $30 to buy a bike. He has $12. He can earn $6 an hour
babysitting. Which equation can be used to find the number of hours, h, Karl has to
babysit to have the money he needs?
30 - 6h + 12 = 0
6+ n = 12
6 + 12 h = 30
6 h + 12 = 30
Answer:
6h + 12 = 30
Step-by-step explanation:
Hence, the equation obtained for number of hours worked is given as 12 + 6h = 30.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
The total money required is given as $30.
Suppose the number of hours for babysitting be h.
Then, the money earned by doing it is $6h.
And, the total money with Karl is 12 + 6h.
As per the question, the following equations can be written as,
12 + 6h = 30
Hence, the equation for finding the number of hours is given as 12 + 6h = 30.
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Determine whether each equation has one solution, no solution or infinitely many solutions. 4x + 10 = 2(2x + 5) 4x - 5 = 4x + 10 4x - 5 = -5
Answer:
see below
Step-by-step explanation:
4x + 10 = 2(2x + 5)
Distribute
4x+10 = 4x+10
Since the left side is identical to the right side, there are infinite solutions
4x - 5 = 4x + 10
Subtract 4x from each side
-5 = 10
This is never true, so there are no solutions
4x-5 = -5
Add 5 to each side
4x = 0
x=0
There is one solutions
What is the answer, what are the steps to solve this, and what do the parts of the equation represent?
Step-by-step explanation:
Just sub 4 into where n is
Decide whether the pair of ratios form a proportion 15/12=4.5/3.6
Answer: Yes they form a proportion. The given equation is a true equation.
==========================================
Explanation:
The idea is that if we have
a/b = c/d
then that it is the same as
a*d = b*c
This is known as cross multiplication. We'll use this rule to get
15/12 = 4.5/3.6
15*3.6 = 12*4.5
54 = 54
We got the same value on both sides, meaning that the last equation is true. Consequently, it means the first equation is true as well (all three equations are true).
--------
You could also use your calculator to see that
15/12 = 1.25
4.5/3.6 = 1.25
showing that 15/12 = 4.5/3.6 is a true equation and the ratios form a proportion.
Answer:
15/12=4.5/3.6 = True
Step-by-step explanation:
Simplify the following: Left-hand
15/12
Hint: | Reduce 15/12 to lowest terms. Start by finding the GCD of 15 and 12.
The gcd of 15 and 12 is 3, so 15/12 = (3×5)/(3×4) = 3/3×5/4 = 5/4:
Answer: 5/4
______________________________
Approximate the following:
4.5/3.6
Hint: | Express 4.5/3.6 in decimal form.
4.5/3.6 = 1.25:
Answer: 1.25 = 5/4
Last question of the day!!
Answer:
Correct options are 2, 5 and 7.
Step-by-step explanation:
Consider the given vertices of triangle are A(-3,-3), B(-3,2) and C(1,2).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{(-3-(-3))^2+(2-(-3))^2}[/tex]
[tex]AB=\sqrt{(0)^2+(5)^2}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5[/tex]
Similarly,
[tex]BC=\sqrt{(1-(-3))^2+(2-2)^2}=4[/tex]
[tex]AC=\sqrt{(1-(-3))^2+(2-(-3))^2}=\sqrt{16+25}=\sqrt{41}[/tex]
From the above calculation it is clear that AC>AB and AC>BC.
According to Pythagoras theorem, in a right angle triangle, the square of largest side is equal to the sum of squares of two small sides.
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex]AC^2=(\sqrt{41})^2=41[/tex]
[tex]AB^2+BC^2=(5)^2+4^2=24+16=41=AC^2[/tex]
So, given triangle is a right angle triangle and AC is its hypotenuse.
Therefore, the correct options are 2, 5 and 7.
At a sale, dresses were sold for $39 each. This price was 65% of a dress's original price. How much did a dress originally cost?
Answer:
Hey there!
We can write the equation:
0.65x=39
x=60
The dress originally sold for 60 dollars.
Hope this helps :)
A study of 200 computer service firms revealed these incomes after taxes: Income After Taxes Number of Firms Under $1 million 102 $1 million up to $20 million 61 $20 million or more 37 What is the probability that a particular firm selected has $1 million or more in income after taxes
Answer:
The probability that a particular firm selected has $1 million or more in income after taxes is 49%.
Step-by-step explanation:
We are given a study of 200 computer service firms revealed these incomes after taxes below;
Income After Taxes Number of Firms
Under $1 million 102
$1 million up to $20 million 61
$20 million or more 37
Total 200
Now, the probability that a particular firm selected has $1 million or more in income after taxes is given by;
Total number of firms = 102 + 61 + 37 = 200
Number of firms having $1 million or more in income after taxes = 61 + 37 = 98 {here under $1 million data is not include}
So, the required probability = [tex]\frac{\text{Firms with \$1 million or more in income after taxes}}{\text{Total number of firms}}[/tex]
= [tex]\frac{98}{200}[/tex]
= 0.49 or 49%
The probability that a particular firm selected has $1 million or more in income after taxes is 0.49 or 49%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
A study of 200 computer service firms revealed these incomes after taxes:
Income After Taxes Number of Firms Under
$1 million 102
$1 million up to $20 million 61
$20 million or more 37.
Then the total event will be
Total event = 102 + 37 +61 = 200
The probability that a particular firm selected has $1 million or more in income after taxes will be
Favorable event = 37 + 61 = 98
Then the probability will be
[tex]\rm P = \dfrac{98}{200} \\\\P = 0.49 \ or \ 49 \%[/tex]
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If you use a 5/8 inch drill bit instead of a 3/16 that the project called for ,your hole will be too . by inches
the difference of 8 and 2, added to x"
Answer:
see below
Step-by-step explanation:
Difference is subtract
(8-2)
Then add this to x
(8-2) +x
6+x
How to evaluate this help me out so lost?
Answer:
5443
Step-by-step explanation:
Order of Operations: BPEMDAS
Always left to right.
Step 1: Add 68 and 5042
68 + 5042 = 5110
Step 2: Add 5110 and 333
5110 + 333 = 5443
And we have our answer!
Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?
Answer:
Step-by-step explanation:
First we start with 12 pounds
On Monday, she and her friends eat 4 pounds. So we have 8 now.
On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.
On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15
On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.
On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.
On Saturday, her mom gives her one more pound. 2 + 1 = 3.
On Sunday, she finally has 3 pounds.
Answer:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
The chart shows a certain city's population by age. Assume that the selections are independent events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.
Answer:
0.000014
Step-by-step explanation:
The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:
City X's Population by Age
0-24 years old 33%
25-44 years old 22%
45-64 years old 21%
65 or older 24%
In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:
P(A and B) = P(A) * P(B)
probability that the first 2 are 65 or older
Let A be the event that the first 2 are 65 or older
The probability of 65 or older 24% i.e. 0.24
So the probability that first 2 are 65 or older is:
0.24(select resident 1) * 0.24(select resident 2)
P(A) = 0.24 * 0.24
= 0.0576
P(A) = 0.0576
probability that the next 3 are 25-44 years old
Let B be the event that the next 3 are 25-44 years old
25-44 years old 22% i.e. 0.22
So the probability that the next 3 are 25-44 years old is:
0.22 * 0.22* 0.22
P(B) = 0.22 * 0.22 * 0.22
= 0.010648
P(B) = 0.010648
probability that next 2 are 24 or younger
Let C be the event that the next 2 are 24 or younger
0-24 years old 33% i.e. 0.33
So the probability that the next 2 are 24 or younger is:
0.33 * 0.33
P(C) = 0.33 * 0.33
= 0.1089
P(C) = 0.1089
probability that last is 45-64 years old
Let D be the event that last is 45-64 years old
45-64 years old 21% i.e. 0.21
So the probability that last is 45-64 years old is:
0.21
P(D) = 0.21
So probability of these independent events is computed as:
P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)
= 0.0576 * 0.010648 * 0.1089 * 0.21
= 0.000014
