Answer:
a) For this case we select a sample size of n=9. And we know that the distribution of X is normal so then the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
b) [tex] SE = \frac{\sigma}{\sqrt{n}} =\frac{5.8}{\sqrt{9}} =1.9333[/tex]
c) [tex] P\bar X >39.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 39.5 we got:
[tex] z = \frac{39.5-38}{\frac{5.8}{\sqrt{9}}}= 0.78[/tex]
And using the complement rule we got:
[tex] P(z >0.78) =1-P(Z<0.78) = 1-0.7823= 0.2177[/tex]
d) [tex] P\bar X >37.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 37.5 we got:
[tex] z = \frac{37.5-38}{\frac{5.8}{\sqrt{9}}}= -0.26[/tex]
And using the complement rule we got:
[tex] P(z >-0.26) =1-P(Z<-0.26) = 1-0.3974= 0.6026[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the life of batteries of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(38,5.8)[/tex]
Where [tex]\mu=38[/tex] and [tex]\sigma=5.8[/tex]
Part a
For this case we select a sample size of n=9. And we know that the distribution of X is normal so then the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
Part b
The standard error is given by:
[tex] SE = \frac{\sigma}{\sqrt{n}} =\frac{5.8}{\sqrt{9}} =1.9333[/tex]
Part c
We want this probability:
[tex] P\bar X >39.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 39.5 we got:
[tex] z = \frac{39.5-38}{\frac{5.8}{\sqrt{9}}}= 0.78[/tex]
And using the complement rule we got:
[tex] P(z >0.78) =1-P(Z<0.78) = 1-0.7823= 0.2177[/tex]
Part d
We want this probability:
[tex] P\bar X >37.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 37.5 we got:
[tex] z = \frac{37.5-38}{\frac{5.8}{\sqrt{9}}}= -0.26[/tex]
And using the complement rule we got:
[tex] P(z >-0.26) =1-P(Z<-0.26) = 1-0.3974= 0.6026[/tex]
The distribution of the mean life of Batteries produced by Power+, Inc. follows Normal distribution. The standard error is calculated to be 1.9333. Using Z scores, it's discovered that approximately 21.77% of samples will have a mean life more than 39.5 hours while around 60.26% samples will have a mean useful life more than 37.5 hours.
Explanation:Understanding the Distribution of the Mean Life of Batteries
a. The distribution of the sample mean should approximate a normal distribution because we know the distribution of the population (life of the batteries) is normal. The expectation is that the sample mean should also follow normal distribution, based on the Central Limit Theorem.
b. The standard error of the distribution of the sample mean, is calculated as the standard deviation divided by the square root of the number of samples. Therefore, the standard error is 5.8 / sqrt(9), that is approximately 1.9333.
c. To find the proportion of samples with a mean useful life of more than 39.5 hours, we first find the Z score for 39.5. The Z score is calculated by (sample mean - population mean) / standard error. Therefore, Z = (39.5 - 38) / 1.9333 = approximately 0.78 (rounded to 2 decimal places). Looking this up on a Z table gives us 0.7823. However, because we want the proportion where it is more than 39.5 hours, we need to subtract this from 1. So, 1-0.7823 = 0.2177 (i.e., 21.77% samples will have a mean useful life more than 39.5 hours).
d. Following the same procedure, the Z score for a sample mean of 37.5 is approx negative -0.26 (rounded to 2 decimal places) using the same calculation as above. Looking this up on a Z table gives us 0.3974. But, because we want the proportion greater than 37.5 hours, we need to subtract this from 1. So, 1-0.3974 = 0.6026 (i.e., 60.26% samples will have a mean useful life more than 37.5 hours).
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What is the equation of the line that passes through the point (6,-5)(6,−5) and has a slope of -\frac{3}{2}−
2
3
The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
WE need to find the equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex].
Given: m=-3/2 and x_1 = -6 and y_1 =-5
So the required equation of a line in a point-slope form;
y+5 = -3/2(x+6)
Hence, The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).
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The equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.
Explanation:To find the equation of the line, we can use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point is (6, -5) and the slope is -3/2. Plugging these values into the equation, we get y - (-5) = -3/2(x - 6), which simplifies to y + 5 = -3/2(x - 6).
Expanding the equation further, we get y + 5 = -3/2x + 9. To isolate y, we can subtract 5 from both sides of the equation, resulting in y = -3/2x + 4. Therefore, the equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.
The function below describes the number of students who enrolled at a university, where f(t) represents the number of students and t represents the time in years.
Initially,_____ students enroll at the university. Every______ , the number of students who enroll at the university increases by a factor of______ .
Answer:
18,500 , 1 , 1.03
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
f(t) =18,500(1.03)^t
1st blank:
19,055
1.03
3
18,500
2nd blank:
t years
2 years
3 years
1 year
3rd blank:
19,055
3
18,500
1.03
My answer:
Given that: f(t) =18,500*[tex]1.03^{t}[/tex]
1st blank:
Initial value when t = 0, so we have:
f(0) =18,500*[tex]1.03^{0}[/tex]
[tex]f(0) =18,500(1)\\ f(0) =18,500[/tex]
So we choose D for 1st blank
2nd and 3rd blank:
Because it's an exponential function f(t) =18,500*[tex]1.03^{t}[/tex] , with every value of t increment f(t) increase by a factor of 1.03 . So Every 1 year the number of students who enroll at the university increases by a factor of 1.03
=> 2nd blank: 1
=> 3rd blank: 1.03
Hope it will find you well.
Answer:
The first blank this is 18,500. Second blank is 1. The third blank is 1.03. hope this helps
Step-by-step explanation:
Pedro is building a playground in the shape of a right triangle he wants to know the area of the playground to help him decide how sand to buy what are the dimensions of the rectangle
Answer:
Amount of sand=Area of triangle(ABC)=1/2*AB*BC
Dimension of rectangle as length=BC and breadth=AB
Step-by-step explanation:
Given:
Pedro building a playground in shape of right angled triangle.
To Find:
How much sand he need to buy
And if playground changed to rectangle what will be the dimensions.
Solution:
Consider a ΔABC be the play ground vertex of playground,
And AB and BC be the sides making right angle.
The sand required to fill ground will be the amount of are covered by the ABC triangle.
So,
Area Of triangle(ABC)=1/2* base* height
Here base will be BC and height =AB
Therefore Area of Triangle(ABC)=1/2*BC*AB
Depending on the lengths of base and height amount of sand will be decided.
Now,
For Rectangle dimensions,
We know that if same sized triangles composes each other forms a rectangle.
It requires two triangle to form one rectangle as follows
(Refer the attachment)
Same sized Triangle ACD is imposed on it to from rectangle ABCD.
So dimension for rectangle will be same as the triangle
Dimension=length and breadth
i.e. length=base of triangle=BC
Breadth=Height of triangle=AB
i.e Breadth =AB.
Euclid’s root beer mug is shaped basically like a cylinder that is eight inches tall with a radius of three inches. Aristotle’s root beer glass is shaped basically like a cone that is 18 inches tall with a diameter of four inches. Which vessel holds the most root beer?
The Euclid's mug holds the most root beer.
Step-by-step explanation:
Euclid's mug :
Height = 8 inches
Radius = 3 inches
Volume = π(r x r) h
= (3.14) (9) 8
= 226.08 cubic inches
Aristotle's mug:
Height = 18 inches
Diameter = 4 inches
Radius = 2 inches
Volume = (1/3) π(r x r) h
= (1/3) (3.14) (4) 18
= 37.68 cubic inches
The Euclid's mug holds the most root beer.
Evaluate Loga√44+ Log a√275- Log 11a
They all have base 10
Answer:
[tex]log(10a)[/tex]
Step-by-step explanation:
[tex]log(a\sqrt{44})+log(a \sqrt275)-log(11a)[/tex]
We can simplify this using these log laws:
[tex]log(a)+log(b)=log(ab)\\log(a)-log(b)=log(\frac{a}{b})[/tex]
[tex]log(\frac{a^2\sqrt{44} \sqrt{275}}{11a})[/tex]
We also have laws to simplify square roots
[tex]\sqrt{a}*\sqrt{b} = \sqrt{ab}[/tex]
So this becomes
[tex]log(\frac{a^2\sqrt{12100}}{11a})[/tex]
[tex]\sqrt{12100} = 110[/tex]
so this becomes
[tex]log(\frac{110a^2}{11a})=log(10a)[/tex]
Mr. and Mrs. Chavez close on a 30 year home loan for $250,000. The monthly payment with no points is $1,580, but if they buy a point it is $1,560. What might you infer if Mr. and Mrs. Chavez choose not to buy a point?
a.
They plan to sell the house at the end of 5 years.
b.
They plan to sell the house at the end of 10 years.
c.
They plan to sell the house at the end of 15 years.
d.
They plan to stay in the house at least 30 years.
Answer: A
Answer: A
Step-by-step explanation:
John is icing 30 cupcakes. He spreads mint icing on 1/5 of the cupcakes and chocolate icing on 1/2 of the remaining cupcakes. How many cupcakes will get chocolate frosting?
Answer: 12 cupcakes will get chocolate frosting
Step-by-step explanation: John started with 30 cupcakes and spresd mint icing on 1/5 of these. That means he did the following
Mint icing = 30 x 1/5
Mint icing = 6
That leaves him with a total of 30 minus 6 cupcakes which equals 24 cupcakes.
Next he spreads chocolate icing on half of the remaining, that is half of 24. That means he did the following;
Chocolate icing = 24 x 1/2
Chocolate icing = 12
Therefore 12 cupcakes will get chocolate frosting
The scale of Miguel's dollhouse is 1in.=2 2/7ft. If the pants of the military uniform of the father in the dollhouse are 1 2/5 inches long, how long would the pants be in real life?
Answer:
3 1/5 ft
Step-by-step explanation:
We can set up a proportion:
[tex]\frac{1}{2\frac{2}{7} } =\frac{1\frac{2}{5} }{x}[/tex] , where x is how long the pants are in real life
Cross multiply:
x = (2 2/7) * (1 2/5)
It's easier if we have improper fractions, so convert the mixed numbers into improper fractions:
2 2/7 = 16/7
1 2/5 = 7/5
Now, put these back in:
x = (16/7) * (7/5) = 16/5 = 3 1/5
Thus, in real life, the pants would be 3 1/5 ft long.
Hope this helps!
Answer:
3⅕ ft
Step-by-step explanation:
1 in --> 2 2/7 ft
2 2/7 = 16/7
1 2/5 in = 7/5 in
7/5 × 16/7 = 16/5 ft
3 1/5 ft
11 + (3)(9) Step 1: 11 + (9)(3) Step 2: (11 + 9)(3) Step 3: 20(3) Step 4: 60 Analyze the work to find the error.
Answer:
Step 2 is where this person went wrong
Step-by-step explanation:
Should be
11 + (9)(3)= x
11 + 27= x
x = 38
Answer:
Step 2 is where the error started. You can see the person did the order of operations wrong. The person was supposed to multiple (9)(3) first because of PEMDAS; (9)(3)=27 and then you add the 27 to 11 and get 38
Step-by-step explanation:
You are making an open box from a rectangular sheet of cardboard by cutting squares of equal length from each corner and folding up the sides. The dimensions of the sheet of cardboard are 15 inches by 12 inches. Write a polynomial that represents the total volume of the open box.
Answer:
[tex]V(x) = 4x^3 - 54x^2 + 180x[/tex]
Step-by-step explanation:
We are given the following in the question:
A rectangular piece of cardboard of side 15 inches by 12 inches is cut in such that a square is cut from each corner.
Let x be the side of this square cut. When it was folded to make the box.
The height of box =
[tex]x\text{ inches}[/tex]
The length becomes
[tex](15-2x)\text{ inches}[/tex]
The width becomes
[tex](12-2x)\text{ inches}[/tex]
Volume of box =
[tex]V =l\times w\times h[/tex]
Putting values, we get
[tex]V(x) = (15-2x)(12-2x)x\\V(x) = (180-30x-24x+4x^2)(x)\\V(x) = (4x^2 - 54x + 180)(x)\\V(x) = 4x^3 - 54x^2 + 180x[/tex]
is the required polynomial for volume of box formed.
The circumference of a circle is 16 ft.
what is the radius?
.
Answer:
The answer is 8. And for the love of God people if you don't know the answer don't waste an answer space just for the points. It makes everyone mad. Stop. Just cut it out.
Step-by-step explanation:
Solve -x^2-9x-20=0 with the quadratic formula
plz help!
Answer:
a = -1 b = -9 c = -20
x1 = [--9 +- (sq root -9^2 - 4 * -1 * -20)] / 2 * -1
x1 = 9 +sq root (81 - 80) / -2
x1 = [9 + 1 ] / -2
x1 = -5
x2 = 9 -sq root (81 - 80) / -2
x2 = 8 / -2
x2 = -4
Step-by-step explanation:
Lena‘s observed that in the last 12 issues of rise over run weekly 384o out of950 pages contain an advertisement what is the probability that the next page she turns to will contain an advertisement
Answer:
Probability thay the next page she turns to will have an advert = 0.4042
Step-by-step explanation:
In the last 12 issues of the magazine, 384 out of 950 pages contain an advertisement.
We now need to find the probability that the next page has an advertisement.
Probability of an event
= n(of that event) ÷ n(total sample spaces)
n(of the event of an advert) = number of pages with adverts in those issues = 384
n(total sample spaces) = total number of pages = 950
Probability that the next page or any page at all will have an advert = (384/950) = 0.4042
Hope this Helps!!!
The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and non smokers uses a preliminary estimate of the proportion who smoke of .30.a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of.02? use 95% confidence.b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population?c. What is the 95% confidence interval for the proportion of smokers in the population?
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
a) From the information given,
Margin of error = 0.02
p = 0.3
q = 1 - 0.3 = 0.7
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.5 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Therefore,
0.02 = 1.96 × √(0.3 × 0.7)/n
0.02/1.96 = √0.21/n
0.0102 = √0.21/n
Taking square of both sides, it becomes
0.00010404 = 0.21/n
n = 0.21/0.00010404
n = 2018
Sample size = 2018
b) if n = 2018
x = 520
Then
p = 520/2018 = 0.26
Point estimate of the proportion of smokers in the population is 0.26
c) q = 1 - 0.26 = 0.74
the 95% confidence interval for the proportion of smokers in the population is
0.26 ± 1.96 × √(0.26)(0.74)/2018
= 0.26 ± 0.019
Answer:
a) n = 2017
b) Point estimate is 0.2578
c) 95% Confidence Interval is Minimum = 0.2387, Maximum 0.2769
Step-by-step explanation:
Here we have
At 95%, we have
[tex]z_{\alpha /2}[/tex] = 1.96
To determine sample size, we have
[tex]n = \frac{(z_{\alpha /2})^2 \hat p \hat q}{E^2}[/tex]
Where:
[tex]\hat p[/tex] = 0.3
[tex]\hat q[/tex] = [tex]1-\hat p[/tex] = 0.7
E = 0.02
Therefore, n = 2016.84 ≈2017
b) The point estimate is given by
[tex]\hat p =\frac{x}{n} = \frac{520}{2017}[/tex] = 0.2578
c) The confidence interval is given by;
[tex]CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Which gives
[tex]CI=0.2578\pm 1.96\times \sqrt{\frac{0.2578(1-0.2578)}{2017}}[/tex]
Hence CI = Min = 0.2387 to Max = 0.2769
What is the proof for this equation?
3x+27=2y+32
I will give brainliest!!!!!! Thx
What is the value of t?
what is domain and range
Answer:
the domain is anything with the x-axis and range the y-axis
Answer:
Domain- is the set of all possible x-values or "input" for the function that gets you to the "output" or y-values. Range- is the difference between the highest and the lowest values.
Step-by-step explanation:
Angle C is inscribed in circle O. AB is a diameter of circle O. What is the radius of circle O?
Answer:
6.5 units
Step-by-step explanation:
In circle with center O, AB is diameter.
[tex] \therefore m\angle ACB = 90°\\[/tex]
(Angle inscribed in a semicircle)
[tex] \therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\[/tex]
By Pythagorean theorem:
[tex]AB = \sqrt{ {12}^{2} + {5}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ AB \: = 13 \\ r = \frac{13}{2} = 6.5 \: units[/tex]
Type the expression that results from the following series of steps:
start with y, subtract 4, then times 9.
Start with y: [tex]y[/tex]
Subtract 4: [tex]y-4[/tex]
Multiply by 9: [tex]9(y-4)=9y-36[/tex]
Answer:
[tex]9(y - 4) \\ = 9y - 36[/tex]
Step-by-step explanation:
[tex]start \: \: \: \: \: \: \: \: \: \: = y \\ subtract \: = y - 4 \\ times \: \: 9 \: \: \: = 9(y - 4) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 9y - 36[/tex]
A shipping container in the shape of a rectangular solid must have a volume of 84 cubic meters. The client tells the manufacturer that, because of the contents, the length of the container must be one meter longer than the width, and the height must be one meter greater than twice the width. What should the dimensions of the container be?
Answer:
The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.
Step-by-step explanation:
Let the width of rectangular solid be x
We are given that the length of the container must be one meter longer than the width
So, Length of solid = x+1
We are also given that height must be one meter greater than twice the width
So, Height of solid = 2x+1
So, Volume of solid = [tex]Length \times Width \times height[/tex]
Volume of solid = [tex](x+1) \times x \times (2x+1)[/tex]
Volume of solid =[tex](x^2+x)(2x+1)[/tex]
Volume of solid =[tex]2x^3+x^2+2x^2+x=2x^3+3x^2+x[/tex]
We are given that a rectangular solid must have a volume of 84 cubic meters
So, [tex]2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\[/tex]
On equating
x-3=0
x=3
So, Length of solid = x+1=3+1 = 4 feet
Height of solid = 2x+1 =2(3)+1=7 feet
Width of solid = 3 feet
Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.
The volume of a rectangular solid shipping container = 84 cubic meters
The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
Given:
The volume of a rectangular solid shipping container = 84 cubic meters
Let: The width of the container be x
The length of the container must be one meter longer than the width.
So, The length of the container be (x + 1)
The height must be one meter greater than twice the width.
So, The height of the container be (2x + 1)
To find the dimensions of the container
The Volume of the container = Length x Width x Height
[tex]84=x(x+1)(2x+1)[/tex]
[tex]84=(x^{2} +x)(2x+1)[/tex]
[tex]84=2x^{3} +3x^{2} +x[/tex]
[tex]2x^{3} +3x^{2} +x-84=0\\(x-3)(2x^{2} +9x+28)=0\\x-3=0\\x=3[/tex]
So, The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
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Apply the distributive property to the expression to write an equivalent expression. Complete the statements. 4x + 16 Find the GCF of . Now factor out the GCF by dividing each term in the expression by . 4x divided by the GCF is , and 16 divided by the GCF is . The equivalent expression is .
Answer:
[tex]4(x+4)=4x+16[/tex]
Step-by-step explanation:
a) The Greatest Common Factor, of both terms 4x and 16 is 16.
4,16|2
2,8|2
1,4|2
1,2|2
1,1| = 2*2*2*2=16
b) Let's divide each term by 4 their
4x+16
[tex]\frac{4x}{4}=x\\\\\frac{16}{4}=4[/tex]
Placing their common divisor outside the parentheses, and inside the sum of this result:
[tex]4(x+4)=4x+16[/tex]
The equivalent expression after factoring out the GCF is [tex]\(4(x + 4)\)[/tex].
To apply the distributive property to the expression \(4x + 16\), we can factor out the greatest common factor (GCF) of the two terms. In this case, the GCF of 4 and 16 is 4. By dividing each term in the expression by 4, we can factor out the GCF.
\(4x\) divided by the GCF (4) is \(x\), and \(16\) divided by the GCF (4) is \(4\). Therefore, the expression \(4x + 16\) can be factored as \(4(x + 4)\) using the distributive property.
To summarize:
- GCF of 4 and 16 is 4.
- \(4x\) divided by the GCF (4) is \(x\).
- \(16\) divided by the GCF (4) is \(4\).
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Simplify an expression for the area of the rectangle.
Answer:
39.6x +26.4
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
A = 13.2 * (3x+2)
Distribute
39.6x +26.4
Which equation represents a circle with a center at (-3,-5) and a radius of 6 units?
(x – 3)2 + (y – 5)2 = 6
(x – 3)2 + (y-5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
va
Answer: (x+3)2 + (y+5)2 =36
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
margot used 1/2 pounds of turkey to make 2/3 liters of turkey chill. If margots recipe is for 1 liter of turkey chill,how many pounds of turkey will she need to make 4 times the recipe
Answer:
2 pounds of turkey?
Step-by-step explanation:
Margot will therefore need 3 pounds of turkey to make 4 liters of her turkey chili.
To find out how many pounds of turkey Margot will need to make 4 times her turkey chili recipe for 1 liter, we first identify the amount needed for 1 liter based on the given ratio, and then multiply that amount by 4.
Margot uses 1/2 pounds of turkey for 2/3 liters of turkey chili. If we need to find out the amount for 1 liter, we can set up a proportion:
1/2 pounds turkey / (2/3 liters) = x pounds turkey / 1 liter
We cross multiply to solve for x:
(1/2) * 1 = x * (2/3)
Now we solve for x:
x = (1/2) * (3/2)
x = 3/4 pounds of turkey for 1 liter of chili
For 4 liters of chili (4 times the recipe), we would multiply:
4 * (3/4 pounds) = 3 pounds of turkey
Find the Perimeter of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
9514 1404 393
Answer:
43.1
Step-by-step explanation:
The perimeter is the sum of the lengths of the two straight edges, each of which is 9 units long, and the circumference of the full circle of diameter 8 units. The circumference is pi times the diameter.
P = 2(9) +8π = 18 +25.13
P ≈ 43.1 . . . units
The perimeter of the combination of a rectangle and two semicircles is found by adding the straight sides of the rectangle and the circumference of the resulting full circle formed by the semicircles. In this case, it's 43.1 units.
To find the perimeter of the combined shape consisting of a rectangle and two semicircles, we need to consider the lengths of the straight parts as well as the circumference of the circles. The perimeter is the sum of the lengths of the straight sides of the rectangle, each of which is 9 units long, and the circumference of the full circle with a diameter of 8 units.
Using the formula for the circumference of a circle (C = πd) where d is the diameter, the circumference of the full circle would be 8π. So, the total perimeter of the shape is:
P = 2*(9) + 8π
That gives us:
P = 18 + 25.13 approximately
So, P ≈ 43.1. . . units
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8) An ultimate frisbee team has to order jerseys, shorts, and hats. They have a budget of $1350 to
spend on $50 jerseys, $20 shorts, and $15 hats. They want to buy 40 items in preparation for the
oncoming season and must order as many jerseys as shorts and hats combined. How many of
each item should they order? Write a system of equations to help you solve this problem.
Answer:
Step-by-step explanation:
By using j, s ,h to represent the number of jerseys,shorts and hats respectively.
System of Equations:
j + s + h = 40
j = s + h
50j + 20s + 15h = 1350
(s + h) + s + h = 40
2s + 2h = 40
s + h = 20
s = 20 – h
50[(20 – h) + h] + 20(20 – h) + 15h = 1350
50(20) + 400 – 20h + 15h = 1350
1400 – 5h = 1350
5h = 50h
h = 10
s = 20 – 10
s = 10
j = 10 + 10
j = 20
20 jerseys, 10 shorts, 10 hats
They order 20 jerseys, 10 shorts, 10 hats
What is system of equation?A system of equations, also known as a set of simultaneous or equation system, is a finite set of equations for which we sought the common solutions.
According to the question
By using j, s ,h to represent the number of jerseys ,shorts and hats respectively.
System of Equations:
j + s + h = 40. . . . . Equation (1)
j = s + h. . . . . . .Equation (2)
50j + 20s + 15h = 1350 . . . . . . Equation (3)
By putting the value of j = s + h in equation (1)
(s + h) + s + h = 40
2s + 2h = 40
s + h = 20
s = 20 – h. . . . . . . .Equation (4)
By putting the value of j = s + h and s = 20 - h in equation (3) we get
50[(20 – h) + h] + 20(20 – h) + 15h = 1350
50(20) + 400 – 20h + 15h = 1350
1400 – 5h = 1350
5h = 50h
h = 10
s = 20 – 10
s = 10
j = 10 + 10
j = 20
Hence , 20 jerseys, 10 shorts, 10 hats
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A restaurant is offering a new buffet with six types of sandwiches, four sides, and five desserts. If customers are allowed to select one sandwich, one side, and one dessert, how many meal combinations are possible?
Answer:
240
Step-by-step explanation:
Multiply everything together. 6*4*5 is 240.
Which of the following lines best fits the data shown in the scatter plot
Answer:
Im pretty sure its A
Step-by-step explanation:
Therefore, the option (A) is the correct answer.
What is the scatter plot?
Scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.
As per the given information, the correct graph is in option (A) because in this graph it is moving upward with respect to the line of curve.
Hence, the option (A) is the correct answer.
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Simplify.
Remove all perfect squares from inside the square root.
Assume x is positive.
\sqrt{20x^8}
Answer:
[tex]2x^4\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{20x^8}[/tex] = [tex]\sqrt{4*5*(x^4)^2}[/tex] = [tex]2x^4\sqrt{5}[/tex]
The solution of the equation after remove all perfect squares from inside the square root is,
⇒ 2x⁴√5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ √20x⁸
Now, We can simplify and remove all perfect squares from inside the square root as;
⇒ √20x⁸
⇒ √2 × 2 × 5 × (x⁴)²
⇒ 2x⁴√5
Thus, The solution of the equation after remove all perfect squares from inside the square root is,
⇒ 2x⁴√5
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Nathan needs some paint for his bedroom. He finds two cans of white paint, four cans of green paint and three cans of pink paint in his garage. If he chooses a can of paint without looking at the color, what is the chance that he will paint his bedroom pink
Answer:
3/9 or 33.33%
Step-by-step explanation:
there are 9 total cans and 3 pink cans. So, that'd be 3/9 or 33.33%
hope this helps!
Answer:
1/3
Step-by-step explanation: