Answer:
The correct answer is "0.7289".
Step-by-step explanation:
The given values are:
Mean,
[tex]\mu = 15.5[/tex]
Standard deviation,
[tex]\sigma = 3.6[/tex]
As we know,
⇒ [tex]z = \frac{(x - \mu)}{\sigma}[/tex]
The probability will be:
⇒ [tex]P(11< x< 19) = P(\frac{11-15.5}{3.6} <z<\frac{19-15.5}{3.6})[/tex]
[tex]=P(z< 0.9722)-P(z< -1.25)[/tex]
By using the z table, we get
[tex]=0.8345-0.1056[/tex]
[tex]=0.7289[/tex]
You invested your summer earnings into and annuity from which you can draw expenses while you are at university. If you need to withdraw $1200 each month for 9 months of university, how much do you need to invest into an account, earning 6% per year, compounded semi-annually, in order to cover your expenses?
Answer:
10538.07
Step-by-step explanation:
find the effective semiannual rate: .06/2= .03
conver this into an effective monthly rate
[tex](1.03)^2=(1+i)^{12}\\(1.03)^{1/6}-1=i\\i=.0049386220312[/tex]
this is our montlhy effective rate. use this to calculate teh present value of 9 1200 dollars payments
[tex]1200(\frac{1-(1+.0049386220312)^{-9}}{.0049386220312})=10538.0729871[/tex]
which rounds to 10538.07
The invested amount would be $10538.52 in order to cover your expenses if you need to withdraw $1200 each month for 9 months of university.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt} \\\\\\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is or borrowed (in years)
It is given that:
You need to withdraw $1200 each month for 9 months of university,
The effective semiannual rate = 0.06/2 = 0.03
[tex]\rm i = (1.03)^{1/6} - 1[/tex]
i = 0.00493
The invested amount:
[tex]= 1200\dfrac{[1- (1 + 0.00493)^{-9}]}{0.00493}[/tex]
After simplification:
= $10538.52
Thus, the invested amount would be $10538.52 in order to cover your expenses if you need to withdraw $1200 each month for 9 months of university.
Learn more about the compound interest here:
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An automobile manufacturer has given its jeep a 51.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 230 jeeps, they found a mean MPG of 51.1. Assume the population variance is known to be 6.25. A level of significance of 0.02 will be used. Make the decision to reject or fail to reject the null hypothesis.
Answer:
The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.
Step-by-step explanation:
An automobile manufacturer has given its jeep a 51.3 miles/gallon (MPG) rating.
At the null hypothesis, we test if the mean is of 51.3, that is:
[tex]H_0: \mu = 51.3[/tex]
An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating.
This means that at the alternative hypothesis, we test if the mean is different of 51.3, that is:
[tex]H_0: \mu \neq 51.3[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
51.3 is tested at the null hypothesis:
This means that [tex]\mu = 51.3[/tex]
After testing 230 jeeps, they found a mean MPG of 51.1. Assume the population variance is known to be 6.25.
This means that [tex]n = 230, X = 51.1, \sigma = \sqrt{6.25} = 2.5[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{51.1 - 51.3}{\frac{2.5}{\sqrt{230}}}[/tex]
[tex]z = -1.21[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the sample mean differing from 51.1 by at least 0.2, which is P(|z| > 1.21), which is 2 multiplied by the p-value of z = -1.21.
Looking at the z-table, z = -1.21 has a p-value of 0.1131.
2*0.1131 = 0.2262
The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.
A certain freezing process requires that room temperature be lowered from 35oC at the rate of 6oC every hour. What will be the room temperature 8 hours after the process begins?
Answer:
-13 degrees celcius.
Step-by-step explanation:
6 degrees are lowered every hour. 6*8 = 48 degrees, 48 degrees are lowered.
35-48 is -13. The room temperature will be -13 eight hours after the process begins.
The angle θ between 5i-j+k & 2i-j+k is
Step-by-step explanation:
Let,
[tex] \sf \vec{a} = 5 \hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{a}| = \sqrt{ {5}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{25 + 1 + 1} \\ = \sqrt{27} \\ \\ \sf \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{b}| = \sqrt{ {2}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{4 + 1 + 1} \\ = \sqrt{6} \\ \\\sf \: \vec{a}. \vec{b} = (5 \hat{i} - \hat{j} + \hat{k}).(2\hat{i} - \hat{j} + \hat{k}) \\ = 5 \times 2 + ( - 1) \times ( - 1) + 1 \times 1 \\ = 10 + 1 + 1 \\ = 12 \\ \\ \sf \: angle \: between \: \vec{a} \: and \: \vec{b} \: = \theta \\ \\ \: so \\ \sf \vec{a}. \vec{b} = | \vec{a}| . | \vec{b}| cos\theta \\ = > \sf \: cos \theta \: = \frac{ \vec{a}. \vec{b}}{ | \vec{a}| . | \vec{b}| } \\ = > cos \theta = \frac{12}{ \sqrt{27} \times \sqrt{6} } = 0.94 \\ = > \theta = {cos}^{ - 1} (0.94) \\ = > \green{\theta = 19.47 ^{ \circ} }[/tex]
the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age?
Answer:
sadia is 32
Step-by-step explanation:
sadia : father : total
3 6 9
Divide 96 by 9
96/9 = 32/3
Multiply each by 32/3
sadia : father : total
3*32/3 6*32/3 9*32/3
32 64 96
PLZZZ HELP
This is due in 15 mins
I need 5
But I already have 4
So one more
Answer:
The hottest month for the northern hemisphere is August.
The hottest month for the southern hemisphere is January and February (these top two might be the opposite)
It's globally warmer during the months of June July and August
During april and november, the southern hemisphere and northern hemisphere are the same, or very close.
During July and August the southern and northern hemispheres have the largest difference in temperature
A box contains two blue cards numbered 1 and 2, and three green numbered 1 through 3. A blue card ins picked, followed by a green card. Select sample space for such experiment
a) {1, 1), (1, 2, (1, 3)(2, 1), (2, 2), (2, 3)}
b) {(1, 1)(1, 2), (2, 1), (2, 2), (3, 1), (3, 2)}
c) {5}
d) {6}
Answer:
The answer is a.
After simplification, how many terms will be there in 4x3 + 9y2 - 3x + 2 - 1?
3
6
5
4.
Answer:
Correct answer is 4 because the last 2 terms can be combined:
Step-by-step explanation:
4x3 + 9y2 – 3x + 2 – 1 = 4x3 – 3x + 9y2 + 1.
Why is the value of -9 is not-3
Answer:
Because it's a negative.
Step-by-step explanation:
The value of a positive number is still a positive number.
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.8 years, and
standard deviation of 1.7 years.
The 10% of items with the shortest lifespan will last less than how many years?
Round your answer to one decimal place.
Answer:
Less than 3.6 years.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.8 years, and standard deviation of 1.7 years.
This means that [tex]\mu = 5.8, \sigma = 1.7[/tex]
The 10% of items with the shortest lifespan will last less than how many years?
Less than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 5.8}{1.7}[/tex]
[tex]X - 5.8 = -1.28*1.7[/tex]
[tex]X = 3.6[/tex]
Less than 3.6 years.
Determine whether the integral from -3 to infinity 1/sqrt (5 - x) is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent .
It's divergent because 1/√(5 - x) is defined only for x < 5, which means the integral from 5 to infinity doesn't exist.
find the value of trigonometric ratio
Pls if anyone knows the answer with work included/steps that will be greatly appreciated :)
Answer:
3. 3x^2 + 15x
4. x=36
Step-by-step explanation:
The area of a rectangle is
A = l*w
A = (3x)*(x+5)
Distribute
3x^2 + 15x
2/3x - 4 = 20
Add 4 to each side
2/3x -4+4 = 20+4
2/3x = 24
Multiply each side by 3/2
2/3*3/2 =24*3/2
x = 12*3
x=36
X/6 - y/3 = 1
please explain in detail!
Answer:
x=12,y=3
Step-by-step explanation:
x/6-y/3=1
x can equal 12 because 12/6 is equal to 2.
y can equal 3 because 3/3 equals 1
2-1=1
The gate of a stadium ha two pillars each of height 10ft.with four visible lateral faces and 3ft*3ft bases .the top of eaxh pillar has combined pyaramid of height2ft.If the combined structures of both pillars and pyramid are painted at the rate of rs 80 persq.ft.calcuate the total cost of painting.
The pillars and the pyramids in the stadium gate means that we have to calculate the area of the items that make up the gate one after the other. At the end of the calculation, the calculated areas are then added up.
The total cost of painting is Rs.21344
First, we calculate the area of 1 side of 1 pillar using:
[tex]A = Height * Base[/tex]
Where
[tex]Height = 10ft[/tex] --- Height of the pillar
[tex]Base = 3ft[/tex] --- Base of the pillar
So:
[tex]A = 10ft * 3ft[/tex]
[tex]A = 30ft^2[/tex]
The area of the 4 sides of the pillar is:
[tex]A_2 = 4 * A[/tex] --- i.e. 4 multiplied by the area of 1 side
[tex]A_2 = 4 * 30ft^2[/tex]
[tex]A_2 = 120ft^2[/tex]
The area of the 2 pillars is:
[tex]Area_1 = 2 * A_2[/tex] --- i.e. 2 multiplied by the area of 1
[tex]Area_1 = 2 * 120ft^2[/tex]
[tex]Area_1 = 240ft^2[/tex]
Because one part of the pyramid won't be visible, we calculate the area of the pyramid using:
[tex]Area = lw + l\sqrt{(w/2)^2 + h^2} + w\sqrt{(l/2)^2 + h^2}[/tex]
Where:
[tex]h = 2[/tex] -- the height
[tex]l = w = 3[/tex] --- the base of the pillar is the length & width of the pyramid.
So, we have:
[tex]Area = 3\sqrt{(2/2)^2 + 2^2} + 3\sqrt{(2/2)^2 + 2^2}[/tex]
[tex]Area = 3\sqrt{1 + 4} + 3\sqrt{1 + 4}[/tex]
[tex]Area = 3\sqrt{5} + 3\sqrt{5}[/tex]
[tex]Area = 6\sqrt{5}[/tex]
For the two pyramids, the area is:
[tex]Area_2 = 2 * 6\sqrt 5[/tex] -- 2 multiplied by area of 1
[tex]Area_2 = 12\sqrt 5[/tex]
[tex]Area_2 = 26.8[/tex]
So, the total area to be painted is:
[tex]Total = Area_1 + Area_2[/tex] --- the sum of the area of the pillars and the pyramids
[tex]Total = 240+26.8[/tex]
[tex]Total = 266.8ft^2[/tex]
The unit cost of paint is:
Rate = Rs80 per sq.ft
The total cost of painting is:
[tex]Cost = 80 * 266.8[/tex]
[tex]Cost = Rs.21344[/tex]
Hence, the total cost of painting is Rs.21344.
Read more at:
https://brainly.com/question/14320476
10. cos c plz help me
Answer:
cos C = 12/13
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
Cos theta = adj/ hyp
cos C = 36/39
Dividing the top and bottom by 3
cos C = 12/13
CosØ=Base/Hypotenuse
cosC=BC/ACcosC=36/39cosC=12/13what is the sign of x/y times 7y^3 when x<0 and y>0? A. Positive B. Negative C. Zero
X <0 means x would be negative.
For x/y, a negative divided by a positive would give a negative answer.
A negative multiplied by a positive would result in a negative.
The answer would be B. Negative
A parent is buying two types of chocolate truffles for their family. The oldest child can eat twice as much as their younger siblings and prefers white chocolate (W), the younger three like dark chocolate (D) and the spouse likes white chocolate (W). Five white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 6 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $34.00, how much was each dark chocolate truffle
Answer:
Each chocolate truffle is $2.125
Step-by-step explanation:
Honestly, I'm not 100% sure if this is correct, and I am truly sorry if this is wrong, but its worth a try :)
What is the value of the expression
below?
(7)3
Answer:
21
Step-by-step explanation:
I want to know how to solve this equation
9514 1404 393
Answer:
B
Step-by-step explanation:
To find the inverse of y = f(x), solve the equation x = f(y) for y. For these functions, that's about the easiest way to do it.
A. x = ∛(3y) ⇒ x³ = 3y ⇒ x³/3 = y . . . . . does not match g(x)
B. x = 11y -4 ⇒ x +4 = 11y ⇒ (x +4)/11 = y . . . . matches g(x)
C. x = 3/y -10 ⇒ x +10 = 3/y ⇒ 3/(x+10) = y . . . . does not match g(x)
D. x = y/12 +15 ⇒ x -15 = y/12 ⇒ 12(x -15) = y . . . . does not match g(x)
_____
Additional comment
This is repeated application of the "solve for ..." process. In general, that process "undoes" what is "done" to the variable. The order of operations can tell you the order of the things that are done. The undoing is in the reverse order.
You need to be completely comfortable with the properties of equality (addition, subtraction, multiplication, division), and you need to understand the inverse functions of the functions we usually use: (powers, roots), (exponentials, logarithms), (trig functions, inverse trig functions). Of course, the inverse of addition is subtraction; the inverse of multiplication is division.
__
Above, we used a "shortcut" a couple of times:
a = b/c ⇒ c = b/a . . . . . equivalent to multiplying both sides by c/a.
what is the value of x
Answer:
c 112⁰
Step-by-step explanation:
cuz the triangle is the same and x is on a straight line so get 180 - 68 = 112
Answer:
the angle opposite to x is 61 degree (being alternate angle)
so
x+ 61 = 180(being linear pair)
or, x = 180 - 61
so, x = 119
the answer is 119(d).
O is the center if the regular polygon beloe. Find its perimeter. Round to the nearest tenth if necessary HURRY
Answer:
24.8 units
Step-by-step explanation:
Given
[tex]n = 10[/tex] --- sides
The attached decagon
Required
The perimeter
The decagon is made up of 10 isosceles triangles.
The angle at the vertex of each is:
[tex]Angle = \frac{360}{10}[/tex]
[tex]Angle = 36[/tex]
Next, we create a right-angled triangle from the shape (see attachment)
[tex]\theta[/tex] is calculated as:
[tex]\theta = \frac{Angle}{2}[/tex]
[tex]\theta = \frac{36}{2}[/tex]
[tex]\theta = 18[/tex]
Next, calculate x using:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(18) = \frac{x}{4}[/tex]
Make x the subject
[tex]x = 4 * \sin(18)[/tex]
[tex]x = 1.24[/tex]
So, the length (L) of one side of the decagon is:
[tex]L = 2x[/tex]
[tex]L = 2 * 1.24[/tex]
[tex]L = 2.48[/tex]
The perimeter (P) of the shape is:
[tex]P = 10 *L[/tex]
[tex]P = 10 * 2.48[/tex]
[tex]P = 24.8[/tex]
The perimeter of the given polygon rounded to the nearest tenth is; 24.7
What is the perimeter of the Polygon?
The given polygon as we can see has 10 sides.
Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.
Thus, the other two angles will be; (180 - 36)/2 = 72° each
Using sine rule, we can find the length of a side of the polygon as;
x/sin 36 = 4/sin 72
x = (4 * sin 36)/sin 72
x = 2.472
Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7
Read more about perimeter at; https://brainly.com/question/397857
The grades in a statistics course for a particular semester were as follows:
Grade ABCDF f 14 18 32 20 16
Test the hypothesis, at the 0.05 level of significance, that the distribution of grades is uniform. (Test that each grade is equally likely) Round your solutions to 3 decimal places where necessary.
Test Statistic =
Critical Value =
Answer:
Test Statistic = 10
Critical Value = 9.488
Step-by-step explanation:
Given :
Grade A _ B _ C _ D _ F
_____14 _ 18 _32_ 20_16
H0 : distribution of grade is uniform
H1 : Distribution of grade is not uniform
Using the Chisquare statistic :
χ² = (observed - Expected)² / Expected
The expected value :
(14+18+32+20+16) / 5 = 20
χ² = (14-20)^2 / 20 + (18-20)^2 / 20 + (32-20)^2 / 20 + (20-20)^2 / 20 + (16-20)^2 / 20
χ² statistic = 10
The χ² critical at df = (n - 1) = 5 - 1 = 4
χ² Critical(10, 4) = 9.488
5 times a certain number plus 2 times that number plus 2 is 16 what is the number
let the number be x
ATQ
[tex]\\ \sf\longmapsto 5x+2x+2=16[/tex]
[tex]\\ \sf\longmapsto (5+2)x+2=16[/tex]
[tex]\\ \sf\longmapsto 7x+2=16[/tex]
[tex]\\ \sf\longmapsto 7x=16-2[/tex]
[tex]\\ \sf\longmapsto 7x=14[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{14}{7}[/tex]
[tex]\\ \sf\longmapsto x=2[/tex]
Answer:
The number is
2
Explanation:
Let
n
represent the number.
Translating the given statement into algebraic notation, we have
XXX
5
n
+
2
n
+
2
=
16
Therefore
XXX
7
n
+
2
=
16
XXX
7
n
=
14
XXX
n
=
2
answered by: Alan P.
The probability that you will make the hockey team is 2/3
The probability that you will make the swimming team is 3/4.
If the probability that you make
both teams is 1/2
what is the probability that you at least make one of the teams?
Answer:
p = [tex]\frac{11}{12}[/tex]
Step-by-step explanation:
Probability that you make the hockey team only: 2/3 * (1-3/4) = 1/6
Probability that you make the swimming team only: 3/4 * (1-2/3) = 1/4
Probability that you make the both team: 1/2
the probability that you at least make one of the teams: 1/6 + 1/4 + 1/2 = 11/12
The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a standard deviation of 0.08 ounce. Every car that has more than 12.20 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that need to be cleaned because of spillage to 3%
Answer:
x = 12.15 oz
Step-by-step explanation:
z = 1.8808
1.8808 = (x - 12)/.08
The coordinates of the preimage are:
A(−8,−2)
B(−4,−3)
C(−2,−8)
D(−10,−6)
Now let’s find the coordinates after the reflection over the x-axis.
A′(−8,
)
B′(−4,
)
C′(−2,
)
D′(−10,
)
And now find the coordinates after the reflection over the y-axis.
A′′(
,2)
B′′(
,3)
C′′(
,8)
D′′(
,6)
This is also the same as a rotation of 180∘.
9514 1404 393
Answer:
A'(-8, 2) ⇒ A"(8, 2)B'(-4, 3) ⇒ B"(4, 3)C'(-2, 8) ⇒ C"(2, 8)D'(-10, 6) ⇒ D"(10, 6)Step-by-step explanation:
Reflection over the x-axis changes the sign of the y-coordinate. Reflection over the y-axis changes the sign of the x-coordinate. We can summarize the transformations as ...
preimage point ⇒ reflection over x ⇒ reflection over y
A(−8,−2) ⇒ A'(-8, 2) ⇒ A"(8, 2)
B(−4,−3) ⇒ B'(-4, 3) ⇒ B"(4, 3)
C(−2,−8) ⇒ C'(-2, 8) ⇒ C"(2, 8)
D(−10,−6) ⇒ D'(-10, 6) ⇒ D"(10, 6)
Some friends are sharing a pizza. If each person gets 1/8 of the pizza, what percent of the pizza does each person get?
Answer:
1/8=12.50%
Step-by-step explanation:
Take the pizza as a whole = 100
Then consider 1/8 of 100
or 1/8 * 100
= 1/4 * 50
= 1/2 * 25
= 12.50
Therefore it is 12.50%
Solve the triangle.
9514 1404 393
Answer:
b = 757.7 mA = 17.2°C = 14.3°Step-by-step explanation:
From the law of cosines, you can find the length of side b to be ...
b = √(a² +c² -2ac·cos(B))
b = √(184041 +128164 -307164cos(148.5°)) ≈ √574105.36
b ≈ 757.7
__
From the law of sines, you can find the measure of angle C to be ...
C = arcsin(c/b·sin(B))
C ≈ arcsin(358/757.7·sin(148.5°)) ≈ arcsin(0.246872)
C ≈ 14.3°
A = 180° -148.5° -14.3°
A = 17.2°
_____
Some graphing calculators have built-in triangle-solving functions. Apps are available for the purpose for phone or tablet. The screenshot shows a web site that does a nice job of solving the triangle.
Which power does this expression simplify to?
[(7)(7)
1
- -
ооо
74
O
Step-by-step explanation:
Answer is in attached image...
hope it helps
Answer:
its a
Step-by-step explanation:
just did it
