This question is incomplete, the complete question is;
A sample of size 86 will be drawn from a population with mean 90 and standard deviation 24. Use the TI-84 calculator Part 1 of 2
Find the probability that x will be more than 89. Round the answer to at least four decimal places. The probability that will be more than 89 is Part 2 of 2 Find the 60 percentile of x. Round the answer to two decimal places. The 60 percentile is
.
Answer:
part 1) the probability that x will be more than 89 is 0.6517
part 2) the 60 percentile of x is 90.65
Step-by-step explanation:
Given that;
u = 90, α = 24, n = 86
Part 1 says Find the probability that x will be more than 89
p ( x > 89 ) = p (( x - u)/α√n > (89-90)/24/√86 ))
= p ( z > - 0.39 ) = 1 - p (z ≤ - 0.39 )
from z table, 0.39 → 0.3483
= 1 - 0.3483 = 0.6517
∴ the probability that x will be more than 89 is 0.6517
part 2 says Find the 60 percentile of x
p( Z < z ) = 0.60
now from the z-table, p(Z < 0.25 ) = 0.60
and we that x = u + z(α/√n)
x = 90 + 0.25( 24 / √ 86
x = 90.64699 ≈ 90.65
∴ the 60 percentile of x is 90.65
a man dropped his keys into the sea, and watched them fall to a depth of -8 meters before landing on a rock. how far are the keys from the surface of the sea?
Sandra calculated the height of a cylinder that has a volume of 576 pi cubic centimeters and a radius of 8 centimeters. Her work is shown below. V = B h Step 1: 576 pi = pi 8 squared h Step 2: 576 pi = 64 pi h Step 3: StartFraction 576 pi Over 64 pi EndFraction = StartFraction 64 pi Over 64 pi EndFraction h Step 4: h = 9 pi cm What error did Sandra make when calculating the height of the cylinder? In step 1, she substituted into the volume formula incorrectly. In step 2, she calculated 8 squared incorrectly. It should be 16 rather than 64. In step 4, the pi should have canceled, making the correct answer 9 cm. Sandra calculated the height of the cylinder correctly.
Answer:
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Step-by-step explanation:
Volume=576π cubic centimeters
Radius=8 cm
h=?
Her work:
Volume of a cyclinder=πr^2h
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h=9π cm
Correct workings:
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h= 9 centimeters
Her error is in step 4
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Answer:
the error was made in step 4, should have also been cancelled making the correct answer as 9 cm.
Step-by-step explanation:
Will Give Brainliest! (And 25 Points) Easy Algebra Question! Please show all steps! Solve for x [tex]b+3/x=f/2[/tex]
Answer:
Step-by-step explanation:
Hello, we assume that x is different from 0 and f different from 2b
[tex]b+\dfrac{3}{x}=\dfrac{f}{2}\\\\\text{Subtract b}\\\\+\dfrac{3}{x}=\dfrac{f}{2}-b\\\\\text{Mulitply by 2x}\\\\+\dfrac{3*2*x}{x}=6=\dfrac{2xf}{2}-2bx=(f-2b)x\\\\\text{Divide by f-2b}\\\\\Large \boxed{\sf \bf x=\dfrac{6}{f-2b}}[/tex]
Thanks
Hi I am a teacher or 52 years old and I am wondering how I can become an online tutor?
Answer:
Go online and do research, I'm pretty sure you have websites around your area that is looking for tutors
Step-by-step explanation:
what is LCM of 2 4 8
Answer:
the LCM would be 8 based on the following set of multiples: Multiples of 2: 2, 4, 6, 8, 10, 12, 14, ... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
Step-by-step explanation:
Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x2 y = 6x − x2
Answer:
81π for the x axis.
Step-by-step explanation:
STEP ONE: Determine the intersection.
we are given from the question that y = x^2 and y = 6x − x^2. Therefore if y = x^2, then we will have;
x^2 = 6x - x^2 ---------------------------------------------------------------------------------[1].
Solving and factorizing the equation [1] above give us x = 0 and x = 3 (that is x[6 -2x] = 0 ). Therefore, the point of intersection = (0,0) and (3,9).
STEP TWO: Determine the value for the cross sectional area.
The cross sectional area= [6x - x^2]π - [x2]^2 π. --------------[2].
The cross sectional area = -12 π[x -3]x^2.
STEP THREE: integrate the cross sectional area taking x =3 and x =0 as the upper and lower integration limits or boundaries with respect to dx to determine the vome in the x axis.
volume =∫-12 π[x -3]x^2 dx.volume = -12 π[ (3)^4/4 - (3)^3 ] = 81π.volume, v with respect to the x axis = 81π
When grading English papers, the instructor checks every 4th paper for plagiarism. What form of sampling is used?
random
convenience
systematic
cluster
Answer: systematic
Step-by-step explanation:
In random sampling researcher choose elements randomly for sample .In convenience sampling individuals are selected as per his convenience and comfort.In systematic sampling individuals are selected in a systematic way by using a fix periodic interval k from the entire population .In cluster sampling clusters (of homogeneous elements) are selected to make a sample.Given, When grading English papers, the instructor checks every 4th paper for plagiarism which expresses a fixed periodic interval.
Hence, this is systematic sampling.
Evacuation and emergency procedures should be displayed in the classroom lab/office. * 4 points True False
Answer:
The answer is true. I hope this helps
Answer:
yes. If there will be Evacuation and emergency procedures then the students can learn about that and can use that when there is an emergency case.
Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function. 5e^(-x)^2 cos(4x)
Answer:
The first three nonzero terms in the Maclaurin series is
[tex]\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
Step-by-step explanation:
GIven that:
[tex]f(x) = 5e^{-x^2} cos (4x)[/tex]
The Maclaurin series of cos x can be expressed as :
[tex]\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+... \ \ \ (1)}[/tex]
[tex]\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0} \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!} -\dfrac{x^6}{3!}+... \ \ \ (2)}[/tex]
From equation(1), substituting x with (4x), Then:
[tex]\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}[/tex]
The first three terms of cos (4x) is:
[tex]\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}[/tex]
[tex]\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}[/tex]
[tex]\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}[/tex]
Multiplying equation (2) with (3); we have :
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }[/tex]
[tex]\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
Finally , multiplying 5 with [tex]\mathtt{ e^{-x^2} cos (4x) }[/tex] ; we have:
The first three nonzero terms in the Maclaurin series is
[tex]\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }[/tex]
PLEASE HELP!!
express as a trinomial
(x-6) (2x-7)
Answer:
2x² - 19x + 42
Step-by-step explanation:
We want to expand (x - 6)(2x - 7) into a trinomial.
We use the FOIL (first, outer, inner, last) method.
First, multiply the first terms of each parenthetical expression; in the first one, that's x, and in the second, that's 2x:
x * 2x = 2x²
Next, multiply the outer terms; in the first one, that's x, and in the second, that's -7:
x * (-7) = -7x
After that, multiply the inner terms; in the first one, that's -6 and in the second, that's 2x:
(-6) * 2x = -12x
Finally, multiply the last terms; in the first one, that's -6 and in the second, that's -7:
(-6) * (-7) = 42
Now, add all these results together:
2x² + (-7x) + (-12x) + 42
2x² - 19x + 42
The answer is thus 2x² - 19x + 42.
~ an aesthetics lover
Answer:
2x²-19x+42
Step-by-step explanation:
x·2x-x·7-6·2x+6·7
2xx-7x-12x+42
2x²-7x-12x
2x²-7x-12+42
Find the solution to the system of equations.
Answer: x=1, y=-4
Step-by-step explanation:
There are different ways to solve system of equation
graphingsubstitutioneliminationIn your case, since they are all put y on one side, then we should use substitution.
we should substitute y
-7x+3=-x-3
-7x+x=-3-3
-6x=-6
x=1
--------------------------
substitute x into any one of the equation to find y
y=-7x+3
y=-7×1+3
y=-7+3
y=-4
y=-x-3
y=-1-3
y=-4
#CarryOnLearning
how to answer the (a) question?
help please
i believe its 4
Step-by-step explanation:
Please help. Calculate the loading dose, in mg of heparin for a 5-year-old with a total body weight of 40 lbs., with 10% body fat (that is, 90% of that 40 lbs. is lean body mass). You may also be interested to know that 1 kg = 2.20 lbs. Think about the steps you need to go through to find the correct dose. Remember, first you need to find the dosing mass.
Answer:
≈ 3 mg
Step-by-step explanation:
Dose rate of heparin is 0.16 mg per kg of DMDosing mass calculation formula is:
DM = LBM + (TBM - LBM)/3, where LBM = lean body mass, TBM = total body massTBM = 40 lbsBody fat = 10%LBM = 90% of TBM = 0.9*TBMDosing mass
DM = 40 *0.9 + ( 40 - 40*0.9)/3 = 37.33 lbsConverting to kg
1 kg = 2.2 lbsDM = 37.33 lbs /2.2 = 16.97 kgLoading dose
dose = DM * dose rate per kgdose = 16.97 kg *0.16 mg/kg = 2.7152 mg ≈ 3 mgRound 467 to the nearest 10
Answer:
470.
Step-by-step explanation:
The units digit 7.
As this is greater than 4 we add 1 to the tens digit. ( 6 + 1 = 7), and the units digit becomes 0.
examples of parallel lines and interesting lines
Answer:
when the lines are opposite and doesnot intersect at any point then the lines are parallel
for example the opposite lines of parallelogram are parallel
when the lines cut each other at one point then we can say that lines are intersecting
hope it helps u
Answer:
Parallel lines :When thè lines are parellel and opposte to each other then it is called parellel lines.
Intersecting lines :When thè lines intersect each other and meet at a point then it is called intersecting lines.
6.2×10 +6×10³ Brainiest if right
Answer: 6062
Add Parentheses
[tex](6.2*10)+(6*10^3)[/tex]
Note: Always Multiply the Parentheses first!
Multiply
[tex]6.2*10=62[/tex]
[tex]6*10^3=6000[/tex]
How is 6×10^3 6000?
Before you multiply the whole equation you first Multiply 10 3 times. This is called an Exponent. In my own words, an exponent is a number that tells you how many times to multiply that number. So if we had 6^2 I will multiply 6×6 2 times. So we multiply 10×10×10 and get 1000. Then we multiply 6×1000 and get 6000.
Add
Since the final step is to add we Add the answer we got for 6.2×10 and 6×10^3.
Therefore we are adding 62*6000 and we get 6062.
Where do the lines y=2x+1 and y=-5x-6 intersect?
Answer:
(-1, -1)
Step-by-step explanation:
To find where two lines in slope-intercept form intersect, set them equal to each other.
2x + 1 = -5x - 6
7x = -7
x = -1
Knowing they intersect at x = -1, substitute -1 into either of the two equations to find the y-value of their intersection.
y = 2(-1) + 1
y = -2 + 1
y = -1
So the intersection point of the two lines is (-1, -1).
i need help with this
Answer:
1a. either AC ≅ DF or AB ≅ DE
1b. <A ≅ <D
2a. B
2b. D
Step-by-step explanation:
paper plus sells reams ofpaper of $5.25 each discount paper sells the same reams of paper for $3.99 each, how much would you save by purchasing 15 reams of paper at discount paper instead of at paper plus?
Answer: $18.90
Step-by-step explanation:
multiply both by 15
subtract from each other
Solve the equation for X 3(x+2)=2(2-x)
Answer:
x = - 2/5Step-by-step explanation:
[tex]3(x+2)=2(2-x)\\\\\mathrm{Expand\:}3\left(x+2\right):\quad 3x+6\\\\\mathrm{Expand\:}2\left(2-x\right):\quad 4-2x\\\\3x+6=4-2x\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\3x+6-6=4-2x-6\\\\3x=-2x-2\\\\\mathrm{Add\:}2x\mathrm{\:to\:both\:sides}\\\\3x+2x=-2x-2+2x\\\\Simplify\\\\5x=-2\\\\Divide\:both\:sides\:by5\\\\\frac{5x}{5}=\frac{-2}{5}\\\\x=-\frac{2}{5}[/tex]
add 5 to me then you divide by 7 if you add 12 then subtract 7 you get 10 what number am i
Answer:
x+5=x÷7+12=x-7=10 it is 30
Answer:
30
Step-by-step explanation:
Given number is x, then:
(x + 5) ÷ 7 + 12 - 7 = 10(x + 5) ÷ 7 + 5= 10(x + 5) ÷ 7 = 5x + 5 = 5*7x + 5 = 35x = 35 - 5x = 30The number is 30
Alastair drives 18.2 miles in 14 minutes.
He passes a sign which gives the speed limit as 50 mph.
By how much, in mph, did Alastair's average speed exceed the speed limit?
Answer:
28 mph
Step-by-step explanation:
Distance
18.2 milesTime
14 min = 14/60 hrAverage speed
d/t = 18.2 ÷ 14/60 = 182/10 × 60/14 = 78 mphThe difference with allowed speed
78 - 50 = 28 mphAnswer:
28mph
Step-by-step explanation:
Simplify the expression:
(10x2 -1 + 4x) + (3 + 5x2 - 4x)
Answer:
15x^2+2
Step-by-step explanation:
(10x^2 -1 + 4x) + (3 + 5x^2 - 4x)
Combine like terms
10x^2+5x^2+4x-4x-1+3
15x^2+2
what is standered form of 6,600,000,000,000,000,000,000
Answer:
6.6×10²¹
Step-by-step explanation:
6,600,000,000,000,000,000,000 → there are 21 place values after the first non-zero number ''6''
to convert to standard form, we move the decimal point after the first non-zero number.
6,600,000,000,000,000,000,000.0 ← decimal in the end
the decimal will be moved, all the digits after the decimal are counted and they will resemble the index.
6.6×10²¹
Multiply.
(-7x - 2) (5x+3)
Simplify your answer.
Answer:
= -35x² - 31x - 6
Step-by-step explanation:
(-7x -2)(5x+3) = -7x*5x -7x*3 -2*5x -2*3 = -35x² - 21x - 10x - 6
= -35x² - 31x - 6
Which figure has one line of symmetry but no rotational symmetry?
Answer:
c because u can split it only once vertically but it’s not a rotationally symmetrical shape
Step-by-step explanation:
A man walks along a straight path at a speed of 3 ft/s. A searchlight is located on the ground 4 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 3 ft from the point on the path closest to the searchlight
Answer:
0.48 rad/sec
Step-by-step explanation:
From the diagram:
We can find 'x' using trigonometry :
Tanθ = opposite / Adjacent
Opposite = x ; adjacent = 4
Tanθ = x / 4
x = 4tanθ
Let u = 4 and v = tanθ
If dx/dt = 3ft/s ;
dθ/dt when x = 3ft
Differentiate x with respect to t
dx/dt (4tanθ)
Let d/dθ tanθ = sec^2θ
Sec^2θ = 1 / cos^2θ
dθ/dt = 1/4cos^2θdx/dt
dθ/dt = 1/4cos^2θ(3)
dθ/dt = 3/4cos^2θ
When x = 3ft
Cosθ = Adjacent / Hypotenus
Hypotenus = √(4^2 + 3^2
Hypotenuse = √16 + 9 = √25 = 5
Cosθ = 4/5
dθ/dt = 3/4(4/5)^2
dθ/dt = 3/4(16/25)
dθ/dt = 48/100 = 12/25 = 0.48 rad/sec
Gunnar’s car gets 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. PART B: Gunnar’s car is close to empty and only has 0.98 gallon of gas left. He stops at a gas station that charges $2.05 per gallon of gas. How much does it cost for Gunnar to refill his tank? Round your answer to the nearest penny.
Answer:
399.17 miles
Step-by-step explanation:
Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.
Gunnar's car travels with one gallon of gas = 22.4 miles
He can travel with 17.82 gallon of gas = 17.82 × 22.4
= 399.168 ≈ 399.17 miles
Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.
Choose the best answer from the four choices given. You may use scratch
paper.
(3x2y3 )3 =
3x5y6
O 9x6yº
O 27x5y6
O 27x6y
Answer:
27x^6y^9
Step-by-step explanation:
(3x^2y^3)^3 = 3^3 * (x^2)^3 * (y^3)^3 =
= 27x^6y^9
A past survey of 1, 068,000 students taking a standardized test revealed that 8.9% of the students were planning on studying engineering in college.
In a recent survey of 1, 476,000 students taking the SAT. 9.2% of the students were planning to study engineering.
Construct a 95% confidence interval for the difference between proportions ^p1−^p2 by using the following inequality. Assume the samples are random and independent.
(^p1−^p2)−zc√^p1^q1n1+^p2^q2n2
The confidence interval is _____
Complete Question
The complete question is shown on the first uploaded image
Answer:
The interval is [tex]-0.0037 < p_1-p_2<-0.0023[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n _1 = 1068000[/tex]
The first sample proportion is [tex]\r p_1 = 0.089[/tex]
The second sample size is [tex]n_2 = 1476000[/tex]
The second sample proportion is [tex]\r p_2 = 0.092[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = (100 - 95 )\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{\alpha }{2} } =z_c= 1.96[/tex]
Generally the 95% confidence interval is mathematically represented as
[tex](\r p_1 - \r p_2 ) -z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}} < (p_1 - p_2 ) < (\r p_1 - \r p_2 ) +z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}}[/tex]
Here [tex]\r q_1[/tex] is mathematically evaluated as [tex]\r q_1 = (1 - \r p_1)= 1-0.089 =0.911[/tex]
and [tex]\r q_2[/tex] is mathematically evaluated as [tex]\r q_2 = (1 - \r p_2) = 1- 0.092 = 0.908[/tex]
So
[tex](0.089 - 0.092 ) -1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}} < (p_1 - p_2 ) < (0.089 - 0.092 ) +1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}}[/tex]
[tex]-0.0037 < p_1-p_2<-0.0023[/tex]