Answer:
Variance=134.8943 kg
Step-by-step explanation:
The relationship between standard deviation and variance is that standard deviation is the square root of the variance.
So given the value of standard deviation to be 11.6144kg, the variance will be the square of the number.
Standard deviation= √variance
Standard deviation ²=√variance²
Standard deviation ² = variance
11.6144²= variance
134.8943
Variance=134.8943 kg
Answer:
122.4409 kg
Step-by-step explanation:
A customer gave her hair dresser a 20% tip, which amounted to $7. What was the price before the tip?
Answer:
The price before tip was 35
Step-by-step explanation:
Let x = original amount
x * 20% = 7
Change to decimal form
x * .20 = 7
Divide each side by .20
x*.20/.20 = 7/.20
x =35
is the midsegment of ABC. If is 30 centimeters long, how long is ?
A.
25 centimeters
B.
20 centimeters
C.
15 centimeters
D.
10 centimeters
Answer:
C. 15 centimeters
Step-by-step explanation:
The Triangle Midsegment Theorem
segment LM = 1/2 of AC
LM = 1/2 * 30
LM = 15 cm
A pile of 55 coins consisting of nickels and dimes is worth $3.90 . Find the number of each.
Answer:
23 dimes, 32 nickels
Step-by-step explanation:
Let n equal the number of nickels and d be the number of dimes. We can use the information given to create a system of equations, as follows:
The total number of coins (the number of nickels plus the number of dimes) is 55, giving us the equation n + d = 55.
The total amount is $3.90. Since each nickel is worth $0.05 and each dime is worth $0.10, we get the equation 0.05n + 0.10d = 3.90.
Multiplying the second equation by 20, we get n + 2d = 78. We can subtract the first equation to get d = 23. Substituting this into the first equation, we get that n = 32.
Therefore, there are 23 dimes and 32 nickels.
Answer: 100 penny 2 qtrs 50 noclke
Step-by-step explanation:
In the given diagram, find the values of x, y, and z.
a. x = 36°, y = 36°, z = 34°
b. x = 44º, y = 44°, z = 44°
c. x = 34º, y = 34°, z = 34°
d. x = 36°, y = 34°, z = 34°
Answer:
a. x = 36°, y = 36°, z = 34°
Step-by-step explanation:
X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°
The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°
Solve the following for x. 3(x-2)-6x=4(x-5)
Answer:
x=2
Step-by-step explanation:
3(x-2)-6x=4(x-5)
Distribute
3x -6 -6x = 4x -20
Combine like terms
-3x-6 = 4x-20
Add 3x to each side
-3x-6+3x = 4x-20+3x
-6 = 7x-20
Add 20 to each side
-6+20 = 7x-20+20
14 = 7x
Divide by 7
14/7 =7x/7
2=x
Answer:
x = 2Step-by-step explanation:
[tex]3(x - 2) - 6x = 4(x - 5)[/tex]
Distribute 3 through the parentheses
[tex]3x - 6 - 6x = 4(x - 5)[/tex]
Distribute 4 through the parentheses
[tex]3x - 6 - 6x = 4x - 20[/tex]
Collect like terms
[tex] - 3x - 6 = 4x - 20[/tex]
Move variable to L.H.S and change it's sign
[tex] - 3x - 4x - 6 = - 20[/tex]
Move constant to RHS and change it's sign
[tex] - 3x - 4x = - 20 + 6[/tex]
Collect like terms
[tex] - 7x = - 20 + 6[/tex]
Calculate
[tex] - 7x = - 14[/tex]
Divide both sides of the equation by -7
[tex] \frac{ - 7x}{ - 7} = \frac{ - 14}{ - 7} [/tex]
Calculate
[tex]x = 2[/tex]
Hope this helps..
Best regards!!
A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.65 lb, the mean of all of the weights is x=2.135 lb, and the standard deviation of the weights is s=2.316 lb. a. What is the difference between the weight of 5.65 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.65 lb to a z score. d. If we consider weights that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the weight of 5.65 lb significant?
Answer:
Explained below.
Step-by-step explanation:
Let the random variable X represent the weights (lb) of plastic discarded by households.
It is provided that the mean weight is, [tex]\bar x=2.135\ \text{lb}[/tex] and the standard deviation of the weights is, [tex]s=2.316\ \text{lb}[/tex].
(a)
Compute the difference between the weight of 5.65 lb and the mean of the weights as follows:
[tex]d=5.65 - \bar x\\\\d=5.65-2.135\\\\d=3.515[/tex]
Thus, the difference is 3.515 lb.
(b)
Compute the number of standard deviations as follows:
[tex]\text{Number of Standard Deviation}=\frac{d}{s}=\frac{3.515}{2.316}=1.518[/tex]
Thus, the number of standard deviation is 1.518.
(c)
Compute the z-score for the weight 5.65 lb as follows:
[tex]z=\frac{a-\bar x}{s}=\frac{5.65-2.135}{2.316}=1.517703\approx 1.52[/tex]
Thus, the z-score is 1.52.
(d)
The z-score for the weight 5.65 lb is 1.52.
This z-score lies in the range -2 and 2.
Thus, the weight of 5.65 lb is neither significantly low nor significantly high.
The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t) = -16t^2 + 32t +128. How long will it take the projectile to hit the ground?
Answer:
It takes 4 seconds for the projectile to hit the ground
Step-by-step explanation:
The height of the projectile after t seconds is given by the following equation:
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
How long will it take the projectile to hit the ground?
It happens when [tex]h(t) = 0[/tex]
So
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
[tex]-16t^{2} + 32t + 128 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]-16t^{2} + 32t + 128 = 0[/tex]
So [tex]a = -16, b = 32, c = 128[/tex]
[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]
[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]
[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]
Time is a positive measure, so:
It takes 4 seconds for the projectile to hit the ground
Prove that tan (pi/4 + A) tan (3pi/4 +A) = -1
Answer:
Step-by-step explanation:
tan(pi\4+A)tan(3pi\4+A) =-1
using the tangent sum of angle formula
What is the product of 3x(x^2+4)?
0 + 3x + 4
3+ 12
31
124
Answer: i honestly dont know this seems very complicated
Step-by-step explanation:
Answer:
3x^3+12x
Step-by-step explanation:
Which of the following can be calculated using the formula ?
A.
Area of a circle
B.
Circumference of a circle
C.
Arc length of a circle
D.
Diameter of a circle
The formula C = π2r
Is used for the circumference.
Which of the following can be calculated using the formula?We know that the number π is defined as the quotient between the circumference of a circle and its diameter, so we can write:
C/d = π
And remember that the diameter is twice the radius, so we can write:
d = 2r
Then we can rewrite the equation for the circumference as:
C = π2r
Then we conclude that the correct option is B.
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Solve for X. pls help asap
Answer:
x=3
Step-by-step explanation:
Use the Pythagorean Theorem to write an equation.
x^2+y^2=z^2
Substitute values from the problem.
x^2 + 6^2 = 9^2
Solve for what you know.
x^2 + 36 = 81
Square root it.
x+6=9
Subtract 6 from both sides.
x=3
In the future, if you see a right triangle with an unknown side, and the other two sides are either 3, 6, or 9, you know that the other one is the missing value out of 3/6/9. This is called a 3/6/9 triangle.
Answer:
6.7Step-by-step explanation:
Hypotenuse (h) = 9
base (b) = X
Perpendicular (p) = 6
Now,
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]
[tex] {b}^{2} = {(9)}^{2} - {(6)}^{2} [/tex]
[tex] {b}^{2} = 81 - 36[/tex]
[tex] {b}^{2} = 45[/tex]
[tex]b = \sqrt{45} [/tex]
[tex]b = 6.7[/tex]
Hope this helps...
Good luck on your assignment..
What is the measure of <A in the triangle below?
Answer:
62
Step-by-step explanation:
180-116 makes us find out that angle C is 64, thus to find out the inner angles you gotta do 64+ (2x+4)+(3x-13)=180
You follow this operation, find out x and perform 3(25)-13, which ends up giving you 62
Answer:
62°
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is not sharing a common side
2x + 4 + 3x - 13 = 116° add like terms
5x - 9 = 116°
5x = 125° divide both sides by 5
x = 25 and angle A is 3x - 13 so 3×25 - 13 = 62°
whats a significant figure
Answer:
Significant figures are any digits that contribute to the number: In 02.400, only 2 and 4 are significant digits. However, in 2.4001, 2, 4, 0, 0, and 1 are significant digits, because the number would not be the same without them.
Step-by-step explanation:
Hope it helps <3
Please answer this correctly without making mistakes
Shortest is Vindale to Wildgrove to Clarksville
18.9 + 13.2 = 32.1 km.
Two trains leave New York at the same time heading in opposite directions. Train A travels at 4/5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A? Can you pls help me fast
=============================================
Work Shown:
x = speed of train A
y = speed of train B
"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y
distance = rate*time
d = x*7
d = (4/5)y*7 = (28/5)y represents the distance train A travels
d = y*7 = 7y represents the distance train B travels
summing those distances will give us 693
(28/5)y + 7y = 693
5*( (28/5)y + 7y ) = 5*693
28y + 35y = 3465
63y = 3465
y = 3465/63
y = 55
Train B's speed is 55 mph
4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph
Train A's speed is 44 mph
The drama club is selling T-shirts and caps to raise money for a spring trip. The caps sell for $5.00 each, and the T-shirts sell for $10.00 each. The drama club needs to raise at least $500.00 for the trip. The inequality that represents this situation is graphed, with x representing the number of caps sold and y representing the number of T-shirts sold. Which solution is valid within the context of the situation?
Answer:
The correct answer to this question is C: (72,24).
Step-by-step explanation:
We are given that:
The cost of 1 cap is $5 each
The cost of 1 t-shirt is $10 each
Let x be the number of caps sold
Let y be the number of t-shirt sold
In the context we are given that the drama club needs to raise at least $500 to go on the trip.
So based on this information we can create a inequality as:
the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500
Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.
Next we need to figure out how many caps and t-shirt were sold.
- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)
Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )
B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500
YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!
C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.
So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.
Answer: C
Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.
First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.
Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.
So, (8,5) is a valid solution in the context of the situation.
if sin theta = 2/3 which is possible
Answer:
C. cos theta = √5/3 and tan theta = 2/√5D. sec theta = 3/√5 and tan theta = 2/√5Step-by-step explanation:
According to SOH in SOH, CAH TOA;
SOH means sin theta = opposite/hypotenuse = 2/3
This shows that opposite = 2 and hypotenuse = 3. Before we can determine which of the expression is possible, we need to find the third side of the rigt angled triangle which is the adjacent.
According to Pythagoras theorem; hyp² = opp²+adj²
adj² = hyp² - opp²
adj² = 3² - 2²
adj² = 9 - 4
adj² = 5
adj = √5
Hence the adjacent side is √5.
From the trigonometry identity above;
cos theta = adj/hyp = √5/3 and tan theta = opp/adj = 2/√5
Since sec theta = 1/cos theta then sec theta = 1/(adj/hyp)
sec theta = hyp/adj = 3/√5
From the above calculation, the following are possible:
cos theta = √5/3, tan theta = 2/√5 and sec theta = 3/√5
The correct options are C and D
PLEASE PLEASE PLEASE HELP TIMEDCan you prove that DE F = HGF Justify your answer. A. Yes, the triangles are congruent by SAS. B. Yes, the triangles are congruent by SSS. C. Yes, the triangles are congruent by SSA. D. No, not enough information is given.
Answer:
A. Yes, the triangles are congruent by SAS.
Step-by-step explanation:
EF = FG and DF = FH-> Given
angle EFD = angle HFG -> Vertical angles are congruent
DE F = HGF -> SAS Triangle Congruence Theorem
We can prove ∠DE F = ∠HGF by SAS congruency.
Hence option A is correct.
In the given triangle,
DE = GE
DF = FH
We know that,
SAS congruency stands for "Side-Angle-Side" congruence,
Which is a rule used in geometry to prove that two triangles are congruent or equal in size and shape.
This rule states that if two sides and the angle between them of one triangle are congruent to the corresponding two sides and angle of another triangle, then the two triangles are congruent.
Since the triangles
DE,GE and DF, FH are the corresponding sides and
DE = GE
DF = FH
Since DEF and FHG are congruent.
Therefore,
∠DE F = ∠HGF
Hence proved.
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A box contains orange balls and green balls. The number of green balls is seven more than three times the number of orange balls. If there are 67 balls altogether, how many green balls and how many orange balls are there in the box?
Answer:
52 green, 15 orange
Step-by-step explanation:
g + o = 67 g = green, o = orange, x = total
g = 3o + 7
use substitution: (3o + 7) + o = 67
solve for o:
4o + 7 = 67
4o = 60
o = 60/4 = 15
solve for g:
g + 15 = 67
g = 52
In an ANOVA the F-calculated for the treatment 4.76 with 3 degrees of freedom in the numerator and 6 degrees of freedom in the error term. What is the approximate p-value
Answer:
0.0499
Step-by-step explanation:
The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.
The p-value shows that the for 5% level of significance the null hypothesis can be rejected.
if one tenth of a number is added to 2. the result is half of that number. what is the number?
Answer:
5
Step-by-step explanation:
According to the given question, the calculation of number is shown below:-
Let the number be x.
[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.
[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]
Now we will solve the above equation
[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]
x = 5
Therefore the correct answer is 5
Hence, the number based on the given information provided in the question is 5
The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − (x − π/2) + 1/6 (x − π/2)3 + R3(x). Using this, estimate cos(86°) correct to five decimal places.
Answer:
The cosine of 86º is approximately 0.06976.
Step-by-step explanation:
The third degree Taylor polynomial for the cosine function centered at [tex]a = \frac{\pi}{2}[/tex] is:
[tex]\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}[/tex]
The value of 86º in radians is:
[tex]86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi[/tex]
[tex]86^{\circ} = \frac{43}{90}\pi\,rad[/tex]
Then, the cosine of 86º is:
[tex]\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}[/tex]
[tex]\cos 86^{\circ} \approx 0.06976[/tex]
The cosine of 86º is approximately 0.06976.
A college financial advisor wants to estimate the mean cost of textbooks per quarter for students at the college. For the estimate to be useful, it should have a margin of error of 20 dollars or less. The standard deviation of prices is estimated to be around 100 dollars. How large of a sample size needs to be used to be 95% confident, with the given margin of error?
Answer:
minimum sample size = 97
Step-by-step explanation:
Margin of error = 20
standard deviation = 100
sample size = n
standard error = 100/sqrt(n)
confidence level, alpha = 95%
Using the standard rule for 95% confidence
standard error <= sample mean [tex]\pm[/tex] 1.96 standard error, or
20 <= 1.96*100 / sqrt(n)
n >= (1.96*100/20)^2 = 9.8^2 = 96.04
=>
n >= 97
What is heron's formula
Answer:
[tex]\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
Step-by-step explanation:
We can use Heron’s formula to determine the area of a triangle when three side lengths of a triangle are given.
[tex]s=\frac{a+b+c}{2}[/tex]
[tex]s : \mathrm{semi \: perimeter}[/tex]
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]A : \mathrm{area}[/tex]
Answer:
Heron's formula gives the area of a triangle when the length of all three sides are known. Use Heron's formula to find the area of triangle ABC, if AB=3,BC=2,CA=4 . Substitute S into the formula . Round answer to nearest tenth.
Step-by-step explanation:
Adult men have heights that a normally distributed with a mean of 69.5 inches and a standard deviation of 2.4 inches. Adult women have heights that a normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches. Between a man with a height of 74 inches and a women with a height of 70 inches, who is more unusually tall within his or her respective sex ?
Answer:
Step-by-step explanation:
From the information given:
For Adult Men
Mean [tex]\mu[/tex] = 69.5
Standard deviation [tex]\sigma[/tex] = 2.4
observed value X = 74
For Adult Women
Mean [tex]\mu[/tex] = 63.8
Standard deviation [tex]\sigma[/tex] = 2.6
observed value X = 70
Therefore ; the values for their z scores can be obtained in order to determine who is more unusually tall within his or her respective sex
For Adult Men :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{74- 69.5}{2.4}[/tex]
[tex]z = \dfrac{4.5}{2.4}[/tex]
z = 1.875
For Adult Women :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]z = \dfrac{70- 63.8}{2.6}[/tex]
[tex]z = \dfrac{6.2}{2.6}[/tex]
z = 2.3846
Thus; we can conclude that , the women is more unusually tall within his or her respective sex
A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
Answer:
number of children ticket sold = 70
number of adult ticket sold = 70 × 3 = 210
number of student ticket sold = 500 - 4(70) = 500 - 280 = 220
The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.
What is an expression? What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.
Adult's ticket = [y]
Children's ticket = [x]
Student's ticket = [z]
and
y = 3x
Now -
x + y + z = 500
x + 3x + z = 500
4x + z = 500 ....[1]
and
12x + 18y + 15z = 8040
12x + 18(3x) + 15z = 8040
12x + 54x + 15z = 8040
66x + 15z = 8040 ....[2]
On solving [1] and [2], we get -
x = 90 and z = 140
and
y = 3x = 3 x 90 = 270
y = 270
Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.
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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.9 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.
b. If 39 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb.
c. When redesigning the ejection seat which probability is more relevant?
Answer:
The answer is below
Step-by-step explanation:
Given that:
mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb
z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%
b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%
c) The probability from part C is more important
In a circle with a radius of 8ft an arc is intercepted by a central angle of 135 degrees. What is the length of the arc?
A: 6.28 ft
B: 9.42 ft
C: 18.84 ft
D: 28.26 ft
Greetings from Brasil...
We know that the entire length of a circle its:
C = 2πR
C = 2π8
C= 16π circumference length
now rule of 3:
length º
16π --------- 360
X --------- 135
360X = 135 · 16π
X = 2160π/360
X = 6π or 18,84Find the volume of each cone.
Answer: 6 cm, V=48π or V=150.8 cm³
It appears the question is asking for the radius, but below I have shown how to find the volume.
Step-by-step explanation:
The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.
The formula to find the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. Now that we have the radius from above, we can use that to plug into the equation along with the given height.
[tex]V=\pi (6^2)\frac{4}{3}[/tex] [expand the exponent]
[tex]V=36\pi \frac{4}{3}[/tex] [combine like terms]
[tex]V=48\pi[/tex] or [tex]V=150.8 cm^3[/tex]
PLEASE PLEASE PLEASE HELP
Answer:
1) 18
2) P
Step-by-step explanation:
1) Multiply the top number by itself and then reverse the digits!
9*9 = 81 reversed is 18
2) Seems to be the number of line ends a letter has when you write it down. P only has one end, at the bottom.
Answer:
P
Step-by-step explanation:
2.
The number of strokes of the letter that come to an end.
The bottom of the A has two sticks that come to an end.
A = 2
The B has no sticks coming to an end.
B = 0
The C and an upper and a lower stroke coming to an end.
C = 2
D has none.
D = 0
E has 3 sticks coming to an end.
E = 3
etc.
M has 3.
N has 2.
O has 0.
P has 1 stick coming to an end.
Q has none.
R has 2.
S has 2.
T has 3.
U has 2.
V has 2.
W has 3.
X has 4.
Y has 3
Z has 2.
Of all letters after L, only P has exactly 1 stroke coming to an end.
Answer: P