Answer:
the line y = x
Step-by-step explanation:
(a, b ) and (b, a ) are reflections of each other in the line y = x.
They are therefore both equidistant from the line y = x
which graph represents a function?
I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.
The only function there is the last one. (Right bottom)
The amount of time to complete a physical activity in a PE class is approximately normally normally distributed with a mean of 32.9 seconds and a standard deviation of 6.4 seconds.
A) What is the probability that a randomly chosen student completes the activity in less than 33.2 seconds?
B) What is the probability that a randomly chosen student completes the activity in more than 46.6 seconds?
C) What proportion of students take between 35.5 and 42.8 seconds to complete the activity?
D) 75% of all students finish the activity in less than____seconds.
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.
The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\[/tex]
a) For x < 33.2 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%
b) For x > 46.6 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%
c) For x = 35.5 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41[/tex]
For x = 42.8 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55[/tex]
From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%
d) A probability of 75% = 0.75 corresponds to a z score of 0.68
[tex]z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3[/tex]
75% of all students finish the activity in less than 37.3 seconds
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $
Question:
Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $20.70? How much was the tip?
Answer:
Price of meal = $18
Tip price = $2.70
Step-by-step explanation:
Let the price of the meal be y;
Let the tip be t
From the question;
15% of y is the tip charge (t). i.e
t = 15%y
=> t = 0.15y --------(i)
The total amount charged is $20.70 (This means that the sum of the price of the meal and the tip is $20.70)
=> y + t = 20.70 [substitute the value of t=0.15y from equation (i)]
=> y + 0.15y = 20.70
=> 1.15y = 20.70
=> y = [tex]\frac{20.70}{1.15}[/tex]
=> y = $18
Therefore the price of the meal, y, is $18.
From equation (i),
t = 0.15y [substitute the value of y = $18]
t = 0.15(18)
t = $2.70
Therefore the tip was $2.70
I need some help, see the picture for the question. Solve for V
Answer:
the answer is A) h=3V/(Pi*r^2)
Step-by-step explanation:
This question is asking to solve for h, the equation is allready solved for V.
to solve for h means to get h by itself on one side of the equation.
1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation
2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.
3) (3*V)/(pi*r^2)=h. Simplify.
4) 3V/(Pi*r^2)=h.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.
Answer:
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Step-by-step explanation:
The amount of Carbon-14 after t years is given by the following equation:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.
This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]
How many years will it take for carbon–14 to decay to 10 percent of its original amount?
This is t for which:
[tex]A(t) = 0.1A(0)[/tex]
So
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]
[tex]e^{-0.000124t} = 0.1[/tex]
[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]
[tex]-0.000124t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]
[tex]t = 18569.2[/tex]
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Find the total area of the prism.
Answer:
A=1,728
Step-by-step explanation:
To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.
The width is 12, the hight is 12, and the depth is 12 so you can write
A=12*12*12
Multiply 12 by 12
A=144*12
Multiply 12 by 144 to get your final total area
A=1,728
Hope this helps, feel free to ask follow-up questions if confused.
Have a good day! :)
the exact derivative of f(x)=x^3 at x=5
Answer:
[tex]75[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx}\left(x^3\right)[/tex]
[tex]=3x^{3-1}[/tex]
[tex]=3x^2[/tex]
[tex]3\left(5\right)^2[/tex]
[tex]=3\cdot \:25[/tex]
[tex]=75[/tex]
Which could be used to evaluate the expression
43)
O (-6)(4)+(-01
0 (-6)(4) «(-6) (
3
O (-6+4)+ -6
G
0 (-6+4)*|-6-
Answer:
[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]
Step-by-step explanation:
The expression, [tex] -6(4\frac{2}{3}) [/tex] , can be understood or interpreted as negative six multiplied by four and two-third.
Thus, it could be evaluated using distributive property of multiplication, as shown below:
[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]
[tex](-6)(4) + (-6)(\frac{2}{3}) \\(-24) + (-2)(2)\\-24 + (-4)\\-24 - 4\\= -28[/tex]
Find the measure of a.
Answer:
a = 37
Step-by-step explanation:
the sum of any triangle angles is 180
then 62 + 81 + a = 180
a = 37
.. ..
Answer:
a = 37 degrees
Step-by-step explanation:
81+62 = 143
We know that all angles of a triangle = 180 degrees
180-143= 37 degrees
a = 37 degrees
Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 6 0.10 12 0.35 18 0.25 24 0.30
Answer:
Mean = 16.5
Variance = 35.55
Step-by-step explanation:
x P(x) x. P(x) x² x². P(x)
6 0.10 0.6 36 3.6
12 0.35 4.2 144 50.4
18 0.25 4.5 324 81
24 0.30 7.2 576 172.8
∑x P (x) 16.5 ∑x² P (x) 307.8
The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.
Mean is given by E(X)= ∑x P (x) = 16.5
Similarly the variance is also calculated using the expected value of X and X².
Variance is given= E(X)²- [E(X)]²= 307.8- (16.5)²= 307.8-272.25 = 35.55
assume the carrying capacity of the earth is 21 billion. use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion. How does the predicted growth rate compare to the actual growth rate of about 1.2% per year?
Answer:
current population growth rate would be -3.1%
Step-by-step explanation:
We have to:
Growth rate = r * (1 - population / carrying capacity)
for 1960,
we have carrying capacity = 21 billion
population = 3 billion
r = Growth rate 1960 / (1 - population / carrying capacity)
replacing:
r = 0.021 / (1 - 3/21)
r = 0.0245
that is to say r = 2.45%
Now the current population would be:
= 0.0245 * (1 - carrying population / carrying capacity)
we replace:
= 0.0245 * (1 - 6.8 / 3)
= -0.031
current population growth rate would be -3.1%
The predicted growth rate compare to the actual growth rate of about 1.2% per year is -3.1% and this can be determined by using the formula of growth rate.
Given :
Assume the carrying capacity of the earth is 21 billion. Use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion.The growth rate is given by the formula:
[tex]\rm Growth \;Rate = r\times \left(1-\dfrac{Populatuion}{Carrying\;Capacity}\right)[/tex]
Given that the carrying capacity of the earth is 21 billion. The growth rate in 1960 is 2.1%. So, put the known values in the equation (1).
[tex]\rm 0.021 = r\times \left(1-\dfrac{3}{21}\right)[/tex]
[tex]0.021=r\times \dfrac{18}{21}[/tex]
0.0245 = r
So, r = 2.45%.
Now, the growth rate of the current population is:
[tex]\rm Growth \;Rate = 0.0245\times \left(1-\dfrac{6.8}{3}\right)[/tex]
[tex]\rm Growth\; Rate = 0.0245 \times \dfrac{-3.8}{3}[/tex]
0.031 = Growth Rate
So, the growth rate is -3.1%.
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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
What is the measure of A? (solve to the nearest WHOLE DEGREE)
Answer:
A = 0.507 or 29 degrees
Step-by-step explanation:
5 = tanA * 9
inv tan = 5/9
angle A = 0.507
angle A = 29 degrees
Quadrilateral RSTQ is a parallelogram.
R
Which of the following relationships must be true?
O RS = RO
O TQ QR
O ZT ZR
O ZSRR
Answer:
[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]
Step-by-step explanation:
According to the Parallelogram definition, every Parallelogram have a pair of congruent sides. In this case, Namely [tex]\overline{RS} \cong \overline{TQ}[/tex] and [tex]\overline{QR} \cong \overline{TS}[/tex]
(not listed as an option)
And the opposite angles are congruent too.
So
[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]
∠R≅∠T relationship is true for the RSTQ parallelogram
What is Quadrilateral?A quadrilateral is a polygon having four sides, four angles, and four vertices.
A parallelogram is a quadrilateral with four sides.
a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
In parallelogram the opposite sides have equal length.
The opposite sides are congruent and the opposite angles are also congruent.
SR=TQ
ST=RQ
These sides are equal and
∠R≅∠T
∠S≅∠Q
In the given options only ∠R≅∠T is given, so we can consider this.
Hence ∠R≅∠T relationship is true for the RSTQ parallelogram
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Researchers recorded that a certain bacteria population declined from 800,000 to 500,000 in 6 hours after the administration of medication. At this rate of decay, how many bacteria would there have been at 24 hours? Round to the nearest whole number
Answer:
We can assume that the decline in the population is an exponential decay.
An exponential decay can be written as:
P(t) = A*b^t
Where A is the initial population, b is the base and t is the variable, in this case, number of hours.
We know that: A = 800,000.
P(t) = 800,000*b^t
And we know that after 6 hours, the popuation was 500,000:
p(6h) = 500,000 = 800,000*b^6
then we have that:
b^6 = 500,000/800,000 = 5/8
b = (5/8)^(1/6) = 0.925
Then our equation is:
P(t) = 800,000*0.925^t
Now, the population after 24 hours will be:
P(24) = 800,000*0.925^24 = 123,166
Answer:
122,070 bacteria.
Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt
Substitute the values in the formula.
500,000=800,000ek⋅6
Solve for k. Divide each side by 800,000.
58=e6k
Take the natural log of each side.
ln58=lne6k
Use the power property.
ln58=6klne
Simplify.
ln58=6k
Divide each side by 6.
ln586=k
Approximate the answer.
k≈−0.078
We use this rate of growth to predict the number of bacteria there will be in 24 hours.
AA0ktA=?=800,000=ln586=24hours=A0ekt
Substitute in the values.
A=800,000eln586⋅24
Evaluate.
A≈122,070.31
At this rate of decay, researchers can expect 122,070 bacteria.
You have $9000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $25 per meter. What is the maximum area you can achieve for the enclosure
Answer:i explained it
Step-by-step explanation:
The total cost of the fence will be 30(2L + 2W) + 2*25 W <= 9000
60L + 110W <= 9000
60 L <= 9000 - 110W
L <= 150 - 11/6 W
For a given width, the maximum area will correspond to the maximum length, so we can just go ahead and say L = 150 - 11/6 W
A = LW = (150 - 11/6 W) W
A = 150 W - 11/6 W2
A' = 150 - 11/3 W = 0
150 = 11/3 W
W = 450/11
Linda earned $13,500 in 3 months. What is her annual salary?
Answer:
$54,000
Step-by-step explanation:
Assuming that her salary does not change. Note that annual means "a year", which would mean 12 months.
First, find how much Linda makes per month. Divide the total earned in 3 months with 3 months:
13,500/3 = 4,500
Next, multiply 4,500 (the amount made per month) with 12 to get your annual salary:
4,500 x 12 = 54,000
Linda makes $54,000 annually.
The lines shown below are parallel.if the green line has a slope of -1,what is the slope of the red line?
Answer:
-1
Step-by-step explanation:
If a line is parallel on a graph, then that means that they will descend/climb at the same rate. Therefore, the slope of this line is also -1.
Hope this helped!
Answer:If they are parallel,
Then their slope will be same...
Step-by-step explanation:
???????????????????
?
?
?
?
Answer:
It should be 10 for the first box, 1000 for the second box and 100 for the third box.
Step-by-step explanation:
Each extra decimal place value added, u have to multiply it by the next value place such as tenths/hundreths/thousandths
A rhombus has interior angle measures of 104∘, 104∘, 76∘ and X degrees. Find the measure of angle X in the rhombus. Enter only the number of degrees in the answer box. Angle X measures degrees.
Answer:
76°
Interior angle of a rhombus =360
104° +104° +76° +X =360
X= 360 - 284
X= 76°
We know that the value of ∠x in the given rhombus is 76°.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal. A rhombus' internal angles add up to 360 degrees, just like in other quadrilaterals, and, like in a parallelogram, the angles of opposite pairs of vertices are identical. The total of the angles of two neighboring vertices is 180 degrees.So, get the ∠x as follows:
We now know that sum of all angles in a rhombus is 360°.Then,
104 + 104 + 76 + x = 360284 + x = 360x = 360 - 284x = 76°Therefore, we know that the value of ∠x in the given rhombus is 76°.
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Problem 2
In the above diagram, circles O and O' are tangent at X, and PQ is tangent to both circles. Given that
OX= 3 and O'X = 8. find PQ.
Answer:
√96
Step-by-step explanation:
PQ is tangent to both lines, so PQ is perpendicular to PO and QO'.
The radius of the smaller circle is 3, and the radius of the larger circle is 8.
If we draw a line from O to O', and another line from point O to line QO' that is parallel to PQ, we get a right triangle where OO' is the hypotenuse, the short leg is 8−3=5, and the long leg is the same length as PQ.
Using Pythagorean theorem:
x² + 5² = 11²
x = √96
A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with accessories for $24,000. The total cost of the car was 8 times as much as the accessories. How much did the accessories cost? Cost of Accessories
Answer:
y = 2666.67
Step-by-step explanation:
Well to solve this we can make a system of equations.
x = cost of car alone
y = cost of accesories,
[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]
So now we plug in 8y for x in x + y = 24000.
(8y) + y = 24000
9y = 24000
Divide both sides by 9
y = 2666.666666
or 2666.67 rounded to the nearest hundredth.
Now that we have y we can plug that in for y in x=8y.
x = 8(2.666.67)
x = 21,333.33 rounded to the nearest hundredth.
Thus,
accessories "y" cost around 2666.67.
Hope this helps :)
The formula for the volume of a right circular cylinder is
V = 72h. If r = 26 and h = 5b + 3, what is the
volume of the cylinder in terms of b?
Answer:
20b^3+12b^2
Step-by-step explanation:
v=(2b)^2 (5b+3) = 4b^2 (5b+3) = 20b3+12b^2
A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 14 respectively. The standard error of the mean is
Answer:
1.4Step-by-step explanation:
The formula for calculating the standard error of the mean is expressed as shown below;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
[tex]\sigma[/tex] is the standard deviation and n is the sample size.
Given [tex]\sigma[/tex] = 14 and n = 100
Substituting this values into the formula fr calculating the standard error of the mean;
[tex]SE = \frac{14}{\sqrt{100} } \\\\SE = \frac{14}{10} \\\\SE = 1.4[/tex]
Hence, standard error of the mean is 1.4
Combine like terms to create an equivalent expression. -3.6-1.9t+1.2+5.1t−3.6−1.9t+1.2+5.1t
Question
Combine like terms to create an equivalent expression.
-3.6-1.9t+1.2+5.1t
Answer:
3.2t - 2.4
Step-by-step explanation:
Given;
-3.6 - 1.9t + 1.2 + 5.1t
Combining like terms means bringing terms that have "t" together and separately, those that don't have "t" together. i.e
=> − 1.9t + 5.1t - 3.6 + 1.2
=> 3.2t - 2.4
Therefore, the equivalent expression is;
3.2t - 2.4
Answer:
3.2t - 2.4
Step-by-step explanation:
right on khan
PLEASE HELP ?
A: 111.6 square centimeters
B: 323 square centimeters
C: 7.75 square centimeters
Answer:
B. 323 square centimeters
Step-by-step explanation:
multiply the inches by the conversion number
50 x 6.45 = 322.5
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
[tex]1 \ inch^2 = 6.45 \ cm^2[/tex]
Multiplying both sides by 50
[tex]1 * 50 \ inch^2 = 6.45 * 50 \ cm^2\\[/tex]
[tex]50 \ inch^2 = 323 \ cm^2[/tex]
What is the range of the function f(x)=3/4|x|-3
Range is [tex]y\in[-3,+\infty)[/tex].
Hope this helps.
The rule r_y-axis ° R_0,90 (x,y) is applied to ABC. Which triangle shows the final image?
a. 1
b. 2
c. 3
d. 4
Answer: 4
Step-by-step explanation:
Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.
The attachment shows the graph rotated 1-turn to the left (90°).
Notice it is in the exact same position as #4.
You pick two students at random, one at a time. What is the probability that the second student is a sophomore, given that the first is a freshman
Answer:
0.40
Step-by-step explanation:
The computation of the probability for the second student be sophomore and the first is a freshman is shown below:
Let us assume
Sophomore = S
Freshman = F
Based on this assumption, the probability is as follows
So,
[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]
= 0.40
Hence, the probability for the second student be sophomore and the first student be freshman is 0.40
One kind of candy (jelly) sells for $5 a pound and another (chocolate) for $10 a pound. How many pounds of each should be used to make a mixture of 10 pounds of candy (both kinds) that sells for a total $80 (i.e. $8/pound)?
Answer:
chocolate: 6 poundsjelly: 4 poundsStep-by-step explanation:
Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...
10x +5(10 -x) = 80
5x +50 = 80
5x = 30
x = 6 . . . . . . . . pounds of chocolate
10 -x = 4 . . . . . pounds of jelly candy
6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.