Answer:
2/3rds of liad's run
Step-by-step explanation:
3 min 45s = 3 3/4 min = 15/4 min; 10/(15/4) = 8/3 laps
2min 30s = 2 1/2 min = 5/2 min; 10/(5/2) = 4 laps
(8/3)/4 = 2/3
A satellite orbits the Earth at a height of 343 kilometers. If the satellite makes 8 revolutions around the Earth, how many kilometers does it travel? (Earth's diameter is 6371 kilometers.) Use 3.14 as the approximate value of pi .
The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.
What is the distance in kilometres covered by the satellite after 8 revolutions?Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;
D = 6371 + (343)×2
Hence, we have; diameter, D = 7057 km.
Hence, the distance travelled after 8 revolutions is;
C = 8 × πd
C = 8 × 3.14 × 7057
C = 177,271.8 km.
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ZAP is a right triangle, with right angle A and sin P = 3/5 What is cos Z?
The ratio of cos Z is cos Z = 3 / 5
How to find the trigonometric ratios of a right triangle?A right triangle has one angle of the triangle as 90 degrees.
The sides of the right triangle can be found using trigonometric ratios.
Therefore,
sin ∅ = opposite / hypotenuse
sin Z = 3 / 5
Using Pythagoras theorem,
c² = a² + b²
5² - 3² = b²
b² = 25 - 9
b² = 16
b = √16
b = 4
Hence,
P + A = 90 degrees (complementary angles)
Therefore,
sin P = cos Z
cos Z = 3 / 5
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Explain how to modify the graphs of f(x) and G(x) to graph the solution set to the following system of inequalities. How can at least solution set be identified?
Give f(x) a dotted boundary and shade it above.
Give g(x) a solid boundary and shade it above.
The solution set is the region that is in the shaded region of both graphs.
What is the component form of the vector that translates the top house figure to the
bottom house figure?
The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).
What is the vector component form?The component form of a vector is known to be depicted as < x, y >.
Note that:
x - tells the distance or how far to the right or left, a vector is known or seen to be going.
y - tells the distance or how far to the upper part or downward a vector is known or seen to be going.
From the question and looking at the image attached, we were able to obtain (-4,4) and (2, 0)
So:
⇒ (-4,4) --------(-4+6)(4-4)-------(2,0)
⇒ (6,-4)
Hence, The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).
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Graph the following conditions. {(x, y): x + 2y > 6}
See attachment for the graph of the inequality expression x + 2y > 6
How to graph the conditions?The condition is given as:
{(x, y): x + 2y > 6}
This means that
x + 2y > 6
The above is an inequality expression, where the variables are x and y
So, we simply plot the graph of the inequality expression x + 2y > 6
See attachment for the graph of the inequality expression x + 2y > 6
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George has 50,000in wage income ,20,000 in gambling winning .10,000 in alimony income and 5,000 in divided income the amount of George income that is subject to withholding is
The amount of George's income that is subject to withholding is $75,000, which excludes the alimony income.
What is alimony income?Alimony income represents the amount received from a spouse or a former spouse under a divorce or separation instrument.
What are the incomes subject to withholding?The incomes subject to withholding include the following:
Regular CommissionsVacation payReimbursementsOther expense allowances PensionsBonusesDividendsGambling winnings.Data and Calculations:Wages income = $50,000
Gambling winning = $20,000
Alimony income = $10,000
Dividend income = $5,000
Income subject to withholding = $75,000 ($20,000 + $20,000 + $5,000)
Thus, George's income that is subject to withholding is $75,000, excluding the alimony income.
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Solve for x. You must show all of your work to receive credit.
Answer:
x = 6
Step-by-step explanation:
The spread of a disease can be modeled as N = 250√ where N is
the number of infected people, and t is time (in days).
How long will it take until the number of infected people reaches
2,500?
The spread of the disease will take a time 100 days to reach 2,500 infected people.
How to find the number of infected people at a certain time
In this problem we have a radical equation that represents the number of infected people as a function of time, we are suppose to find the time when that number will be 2,500 by algebra properties: (N = 2,500)
2,500 = 250 · √t
√t = 2,500 / 250
√t = 10
t = 10²
t = 100
The spread of the disease will take a time 100 days to reach 2,500 infected people.
Remark
The statement is poorly formatted and presents typing mistakes, correct form is shown below:
The spread of a disease can be modeled as N(t) = 250 · √t, where N is the number of infected people, and t is time (in days). How long will it take until the number of infected people reaches 2,500?
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Find the missing side length in the image below 12 18 and 10
The missing length of the right triangle is 13.41 inches.
How to find the side of a right triangle?A right angle triangle has one of its angles as 90 degrees.
The side length of a right triangle can be found using Pythagoras theorem.
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the other legs.Therefore,
x² = 18² - 12²
x² = 324 - 144
x² = 180
x = √180
x = 13.416407865
x = 13.41 inches
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The Two sets A and B are said to be disjoint sets if A n B=_____
The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
What does it mean for two sets to be disjoint?Disjoint sets are a pair of sets that do not share any elements. For instance, sets A=2,3 and B=4,5 are not connected sets.When two sets don't share elements, they are considered disjoint sets. In other words, the null set will result if we find the intersection of two sets. The process is straightforward; two sets are given in this procedure.When using a disjoint set union, it is possible to add new sets, combine existing sets, and check whether two sets of elements are the same in almost real-time.The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
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Gia is participating in a jump-a-thon to raise money for her school. After completing
20 jumps, she raised $50. Gia wants to know how much money she raises per jump.
Which rate shows how much money Gia raises per jump?
50
20
20
50
jumps per dollar
dollars per jump
20
50
50
20
jumps per dollar
dollars per jump
Answer:
50/20
Step-by-step explanation:
Rate of money raised raises per jump is
money raised / jumps
$50/ 20 jumps
We can think that if we divide the $50 into 20 equal parts,
each part will represent 1 jump and will have 50/20 = $2.5 per 1 jump.
A vector v has an initial (2,-3) point and terminal point (3,-4)
Write in component form.
The vector in component form is given by:
V = i - j.
How to find a vector?A vector is given by the terminal point subtracted by the initial point, hence:
(3,-4) - (2, -3) = (3 - 2, -4 - (-3)) = (1, -1)
How a vector is written in component form?A vector (a,b) in component form is:
V = a i + bj.
Hence, for vector (1,-1), we have that:
V = i - j.
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Write 636,000 in scientific notation.
HELP ME PLEASE
. Find the perimeter of a regular pentagon with each side measuring 4.5 inches.
Answer: 22.5 inches
Step-by-step explanation:
the general formula for finding perimeter is [tex]p=s+s+s...[/tex]a pentagon contains 5 sides[tex]p=s+s+s+s+s[/tex]
note that this is a regular pentagon so it must contain 5 congruent sideseach side will be 4.5 inchesthe formula can be changed to [tex]5(s)[/tex] and solved:[tex]5(4.5 in)=p[/tex]
∴ 22.5 inches = perimeter of the pentagon
Choose the equation that
matches the graph.
a. (1/2)x-4
b. y = 4x-1
C.
y = (1/1)
(¹²) ² − 4
-
d.
e.
x-4
y = (1/1)
y = 4x + 1
y = 4x+1
Answer: d
Step-by-step explanation:
The graph is increasing, so the base must be more than 1.
Eliminate a and c.Also, the y-intercept is 2.
Eliminate b and e.This leaves d.
Sketch the region enclosed by the given curves and find its area.
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
How to determine the area of a region enclosed by four functions
In this question we must determine the area generated by four functions: three linear functions and a radical function. First, we plot the four functions to determine the required combinations of definite integrals need for calculation:
[tex]A = \int\limits^{0.382}_0 {[f(x) - g(x)]} \, dx + \int\limits^2_{0.382} {[h(x) - g(x)]} \, dx[/tex], where f(x) = √x, g(x) = x - 3 and h(x) = - x + 1.
[tex]A = \int\limits^{0.382}_{0} {[\sqrt{x} - x + 3]} \, dx + \int\limits^{2}_{0.382} {[- 2 \cdot x + 4]} \, dx[/tex]
[tex]A = \int\limits^{0.382}_{0} {\sqrt{x}} \, dx - \int\limits^{0.382}_{0} {x} \, dx + 3 \int\limits^{0.382}_{0}\, dx - 2 \int\limits^{2}_{0.382} {x} \, dx + 4 \int\limits^{2}_{0.382}\, dx[/tex]
[tex]A= 2 \cdot x^{\frac{3}{2} }|_{0}^{0.382} - \frac{x^{2}}{2}|_{0}^{0.382} + 3\cdot x |_{0.382}^{2} - x^{2} |_{0.382}^{2}+4\cdot x |_{0.382}^{2}[/tex]
[tex]A = 2 \cdot (0.382^{\frac{3}{2} }-0^{\frac{3}{2} })-\left(\frac{1}{2} \right)\cdot (0.382^{2}-0^{2}) + 3 \cdot (2 - 0.382) - (2^{2}-0.382^{2})+4\cdot (2^{2}-0.382^{2})[/tex]
A = 16.815
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
Remark
The statement reports an inconsistency with at least one function and needs to be modified in order to apply definite integrals in a consistent manner. New form is shown below:
Sketch the region enclosed by the given curves and find its area: (i) x + y = 1, (ii) x - 3 = y, (iii) y = √x, (iv) x = 0.
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I NEED HELP ASAP PLS!!!
Answer:
C looks most correct
Step-by-step explanation:
In a student club, the probability that a randomly selected member volunteered for a recent activity was 24/43. What is the probability that a randomly selected member did not volunteer for the recent activity?
The probability that a randomly selected member did not volunteer for the recent activity is 19/43.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered
1 - 24/43
(43/43) - (24/43) = 19/43
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In a mathematics class, half of the students scored 87 on an achievement test.
With the exception of a few students who scored 52, the remaining students
scored 71. Which of the following
statements is true about the distribution of
scores?
Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Therefore, the correct answer is option A. The mean is less than the median.
What are statistics?Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Half the students scored 87.
The next highest score exists at 71.
Then the median will be (71+ 87) / 2 = 79
A few students scored 52, so the mean exists a little lower than the mean of 71 and 87.
Therefore, the correct answer is option A. The mean is less than the median.
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The complete question is:
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
the measure of the angels of a quadrilateral are in ratio 2:4:5:7 find the measure of each of it's angles
Answer:
Step-by-step explanation:
If they all exist in proportion to one another (READ: ratio) then multiplying each of the angles by the same number (here, some unknown "x" value) will maintain the proportionality. Since all the angles of a quadrilateral have to add up to equal 360, then
2x + 4x + 5x + 7x = 360 and
18x = 360. Divide both sides by 18 to get that
x = 20. That means that
2x = 2(20) = 40 and
4x = 4(20) = 80 and
5x = 5(20) = 100 and
7x = 7(20) = 140. Adding all of those up:
40 + 80 + 100 + 140 = 360
Answer:
40,80,100,140
Step-by-step explanation:
Let the ratio 2:4:5:7 angles be 2x, 4x, 5x, 7x
Now
2x + 4x + 5x + 7x=360 degrees
18x = 360 degrees
x =360/18
x=20
2x=2 *20=40
4x=4 *20=80
5x=5 *20=100
7x=7* 20=140
se the FOIL method to evaluate the expression: (5+2)(4-5)
The FOIL method is a method of expanding two given brackets by following the required steps. Thus using the FOIL method, the required answer is: -7
Expansion of brackets may be done using different methods, but these methods would give the same answer. Some methods that can be used are the binomial expansion method, FOIL method, etc.
The FOIL method is a shortened form of the steps required for the process. These required steps are First, Outside, Inside, and last.
Thus to expand the given brackets in the question, we have;
(5+2)(4-5) = 5(4 - 5) + 2(4 - 5)
= 20 - 25 + 8 - 10
= 28 - 35
(5+2)(4-5) = -7
Thus using the FOIL method, the answer to the question is -7.
Quick check: (5+2)(4-5) = (7)(-1)
= -7
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A two digit number has 6 more ones than tens. Twice the sum of the number and its reverse is 6 more than ten times the number. Find the number.
The number with the given properties is 17
How to determine the numbers?Let the tens be x and the units be y.
So, the number is 10x + y
The relationship between the digits is
[tex]y = x + 6[/tex]
The relationship between the number and the reverse is
[tex]2(10x + y + 10y + x) = 6 + 10 * (10x + y)[/tex]
Simplify the second equation
[tex]2(11x + 11y) = 6 + 100x + 10y[/tex]
Open the brackets
[tex]22x + 22y = 6 + 100x + 10y[/tex]
Substitute y = x + 6
[tex]22x + 22(x + 6) = 6 + 100x + 10(x + 6)[/tex]
Expand
[tex]22x + 22x + 132 = 6 + 100x + 10x + 60[/tex]
Collect like terms
[tex]22x + 22x - 100x - 10x = 6 + 60 - 132[/tex]
Evaluate the like terms
[tex]-66x = -66[/tex]
Divide by -66
x = 1
Substitute x = 1 in y = x + 6
[tex]y = 1 + 6[/tex]
y = 7
Recall that the number is 10x + y
So, we have
Number = 10 * 1 + 7
Evaluate
Number = 17
Hence, the number is 17
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just need all answers to 19 asap please
Answer:
1&2)
GH = 28
FH = 56
XY = 7
XZ = 14
3-6) Acute, Obtuse, Acute, Right
7) Perimeter: 40 in. Area: 84 in^2
8) Perimeter: 42 m. Area: 84 m^2
9) Perimeter: 15.2 yd. Area: 14.44 yd^2
10) 1, 8, 27, 64, 125 These are the cubes of 1, 2, 3, 4, 5 so it's just the cube of the next number that was cubed before.
11) 128, 32, 8, 2, 1/2 Divide the previous number by 4.
12) 2, -6, 18, -54, 162 Multiply the previous number by -3
13-15) I'm sorry we didn't do those so I don't really know how that works sorry.
16) 3x - 14 = 34
3x = 48 Add 14 to each side (to isolate 3x)
x = 16 Divide by 3 both sides (to get x)
17) -4(x+3) = -28
x+3 = 7 divide by -4 on both sides (to get a step closer to solving for x and isolating x+3)
x = 4 subtract 3 from both sides (to get x (isolating x))
18) 43 - 9(x-7) = -x - 6
43 - 9x + 63 = -x - 6 distribute 9 to x and 7 (to expand)
106 - 9x = -x - 6 combine like terms (easier to deal with)
106 - 8x = -6 add x to both sides (so there's only x on one side)
112 - 8x = 0 add 6 to both sides (only one number left)
112 = 8x move -8x to the right side
x = 14 divide by 8 (to isolate x)
19) x = 29 degrees
20) x = 13 degrees
21) x = 9 degrees, y = 31 degrees
Step-by-step explanation:
4x = 5x-7
x = 7
GH = 5(7) - 7 = 35 - 7 = 28
FH = 4x + 5x - 7 = 4(7) + 28 = 28*2 = 56
3x - 5 = x + 3
x = 4
XY = 3(4) - 5 = 12 - 5 = 7
XZ = 7*2 = 14
Acute is < 90
Obtuse is > 90
Right is = 90
Straight is = 180
7) 2(6+14) = 2(20) = 40 in
6*14 = 84 in^2
8) 13+14+15 = 42 m
(12*14)/2 = 6*14 = 84 m^2
9) 3.8*4 = 15.2 yd
3.8^2 = 14.44 yd^2
19) 34 + 4x + 30 = 180
64 + 4x = 180
4x = 116
x = 29
20) 4x + 7x + 37 = 180
11x = 143
x = 13
21) 3y + 42 = 9x + 54
y + 14 = 3x + 18
y = 3x + 4
3y + 42 + 5x + 9x + 54 + 5x = 360
3y + 19x = 264
substitute y with 3x + 4
3(3x + 4) + 19x = 264
9x + 12 + 19x = 264
28x = 252
x = 9
so y = 3(9) + 4 = 27 + 4 = 31
Patrick is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. He uses the following formula to calculate voltage: voltage=(current) × (resistance) The circuit he tests had a current of 4+j2 amps and a resistance of 2-j3 ohms. What is the voltage of the current?
Based on the given current and the given resistance, the voltage of the current is 14 + j8
How to determine the voltage of the current?From the question, we have the following parameters
current of 4+j2 amps and a resistance of 2-j3 ohms.
This can be rewritten as:
Current (I) = 4+j2 amps
Resistance (R) = 2-j3 ohms.
The formula to calculate voltage is given as
Voltage=(current) × (resistance)
Rewrite as:
V = I * R
Substitute the known values in the above equation
V = (4 + j2) * (2 - j3)
Expand the brackets
V = 8 - j4 + j12 + 6
Collect the like ters
V = 8 + 6 - j4 + j12
Evaluate the like term
V = 14 + j8
Based on the given current and the given resistance, the voltage of the current is 14 + j8
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A group of people were asked which of three ice cream flavors they prefer. The results are shown in the table.
Ages Vanilla Strawberry Chocolate
20 years and younger 8 10 6
Over 20 years 8 6 12
What is the probability of a person being over 20 years old and preferring vanilla ice cream?
8%
13%
16%
26%
Answer: 8/50 = 16%
Step-by-step explanation:
Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below:
6E+10
Write the number shown on the calculator display in standard form.
The number shown on the calculator display can be written in standard form as 6 x 10¹⁰.
Product of 200,000 and 300,000The product of 200,000 and 300,000 is calculated as follows;
200,000 × 300,000 = 6E+10
What is standard form?Standard form is a mathematical way or a standard way of presenting numbers as a mathematical expression.
It presents numbers in the simplest form.
Product of 200,000 and 300,000 in standard form200,000 × 300,000 = 6 x 10¹⁰
Thus, the number shown on the calculator display can be written in standard form as 6 x 10¹⁰.
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Is TriangleMNL ≅ TriangleQNL? Why or why not?
Yes, they are congruent by either ASA or AAS.
Yes, they are both right triangles.
No, AngleM is not congruent to AngleNLQ.
No, there are no congruent sides.
Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
What are congruent triangles?A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angle triangle. Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other.
From triangle MNL and triangle QNL, in triangle MNL:
∠M + ∠N + ∠L = 180° (sum of angles in a triangle)
90 + 58 + ∠L = 180
∠L = 32°
Hence Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
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Rabbits are known for being extremely prolific—having a high reproductive rate. The average gestation period for rabbits is about 28 days and they have an unusual reproductive system that permits a female rabbit to be pregnant with two litters at once. This is an adaptation that allows rabbits to survive in the wild where they have a high mortality rate—they’re a source of food for many species of predators! In situations where there are no natural predators, two adult rabbits could easily become 1000 in one year’s time. i. Using this information, construct an exponential model to predict the number of rabbits after “x” years if there are no natural predators. ii. If the rabbit population were left unchecked (no predators and an abundance of food), how many rabbits would there be at the end of 3 years?
(i) The exponential growth model to predict the number of rabbits after 'x' years is [tex]A = 2e^{6.21460809842x}[/tex].
(ii) The number of rabbits at the end of 3 years will be 250000000.
A continuous exponential growth function is of the form [tex]A = Pe^{rt}[/tex], where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.
In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.
We assume the exponential growth model to be a continuous model, of the form [tex]A = Pe^{rt}[/tex], where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.
The initial quantity of rabbits, P = 2.
Time, t = x years.
Substituting the values, we get:
[tex]A = 2e^{rx}[/tex] ... (i)
We have been told that after 1 year, the number of rabbits was 1000.
Thus, substituting A = 1000, and x = 1, we get:
[tex]1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500[/tex]
Taking log on both sides, we get:
[tex]log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842[/tex]
Thus, the rate of growth, r = 6.21460809842.
Substituting r = 6.21460809842 in (i), we get:
[tex]A = 2e^{6.21460809842x}[/tex], which is the required model.
To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:
[tex]A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000[/tex]
Thus, there would be 250000000 rabbits at the end of 3 years.
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Find the midpoint of the segment with the following endpoints.
(10, 3) and (2, 9)
Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 18 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 150 and 156 miles in a day. Round your answer to four decimal places.
The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.
How to calculate the probability distribution?The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,
Z = (X - μ)/σ
Where X - random variable; μ - mean; σ - standard deviation;
Then the probability is calculated by P(Z < x), using the values from the distribution table.
Calculation:The given data has the mean μ = 120 and the standard deviation σ = 18
Z- score for X =150:
Z = (150 - 120)/18
= 1.67
Z - score for X = 156:
Z = (156 - 120)/18
= 2
So, the probability distribution over these scores is
P(150 < X < 156) = P(1.67 < Z < 2)
⇒ P(Z < 2) - P(Z < 1.67)
From the standard distribution table,
P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254
On substituting,
P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471
Rounding off to four decimal places,
P(150 < X < 156) = 0.0247
Thus, the required probability is 0.0247.
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