The distance that Anthony will ride down Pine Avenue would be D.) 24 miles .
How to find the distance ?Anthony's route distance along Pine Avenue can be calculated using the Pythagorean Theorem. This theorem confirms that in a right triangle, when one angle is 90 degrees, the sum of squares of the lengths of the two non-hypotenuse sides equals the square of length of the hypotenuse or the longest side.
Hypothenuse ² = Forrest Lane ² + Pine Avenue ²
26 ² = 10 ² + x ²
676 = 100 + x ²
x ² = 576
x = 24
In conclusion, Anthony will ride down Pine Avenue for 24 miles.
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Full question is:
Anthony was mapping out a route to ride his bike. The route he picked forms a right triangle, as shown in the picture below. If the route takes him 10 miles on Forrest Lane and 26 miles up Cedar Drive, how far will Anthony ride down Pine Avenue?
A.) 16 miles
B.) 36 miles
C.) 30 miles
D.) 24 miles
A town’s population doubles in 23 years. Its percentage growth rate is approximately *
23% per year.
70/23 per year
23/70 per year
The answer is that the town's percentage growth rate is approximately 3% per year.
What is the approximate percentage growth rate per year of a town whose population doubles in 23 years?To find the town's percentage growth rate, we can use the formula:
growth rate = (final population - initial population) / initial population * 100%
Let P be the initial population of the town, and let t be the time it takes for the population to double, which is 23 years in this case. We know that:
final population = 2P (since the population doubles)
t = 23 years
Substituting these values into the formula, we get:
growth rate = (2P - P) / P * 100% / 23
= P / P * 100% / 23
= 100% / 23
≈ 4.35%
However, this is the annual growth rate that would result in a doubling of the population in exactly 23 years. Since the question asks for the approximate percentage growth rate per year.
We need to find the equivalent annual growth rate that would result in a doubling time of approximately 23 years.
One way to do this is to use the rule of 70, which states that the doubling time (t) of a quantity growing at a constant percentage rate (r) is approximately equal to 70 divided by the growth rate:
t ≈ 70 / r
In this case, we want t to be approximately 23 years, so we can solve for r:
23 ≈ 70 / r
r ≈ 70 / 23
r ≈ 3.04%
Therefore, the town's percentage growth rate is approximately 3% per year.
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in 2018, coolville, california had a population of 72,000 people. in 2020, the population had dropped to
70,379. city officials expect the population to eventually level off at 60,000.
a. what kind of function would best model the population over time? how do you know?
b. write an equation that models the changing populaion over time.
a. The function that would best model the population over time is Exponential decay
b. write an equation that models the changing population over time P(t) = [tex]72,000 * e^(-0.035t)[/tex]
a. Exponential rot (Exponential decay) work would best demonstrate the populace over time.
Usually, the populace has diminished from 72,000 to 70,379 in fair 2 years, which could be a generally brief time period. Also, city authorities anticipate the populace to level off at 60,000, which is a sign of exponential rot.
b. The exponential rot work can be composed as:
P(t) = P0 *[tex]e^(-kt)[/tex]
Where P(t) is the populace at time t, P0 is the starting populace, e is the scientific steady around rise to 2.718, and k is the rot consistent.
Utilizing the given data, able to substitute the values:
P(0) = 72,000 (populace in 2018)
P(2) = 70,379 (populace in 2020)
To illuminate for k, able to utilize the equation:
k = ln(P0/P(t))/t
k = ln(72,000/70,379)/2
k ≈ 0.035
Subsequently, the condition that models the changing populace over time is:
P(t) = [tex]72,000 * e^(-0.035t)[/tex]
where t is the time in a long time since 2018.
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Antawn Jamison lanza tiros libres. Anotar o fallar los tiros libres no cambia la probabilidad de que anote en el siguiente tiro, y él anota 73\%73%73, percent de sus tiros libres. ¿Cuál es la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres?
la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
La probabilidad de que anote un tiro libre es del 73%, lo que significa que la probabilidad de que falle es del 27%.
La probabilidad de que anote sus próximos 9 tiros libres es:
0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 = 0.0733
Por lo tanto, la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.
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Un termómetro con resistencia de platino de ciertas especificaciones
opera de acuerdo con la ecuación R = 10000 + (4124 x 10-2) T – (1779 x 10-5) T2
Donde R es la resistencia (en ohms) a la temperatura T (grados Celsius).
Si R = 13946, determine el valor correspondiente de T. Redondee al grado
Celsius más cercano. Suponga que tal termómetro sólo se utiliza si T ≤
600° C
The value of T is 428°C.
How to calculate temperature from resistance?To solve the problem, we can start by substituting the given value of R = 13946 into the equation R = 10000 + (4124 x 10^-2)T – (1779 x 10^-5)T^2 and solving for T. This gives us a quadratic equation in T which can be solved using the quadratic formula.
After simplifying, we get T = 427.67°C or T = -88.22°C. However, we know that the thermometer is only used if T ≤ 600°C, so the only valid solution is T = 427.67°C.Therefore, the temperature corresponding to a resistance of 13946 ohms is approximately 428°C.
It's important to note that this assumes the thermometer is operating within its specified range and that the resistance-temperature relationship remains linear over the given temperature range.
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FILL IN THE BLANK. Determine the direction in which f has maximum rate of increase from P. f(x,y,z) x²y√ z, P= (-1,7,9) = (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) direction of maximum rate of increase:_______ Determine the rate of change in that direction. (Give an exact answer. Use symbolic notation and fractions where needed.) rate of change:_______
Direction of maximum rate of increase: (-14, 3, 7/3).
The rate of change in that direction:√(196 + 9 + 49/9).
To determine the direction in which f has a maximum rate of increase from point P(-1, 7, 9):
We need to find the gradient of the function f(x, y, z) = x²y√z.
The gradient is given by the vector of partial derivatives with respect to x, y, and z:
∇f = (df/dx, df/dy, df/dz)
First, find the partial derivatives:
df/dx = 2xy√z
df/dy = x²√z
df/dz = (1/2)x²y*z^(-1/2)
Now, evaluate the gradient at point P(-1, 7, 9):
∇f(P) = (2(-1)(7)√9, (-1)²√9, (1/2)(-1)²(7)*(9^(-1/2)))
∇f(P) = (-14, 3, 7/3)
The direction of maximum rate of increase is given by the gradient at point P, which is (-14, 3, 7/3).
To determine the rate of change in that direction:
The rate of change is given by the magnitude of the gradient vector:
Rate of change = ||∇f(P)|| = √((-14)^2 + (3)^2 + (7/3)^2)
Rate of change = √(196 + 9 + 49/9)
The rate of change is the square root of this value, which is an exact representation of the rate of change in the direction of maximum increase.
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HELP PLS
Interpret the following sine regression model.
y= 0. 884 sin(0. 245x - 1. 093) + 0. 400
What is the value of c in this equation?
a. 0. 400
b. 1. 093
c. 0. 245
d. 0. 884
The value of c in equation y= 0. 884 sin(0. 245x - 1. 093) + 0. 400 is c. 0. 245.
The given equation represents a sine regression model, where y is the dependent variable and x is the independent variable. The equation includes a sine function with a frequency of 0.245 and an amplitude of 0.884. The constant term, 0.400, represents the vertical shift or the y-intercept of the graph. The phase shift, 1.093, determines the horizontal shift of the graph.
To find the value of c, we need to look at the coefficient of x in the sine function. In this case, the coefficient of x is 0.245, which represents the frequency or the number of complete cycles that occur in a given interval. Therefore, the answer is (c) 0.245.
It's important to note that the coefficient of x in a sine regression model represents the frequency and not the phase shift or the horizontal shift. The phase shift is determined by the constant term in the sine function.
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Rectangle ABCD is graphed in the coordinate plane. The following are
the vertices of the rectangle: A(-6,-4), B(-4,-4), C(-4,-2), and
D(-6, -2).
What is the perimeter of rectangle ABCD?
units
Stuck? Review related articles/videos or use a hint.
Report a problem
Answer:
The perimeter of rectangle ABCD can be calculated by adding up the lengths of its sides. Using the distance formula, we can find that AB has a length of 2 units, BC has a length of 2 units, CD has a length of 2 units, and AD has a length of 4 units. Therefore, the perimeter of rectangle ABCD is 10 units.
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28 is the geometric mean of 13 and another number. Find the number and round your answer to the nearest hundredth
To find the number when 28 is the geometric mean of 13 and that number, we'll use the formula for the geometric mean: √(a * b) = GM, where a and b are the two numbers, and GM is the geometric mean. In this case, a = 13, GM = 28.
Step 1: Substitute the given values into the formula:
√(13 * b) = 28
Step 2: Square both sides to get rid of the square root:
(√(13 * b))^2 = 28^2
13 * b = 784
Step 3: Divide both sides by 13 to isolate b:
b = 784 / 13
b ≈ 60.31
So, the other number is approximately 60.31 when rounded to the nearest hundredth. In summary, 28 is the geometric mean of 13 and 60.31, as √(13 * 60.31) ≈ 28.
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The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 42 meters. Find the length and width of the rectangle
the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters. So the dimensions of the rectangle are 10 meters by 11 meters.
what is rectangle ?
A rectangle is a geometric shape that has four straight sides and four right angles (90-degree angles) between them. The opposite sides of a rectangle are parallel and have the same length, so the shape is symmetrical along its horizontal and vertical axes.
In the given question,
Let's assume that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is x + 1 meters, since the length and width are consecutive integers.
The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 42 meters, so we can write:
2(length + width) = 42
Substituting the expressions for the length and width in terms of x, we get:
2(x + x + 1) = 42
Simplifying this equation, we get:
4x + 2 = 42
Subtracting 2 from both sides, we get:
4x = 40
Dividing both sides by 4, we get:
x = 10
Therefore, the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters.
So the dimensions of the rectangle are 10 meters by 11 meters.
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A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
Part A: Dillon and Chelsey are discussing how to write the equation of a tangent line
to circle A through point B. Both agree that they start the problem by drawing the
radius AB and find the slope of that segment. They also know that a tangent line is
perpendicular to the radius.
The area of the shaded region is (9/500)π.
To find the area shaded below in circle K, we first need to find the radius of the circle.
Let O be the center of the circle, and let N be the midpoint of segment LM. We can draw a radius ON to segment LM such that it is perpendicular to LM, and then draw another radius OL to point L. This forms a right triangle LON with the hypotenuse equal to the radius of circle K.
Since segment LM is given to have a length of 11/9π, we can find the length of LN by dividing it in half:
LN = (11/9π)/2 = 11/18π
We can then use trigonometry to find the length of OL:
sin(55°) = OL / LN
OL = LN sin(55°)
OL = (11/18π) sin(55°)
Next, we can use the Pythagorean theorem to find the length of ON:
ON² = OL² + LN²
ON² = [(11/18π) sin(55°)]² + [11/18π]²
ON ≈ 1.022
Therefore, the radius of circle K is approximately 1.022.
The area of the shaded region can now be found by subtracting the area of sector LOM from the area of triangle LON:
Area of sector LOM = (110/360)π(1.022)² ≈ 0.317π
Area of triangle LON = (1/2)(11/18π)(1.022) ≈ 0.326π
Area of shaded region = (0.326π) - (0.317π) = (9/500)π
So the area of the shaded region is (9/500)π.
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The greenery landscaping company puts in an order for 2 pine trees and 5 hydrangea bushes for a neighborhood project. the order costs $150. they put in a second order for 3 pine trees and 4 hydrangea bushes that cost $144. 50.
what is the cost for one pine tree?
$: ?
The cost of one pine tree is $17.50.
To find the cost of one pine tree, we can use the information provided about the orders from the Greenery Landscaping Company. We have the following two equations:
1) 2P + 5H = $150 (2 pine trees and 5 hydrangea bushes)
2) 3P + 4H = $144.50 (3 pine trees and 4 hydrangea bushes)
Now, let's solve these equations using the substitution or elimination method. Here, we'll use the elimination method.
Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of H the same:
1) 6P + 15H = $450
2) 6P + 8H = $289
Step 2: Subtract the second equation from the first equation:
(6P + 15H) - (6P + 8H) = $450 - $289
0P + 7H = $161
Step 3: Divide by 7 to find the cost of one hydrangea bush (H):
H = $161 / 7
H = $23
Step 4: Substitute the value of H back into one of the original equations to find the cost of one pine tree (P). We'll use the first equation:
2P + 5($23) = $150
2P + $115 = $150
Step 5: Subtract $115 from both sides of the equation:
2P = $35
Step 6: Divide by 2 to find the cost of one pine tree (P):
P = $35 / 2
P = $17.50
So, the cost of one pine tree is $17.50.
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Solve the equation. ㏒₃(1/9)=2x-1
Enter your answer in the box. Enter a fractional answer as a simplified fraction.
The solution to the given equation which is log₃(1/9) = 2x - 1 is equal to x = -1/2.
To solve the equation log₃(1/9) = 2x - 1, we need to isolate the variable x on one side of the equation. We can start by using the logarithm property that states that the logarithm of a number to a base is equal to the exponent to which the base must be raised to obtain that number. In other words, log₃(1/9) = x if and only if [tex]3^x[/tex] = 1/9.
So, let's rewrite the given equation using this property as follows:
[tex]3^{(log(1/9))[/tex] = [tex]3^{2x-1[/tex]
Simplifying the left-hand side using the logarithm property, we get:
1/9 = [tex]3^{(2x - 1)[/tex]
Now, we can solve for x by taking the logarithm of both sides to base 3:
log₃(1/9) = log₃([tex]3^{(2x - 1)[/tex])
-2 = (2x - 1) * log₃(3)
-2 = 2x - 1
2x = -1
x = -1/2
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Kirk pays an annual premium of $1,075 for automobile insurance, including comprehensive coverage of up to $500,000. He pays this premium for 8 years without needing to file a single claim. Then he gets into an accident during bad weather, for which no one is at fault. Kirk is not injured, but his car valued at $22,500 is totaled. His insurance company pays the claim and Kirk replaces his car. If he did not have automobile insurance, how much more would have Kirk paid for damages than what he had invested in his insurance policy?
$8,600
$13,900
$21,425
$31,100
Kirk would have paid $13,900 more for damages than what he had invested in his insurance policy if he did not have automobile insurance.
The amount that Kirk would have paid for damages than what he had invested in his insurance policy if he did not have automobile insurance can be determine as follows. Hence,
1. Calculate the total amount Kirk paid in insurance premiums over 8 years:
$1,075 * 8 = $8,600
2. Determine the total value of the car that was totaled:
$22,500
3. Subtract the total amount Kirk paid in insurance premiums from the value of the totaled car:
$22,500 - $8,600 = $13,900
Kirk would have paid $13,900 more for damages.
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Solve system of equations by the substitution method.
Chris has $3.85 in dimes and quarters. There are 25 coins in all. How many of each type of coin does he have?
Solving a system of equations we can see that he has 9 quarters and 16 dimes.
How to solve the system of equations?Let's define the variables:
x = number of dimes
y = number of quarters.
There are 25 coins, so:
x + y = 25
The value is $3.85, so:
x*0.10 + y*0.25 = 3.85
So the system of equations is:
x + y = 25
x*0.10 + y*0.25 = 3.85
We can isolate x on the first equation to get:
x = 25 - y
Replacing that in the other one we get:
(25 -y)*0.10 + y*0.25 = 3.85
2.5 + y*0.15 = 3.85
y = (3.85 - 2.5)/0.15
y = 9
Then the other 16 coins are dimes.
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What’s the answer I need help pls?
Answer:
(E). y = 2cos(3x)
Step-by-step explanation:
First, amplitude of cos(x) is 1 , then 2cos(x) has amplitude 2
Second, period of cos(x) is 2[tex]\pi[/tex] , then 3 × [tex]\frac{2\pi }{3}[/tex] = 2[tex]\pi[/tex]
So, the answer is y = 2cos(3x)
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2. The data in the table represent the training times (in seconds) for Adam and Miguel.
Adam 103 105 104 106 100 98 92 91 97 101
Miguel 88 86 89 93 105 85 92 96 97 94
(a) All of the training times of which person had the greatest spread? Explain how you know.
(b) The middle 50% of the training times of which person had the least spread? Explain how you know.
(c) What do the answers to Parts 2(a) and 2(b) tell you about Adam’s and Miguel’s training times?
(a) Miguel had the greatest spread in training times.
(b) Adam had the least spread in the middle 50% of training times.
(c) Miguel's training times had a greater range, indicating more variability, while Adam's training times were more consistent and tightly grouped.
(a) Who had the greatest spread?(b) Who had the least spread?(c) how do the answers indicate?(a) To determine which person had the greatest spread, we need to compare the range or variability of their training times. By observing the given data, we can see that Adam's training times range from 92 to 106, resulting in a spread of 14. On the other hand, Miguel's training times range from 85 to 105, resulting in a spread of 20. Therefore, Miguel had the greatest spread of training times.
(b) To determine which person had the least spread in the middle 50% of training times, we need to compare the interquartile range (IQR). By calculating the IQR, we find that Adam's IQR is 9 (from the 25th to the 75th percentile), whereas Miguel's IQR is 7. Since Adam's IQR is greater, it means Miguel had the least spread in the middle 50% of training times.
(c) The answers to parts (a) and (b) indicate that while Miguel had a greater spread of training times overall, Adam's training times had a greater spread in the middle 50%. This suggests that Adam's training times were more concentrated around the median, while Miguel's training times were more spread out.
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a) All of the training times of Adam had the greatest spread.
(b) The middle 50% of the training times of Adam had the least spread.
(c) The answers to Parts (a) and (b) tell us that Adam's training performance may be more stable within that middle 50%, while Miguel's performance is more variable.
(a) Adam's training times had the greatest spread.
To determine this, we can calculate the range of the data sets. For Adam, the range is 106-92 = 14 seconds, while for Miguel, the range is 105-85 = 20 seconds. However, a better measure of spread is the interquartile range (IQR), which focuses on the middle 50% of the data. For Adam, the IQR is 101-97 = 4 seconds, while for Miguel, the IQR is 96-89 = 7 seconds. In both cases, Miguel's data has a greater spread.
(b) Adam's training times had the least spread for the middle 50% of the data. This is demonstrated by the IQR, as mentioned above. For Adam, the IQR is 4 seconds, while for Miguel, it is 7 seconds.
(c) The answers to Parts 2(a) and 2(b) tell us that while Miguel's overall training times have a greater spread, the middle 50% of Adam's training times are more consistent, with less variation. This suggests that Adam's training performance may be more stable within that middle 50%, while Miguel's performance is more variable.
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Find the critical point(s) of the function
f(x)=x3+x −3+2
. (Give your answer in the form of a comma-separated list of values. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no critical points.) critical point(s): Determine the
x
-coordinates of the critical point(s) that correspond(s) to a local minimum or a local maximum. (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no local minimum or local maximum.)
The critical point(s) of the function f(x) = x^3 + x - 3 + 2 are determined to find the x-coordinate(s) of the local minimum or local maximum.
To find the critical point(s) of the given function, we need to first find the derivative of the function and then solve for the value(s) of x that make the derivative equal to zero.
Given function: f(x) = x^3 + x - 3 + 2
Find the derivative of the function f(x) with respect to x.
f'(x) = 3x^2 + 1
Set the derivative f'(x) equal to zero and solve for x.
3x^2 + 1 = 0
Subtract 1 from both sides of the equation.
3x^2 = -1
Divide both sides of the equation by 3.
x^2 = -1/3
Take the square root of both sides of the equation.
x = ±√(-1/3)
Since the square root of a negative number is not a real number, the function f(x) does not have any real critical points. Therefore, the critical point(s) for the function f(x) = x^3 + x - 3 + 2 is DNE (Does Not Exist) in terms of real numbers.
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Cîte numere de trei cifre se pot alcătui din cifrele 1, 2, 3, 4 încît:1) cifrele să nu se repete;2) cifrele să se repete.
There are 24 three-digit numbers without repeating digits, and 64 three-digit numbers with repeating digits.
How many three-digit numbers can be formed?1) Pentru a alcătui numere de trei cifre în care cifrele să nu se repete, putem utiliza principiul combinatoric al permutărilor. Având la dispoziție cifrele 1, 2, 3 și 4, vom avea 4 posibilități pentru a alege prima cifră, 3 posibilități pentru a alege a doua cifră și 2 posibilități pentru a alege a treia cifră. Prin înmulțirea acestor numere, obținem:
4 * 3 * 2 = 24
Există deci 24 de numere de trei cifre în care cifrele nu se repetă, utilizând cifrele 1, 2, 3 și 4.
2) Pentru a alcătui numere de trei cifre în care cifrele se repetă, vom avea 4 posibilități pentru a alege oricare dintre cele trei cifre și anume 1, 2, 3 și 4. Prin urmare, avem:
4 * 4 * 4 = 64
Există 64 de numere de trei cifre în care cifrele se pot repeta, utilizând cifrele 1, 2, 3 și 4.
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How many solutions does the equation 4p 7 = 3 4 4p have? one two infinitely many none
Answer:
one
Step-by-step explanation:
The equation 4p + 7 = 3(4p) can be simplified by distributing the 3 on the right-hand side of the equation:
4p + 7 = 12p
Subtracting 4p from both sides of the equation, we get:
7 = 8p
Dividing both sides of the equation by 8, we get:
p = 7/8
Therefore, the equation has only one solution, which is p = 7/8. Answer: one.
Justice has a box of trading cards. There are three types of trading cards in the box, a basketball, a football, and a soccer ball. The probability of picking out a basketball card is 2/5, and the probability of picking out a football card is 1/3. What is the probability Justice will randomly pick out a soccer card?
If the probability of picking out a basketball card is 2/5, and the probability of picking out a football card is 1/3, the probability of Justice randomly picking out a soccer card is 4/15.
To find the probability of Justice picking out a soccer card, we need to know the total probability of all three types of cards adding up to 1. Since there are only three types of cards, we can subtract the probability of picking a basketball card and the probability of picking a football card from 1 to find the probability of picking a soccer card.
Let P(S) be the probability of picking a soccer card.
We know that P(B) = 2/5 and P(F) = 1/3.
Therefore, the total probability of picking one of the three cards is:
P(B) + P(F) + P(S) = 1
Substituting the values we know, we get:
2/5 + 1/3 + P(S) = 1
Simplifying the equation, we get:
6/15 + 5/15 + P(S) = 1
11/15 + P(S) = 1
P(S) = 1 - 11/15
P(S) = 4/15
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3.3 Dr Seroto travelled from his office directly to the school 45 km away. He travelled at an average speed of 100 km per hour and arrived at the school at 11:20. Verify, showing ALL calculations, whether Dr Seroto left his office at exactly 10:50. The following formula may be used: Distance = average speed x time
[tex]distance= average sped \times time[/tex]
Answer: We can use the formula Distance = Average speed x time to verify whether Dr Seroto left his office at exactly 10:50.
Let t be the time Dr Seroto left his office. Then, the time he arrived at the school can be expressed as:
t + (Distance/Average speed) = 11:20
We know that the distance is 45 km and the average speed is 100 km/hour. Substituting these values, we get:
t + (45/100) = 11:20
We need to convert the time on the right-hand side to hours. 11:20 can be written as:
11 + 20/60 = 11.33 hours
Substituting this value, we get:
t + 0.45 = 11.33
Solving for t, we get:
t = 11.33 - 0.45
t = 10.88 hours
This is not equal to 10:50, which is 10.83 hours. Therefore, Dr Seroto did not leave his office at exactly 10:50.
(8-6b)(5-3b)=
You have to find the product this is geometry
The product of (8-6b)(5-3b), using the distributive property of multiplication is [tex]18b^2 - 54b + 40[/tex].
This problem is actually an algebraic expression involving variables and constants. To find the product of (8-6b)(5-3b), we need to use the distributive property of multiplication.
We can start by multiplying 8 by 5, which gives us 40. Next, we multiply 8 by -3b, which gives us -24b. Then, we multiply -6b by 5, which gives us -30b. Finally, we multiply -6b by -3b, which gives us[tex]18b^2[/tex].
Putting all of these terms together, we get:
(8-6b)(5-3b) = [tex]40 - 24b - 30b + 18b^2[/tex]
Simplifying this expression, we can combine the like terms -24b and -30b to get -54b. So the final answer is:
(8-6b)(5-3b) = [tex]18b^2 - 54b + 40[/tex]
Therefore, the product of (8-6b)(5-3b) is [tex]18b^2 - 54b + 40[/tex].
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PLEASE HELP AND SHOW WORK!! 10 PTS IF U ANSWER
Answer:
Step-by-step explanation:
You're going to want to break up the shape into three parts, two triangles, and the rectangle.
Starting with the left-most triangle: A=(L*W)/2
The length is 4ft and the width is 3ft, multiply and divide by 2 to get: A=6 square feet.
Do the same with the second triangle on the bottom left (L=2ft, W=2ft) to get A=2 square feet.
Now the rectangle, A=L*W and total length is 10ft (8ft+2ft) and the width is 3ft. Multiply these values to get A=30 square feet.
Last step: add up all three areas for the total area of the entire shape, 6+2+30=38.
Area= 38 square feet.
Jayden just accepted a job at a new company where he will make an annual
salary of $41000. Jayden was told that for each year he stays with the
company, he will be given a salary raise of $2500. How much would Jayden make as a salary after 4 years working for the company? What would be his salary after t years?
Jayden's starting salary is $41000 per year. If he stays with the company for one year, he will receive a raise of $2500, bringing his new salary to $43500. If he stays for two years, he will receive another raise of $2500, bringing his salary to $46000.
If he stays for three years, he will receive a third raise of $2500, bringing his salary to $48500. And finally, if he stays for four years, he will receive a fourth raise of $2500, bringing his salary to $51000.
Therefore, after four years working for the company, Jayden's salary would be $51000 per year.
After t years, Jayden's salary would be calculated as follows:
- After one year: $41000 + $2500 = $43500
- After two years: $41000 + ($2500 x 2) = $46000
- After three years: $41000 + ($2500 x 3) = $48500
- After four years: $41000 + ($2500 x 4) = $51000
- After t years: $41000 + ($2500 x t).
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COMPARE BY USING <,>,=,<=,>=
The product of the middle two sums is greater than or equal to the product of the least and the greatest of the sums.
How can the two products be compared?To compare two products, we need to compare the values of the products using the comparison operators (<, >, <=, >=, or =).
We can start by finding the sums of the original numbers (0, 1, 2, 3):
Sum of the original numbers = 0 + 1 + 2 + 3 = 6
Now, we add the number k to each of the numbers:
Sum of the new numbers = (0 + k) + (1 + k) + (2 + k) + (3 + k)
= (0 + 1 + 2 + 3) + 4k
= 6 + 4k
So, the new sums range from 6 + 4k (the smallest) to 9 + 4k (the largest).
The product of the least and the greatest of the sums is:
(6 + 4k) × (9 + 4k) = 54 + 60k + 16k^2
The product of the middle two sums is:
(7 + 4k) × (8 + 4k) = 56 + 60k + 16k^2
Comparing the two products using the comparison operators:
54 + 60k + 16k^2 < 56 + 60k + 16k^2 (since 54 < 56)
or
54 + 60k + 16k^2 <= 56 + 60k + 16k^2 (since the products are equal when k=0)
In conclusion, the product of the middle two sums is greater than or equal to the product of the least and the greatest of the sums.
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We want to evaluate the integral X +34 +16 dx, we use the trigonometric substitution X and dx = do and therefore the integrar becomes, in terms or o, de The antiderivative in terms of 8 is (do not forget the absolute value) 1 = + Finally, when we substitute back to the variable x, the antiderivative becomes T Use for the constant of integration
The antiderivative of the given integral is (X^2/2) + 50X + C, where C is the constant of integration.
This is obtained by integrating the given polynomial directly without the need for trigonometric substitution.First, let's rewrite the integral: ∫(X + 34 + 16) dx. Since the integrand is a polynomial, we don't need trigonometric substitution. Instead, we can find the antiderivative directly:
∫(X + 34 + 16) dx = ∫(X + 50) dx.
Now, find the antiderivative:
(X^2/2) + 50X + C, where C is the constant of integration.
So, the antiderivative of ∫(X + 34 + 16) dx is (X^2/2) + 50X + C.
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If the probability of an event is 88/83 what is the probability of the event not happening? 88' Write your answer as a simplified fraction.
The probability of the event not happening is 5/83.
Here, probability refers to the likelihood of a given event occurring and that the inequality f(x) > 3g(x) holds for all x > 0.
If the probability of an event happening is 88/83, then the probability of the event not happening is 1 minus the probability of the event happening. This can be expressed as:
1 - 88/83
To simplify this expression, we can first find a common denominator for 1 and 88/83, which is 83/83:
83/83 - 88/83
-5/83
Therefore, the probability of the event not happening is 5/83.
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a scientist recorded the growth (g) of pine trees and the amount of rain fall (r) they received in their first year. which equation best fits the data
An equation that best fits the data is: C. g = -0.019r² + 0.797r + 1.94.
How to determine the line of best fit?In this scenario, the r (inches) would be plotted on the x-axis (x-coordinate) of the scatter plot while the G (inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the r (inches) and the G (inches), an equation for the line of best fit is given by:
g = -0.019r² + 0.797r + 1.94
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis.
Ilull = 5, Ou = 0°
I|v|I = 2, Ov = 60°
The component form of u + v can be found using the given lengths and angles and it is (6, √3).
To find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis we will sum the u and v.
Given Ilull = 5 and Ou = 0°, we can represent vector u as (5, 0) in component form. Given |Iv|I = 2 and Ov = 60°, we can represent vector v as (2cos60°, 2sin60°) = (1, √3) in component form.
To find u + v, we add the corresponding components of u and v. This gives us:
u + v = (5, 0) + (1, √3) = (5+1, 0+√3) = (6, √3)
Therefore, the component form of u + v is (6, √3).
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The average price, in dollars, of a gallon of orange juice r years after 1990 can be modeled by the
exponential function f(x) - 1. 07(103) +3. 79.
Use the exponential function to estimate the average price of a gallon of orange juice in 2020.
Round your answer to the nearest cent.
Using the exponential function to estimate the average price of a gallon of orange juice in 2020, the average price in 2020 is $6.39
To estimate the average price of a gallon of orange juice in 2020 using the given exponential function f(x) = 1.07(1.03^x) + 3.79, first, determine the number of years after 1990, which is r:
r = 2020 - 1990 = 30
Next, substitute r with 30 into the function:
f(30) = 1.07(1.03^30) + 3.79
Calculate the value of f(30):
f(30) ≈ 1.07(2.427) + 3.79 ≈ 2.599 + 3.79 ≈ 6.389
Round your answer to the nearest cent:
Average price in 2020 ≈ $6.39
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