Answer:
m = 25 + 6n
Step-by-step explanation:
To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.
100 people questioned, 37 say they eat fruits, 33 say they eat vegetables, 9 say they eat cheese and fruits, 12 eat cheese and vegetables, 10 eat fruits and vegetables, 12 eat only cheese, and 3 report they eat all three offerings. How many people surveyed eat cheese? How many do not eat any of the offerings?
Answer:
Done
Step-by-step explanation:
To solve the problem, we can use a Venn diagram to visualize the information provided in the question.
Let's draw three overlapping circles to represent the three groups of people: those who eat fruits, those who eat vegetables, and those who eat cheese.
We know that:
- 37 people eat fruits, so we write "37" in the circle representing fruits.
- 33 people eat vegetables, so we write "33" in the circle representing vegetables.
- 9 people eat both cheese and fruits, so we write "9" in the overlap between the cheese and fruits circles.
- 12 people eat both cheese and vegetables, so we write "12" in the overlap between the cheese and vegetables circles.
- 10 people eat both fruits and vegetables, so we write "10" in the overlap between the fruits and vegetables circles.
- 12 people eat only cheese, so we write "12" in the part of the cheese circle that does not overlap with the other circles.
- 3 people eat all three offerings, so we write "3" in the intersection of all three circles.
Here's what the Venn diagram looks like:
```
Cheese
+----9----+----3----+----12---+
| | Cheese | | |
| Fruits +----6----+--4 | |
| | | | |
+----10---+----3----+----8---+---+
| Vegetables |
+------------+
9 24 15
```
To find out how many people eat cheese, we add up the numbers in the cheese circle: 9 + 3 + 12 = 24. So, 24 people eat cheese.
To find out how many people do not eat any of the offerings, we need to add up the numbers in the regions that are not part of any circle: the region outside of all circles, and the region in the center of the Venn diagram. These regions add up to 9 + 15 = 24. So, 100 - 24 = 76 people do eat at least one of the offerings.
show the solution of the problem
The %RE value for the Improved Euler (Heun) method is zero, which means that the method is exact. The %RE value for the Explicit Euler's method is 0.14%, which means that the method is a good approximation.
How to use Explicit and Improved Euler's method?First rewrite the differential equation as follows:
[tex]\frac{dy}{dt } = (\frac{4}{t } - 6t^2)y[/tex]
Now integrate both sides of the equation:
[tex]\int\limits{\frac{dy}{dt}} \, = \int\limits\, (\frac{4}{t } - 6t^2)y dt[/tex]
This gives us:
[tex]y = 4ln(t) - 2t^3 + C[/tex]
where C = arbitrary constant.
Now, use the initial condition y(1) = 2 to find the value of C:
[tex]2 = 4ln(1) - 2(1)^3 + C[/tex]
This gives us C = 6.
Therefore, the solution of the initial-value problem is:
[tex]y = 4ln(t) - 2t^3 + 6[/tex]
Now, use the Explicit Euler's and Improved Euler (Heun) methods to compute y(1.3) numerically:
Explicit Euler's method:
First find the step size h:
h = (1.3 - 1) = 0.3
Now, use the Explicit Euler's method to compute y(1.3) as follows:
[tex]y(1.3) = y(1) + \frac{h}{2} * \frac{dy}{dt}[/tex]
[tex]y(1.3) = 2 + 0.3 * (4ln(1.3) - 2(1.3)^3 + 6)[/tex]
y(1.3) = 2.119
Improved Euler (Heun) method:
First find the step size h:
h = (1.3 - 1) = 0.3
Now, use the Improved Euler (Heun) method to compute y(1.3) as follows:
[tex]y(1.3) = y(1) + \frac{h}{2} * (\frac{dy}{dt} + \frac{dy}{dt'})[/tex]
where dy/dt' is the value of dy/dt evaluated at t = 1.3:
[tex]\frac{dy}{dt'} = 4ln(1.3) - 2(1.3)^3 + 6[/tex]
[tex]y(1.3) = 2 + \frac{0.3}{2} * (4ln(1.3) - 2(1.3)^3 + 6 + 4ln(1.3) - 2(1.3)^3 + 6)[/tex]
y(1.3) = 2.122
Now, calculate the %RE values for both methods:
Explicit Euler's method:
%RE = [tex]\frac{(y(1.3) - y_{true})}{y_{true}} * 100[/tex]
where y_true is the exact value of y(1.3) = 2.122:
%RE = (2.119 - 2.122)/2.122 × 100 = 0.14%
Improved Euler (Heun) method:
%RE = [tex]\frac{(y(1.3) - y_{true})}{y_{true}} * 100[/tex]
%RE = (2.122 - 2.122)/2.122 × 100 = 0%
The %RE value for the Improved Euler (Heun) method is zero, which means that the method is exact. The %RE value for the Explicit Euler's method is 0.14%, which means that the method is a good approximation.
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A recent concert sold $916 worth
of tickets. Students were charged
$1.25 and adults were charged
$2.25. If 560 people attended, how
many adults attended the concert?
How many students?
Answer:
250 students and 310 adults
Step-by-step explanation:
so if students are charged 1.25 and adults are charged 2.25 and 560 people attended if you divided from it should equal
If anyone can help me on this please
true or false if two squares have equal side length then they are congruent
A ) find the perimeter of the plot land
B) find the area of the plot land without the building and parking lot
The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units
Finding the perimeter of the plot landFrom the graph, the vertices of the land are
A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)
Calculate the distance between adjacent vertices
So, we have
AB = √[(0 - 25)² + (20 - 19)²] = 25.02
BC = √[(20 - 25)² + (2 - 19)²] = 17.72
DC = √[(20 - 5)² + (2 - 0)²] = 15.13
AD = √[(0 - 5)² + (20 - 0)²] = 20.62
The perimeter of the plot land is
P = 25.02 + 17.72 + 15.13 + 20.62
P = 78.49 units
Finding the area of the plot landThis is calculated as
Area = Plot land - Building - Parking lot
Using the vertices, we have
Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]
This gives
Area = 295 - 45 - 40
So, we have
Area = 210
Hence, the area is 210 square units
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Austin takes1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is
/
radians per second.
Austin's rate of motion is (1/70)π Radians per second.
To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:
ω = Δθ / Δt
Where:
ω = angular velocity (in radians per second)
Δθ = change in angular displacement (in radians)
Δt = change in time (in seconds)
We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:
s = (3/4) * 2πr
s = (3/2)πr
We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).
So, Δt = 105 seconds
Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:
Δθ = (3/4) * 2π
Δθ = (3/2)π
Therefore, Austin's rate of motion (ω) in radians per second is:
ω = Δθ / Δt
ω = [(3/2)π] / 105
ω = (3/210)π
ω = (1/70)π radians per second
So, Austin's rate of motion is (1/70)π radians per second.
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192 airplanes leave Abuja Airport each day. 5/8 of them are international flights, while others are domestic flights. Find the total number of domestic flights that leave the airport each day.
Find the area of the given shapes.
Area of a Triangle - Pre-Algebra
A
48 units2
B
24 units2
C
54 units2
D
30 units2
The area of the triangle given at the end of the answer is of:
B. 24 units².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
Considering the image presented for this problem, the dimensions for the triangle are given as follows:
b = 12, h = 4.
Hence the area is given as follows:
A = 0.5 x 4 x 12
A = 24 units².
This means that option B is the correct option in the context of this problem.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B)
Step-by-step explanation:
Geometric mean:
[tex]\sf 5 , a_2,a_3, a_4, a_5,1215[/tex]
[tex]\bf a_1 = first \ term = 5[/tex]
n = number of terms = 6
r = common ratio
[tex]\boxed{\bf a_n = a_1 * r^{n-1}}[/tex]
[tex]a^{6} = 5 *r^{6-1}\\\\1215 = 5*r^5\\\\ \dfrac{1215}{5}=r^5\\\\243=r^5\\\\3^5=r^5[/tex]
As powers are same, compare the bases,
r = 3
Each term is obtained by multiplying the previous term by the common ratio. r = 3
[tex]\sf a_2 = 5*3 = 15\\\\a_3= 15*3 = 45\\\\a_4 = 45 *3 =135\\\\ a_5 = 135*3 = 405[/tex]
how do u find the answer to this pls help
59P₂ = (Type a whole number.)
The value of permutation expression ₅₉P₂ is 3422.
What is permutation?A permutation is an arrangement of objects in a definite order.
To find the value of ₅₉P₂, we use the formula below
Formula:
Pₐ = (n!)/(n-r)!...................... Equation 1Where:
Pₐ = ₅₉P₂n = 59r = 2! = FactorialSubstitute these values into equation 1
₅₉P₂ = 59!/(59-2)! ₅₉P₂ = (59×58×57!)/(57!) ₅₉P₂ = 3422Learn more about about permutation here: https://brainly.com/question/29595163
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You have a rectangular fabric swatch with an area of 14 cm2 and a
perimeter of 18cm. Find the dimensions of the fabric.
Answer:
length = 7 width = 2
Step-by-step explanation:
for the perimeter 7+7+2+2 is 18 and the area is 7×2 is 14 so the length is 7 and width is 2
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)
Identify the surface area of the composite figure to the nearest tenth.
Answer:
D.
Step-by-step explanation:
6a² = surface area for cube
6(5)² = 150
2[tex]\pi[/tex](r)(h)+2[tex]\pi[/tex]r² = surface area cylinder
2[tex]\pi[/tex](2)(3)+2[tex]\pi[/tex](4) = 20pi
150 + 20pi = 212.8318531
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
a. bus
b. car
c. subway
d. train
Answer:
train is the mode of transportation that can be use
Guests are filling out RSVP cards for Maria's wedding. They must choose which type of entree they would prefer for dinner. The choices are chicken, beef, or vegetarian dinners. Abigail chooses an entree; on the other side of town, Zeke also chooses. Are these two events dependent or independent?
These two events are independent because the outcome of both doesn't affect each other.
What is an independent and dependent events?An independent event is the type of event that occurs when the outcome of one event does not affect the outcome of the second event it is compared with.
A dependent event is the type of event that it's outcome affects the outcome of the second event it is compared with.
That Abigail chose an entree in a town different from Zeke doesn't affect her ability to attend the wedding.
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The table shown below provides statistical data on the bowling scores for David and Elise.
Bowling Score Data
David
145
Interquartile Range 30
Mean
Elise
120
20
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
t
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
David's claim is correct because his mean score is greater than Elise's mean score.
David's claim is correct because the interquartile range for his scores is greater than the interquartile range
for Elise's scores.
David's claim is incorrect because his mean score is greater than Elise's mean score.
David's claim is incorrect because the interquartile range for his scores is greater than the interquartile
Answer:
Step-by-step explanation:
Let's set David's score to D, and Aaron's score to A. If so, we get the equation that satisfies the constraints:
D = 3*A-5, D + A = 215
Set D in terms of A:
D = 215 - A
Input it into the equation:
215 - A = 3*A - 5 -> add 5 and A to both sides to set numbers to the left and variables to the right
215 + 5 = 3* A + A ->
220 = 4A -> divide by 4
220/4 = A ->
55 = A -> substitute A into D + A = 215
D + 55 = 215 -> subtract 55 from both sides
D = 215 - 55 = 160
So, out final answer is:
D = 160, A = 55
I think of a number multiply by 3 add 4 and square the result
Select the correct answer from each drop-down menu.
C
A
B
D
In the figure, the radius of the partial circle with center A is 4 feet.
The perimeter of the figure is
feet, and the area of the figure is
Assume = 3.14, and round your answers to the nearest hundredth.
square feet.
The perimeter of the figure is 24.50 feet feet, and the area of the figure is 45.68 square feet
Calculating the perimeter and the area of the partial circleFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 4 feet (see attachment)
The perimeter of the figure is
Perimeter = Circumference of 3/4 circle + Perimeter of triangle - 2r
So, we have
Perimeter = 3/4 * 2 * 3.14 * 4 + 4 + 4 + 4√2 - 2 * 4
Evalate
Perimeter = 24.50 feet
The area of the figure is:
Area = Area of 3/4 circle + Area of triangle
So, we have
Area = 3/4 * 3.14 * 4² + 1/2 * 4 * 4
Evaluate
Area = 45.68
Hence, the area is 45.68 square feet
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17. Find the circumference given KL= 4.6 in. Round to the nearest tenth.
The circumference of the circle 48.4 inches.
How to find the circumference of a circle?The circumference of a circle is the perimeter of the circle. Therefore, let's find the circumference of the circle as follows:
length of arc = ∅ / 360 × 2πr
where
∅ = central angler = radiusTherefore, let's find the radius
length of arc = 35 / 360 × 2 × 3.14 × r
4.6 = 219.8 / 360 r
4.6 = 0.61055555555 r
divide both sides by 0.61
r = 4.6 / 0.6
r = 7.7 inches
Therefore,
circumference = 2 × 3.14 × 7.7
circumference = 48.356
circumference = 48.4 inches
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The width of a rectangle is 15 feet more than the length. The perimeter is 290 feet. Find the length and width.
Answer:
The length = 65 The width = 80
Step-by-step explanation:
w = 15^2 = 290
225 =290
290-225 =80
w=80
80 - 15 = 65
l = 65
65+65+80+80=290
Answer:
Length: 65
Width: 80
Step-by-step explanation:
Lets turn it into an algebraic expression. x is the length.
length width
x x+15
2x + 2(x+15) = 290
2x +2x +30 =290
4x = 260
x = 65
65+15 = 80
Find the range, variance, and standard deviation for the given sample data.
Merriam-Webster’s Collegiate Dictionary, 11th edition, has 1459 pages of defined words. Listed below are the numbers of defined words per page for a simple random sample of those pages. If we use this sample as a basis for estimating the total number of defined words in the dictionary, how does the variation of these numbers affect our confidence in the accuracy of the estimate?
51 63 36 43 34 62 73 39 53 79
After considering all the given data we conclude that the range is 45, the variance is 422.21, the standard deviation is 20.55
To evaluate the range of the given sample data, we subtract the smallest value from the largest value. For the given case, the largest value is 79 and the smallest value is 34. Therefore, the range is 79 - 34 = 45.
To evaluate the variance of the given sample data, we first need to find the mean. The mean is evaluated by adding up all of the values and dividing by the number of values. Including the given case, we have 10 values, so we add them up and divide by 10:
(51 + 63 + 36 + 43 + 34 + 62 + 73 + 39 + 53 + 79) / 10
= 51.3
Finally , we have to apply subtraction the mean from each value and square the result. Then we add up all of these squared differences and apply division by n-1 (here n is the number of values). This gives us the variance:
((51 - 51.3)² + (63 - 51.3)² + (36 - 51.3)² + (43 - 51.3)² + (34 - 51.3)² + (62 - 51.3)² + (73 - 51.3)² + (39 - 51.3)² + (53 - 51.3)² + (79 - 51.3)²) / (10-1) = 422.21
Lastly, to evaluate the standard deviation, we take the square root of the variance:
√(422.21) = 20.55
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Overnight, a pipe cracked and started to leak into a basement. The graph shows the depth of the water in relation to time.
The water rises 10 inches each hour. The water is 4 inches deep is the water after four hours. It will take 8 hours for the water to reach a depth of 80 inches.
A pipe cracked overnight and started to leak into a basement.
The graph represents the depth (d) of the water over time (t).
As per the given graph, the required solution would be as:
Take two points (1, 10) and (5, 50) in the given graph
The linear function will be :
d - 10 = (50-10)/(5-1)(t - 1)
d - 10 = (40/4)(t - 1)
d = 10(t - 1) + 10
d = 10t - 10 + 10
d = 10t
Here slope of the given function is 10, which means 10 inches the water rise each hour.
The value of time (t) = 4 hr corresponds to the depth of water (d) is
d = 10(4) = 40
So, the water is 40 inches deep is the water after four hours
The value of depth of water (d) = 80 in corresponds to the time (t) is
80 = 10t
t = 80/10 = 8
So, It will take 8 hours for the water to reach a depth of 80 inches
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please help with question 2(iii)
The value of c for same sign of roots are,
⇒ c > 0
Given that;
Quadratic equation is,
⇒ x² - 2x + c = 0
Since, We know that;
For the roots of ax²+bx+c=0 to have same signs,
a(x2+b/ax+c/a), the last term, i.e. c/a>0, because if you factorize the quadratic, to arrive at positive constant you either have to have two negative numbers multiplied or two positive multiplied by each other.
Here,
Quadratic equation is,
⇒ x² - 2x + c = 0
Hence, The condition for same sign of roots are,
⇒ c > 0
Thus, The value of c for same sign of roots are,
⇒ c > 0
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Answer:
2. (i) p = 4
(ii) p < -4
(iii) 0 < c ≤ 1
Step-by-step explanation:
To find the value(s) of p for which x² - 2x - 3 = p will have the equal or real roots, we can use the discriminant formula.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root (equal roots).\\when $b^2-4ac < 0 \implies$ no real roots (two complex roots).\\\end{minipage}}[/tex]
Part (i)Rearrange the given equation so that it is in the form ax² + bx + c = 0:
[tex]x^2-2x-3-p=0[/tex]
Therefore, the values of a, b and c are:
a = 1b = -2c = (-3 - p)To find the value of p for which the given quadratic has equal roots, substitute the values of a, b and c into the discriminant formula, set it equal to zero, and solve for p:
[tex]\begin{aligned}b^2-4ac&=0\\(-2)^2-4(1)(-3-p)&=0\\4-4(-3-p)&=0\\4+12+4p&=0\\16+4p&=0\\4p&=-16\\p&=-4\end{aligned}[/tex]
Therefore, the value of p for which the given quadratic will have equal roots is p = -4.
Part (ii)Rearrange the given equation so that it is in the form ax² + bx + c = 0:
[tex]x^2-2x-3-p=0[/tex]
Therefore, the values of a, b and c are:
a = 1b = -2c = (-3 - p)To find the values of p for which the given quadratic has no real roots, substitute the values of a, b and c into the discriminant formula, set it to less than zero, and solve for p:
[tex]\begin{aligned}b^2-4ac& < 0\\(-2)^2-4(1)(-3-p)& < 0\\4-4(-3-p)& < 0\\4+12+4p& < 0\\16+4p& < 0\\4p& < - 16\\p& < -4\end{aligned}[/tex]
Therefore, the value of p for which the given quadratic will no real roots is p < -4.
Part (iii)For the roots of x² - 2x + c = 0 to have the same sign, both roots either have to be less that 0 or more than 0.
From part (i), we know that x² - 2x - 3 - p = 0 has equal roots when p = -4.
Substitute p = -4 into the equation:
[tex]\begin{aligned}x^2 - 2x - 3 - p &= 0\\x^2-2x-3-(-4)&=0\\x^2-2x-3+4&=0\\x^2-2x+1&=0\end{aligned}[/tex]
Comparing this to x² - 2x + c = 0, we can see that x² - 2x + c = 0 has equal roots when c = 1.
The leading coefficient of x² - 2x + c = 0 is positive, so the parabola opens upwards. We know it has equal roots when c = 1, so the vertex touches the x-axis when c = 1. Therefore, it has no real roots when c > 1 (since the vertex will be above the x-axis in this interval).
Therefore, we can determine that x² - 2x + c = 0 has two real roots when c ≤ 1.
When c = 0, the equation of the parabola is y = x² - 2x.
The roots are the points at which the curve crosses the x-axis (when y = 0). As y = 0 when x = 0, one of the roots is (0, 0) when c = 0.
Therefore, when c < 0, one root will be negative and the other will be positive.
Note there is no value of c where both roots are negative, as the x-value of the vertex is positive.
So the values of c for which the roots of x² - 2x + c = 0 will have the same sign (positive) are 0 < c ≤ 1.
What is the probability that both events occur?
Answer:
0.17
Step-by-step explanation:
Probability for Event A: 1/3
Probability for Event B: 1/2
Total Probability: 1/6
C) John, a meteorologist, recorded the temperatures from Monday to Frida and the mean temperature of five days was 40°F. The temperatures recorded on four consecutive days were 40°F, 39°F, 44°F, and 40°F. What temperature was recorded on the fifth day?
Average is the total sum of the given values divided by the number of values.
The average low temperature for the week is -3°F.
We have,
It is the total sum of the given values divided by the number of values.
We have,
Temperatures for one week:
Day Temperature
Sunday −5 °F
Monday −8 °F
Tuesday −6°F
Wednesday −8°F
Thursday −3 °F
Friday 2° F
Saturday 7° F
The average of the low temperature:
= [ -5 + (-8) + (-6) + (-8) + (-3) + 2 + 7 ] / 7
= (-5 - 8 - 6 - 8 - 3 + 2 + 7) / 7
= -30 + 9 / 7
= -21 / 7
= -3
Thus,
The average low temperature for the week is -3°F.
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complete question:
Christopher recorded the low temperature each day for 1 week and recorded his results in this table.
Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Low −5 °F −8 °F −6 °F −8°F −3 °F 2° F 7° F
What is the average low temperature for the week?
Find the surface area of the triangular prism.
3,360 m2
1,662 m2
6,720 m2
1,872 m2
The total surface area of the triangular prism is is 1872 square meters
Finding the surface area of the triangular prismFrom the question, we have the following parameters that can be used in our computation:
The triangular prism
The surface area of the triangular prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the of the triangular prism
Using the above as a guide, we have the following:
Area = 1/2 * 12 * 16 * 2 + 35 * (20 + 16 + 12)
Evaluate
Area = 1872
Hence, the surface area is 1872 square meters
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I NEED HELP STATISTICS
The 10th percentile is 164 milliseconds, and the 75th percentile is 261 milliseconds.
To find the percentiles for the given data, we first need to arrange the data in ascending order:
152, 164, 175, 193, 212, 217, 222, 235, 250, 257, 261, 273, 296, 311
There are 15 data points, so the 10th percentile can be calculated as follows:
10th percentile = (10/100) * (15 - 1) + 1 = 1.4
The 10th percentile corresponds to the 2nd data point in the ordered list:
10th percentile = 164
Similarly, the 75th percentile can be calculated as follows:
75th percentile = (75/100) * (15 - 1) + 1 = 11.4
The 75th percentile corresponds to the 11th data point in the ordered list:
75th percentile = 261
Therefore, the 10th percentile is 164 milliseconds, and the 75th percentile is 261 milliseconds.
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The sum of my digits is 14. their difference is 4. I am less than 60. What number am I?
Hi can you help me? thanks!
Juanita is an accident reconstruction expert. She measured a 70-foot chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured 9 feet in length. The drag factor of the road surface was determined to be 1.13. What is the minimum speed that the car was traveling when the skid occurred? Record your answer to the nearest tenth.
The minimum speed at which the car was traveling is 52.9 miles per hour.
To find the minimum speed at which the car was traveling during the skid, we can use the formula for calculating skid speed:
Skid speed = (Chord length x Chord length x Drag factor) / (2 x Middle ordinate)
Plugging in the given values:
Chord length = 70 feet
Middle ordinate = 9 feet
Drag factor = 1.13
Skid speed = (70 x 70 x 1.13) / (2 x 9)
Skid speed = 1391 / 18
Skid speed ≈ 77.3 feet per second
To convert the speed to miles per hour, we can multiply it by 3600/5280
= 77.3 x (3600/5280)
≈ 52.9 miles per hour
Therefore, the minimum speed at which the car was traveling is 52.9 miles per hour.
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Which statement is true about the functions f(x) = -15x2 + 32 and g(x) = -17x2 + 5x + 32?
The true statement is that f(x) and g(x) have the same y-intercept. Option C.
Function problemBoth f(x) and g(x) have the same y-intercept. We can see this by setting x = 0 for both functions.
For f(x), we get:f(0) = -15(0)^2 + 32 = 32
For g(x), we get:g(0) = -17(0)^2 + 5(0) + 32 = 32
The other statements are not necessarily true. f(x) and g(x) do not necessarily have the same zeros, as the coefficients and constants in the functions are different.
The maximum value of f(x) and g(x) would depend on the vertex of each function, which may or may not be the same.
Finally, neither f(x) nor g(x) are odd functions, as they do not satisfy the property of f(-x) = -f(x) or g(-x) = -g(x) for all x.
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