Answer:
Mean: 19.366666666667
Step-by-step explanation:
Mean: Average of the Data set
If you add the numbers below and divide them by the amount of numbers there are, you will get the average of the data set.
14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25
Average= sum/count
Mean= 1162 / 60
Mean= 19.366666666667
Rounded to the nearest tenth: 19.4
Rounded to the nearest hundredth: 19.37
the perimeter of a rectangle is 70 cm . if the ratio of the width to the length is 2:5 what is the width ?
Answer:
width = 10 cm
Step-by-step explanation:
the ratio of width to length is 2 : 5 = 2x : 5x ( x is a multiplier )
the perimeter (P) of a rectangle is calculated as
P = 2 × width + 2 × length
given P = 70 then
2(2x) + 2(5x) = 70
4x + 10x = 70
14x = 70 ( divide both sides by 14 )
x = 5
Then
width = 2x = 2 × 5 = 10 cm and length = 5x = 5 × 5 = 25 cm
If y=4 when x=12, find y when x=-24
The value of y is -8 if the x -24 and y varies directly with x, and If y = 4 when x = 12.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
The question is incomplete.
The complete question is:
If y varies directly with x, and If y = 4 when x = 12, how do you find y when x = -24?
y ∝ x (given)
y = kx
k is the constant of proportionality.
4 = 12k (y = 4, and x = 12)
k = 1/3
y = x/3
Plug x = -24
y = -24/3
y = -8
Thus, the value of y is -8 if the x -24 and y varies directly with x, and If y = 4 when x = 12.
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If you bought a stock last year for a price of $66, and it has gone down 13.9% since then, how much is the stock worth now, to the nearest cent?
The stock worth now, to the nearest cent, is $58.14.
How to find the current worth of stock?The current worth of stock = initial price of stock+increase in the price of stocks
If you bought stock last year for a price of $66, and it has gone down 13.9% since then,
Let X be the worth of stock;
66 × 100 = (13.5% + 100%) × X
6600 = 113.5X
X = 6600/113.5
X = 58.14458
X = $58.14
Hence, The stock worth now, to the nearest cent is $58.14.
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See photo for questions.
Answer:
1. "a" [tex]u'=6x[/tex]
2. "d" [tex]v'=15x^2[/tex]
3. "b" [tex]y'=75x^4+30x^2+6x[/tex]
Step-by-step explanation:
General outline:For parts 1 & 2, apply power ruleFor part 3, apply product rulePart 1.
Given [tex]u=3x^2+2[/tex], find [tex]\frac{du}{dx} \text{ or } u'[/tex].
[tex]u=3x^2+2[/tex]
Apply a derivative to both sides...
[tex]u'=(3x^2+2)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]u'=(3x^2)'+(2)'[/tex]
Scalars factor out of derivatives...
[tex]u'=3(x^2)'+(2)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]u'=3(2x)+0[/tex]
Simplify...
[tex]u'=6x[/tex]
So, option "a"
Part 2.
Given [tex]v=5x^3+1[/tex], find [tex]\frac{dv}{dx} \text{ or } v'[/tex].
[tex]v=5x^3+1[/tex]
Apply a derivative to both sides...
[tex]v'=(5x^3+1)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]v'=(5x^3)'+(1)'[/tex]
Scalars factor out of derivatives...
[tex]v'=5(x^3)'+(1)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]v'=5(3x^2)+0[/tex]
Simplify...
[tex]v'=15x^2[/tex]
So, option "d"
Part 3.
Given [tex]y=(3x^2+2)(5x^3+1)[/tex]
[tex]\text{Then if } u=3x^2+2 \text{ and } v=5x^3+1, y=u*v[/tex]
To find [tex]\frac{dy}{dx} \text{ or } y'[/tex], recall the product rule: [tex]y'=uv'+u'v[/tex]
[tex]y'=uv'+u'v[/tex]
Substituting the expressions found from above...
[tex]y'=(3x^2+2)(15x^2)+(6x)(5x^3+1)[/tex]
Apply the distributive property...
[tex]y'=(45x^4+30x^2)+(30x^4+6x)[/tex]
Use the associative and commutative property of addition to combine like terms, and rewrite in descending order:
[tex]y'=75x^4+30x^2+6x[/tex]
So, option "b"
What is −7.6 − 2(2.2)
Answer:
-12
Step-by-step explanation:
Order of operations:
PEMDAS
First, do parenthesis, 2 x 2.2 = 4.4 then do -7.6 - 4.4 = -12
HELP THIS IS URGENT WILL GIVE BRANLIEST ANSWER 3 AND 6
Find the area of the shaded region
O100 m²
O 105 m²
O 75 m²
O 50 m²
5m
10 m.
5m
15 m
3z^2-4z+11 -(12z^2+2z-11 find the difference . polynomials functions
Answer:
−135z
2
−2z
The 2 is representing Square
Step-by-step explanation:
(3z)
2
−4z+11−(12z)
2
+2z−11
Expand (3z)
2
.
3
2
z
2
−4z+11−(12z)
2
+2z−11
Calculate 3 to the power of 2 and get 9.
9z
2
−4z+11−(12z)
2
+2z−11
Expand (12z)
2
.
9z
2
−4z+11−12
2
z
2
+2z−11
Calculate 12 to the power of 2 and get 144.
9z
2
−4z+11−144z
2
+2z−11
Combine 9z
2
and −144z
2
to get −135z
2
.
−135z
2
−4z+11+2z−11
Combine −4z and 2z to get −2z.
−135z
2
−2z+11−11
Subtract 11 from 11 to get 0.
−135z
2
−2z
You have loaned a friend %100 and will charge him 5% annual simple interest when he pay it back.
Answer:
bro nobody can figure this out you need to word the entire question with numbers and all. and proper English pls
x=7-3y
2(7-3y)+4y=8
14-6y +4y=8
14-2y=8
-2y = -6
y=3
x + 3(3) = 7
Answer:
(-2,7)
Step-by-step explanation:
x=7-3y
2(7-3y)+4y=8
14-6y +4y=8
14-2y=8
-2y = -6
y=3
x + 3(3) = 7
x + 9 = 7
x = -2
(-2,7)
Answer: -2,3
Step-by-step explanation:
1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water. Water flows out of the tank at a rate of 4 per minute. At this rate, how long will the tank be completely drained out of water? 80 cm 40 cm 30 cm 1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water . Water flows out of the tank at a rate of 4 per minute . At this rate , how long will the tank be completely drained out of water ? 80 cm 40 cm 30 cm
Answer:
6.34 min to empty
Step-by-step explanation:
80 cm x 40 cm x 30 cm = 96000 cm^3
this volume represents 25.36 gallons of water (US)
25.36 gal / 4 gal/min = 6.34 min to empty
The linear function that is represented by which table has the same slope as the graph? On a coordinate plane, a line goes through points (0, negative 3) and (2, 1). a A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries negative 9, negative 7, negative 5, negative 3, negative 1. b A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries 9, 7, 5, 3, 1. c A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. d A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 5, 7, 9. Column 2 is labeled y with entries negative 9, negative 13, negative 17, negative 21, negative 25.
Option C. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. This labeled is correct.
According to the linear function,
Every linear function is characterized by a constant rate of change; the slope. The slope of a linear function is a measure of the “steepness” of the line. We use the symbols Δx and Δy which mean respectively the “change in x ” and the “change in y ”.
So Option C is correct after all assumptions.
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The Carter family just left the local pet store with Rex, their new family dog. The pet store owner told the Carter family that for the next 6 months, Rex would grow at an average rate of 9 pounds per month. Currently, Rex is 2 months old and weighs 6 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 6 Part A: Complete the given table that represents Rex’s current weight, in pounds, as a function of his age, in months Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. Part D: If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old? Upload your table, graph, and solution below.
The graph is attached and all the sub parts have been answered.
What is a function ?A function is away of relating a dependent variable to an independent variable .
It is given that
Current weight of Rex at 2 months =6 pounds
Let x represents the age in months of Rex
then a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. is
Let y be the current weight of Rex
then
y = 6 + 9(x -2)
The table that represents Rex’s current weight, in pounds, as a function of his age, in months
2 6
3 15
4 24
5 33
6 42
7 51
8 59
The graph is plotted for the given data and attached .
If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old
6 + 9*(12-2)
96 pounds.
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Construct a polynomial function with the following properties fifth degree, 3 is a zero of multiplicity 3, - 4 is the only other zero, leading coefficient is 3
The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²
How to construct polynomial functions?Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
We need to form a polynomial expression with the following properties;
fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;
y = 2(x - 3)³(x + 4)²
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Megan bought 3 tickets to the ballet for $57.50. How much would it cost for her to buy 15 tickets?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction
Which point is a reflection of Z(5/1, 3) across the x-axis? Please I will give the brainliest
Answer: (5/1, -3)
Hope this helps :)
Answer:
Look at the attachment.
Step-by-step explanation:
Look at the attachment.
Select the correct answer. Which set of vertices forms a parallelogram? OA A2,4), B(3, 3), C6, 4), D(5, 6) OB. A(-1, 1), B(2, 2), C(5, 1), D(4, 1) OC. A(-5, -2), B(-3, 3), C3, 5), D(1, 0) OD. A(-1, 2), B(1, 3), C5, 3), D(1, 1).
Answer:
(6,4)
Step-by-step explanation:
^^^
What is the mode of 1,1,2,2,3,3,4,4
Answer: There is no mode.
Step-by-step explanation:
The mode is the number that appears the most in a given set of data. Each number in this data set is repeated twice. Therefore, there is no mode.
I hope this helped!! :)
Answer:
1, 2, 3, 4
or none
Step-by-step explanation:
Mode is the value or values in the data set that occurs most frequently.
example:
For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.
in 1, 1, 2, 2, 3, 3, 4, 4 all numbers occur the same amount of times, therefore they all (or none) are the mode
hope this helps:)
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a -credit course, a B in each of -credit courses, a C in a -credit course, and a D in a -credit course?
Answer: 2.7545
The question was a little off, but I can understand enough
Step-by-step explanation:
Grade Grade Point(x) Course Credit(y) Product(xy)
A 4 3 12
B 3 4 12
B 3 4 12
B 3 4 12
C 2 2 4
D 1 3 3
Total 20 55
This means, the GPA of the student is :
[tex]GPA=\frac{55}{20}[/tex]
[tex]2.75[/tex]
The scatter plot shows a correlation between the years and the rainfall in centimeters in Tennessee.
The line of regression models that correlation.
Enter a number to complete each statement.
please help
Answer:
7
4
Step-by-step explanation:
The actual values are shown on the given graph as blue points.
The line of regression is shown on the given graph as the red line.
From inspection of the graph, in the year 2000 the actual rainfall was 43 cm, shown by point (2000, 43). It appears that the regression line is at y = 50 when x is the year 2000.
⇒ Difference = 50 - 43 = 7 cm
In 2000, the actual rainfall was 7 centimeters below what the model predicts.
From inspection of the graph, in the year 2003 the actual rainfall was 44 cm, shown by point (2003, 40). It appears that the regression line is at y = 40 when x is the year 2003.
⇒ Difference = 44 - 40 = 4 cm
In 2003, the actual rainfall was 4 centimeters above what the model predicts.
Examples for Continuous rv X
1. Given the pdf:
f(x) {1/4 e^-1/4x} x>0
0, otherwise
Find: a. E(X) and b. Var(X)
Use the definitions of expectation and variance.
Expectation[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]
Integrate by parts,
[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]
with
[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]
[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]
(since the integral of the PDF is 1, and this integral is 4 times that)
Variance[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]
Compute the so-called second moment.
[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]
Integrate by parts, with
[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]
[tex]E(X^2) = 8 E(X) = 32[/tex]
and the variance is
[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]
please help with this question
find the value of x ( fast fast fast)
The value of x is calculated with the help of a similar triangle is 24.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In a triangle, if there is a parallel line with any side of the triangle, then the line divides the other sides in the same ratio.
Then we have
x / 12 = 32 / 16
x = 24
Then the value of x is 24.
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0 1 3 6 10 what goes after 10?
Answer:
15
Step-by-step explanation:
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
The two triangles are similar What is the value of x? Enter your answer in the box x =
Answ x=59
Step-by-step explanation:
ments
nts
ns
Mai says, "I know how to find the area of a sector or the length of an arc for central angles like 180
degrees or 90 degrees. But I don't know how to do it for central angles that make up more complicated
fractions of the circle."
1. In the diagram, the sector's central angle measures 8 degrees and the circle's radius is r units. Use
the diagram to tell Mai how to find the area of a sector and the length of an arc for any angle and
radius measure.
2. This image shows a circle with radius and central angle measurements. Find the area of the shaded
sector, and the length of the arc defined by the sector.
160%
5 in
The sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
How to find a sector area, and arc length?For a sector that has a central angle of θ, and a radius of r;
The sector area, and the arc length are:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] --- sector area
[tex]L = \frac{\theta}{360} * 2\pi r[/tex] ---- arc length
How to find the given sector area, and arc length?Here, the given parameters are:
Central angle, θ = 160
Radius, r = 5 inches
The sector area is
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]A = \frac{160}{360} * \frac{22}{7} * 5^2[/tex]
Evaluate
A = 34.92
The arc length is:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{160}{360} * 2 * \frac{22}{7} * 5[/tex]
L = 13.97
Hence, the sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
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The United States Postal Service reports that 90% of first-class mail within the same city is delivered in two days of the time of mailing. Ten letters are randomly sent to different locations. a. What is the probability that all 10 will arrive within two days? b. What is the probability that exactly 8 will arrive within two days? c. What is the probability that 5 or fewer will arrive within two days? d. What is the mean number of letters that will arrive within two days? e. What is the standard deviation of the number of letters that will arrive within two days?
a)The probability that all 10 will arrive within two days is 0.3486.
b) P(x = 8) = 0.1937
c) P(x=5)= 0.0014
d) mean = 9
e) Standard deviation = √0.90 = 0.9486
What is Binomial Probability?The binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times and the outcome for a given patient is either a success or a failure.
Given:
p = 90/100 = 0.90
q(probability of success) = 1 - p = 1 - 0.90 = 0.10
n = 10
a)The probability that all 10 will arrive within two days
P(x = 10) = 0.3486
b) P(x = 8) = 0.1937
c) P(x=5)= 0.0014
d) mean = np = 10 × 0.90 = 9
e) Variance = npq = 10 × 0.90 × 0.10 = 0.90
Standard deviation = √0.90 = 0.9486
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Prove that the function
Answer:
See proof below
Step-by-step explanation:
Important points
understanding what it means to be "onto"the nature of a quadratic functionfinding a value that isn't in the rangeOnto
For a function with a given co-domain to be "onto," every element of the co-domain must be an element of the range.
However, the co-domain here is suggested to be [tex]\mathbb R[/tex], whereas the range of f is not [tex]\mathbb R[/tex] (proof below).
Proof (contradiction)
Suppose that f is onto [tex]\mathbb R[/tex].
Consider the output 7 (a specific element of [tex]\mathbb R[/tex]).
Since f is onto [tex]\mathbb R[/tex], there must exist some input from the domain [tex]\mathbb R[/tex], "p", such that f(p) = 7.
Substitute and solve to find values for "p".
[tex]f(x)=-3x^2+4\\f(p)=-3(p)^2+4\\7=-3p^2+4\\3=-3p^2\\-1=p^2[/tex]
Next, apply the square root property:
[tex]\pm \sqrt{-1} =\sqrt{p^2}[/tex]
By definition, [tex]\sqrt{-1} =i[/tex], so
[tex]i=p \text{ or } -i =p[/tex]
By the Fundamental Theorem of Algebra, any polynomial of degree n with complex coefficients, has exactly n complex roots. Since the degree of f is 2, there are exactly 2 roots, and we've found them both, so we've found all of them.
However, neither [tex]i[/tex] nor [tex]-i[/tex] are in [tex]\mathbb R[/tex], so there are zero values of p in [tex]\mathbb R[/tex] for which f(p)= 7, which is a contradiction.
Therefore, the contradiction supposition must be false, proving that f is not onto [tex]\mathbb R[/tex]
A 20-ft by the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 256 ft2, how wide is the walkway?
========================================================
Explanation:
x = width of the walkway in feet
This is some positive real number.
The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x
Refer to the diagram below.
The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft
The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.
-----------
Area = length*width
1056 = (20+2x)*(40+2x)
1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule
1056 = 800 + 40x + 80x + 4x^2
0 = 4x^2 + 40x + 80x + 800 - 1056
0 = 4x^2 + 120x - 256
4x^2 + 120x - 256 = 0
4(x^2 + 30x - 64) = 0
x^2 + 30x - 64 = 0
Let's use the quadratic formula to finish solving for x.
Plug in a = 1, b = 30, c = -64
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\[/tex]
Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.
The only practical solution is x = 2
Therefore, the walkway is 2 feet wide
A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s^2. How much time does it take to travel 95.1 m?
The school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
A school bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
From the second equation of motion:
[tex]\rm s = u + \dfrac{1}{2}at^2[/tex]
We have given:
s = 95.1 m
u = 26.8 m/s
a = 4.73 m/s²
[tex]\rm 95.1 = 26.8 + \dfrac{1}{2}(4.73)t^2[/tex]
The above equation is a quadratic equation:
After simplification:
[tex]\rm \dfrac{4.73}{2}t^2=68.3[/tex]
[tex]\rm t^2=28.879[/tex]
t = 5.373 seconds ≈ 5.34 seconds
Thus, the school bus will take 5.34 seconds to travel 95.1 m if the bus is moving 26.8 m/s on flat ground when it begins to accelerate at 4.73 m/s².
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