The mean of the number of shoes according to the obtained results is; 8.49.
The median of the number of pairs of shoes obtained is; 9.
What is the mean and median of the frequency distribution?It follows from the complete task content that the mean and median of the data set are to be evaluated;
Since the mean is the average of all obtained data values, it follows from the mean formula;
Mean = Sum Total/Total Frequency
Mean = { ( 8 × 4 ) + ( 4 × 5 ) + .......+ (13 × 4) } / 65
Mean = 552/65
Mean = 8.49.
Also, the median of the set of 65 data values can be guessed to be the 33rd term.
On this note, the data value which corresponds to a cumulative frequency of 33 upon orderly arrangement is the median term.
Hence, since; 8 + 5 + 4 + 4 + 7 = 28; Hence, upon addition of 14, we have; 42.
Therefore, the median of the number of pairs of shoes is; 9 pairs of shoes.
Remark; The complete task requires that the mean and median be determined.
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Act 3 of the 2003 Leonid meteor shower was expected to last 24 hours. The margin of error for this prediction was
0.7 days. Set up and solve an absolute value equation to find the limits of the range for the length of time that Act 3
could last. Show your work.
The limits of the range for the length of time that Act 3 could last is 33.6
What is limit ?The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category. In general, integrals are divided into two categories: definite integrals and indefinite integrals.
A 24-hour period was predicted for Act 3 of the 2003 Leonid meteor shower. This prediction had a 0.7-day error window. How long could Act 3 potentially last, in the range
Lower Limit: 24-0.7(24) = 0.3(24) = 7.2 hrs
Upper Limit: 24+0.7(24) = 40.8 hrs
Range = Upper Limit - Lower Limit
= 40.8 - 7.2
=33.6
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Question 10
What is the equation of a line parallel to y = 3x + 2 and passes through the point (2, 1)?
Oy = 3x - 5
Oy=2x+3
Oy=3x + 7
Oy=1/3x+7
10 pts
The equation for a line parallel to y = 3x + 2 that passes through the point (2, 1) is y = 3x - 5.
What exactly is Point Slope Form?The point slope form is used to calculate the equation of a straight line that is inclined to the x-axis at a given angle and passes through a given point.
What are the methods for solving the line equation?Depending on the information available, the equation of a line can be found using a variety of methods. Among the methods are:
Point slope formSlope-intercept formIntercept formTwo-point formThe given equation of line is y = 3x + 2.
We need to find the equation of line parallel to the given line and it passes through the point (2, 1).
Slope of line y = 3x + 2 is given as:
By comparing the given equation with y = mx + c, we can say that the slope(m) = 3
Let, a point with coordinates (x, y) be on the line parallel to given line.
Finding slope again we get,
[tex]\frac{y-1}{x-2}[/tex] = 3
y-1 = 3x - 6
∴ y = 3x - 5
As a result, a line parallel to y = 3x + 2 that passes through the point (2, 1) has the equation y = 3x - 5.
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for 1 and 2 draw front side and top views of each stack of unit blocks
1.
2.
3.
In the figure of the second exercise there is one block which is not visible.
4.
We can see that the figure is made with 8 blocks
5.
The maximum length of the figure would be 6. You need 3 blocks to get a heigth of 3 units. Then you can add the other 5 blocks to the one which is in the base to make the figure with a length of 6 units.
Raina runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
raina runs 6 miles in 55 minutes
so it speed is 6/55 miles per minute
that means in one minute he runs 6/55 miles
so in 44 minutes
[tex]\begin{gathered} =\frac{6}{55}\times44 \\ =\frac{6\times4}{5}=\frac{24}{5} \end{gathered}[/tex]in 44 minutes he will run 24/5 miles or 4.8 miles
What is the solution to x-8=-8 hint is not zero
IT HAS TO BE X=0 BECAUSE YOU ADD 8 TO X-8 THAT REMOVES THAT 8 THEN THE ADD 8 TO THE OTHERSIDE OF THE EQUAL SIGN
Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
Find the area of the sector of the circle.
Answer:
D
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{\frac{5\pi }{8} }{2\pi }[/tex]
= π × 12.8² × ([tex]\frac{5}{8}[/tex] ÷ 2)
= π × 163.84 × [tex]\frac{5}{16}[/tex]
≈ 160.8 cm² ( to the nearest tenth )
uppose that the rela
S={(-1, -9), (-9, 1), (3, 1)}
ve the domain and range of S.
rite your answers using set notation.
domain =
range =
Answer:
Domain = {-9, -1, 3}Range = {-9, 1}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A ball is thrown in the air. The function
h = 30t-5t²
can be used to find the height (h) of the ball in meters after 6 seconds. How long does it take the ball to reach a height of 45 meters?
Using given function, we conclude that it will take 3 seconds the ball to reach a height of 45 meters.
In this question, we have been given a function h = 30t - 5t²
This function is used to find the height (h) of the ball in meters after 6 seconds.
We need to find the amount of time required to reach ball to a height of 45 meters.
here, height h = 45 meters
to find : time t
h = 30t - 5t² ........................(Given function)
45 = 30t - 5t²
30t - 5t² - 45 = 0
5t² - 30t + 45 = 0
t² - 6t + 9 = 0
(t - 3)² = 0
t - 3 = 0
t = 3 seconds
Therefore, it will take 3 seconds the ball to reach a height of 45 meters.
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what is the value of 6a+9b?
Please help me factor.
49 - 9x²
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
7
and
b
=
3
x
.
(
7
+
3
x
)
(
7
−
3
x
)
Answer: -(3x - 7)(3x + 7)
Step-by-step explanation:
1. Rewrite the formula:
-[tex]9x^{2} + 49[/tex]
2. Factor -1 out of [tex]-9x^{2} + 49[/tex]
[tex]-(9x^{2} - 49)[/tex]
3. [tex]9x^{2} - 49 = (3x)^{2} - 7^{2}[/tex]
[tex]((3x)^{2} - 7^{2})[/tex]
4. Factor the difference of two squares. [tex](3x)^{2} - 7^{2} =[/tex]
[tex](3x-7)(3x+7)[/tex]
5. Add back negative:
Answer: [tex]-(3x-7)(3x+7)[/tex]
If
f(x) = 2x² – 5
and
g(x) = 5x + 7
Find
g(f(x)) = [?]x² + [ ]
⇒g(f(x)) means that in the place of x in the function g you will plug in the function f.
⇒This means that [tex]2x^{2} -5[/tex] will be plugged in the place of x in 5x+7 and the simplify.
⇒[tex]=5(2x^{2} -5)+7\\\\=10x^{2} -25+7\\=10x^{2} -18[/tex]
⇒Now you have the unknowns The coefficient of the variable [tex]x^{2}[/tex] is 10 and the constant number is -18.
Helppp
Express 27^1/2 as a power of 3
Express root 2 as a power of 8
Express root 2/16 as a power of 2
FOR THE FURST QUESTION.
[tex] {27}^{ \frac{1}{2} } \\ = (3^{3} )^{ \frac{1}{2} } \\ = {3}^{3 \times \frac{1}{2} } \\ = 3^{ \frac{3}{2} } [/tex]
FOR THE SECOND QUESTION
[tex] \sqrt{2} \\ = ( \sqrt[3]{8} )^{ \frac{1}{2} } \\ = ( {8}^{ \frac{1}{3} } )^{ \frac{1}{2} } \\ = 8^{ \frac{1}{3} \times \frac{1}{2} } ) \\ = 8^{ \frac{1}{6} } [/tex]
FOR THE THIRD ONE
[tex] \frac{ \sqrt{2} }{16} \\ = \frac{ \sqrt{2} }{16} \\ = \frac{ {2}^{ \frac{1}{2} } }{ {2}^{4} } \\ = 2^{ \frac{1}{2} - 4 } \\ = 2^{ - \frac{7}{2} } [/tex]
ATTACHED IS THE SOLUTION
A large tank of sterile water holds 200 gallons . It is leaking at an unknown rate. At 8:30 am the tank had 137 gallons and at 11:00 am the tank had 115 gallons. Assuming the tank was full when the leak began , write a function to estimate how much water is in the tank. now find the time at which the tank began leaking and the time at which the tank will be empty.
The time that the tank began leaking water is 12:40am
The time the tank will be empty is 11 : 23 pm.
What is the time the tank began leaking water?The function that would determine the amount of water in the tank is a linear function. A linear function is a function that has a single power that is raised to the power of one. When drawn on a graph, a linear function is a straight line.
The first step is to determine the rate of leakage of the tank.
Rate = (water in the tank at 11am - water in the tank at 8:30am) / change in time
(137 - 115) / (11 - 8:30)
22 / 2:30
22 ÷ 2 1/2 hours = 8.8 gallons per hour
Linear function would have this form:
Water in the tank = water in the tank when full - (rate of leakage x number of hours)
137 = 200 - (8.8xh)
137 = 200 - 8.8h
200 - 137 = 8.8h
63 = 8.8h
h = 63 / 8.8
h = 7.16 hours = 7 4/15 hours
8 - 7 4/15 hours = 12 10/15 hours = 12.40am
When the tank is empty:
0 = 200 - 8.8h
200 - 0 = 8.8h
200 / 8.8 = 22.72 = 22 hours 43 minutes
22 hours 43 minutes + 12 : 40M = 11 : 23 pm
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Express 36 cookies divided equally among 24 students as a fraction and a decimal.
Answer:
3/2, 1.5
Step-by-step explanation:
When you put 36 cookies divided amongst 24 students, each student cookies one and a half cookies
hello i need help on this
A rational number is a number that can be expressed as a ratio of two integers. Integers can be positive or negative. Rational numbers are simply fractions. For example;
-5/2, -1/5, 3/1, 4/5 etc are all rational numbers because we can write them as a ratio of two integers.
Since some of this fractions can lead to both negativa and positive integers, hence rational number is a positive or negative whole number including 0.
Hence all the options are correct since rational numbers are are also repeating decimals
Question
Find the equation of a line that contains the points (-7,-4) and (−2, 3).
(Write the equation in standard form.)
Answer:
y=1.4x+5.8
You have to do y2-y1 over x2-x1.
which of the following is the graph of the function f(x)=1/2Ix+4I-3
we have the function
f(x)=1/2Ix+4I-3
the vertex of the given function is the point
(-4,-3) ---------> III quadrant
therefore
the answer is the option CI need help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Root of the equation 3x-8=1 is
Answer:
x= 3
Step-by-step explanation:
Add
8
to both sides
3x-8=1
2
Simplify
Add the numbers
3x=9
3
Divide both sides by the same factor
3x=9
4
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
Answer:
x = 3
You first add 8 to both sides:
3x - 8 + 8 = 1 + 8
Simplify:
3x = 9
The divide both side by the same factor:
3x/3 = 9/3
9 divided by 3 is 3 so the solution is:
x = 3
Step-by-step explanation:
Hope it helps! =D
I really need help I hate Sparx maths
Answer:
[tex]x=\dfrac{1}{5}, \quad y=6[/tex]
Step-by-step explanation:
Given equations:
[tex]\begin{cases}y=10x+4\\2y+5x=13\end{cases}[/tex]
To solve the given equations by substitution, substitute the first equation into the second equation and solve for x:
[tex]\begin{aligned}\textsf{Equation 2}: \quad 2y+5x&=13\\\\y=10x+4 \implies 2(10x+4)+5x&=13\\20x+8+5x&=13\\25x+8&=13\\25x+8-8&=13-8\\25x&=5\\\dfrac{25x}{25}&=\dfrac{5}{25}\\x&=\dfrac{1}{5}\end{aligned}[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}\textsf{Equation 1}: \quad y &=10x+4\\\\x=\dfrac{1}{5} \implies y&=10\left(\dfrac{1}{5}\right)+4\\y&=\dfrac{10}{5}+4\\y&=2+4\\y&=6\end{aligned}[/tex]
Therefore, the solution to the equations is:
[tex]x=\dfrac{1}{5}, \quad y=6[/tex]
The difference between 7 times a number and 9 more than 2 times the number.
Answer:
Step-by-step explanation:
Equation: 7x - 9 = 5 (x+2) 7x - 9 = 5x + 10 2x = 19 x = 9.5
What’s the correct number and label for the
denominator of the ratio.
Answer:
see explanation
Step-by-step explanation:
ratio required is houses : turbines
let x be the number of turbines required for 26 houses , then
[tex]\frac{6houses}{18turbines}[/tex] = [tex]\frac{26houses}{x}[/tex] ( cross- multiply )
6x = 26 × 18 = 468 ( divide both sides by 6 )
x = 78
78 turbines are required for 26 houses
Write your equation:
plsssssss helppppp
Answer:
The equation is y = 50 + 25x. The slope is the additional cost per hour, and the y-intercept is the cost of the service call to appear at the house.
What is the correct answer to this question
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: State the Angle-Arc relationship
STEP 2: Interpret the given image
[tex]\angle HIJ=\frac{1}{2}HJ[/tex]STEP 3: Find the required angle
By substitution
[tex]\begin{gathered} \angle HIJ=\frac{1}{2}\cdot100 \\ \\ HJ=100 \\ \angle HIJ=\frac{1}{2}\cdot100=50\degree \end{gathered}[/tex]Hence, the answer is 50°
11=t/-12. Find the value of T
Answer:
t=-132
Step-by-step explanation:
multiply -12 on both sides.
-12x11=t
t=-132
Can someone help me step by step to the answer please? thank you!
What is the distance between a and b on the number line below?0.550.652.484.85
Choose the correct simplification of (5xy^7)^2(y^4)^3.
25x^2y^22
10x^2y^14
25x^2y^14
10x^2y^20
The simplified form of the given expression is 25 x² y ²⁶.
What is the simplified form of the expression?
Simplifying expressions mean rewriting the same algebraic expression in a compact form such that there are no like terms.
What are the exponent rules?
The different Laws of exponents used to solve the above mentioned question are:
[tex]x^{m}.x^{n} = x^{m+n} \\\frac{x^{m} }{x^{n} } = x^{m-n} \\(x^{m})^{n} } = x^{mn }[/tex]
According to the given question.
We have an expression (5xy⁷)²(y⁴)³
To simplify the above expression we use the exponent rules.
Therefore,
(5xy⁷)²(y⁴)³
(5² x² y²×⁷) (y ⁴׳)
(25 x² y¹⁴ ) (y¹²)
25 x² y¹⁴⁺¹²
25 x² y ²⁶
Therefore, the simplified form of the given expression is 25 x² y ²⁶
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Determine which function has the greatest rate of change as x approaches infinity.
For the given options, we will find the function that has the greatest rate of change as x approaches infinity
[tex]\begin{gathered} a)f(x)=2x-8 \\ b)g(x)=5x^2-x+7 \\ c)h(x)=4^x-6 \end{gathered}[/tex]The first function is a linear
The second function is quadratic
The third function is exponential
By reviewing the graph of the three functions, we can know that the exponential function has the greatest rate of change as x approaches infinity
So, the answer will be option C) h(x)