The mean net worth of the 42 national corporations is approximately 31.5 million dollars. The modal class is the class with the highest frequency, which is the class with class limits of 10-15 and a frequency of 14.
To find the mean, we add up all the net worth values and divide by the total number of corporations. However, since we only have the frequency of each class, not the actual net worth values, we need to estimate the mean using the midpoint of each class and the frequency as the weight. The midpoint of a class is calculated by averaging the lower and upper-class limits.
In this case, the midpoint for a class with class limits of 10-15 is 12.5 million dollars and the midpoint for a class with class limits of 40-45 is 42.5 million dollars. By multiplying the midpoint of each class by its frequency and summing up the results, we can estimate the mean net worth of the corporations.
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Complete Question:
Net Worth of Corporations These data represent the net worth (in millions of dollars) of 42 national corporations. Find the mean and modal class for the data.
Class limits Frequency
10-15 14
16-21 2
22-27 4
28-33 8
34-39 3
40-45 11
How many solutions does the system 3x+y=4 and 6x+2y=8 have show work
Considering the systems of equations, the system of equations has infinite solutions.
Definition of systems of equationsSystems of equations are a set of two or more equations with two or more variables.
To find the solution to a system of equations, you have to solve the equations simultaneously. However, not all systems of equations have a solution. You can have systems with no solutions or even systems with infinitely many solutions.
hat is, there are three possible results that we can find when working with systems of linear equations:
A solution: A system of linear equations of two or more equations with two or more variables will have only one solution when the equations of the system are different from each other and are not parallel.No solution: In this case, the equations of the system are parallel, so a have no point in common and there is no solution that can satisfy all the equations of the system.Infinite solutions: Occurs when the graphs of the equations overlap one another due to having equivalent versions of the same equation. Algebraically, you can determine if the equations of the system are equivalent by simplifying and manipulating them. For example, you might have that one of the equations is equal to the other multiplied by 2.Solutions in this caseThe system of equations is:
3x+y=4
6x+2y=8
You can see that the second equation is obtained by multiplying the first equation by 2. Therefore, the system of equations has infinitely many solutions.
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the dimensions of a rectangle are shown. write the area of the rectangle as a sum of cubes. x 3 and x^2-3x 9
The area of a rectangle with length x and width [tex]x^2-3x[/tex] can be written as a sum of cubes as [tex]x^3 + (x^2-3x)^3[/tex].
[tex]x^3 + (x^2-3x)^3[/tex]
We are asked to write the area of the rectangle as a sum of cubes. The area of a rectangle is calculated with length times width.
The length of the rectangle is given as x and the width of the rectangle is given as [tex]x^2-3x.[/tex]
The area of the rectangle can be written as:
Area = [tex]x^2-3x.[/tex]
The area can then be written as a sum of cubes as:
Area = [tex]x^3 + (x^2-3x)^3[/tex]
Therefore, the answer is [tex]x^3 + (x^2-3x)^3.[/tex]
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Nate is culturing bacteria that have a growth rate of 10% per hour. If the current population is 12,800 bacteria, how many bacteria will there be in 8 hours?A growing farming conglomerate increases its water usage at a rate of 10% every year. If it used 13,000 megaliters of water this year, then how much water will it use 17 years from now?
27438 be the number of bacteria there be in 8 hours.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Nate is culturing bacteria that have a growth rate of 10% per hour.
The current population is 12,800 bacteria.
We need to find the number of bacteria will there be in 8 hours
[tex]A=P(1+r)^{t}[/tex]
[tex]A=12800(1+10/100)^{8}[/tex]
[tex]A=12800(1+0.1)^{8}[/tex]
A = 12800×(2.14)
A=27438
Hence, 27438 be the number of bacteria there be in 8 hours.
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for the charge distribution provided, indicate the region (a to e) along the horizontal axis where a point exists at which the net electric field is zero. (figure 3)
The region along the horizontal axis where the net electric field is zero is region C.
In region C, the electric field produced by the positive charge is equal and opposite to the electric field produced by the negative charge. Therefore, the net electric field in this region is zero. The electric field is proportional to the gradient of the potential, and thus, the potential is constant in region C. Points in region C are equipotential points, meaning that they have the same electrical potential and the electric field is perpendicular to the equipotential surface.
In regions A, B, D, and E, the electric field is non-zero because the charges are not symmetrically placed with respect to the point in question, and thus, the electric field will have a net non-zero value in these regions.
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One leg of a right triangle has a length of 7m. The other sides have lengths that are consecutive integers. Find the lengths
Answer:
24 m, 25 m
Step-by-step explanation:
You want the two sides of a right triangle that are consecutive integers when one side is 7 m.
Pythagorean theoremLet the shorter side be represented by x. Then the longer side is x+1, and the Pythagorean theorem tells you ...
7² +x² = (x+1)²
49 +x² = x² +2x +1
48 = 2x . . . . . . subtract (x²+1)
24 = x
x+1 = 25
The other sides are 24 and 25 meters.
__
Additional comment
You know that 7 is not the hypotenuse, because a 3-4-5 right triangle is the only right triangle with consecutive integer leg lengths and a hypotenuse of 7 or less. (The next nearest right triangle with consecutive leg lengths is {20, 21, 29}, with a hypotenuse of 29.)
You may recognize the side lengths as the Pythagorean Triple {7, 24, 25}, one of the triples commonly seen in algebra and trig problems.
The school cafeteria is selling hot dogs for $2 and chili dogs for $2.50. They sold 53 items for a total of $120. How many hot dogs were sold. How many chili dogs were sold
Answer:
Hotdogs = 25 Chili dogs = 28
I believe it correct
Which equation represents the written description?
Five times the difference between 26.8 and a number is equal to 63.7.
5(m − 26.8) = 63.7
5m − 26.8 = 63.7
5(26.8 − m) = 63.7
5(26.8) − m = 63.7
Answer:
The first one is the answer
Step-by-step explanation:
let m be the other number,
so 5(m-26.8) = 63.7
What kind of angle is this
Answer:
no they are not similar
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation: :)
Estimate the perimeter of the figure.
The perimeter of the figure is 28 units.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners.
Let us split the given figure to three shapes
Rectangle, Two right triangles
The rectangle has 4 units of length and 3 units of width
Perimeter of rectangle=2(length+width)
=2(4+3)
=14
Now the three sides of triangle are 2, 2 and 2.82 (pythagoras theorem)
Perimeter of triangle=2+2+2.82
=7 units
as there are two right triangle the total perimeter is 2×7=14 units.
So Total perimeter=14+14 units
28 units
Hence, the perimeter of the figure is 28 units.
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Determine the slant asymptote of the rational function f of x is equal to the quantity 10x cubed minus 8x squared plus 6 end quantity over the quantity 2x squared plus 2x minus 4 end quantity.
y = 5x – 9
y = 5x + 9
y = 5x – 1
y = 5x + 1
The correct statement is y=5x-9
What is Meant by Slant Asymptote?In Mathematics, a slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.
Given here: The function f(x)=10x³-8x²+6 over 2x²+2x-4
Thus 2x²+2x-4)=10x³-8x²+6 (5x-9
10x³+10x²-20x
__________________
-18x²+4x+6
-18x²-18x-36
___________________
22x+42
Thus the required oblique slant asymptote is given by 5x-9
Hence, The correct statement is y=5x-9
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A cell phone is plugged in to be charged. The table shows the percent of battery power at some times after it was plugged in.
The equation representing the table is y = 0.9x + 6 and at 104.44 minutes the phone will be fully charged.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Let, The x coordinate represents time in minutes and the y coordinate represents battery percentage.
So, The ordered pairs are, (0, 6), (10, 15).
Slope(m) = (15 - 6)/(10 - 0).
Slope(m) = 9/10 = 0.9.
y = 0.9x + b.
6 = 0.9(0) + b.
b = 6.
y = 0.9x + 6.
When it is fully charged it is,
100 = 0.9x + 6.
0.9x = 94.
x = 94/0.9.
x = 104.44 minutes or 104 minutes and 26 seconds.
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the endpoints of $\overline{ab}$ are $a\left(2,\ 5\right)$ and $b\left(-4,\ 7\right)$ . find the coordinates of the midpoint.
The endpoints of AB are (2, 5) and (-4, 7). So the coordinates of the midpoint are (-1, 6).
Determine the coordinates of the midpointThese are the specified parameters:
AB are (2, 5) and (-4, 7)
Here,
x₁ = 2 and y₁ = 5
x₂ = -4 and y₂ = 7
The coordinates of the midpoint
= ((x₁ + x₂)/2 , (y₁ + y₂)/2)
= ((2 + (-4))/2 , (5 + 7)/2)
= (-2/2 , 12/2)
= (-1, 6)
So the coordinates of the midpoint of segment AB are (-1, 6).
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Last year, Mrs. Larson’s annual salary was $67,438. This year she received a raise and now earns $75,530 annually. She is paid biweekly. a. What was her biweekly salary last year? Round to the nearest cent. b. What is Mrs. Larson’s biweekly salary this year? Round to the nearest cent. c. On a biweekly basis, how much more does Mrs. Larson earn as a result of her raise to the nearest cent, and as a percent increase?
The biweekly salary last year is $2,593.77.
The biweekly salary this year is $2,905.
The amount she earns more is $311.23.
What is the biweekly salary?If an event occurs biweekly, it means that it occurs every two weeks.
Total number of times she was paid = number of weeks in a year / frequency she is paid
52 /2 = 26
Biweekly salary last year = salary last year / number of times she was paid
$67,438 / 26 = $2,593.77
Biweekly salary this year = annual salary / number of times she was paid
= $75,530 / 26
= $2,905
Increase in biweekly salary = $2,905 - $2,593.77 = $311.23
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ii. The first four moments of a distribution about the value 4 of the variable are -1.5, 17,-30 and 108. Find the moments about mean.
Answer:2.5,21,166,1132
Step-by-step explanation:
. State whether the image below is an enlargement
or a reduction. Identify the scale factor.
4cm
15
3cm
5cm
20cm
25cm
15cm
Enlargement OR Reduction? (circle one)
Scale Factor =
The image below is a reduction, the scale factor is 1/5.
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Thus, scale factor is the ratio of the new measurement to the old measurement.
Given;
The two triangle with 4cm, 5cm, 3cm and 20cm, 25cm, and 15cm.
Now,
s=4/20=1/5
s=5/25=1/5
s=3/15=1/5
Therefore, the scale factor will be 1/5.
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The height of the triangle is 12 cm greater than the base of the triangle
b. What is the area of the triangle? Show your work.HELP
The required area of the triangle is represented by the expression A = (1/2)b² + 6b. where b is the base of the triangle.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
To find the area of a triangle, we need to know the base and height of the triangle. The height of the triangle is given as 12 cm greater than the base of the triangle, so let's call the base of the triangle "b".
The height would then be h = b + 12.
The formula for the area of a triangle is:
A = (1/2)bh
So, the area of the triangle would be:
A = (1/2)(b)(b + 12)
A= (1/2)b² + (1/2)12b
A = (1/2)b² + 6b
In this case, the area of the triangle is a function of the base, so the exact value of the area depends on the value of b.
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A rocket is launched from the top of a building. The flight path is modelled by h = -4t2 + 16t + 24
where h is the height of the rocket from the ground in metres, and t is the time in seconds. What is the initial height of the rocket, when will the rocket hit the ground and what height is the rocket after 4 seconds
The initial height of the rocket is 24 meters. The rocket would hit ground after 5.16 seconds. The height of the rocket after 4 seconds is 84 meters.
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The height of the rocket after t seconds is:
h(t) = -4t² + 16t + 24
a) The initial height is at t = 0, hence:
h(0) = -4(0) + 16(0) + 24
h(0) = 24
The initial height of the rocket is 24 meters
b) The rocket hit the ground at h = 0, hence:
0 = -4t² + 16t + 24
4t² - 16t - 24 = 0
t = 5.16 seconds
c) The height of the rocket after 4 seconds:
h(5) = -4(5) + 16(5) + 24 = 84 meter
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PLEASE HELP 20 points
Answer: Im pretty sure the answers are B and C
Step-by-step explanation:
if you start with [tex]\frac{2(3x-6)}{3}[/tex] and distribute the 2
[tex]2*3=6[/tex]
[tex]2*-6=-12[/tex]
So you are left with [tex]\frac{6x-12}{3}[/tex]
[tex]\frac{6x}{3}=2x[/tex]
[tex]\frac{-12}{3}=-4[/tex]
[tex]2x-4[/tex]
b) In a certain airport, planes landed at random times with a constant average rate of one every 10 minutes.
i. Find the probability that between two (2) and six (6) planes will landed in 10 minutes. (3 marks)
Answer:
The number of planes that land in a given time period follows a Poisson distribution with parameter lambda equal to the average rate of landing per unit time. In this case, lambda is equal to 0.1 planes per minute.
The probability that between 2 and 6 planes will land in 10 minutes is given by the cumulative distribution function of the Poisson distribution:
P(2 <= X <= 6) = P(X <= 6) - P(X <= 1)
Where X is the number of planes that land in 10 minutes.
Using the cumulative distribution function for the Poisson distribution, we have:
P(X <= 6) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)
P(X <= 1) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10)
Therefore,
P(2 <= X <= 6) = (1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)) - (1 - e^(-0.1 * 10) * (1 + 0.1 * 10))
The exact value of this probability can be calculated using a calculator or computer software.
Answer:
0.3
Step-by-step explanation:
A) Find the slope of the line passing through the points (−8, -4) and (−8, 8).
B) Find the slope of the line passing through the points (3, 4) and (−3, 4).
The slope of the line passing through the points (−8, -4) and (−8, 8) is undefined
The slope of the line passing through the points (3, 4) and (−3, 4) is 0
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
A) Find the slope of the line passing through the points (−8, -4) and (−8, 8).
m = (8 - (-4)) / (-8 - (-8)) = undefined
The slope is undefined
B) Find the slope of the line passing through the points (3, 4) and (−3, 4).
Slope = (4 - 4) / (-3 - (-3)) = 0
The slope is 0
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PLEASE HELP ME!!! I NEED YOUR HELP!!!!
Answer:
0 0
3 9
5 15
10 30
Step-by-step explanation:
Since y=3x plug in the various x values to attain your y values.
A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b)x + 0 as the parent function. Which graph shows the boat's value increasing at a rate of 25% per year? Group of answer choices The graph starts on the left near the x-axis, and near the point negative 20 comma 5 curves upward to the right. The graph starts on the left near the horizontal line x equal 25, and near the point negative 20 comma 30, the graph curves upward to the right. The graph starts on the top left near the y-axis and moves downward to the right. The graph makes a sharp turn near the point 10 comma 2.5 and continues to the right along the x-axis. The graph starts on the top left near the y-axis and moves downward to the right. The graph makes a sharp turn near the point 5 comma negative 30 and continues to the right along the horizontal line x equals negative 25.
The graph of the exponent function A(x) = 400 (1.25)ˣ + 0 will be drawn below. Then the correct option is A.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
y = a (1 ± r)ˣ
A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b)ˣ + 0 as the parent function.
The increasing at a rate of 25% per year. value of 'b' is given as,
b = 1 + 0.25
b = 1.25
Then the equation is given as,
A(x) = 400 (1.25)ˣ + 0
The graph of the exponent function A(x) = 400 (1.25)ˣ + 0 will be drawn below. Then the correct option is A.
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sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle. 2x y2
The area between the curves is 18 square units.
First, we should find the area between the curves 2x+y²=8 and y=x, we can find the area of curves by substituting y for x in equation 2x+y²=8.
The given equation is 2x+y²=8 and for this, we have to find the roots:
2y+y²=8
y²+2y−8=0
(y+4)(y−2)=8
so the line y=x intersects the parabola 2x+y²=8 at the points (−4,−4) and (2,2). Solving the equation 2x+y²=8 for x yields x=4−1/2y²
From sketching the graphs of the parabola and the line, we can see that the x-values on the parabola lie on the line in the interval of −4≤y≤2.
The area between curves is:
[tex]A=\int\limits^2_4 {(4-\frac{1}{2}y^2-y) } \, dy\\\\A=(4y-\frac{1}{6} y^3-\frac{1}{2} )^2_-_4[/tex]
A=(8-4/3-2)-(-16+32/3-8)
A =18 square units.
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.
a chi-square test is calculated for the observed and expected numbers of progeny from a genetic cross. the probability associated with the chi-square value is 0.023. this is the probability that
The probability associated with the chi-square value of 0.023 in a chi-square test is the probability of obtaining the observed results, assuming that the expected results are true.
In other words, it is the probability of observing the deviation between the observed and expected values purely due to chance. A low probability value, such as 0.023, indicates that the deviation is unlikely to have occurred by chance, and suggests that there may be some other factor affecting the results of the genetic cross.
In this case, the researcher may reject the null hypothesis that the observed and expected values are in agreement, and conclude that there is a significant difference between the observed and expected values.
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Morgan has two sisters. Morgan is x years old. Her sister Megan is 3 years older. Her sister Marie is 2 years older. Which expression represents the sum ○ A. x+5 ○ B. x+8 o C. 3x+5 o D. 3x+8
Answer:
C
Step-by-step explanation:
morgan = x
megan = x+3
marie = x+2
x+x+3+x+2=3x+5
nUmeRIC
For the following exercises, perform the indicated operation and express the result as a simplified complex number.
(3 + 2i) + (5 − 3i)
. (−5 + 3i) − (6 − I)
(−4 + 4i) − (−6 + 9i)
(2 + 3i)(4 − i)
2-3i/4+3i
The simplified form of complex number (2+3i)(4-i) is 11+10i.
What is the complex number?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
Here,
A) (3 + 2i) + (5 - 3i)
= 3+2i+5-3i
= 8-i
B) (-5 + 3i) - (6 - i)
= -5+3i-6+i
= -11+4i
C) (-4+4i)-(-6+9i)
= -4+4i+6-9i
= 2-5i
D) (2+3i)(4-i)
= 8+12i-2i-3i²
= 8+10i+3
= 11+10i
E) (2-3i)/(4+3i)
Rationalize denominator, that is
(2-3i)×(4-3i)/(4+3i)×(4-3i)
= (8-12i-6i+9i²)/(16-9i²)
= (8-18i-9)/25
= (-18i-1)/25
Therefore, the simplified form of (2+3i)(4-i) is 11+10i.
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a random number is selected uniformly from 0; 1; 2; 3; 4; 5; 6; 7 without replacement until 3 is chosen. let x denote the number of selection. find the entropy h(x) in bits
The entropy of the random variable X in this case is approximately 1.585 bits.
The entropy of a random variable X is a measure of the uncertainty associated with it. In this case, the random variable X is the number of selections required to choose the number 3.
Since the numbers are selected without replacement, the possible values for X are 1, 2, and 3, and the probabilities for each value are:
P(X=1) = 1/3
P(X=2) = 2/7
P(X=3) = 4/7
The entropy of a random variable X in bits is given by the formula:
H(X) = -∑P(X) log2(P(X))
Plugging in the probabilities above:
H(X) = -(1/3 log2(1/3) + 2/7 log2(2/7) + 4/7 log2(4/7))
H(X) = 1.585 bits
So, the entropy of the random variable X in this case is approximately 1.585 bits.
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Hi can someone please help me with these questions I'm really struggling with them!!!
(Is anyone really good at math? )
Image 1
1.
2.
3.
Image 2
1.
2.
3.
Answer:
image 2
1. SSS
2. AAS
3. SAS
rearrange w=3(2a+b)-4
make a the subject
Step-by-step explanation:
Rearrange w = 3(2a + b) - 4 to make a the subject:
w = 3(2a + b) - 4
expand right side:
w = 6a + 3b - 4
add 4 to both sides:
w + 4 = 6a + 3b - 4 + 4
w + 4 = 6a + 3b
subtract 3b from both sides:
w + 4 - 3b = 6a + 3b - 3b
w + 4 - 3b = 6a
flip flop equation for readability ease:
w + 4 - 3b = 6a becomes:
6a = w + 4 - 3b
divide both sides by 6:
6a/6 = (w + 4 - 3b)/6
a = [tex]\frac{1}{6}w + \frac{4}{6} -\frac{3}{6}b[/tex]
reduce:
a = [tex]\frac{1}{6}w + \frac{2}{3} -\frac{1}{2}b[/tex]
Now, arrange right side of equation so variables are ordered alphabetically.
Answer: [tex]a = -\frac{1}{2}b +\frac{1}{6} w+\frac{2}{3}[/tex]
Select each equation that the number 10² makes true.
Equations that the number 10² makes true are:
4.08 × 10² = 408
0.97 × 10² = 97
What is equation?An equation is a mathematical statement that expresses equality, is made up of two expressions connected by an equal sign.
Given equations,
a) 0.031 × 10² = 31
0.031 × 100 = 31
3.1 ≠ 31
LHS ≠ RHS
Equation is not true
b) 0.501 × 10² = 501
0.501 × 100 = 50.1
50.1 ≠ 50.1
LHS ≠ RHS
Equation is not true
c) 4.08 × 10² = 408
4.08 × 100 = 408
408 = 408
LHS = RHS
Equation is true
d) 0.97 × 10² = 97
0.97 × 100 = 97
97 = 97
LHS = RHS
Equation is true
e) 0.55 × 10² = 550
0.55 × 100 = 550
55 ≠ 550
LHS ≠ RHS
Equation is not true
Hence, 4.08 × 10² = 408 and 0.97 × 10² = 97 are equations that the number 10² makes true.
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