two families with four people in each family go to a movie theater. in how many ways can they be seated
According to probability, if both families want to sit together, they can be seated in a row a maximum of two times.
What seating configuration?The direction that each person is facing is crucial when arranging the people.
In order to determine how many ways they can be seated in a row if both families want to sit together, imagine that two families with four members each attend a movie theatre.
Given that the arrangement is important, we will apply the permutation rule. We'll divide the remaining four into two groups of four each.
There are two different ways to arrange the groups so they can sit together.
2! = 2 * 1
2! = 2ways
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to
5.2.2 Guided Instruction: Solutions to the
Products and Quotients of Polynomials on a
Graph
Graphs can be used to determine the products and
quotients of polynomials similarly to using graphs when
adding and subtracting polynomials.
The functions a(x) and b(x), and their product, a(x) b(x),
represented by c(x), are shown on the coordinate plane.
35A
(10, 34)
-10
-30
-25-(-0,24)
MATH
20
(0.805, 105)
10
(1.5, 6)
0
(0-3)
b(x10
-15
(8,13)
C(x)
(6.5, 10)
5
(0-8)
(10, 17)
(8.695-10)
3. Find the value of c(10).
2. What is the product of a(10) · b(10)?
10, 2
15
(8,0)
-20
1. Describe how to use the graph to determine the value
of a (10) b(10).
20
25
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
Definition of the cubic function .f(x)=ax3+bx2+cx+d, where 0 and the coefficients a, b, c, and d are complex numbers, and where the variable x has real values. In other words, it is both a three-degree polynomial function and a real function.
Here,
Our role in this situation is:
y = ∛(x - 5) (x - 5)
so the cubic root is given.
In this case, we see that when x = 0, we have:
The y-intercept is y = -5.
And if x = 5, we get:
Because of the sign change, the x-intercept and inflection point are both equal to y = ∛0 = 0
Thus, the choice that best describes the graph is A cubic function on a coordinate plane has an inflection point at x = 5 and crosses the x-axis at x = 5.
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x^y=y^x and x=2y prove that y=2.
Answer:
[tex] {x}^{y} = {y}^{x} \: - - - (1)[/tex]
[tex]x = 2y \: - - - (2)[/tex]
Substitute (2) into (1):
[tex] {2y}^{y} = {y}^{2y} [/tex]
Log both sides:
[tex]lg(2 {y}^{y} ) = lg(y^{2y} )[/tex]
[tex]y \: lg(2y) = 2y(lg \: y)[/tex]
[tex]y \: lg(2) + y \: lg(y) = 2y \: lg(y)[/tex]
[tex]y \: lg(2) = 2y \: lg(y) - y \: lg(y)[/tex]
[tex]y \: lg(2) = y \: lg(y)[/tex]
Divide by y on both sides:
[tex]lg(2) = lg(y)[/tex]
[tex] {10}^{lg(2)} = {10}^{lg(y)} [/tex]
2= y
y= 2 (proved)
Explanation:
• step 5: lg(m)^n= nlg(m)
• Step 6: lg(mn)= lg(m) +lg(n)
During a science experiment, a chemist boils a liquid and then sets it on the lab table and records the temperatures as it cools. The graph shows , the temperature in degrees Centigrade, and is the number of after the liquid is set on the table. Liquid Temperature Time () Which equation is the best model for this data?
The exponential function that best models this data is given as follows:
C. y = 80(0.75)^x + 20.
How to define the exponential function?An exponential function, considering it's asymptote, is defined as follows:
y = a(b)^x + c.
In which the parameters are given as follows:
a is used to define the initial value.b is the rate of change.c is the horizontal asymptote.From the graph, the horizontal asymptote is at y = 20, hence the parameter c is defined as follows:
c = 20.
When x = 0, y = 100, hence the parameter a is obtained as follows:
100 = a(b)^0 + 20
a + 20 = 100
a = 80.
When x = 5, y = 40, hence the parameter b is obtained as follows:
40 = 80b^5 + 20
80b^5 = 20
b^5 = 1/4
b = (1/4)^(1/5)
b = 0.75. (approximately).
Hence the function is defined as follows:
y = 80(0.75)^x + 20.
Meaning that the correct option is given by option C.
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Wendall designs a tower with a height in feet that can be represented by the function T(x) = 9(x + 6.9), where x is the height of the visible space in a standard office. Then, he decides to include an above ground parking garage under the tower. The height of the parking garage can be represented by the function G(x) = 3x.
Answer:
[tex]G(T(x)) = 27(x + 6.9)[/tex]
Step-by-step explanation:
Given
[tex]T(x) = 9(x + 6.9)[/tex]
[tex]G(x) = 3x[/tex]
Required [Missing from the question]
G(T(x))
We have:
[tex]G(x) = 3x[/tex]
This implies that:
[tex]G(T(x)) = 3(T(x))[/tex]
Substitute: [tex]T(x) = 9(x + 6.9)[/tex]
[tex]G(T(x)) = 3[9(x + 6.9)][/tex]
Open bracket
[tex]G(T(x)) = 27(x + 6.9)[/tex]
What is the XYZ axis called?
The XYZ axis is called as X-axis, Y-axis, and Z-axis, respectively.
The term axis in math is defined as a line with respect to which a curve or figure is drawn, measured, rotated, etc.
Here we have given that XYZ axis, in math are no standard names for the coordinates in the three axes
Based on these the coordinates are often denoted by the letters X, Y, and Z, or x, y, and z.
And these axes may then be referred to as the X-axis, Y-axis, and Z-axis, respectively.
Here in the graph x-axis and y-axis represent the first two dimensions where as the z-axis, the third dimension. Which is also defines the x and y denote width and height and the z denotes depth.
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Unit rates are ALL AROUND US. If you have a phone, take a picture of a unit rate that you find at the grocery store, gas station, or as you are simply out and about. For your post, describe the picture and where you found your unit rate and what the unit rate was.
For your replies, think back and see if you recall seeing unit rates in those places. Describe how a unit rate could be used at the location where it was found.
A unit rate I found at the grocery store was 10 bananas/ $5 this describe the price for 10 bananas but can also be used to identify the price for 1 banana.
What is a unit rate?In mathematics, a unit rate can be defined as a mathematical expression that includes two units to show the rate of a specific activity. For example, the expression 50 kilometers/2 hours shows a car covers a distance of 50 kilometers in two hours, which can be simplied as 25 kilometers per hour.
What is an example of a unit rate that you can find at a grocery store?A unit rate I could observe last weekend while buying fruits and vegetables was 10 bananas/ $5. This unit rate is mainly used to inform buyers about the price of 10 bananas. However, this can also be simplified as $0.5 per banana and this would inform the buyers about the price per unit.
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Maggie made the following quilt from 64 square pieces of fabric.
A square array of eight squares wide by eight squares long. The length of the total square is seven and fifty-two hundredths feet.
What is the side length of each square piece of fabric? Enter your answer in the box.
11.75
feet
Answer:
11.75
Step-by-step explanation:
The quilt consists of a square array of 8 x 8 = <<8*8=64>>64 square pieces of fabric.
Since the length of the total quilt is 7.52 feet, the side length of each square piece of fabric is 7.52 / 8 = <<752/8=0.94>>0.94 feet.
However, since you are asked to enter your answer in the box in feet, you should express 0.94 feet as a decimal to the nearest hundredth. The nearest hundredth of a foot to 0.94 feet is 0.95 feet. Therefore, the side length of each square piece of fabric is approximately 0.95 feet, or approximately 11.75 inches.
So the answer is 11.75 feet.
BANKING Twin brothers Amare and Jermaine each received $1000 for graduation. Amare invests his money in an account that pays 2.25% compounded daily. Jermain invests his money in an account that pays 2.25% compounded
annually.
Part A
Which brother will have more money at the end of 10 years?
A) Amare
B) Jermaine
C) The accounts will be equal.
Part B
To the nearest cent, how much more money? $
A) Amaire have more money than Jermaine after 10 years.
B) By [tex]5.387*10^{11}[/tex]% Amaire has more money than Jermaine.
What is compound interest?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.
Amare and Jermaine has initial amount = $1000
Amare spend his money that pays 2.25% compounded daily.
where are Jermain invest his money that pays 2.25% compounded annually.
Formula of Compound interest that compounded daily
final amount = [tex]A(1+\frac{r}{365})^{365t}[/tex]
where A is initial amount and t is time in years .
final amount after 10 years
final amount = [tex]1000(1+\frac{2.25}{365})^{365*10}[/tex]
final amount = 1000×[tex]1.00616^{3650}[/tex]
final amount = 1000×5.51×[tex]10^{9}[/tex]
final amount = $5.51 ×[tex]10^{12}[/tex]
Formula of Compound interest that compounded annually
final amount = [tex]A(1+\frac{r}{100})^{t}[/tex]
where A is initial amount and t is time in years .
final amount after 10 years
final amount = [tex]1000(1+\frac{2.25}{1000})^{10}[/tex]
final amount = 1000×[tex]1.00225^{10}[/tex]
final amount = 1000×1.0227
final amount = $1022.7
Part A :
Amare has more money after 10 years.
part B :
percent more money = [($5.51 ×[tex]10^{12}[/tex] - 1022.7)/1022.7]*100=[tex]5.387*10^{11}[/tex]%
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PLEASE PLEASE HELP ME WILL MARK BRAINLISTS!!!!!!
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELP
Answer:
All of them approach 9 when x=0
Step-by-step explanation:
what is the area of this figure?
Answer:
602
Step-by-step explanation:
First find area of the rectangle portion
L x W
22 x 15
330
Second find area of trapezoid
B1+B2/2 times height
12+22/2 times 16
34/2 times 16
17 times 16
272
Lastly, add areas together
Rafael claims it's easiest to score points when a scatterplot has a linear association. Sahana says it's easiest when a scatterplot has a strong association.
Who is correct?
Rafael claims it's easiest to score points when a scatterplot has a linear association. Sahana says it's easiest when a scatterplot has a strong association. Both Rafael and Sahana are correct, in their own way.
A scatterplot with a linear association means that there is a straight line relationship between the two variables being plotted. In such a scatterplot, it is relatively easy to make predictions based on the line of best fit, as well as to calculate the correlation coefficient(r), which can indicate the strength and direction of the linear relationship.
On the other hand, a scatterplot with a strong association means that the points in the plot are closely grouped together, indicating a high degree of correlation between the variables. It is relatively easy to make predictions based on the overall pattern of the points in the scatterplot, even if there is no clear linear relationship.
So, Rafael is correct that scoring points is easiest when a scatterplot has a linear association because it is relatively easy to make predictions based on the line of best fit and correlation coefficient. And Sahana is correct that scoring points is easiest when a scatterplot has a strong association because it is relatively easy to make predictions based on the overall pattern of the points in the scatterplot.
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A line with a slope of 0 passes through the points (-2,0) and (-8,c). What is the value of c?
The value of c will be 0.
What is a slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
m = y2 - y1 / x2 - x1
where m = 0
y2 = c
y1 = 0
x1 = -2
x2 = -8
0 = c - 0 / -8 - -(2)
0 = c - 0 / -8 + 2
0 = c - 0 / -6
c - 0 = -6(0)
c - 0 = 0
c = 0
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which of these functions is linear?
Answer:
Function 2, y = x - 5
Step-by-step explanation:
Function 1 is called an Absolute Value Function (where there is absolute value symbol around the whole or a part of the equation, its parent function is; y = |x| )
Function 2 is called a Linear Function (which could be written as y = mx + b, here m and b are integer values, b value is the y-intercept, m is the slope)
Function 3 is called an Inverse Function ( where a value is divided by a variable like "x", it's parent function is; y = [tex]\frac{1}{x}[/tex] )
Function 4 is called a Quadratic Function (it's a function where the variable is squared, it's parent function is; y = x² )
Hope this helps!
The function that represents the linear function is y = x - 5. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let's check all the options, then we have
A) y = |x| - 5, the function is an absolute function.
B) y = x - 5, the function is a linear function.
C) y = 1/x - 5, the function is a rectangular hyperbolic function.
D) y = x² - 5, the function is a quadratic function.
The function that represents the linear function is y = x - 5. Then the correct option is B.
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18. Rachel paid $46 in tax for the money she earned
as a camp counselor. How much money did
Rachel earn?
Helpp!
Answer:
$1022.22Step-by-step explanation:
The tax is 4.5%Amount of tax paid is $46Total amount of money earned is x.
4.5% of x = $46x*4.5/100 = 46x * 0.045 = 46x = 46/0.045x = 1022.22Answer:
Solution given
tax = 4.5%
Amount of tax = $46
Let total amount of money earned is x.
we have
4.5% of x = $46
x×4.5/100 = 46
x×0.045 =46
x = 46/0.045
x= 1022.22
So Racheal earn $ 1022.22.
What is true about the sum of the two polynomials 6 s 2 t − 2 st 2 4 s 2 t − 3 st 2?
The sum of the two polynomials 6s²t – 2st² and 4s²t – 3st² is 5(2s²t – st²) in factorized from.
What is polynomials?One or more algebraic terms (monomials) are combined mathematically to form a polynomial. Poly- (many) and -nomial (terms) are the roots of the word "polynomial".
A polynomial can have exponents (powers), constants (numbers), and variables (letters), but never negative exponents or division by a variable.
In standard form, polynomials prefer to be expressed. In addition, the exponents are arranged in descending order because they don't contain any similar terms (largest to smallest).
The sum of two polynomial is
⇒6s²t – 2st² + 4s²t – 3st²
= 6s²t + 4s²t – 3st²– 2st²
= 10s²t – 5st²
= 5(2s²t – st²)
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Full question
What is true about the sum of the two polynomials?
6s²t – 2st² and 4s²t – 3st²
Given this unit circle, what is
the value of x?
(x,-√2)
X =
(1,0)
[?]
Enter
Answer:
x = - √2/2
Step-by-step explanation:
We know that x = rcosθ and y = rsinθ. The unit circle always have radius of 1 unit. Therefore, r = 1 as defined. Hence:
x = cosθ, y = sinθ
x = cosθ, θ = arcsin(y)
x = cos{arcsin(-√2/2)}
Find the measurement or θ that makes sinθ = -√2/2 and that is π + π/4 = 5π/4.
x = cos(5π/4)
And cos(5π/4) = - √2/2 as well. Hence, x = - √2/2.
HELP ME PLEASE aAA REEE NO SCAMS
Answer:
5
Step-by-step explanation:
Each value of ADCB is 2x as much as EHGF
No links will mark brainliest if correct!
12,000$Step-by-step explanation
What are sin 0 and cos 0 for each value of 0?
Answer:
a. sin 300 = -∛3/2, cos 300 = 1/2
b. sin -225 = √2/2, cos -225 = √2/2
c. sin 5π/6 = 1/2, cos 5π/6 = -3√2
d. sin -4π/3 = √3/2, cos -4π/3 = -1/2
Step-by-step explanation:
See unit circle
i don’t know this pls help
The perimeter of the right triangle is 228 inches
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.
Since it is a right triangle,
c² = 57² +76²
c² = 3249 + 5776
c² = 9025
c= √ 9025 = 95
Perimeter is the sum of all sides
Perimeter = 57+76+95 = 228 inches
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A $280 suit is marked down by 30%. Find the sale price.
Answer:
To find the sale price of the suit, we need to first calculate the discount. The discount is equal to the original price multiplied by the discount rate, which in this case is $280 * 30% = $84.
Then we subtract the discount from the original price to find the sale price: $280 - $84 = $196.
So the sale price of the suit is $196.
Step-by-step explanation:
help plz 20 points help plz its math
Answer: A
Step-by-step explanation:
Daphine flips a coin four times. What is the probability that it lands on rails all four times?
Answer:
4/8 if you need simplified version its 1/2
Step-by-step explanation:
A coin has 2 sides. If you flip a coin one time, the possibility of getting a tails would be 1/2.
times 1/2 by 4 (since your flipping it four times)
Find the height of the triangle.
Answer:
72.83
Step-by-step explanation:
61²+x²=95²
3721+x²=9025
x²= 5304
x= 72.83
What type of correlation (association)? The outside temperature and the amount of layers you wear.
Answer:
negitive corralation
Step-by-step explanation:
The outside temperature and the number of layers you wear. represents a negative correlation.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
As we know a negative correlation is a relationship between two variables in which one increases while the other decreases and a positive correlation is a relationship in which one variable increases while the other decreases.
The case of the two variables that are outside temperature and the number of layers you wear represents the negative correlation because in the summer temperature increases and the number of layers decreases that you wear.
In the winter when the temperature goes down the number of layers increases that you wear.
Thus, the outside temperature and the number of layers you wear. represents a negative correlation.
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I need help with my math final!!
Answer:
8
Step-by-step explanation:
90x5=450
548-450=98
98divede12=8..2
Answer: is 14
Step-by-step explanation: its 14 but i dont know how to explain it
Which number is the prime factorization for: 2 x 3 x 3 x 5
Answers:
90
180
18
95
Answer:
90
Step-by-step explanation:
2*3*3*5=
90
Answer:
90
Step-by-step explanation:
2 × 3 × 3 × 5
2 × 3 × 15
2 × 45
90
Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is l. Use function notation.
what does P(11) represent in this situation? What is its value?
For a roll of paper with dimensions 3 feet cut to any desire length,
a) The value of perimeter when cut to 2.5 feet is 11 feet.
b) The complete table with filled perimeter column is present above . The function notation for perimeter is , P =2(L+ W)
c) P(11) , represents the length of paper cut to 11 feet in this situation. It's value i.e., P(11) = 28 feet .
Perimeter is defined as the sum of all boundary length of any geometry. We have a roll of paper with dimensions 3 feet ( i.e, width) is cut to any length. From, it we conclude that that paper is like quadrilateral shape but not square.
a) when the paper cut in a length of 2.5 feet , so, length (L) = 2.5 feet
The perimeter of quadilateral ( rectangle in this case ) is 2(L+W) so, perimeter
= 2( 2.5 + 3)
= 11.0 feet
b) Now, we have to complete "perimeter coulmn ," in the table and side lengths are provided.
Width (w) = 3 feet
length (l) = 1 feet
perimeter = 2(4) = 8
similarly, side lengths (ft.) perimeter ( ft.)
2.5 11
1 8
2 10
11 28
L 2( L + W)
The functional notation for perimeter is
P = 2(L+W) .
c) P(11) represents the length of paper in feet when the paper is cut at a length of 11 feet . It's value is 28 feet . So, the value of P(11) is 28 feet.
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Complete question:
A roll of paper that is 3 feet wide can be cut to any length.
a. If we cut a length of 2.5 feet, what is the perimeter of the paper?
b. Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation.
c) what does P(11) represent in this situation? What is its value?
A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 41 miles north of the transmitter to a second city 42 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter
On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
city - north at (0,65)
city-east at (59,0)
Slope is m=(-65/59)
[tex]B= y - mx = 65 - (-65/59)(0) = 65[/tex]
The equation of the line between the cities is y = (-65/59)x + 65
[tex]x^2 + ( (-65/50)x + 65) )^2 = 47^2[/tex]
the intersection points are:
(20.698, 42.197) and (43.998,16.527)
The transmitter is within range between those to points along the line.
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