The events are not independent.
The probability of selecting a football card and a basketball card is 0.16.
What is the probability?Probability is the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of selecting a football card and a basketball card = (number of football cards / total number of cards) x (number of basketball cards / total number of cards)
2/10 x 8/10 = 0.16
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f(x) = 4x² + 5x - 3
g(x) = 4x³
3x² + 5
Find (f+g)(x).
Answer:
[tex]4x^3+7x^2+5x+2[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=4x^2+5x-3[/tex]
[tex]g(x)=4x^3+3x^2+5[/tex]
[tex]\begin{aligned}\implies (f+g)(x)=f(x)+g(x) & = (4x^2+5x-3) + (4x^3+3x^2+5) \\& = 4x^2+5x-3+4x^3+3x^2+5 \\& = 4x^3+4x^2+3x^2+5x-3+5 \\& = 4x^3+7x^2+5x+2 \\\end{aligned}[/tex]
Audrey takes a sheet of paper and makes a diagonal cut from one corner to the opposite
corner, making two triangles. The cut she makes is 87 inches long and the width of the paper
is 60 inches. What is the paper's length?
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Solution:}}}}}}[/tex]
Let us take the width of the paper as base, the cut she made be hypotenuse and the paper's length be perpendicular.
Here,
Hypotenuse (H) = 87 inch
Base (B) = 60 inch
Perpendicular (P) = [To be calculated]
As, we can use Pythagoras theorem to find. So by using Pythagoras theorem :
H² = P² + B²
[tex] {87}^{2} = {P}^{2} + {60}^{2} \\ \\ \implies \: 7569 = {P}^{2} + 3600 \\ \\ \implies \: 7569 - 3600 = {P}^{2} \\ \\ \implies3969 = {P}^{2} \\ \\ \implies \: P = \sqrt{3969} \\ \\ \implies \: P = 63[/tex]
The length of the paper is 63 inches.
[tex] \boxed{ \frak \pink{BrainlyDamurai}}[/tex]
Simplify the expression to a + bi form:
√4+ √−4+√36 + √−4
Answer:
8 + 4i
Step-by-step explanation:
according to the bi form, the solution to the expression √4+ √−4+√36 + √−4 would be 8 + 4i
Which polynomial function could be represented by the graph below?
A. [tex]f(x) = x^2 - 4x[/tex]
B. [tex]f(x) = x^2 + 4x[/tex]
C. [tex]f(x) = -x^2 - 4x[/tex]
D. [tex]f(x) = -x^2 + 4x[/tex]
Answer:
[tex]f(x) = {x}^{2} + 4x[/tex]
Step-by-step explanation:
The graph is concave up, this means that the leading term x^2 is positive.
[tex]f(x) = {x}^{2} + 4x[/tex]
[tex]y = {x}^{2} + 4x[/tex]
For the x intercept, let y = 0[tex] {x}^{2} + 4x = 0[/tex]
[tex]x(x + 4) = 0[/tex]
[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]
The x intercepts are:
(0 , 0) and (-4 , 0)
For the y intercept, let x = 0
[tex]y = {0}^{2} + 4(0) = 0[/tex]
y intercept :(0, 0)
For the turning point:[tex]t.p = \frac{x1 + x2}{2} [/tex]
[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]
[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]
Turning point:(-2 , -4)
If you connect all these coordinates you will get the parabola shown in the picture.
please help !!!! and please answer every question not just one part.
Answer:
1) C. x-1 tells us that it has decreased by a value
2) original number of apples
3) 4(x-1)=28. Divide by 4, then take the 1 over
To predict the outcome of the vote for the town budget, the town manag assigned random numbers and selected 12F registered voters. He then called these vote and asked how they planned to vote. Is th town manager's sample representative of population? Explain.
The town manager's sample is not representative of population as he only picked females.
What is a sample representative?It should be noted that a sample representative simply means a subset of a population which seeks to reflect the characteristics of the larger group.
In this case, the town manager's sample is not representative of populationas he only picked females. The males too ought to be given an equal chance.
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solve for x.
2-[x+4(6-x)+16]-10=38-8x
Exact form is x = 86/11
Mixed number form is x = 7 whole number 9/11
What effect does the circled point have on the standard deviation of the residuals? This point will increase the value of the standard deviation of the residuals because it has a large positive residual. This point will increase the value of the standard deviation of the residuals because it has a large negative residual. This point will not affect the value of the standard deviation of the residuals because it has a large positive residual. This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.
The effect of this circled point is that: A. it will increase the value of the standard deviation of the residuals because it has a large positive residual.
What is the standard deviation of residuals?The standard deviation of residuals is also referred to as root mean square deviation and they are typically used in statistics to calculate the rate at which data points spread around a given regression line.
By critically observing the scatter plot shown in the image attached below, we can infer and logically deduce that the circled point will increase the value of the standard deviation of the residuals because it has a large positive residual.
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Complete Question:
A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect does the circled point have on the standard deviation of the residuals?
If x1 = 4, then x² + 1/x² =
Answer:
257/16
Step-by-step explanation:
Given :
x¹ = 4Then :
x² + 1/x²(x¹)² + 1/(x¹)²(4)² + 1/(4)²16 + 1/16257/16A shop has 4 fruits (bananas, oranges, apples, and grapes) and 2 dips (peanut butter and caramel).
Zeke's mom randomly buys 1 fruit and 1 dip for his lunch.
What is the probability that she selects his favorite option: bananas and peanut butter?
Answer:
total fruits and dips=4+2=6
P(select banana&peanut butter)=banana+peanut /total fruits and d
Step-by-step explanation:
total fruits and dips=4+2=6
P(select banana&peanut)=banana+peanut/total fruits and dips
P(select banana&peanut)=1+1=2/6
=1/3
Write an equation for the line through the point (1,3) parallel to
the line y =
1/2x + 10.
Answer:
y=1/2x+5/2
Step-by-step explanation:
The slope will not change if the line is parallel.
So start with 1/2x and plug in 1.
You will get 1/2 and you need to get a total of 6/2 to get a y of 3.
since you already have 1/2 the remanding value needed is 5/2 and once you add the two you will get 6/2 which equals a y of 3.
The diagram shows triangles ABC and PQR. ABC is mapped to PQR by combining two single transformations
Any ideas for this question
===========================================================
Explanation:
Let x = length of side BC
This is the height of the cylinder. Think of a can that is laying on its side. The radius of this can or cylinder is CD
If point B has x coordinate of 12, and BC is 12 units long, this must mean point C has x coordinate of 12-x. This is plugged into the function to show that CD has a length of exactly [tex]\sqrt{12-x}[/tex]
This is the radius of the cylinder
The volume of a cylinder is [tex]V = \pi*r^2*h[/tex]
Plug in the radius and height mentioned to get this function in terms of x
[tex]V = \pi*\left(\sqrt{12-x} \ \right)^2*x[/tex]
That simplifies to
[tex]V = \pi(12-x)x[/tex]
or
[tex]V = \pi(12x-x^2)[/tex]
Ignore the pi portion for now.
We wish to maximize the function f(x) = 12x-x^2
Use either calculus (specifically derivatives) or a graphing calculator to find that the vertex is at (6, 36)
This means x = 6 leads to the largest f(x) value being 36.
Therefore, the volume V is maxed out when x = 6 and we get a max volume of 36pi cubic units.
how many significant figures are there in the number 11
Answer: the maximum of three
Step-by-step explanation: each number has 2 significant figures. so 10.85 has four significant figures and must be rounded to 11 so it can have a maximum of three
15.23*3.6=54.83
For what value of x does 4 superscript x baseline = (one-eighth) superscript x 5?
An equation is formed of two equal expressions. The value of x for which 4ˣ=(1/8)ˣ⁺⁵ is 3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The value of x for which 4ˣ=(1/8)ˣ⁺⁵ is,
4ˣ=(1/8)ˣ⁺⁵
(2²)ˣ = (2⁻³)ˣ⁺⁵
2²ˣ = 2⁽⁻³ˣ⁺¹⁵⁾
2x = -3x + 15
5x = 15
x = 3
Hence, the value of x for which 4ˣ=(1/8)ˣ⁺⁵ is 3.
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You have been given data about gas prices in 15 states. Comparing the two data sets below, what does the larger standard deviation, range, and variance say about gas prices in 2022 compared to gas prices in 2018?
Gas Prices in 2018 Gas Prices in 2022
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.11
Max: $5.87
Min: $4.48
Mean: $4.83
Median: $4.72
Mode: $4.72
Variance: 0.0142
Standard Deviation: $0.38
Comparing the two data sets shown below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
Both the mean and the median can be used to describe where the “center” of a dataset is located.
So, the mean of data in 2022 is more than mean of data in 2018.
It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.
As the variance of 2022 more than in variance in 2018.
A high variance indicates that the data points are very spread out from the mean, and from one another.
As the standard deviation of 2022 more than in standard deviation in 2018.
The high standard deviation indicates data are more spread out.
The bigger the range, the more spread out the data.
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Write in point-slope form an equation of the line that passes through the given point and has the given slope. Point: (4, 8); m = 3/4
Answer:
[tex]\mathsf{y-8=\cfrac{3}{4}(x-4)}[/tex]
Step-by-step explanation:
Hi student, let me help you out!
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ..... ........ ...... ... ......... .... ....
First, let's recall the point-slope form equation: ↪ [tex]\mathrm{y-y_1=m(x-x_1)}[/tex].
where: y₁ = y-coordinate of the point (the second coordinate), m=slope, x₁=x-coordinate (the first coordinate).
Let's stick in the values accordingly. We obtain the following: [tex]\mathrm{y-8=\cfrac{3}{4}(x-4)}[/tex], which is our point-slope form equation.
Hope this helped you out, ask in comments if any queries arise.
Best Wishes!
[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{4}}[/tex]
What is the name of the numeral system we use today?.
I need help in this question if highly appreciate it if someone can help me solve this problem
Answer:
The one you chose is correct.
Step-by-step explanation:
The scale factor is 1.5. We know QP is 5. QP is the corresponding side to KJ. So, we multiply 5 with 1.5 and get 7.5 which is equal to 15/2
I found the scale factor by dividing LK which was 9 and QR which was 6.
9/6=1.5.
Hope this helps
Write the following ratio using two other notations.
[tex] \frac{1}{3} [/tex]
Answer:
1:3
1 to 3
Step-by-step explanation:
The other notations a ratio [tex]\frac{a}{b}[/tex] can be written in are a:b and a to b.
From what we are given, a = 1 and b = 3, so in the form a:b, the ration would be 1:3 and in the form a to b it would be 1 to 3.
help im being timed plssss
The value of cos 45 in a right angle triangle is 1/√2.
What is the trigonometry ratio?The trigonometry ratios are ratios that can be used to determine the side and angles of a triangle depending on the known parameter. The basic trigonometry ratios are denoted by the acronym: SOH CAH TOA
i.e.
Sin θ = opp/hypCos θ = adj/hypTan θ = opp/adjFrom the given diagram, we are to find the Cos 45°
i.e.
θ = 45°
Let's recall the angle 45 45 90 theorem that states that right angles have the following values for the sides:
hypotenuse = √2opposite = 1adjacent = 1Since
Cos θ = adj/hyp
Cos 45 = 1/√2
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please answer, much appreciated!!!!!
Answer:
i don't understand your question
Step-by-step explanation:
the simplification lf (x^3+2x-3)-(x^2-2x+4)
Answer:
x³ - x² + 4x - 7
Step-by-step explanation:
(x³ + 2x - 3) - (x² - 2x + 4)
remove first parenthesis and distribute second parenthesis by - 1
= x³ + 2x - 3 - x² + 2x - 4 ← collect like terms
= x³ - x² + 4x - 7 ← in standard form
How to find a fraction from a decimal
Answer:
0.6= 6/10
[tex]0.6 = 6 \div 10[/tex]
Step-by-step explanation:
To convert a decimal to a fraction
place the decimal number over its place value
For example
in 0.8 the 8is in the tenths place,
so we place 6 over 10 to create the equivalent fraction, 8/10.
example 2
=6.25
625/100
25/4
What is the slope of the line that passes through the pair of points?
(5, 8), (9,-3)
Answer:
-11/4
Step-by-step explanation:
slope = [tex]\frac{-3-8}{9-5} =\frac{-11}{4}[/tex]
Hope this helps
Answer:
-11/4
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (-3 - 8)/(9 - 5) = -11/4
Johnni guessed on all 8 questions of a multiple-choice quiz. each question has 4 answer choices. what is the probability that she got exactly 3 questions correct? round the answer to the nearest thousandth. p (k successes) = subscript n baseline c subscript k baseline p superscript k baseline (1 minus p) superscript n minus k. subscript n baseline c subscript k baseline = startfraction n factorial over (n minus k) factorial times k factorial endfraction 0.004 0.208 0.422 0.792
The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
What is Probability ?Probability can be defined as the likeliness of
If you use the formula P(r)=[tex]^nC_r P^rq^{n-r}[/tex]
P is the probability of success = 3/4 = .25
the total number of questions is n = 8
the total number of questions that Johnni got correct is r = 3
the probability of getting an answer wrong is q = 1-0.25 = 0.75
Substituting all of these values
[tex]^8C_3 P^3 (0.75)^{8-3}[/tex]
= .208.
The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
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Answer:
B. 0.208
Step-by-step explanation:
edge 2023
Solve the system of equations x + y = 14 and 5x - 3y = 38 by combining equations. +y = 14) -3y =38) (5x X +y = 14 5x -3y = 38 try 0x0y= You must answer all questions above in order to submit.
Answer:
6x+2y=52
Step-by-step explanation:
If you just drop down the answers, like for the first set x+5x=6x, so thats the first term and so on.
Consider function g.
g(x)={(6,-8<=(-2)<-2 ),(0,-2<=(-2)<4),(-4,4<=(-2)<10):}
What are the values of the function when x = -2 and when x = 4?
g(-2) = __
g(4) = __
By evaluating the piecewise function, we get:
g(-2) = 0.
g(4) = 4.
How to evaluate the piecewise function?A piecewise function is a function that behaves differently in different parts of its domain.
Here, we first want to get g(-2). x = -2 belongs to the second domain, then we use that part:
g(-2) = 0.
For x = 4, it belongs to the third domain, then we have:
g(4) = 4.
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Add the polynomials.
(3x^2+5x−3)+(4x^2+2x)
7x^2+7x−3
7x^2+5x+5
3x^2+9x−1
x^2+5x−3
Nashville is 595 feet above sea level. You board an airplane and the pilot ascended 39000 feet. Write the two integers that represent this scenario.
To solve this problem, let's simply find the difference in the distance between the two locations.
EquationTo express this integer, we need to define the locations with variables and then calculate the difference.
Nashville = A = 595ftPilot = B = 39000ftThe difference between the two location can be written as
[tex]Pilot - Nashville = B - A = 39000 - 595 = 38405ft[/tex]
The two integers that represent this scenario are 595 and 39000 respectively.
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