She has cards that go from 9 to 21.
We assume she has one card with each number that goes from 9 to 21:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
If we want to calculate the probability she pulls a card lower than 17, we have to count how many cards are lower than 17 and then divide this number by the total amount of cards.
NOTE: each card is a possible event. We will calculate the probability as the quotient between the number of successful events (cards lower than 17) and the total possible events (number of cards available).
We have 17-9 = 8 cards that are lower than 17.
The total number is 22-9 = 13 cards (all the cards lower than 22).
Then, we can calculate the probability as:
[tex]P(C<17)=\frac{8}{13}[/tex]Answer: The probabilty she pull a card lower than 17 is P=8/13
A line passes through(1,-5) and (-3,7) write an equation for the line in point-slope form Rewrite the equation in slope-intercept form A. Y-5=1/3(x+1) ; y =1/3x + 16/3 B. Y+5=-3(x-1); y=-3x-2 C. Y-1=1/3(x+5);y=-1/3x+3/8 D. Y-5=3(x-1);y=3x+8
Step 1: Concept
Write the formula for the equation of a line in terms of point-slope form
and in slope-intercept form.
[tex]\begin{gathered} Pi\text{ont slope form is given below} \\ y-y_1=m(x-x_1) \\ \text{Slope}-\text{intercept form} \\ y\text{ = mx + c} \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Where
m = slope
c = intercept
Step 2: Represent the coordinates
[tex]\begin{gathered} (x_1,y_1\text{ ) = (1, -5)} \\ (x_2,y_2\text{ ) = ( -3, 7)} \end{gathered}[/tex]Step 3: Find the slope, using slope formula.
[tex]\begin{gathered} m\text{ = slope} \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{7\text{ -(-5)}}{-3\text{ -1}} \\ m\text{ = }\frac{7\text{ + 5}}{-4} \\ m\text{ = }\frac{12}{-4} \\ m\text{ = -3} \end{gathered}[/tex]Step 4: Write an equation for the line in point-slope form.
[tex]\begin{gathered} \text{y - y}_1=m(x-x_1) \\ y\text{ -(-5) = -3(x - 1)} \\ \text{y + 5 = -3(x - 1)} \end{gathered}[/tex]Step 5: Simplify the equation in 4 to write the equation in slope-intercept form.
y + 5 = -3(x - 1)
y + 5 = -3x + 3
y = -3x + 3 - 5
y = -3x - 2
Final answer
Option B
y + 5 = -3(x - 1)
y = -3x - 2
Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.
SOLUTION
The given expression is:
[tex](x-4)^5[/tex]Using binomial theorem, the function is expanded as follows:
[tex](x-4)^5=x^5+5(x)^4(-4)^+\frac{5(5-1)}{2!}x^3(-4)^2+\frac{5(5-1)(5-2)}{3!}x^2(-4)^3+\frac{5(5-1)(5-2)(5-3)}{4!}x^(-4)^4+(-4)^5[/tex]This gives:
[tex](x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024[/tex]The pascal triangle is shown:
Using pascal triangle the expansion is shown:
[tex]\begin{gathered} (x-4)^5=x^5+5x^4(-4)+10x^3(-4)^2+10x^2(-4)^3+5x(-4)^4+(-4)^5 \\ (x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024 \end{gathered}[/tex]4(3y-7)=-3(-2y) - 4
What is the y
Answer:
y=4
Step-by-step explanation:
first we have to distribute
4(3y)+(4)(-7)=-3(-2y)-4
12y-28=6y-4
6y-28=-4
6y=24
y=4
Hopes this helps please mark brainliest
f(x) = 3x² +5
g(x) = 4x - 2
h(x) = x²-3x+1
Find f(x) + g(x) - h(x).
O 2x² + 7x + 2
O 2x² + x + 2
O 5x² + 4
O 7x² + x +4
Answer:
f(X)+g(X)-h(X)
3x²+5+4x+2-(x²-3x+1)
3x²+5+4x+2-x²+3x-1 [opened the brackets and changed the signs]
3x²-x²+4x+3x+5+2-1 [arranged the liked terms]
2x²+7x+7-1
2x²+7x+6
I don't see my answer in your options but trust me I have learned this and I am pretty sure that my answer is correct!!!!!!!
What is 32/3 as a proper fraction also I am gay if you don't agree don't help and my name is Oliver
A fraction can be proper or improper.
When a fraction is proper, the numerator is less than the denominator, and therefore, the fraction is less than unity. For example:
[tex]\frac{3}{4}=0.75<1[/tex]When a fraction is improper the numerator is greater than the denominator and therefore the fraction is greater than unity. For example:
[tex]\frac{9}{5}=1.8>1[/tex]So, in this case, you have
[tex]\frac{32}{3}=10.67>1[/tex]Then, as you can see 32/3 is an improper fraction.
To take it to a proper fraction, you can convert this fraction into a mixed number.
A mixed number is made up of an integer part and a proper fraction.
So, you have
[tex]\begin{gathered} \frac{32}{3}=\frac{10\cdot3+2}{3}=\frac{10\cdot3}{3}+\frac{2}{3}=10+\frac{2}{3}=10\frac{2}{3} \\ \text{ Then,} \\ \frac{32}{3}=10\frac{2}{3} \end{gathered}[/tex]Therefore, 32/2 as a proper fraction will be
[tex]10\frac{2}{3}[/tex]Explain the different ways a linear equation can be transformed. Then give an example and describe the transformation. (It's not a Test, I don't know how to explain that's why)
Answer: Translation, Rotation, or Reflection
Step-by-step explanation: The graphs of linear functions can be transformed without changing the shape of the line by changing the location of the y-intercept or the slope of the line. Those lines can be transformed by translation, rotation, or reflection, and still follow the slope-intercept form y = MX + b
A self-tanning lotion advertises that a 4-oz bottle will provide six applications. Jen found a great deal on a 19-oz bottle of the self-tanning lotion she had been using. Based on the advertising claims, how many applications of the self-tanner should Jen expect?
The number of applications of the self-tanner that Jen should expect would be= 28.5 applications
What is self-tanning lotion?A self-tanning lotion is defined as the type of lotion that can be used to artificially tan the skin and it is applied topically.
The number of applications for 4oz of the lotion= 6
The number of applications for 19oz of the lotion= X
Make X the subject of formula;
X = 19×6/4
X = 114/4
X= 28.5 applications
Therefore, based on the advertisement claims of a 19 Oz bottle of self-tanning lotion, the number of applications Jen should expect is 28.5.
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in general the ____ of a linear model represents how the two types of data change in correlation of each other.1. trend line2. y-intercept3. slope4. x intercept5. correlation coefficient
How 2 tipes of data change
it could be two options
Trend line
Coefficient of correlation
On a school trip, there are 9 boys, 10 girls and 4 adults. Write each as a ratio.Girls to Boys10:9Boys and Girls to Adults9:10:4Adults to Boys and Girls4:9:10
Given
Boys = 9
Girls = 10
Adults = 4
Find
ratio
Explanation
girls to boys
as girls are 10 and boys are 9 ,
so the ratio =
[tex]10\colon9[/tex]boys and girls to adults
boys and girls = 9 + 10 = 19
so the ratio =
[tex]19\colon4[/tex]adults to boys and girls
[tex]4\colon19[/tex]Final Answer
a) 10:9
b) 19:4
c) 4:19
2. Microsoft Corp. has made an offer to acquire 1.5 million shares of Apple$374 per share. They offered Apple 10 million shares of Microsoft worth $25 pershare, but they need to make up the difference with other shares. They have othershares worth $28 per share. How many of the $28 shares (to the nearest share) dothey also have to offer to make an even swap? Explain your work using words,numbers, and/or pictures
A sun is a distant of galaxy what is the distance
We would divide the mass of the sun by the mass of the earth. From the information given,
mass of earth = 5.972 x 10^24
mass of sun = 1.61244 x 10^31
Number of earths = 1.61244 x 10^31/5.972 x 10^24 = 2.7 x 10^6
It will take 2.7 x 10^6 to equal the mass of the sun
The graph of a function is shown on the coordinate plane below. Which relationship represents a function with the same slope as the function graphed?
If (x_1, y_1) and (x_2, y_2) are points of a line, its slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]From the graph of the function, we see that the line passes through the points:
• (x_1, y_1) = (-1, 6),
,• (x_2, y_2) = (0, 1).
The slope of the line is:
[tex]m=\frac{1-6}{0-(-1)}=-5.[/tex]A) Using the points:
• (x_1, y_1) = (-2, 0),
,• (x_2, y_2) = (2, 10).
We find that the slope of this line is:
[tex]m=\frac{10-0}{2-(-2)}=\frac{10}{4}=2.5.[/tex]This function has not the same slope as the line of the graph.
B) The general equation of a line is:
[tex]y=m\cdot x+b\text{.}[/tex]Where m is the slope and b is the y-intercept.
Comparing the general equation with the equation:
[tex]y=-5x+3,[/tex]we see that the slope of the line of this equation is m = -5.
This function has the same slope as the line of the graph.
C) Using the points:
• (x_1, y_1) = (-4, 8),
,• (x_2, y_2) = (0, 5).
We find that the slope of this line is:
[tex]m=\frac{5-8}{0-(-4)}=-\frac{3}{4}=-0.75.[/tex]This function has not the same slope as the line of the graph.
D) Comparing the general equation with the equation:
[tex]y=-\frac{5}{4}x+2.[/tex]we see that the slope of the line of this equation is m = -5/4.
This function has not the same slope as the line of the graph.
Answer
B. y = -5x + 3
Find an equation of the line that goes through the points (-10,13) and (-4,7). Write your answer in the formY=mx+b
1) In this problem, let's plug those points into the slope formula to get the slope, i.e. the measure of how steep is the line between those points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-13}{-4-(-10)}=\frac{-6}{6}=-1[/tex]2) Now, let's find the y-intercept, a.k.a. the linear coefficient "b". To do that we need to plug into the Slope-Intercept Formula one of those points, the slope, and solve it for "b"
[tex]\begin{gathered} (-4,7),m=-1 \\ y=mx+b \\ 7=-4(-1)+b \\ 7=4+b \\ 7-4=b \\ b=3 \end{gathered}[/tex]3) Therefore, the equation of the line is:
[tex]y=-x+3[/tex]If a1=2 and an+1 =(an)² - 4 then find the value of a4
From the Question given, we are able to write the following relationship:
[tex]\begin{gathered} a_1=2 \\ a_{n+1}=(a_n)²-4 \end{gathered}[/tex]By substituting the values 1, 2, and 3, we are able to calculate as follows:
[tex][/tex]Suppose that the demand and supply for artificial Christmas trees is given by the functions below where p is the price of a tree in dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold/bought at this price.p=109.70−0.10q (demand function)p=0.01q2+5.91 (supply function)
The equilibrium price is the price at which the demand function is equal to the supply function.
Hence it is given by:
[tex]\begin{gathered} 109.70-0.10q=0.01q^2+5.91 \\ 0.01q^2+0.10q-103.79=0 \end{gathered}[/tex]Solve the quadratic equation to get:
q=97,-107.
Now the quantity cannot be negative hence the value of q=97. Hence 97 hundred trees is the demand.
The equilibrium price is given by:
[tex]p=109.70-0.10q=100\text{ dollars}[/tex]Hence Option A is correct and the boxes to be filled is given by the statement given below:
The equilibrium price of $100 gives a demand that is equal to a supply of 97 hundred trees.
Convert the repeated decimal 0.47 into a fraction using infinite geometric series.
Answer:
47/99
Explanation:
Given the repeated decimal 0.4747...
This can be splitted into;
0.47 + 0.0047 + 0.000047 + ...
On rewriting;
47/100 + 47/10000 + 47/1000000 + ...
The given series is a geometric progression
The sum to infinity of a geometric progression is expressed as;
[tex]S\infty\text{ = }\frac{a}{1-r}[/tex]a is the first term
r is the common ratio
From the sequence;
a = 47/100
r = (47/10000)/(47/100)
r = 47/10000 * 100/47
r = 1/100
Substitute;
[tex]\begin{gathered} S\infty\text{ = }\frac{\frac{47}{100}}{1-\frac{1}{100}} \\ S\infty\text{ = }\frac{\frac{47}{100}}{\frac{99}{100}} \\ S\infty\text{ = }\frac{47}{100}\cdot\frac{100}{99} \\ S\infty\text{ = }\frac{47}{99} \end{gathered}[/tex]Henec the repeated fraction to decimal is 47/99
7.) Write the equations below in words m=2×7÷9
Given
[tex]m=2\cdot\frac{7}{9}[/tex]
Procedure
m is equal to the multiplication of 2 by 7 and then divided by 9.
x^2- 20x = -2x – 80In (x+a)^2=b form please hurry
Completing Squares
It's given the following equation:
[tex]x^2-20x=-2x-80[/tex]We are required to express the equation in the form:
[tex](x+a)^2=b[/tex]The first step is sending all the variables to the left side of the equation.
Adding 2x:
[tex]\begin{gathered} x^2-20x+2x=-80 \\ \\ \text{Simplifying:} \\ x^2-18x=-80 \end{gathered}[/tex]To complete squares, we need to recall the following identity:
[tex]p^2+2pq+q^2=(p+q)^2[/tex]The expression on the left side is missing the third term to be a perfect square. Note that comparing
p=x
2pq = -18x
This means that
q = -18x/2p
q = -18x/2x
q = -9
Now we know the value of the second term, we need to add q^2=81:
[tex]x^2-18x+81=-80+81[/tex]The left side of the equation is the square of x-9, and the right side can be calculated:
[tex](x-9)^2=1[/tex]Now we have the required expression, where a=-9 and b = 1
-------------------
Describe how the graph of the function is a transformation of the original function f.y=f(x+16)This results in a Answer shift to the graph Answer units Answer.
When we add a constant to the argument of a function, we are shifting the graph horizontally. If the constant is positive, the graph gets shifted to the left, if it's negative, the graph gets shifted to the right.
With this in mind we can solve the problem. The constant "16" was added to the argument of the function "f(x)". This results in a "horizontal" shift to the graph "16" units "to the left".
Which of the following equations is the translation 2 units down of the graph of y = Ixl?y = |x - 2|y = |x + 2|y = |xl - 2y = Ixl + 2
Answer:
y = | x | - 2
Explanation:
If we have a function g(x) = f(x) + c, we can say that g(x) is a translation of c units up or down of f(x)
If c is negative, the translation is c units down.
Therefore, the translation of 2 units down of the graph y = | x | is:
y = | x | - 2
An employee makes $10.51 per hour but is getting a 3% increase. What is his new wage per hour to the nearest cent?
First, we find 3% of $10.51.
[tex]0.03\cdot10.51=0.32[/tex]Then, we add this increase to $10.51.
[tex]10.51+0.32=10.83[/tex]Hence, the new wage per hour is $10.83.write a cubic function with the three open blue points as roots
Okay, here we have this:
Considering the provided points, we are going to write a cubic function with these points as roots, so we have this:
The factored function will be equal to the multiplication of three binomials, where the first term will be x and the second will be each root with an inverse sign. Then we have:
[tex]f(x)=\mleft(x+2\mright)\mleft(x-2\mright)\mleft(x-6\mright)[/tex]Now we are going to operate each term to obtain the expanded function:
[tex]\begin{gathered} f(x)=x^2x+x^2\mleft(-6\mright)-4x-4\mleft(-6\mright) \\ f(x)=x^3-6x^2-4x+24 \end{gathered}[/tex]The last one we write is the function we are looking for and satisfies the requested roots.
Find F-1(x), the inverse of F(x), for 3 and 4
Solving for number 3:
Step 1. Define the function.
The original function we have is:
[tex]F(x)=x-10[/tex]Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:
[tex]y=x-10[/tex]Step 3. Now, we are going to interchange the letters x and y (swap x and y):
[tex]x=y-10[/tex]Step 4. Finally, the last step is to solve for y:
[tex]y=x+10[/tex]change y for F-1(x), and the inverse function is:
[tex]F^{-1}(x)=x+10^{}[/tex]Answer:
[tex]F^{-1}(x)=x+10[/tex]Answer:
Solving for number 3:
Step 1. Define the function.
The original function we have is:
Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:
Step 3. Now, we are going to interchange the letters x and y (swap x and y):
Step 4. Finally, the last step is to solve for y:
Change y for F-1(x), and the inverse function is:
Answer:
Step-by-step explanation:
9Philip is saving money to buy a new computer. He saves the same amount ofmoney each week.After 2 weeks of saving, Philip still needs $520 to buy the computer.After 6 weeks of saving, Philip still needs $300 to buy the computer.How much does the computer cost?
First let's calculate how much money Philip saves each week.
In 4 weeks, he saved 520 - 300 = $220, so he saved 220/4 = $55 per week.
Then, we have that after 2 weeks of saving, he still needed $520, so before this saving, he needed:
[tex]\begin{gathered} 520+2\cdot55 \\ =520+110 \\ =630 \end{gathered}[/tex]So the computer costs $630.
jon: 1 ptgiven by f(x) = |x| – 4. Find each of the indicated function values.(b) f(4)(c) f(a + 4)(Simplify your answer.)
we have
f(x) = |x| – 4
Part b
f(4)
so
For x=4
substitute in the expression above
f(4) = |4| – 4
f(4)=4-4
f(4)=0
Part c
f(a+4)
so
For x=(a+4)
substitute
f(a+4) = |(a+4)| – 4
f(a+4)=a+4-4
f(a+4)=a
A student cafeteria has 24 tables, tables X has 4 seats each, tables Y has 6 seats each, and tables Z has 10 seats each. The total seating capacity of the cafeteria is 148. For a student meeting, half of tables X, 1/4 of tables Y, and 1/3 of tables Z will be used, for a total of 9 tables. Determine X, Y, and Z. ( Answer the final answer in a full sentence. )
Answer: For a meeting, half of x, 1/4 of y, and 1/3 of z will be used for a total of 9 tables:
[tex]\begin{gathered} x+y+z=9 \\ \\ \\ \\ \frac{1}{2}x=\frac{4}{2}=2 \\ \\ \frac{1}{4}y=\frac{6}{4}=\frac{3}{2} \\ \\ \frac{1}{3}z=\frac{10}{3} \\ \\ \text{ Since we have a total of 9 tables therefore we have:} \\ \\ 3x+3y+3z\Rightarrow\text{ Total number of chairs.} \\ \\ 3(2)+3(\frac{3}{2})+3(\frac{10}{3})=6+\frac{9}{2}+10 \\ \\ \\ \text{Therefore:} \\ \\ ------------------------------- \\ \\ x=6 \\ \\ y=\frac{9}{2} \\ \\ z=10 \end{gathered}[/tex]Therefore the x = 6 and y = 9/2 and z = 10 is the answer.
which graph represents the inequalities.2x+y>4. i attatched the graphs below.
Answer:
Explanations:
According to the given question, you are to find the graph that represents the inequality 2x+y>4.
First, we need to find the x and y-intercept of the line.
For x-intercept
x-intercept occurs at the point where y = 0.
[tex]\begin{gathered} 2x+y=4 \\ 2x+0=4 \\ 2x=4 \\ x=2 \end{gathered}[/tex]Hence the x-intercept occur at (2, 0)
For the y-intercept
y-intercept occurs at the point where x = 0
[tex]\begin{gathered} 2(0)+y=4 \\ y=4 \end{gathered}[/tex]Hence the y-intercept s at (0, 4)
To get the correct graph, we will look at the line that has an x-intercept at (2, 0) and y-inercept at (0, 4)
Use the Remainder Theorem to explain whether or not (x − 2) is a factor of F(x) = x4 − 2x3 + 3x2 − ax+ 3
The remainder theorem states that when a polynomial P(x) is divided by (x - a), for some number a, the remainder r is equal to P(a). Also states that when P(a) = 0, then (x - a) is a factor of P(x).
Then, let us see the result of evaluating the given polynomial when x = 2.
[tex]\begin{gathered} x=2 \\ F\lparen x)=x^4−2x^3+3x^2−ax+3 \\ F(2)=2^4−2(2)^3+3(2)^2−a(2)+3 \end{gathered}[/tex]starting at 00 if you were to go up 7 units and left for you is what coordinates would you end up at what quadrant would you be in
The coordinate is starting from the origin
7 units up and 4 units to the left
My coordinate will be (4, 7)
This is because the up is positive y- axis and the left is postive x - axis as well
X = 4 and y = 7
Joining the two points together will end up in the first quadrant
The answer is (4, 7) and First quadrant
At a party, there are 40 prizes, which are either kazoos or whistles. The tape diagram shows the ratio of kazoos to whistles.
kazoos: 3-15
whistles: 5-25
Total Prizes: 8-40
Khan Academy
Using ratios we know that there are 15 kazoos and 25 whistles out of the total 40 gifts.
What are ratios?In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons. Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.So, the complete number of prizes—is 40 kazoos or whistles.
The ratio of whistles to kazoos is shown in the diagram.The original proportion of kazoos to whistles was therefore 3:5.Using this ratio, the total prize equals 3 + 5 = 8.Assume that there are 3 times as many Kazoos.Whistles = number of times 5We can state that 3/8 of the total rewards will be kazoos and 5/8 of the total awards will be whistling in this case.
Quantity of kazoos: 3/8 × 40 = 15The quantity of whistling: 5/8 × 40 = 25Therefore, using ratios we know that there are 15 kazoos and 25 whistles out of the total 40 gifts.
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