Given
Table of names
Procedure
Names end with an E
Gabe
Steve
The probability would be independent and equal to:
[tex]\begin{gathered} \frac{2}{6}\cdot\frac{2}{6} \\ \frac{4}{36} \\ \\ \frac{1}{9} \end{gathered}[/tex]The probability would be 1/9
The table represents a linear function.What is the slope of the function?y08-2.04х-4-2-112-10-14-22-26O 2O 5
Answer
Option B is correct.
The slope of this function = -4
Explanation
For a linear function, the slope of the line can be obtained when the coordinates of two points on the line or the values of the linear function (y) at different values of x are known. If the two points are described as (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the two extreme points, (x₁, y₁) and (x₂, y₂) are (-4, -2) and (2, -26).
x₁ = -4
y₁ = -2
x₂ = 2
y₂ = -26
[tex]\text{Slope = }\frac{-26-(-2)}{2-(-4)}=\frac{-26+2}{2+4}=\frac{-24}{6}=-4[/tex]Hope this Helps!!!
suppose that the amount of time it takes to build a highway vadies directly with the length of the highway and inversely with the number of workers. suppose also that it takes 300 workers 22 week to build 24 miles of highway. how long will it take 225 to build 27 miles of highway
4.) explain clearly in your own words why the triangles and figure 12.3 to have area 1/2 (b•h) for the given choice of base B and height h
The area of the right angled triangle as well as that of the isosceles triangle is calculated as
Area = 1/2 (b * h)
The explanation is logical, observe the right angled triangle (the one on the left) and you'll see that the length covered by the height (labelled as h) is not the entire width covered by the base (labelled as b) unlike what you have in a rectangle or square. Its only logical to multiply the base by half of the height, otherwise you might end up calculating the area of a rectangle.
That applies to all triangles in general, the area is calculated as
[tex]A=\frac{1}{2}bh[/tex]a bread recipe calls for 3 3/8 cups of white flour and 2 1/2 cups of whole wheat flour. How many cups of flour in all?
Answer:
5 complete cups and 7/8 of a cup
[tex]5\frac{7}{8}[/tex]Cube A has a side length of 8 inches and cube B has a side length of 2 inches. What isthe ratio of the volumes of cube B to cube A?ABMath Bits.com8"2"O 16Submit AnswerOhO 30da
The ratio of the volume of cube B to the volume of cube A is 1/64
Explanation:The volume of cube A is 8^3 = 512 cubic inches
The volume if cube B is 2^3 = 8 cubic inches
The ratio of the volume of cube B to the volume of cube A is:
8/512 = 1/64
Ashlee was born on 09/08/1981. How many eight digit codes could she make using the digits in her birthday
Ashlee could make 2520 eight digit codes using the digits in her birthday .
In the question
it is given that
the birthdate of Ashlee is 09/08/1981.
So, the number of digits are 0,0,1,1,8,8,9,9 .
number of digits = 8
So, 8 digits can be arranged in 8! ways
8! = 8*7*6*5*4*3*2*1 = 40320
Repeating digits are
0 repeated 2 times = 2! = 2
1 repeated 2 times = 2! = 2
8 repeated 2 times = 2! = 2
9 repeated 2 times = 2! =2
So, the number of 8 digits codes is = 8!/(2!*2!*2!*2!)
= 8!/(2*2*2*2)
= 40320/16
= 2520
Therefore , Ashlee could make 2520 eight digit codes using the digits in her birthday .
The given question is incomplete , the complete question is
Ashlee was born on 09/08/1981. How many eight digit codes could she make using the digits in her birthday ?
Learn more about Arrangement here
https://brainly.com/question/22670644
#SPJ1
1)Find the probability of randomly selecting the correct access code on the first try 4 digits (0 through 9)2)find the probability of NOT selecting the correct access code on the first try
There are 10 digits from 0 to 9.
First digit 10 ways
Second digit 10 ways
Third digit 10 ways
Fourth digit 10 ways
[tex]\text{There are 10}\times10\times10\times10\text{ ways for four digits.}[/tex][tex]\text{There are 10}000\text{ ways for four digits.}[/tex]Hence the total outcomes =10000
Selecting the correct access code on the first try given favorable outcomes =1.
[tex]\text{The probability of randomly selecting the correct access code on the first try=}\frac{favorable\text{ outcome}}{\text{Total outcomes}}[/tex][tex]\text{=}\frac{1}{10000}[/tex][tex]=0.0001[/tex]Hence the probability of randomly selecting the correct access code on the first try is 0.0001.
The probability of not selecting the correct access code on the first try=1-The probability of selecting the correct access code on the first try
The probability of not selecting the correct access code on the first try=1-0.0001
Hence the probability of not selecting the correct access code on the first try=0.9999.
100 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degrees and classifications of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
The expression that represents the area of the rectangle is 6x² + 29x + 35. The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
Area of the rectangle = L × W square units
The sides of a rectangle are (2x + 5) units and (3x + 7) units, respectively. Then the area of the rectangle will be given as,
A = (2x + 5)(3x + 7)
A = 2x(3x + 7) + 5(3x + 7)
A = 6x² + 14x + 15x + 35
A = 6x² + 29x + 35
The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.
More about the area of the rectangle link is given below.
https://brainly.com/question/20693059
#SPJ1
Answer:
[tex]\textsf{A.} \quad \textsf{Area}=(2x+5)(3x+7)[/tex]
B. Degree = 2.
Classification = Quadratic trinomial.
C. Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).
Step-by-step explanation:
Part AArea of a rectangle
[tex]\boxed{A=lw}[/tex]
where l is the length and w is the width.
Given that a rectangle has sides measuring (2x + 5) units and (3x + 7) units, the area can be expressed as a product of the two sides:
[tex]\implies \textsf{Area}=(2x+5)(3x+7)[/tex]
Part BFOIL method
[tex]\boxed{(a + b)(c + d) = ac + ad + bc + bd}[/tex]
Expand the brackets of the equation found in part A by using the FOIL method:
[tex]\implies \textsf{Area}=6x^2+14x+15x+35[/tex]
[tex]\implies \textsf{Area}=6x^2+29x+35[/tex]
The degree of a polynomial is the highest power of a variable in the polynomial equation. Therefore:
The degree of the function is 2.A polynomial is classified according to the number of terms and its degree.
The number of terms in the polynomial is three, therefore it is a trinomial.The degree of the function is 2, therefore it is quadratic.Part CClosure property under Multiplication
A set is closed under multiplication when we perform that operation on elements of the set and the answer is also in the set.
Therefore, Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).
What percent of 120 is 30?
To find what percent of 120 is 30.
We will use the relationship
[tex]\frac{is}{of}\times100\text{ \%}[/tex]In our case
[tex]\begin{gathered} is=30 \\ of=120 \end{gathered}[/tex][tex]\frac{30}{120}\times100\text{ \%=25\%}[/tex]Thus, the answer is 25%
Identify the function rule from the values in the table.
we are given a table of inputs and ouputs of a function. We notice that each output is obtained by multiplying the input by -4:
[tex]\begin{gathered} (-2)(-4)=8 \\ (0)(-4)=0 \\ (1)(-4)=-4 \\ (3)(-4)=-12 \end{gathered}[/tex]Therefore, the right answer is A.
Sq root of z +3 + Sq root of Z -2 = 5
Find sin 2x, cos 2x, and tan 2x if tan x= -3/2 and x terminates in quadrant IV.
• sin 2x = -12/13
,• cos 2x = -5/13
,• tan 2x = 12/5
Explanation:Given that
[tex]\tan x=-\frac{3}{2}[/tex]Then
[tex]\begin{gathered} \sin2x=\frac{2\tan x}{1+\tan^2x} \\ \\ =\frac{2(-\frac{3}{2})}{1+(-\frac{3}{2})^2}=\frac{-3}{\frac{13}{4}} \\ \\ =-3\times\frac{4}{13}=-\frac{12}{13} \end{gathered}[/tex][tex]\begin{gathered} \cos2x=\frac{1-\tan^2x}{1+\tan^2x}=\frac{1-(-\frac{3}{2})^2}{1+(-\frac{3}{2})^2} \\ \\ =\frac{1-\frac{9}{4}}{1+\frac{9}{4}}=\frac{-\frac{5}{4}}{\frac{13}{4}}=-\frac{5}{4}\times\frac{4}{13}=-\frac{5}{13} \end{gathered}[/tex][tex]\begin{gathered} \tan2x=\frac{2\tan x}{1-\tan^2x}=\frac{2(-\frac{3}{2})}{1-(-\frac{3}{2})^2} \\ \\ =\frac{-3}{1-\frac{9}{4}}=\frac{-3}{-\frac{5}{4}}=-3\times\frac{-4}{5}=\frac{12}{5} \end{gathered}[/tex]random variables, probability distributions and expected value Alyssa likes to play roulette, but she doesn't like the low probability of betting on a single number. Therefore, she bets on a block of 4 numbers, increasing her probability of winning to 38. She generally places a $5 chip on her block of 4. If any other number comes up she loses her bet, but if one of her 4 numbers come up, she wins $40 (and gets to keep her bet!). What is the expected value for Alyssa playing roulette? Round to the nearest cent. Do not round until your final calculation.
We have to calculate the expected value for Alyssa playing roulette.
The expected value is calculated as the weighted sum of all the possible the outcomes, weighted by the probabilities of occurrence of this outcomes.
Then, we start by listing all the outcomes:
1) One of the numbers of the block comes up.
This will happen with a probability of 4 out of 38 (P=4/38). NOTE: The total numbers of the roulette are 38.
The net prize, that is excluding the $5 she bets, is $40.
2) None of the numbers of the block comes up.
That will happen with probability 34 out of 38 (P=34/38).
The net prize, as she will lose the $5 she bets, is -$5.
The expected value can be calculated as:
[tex]E=\sum ^2_{i=1}p_i\cdot X_i=\frac{4}{38}\cdot40+\frac{34}{38}\cdot(-5)=\frac{160}{38}-\frac{170}{38}=\frac{-10}{38}\approx-0.26[/tex]The expected value for Alyssa is -$0.26.
What is the first operation that should be performed to calculate (3 + 2) × 6÷5 - 4?
A) addition
B) division
C) subtraction
D) multiplication
Answer: A) addition
Step-by-step explanation:
because of BODMAS, you need to do the bracket first
A medical experiment on tumor growth gives the following data table.
x y
61 48
95 76
97 82
101 95
115 118
The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 2640.8 and the sum of squares of regression (SSR) was 2429.8. Calculate R2, rounded to three decimal places.
Provide your answer below:
The calculation of the coefficient of determination, or R² rounded to three decimal places is 0.080.
What is the coefficient of determination (R²)?The coefficient of determination, R², is a statistical measurement that determines the proportion of variance in the dependent variable that the independent variable can explain.
In other words, R² shows how well the actual data is approximated by the regression line.
R-Squared (R²) is widely used to predict future outcomes and for hypothesis testing because it provides information about the goodness of fit of the statistical model.
x y
61 48
95 76
97 82
101 95
115 118
The total sum of squares (SST) = 2640.8
The sum of squares of regression (SSR) = 2429.8
R² = 1 - SSR/SST
R² = 1 - 2429.8/2640.8
R² = 1 - 0.92
R² = 0.080
R² = 8%
Thus, with R² = 8%, we can conclude that the y values are only accountable for 8% of the variation in x.
Learn more about the coefficient of determination (R²) at https://brainly.com/question/17237825
#SPJ1
Adele opens an account with $140 and deposits $35 a month. Kent opens an account with $50 and also
deposits $35 a month. Will they have the same amount in their accounts at any point? If so, in how many
months and how much will be in each account? Complete the explanation.
have the same amount in their accounts at a certain point. Setting the expressions equal
which is (select)
and solving them gives 140=
They (select)
to each other gives 140 + 35x =
View Exampl
Step-by-Stepm
Textbook
Print
Turn it in
Save & Close
Answer: No
Step-by-step explanation:
If Adele opens an account with more money than Kent, and they deposit the same amount each month, Adele will always have more money than Kent.
Which steps show how to use the distributive property to evaluate 9 - 32? A. 9(32) = 9(30 + 2) = 9.30 + 9 - 2 = 270 + 18 = 288 0 B. 9(32) = 9(30 + 2) = 9 - 30 + 30 - 2 = 270 + 60 = 330 OC. 9(32) = 9(30 + 2) = 9.30 – 9.2 = 270 – 18 = 252 O D. 9(32) = 9(30 + 2) = 9.30 + 2 = 270 + 2 = 272
to find the distribution of
[tex]9\cdot32[/tex]rewrite 32 as an addition
[tex]32=30+2[/tex]rewrite the product
[tex]9\cdot(30+2)[/tex]distribute the 9
[tex]\begin{gathered} 9\cdot30=270 \\ 9\cdot2=18 \\ \\ 9\cdot(30+2)=9\cdot30+9\cdot2 \\ 9\cdot(30+2)=270+18 \\ 9\cdot32=288 \end{gathered}[/tex]Mr. Hanes places the names of four of his students, Joe, Sofia, Hayden, and Bonita, on slips of paper. From these, he intends to randomly select two students to represent his class at the robotics convention. He draws the name of the first student, sets it aside, then draws the name of the second student. Whats the probability he draws he draws Sofia then joe?
Given:
Total student = 4
Joe, Sofia, Hayden, and Bonita.
Find-:
Probability he draws Sofia then Joe.
Explanation-:
Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The formula of probability:
[tex]P(A)=\frac{\text{ Number of favorable outcomes to A}}{\text{ Total number of possible outcomes}}[/tex]For Sofia.
Total number of possible outcomes = 4
Favorable outcomes for Sofia = 1
So probability for Sofia :
[tex]P(S)=\frac{1}{4}[/tex]After the first student set it aside.
For Joe.
Total number of possible outcomes = 3
A favorable outcome for Joe = 1
So probability for Joe.
[tex]P(J)=\frac{1}{3}[/tex]So probability for Sofia then joe is:
[tex]\begin{gathered} P=\frac{1}{4}\times\frac{1}{3} \\ \\ P=\frac{1}{12} \end{gathered}[/tex]
can you help me with number 2? I am confused
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The equation of a circle is given as :
[tex](x-a)^2+(y-b)^2=r^2[/tex]comparing with the given equation:
[tex]\text{( x+5)}^2+(y-4)^2=9[/tex]we have that:
[tex]\begin{gathered} \text{Centre ( a, b ) = ( -5, 4)} \\ and\text{ } \\ \text{Radius = }\sqrt[]{9}=\text{ 3} \end{gathered}[/tex]CONCLUSION:
From the detailed explanation, we can see that the correct answer is:
[tex](-5,\text{ 4); r = 3 ( OPTION }C)[/tex]Figure A is a scale image of Figure B.27Figure AFigure B4535What is the value of x?
Answer:
x = 21
Explanation:
Figure A is a scaled version of figure B. This means that the ratio between any two sides must be the same for both figures.
It follows then
[tex]\frac{27}{45}=\frac{x}{35}[/tex]which just means that the ratio f sides 27 with 45 must be the same as the ratio between side x and 35. Why? Because these two sides are the same across the two figures and therefore their size with respect to each other must not change.
Now to find the value of x, we simply need to solve for x.
We do this by multipying both sides by 35:
[tex]undefined[/tex]g(x)=2x-2f(x)=4x-1Find (g*f) (-9)
Given:
[tex]\begin{gathered} g(x)=2x-2 \\ f(x)=4x-1 \end{gathered}[/tex]The expression for g(f(x)) is,
[tex]\begin{gathered} g(f(x))=2(f(x))-2 \\ =2(4x-1)-2 \\ =8x-2-2 \\ =8x \end{gathered}[/tex]Substitute x=-9 in the above expression.
[tex]\begin{gathered} g(f(-9))=8\times-9 \\ =-72 \end{gathered}[/tex]Thus, the final value of the expression is -72.
Hi could you help me find out the correct answer to this?
Given:
There are given two triangles.
Explanation:
According to the question:
We need to find the tall of Ariadne.
So,
To find the value, we need to use triangle proportion properties.
So,
Suppose the value of tall is x.
So,
[tex]\frac{x}{6}=\frac{15}{18}[/tex]We need to find the value of x.
Then,
[tex]\begin{gathered} \frac{x}{6}=\frac{15}{18} \\ x\times18=15\times6 \\ x=\frac{15\times6}{18} \\ x=5 \end{gathered}[/tex]Final answer:
Hence, the solution is 5 ft tall.
Sarah wanted to lose some weight, so she planned a day of exercising. She spent a total of 4 hours riding her bike and jogging. She biked for 35 miles and jogged for 6 miles. Her rate for jogging was 10 mph less than her biking rate. What was her rate when jogging?
Consider the relation,
[tex]\text{Speed}=\frac{\text{ Distance}}{\text{ Time}}[/tex]The total time taken by Sarah for biking and jogging is 4 hours.
Given that her speed for biking was 10 mph, the time taken to bike 35 miles is calculated as,
[tex]\begin{gathered} T_b=\frac{35}{10} \\ T_b=3.5\text{ hours} \end{gathered}[/tex]So, out of the total 4 hours of exercise, Sarah spent 3.5 hours riding her bike.
The remaining 0.5 hour must have been spent on jogging,
[tex]undefined[/tex]The width of a rectangle is 6x + 8 and the length of the rectangle is 12x + 16 determine the ratio of the width to the perimeter.Supply the following:Perimeter = 21 + 2w = Ratio= w/p Final answer in simplest form:
Solution:
For this case we know that the width is given by:
w = 6x +8
The lenght is given by:
l= 12x +16
And the perimeter would be given by:
P= 2l +2w = 2(12x+16)+ 2(6x+8)= 24x+32 +12x+16=36x + 48
And then the ratio would be:
[tex]\text{ratio}=\frac{6x+8}{36x+48}=\frac{3x+4}{18x+24}[/tex]Given that line S and line T are parallel, and line R is a transversal that cuts through lines S and T, which angles are alternate interior anglesZА A
The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, the resulting alternate inferior angles are congruent.
In this case:
You have a total of 21 coins, all nickels and dimes. The total value is $1.70. Which of the following is the system of linear equations that represent this scenario? Let n = the number of nickels and let d = the number dimes.
n = number of nickels
d = number of dimes
1 nickel = 5 cents
1 dime = 10 cents
total number of 21 coins:
n + d = 21
Total value = $1.70
5n + 10 d = 170
Divide by 100
0.05n + 0.10 d = 1.70
Answer:
n + d = 21
0.05n + 0.10 d = 1.70
The distance to your grandparent's house is 259 miles, and the distance to Atlanta is 555 miles. If it took 7 hours to drive to your grandparent's house, how long would you estimate the drive to Atlanta to take?
Answer:
15 Hours
Step-by-step explanation:
259miles = 7 hours
555miles = x
Cross Multiply
259x = 555×7
259x = 3885
Divide Both sides by 259
x = 3885 ÷ 259
x = 15 hours
It would take the driver 15 hours to get to Atlanta
Growth Models 19515. In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wagewas $2.30 per hour. Assume the minimum wage grows according to an exponentialmodel where n represents the time in years after 1960.a. Find an explicit formula for the minimum wage.b. What does the model predict for the minimum wage in 1960?c. If the minimum wage was $5.15 in 1996, is this above, below or equal to whatthe model predicts?
In general, the exponential growth function is given by the formula below
[tex]f(x)=a(1+r)^x[/tex]Where a and r are constants, and x is the number of time intervals.
In our case, n=0 for 1960; therefore, 1968 is n=8,
[tex]\begin{gathered} f(8)=a(1+r)^8 \\ \text{and} \\ f(8)=1.6 \\ \Rightarrow1.6=a(1+r)^8 \end{gathered}[/tex]And 1976 is n=16
[tex]\begin{gathered} f(16)=a(1+r)^{16} \\ \text{and} \\ f(16)=2.3 \\ \Rightarrow2.3=a(1+r)^{16} \end{gathered}[/tex]Solve the two equations simultaneously, as shown below
[tex]\begin{gathered} \frac{1.6}{(1+r)^8}=a \\ \Rightarrow2.3=\frac{1.6}{(1+r)^8}(1+r)^{16} \\ \Rightarrow2.3=1.6(1+r)^8 \\ \Rightarrow\frac{2.3}{1.6}=(1+r)^8 \\ \Rightarrow(\frac{2.3}{1.6})^{\frac{1}{8}}=(1+r)^{}^{} \\ \Rightarrow r=(\frac{2.3}{1.6})^{\frac{1}{8}}-1 \\ \Rightarrow r=0.0464078 \end{gathered}[/tex]Solving for a,
[tex]\begin{gathered} r=0.0464078 \\ \Rightarrow a=\frac{1.6}{(1+0.0464078)^8}=1.113043\ldots \end{gathered}[/tex]a) Thus, the equation is
[tex]\Rightarrow f(n)=1.113043\ldots(1+0.0464078\ldots)^n[/tex]b) 1960 is n=0; thus,
[tex]f(0)=1.113043\ldots(1+0.0464078\ldots)^0=1.113043\ldots[/tex]The answer to part b) is $1.113043... per hour
c)1996 is n=36
[tex]\begin{gathered} f(36)=1.113043\ldots(1+0.0464078\ldots)^{36} \\ \Rightarrow f(36)=5.6983\ldots \end{gathered}[/tex]The model prediction is above $5.15 by $0.55 approximately. The answer is 'below'
If 40% of the selling price of eight $65 sweater is profit then how much money profit does the store make when the sweater is sold
Remember that 40%=0.4.
Per sweater, the profit is
[tex]65\cdot0.4=26[/tex]$26 of profit per sweater.
Finally, for the eight sweaters, the total profit is
[tex]26\cdot8=208[/tex]$208 is the profit for 8 sweaters
Solve the system of two linear inequalities graphically. Graph the solution set of the first linear inequality? Type of boundary line? Two points on boundary line? Region to be shaded?
Answer:
Explanation:
Given the below system of linear inequality;
[tex]\begin{gathered} y<3 \\ y\ge-5 \end{gathered}[/tex]The graph of the linear inequality y < 3 will be a graph with a dashed line with a y-intercept of 3 since the inequality is not with an equal sign as seen below;
The graph of the 2nd linear inequality y >= -5 will be a graph with a solid line with a y-intercept of -5 since it has both the inequality sign and an equality sign as seen below;
