Answer:
[tex]a = \frac{1}{15}[/tex]
Step-by-step explanation:
Hey there!
To solve the given we'll use keep change flip.
[tex]\frac{1}{5} / 3 = a\\\\\frac{1}{5} *\frac{1}{3} = a\\\\\frac{1}{15} = a[/tex]
Hope this helps :)
Give an expression for the answer using permutation notation, combination notation, factorial notation, or other operations. Then evaluate. Of the first questions on a test, a student must answer . Of the second questions, the student must answer . In how many ways can this be done?
Answer:
This question is not complete. Let me explain the concept of combination and permutation.
Step-by-step explanation:
The general formula for factorial is n! = n×(n - 1)×(n - 2)×...×2×1
0! = 1
Example 1:
How many different words can we make using the letters D, S, K and Z?
Solution:
We have 4 letters here.
Therefore, to get the possibility of the numbers, we will use:
4! = 4 x 3 x 2 x 1 = 24. We have 24 different words that can be made with the letters.
Permutation
The general formula for permutation is n P r = n! / (n - r)!
Example 2:
Find 5 [tex]P_{3}[/tex]
Solution: This will give 5!/(5-3)! = (5 x 4 x 3 x 2 x 1) / 2!
= 120 / 2 x 1 = 120 / 2 = 60
Combinations
The general formula for combination is n C r = n! / [ (n - r)! r! ]
Example 3:
Find 4[tex]C_{3}[/tex]
Solution: 4[tex]C_{3}[/tex] will give 4!/(4-3)!3! = (4 x 3 x 2 x 1) / 1!3!
= 24 / 1(3 x 2 x 1) = 24 / 6 = 4
Example 4: In Nigeria, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates will be formed if neither the digits nor the letters are repeated?
Solution: Note that we have 26 letters in the alphabet chart.
(9 P 4) × (26 P 3) = 9!/(9-4)! x 26!/(26-3)! = 47,174,400
If 13 ounces of tea costs $3.19, how much would you expect to pay for 15 ounces of tea? (Round your answer to the nearest cent.
Answer: $3.68
Step-by-step explanation:
Calculate. (3 1/3 −1 5/6 ) ÷ 2 1/7 −1 1/3 · 2.4
A fair coin is tossed 3 times. What
is the probability of getting 2
heads in a row, given that exactly
2 heads occur?
Answer:
The ratio of successful events A = 3 to total number of possible combinations of sample space S = 8 is the probability of 2 heads in 3 coin tosses.
Step-by-step explanation:
Answer: [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
Given that there are exactly two heads out of three coins, we have the following possibilities:
H H T
H T H
T H H
Two of the three possible outcomes have two heads in a row.
[tex]\dfrac{\text{Number of "two heads in a row"}}{\text{Number of "exactly two heads"}}=\large\boxed{\dfrac{2}{3}}[/tex]
Using cross multiplication, which of the following is the solution to 7/3x = 2/(x+5)?
Step-by-step explanation:
Hey, there!!
[tex] \frac{7}{3x} = \frac{2}{x + 5} [/tex]
By cross multiplication,
[tex]7.(x + 5) = 2 \times 3x[/tex]
[tex]7x + 35 = 6x[/tex]
[tex]7x - 6x = -35[/tex]
Therefore, x= -35.
Hope it helps...
You have 19 shirts to choose from, 5 pants, and 2 pairs of shoes. How many different outfits can you make?
I am 2 digit number my ones place is a digit that is 2 less than six my tens place is double the amount of my ones place What number am I?
Answer:
I believe it is 48
Step-by-step explanation:
because 4 is two less than 6, and 4 doubled would be 8
Factoriseeeee COMPLETELY 12x²y² - 17xy- 40 (Show all steps) :D be quickkkk
12x²y² - 17xy - 40
xy (12xy - 17) - 40
As the x and y are shown in both variables but there is no other common factors. I didn't include the 40 as it didn't share any common factors with all of them.
Linda earns 10 dollars each hour working part-time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount (in dollars) that Linda earns in an hour if she sells B books. Write an equation relating A to B . Then graph your equation using the axes below. I get this right all up until the graphing. Can someone help me graph the equation properly? I have tried a question like this 2 times and we only have 3 attempts. It keeps switching on the test. My last attempt is next...
I’m thinking the graph should look like this since it starts at (0,10) and $1 for each book which is the x. I apologize if it’s wrong
A sector subtends an angle of 70 at the centre of a circle of radius 21cm. Calculate the area of the sector?
Answer:
12.8 cm^2
Step-by-step explanation:
Angle subtended by the sector=70
Radius of the circle= 21 cm
Area of the sector =[tex]\frac{given angle}{360}[/tex] x [tex]\pi r^{2}[/tex]
= [tex]\frac{70}{360}* \frac{22}{7}*21\\\\\frac{70}{360 } *22*3\\\frac{77}{6}\\ 12.8[/tex]
The number 430,290,100 in expenden form
Answer:
400,000,000+30,000,000+200,000+90,000+100
walk block.
a)sentence
b)fragment
Answer is fragment because is fragment walk block
Increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis. steepness.
The increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis which is stepness
What is stepness of line?The slope of a line is a measure of its steepness. In mathematics, the stepness or gradient of a line is a number that describes both the direction and the steepness of the line. The stepness of a line is defined as the change in y-values divided by the change in x-values.How to solve this problem?The steps are as follow:
Decreasing the value b decreases the line’s intersection with the y-axisSo the answer is stepnessTherefore the increasing the value of m increases the line’s intersection with the y-axis. intersection with the x-axis which is stepness
Learn more about Stepness of line here:
https://brainly.in/question/41191772
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Answer: C
Step-by-step explanation:
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us? 14 75 31 23 77 63 88 40 68 11 60 Range=nothing (Round to one decimal place as needed.)
Answer:
The range is 77.
The variance is 739.8.
The standard deviation is 27.2.
Step-by-step explanation:
The data provided, in ascending order is as follows:
S = {11 , 14 , 23 , 31 , 40 , 60 , 63 , 68 , 75 , 77 , 88}
The range of a data set is the difference between the maximum and minimum values.
From the above data set we know,
Maximum = 88
Minimum = 11
Compute the range as follows:
Range = Maximum - Minimum
= 88 - 11
= 77
The range is 77.
Compute the mean of the data as follows:
[tex]\bar x=\frac{1}{n}\sum x_{i}=\frac{1}{11}\times [11+14+23+...+88]=50[/tex]
Compute the variance as follows:
[tex]\sigma^{2}=\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}[/tex]
[tex]=\frac{1}{11-1}\times [(11-50)^{2}+(14-50)^{2}+...+(88-50)^{2}]\\\\=\frac{1}{10}\times 7398\\\\=739.8[/tex]
The variance is 739.8.
Compute the standard deviation as follows:
[tex]\sigma=\sqrt{\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}}=\sqrt{739.8}=27.199265\approx 27.2[/tex]
The standard deviation is 27.2.
Find the value of N: 1/N = 1/5 + 1/4 - 1/3 + 1/12
Answer:
1/ N = 1 / 5 + 1/ 4 - 1/ 3 + 1/12
taking L.C.M
Then,
or, 1/N = 5 + 6 / 20 - 13+ 4 / 12
or, 1/N = 11/ 20 - 7/12
or, 1/N = 14 - 12 / 60
or, 1/N = 2 / 60
NOW,
Do cross multiplication,
60 = 2N
or, 60 / 2 = N
so, N = 30
ANS
Evaluate the expression shown below and write your answer as a fraction in simplest form. 3 •1. 2 3
Answer:
[tex] \frac{9}{14} [/tex]
Step-by-step explanation:
Evaluate, [tex] -\frac{3}{2} [/tex] ÷ [tex] -\frac{7}{3} [/tex] by first changing the operation from division to multiplication and flipping the fraction by your right upside down.
Thus,
[tex] -\frac{3}{2} * -\frac{3}{7} [/tex]
Negative multiplied by negative = positive
[tex] \frac{3*3}{2*7} = \frac{9}{14} [/tex]
A recreation park measures 560 m long by 700 m wide. A 250-m by 150-m area of the park is used for soccer and baseball fields. How much of the area remains?
Answer:
354,500 square m
Step-by-step explanation:
Remaining area = Area of park - Area used for soccer and baseball field
= 560 * 700 - 250* 150
= 392,000 - 37,500
= 354,500 square m
The similarities and differences between correlation and regression Correlation and regression are two closely related topics in statistics. For each of the following statements, indicate whether the statement is true of correlation, true of regression, true of both correlation and regression, or true of neither correlation nor regression. Regression Correlation Both Correlation and Regression Neither Correlation nor Regression Can tell you whether one variable (such as smoking) causes another (such as cancer) Can be influenced by extreme values on one or both variables Can tell you the degree to which a linear relationship exists between two variables?
Answer:
Both variables Can tell you the degree to which a linear relationship exists between two variables.
Step-by-step explanation:
Correlation and regression are two statistical concepts that are closely related and complement each other. They are powerful tools used in modern-day machine learning and artificial intelligence.
Correlation evaluates the linear relationship between two variables, using regression as a tool to assess the degree at which a dependant variable changes ( either increasing or decreasing ) based on the value of an independent variable.
The correlation coefficient is the degree of the linear relationship between two variables, ranging from zero ( for non-linear) to one ( for highly linear).
Solve the system of inequalities by graphing.
2x+ 5y <25
y < 3x - 2
5x - 7 <14
Answer:
b
Step-by-step explanation:
Choice b is the only one that has the first equation properly graphed. The boundary line for that equation will have intercepts that can be found by setting the opposite variable to zero.
x-intercept = 25/2 = 12.5 (on the positive x-axis)
y-intercept = 25/5 = 5 (on the positive y-axis)
That is, the boundary line has a shallow negative slope, and is shaded below. Only graph 'b' has such a line.
Evaluate |3 - 5 + 7|.
-5
5
-15
15
Answer:
B. 5
Step-by-step explanation:
|3 - 5 + 7|=|- 2 + 7 | =| 5 | =5Answer is: B. 5
If f(x) = −-4x^{2} + 15, then f(−3) =
Answer:
f(-3) = -21
Step-by-step explanation:
To find f(-3), we just need to plug x = -3 into f(x) so:
f(-3) = -4 * (-3)² + 15
= -4 * 9 + 15 = -36 + 15 = -21
Answer:
[tex]\Huge \boxed{-21}[/tex]
Step-by-step explanation:
[tex]f(x) = -4x^{2} + 15[/tex]
f(-3), the input is -3 for the function f(x).
The value of x = -3
[tex]f(-3) = -4(-3)^{2} + 15[/tex]
Evaluate the expression.
[tex]f(-3) = -4(9)+ 15[/tex]
[tex]f(-3) = -36+ 15[/tex]
[tex]f(-3)=-21[/tex]
The value of f(-3) is -21.
Order these numbers from least to greatest.
5.09, 5.7, 5.7081, 5.009
Answer:
5.009, 5.09, 5.7, 5.7081
Answer:
5.009, 5.09, 5.7, 5.7081
Find the sum of (x + 5) and (2x + 3) *
A) 9x + 1
B) 5x + 2
C) 8x + 3
D) 3x + 8
Answer:
D
Step-by-step explanation:
We know that we are adding the two expressions because the question says "sum" which means that we need to add. Let's combine like terms. We know that x + 2x = 3x and 5 + 3 = 8 so the answer is 3x + 8.
Answer:
D. 3x+8
Step-by-step explanation:
We want to find the sum of (x+5) and (2x+3). Sum means addition, so we must add the 2 expressions.
(x+5)+(2x+3)
Now, we must simplify by combining like terms.
First, combine the terms with variables.
(x+2x) + (5+3)
3x + (5+3)
Next, add the constants, or terms without variables.
3x+ 8
The sum of (x+5) and (2x+3) is 3x+8. This makes choice D the correct answer.
The southward translation of the rose garden is along which axis? What integer represents a change of four yards south?
Going south means you're going in the negative direction along the y axis
Going 4 yards south would be represented as -4 on the y axis number line (this is the vertical number line)
Answer:
Southward translation of the rose garden will move it in the negative y-direction. The integer that represents a change of four yards south is -4.
Step-by-step explanation:
What are the next three terms in the sequence 2, -4, 8, -16, 32, ...?
Answer:
Hey there!
The next three terms are: -64, 128, -256.
Let me know if this helps :)
Answer:
-64, 128, -256
Step-by-step explanation:
Times -2 every step
The formula for the size of a file that was downloaded over time t and at an average rate r is r.t.
Siena downloaded a file at a rate of 800 kilobytes per second for about 110 seconds.
What calculation will give us the estimated size of the file Siena downloaded, in megabytes?
Answer:
The size of file downloaded is 88 megabytes.
Step-by-step explanation:
Given that:
Average rate of downloading the file = [tex]r[/tex]
Time taken to download = [tex]t[/tex]
Formula for the size of file downloaded = [tex]r.t[/tex]
Rate of downloading, [tex]r = 800\ kilobytes/sec[/tex]
Time taken, [tex]t[/tex] = 110 seconds
To find:
Size of file downloaded in megabytes = ?
Solution:
First of all, let us apply the given formula to find the size of file downloaded:
Size of file downloaded = [tex]r.t[/tex]
Size of file downloaded = 800 kilobytes seconds [tex]\times[/tex] 110 seconds =
88000 kilobytes.
Now, let us convert the unit kilobytes to megabytes to find the answer.
Conversion formula:
1000 kilobytes = 1 megabyte
Let us use unitary method to find the number of megabytes in 88000 kilobytes.
1 kilobytes = [tex]\frac{1}{1000}[/tex] megabytes
88000 kilobytes = [tex]\frac{1}{1000} \times[/tex] 88000 megabytes
[tex]\Rightarrow[/tex] 88 megabytes.
Therefore, the size of file downloaded is 88 megabytes.
Answer:
800/1000*110
Step-by-step explanation:
What is corrrectly plotted points for y=-x+3
Answer:
Here. I have graphed this for you. The points are at +3 and +3
Step-by-step explanation:
Write an inequality to represent the graph. a dashed line passing through points 0 comma negative 3 and 2 comma 2 with shading above it
A.y is greater than two fifths times x minus 3 B. y is less than two fifths times x minus 3 C. y is greater than five halves times x minus 3 D. y is less than five halves times x minus 3
Answer: y > (5/2)*x - 3
Step-by-step explanation:
Ok, the thins we should notice.
The line is shaded, so the values of the line are not solutions of the inequality, then we should use < or >.
The shaded part is above the line, so we have:
y > a*x + b.
A linear relationship can be written as:
f(x) = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now, we know that our line passes through the points (0, -3) and (2, 2)
Then the slope is:
a = (2 -(-3))/(2 - 0) = 5/2.
f(x) = (5/2)*x + b.
To find the value of b, we can replace the values of one of the points in the equation, let's use the point (0, -3)
f(0) = -3 = (5/2)*0 + b
-3 = b
Then the line is:
f(x) = (5/2)*x - 3
Then the inequality is:
y > (5/2)*x - 3
I don't know how to commit on these posts but the guy above is wrong.
Find the area of the shape shown below.
6
2.
units2
Answer:
12 [tex]units^{2}[/tex]
Step-by-step explanation:
square: 2 x 2 = 4 units sq
small triangle: 2 x 2 = 4, 4 / 2 = 2 units sq
big triangle: 2 x 6 = 12, 12 / 2 = 6 units sq
4 + 2 + 6 = 12 units sq
Answer:
12 units²
Step-by-step explanation:
we need to notice that the shape has two right triangles and a rectangle
the area of right triangles is b*h/2 and of the rectangle side*length
area of first triangle
Base=2
Height=2
[tex]A=\frac{2*2}{2} =2[/tex]
Area of the square
Side=2
Length=2
[tex]A_2=2*2=4[/tex]
Area of the second triangle
Base=2
Height=6
[tex]A_3=\frac{2*6}{2} =6[/tex]
so we need to add all three areas
[tex]A_T=A_1+A_2+A_3\\\\A_T=2+4+6=12\\\\A_T=12[/tex]
So the area is 12 units²
You have a lead ball with a mass of 420 g. The density of lead is 10.5 g/cm square. What is the volume of the ball?
Answer: Volume = 40 cm3
Step-by-step explanation: