Answers
Solution
We draw a venn diagram to illustrate the information
Without the loss of generality
From the question we have that
[tex]\begin{gathered} n(C\cup Ch)=78 \\ \\ 58-x+x+57-x=78 \\ \\ 115-x=78 \\ \\ x=115-78 \\ \\ x=37 \end{gathered}[/tex]Therefore, the probability that a chosen customer carries both cash and checks is
[tex]\begin{gathered} p=\frac{37}{100} \\ \\ p=0.37 \end{gathered}[/tex]The answer is
[tex]0.37[/tex]
Related Questions
For a standard normal distribution, find:P(Z > c) = 0.7051Find C rounded to four decimal places.
Answers
Answer:
Explanation:
The given expression is
P(Z > c) = 0.7051
P(Z > c) = 1 - P(Z < c)
1 - P(Z < c) = 1 - 0.7051 = 0.2949
From the normal distribution table, the z score for a probability value of
factored from of polynomial need answer fast.(im sorry henry im very confused )
Answers
We have:
[tex]5p^3-10p^2+3p-6[/tex]We factor as follows:
[tex]p(5p^2-10p+3)-6[/tex][tex]\Rightarrow p(-\frac{1}{5}(-5x+\sqrt[]{10}+5)(5x+\sqrt[]{10}-5)-6[/tex]Solve for x.
-
5(x − 2) = -x + 2
3
x = [?]
I
Enter
Answers
5x-10= -x+2
5x+x = 2+10
6x=12
x=2
Answer: x= -13/4 OR -13=4
Step-by-step explanation: There you go just follow the distribution and then the multi step equations to solve the answer
−5(−2)=−+23
−5+10=−+23
−5=−+13
x = -13/4
pls help a washer and a dryer cost $649 combined.The washer costs $51 less than the dryer.What is the cost of the dryer?
Answers
Given in the question:
a.) A washer and a dryer cost $649 combined.
b.) The washer costs $51 less than the dryer.
From the given description, let's transform them into an equation.
Let,
x = Cost of washer
y = Cost of dryer
a.) A washer and a dryer cost $649 combined.
[tex]\text{ x + y = \$649}[/tex]b.) The washer costs $51 less than the dryer.
[tex]\text{ x = y - \$51}[/tex]From the generated equation, substitute x = y - $51 to x + y = $649.
We get,
[tex]\text{ x + y = \$649}[/tex][tex]\text{ (y - \$51) + y = \$649}[/tex][tex]\text{ y - \$51 + y = \$649}[/tex][tex]\text{ 2y = \$649 + \$51}[/tex][tex]\text{ 2y = \$7}00[/tex][tex]\text{ }\frac{\text{2y}}{2}\text{ = }\frac{\text{\$7}00}{2}[/tex][tex]\text{ y = \$350}[/tex]Therefore, the cost of the dryer is $350.
Let's find the cost of the washer.
[tex]\text{ x = y - \$51}[/tex][tex]\text{ x = \$350 - \$51}[/tex][tex]\text{ x = \$}299[/tex]Therefore, the cost of the washer is $299.
Owen bought 15 bananas for $9. What was the cost in banana per dollar
Answers
Answer: 0.6 I think.
Step-by-step explanation:
9 / 15 is 0.6
if I'm wrong I'm sorry!
I don't want to give people the wrong answers!
The life, in years, of a certain type of electrical switch has an exponential distribution with an average life of β = 5 years. If 200 of these switches are installed in different systems, what is the probability that at most 30 fail during the first year?
Answers
The probability that at most [tex]30[/tex] fail during the first year is 0.14550.
A certain type of electrical switch has an exponential distribution with an average life of [tex]\beta =5[/tex] years.
The installed switches in different systems n = 200.
We have to find the probability that at most 30 fail during the first year.
We can find the probability using,
P [tex]=1-e^{-1/\beta }[/tex]
Putting the value
P [tex]=1-e^{-1/5 }[/tex]
P [tex]=1-e^{-0.2}[/tex]
P [tex]=1-0.8187[/tex]
P = 0.1813
Now we find the mean[tex](\mu)[/tex].
[tex]\mu=n\times[/tex] P
[tex]\mu=200\times 0.1813[/tex]
[tex]\mu=36.26[/tex]
Now finding the standard deviation[tex](\sigma)[/tex].
[tex]\sigma=\sqrt{\mu(1-P)}[/tex]
Now putting the value
[tex]\sigma=\sqrt{36.26(1-0.1813)}[/tex]
[tex]\sigma=\sqrt{36.26\times0.8187}[/tex]
[tex]\sigma=\sqrt{29.686}[/tex]
[tex]\sigma=5.448[/tex]
z score,
[tex]z=\frac{(x-\mu)}{\sigma}[/tex]
Now probability that at most 30 fail during the first year.
From the continuity correction,
P(x ≤ 30) [tex]=P(x < 30.5)[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < \frac{30.5-36.26}{5.448})[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < \frac{-5.76}{5.448})[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < -1.058)[/tex]
From the standard table
P(x ≤ 30) = 0.1455
Hence, the probability that at most [tex]30[/tex] fail during the first year is [tex]0.1455[/tex].
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write the slope intercept form:through: (5, 1), perp. to x= -1
Answers
Select ALL parts of the triangle that are labeled ascongruent.
Answers
Given
Answer
AC congruent to GF
Angle A congurent to Angle G
AB congurent GH
B congurent to H
C congurent to F
BC congurent to FH
Given the equation 6x-y=98, find x if y=-2
Answers
x=16
Explanationgiven the function
[tex]6x-y=98[/tex]Step 1
as we need x is terms of y, let's solve for x
[tex]6x-y=98[/tex]a) add y in both sides
[tex]\begin{gathered} 6x-y+y=98+y \\ 6x=98+y \end{gathered}[/tex]b) divide both sides by 6
[tex]\begin{gathered} 6x=98+y \\ \frac{6x}{6}=\frac{98+y}{6} \\ x=\frac{98}{6}+\frac{y}{6}\Rightarrow equation \\ \end{gathered}[/tex]Step 2
now, evaluate for y=-2
[tex]\begin{gathered} x=\frac{98}{6}+\frac{y}{6}\operatorname{\Rightarrow}equat\imaginaryI on \\ replace \\ x=\frac{98}{6}-\frac{2}{6} \\ x=\frac{96}{6}=16 \\ x=16 \end{gathered}[/tex]therefore, the answer is
x=16
I hope this helps you
Yesterday, Reuben had 143 baseball cards. Today, he gave b away. Using b, write an expression for the number of cards Reuben has left. II +0 O-O ローロ Х 5 ? Continue Save For La 2022 McGraw Hill LLC. All Rights Reserved. Terms of U hp
Answers
ANSWER:
143 - b
STEP-BY-STEP EXPLANATION:
Given:
Original quantity: 143
Amount given away: b
The amount of cards Ruben has today will be equal to the difference between the original amount and the given amount, it will be written as the following expression:
[tex]143-b[/tex]ProgScore: 2/101/5 answeredQuestion 2<>A population has parameters u = 245.9 and o= 16.7. You intend to draw a random sample of size n = 83.What is the mean of the distribution of sample means?Hy =What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)=Question Help: D VideoSubmit Question
Answers
For a population with parameters as shown in the image below
(a) Mean of the distribution
[tex]\begin{gathered} \mu_{\bar{x}}\text{ = }\mu\text{ = 245.9} \\ \operatorname{mean}\text{ of the distribution = 245.9} \end{gathered}[/tex](b)Standard deviation of the distribution
[tex]\begin{gathered} \sigma_{\bar{x}\text{ }}\text{ = }\frac{\sigma}{\sqrt[]{n}} \\ \sigma_{\bar{x}\text{ }}\text{ = }\frac{16.7}{\sqrt[]{83}} \\ \sigma_{\bar{x}\text{ }}\text{ = }\frac{16.7}{9.11} \\ \sigma_{\bar{x}\text{ }}\text{ = 1.833} \\ \sigma_{\bar{x}\text{ }}\text{ = 1.83 (2 d.p)} \end{gathered}[/tex]Hence the value of the mean of the distribution = 245.9 and the standard deviation of the distribution = 1.83
Divide monomials ( -18p^4 q^7) (-6p^3 q^8) / -36p^12 q^10
Answers
Given:
[tex]\frac{(-18p^4q^7)(-6p^3q^8)}{-36p^{12}q^{10}}[/tex]We will use the following rules of the exponents:
[tex]\begin{gathered} \frac{a^m}{a^n}=a^{m-n} \\ a^m\cdot a^n=a^{m+n} \end{gathered}[/tex]So, the given expression will be as follows:
[tex]\begin{gathered} \frac{(-18p^4q^7)(-6p^3q^8)}{-36p^{12}q^{10}}=(\frac{-18\cdot-6}{-36})\cdot p^{4+3-12}\cdot q^{7+8-10} \\ \\ =(-3)\cdot p^{-5}\cdot q^5 \\ \\ =\frac{-3q^5}{p^5} \end{gathered}[/tex]so, the answer will be:
[tex]\frac{-3q^5}{p^5}[/tex]Help!!!A copying service charges a uniform rate for the first one hundred copies or less and a fee for each additional copy. Nancy Taylor paid $7.00 to make 200 copies and Rosie Barbi paid $9.20 to make 310 copies.
What is the cost of the first one hundred copies?
Answers
The answer to both the subparts using equations are:
(A) The initial 100 copies are $5 each.(B) Each extra copy will cost you $0.02.What are equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others.So, the equations can be formed as:
100a + [(200 - 100)b] = 7 ⇒ 100a + 100b = 7 ..(1)100a + [(310 - 100)b] = 9.20 ⇒ 100a + 210b = 9.2 ..(2)Where a is the price of each of the first 100 copies and b is the price of the extra copies.The elimination method would be used to resolve the two equations that were formed above.
(B) Calculate equation 1 minus equation 2.
110b = 2.2B = 2.2 / 110 is the result of multiplying both sides by 110.
b = 0.02Each extra copy will cost: $0.02
(A) Replace b in equation 1 with:
100a + 100(0.02) = 7100a + 2 = 7Put similar terms together: 100a = 7 - 2
Add comparable terms: 100a = 5
A = 5 / 100, or multiply both sides of the equation by 100.a = 0.05The price for the first 100 copies is $0.05 x 100 = $5.
Therefore, the answer to both the subparts using equations are:
(A) The initial 100 copies are $5 each.(B) Each extra copy will cost you $0.02.Know more about equations here:
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Deductive Reasoning / 5913. Copy and complete the proof of Theorem 2-6: If the exterior sides of twoadjacent acute angles are perpendicular, then the angles are complementary.Given: OAI OGProve: Z AOB and 2 BOC are comp. 4.BProof:Statements0Reasons1?1. OA 1 OC2. m ZAOC = 903. m ZAOB + m2 BOC = m 2 AOC4.25. 22. Def. of 1 lines3. 24. Substitution Prop.5. Def. of comp. 4
Answers
Reasons
1. Given
3. Angle addition postulate
Statements
4.
[tex]m\angle\text{AOB}+m\angle\text{BOC}=90º[/tex]5.
[tex]\angle\text{AOB and}\angle\text{BOC are complementary}[/tex]stephen needs to place several cubic packages in a shipping box that measures 12 inches by 18 inches by 24 inches.
Answers
648cubes
Explanations
The formula for calculating the volume of a box is expressed as
[tex]V=lwh[/tex]where;
l is the length
w is the width
h is the height
Find the volume of the shipping box
[tex]\begin{gathered} V=12in\times18in\times24in \\ V=5184in^3 \end{gathered}[/tex]Determine the dimension of the cubic package
[tex]\begin{gathered} V_c=2in\times2in\times2in \\ V_c=8in^3 \end{gathered}[/tex]Determine the number of cubes that can fit in the shipping box.
[tex]\begin{gathered} number\text{ of cubes}=\frac{5184in^3}{8in^3} \\ number\text{ of cubes}=648cubes \end{gathered}[/tex]Therefore the maximum number of cubes that can fit into the box is 648cubes
What is 4 x 1/7
Give your answer in simplify fully
Answers
Answer: 4/7 or 0.571428
Step-by-step explanation:
convert the expression
4/1 x 1/7
multiply the fractions
4x1 / 1x7
calculate the products
4/7 or 0.571428
Answer:
4 * 1/7 simplified is 4/7
Step-by-step explanation:
let me know if you want a thorough explanation!
Doreen Schmidt is a chemist. She needs to prepare 32 ounces of a 9% hydrochloric acid solution. Find the amount of
16% solution and the amount of 8% solution she should mix to get this solution.
how many ounces of the 16% acid solution should be in the mixture?
how many ounces of the 8% acid solution should be in the mixture?
Answers
Answer:
See below
Step-by-step explanation:
She needs 32 ounces finshed product
x = 16 % amount amount of acid = .16x
then (32-x) = 8% amount amount of acid = .08(32-x)
final product 9% acid = .09 (32)
.16x + .08 ( 32-x) = .09(32)
solve for x = 16% amount = 4 ounces 8% then is 28 ounces
Find the equation of a line perpendicular to y= 1/2x+1that passes through the point (6,-2).
Answers
the slope must be the opposite reciprocal of 1/2,so it is -2 after you find the slope. use the point slope formula to find the answer
y+2=-2(x-6)
distribute the -2
y+2=-2x+12
subtract 2 to both sides to leave the y by itself
y=-2x+10
Hi - I am trying to get help with a math prob
Answers
1) In this case, let's do it by PEMDAS order of operations.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
2) So let's begin with the parentheses:
[tex]\begin{gathered} 8\div2(2+2)= \\ 8\div2(4) \\ 4(4) \\ 16 \end{gathered}[/tex]Round the following number to 2 decimal places 3.083
Answers
3.083 when rounded up to 2 decimal places is equal to 3.08.
given the graph of the function f(x) below what happens to f(x) when x is a very small postitive number
Answers
Hello!
This exercise asks the value of f(x) when x is a very small positive number. To solve it, we can analyze the attached graph below:
So, we are talking about the numbers that are positive and very close to 0 and its corresponding range.
I put a rectangle to show you the range (we have to analyze it).
So, let's look at it:
Each time the value of X gets closer to zero Y (or f(x)) tends to increase.
So, the answer will be the alternative C.
under the pink line is the answer, simply explain the process
Answers
The function is continuous at a = 5
Explanation:Given:
[tex]18)\text{ }f(x)\text{ = }\frac{2x^2+3x+1}{x^2+5x};\text{ a = 5}[/tex]To find:
If the function is continuous at a = 5
For a function to be continuous at a point, the limit exists for the point and the value of the function at that point must be equal to the limit at the point.
when x = 5
[tex]\begin{gathered} f(x)\text{ = }\frac{2(5)^2+3(5)+1}{(5)^2+5(5)} \\ \\ f(x)\text{ = }\frac{50\text{ + 15 + 1}}{25\text{ + 25}} \\ \\ f(x)\text{ = }\frac{66}{50} \\ \\ f(x)\text{ = }\frac{33}{25} \end{gathered}[/tex]Finding the limit at the point:
[tex]\begin{gathered} \lim_{a\to5}\frac{2x^2+3x\text{ + 1}}{x^2+5x} \\ \\ To\text{ get the limit at the point a = 5, we will susbtitute x with 5} \\ =\text{ }\frac{2(5)\placeholder{⬚}^2+3(5)+1}{(5)\placeholder{⬚}^2+5(5)} \\ \\ =\text{ }\frac{50+15+1}{25+25}\text{ = }\frac{66}{50} \\ \\ =\text{ }\frac{33}{25} \end{gathered}[/tex]The value of the function at that point is equal to the limit at the point.
Hence, the function is continuous at a = 5
A bacteria population grows by 10% every 2 years. Presently, the population is 80 000 bacteria. Find the population 12 years ago. (Can use log if needed but not “in”)
Answers
In this problem
we have an exponential growth function of the form
[tex]y=a(1+r)^{\frac{t}{2}}[/tex]where
r=10%=0.10
Let
t=0 ---------> 12 years ago
so
Presently -------> t=12 years, y=80,000 bacteria
substitute
[tex]\begin{gathered} 80,000=a(1+0.10)^{\frac{12}{2}} \\ a=\frac{80,000}{1.10^6} \\ \\ a=45,158\text{ bacteria} \end{gathered}[/tex]therefore
The population 12 years ago was 45,158 bacteriaEthan says that the value of 40.7 is 10 times the value of 4.07
Answers
The assumption Ethan made was correct
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Ethan said that the result of 10 and 4.07 is 40.7, thus we must verify that his computation is accurate.
In order to do such, we must multiply 10 by 4.07 as illustrated below:
= 10 x 4.07
= 10 x 407/100
= 4070/100
= 40.70
Since the outcome matches Ethan's hypothesis,
The conclusion is valid.
Hence, The result of Ethan is correct
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Given the function p(c)=c² +c:
a. Evaluate p(-3).
b. Solve p(c) = 2.
Answers
Answer: a. p(-3) = 6 b. c = -2 , c = 1
Step-by-step explanation:
a. Evaluate p(-3):
Step 1: Plug in -3 into c
p(-3) = (-3)^2-3
Step 2: Use PEMDAS
p(-3) = 9-3
Step 3: Subtract
p(-3) = 6
b. Solve p(c) = 2:
Step 1: Set the equation equal to 2
2 = c^2+c
Step 2: Bring the 2 to the right
c^2+c-2 = 0
Step 3: Factor
(c+2)(c-1) = 0
Step 4: Use the Zero Product Property
c = -2 , c = 1
Step-by-step explanation:
a.
this is totally easy.
we need to put the given value for c (-3) into all the places of c in the functional expression and then calculate.
p(-3) = (-3)² + -3 = 9 - 3 = 6
b.
this is a bit trickier.
p(c) = 2
so,
c² + c = 2
c² + c - 2 = 0
remember, how 2 sums are multiplied with each other :
(a + b)(c + d) = ac + ad + bc + bd
to make it clearer, the functional expression suggests that a = c.
so,
(c + b)(c + d) = c² + cd + bc + bd = c² + c(d + b) + bd
when we compare this to our equation c² + c - 2 = 0, that means
d + b = 1
-2 = bd
when we think about integer numbers, what comes to mind ?
d = 2
b = -1
or vice versa. but the sequence does not matter, because we bring them together in an addition and in a multiplication, where the commutative principle is active (the sequence does not matter).
so,
c² + c - 2 = (c + 2)(c - 1)
and that must be 0.
so,
(c + 2)(c - 1) = 0
when is a product 0 ? when at least one of the factors is 0.
therefore, either
c + 2 = 0
c = -2
or
c - 1 = 0
c = 1
the solution is
c = -2
or
c = 1
Mrs. lin is making several trays of her famous lasagna. She finds the mozzarella cheese on sale for $4.89 per pound at her local grocery store. How much will she pay for four pounds of cheese
Answers
We have the following:
since we have the value of per unit (that is, 1 pound) we only have to multiply by the number of pounds like this:
[tex]4.89\cdot4=19.56[/tex]Therefore, she will pay in total $19.56
Ben bought a book for $10.75 and a magazine for $3.99. Sales tax was $1.03. He paid with a $20 bill. How much change did he receive?
$4.77
$5.77
$5.23
$4.23
Can someone help I'm way too lazy to do the work rn
Answers
Answer:
4.23
Step-by-step explanation:
10.75+1.03=14.74+1.03=15.77. 20-15.77=4.23
Answer:
$4.23
Step-by-step explanation:
$10.75+3.99=$14.74
$14.74+ $1.03=$15.77
$20.00-$15.77= $4.23
Ben received $4.23 as his change.
State whether the following statement is true or false.Matrices of different orders can sometimes be multiplied.Choose the correct answer below.FalseTrue
Answers
ANSWER
True
EXPLANATION
We want to verify if matrices of different orders can sometimes be multiplied.
The order of a matrix refers to the configuration of the rows and columns of the matrix.
For matrix multiplication to occur, the dimensions of the matrices must be compatible. In other words, the number of columns inn the first matrix must be the same as the number of rows in the second matrix.
This is not affected by the number of rows in the first matrix or the number of columns in the second matrix.
Hence, under the right condition, matrices of different orders can sometimes be multiplied.
The answer is True.
Write four properties of cube numbers?
Answers
1. Cubes of all even natural numbers are even.
2. Cubes of all odd natural numbers are odd.
3. The sum of the cubes of first \ (n\) natural numbers is equal to the square of their sum.
4. Cubes of the numbers ending with \ (4, 5, 6\) and \ (9\) are the numbers ending in the same digit. ...
Hope this helps!
The table shows the results of a survey of students. The survey asked the students whether they have a job and whether they have a car. Job No Job Total Car 38 22 60 No Car 16 18 34 Total 54 40 94 What percentage of the students in the survey have a car?
Answers
Answer:
57.44%
Explanation
Total number of students that has a car = 38 + 16 + 54
Total number of students that has a car = 108
Total number of students = 60 + 34 + 94
Total number of students = 188
Percentage of those that have a car = 108/188 * 100
Percentage of those that have a car = 10800/188
Percentage of those that have a car = 57.44%
Hence the Percentage of those that have a car is 57.44%
