Using the normal approximation to the binomial distribution, there is a 0.0060 = 0.60% probability that at least 12 sales will result from mailing to the 30 prospects.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in the context of this problem are given as follows:
n = 30, p = 0.2.
Hence the mean and the standard deviation for the approximation are given as follows:
[tex]\mu = np = 30 \times 0.2 = 6[/tex].[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{30 \times 0.2 \times 0.8} = 2.19[/tex]Using continuity correction, the probability that at least 12 sales will result from mailing to the 30 prospects is P(X > 11.5), which is one subtracted by the p-value of Z when X = 11.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (11.5 - 6)/2.19
Z = 2.51
Z = 2.51 has a p-value of 0.9940.
1 - 0.9940 = 0.0060.
Hence the probability is of 0.0060 = 0.60%.
More can be learned about the normal distribution at https://brainly.com/question/4079902
#SPJ1
Match the following.
Matching the given mathematical operation equations to the specified choices, gives;
A•B = B•A ; Commutative Property of Multiplication
A + B = B + A ; Commutative Property of Addition
(A•B)•C = A•(B•C); Associative Property of Multiplication
A•0 = 0; Multiplicative Property of 0
(A + B) + C = A + (B + C); Associative Property of Addition
A•1 = A; Multiplicative Identity
A + 0 = A; Additive Identity
What are the properties of mathematical operations?The properties of mathematical operations includes; inverse, associative, distributive, associative and commutative properties
Commutative propertyCommutative property in mathematics is one in which for a binary operation, the result of an operation remains unchanged when the order in which the operands appears in the expression is changed.
Therefore;
Commutative property of multiplication is therefore; A•B = B•A
Commutative property of addition is; A+B = B+A
Associative propertyAssociative property relates with operations that have results which remains the same when the parentheses in the expressions are rearranged.
Therefore;
(A•B)•C = A•(B•C) represents the associative property of multiplication
The associative property of addition is represented by (A+B)+C = A+(B+C)
Multiplicative property of 0The multiplicative property of 0, which can be understood as the zero product property, states that the product of any number and 0 is 0
Therefore, the equation, A•0 = 0, represents the multiplicative property of 0
Multiplicative and additive identityThe multiplicative and additive identity states that an expression remains the same following the product of the expression with an identity element such as 1, or following the addition of the expression with an identity element such as 0
The multiplicative and additive identity are therefore represented by A•1 = A and A + 0 = A respectively
Learn more about properties of mathematical operations here:
https://brainly.com/question/11035245
#SPJ1
Let f(x) = 5x²-2 and let g(x) = 3x + 1. Find (f + g)(2).
(f+g)(2)= (Simplify your answer.)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:(f+g)(x) = 5x² + 3x - 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 5 {x}^{2} - 2[/tex]
and
[tex]\qquad \tt \rightarrow \: g(x) = 3x + 1[/tex]
We need to find : (f + g) (x) = ?
[tex]\qquad \tt \rightarrow \: (f + g)(x) = f(x) + g(x)[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} - 2 + 3x + 1[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} + 3x - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Simplify: (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
7r³ + 11r²s -9rs² - 8s³ is the simplification of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
How to simplify equation?The process of writing an expression in the most effective and compact way possible without affecting the original expression's value is known as simplification of an algebraic expression.
Collecting similar terms is the process, which entails expanding or contracting the terms in an expression.
Let's review some of the crucial words used during expression simplification:
In an algebraic expression, a variable is a letter with an undetermined value.
A coefficient is a number that is used with a variable.A term with a fixed value is called a constant.Variables with the same letter and power are known as like terms. Sometimes, similar terms will have different coefficients.We have been asked to simplify the expression
(7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
Let's simplify
⇒ (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
⇒ 7r³ + 10r²s −3rs² − 8s + r²s -6rs²
⇒ 7r³ + 11r²s -9rs² - 8s³
Thus, 7r³ + 11r²s -9rs² - 8s³ is the simplified form of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
Learn more about simplification
https://brainly.com/question/13742517
#SPJ13
The city of St. Louis is creating a welcome sign on a billboard for visitors to see as they enter the city. The following picture needs to be enlarged so that 1/2 inch represents 7 feet on the actual billboard. Will it fit on a billboard that measures 14 feet in height if the height of the figure is 1 in?
The scale is 1/2 to 7 feet. That means that for each half of an inch of the original picture, the scaled figure will have 7 feet.
Now,
[tex]1\text{ in = }\frac{1}{2}in\text{ +}\frac{1}{2}in.[/tex]That means that 1 inch corresponds to 7ft +7ft= 14ft.
Therefore, if my original figure is 1 inch in height the scaled picture will be 14 ft in height.
Answer: The scaled figure will fit in the billboard.
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Lauren had brochures printed for her new business venture. She originally ordered 4 boxes of black-and-white brochures and 4 boxes of color brochures, which cost a total of $148. After those ran out, she spent $125 on 4 boxes of black-and-white brochures and 3 boxes of color brochures. Given that the prices didn't change, what was the price of each type of brochure?
Let the price of black and white brouchers be x
The price of color brochures be y.
A/q,
4x+4y=148.....(1)
4x+3y=125 .....(2)
The equation (1) becomes,
x+y=37
y=37-x.......(3)
Putting (3) in (2) we have,
4x+3(37-x)=125
4x+111-3x=125
x=14
Putting the value of x in (3) we have,
y=37-14=23
The price of black and white brouches is $14
The price of color brouchers is $23.
Phillip added 15 pencils to his collection. He then gave 30 pencils to a friend. Write and evaluate an expression
Answer:
x + 15 - 30
x -15
Step-by-step explanation:
please help me out i’ll give you brainlist !
Answer:
In order, the answers are d, b, c, a
Step-by-step explanation:
[tex] \frac{ {x}^{7} }{ {x}^{4} } = {x}^{3} [/tex]
[tex] {x}^{ - 3} = \frac{1}{ {x}^{3} } [/tex]
[tex] {x}^{0} = 1[/tex]
[tex] \frac{ {x}^{4} }{ {x}^{3} } = x[/tex]
For the triangle shown, find the length AD. (Assume u = 17, v = 17, ∠x = 25°, and ∠y = 25°
Using the law of Sines, the length of side AD, |AD|, is 7.44
Calculating lengthFrom the question, we are to determine the length of side AD
From the given information, we have that
u = 17 and v = 17
Then,
ΔBCD is an isosceles triangle
∴ m ∠DBC = m ∠ BCD
m ∠DBC = x = 25°
∴ m ∠BCD = 25°
Also,
m ∠BCA = ∠y + m ∠BCD
m ∠BCA = 25° + 25°
m ∠BCA = 50°
Now, we will determine the measure of ∠CAD.
m ∠CAD + m ∠DBC + m ∠BCA = 180° (Sum of angles in a triangle)
m ∠CAD + 25° + 50° = 180°
m ∠CAD = 180° - 25° - 50°
m ∠CAD = 105°
Now,
From law of Sines, we can write that
|AD| / sin DCA = |DC| / sin CAD
|AD| / sin y = u / sin CAD
|AD| / sin 25° = 17 / sin 105°
|AD| = (17 × sin 25°) / sin 105°
|AD| = 7.43795
|AD| ≈ 7.44
Thus,
Length AD is 7.44
Learn more on Calculating length here: https://brainly.com/question/22053910
#SPJ1
f(x) = x + 3g(x) = 2x2 - 4Find (f ·g)(x)
SOLUTION
f(x) = x + 3
[tex]undefined[/tex]Karen the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday therewere 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Karen trained her Monday clients fora total of 10 hours and her Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
ive n
lan A
Plan B
Monday: 3 clients - Plan A
5 clients - Plan B
Total 10 hours
Tuesday
6 clients - Plan A
2 clients - Plan B
Total 10 hours
rocedure
Let's define a system of linear equations that represents the above problem.
A: Number of hours of workout in plan A
B: Number of hours of workout in plan B
[tex]\begin{gathered} 3A+5B=10 \\ 6A+2B=10 \end{gathered}[/tex]The goal here is to solve
3A+5B=10 and
6A+2B=10 for the variables A and B.
The solutions to your equations are:
A = 5/4 hour
B = 5/4 hour
pls help i dont get it
Answer:
Step-by-step explanation:
Answer: You can add 5. The question is asking you what can you do to make both sides equal 8. I am not a professional but I hope that helped.
highest common factor of 106 and 104
The Greatest Common Factor (GCF) for 104 and 106, notation GCF(104,106), is 2.
Given that,
The numbers 106 and 104.
We have to find the greatest common factor of 106 and 104.
The greatest commo factor is nothing but the greatest common factor, which is the product of two or more numbers, is the largest number (GCF). By dividing them by the largest number, a natural number is produced (factor).There are a few factors that both share once all the number's factors have been identified. The common factor with the highest number among the others is said to be the greatest common factor. The GCF is often referred to as the highest common factor (HCF)
The factors of 104 are 1,2,4,8,13,26,52,104;
The factors of 106 are 1,2,53,106.
Therefore, as we can see, the Greatest Common Factor or Divisor is 2, because it is the greatest number that divides evenly into all of them.
To learn more about factor visit: https://brainly.com/question/24182713
#SPJ1
thank u plssssssss do it
Answer:
63
Step-by-step explanation:
23 + 94 = 117
180 degrees ( sum of all angles in a triangle)
180 - 117 = 63
A retailer owes a wholesaler $300,000 due in 45 days. If the payment is 15 days late, there is a 1% penalty charge. Since the bill isn't due immediately, the retailer can invest the $300,000 in a certificate of deposit and make money on the interest. The retailer has two options: a 45-day certificate of deposit (CD) earning 6% per year simple interest or a 60-day certificate earning 7% per year simple interest.
A 45-day certificate of deposit (CD) earning 6% per year simple interest. Simple interest and precise simple interest are the two types of simple interest. $2250 is simple interest for the 6% interest.
What is simple interest ?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest is the amount repaid for using borrowed funds over a predetermined amount of time.
Simple interest=p*n*r
=300000*6/100*45/365
=2250
Ordinary simple interest and precise simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest.
To learn more about simple interest refer to:
https://brainly.com/question/20690803
#SPJ1
f(x) = c f(-x) = c
Does f(x) = f(-x)?
Does f(-x) = f(x)?
+c does not equal -c
The equation of the functions given as f(x) =f(-x) and f(-x) = f(x) are true
How to determine the true statements?The functions are given as
f(x) = c
Also, we have
f(-x) = c
In the above function definitions, we can see that
The functions f(x) and f(-x) have the same value
i.e. f(x) = f(-x) = c
This means that f(x) =f(-x)
By the symmetric property of an equation, the above can also be rewritten as
f(-x) = f(x)
Hence, the functions f(x) =f(-x) and f(-x) = f(x) are true
Read more about functions at
https://brainly.com/question/2946572
#SPJ1
please its due tomorrow
1 Answer:
Evaluate the following expression when q = 13.
q-10
2 Answer:
Evaluate the following expression when x = 4.2.
34.5x
3 Answer:
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
1. The value of the expression when q = 13 in q - 10 is 3.
2. The value of the expression when x = 4.2.
34.5x is 144.9
3. The interest will be $5.25.
How to illustrate the information?It should be noted that an expression is simply used to show the relationship between the variables.
1. The expression when q = 13 in q - 10 will be:
= q - 10
= 13 - 10
= 3
2. The value in the expression when x = 4.2 will be:
= 34.5x
= 34.5 × 4.2
= 144.9
3. Principal = $70
Rate = 3%
Time = 2.5 years
Interest = PRT / 100
= (70 × 3 × 2.5) / 100
= $5.25
The simple interest would you earn in 2.5 years is $5.25.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2)
The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)
Which of these equations is quadratic?An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.
The initial constant, “a,” cannot be 0, and this is an unbreakable rule.
How do you translate a graph into some equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.
Thereafter draw a sloping triangle connecting the two spots you find on the line.
If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:
-2 = a(0+3)(0+1)
-2 = 4a
a = -1/2
So the equation can be written as y = -1/2 (x+3)(x+1)
To know more about quadratic equation, visit:
https://brainly.com/question/17177510
#SPJ13
What is the equation of the following graph
Answer:
y = 1
The graph has no gradient and only intersects at the y-axis.
When your spel of dice, there are several homes, showWhen rolling the dice, the outcome is expressed as a sum of the two dice. Forcrample, il after you rolled the dice, and one die was 33 and the other was 34 youwill have rolled aSelect all of the TRUE statements below There may be more than oneThe probabiliny troling the same digit with cach die is 1/4The odds in favour of roliga 10 is 1:13.The odds against rolling a nurther leathan 7 is 7:5.1$
The total possible outcome for the experiment is 36.
The ossible outcomes for same number on each dice is 6.
So probability for the same number on dice is,
[tex]\frac{6}{36}=\frac{1}{6}[/tex]So probability for the same number on dice is 1/6. So first statement "The probability of rolling the same digit with each die is 1/4" is false.
if f(x)=-5, what is x?
Answer:
x is any real number from -infinity to infinity.
Which relation is a function?
Determine the distance between A(-3, 4) and B(2, -4).
5 units
Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1_{})^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Let
P1=A(-3,4)
P2=B(2,-4)
Step 2
put the values into the equation
[tex]\begin{gathered} \text{distance}=\sqrt[]{(-4-4)^2+(2-(-3))^2} \\ \text{distance}=\sqrt[]{(0)^2+(2+3)^2} \\ \text{distance}=\sqrt[]{(0)^2+(5)^2} \\ \text{distance}=\sqrt[]{(25} \\ \text{distance}=5 \end{gathered}[/tex]Donna bought a desk on sale for $343. This price was 35% of the original price.
The original price for the desk is $980.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
Given:
Sale price = 343
price was 35% of the original price.
let the original price be x
35% of x = 343
35 / 100 * x = 343
x= 343 * 100/ 35
x=980
Hence, the original price of the desk was $980.
Learn more about percentage here:
https://brainly.com/question/13244100
#SPJ1
Use the following information to prepare a classified balance sheet for Alpha Co. at the end of Year 1. Accounts receivable $ 26,500 Accounts payable 12,200 Cash 20,500 Common stock 30,000 Land 10,000 Long-term notes payable 17,500 Merchandise inventory 26,300 Retained earnings 23,600
The classified balance sheet for Alpha Co. at the end of Year 1 is illustrated below.
What is a classified balance sheet?A financial statement incorporating classifications as current assets and liabilities, long-term liabilities, and other things is called a classified balance sheet. It may be simpler to read and extract the information you need by categorizing the information than if it were just listed in a lot of line items.
It is a financial report that includes totals for all of the different revenue and expense classifications and displays revenues, expenses, and profits.
The balance sheet is illustrated below:
Current Assets
Accounts Receivable 26500
Cash 20500
Merchandise Inventory 26300
Total Current Assets 73300
Property, Plant and Equipment
Land 10000
Total Property, Plant and Equipment 10000
Total Assets 83300
Current Liabilities
Accounts Payable 12200
Long Term Liabilities
Long-Term Notes Payable 17500
Stockholders' Equity
Common Stock 30000
Retained Earnings 23600
Total 53600
Total Liabilties 83300
Learn more about balance sheet on:
https://brainly.com/question/1113933
#SPJ1
i need help with question 17
Answer:
[tex]42[/tex]Step-by-step explanation:
To find the median of a stem and leaf plot, use the equation:
[tex]\begin{gathered} median=\frac{n+1}{2} \\ where, \\ n=\text{ number of data} \end{gathered}[/tex]Therefore, for the given plot, there are 16 elements.
[tex]\begin{gathered} \text{ median=}\frac{16+1}{2} \\ \text{ median=8.5} \end{gathered}[/tex]When there are two middle values, the median is the mean of these two values:
[tex]\begin{gathered} \frac{3+1}{2}=2 \\ \text{ Hence, the median is 42.} \end{gathered}[/tex]Can you help me solve this question?
SOLUTION
Step1:
hence from the diagram above, the dimension of the rug is
[tex]\begin{gathered} 34-2x\text{ and } \\ 24-2x \end{gathered}[/tex]Since we have area of the rug,
then we have
[tex](34-2x)(24-2x)=704[/tex]We now solve the equation above quadratically
[tex]\begin{gathered} (34-2x)(24-2x)=704 \\ \text{expand the parenthesis } \\ 16-116x+4x^2=704 \\ \text{subtract 704 from both sides } \\ 816-116x+4x^2-704=704-704 \end{gathered}[/tex]Then we have
[tex]4x^2-116x+112=0[/tex]Solve using factor method we obtain
[tex]\begin{gathered} \text{Divide through by 4} \\ x^2-29x+28=0 \\ x^2-28x-x+28=0 \\ x(x-28)-1(x-28)=0 \\ (x-28)(x-1)=0 \end{gathered}[/tex]Equating each factor to zero we have
[tex]\begin{gathered} x-28=0,x-1=0 \\ x=28,1 \end{gathered}[/tex]Since x can not be 28, the value of x is 1
The Dimension of the rug becomes
[tex]\begin{gathered} 34-2x=34-2(1)=32 \\ \text{and } \\ 24-2x=24-2(1)=22 \end{gathered}[/tex]Hence the dimension of the rug is 32 ft by 22ft (22,32)
Please help I’ll mark you as brainliest if correct!
The value of a in the magic square is 25
The value of b in the magic square is 3
The value of c in the magic square is 14
The value of d in the magic square is 7
What are the missing values?The mathematical operations that would be used to determine the missing numbers are addition and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of determining the difference of two or more numbers.
According to the information provided in the question, all rows, diagonals and columns add to the same number. Thus, the first step is to determine the sum of all the squares.
The three squares of the diagonal from left to right has all the complete numbers.
Sum of the the squares = 5 + 16 + 27 = 48
a = 48 - 18 - 5 = 25
b = 48 - 18 - 27 = 3
c = 48 - 29 - 5 = 14
d = 48 - 27 - 14 = 7
To learn more about subtraction, please check: https://brainly.com/question/854115
#SPJ1
Find a with the given information.
m=-6/7 (-10,0) and (a,-6)
Based on the slope formula for a line, the value of a is: a = -3.
How to Calculate the Slope of a Line?If two points on a line have the following coordinates, (x1, y1) and (x2, y2), to find the slope (m) of the line, the formula that is applied is given as:
Slope (m) = change in y /change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = rise/run.
The given line has the following:
(-10, 0) = (x1, y1)
(a, -6) = (x2, y2)
Slope (m) of the line = -6/7.
Plug in the values into the slope formula for a line:
(-6 - 0) / (a - (-10)) = -6/7
-6/(a + 10) = -6/7
Cross multiply and solve to find the value of a in the equation:
-6(a + 10) = -6(7)
Apply the distributive property
-6a - 60 = -42
Add 60 to both sides
-6a - 60 + 60 = -42 + 60 [addition property of equality]
-6a = 18
Divide both sides by -6
-6a/-6 = 18/-6 [division property of equality]
a = -3
Therefore, the value of a is -3.
The line that has a slope of -6/7 will have the following points, (-10, 0) and (-3, -6).
Learn more about the slope of a line on:
https://brainly.com/question/16949303
#SPJ1
Check all the angles that are congruent to angle 5.
The angles congruent to ∠5 are as follows:
∠8∠1∠4∠9∠12How to find angles in parallel lines?According to the diagram, line l, m and n are parallel lines.
Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.
Hence, the angles that are congruent to ∠5 can be solved as follows:
∠5 ≅ ∠8 (vertically opposite angles)
Vertically opposite angles are congruent.
∠5 ≅ ∠1 (corresponding angles)
Corresponding angles are congruent.
∠5 ≅ ∠4 (alternate angles)
Alternate angles are congruent.
∠5 ≅ ∠9 (corresponding angles)
∠5 ≅ ∠12 (alternate exterior angles)
learn more on angles here: https://brainly.com/question/9299801
#SPJ1
g(x) = 5x – 3g(-2) =?