If 3 times a number is decreased by 2 the principal square root of this difference is 4 less than the number. Find the number(s).
The numbers are -3 and 6
How to determine the numberFrom the information given, let the number be x;
the expression is given as;
(√3x + 2) = x - 4
To determine the number, find the square of both sides, we have;
(√3x + 2) ^2 = (x - 4)^2
Find the square of both sides
3x + 2 = ( x - 4)(x + 4); difference of two squares
expand the bracket
3x + 2 = x^2 + 4x - 4x - 16
collect like terms
x^2 - 3x - 16 - 2
x^2 - 3x - 18
x^2 - 6x + 3x - 18
Factorize the expression
x( x - 6) + 3( x - 6)
(x + 3) or (x - 6)
x = -3 or x = 6
Thus, the numbers are -3 and 6
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Sports regulations usually give the sizes and weights of most sports equipment over a range of values. For each type of sports equipment, the diameters and weights to the appropriate type of ball are given in the accompanying table.
A box contains 30 baseballs. Write a compound inequality that shows the range of the weight of the balls. Graph the inequality.
Type of Ball Range of Diameters Range of Weights Tennis ball 2 1/2 inches to 2 5/8 inches no less than 2 ounces, no greater than 2 1/6 ounces Baseball 2 7/8 inches to 3 inches 5 to 5 1/4 ounces Basketball (women's) no less than 9.07 inches, no greater than 9.23 inches no less than 20 ounces, no greater than 22 ounces Soccer ball (size 5) no less than 21.64 inches, no greater than 22.28 inches 14.46 ounces to 15.87 ounces
The compound inequalities for all the balls that are sports regulated are { (x,y) : 2(1/2) ≤ x ≤ 2(5/8) and 2 ≤y≤ 2(1/6) } for Tennis ball.
{ (x,y) : 2(7/8) ≤ x≤ 3 and 5≤ y ≤ 5(1/4) } for Baseball.
{ (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 } for women's Basket ball.
{ (x,y) : 21.64 ≤x ≤ 22.28 and 14.46 ≤ y ≤ 15.87 } for Scoccer Ball.
What is the correct way of pronouncing a set in roaster form?Suppose we are given { (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 } this reads as The set of all x comma y such that x is between this range and y is between in this range.
Sports regulations have some rules that the diameters and weights of sports pieces of equipment must lie between the regulations that have been set.
We are denoting the Diameters of the balls as x in inches and the weights of the balls as y in ounces.
Now for a Tennis ball the range for x and y can be written in roaster form of set is { (x,y) : 2(1/2) ≤ x ≤ 2(5/8) and 2 ≤y≤ 2(1/6) }.
For Baseball it is { (x,y) : 2(7/8) ≤ x≤ 3 and 5≤ y ≤ 5(1/4) }.
For women's Basketball it is { (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 }.
For Soccer ball the set in roaster form can be written as
{ (x,y) : 21.64 ≤x ≤ 22.28 and 14.46 ≤ y ≤ 15.87 }.
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Clearcut Lumber sells its dimensional lumber with a markup of 60%
a. What rate of margin do they use?
b. A batch of plywood sells for $500 what was the cost?
c. Fence posts with a cost of $10 would sell for how much?
d. The gross profit on the sale of some 4 by 4’s was $50 what was the selling price?
Answer:
c. Fence posts with a cost of $10 would sell for how much?
Step-by-step explanation:
The box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection.
What is the first quartile? Interpret this value in the situation.
About *insert fraction* of the cars going through the intersection were going *Q1* or slower.
Answer:
Step-by-step explanation:
Given,
N= 100
Q1=?
We know that,
Q1= N/4
= 100/4
= 25
8.2% of what amount is $2.87
Answer:
35Step-by-step explanation:
8.2% of what amount is $2.87
we find unity and multiply by 1002.87 : 8.2 * 100 =
35
Identify the set of X-values for which f(X) is greater than or equal to 0.
The given function is greater than or equal to 0 for the interval given as follows:
{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.
When a function is positive and when it is negative?A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.For this problem, with a closed interval, we have that the function is above for:
x ≤ -3, -1 ≤ x ≤ 0, x ≥ 2.
Hence the interval notation is:
{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.
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Determine whether the given ordered pair is a solution of
the system of equations.
(8, 7); -x+y= - 1
6x + y = 41
Answer:THE ANSWER IS NO.
Step-by-step explanation:
As we have given that x=8 and y=7
put theses values in given equations :-
-x + y= -1
-8+7= -1,true
But, for 6x+y=41
We get 6*8+7=41
55 ≠41
Hence the answer is NO.
Answer:
Step-by-step explanation: if the ordered pair (8,7) is a solution of a system of equations; the values x=8, y=7 substituted in the system must make both equations true. -8+7=-1 -1=-1 √ 6×8+7=41 48+7=41 55=41(8,7) is not a solution of the systems.
You sell a smartphone that was originally priced at $600 but is now on sale for 20% off. You give a loyal customer an additional 10% discount. What is the total percent of discount the customer receives on the purchase? A.
Answer: 30%
Step-by-step explanation: just add the 20% and 10% and you get 30%
Kon'nichiwa, everyone! just to make sure you are correct if you answer this question make sure you have a explaination, and a good one with that.
ex; you took the test and have proof you took it.
ex; explaining how you got your answer
also if you happen to need this "⎯⎯" you can just copy paste that and put it in the answer
that's all, thanks for reading this :D
Answer:
Hey there i see that you are doing scientific notation things well i will help you
Step-by-step explanation:
so 5.2 X 10 to the 5th power = 520000
3.9 X 10 to the 8th power = 390000000
and 4.7 X 10 to the 5th power = 470000
so on that info the answer is
4.7 x 10(5), 5.2 x 10(5), 3.9 x 10(8)
hope you have a nice day
Answer and work is all shown in the provided screenshot! I hope this helps! :)
What is an angle that is adjacent to BEC?
Answer:
angle BEAStep-by-step explanation:
What is an angle that is adjacent to BEC?
two angles that have the same vertex and a side in common
so
angle BEA
The Saavedras purchased a home for $220,000 by making a 15% down payment
and borrowing the rest at 4.2% interest compounded monthly for 20 years. This
made their monthly payment $1152.99. The table below represents the first row
of an amortization table for the first period of the loan.
PLEASE. HURRY
Using proportions, the financial measures for the home purchase are given as follows:
Beginning Balance: $220,000.Interest owed: $228,076.4.Payment toward principal: $33,000.Ending balance: $448,076.4.What is a proportion and what is an example of application?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates, which along with operations such as multiplication or division are used to find the equivalent measures.
For this problem, the beginning balance is the purchase value of the home, hence:
Beginning Balance: $220,000.
15% of that goes towards the down payment, hence:
0.15 x 220,000 = $33,000.
Payment toward principal: $33,000.
The number of monthly payments is given by:
20 x 12 = 360 monthly payments.
Considering the monthly payment, the ending balance is given as follows:
33,000 + 360 x 1,152.99 = $448,076.4.
Hence the interest owed is:
448,076.4 - 220,000 = $228,076.4.
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Last year, Salma invested her money in two purchases. She purchased a certificate of deposit for $3000 that paid 5% interest per year and purchased $7000 in corporate bonds paying 4% interest per year. Answer the questions below. Do not do any rounding.
Answer:
a. $2850
b. $6720
Step-by-step explanation:
a.
3000(1-0.05) = $2850
b.
7000(1-0.04) = $6720
What is the slope please help
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 7.5%, and the tax in the second city was 5.5%. The total hotel tax paid for the two cities was $700. How much was the hotel charge in each city before tax?
The hotel charge in city one is $767 and the hotel charge in city two is $2276.
Let x = the charge in 1st city before taxes and
Let y = the charge in 2nd city before taxes
The equation before taxes:
y = x ₊ 1500 ..eq(1)
The equation for total tax paid:
0.075x ₊ 0.055y = 700 ..eq(2)
Substitute equation 1 that is y value in equation 2.
0.075x ₊ 0.055(x₊1500) = 700
0.075x ₊ 0.055x ₊ 82.5 = 700
add the variables and subtract the constants.
0.805x = 700 ₋ 82.5
0.805x = 617.5
x = 617.5/0.805
x = 767
now substitute x value in equation 1.
y = 767 ₊ 1500
y = 2267
Hence the hotel charge before the tax in the first city was $767 and in the second city was $2267.
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What is the product of 6+3i and its conjugate
Answer:
45
Step-by-step explanation:
You want the product of 6+3i and its conjugate.
ConjugateThe conjugate of a complex number is created by reversing the sign of the imaginary part.
(6 +3i)* = 6 -3i
Product of squaresThe product of a complex number and its conjugate is recognizable as the factored form of the difference of squares:
(6 +3i)(6 -3i) = (6)² -(3i)²
Of course, i² = -1, so this becomes ...
6² -(3i)² = 36 -(-9) = 36 +9 = 45
The product of 6+3i and its conjugate is 45.
__
Additional comment
The product of a complex number and its conjugate is the sum of the squares of the magnitudes of the real and imaginary parts. It is always a real number. This fact is used to simplify expressions involving complex numbers.
24. Knowing a Person Who Was Murdered In a sample of 11,771 children
ages 2 to 17, 8% have lost a friend or relative to murder. Four children are
selected at random. (Adapted from University of New Hampshire)
(a) Find the probability that all four have lost a friend or relative to murder.
(b) Find the probability that none of the four has lost a friend or relative to
(c) Find the probability that at least one of the four has lost a friend or
relative to murder.
Using the binomial distribution, the probabilities are given as follows:
a) 0.000041 = 0.0041%.
b) 0.7164 = 71.64%.
c) 0.2836 = 28.36%.
For each person, there are only two possible outcomes, either they have lost a friend, or they have not. The probability of a person having lost a friend is independent of any other person, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For this problem, the values of the parameters are:
n = 4, p = 0.08.
The probability of all four is P(X = 4), hence:
P(X = 4) = (0.08)^4 = 0.000041.
0.000041 = 0.0041% probability that all four have lost a friend or relative to murder.
The probability of none is P(X = 0), hence:
P(X = 0) = (0.92)^4 = 0.7164.
0.7164 = 71.64% probability that none have lost a friend or relative to murder.
The probability of at least one is given by:
P(X >= 1) = 1 - P(X = 0)
Then:
1 - 0.7164 = 0.2836.
0.2836 = 28.36% probability that at least one have lost a friend or relative to murder.
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How many platelets are in 3 milliliters of blood write your answer in standard form
Please help!
Simplify:
Answer: Raise
5
to the power of
4
= 625
Answer:
[tex]5^{4} =625..[/tex]
Step-by-step explanation:
[tex]5^{4} = 625[/tex]
[tex]=625[/tex]
hopefully this helps you :)
The average American dollar bill ($1) weighs about 1.000 gram. Five students weighed the same dollar bill on the same balance. Their results were:
Student 1: 1.040 grams
Student 2: 0.989 grams
Student 3: 1.009 grams
Student 4: 1.026 grams
Student 5: 0.999 grams
Determine:
a) the average
b) the average deviation
c) the relative of percent deviation
Using their concepts, we have that the measures are given as follows:
a) Mean of 1.0126.
b) Average deviation of 0.01632.
c) Percent deviation of 1.6%.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
For this problem, the 5 observations are given as follows:
1.040, 0.989, 1.009, 1.026, 0.999.
Hence the mean is given by:
M = (1.040 + 0.989 + 1.009 + 1.026 + 0.999)/5 = 1.0126.
What is the average deviation?The average deviation of a data-set is given by the sum of the absolute values of the difference between each value and the mean, divided by the number of observations.
Hence:
Ad = (|1.040-1.0126| + |0.989-1.0126| + |1.009-1.0126| + |1.026-1.0126| + |0.999-1.0126|)/5 = 0.01632.
What is the percent deviation?The percent deviation of a data-set is given by the absolute deviation divided by the mean and multiplied by 100%.
Hence:
0.01632/1.0126 x 100% = 1.6%.
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Solve for the remaining angle and sides of the triangle described below. Round to the nearest hundredth:
C=100°
B=60°
, c=3
A = 20
Use sine rule to find the other angles,
If a new van is valued at $34,600, what will its value be in 3 years if it depreciates 14.2% each year?
Answer:
The answer is $21,854. 35
Step-by-step explanation:
rate = 14.2%
Time = 3 years
Value = 34600
V = (1-r)^t
V=34600(1-0.142)^3
V=34600 (0.858)^3
V=$21,854.35
Find the area of the figure. (Sides meet at right angles.)
Answer:
70 in^2
Step-by-step explanation:
Make a line through the middle separating the 5 by 5 square and the rectangle. Then you find the individual areas of each. The bottom shape is a 5 by 5 square, so 5*5 is 25. The top shape's length is 5+2+2 because the bottom shape is a square, so each side=5. Then the blank space between both of the length 2's is 5. As a result, the rectangle's dimensions is 9 by 5. 9*5=45. When we add both areas, we get 45+25=70
suppose an isosceles triangle abc has a=pi/4 and b=c=4. what is the length of a squared
The Isosceles triangle length of a² will be equal to (32 - 16√2).
What is an isosceles triangle?
The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.
A triangle that has at least two sides of equal length is said to be isosceles. Sometimes it is stated to have exactly two sides that are the same length, while other times it is stated to have at least two sides that are the same length, with the latter version mentioning the equilateral triangle as an exception.
It is given that in an isosceles triangle abc has a=π/4 and b=c=4. Then the value of a² will be calculated as below:-
Using the cosine formula to calculate the value of a².
a² = b² + c² -2bc cosФ
a² = 16 + 16 - 2(4)(4)cos(π/4)
a² = 32 - ( 32 x {√2/2})
a² = 32 - 16√2
Therefore, the length of a² will be equal to (32 - 16√2).
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Answer:
4^2(2-root2)
Step-by-step explanation:
You need 6 cups of fruit punch. use 2 cups of pineapple juice add 1 cup of cranberry juice. How many cups of orange juice should you add?
Answer:3
Step-by-step explanation:easy 2 cups of pj plus cranberry juice is 3, get 6 by adding 3 again
Marty needs to subtract a number by 0.01. What decimal place should he subtract from?
A.
tenths
B.
hundredths
C.
thousandths
D.
ones
Answer:
A. tenths
because there's only two digits after a comma
Andres Michael bought a new boat. He took out a loan for $24,440 at 3.75% interest for 4 years. He made a $4,410 partial payment at 4 months and another partial payment of $2,590 at 8 months. How much is due at maturity?
The amount due at maturity on Andres Michael's loan of interest rate of 3.75% is $20,431.75
What is effective monthly loan interest rate?
The loan effective monthly interest rate can be determined as the annual interest rate of 3.75% divided by 12 since there are 12 months in a year
effective monthly interest rate=3.75%/12
effective monthly interest rate=0.003125
loan balance after 4 months=$24,440*(1+0.003125)^4- $4,410
loan balance after 4 months=$20,336.94
loan balance after 12 months=$20,336.94*(1+0.003125)^8-$2,590
loan balance after 12 months=$18,260.96
balance at the 4 year(after another 36 months)=$18,260.96*(1+0.003125)^36
balance at the 4 year(after another 36 months)=$20,431.75
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Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 71 and a standard deviation of 5. Find the percent of juniors whose score is at least 71. % of juniors scored at least 71.
The percent of juniors whose score is at least 71 % is 69.15 %.
We are given that:
Test of the students are normally distributed.
Mean = μ = 71
Standard deviation = σ = 5
We need to find the percent of juniors whose score is at least 71 %.
Now, we know that:
z = ( x - μ) / σ
z = 100 - 71 / 5
z = 29 / 5
z = 5.8
So, percentage = 69.15 %
Therefore, we get that, the percent of juniors whose score is at least 71 % is 69.15 %.
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Which list shows the numbers in increasing order?
A) -0.5, 1.5, -2, -0.75, √7
C) -2, -0.75, -0.5, 1.5, √7
B) -0.5, -2, -0.75, 1.5, √7
D) √7, 1.5, -0.5, -0.75, -2
Answer:
Step-by-step explanation:
its ''C''
Ettwice is three times as old as mavis. the sum of their age is 60. how old each
the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps
Step-by-step explanation:
15 * 3 = 45
45 + 15 = 60
What is a set of values in math?
Answer:
Step-by-step explanation:
Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4}
Finite And Infinite Sets: Union Of Sets
Power Set: Complement Of A Set
Equivalent Sets: Universal Set
Types Of Sets: Set Theory