Answer:
the number is 5
Step-by-step explanation:
let the number be x
4*(x)+-7=3+2x
4x-7=3+2x
2x=10
x=5
4.
Calculate 3% of $600
Hey there!
3% of $600.00
= 3% * $600.00
= 0.03 * 600
= 3/100 * 600/1
= 3(600) / 100(1)
= 1800/100
= 1800 ÷ 100 / 100 ÷ 100
= 18/1
= 18 ÷ 1
= 18
Therefore, your answer should be:
18
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 10 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.
According to Chebyshev's theorem, at least 56% of the home buyer's ages lie between __ years and __ years. (Round your answer to the nearest whole number)
According to Chebyshev's theorem, at least what percent of the home buyers' ages lie between 25 years and 65 years.
Step-by-step explanation:
Given that
A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 10 years.That these measures are valid for the population of all home buyers.To find
Complete the given statements about the distribution of all ages of home buyers.So, according to the question
We have,
Mean of ages = 45, andStandard deviation = 10We know that,
Chebyshev's Theorem
The smallest percentage of observations that fall within a precise range of current standard deviations from the mean is estimated by Chebyshev's Theorem. There are many different chance distributions that are covered by this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.When the distribution is not normal, Chebyshev's Theorem is used. It states that:
Measures are all within 2 standard deviations of the mean in at least 75% of cases.Measures are all within 3 standard deviations of the mean in at least 89% of cases.The percentage of measurements that are within k standard deviations of the mean is represented by an in general:[tex]P = 100(1-\frac{1}{k^2} )[/tex]
Chebyshev's Theorem is used to determine that:
At least 56% of home buyers are between the ages of 30 and 60.At least 75% of home buyers are between the ages of 25 and 65.For the 1sr item, we have to find k at P = 56,
[tex]P = 100(1-\frac{1}{k^2} )[/tex]
[tex]56 = 100(1-\frac{1}{k^2} )[/tex]
0.56 = 1 - [tex]\frac{1}{k^2}[/tex]
[tex]\frac{1}{k^2} = 0.44[/tex]
k² = 1/0.44
k = [tex]\sqrt{\frac{1}{0.44} }[/tex]
k = 1.5
The bounds are, therefore, within 1.5 standard deviations:
45 - 1.5 × 10 = 30 years old.45 + 1.5 × 10 = 65 years old.Ages 25 and 65 are both 2 standard deviations away from the mean, so:
At least 75% of the home buyers' age lie between 25 years and 65 years.Answer:
According to Chebyshev's theorem, at least 56% of the home buyer's ages lie between 30 years and 65 years.According to Chebyshev's theorem, at least what 75% of the home buyers' ages lie between 25 years and 65 years.To learn more about Chebyshev's theorem, please click on the link:
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what is 8,2 equivalent to
Answer: 4,6
Step-by-step explanation:
What is the five-number summary for the data set?
Answer:B
Step-by-step explanation:A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.
Identify the correct justification for each step, given that m/1 = 30° and m/2 = 30°.
30 = m<1 = m<2
m<1 is equals to m<2 because these two angles are transitive property.
How to identify the correct justification for m<1 = 30° and m<2 = 30°?given that m<1 = 30° and m<2 = 30°.
m<1 = 30
m<2 equals to m<1
m<2 = 30 can be obtained by substituting 30 into the second equation.
The proof is now complete.
The Transitive Property of Equality can also be used, which asserts that if X = Y and Y = Z, then X = Y = Z. In other words, if one number is equal to another, and that other number is equal to a third, then all three numbers must be the same.
thus, 30 = m<1 = m<2, m<1 is equals to m<2 because these two angles are transitive property.
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im confused on this !
Answer:
P = 35x + 18(140-x)
Step-by-step explanation:
I think they are just asking for the expression, not to solve it. We would need more info (like the total profit) to solve it.
W Work out the area of the triangle below. 4 cm 10 cm 7 cm Not to scale
The area of the triangle is = 19.4 cm²
What is the area of triangle?Triangle's area is equal to 1/2 (b × h) square units.
where the triangle's base and height, respectively, are denoted by b and h. Let's now examine how to use the provided formula to get a triangle's area.
Area of triangle = 1/2 × B × H
We will calculate the height of the triangle with the help of Pythagoras theorem.
Consider a straight line representing the height of the triangle.
⇒ base = 4cm, half of base = 2cm
⇒ hypotonus = 10cm
(h²) = b² + a²
⇒ 10² = 2² + a²
⇒ 100 = 4 + a²
⇒ √96cm = a
a = 9.7cm
area of triangle = 1/2 × 4 × 9.7
= 19.4 cm²
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When subtracting 2.9 from a certain number, the result is 64.24, as seen below. What number should go in the box to complete the subtraction problem?
The decimal 2.9 is subtracted from an unknown whole number to get 64.24. The unknown whole number has 6 in the tens place, an unknown number in the ones place, 1 in the tenth place, and 4 in the hundredth place.
(5points)
https://lms.lausd.net/assignment/6055492281/assessment#:~:text=When%20subtracting%202.9,Blank%201%3A
Blank 1:
Answer:
can you take a picture of the sum
7 will go in the box. The full number would be 67.14.
work: 64.24 + 2.9 = 67.14.
Find the following given the function f(x)=
Answer:
[tex]-\frac{3+\sqrt{5}}{4}[/tex]
Step-by-step explanation:
[tex]\sqrt{20} \leq 5 \implies f(\sqrt{20})=\frac{2}{\sqrt{20}-6} \\ \\ =\frac{1}{\sqrt{5}-3} \\ \\ =\frac{\sqrt{5}+3}{-4} \\ \\ =-\frac{3+\sqrt{5}}{4}[/tex]
James is saving $15 per week in order to purchase a gaming console. Create a table to represent the relationsip between x, the number of weeks and y, the total amount James has saved.
The total amount saved by the James is: $330.
Equation: What is it?The relationship between two expressions is expressed by the word equation. It employs many mathematical symbols, including greater-than, less-than, and equal.
The amount James has saved, according to the query, is $15 each week.
It is now time to generate the table that shows how the variable "x" and the number of weeks relate to one another.
The following are the possible possibilities for the necessary parameters "x" and "y":
x = [1 2 3 4]
y = [15 30 45 60]
The last formula may now be written as y = 15x.
The formula will be y = 15x = 15x22 = 330 dollars after 22 weeks.
As a result, the James have saved $330.
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Which of these numbers has a lesser value in the hundred thousands place than that of the number in the box? 6,318,219 1,749,803 3,401,182 4,237,639 J 5,893,254
The number that has a lesser value in the hundred thousands place than 6,318,219 is: 4,237,639.
What is the digit of the hundred thousands place?Starting from the end of the number and moving left, the hundred thousands digit is the 6th digit of the number.
The values of the digit for each number are given as follows:
6,318,219: 3.1,749,803: 7.3,401,182: 4.4,237,639: 2.5,893,254: 8.2 < 3, hence, the number that has a lesser value in the hundred thousands place than 6,318,219 is: 4,237,639.
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Dan is making a model volcano for the science fair. He wants an awesome eruption, so he tries different amounts of baking soda and vinegar. First, he tries 2 tablespoons of baking soda and 6 tablespoons of vinegar. Next, he tries 3 tablespoons of baking soda and 9 tablespoons of vinegar. Did Dan use the same ratio of baking soda to vinegar in both eruptions?
In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one is relative to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent.A ratio divides two numbers to compare them.
a: The ratio of two mathematical expressions that is indicated.
b: the proportions of two or more items in terms of quantity, amount, or size: proportion.
based on the available facts;
2/6 for the first ratio can be converted to 1/3, as can 3/9 for the second ratio.
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C. Julia has six novels she wants read, one of them
which is in the chest of a woman' by Efo Kodjo
Mawugbe. She plans to create a reading list of four of
these novels for an upcoming trip, and different orders
count as different lists. How many reading lists are
possible if 'in the chest of a woman' must be on the
list?
She can have 60 reading list to plan to read the 6 novels that she wants to read including the 'in the chest of a woman' in the list.
We are given that:
Number of novels that Julia wants to read = 6
She plans to read = 4
1 novel is fixed that is "in the chest of a woman' by Efo Kodjo"
We need to tell the number of possible reading list that she can have.
We will use permutation for it
By using permutation, we get that:
Number of reading list = 1 × 5 × 4 × 3
Number of reading list = 5 × 12
Number of reading list = 60 lists
Therefore, she can have 60 reading list to plan to read the 6 novels that she wants to read including the 'in the chest of a woman' in the list.
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what is 38-12x3 equal
Answer: 2
Step-by-step explanation: 12 x 3 first becuase pemdas
Tane and Pete are raising funds for their sports trip.
Between them they need to raise $1000.
There are only 5 weeks until they need the money.
Tane gets paid $15 an hour, and Pete gets paid $16 an hour as he has more experience.
Between them they work for a total of 13 hours each week.
What is the average number of hours that each of them work per week if they are to have
exactly the amount of money they need?
Answer: Tane needs to work 8 hours per week while Pete needs to work 5 hours per week
Step-by-step explanation:
T=Tane. P=Pete
5*13=65
T+P=65
15T+16P=1000
T=65-P
15(65-P)+16P=1000
975-15P+16P=1000
975+P=1000
P=25 hours for 5 weeks
T=65-25
T=40 hours for 5 weeks
P: 25/5=5 hours per week
T: 40/5=8 hours per week
Tane needs to work 8 hours per week while Pete needs to work 5 hours per week
How can you represent the number of bacteria after 6 days in terms of exponents?
Answer:
b⁶
Step-by-step explanation:
Where b is the variable, we multiply b by itself six times to represent its multiplications every 6 days.
Could someone help me with this I will give you brainlist
Confused please help
Answer:
Step-by-step explanation:
if you are trying to find x in the equation
3(2x+2)-3x= 6+3x you have to distribute the 3 (which you did correctly.)
6x+6-3x=6+3x
what you did wrong was canceling out the threes. you cannot cancel out the threes here because the one on the left is negative. What you should do is add 3x to each side like this.
6x+6-3x=6+3x
+3x +3x
6x+6=6+6x
since both sides are equal and we obtain 0=0, this means the equation is in fact an identity which is true for all values of x.
5 out of every 8 students sureyed owns a bicycle. There are 65 bicycles. How many students were surveyed?
Answer:
104
Step-by-step explanation:
You would do this by diving 65 by 5, you get 13 then multiple that by 8.
Ken received his bank statement in the mail and checked it to verify his recent pay increase.
Ken has direct deposit so his paycheck is sent electronically to his account. The previous
month's pay was $5,320.10. Ken's account activity showed a $651.22 previous balance,
checks of $5,211.39, ATM withdrawals of $250 and a service charge of $4.50. If Ken's new
balance is $982.01, what increase in pay was direct deposited?
The pay increase that was directly deposited into Ken's account is $476.58.
In the question, we are asked to find the pay increase, that was directly posited in Ken's account, given that Ken received his bank statement in the mail and checked it to verify his recent pay increase. He has direct deposit so his paycheck is sent electronically to his account. The previous month's pay was $5,320.10. His account activity showed a $651.22 previous balance, checks of $5,211.39, ATM withdrawals of $250, and a service charger of $4.50. Also, we are informed that his new balance was $982.01.
We assume the pay increase to be $x.
Thus, his this month's pay will be $(5,320.10 + x).
This will be added in his previous month's balance, to get $651.22 + $(5,320.10 + x) = $(5,971.32 + x).
Now, the check of $5,211.39, ATM withdrawal of $250, and the service charge of $4.50 will be deducted from this to get $(5,971.32 + x) - $5,211.39 - $250 - $4.50 = $(505.43 + x).
This is the final balance of Ken's account.
But, we are given that Ken's new balance was $982.01.
Thus, we get an equation 505.43 + x = 982.01, which can be solved by subtracting 505.43 from both sides to get:
505.43 + x - 505.43 = 982.01 - 505.43,
or, x = 476.58.
Thus, the pay increase that was directly deposited into Ken's account is $476.58.
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Suppose a computer manufacturer has the total cost function
C(x) = 76x + 3600
(in dollars) and the total revenue function
R(x) = 376x
(in dollars).
(a) What is the equation of the profit function P(x) (in dollars) for this commodity?
The equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600
It is given in the problem that,
The total cost function C(x) = 76x + 3600 (in dollars)
Also,
The total revenue function R(x) = 376x (in dollars)
We need to find the equation of the profit function P(x) (in dollars) for this commodity
First we need to understand the following terms
Cost is the price of a commodity which is paid or charged in exchange of something. Example - 1 kg of apple are of 3 Dollars
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations.
So,
The equation of the profit is given by = Total Revenue - Total Cost
P(x) = R(x) - C(x)
Putting values, we get
P(x) = 376x - (76x + 3600)
P(x) = 376x - 76x - 3600
P(x) = 300x - 3600
Hence, the equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600
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A picture frame has a width of 2 inches. If the area of the frame is 128 square inches, and if the picture
itself is 4 inches longer than it is wide, what are the dimensions of the Picture
The dimensions of the picture will be 60 inches and 2 inches.
We are given that:
The width of the frame is = 2 inches.
The area of the frame is 128 inches².
Let the length of the frame be x.
So, according to the question, we get the length of the picture as:
length = x + 4
Area of picture frame = l × b
128 = (x + 4) × 2
128 = 2 x + 8
2 x = 128 - 8
2 x = 120
x = 120 / 2
x = 60 inches.
Therefore, the dimensions of the picture will be 60 inches and 2 inches.
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HELP HELP HELP HELP HELP
please...
Answer:
-10
Step-by-step explanation:
[tex]f(x) = 2 - 3x \\ [/tex]
So,
[tex]f(4) = 2 - (3 \times 4) = 2 - 12 = - 10[/tex]
Therefore, Option A is correct
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Zachary Company reported the following data regarding the product it sells: Sales price $48 Contribution margin ratio 25% Fixed costs $336,000 Required Use the contribution margin ratio approach and consider each requirement separately. What is the break-even point in dollars? In units?
Answer:
The break-even point in dollars is 1,344,000 and in units is 28,000. The break-even point is calculated by dividing the fixed costs by the contribution margin. In this case, 336,000 ÷ .25 = 1,344,000. The break-even point in units is then calculated by dividing the break-even point in dollars by the sales price. In this case, 1,344,000 ÷ 48 = 28,000.
Step-by-step explanation:
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Kyle wants to buy a television on a hire purchase agreement. The cash price of the television is R5 600 R5 600. She is required to pay a deposit of 15%
15% and pay the remaining loan amount off over 24 24 months at an interest rate of 14% 14% p.a.
What are Kyle's monthly repayments?
The monthly repayment Kyle has to pay on the television based on the hire purchase agreement is R229.
What is the monthly repayment?The monthly repayment is the amount to be paid monthly with interest on the given loan amount.
We have,
Price of the television = R5600
Deposit amount:
= 15% of 5600
= 15/100 x 5600
= 0.15 × 5600
= 840
Now,
The remaining amount:
= 5600 - 840
= 4760
The monthly repayment amount of 14% per annum is:
A = [ P( R/12 )( 1 - R/12 [tex])^{n}[/tex] ] / ( 1 + r/12 [tex])^{n}[/tex] - 1
A = [ 4760 ( 0.14/12 )( 1 - 0.14/12 [tex])^{24}[/tex] ] / [ ( 1 + 0.14/12 [tex])^{24}[/tex] - 1 ]
A = 228.54
A ≅ 229
Thus the monthly repayment Kyle has to pay on the television based on the hire purchase agreement is R229.
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please help, it would mean a lot to me! :) I need to understand these type of math problems and I need help on this one! I am having a test next week!
Answer:
2A/h = b
Step-by-step explanation:
To get b by itself, you have to reverse each operation for the other variables.
h is being multiplied by b here, so to reverse it, you would divide h on both side of the equation. This will give you...
A/h = 1/2b (h is not on the right side anymore because it got canceled out.)
Next you will get rid of the 1/2 by multiplying both sides of the equation with the reciprocal. The reciprocal of 1/2 is 2/1. This will give you..
2A/h = b (1/2 is not on the right side anymore because it got canceled out by 2/1 (1/2 x 2/1 = 1))
Step-by-step explanation:
this is the formula for the area of a triangle :
half off the baseline times the height (to this baseline).
to solve an equation for one variable involved means to end up with only that variable on one side, and everything else on the other side.
the whole time we keep the equality alive, so any change done on one side has to be done on the other side as well.
A = 1/2 × b × h
to solve for b means we want to get rid of the 1/2 and the h factor.
let's start with the 1/2 factor : we multiply both sides by 2.
2A = b × h
and to get rid of h, we need to divide both sides by h :
2A/h = b
and that's it.
Use this limit to find f′(11) given f(x)=sqrt(x-2)
Answer: f'(11)=1/6
Step-by-step explanation:
f(x)=sqrt(x-2)
f(x)=(x-2)^1/2
f'(x)=1/2 * (x-2)^(1/2-1)
f'(x)=1/2 * (x-2)^(-1/2)
f'(11)=1/2 * (11-2)^(-1/2)
f'(11)=1/2 * (9)^(-1/2)
f'(11)=1/2 * (9)^(1/2 * (-1))
f'(11)=1/2 * (9^1/2)^(-1)
f'(11)=1/2 * (3)^(-1)
f'(11)=1/2 * 1/3
f'(11)=1*1/(2*3)
f'(11)=1/6
Using the definition of the derivative, we have
[tex]\displaystyle f'(11) = \lim_{x\to11} \frac{\sqrt{x-2} - \sqrt{11-2}}{x - 11} = \lim_{x\to11} \frac{\sqrt{x-2} - 3}{x - 11}[/tex]
Rationalize the numerator.
[tex]\displaystyle \frac{\sqrt{x-2}-3}{x-11} \cdot \frac{\sqrt{x-2}+3}{\sqrt{x-2}+3} = \frac{\left(\sqrt{x-2}\right)^2 - 3^2}{(x-11)\left(\sqrt{x-2}+3\right)} = \frac{x - 11}{(x - 11) \left(\sqrt{x-2} + 3\right)}[/tex]
If [tex]x\neq11[/tex], we can simplify the limit to
[tex]\displaystyle f'(11) = \lim_{x\to11} \frac{x-11}{(x-11)\left(\sqrt{x-2}+3\right)} = \lim_{x\to11} \frac1{\sqrt{x-2} + 3}[/tex]
The function in the remaining limit is continuous at [tex]x=11[/tex], so we end up with
[tex]\displaystyle f'(11) = \frac1{\sqrt{11-2} + 3} = \boxed{\frac16}[/tex]
rewrite 100 as a base and exponent without using an exponent of 1
Answer:
10^2
Step-by-step explanation:
The function F(x) = −0.005x^2 + 0.8x + 12 models the relationship between a certain vehicle’s speed and the fuel economy, where F(x) is the fuel economy in kilometres per litre and x is the speed of the vehicle in kilometre per hour.
a) Determine the average rate of change in the fuel economy in the interval of speed [60,80].
b) b) Interpret your result.
a) The average rate of change on that interval is 0.1
b) as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1
How to find the average rate of change on the given interval?For any function f(x), the average rate of change on an interval (a, b) is given by:
(f(b) - f(a))/(b - a)
In this case, the function is:
F(x) = −0.005x^2 + 0.8x + 12
And the interval is [60, 80]
Then we have:
F(60) = −0.005*60^2 + 0.8*60 + 12 = 42
F(80) = −0.005*80^2 + 0.8*80 + 12 = 44
Then the average rate of change on that interval is:
R = (44 - 42)/(80 - 60) = 0.1
b) What does that rate means?
F(x) relates the fuel economy and x the speed of the vehicle.
This means that as we increase the speed in the interval [60, 80], the fuel economy increases at a rate of 0.1.
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If f(x) = x³ +8, g(x) = x - 2, h(x) = √, then (fogoh)(x)=
The value of (fogoh)(x) is [tex]\sqrt{x^{3} }[/tex] + 6x + 12[tex]\sqrt{x}[/tex]
Here, we are given 3 functions as listed below:
f(x) = [tex]x^{3}[/tex] +8
g(x) = x - 2
and, h(x) = [tex]\sqrt{x}[/tex]
now, (fogoh)(x) can be written as follows-
f[g{h(x)}] = f{g([tex]\sqrt{x}[/tex])}
here, g([tex]\sqrt{x}[/tex]) = [tex]\sqrt{x}[/tex] - 2
Thus, f{g([tex]\sqrt{x}[/tex])} = f([tex]\sqrt{x}[/tex] - 2)
Substituting x = [tex]\sqrt{x}[/tex] - 2 in the function f(x) we get,
[tex](\sqrt{x} - 2)^{3}[/tex]+8
using the algebraic property [tex](a+b)^{3}[/tex] = [tex]a^{3} + b^{3}[/tex] + 3ab(a + b), we get-
= [tex]\sqrt{x^{3} }[/tex] - [tex]2^{3}[/tex] + 3[tex]\sqrt{x}[/tex](-2){[tex]\sqrt{x}[/tex] - 2} + 8
= [tex]\sqrt{x^{3} }[/tex] - 8 + 6x + 12[tex]\sqrt{x}[/tex] + 8
= [tex]\sqrt{x^{3} }[/tex] + 6x + 12[tex]\sqrt{x}[/tex]
Thus the value of (fogoh)(x) = [tex]\sqrt{x^{3} }[/tex] + 6x +12[tex]\sqrt{x}[/tex]
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