how many positive integers under 50 are multiples of neither 4 nor 6
Answers
50/4=12 positive integers are multiples of 4
50/6=8 positive integers are multiples of 6
50/12=4 positive integers are multiples of 12 (LCM of 4 and 6)
By the inclusion/exclusion principle, the number of multiples of either 4 or 6 is equal to 12+8-4=16.
Therefore, the complement is the number of positive integers that are multiples of neither 4 nor 6 = 50-16=34.
Related Questions
When constructing an inscribed equilateral triangle, how many arcs will be drawn on the circle?
a. 3
b. 4
c. 5
d. 6
Answers
Perhaps a more usual method would be to start at D, draw an arc at E, then from there at B. Resetting the compass to have radius, DB, a third arc can be drawn at C using either B or D as the center. This method would give you
.. selection A: 3 arcs
If you didn't want to reset the compass, you could draw two more arcs, say from B to A, then from A to C. This method would give you
.. selection B: 4 arcs.
A cylindrical tank has a height of 12 feet and a diameter of 16 feet. Jane fills the tank with water at a rate of 6 cubic feet per minute. Calculate how long it would take Jane to fill the tank without overflowing it. Explain your reasoning. Round as needed.
Answers
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=8\\ h=12 \end{cases}\implies V=\pi \cdot 8^2\cdot 12\implies V=\stackrel{ft^3}{768\pi} [/tex]
now, that's how many ft³ of water the tank can hold, since she is filling it up at a rate of 6 ft³ per minute, namely in 1 minute 6 ft³ have gone in, then it'll be
768π/6 how many minutes it'll take.
namely, how many times does 6 go into 768π? well, 768π/6.
The formula for the volume of a sphere is V=4/3 3.14r^3. What is the formula solved for r?
Answers
Which list of decimals is ordered from least to greatest? A) 0.11, 0.101, 0.21 B) 0.27, 0.35, 0.41 C) 0.35, 0.056, 4.2 D) 1.09, 0.91, 1.90. I need it quick
Answers
tim has 30 grapes. he keeps 9 grapes for himself. then he gives 7 grapes each to some of his friends. to how many friends does tim give grapes?
Answers
30-9 he kept = 21
21÷7 he gives out per friend =3
Alice has 1/5 as many miniature cars as Sylvester has Sylvester has 35 miniature cars how many miniature cars does alic have?
Answers
Final answer:
Alice has 1/5 as many miniature cars as Sylvester, who owns 35. By multiplying 35 cars by 1/5, we find that Alice has 7 miniature cars.
Explanation:
The student's question is about finding the number of miniature cars Alice has if she has 1/5 as many as Sylvester, who has 35 miniature cars. To solve this, we use the following mathematical operation:
Alice's miniature cars = 1/5 of Sylvester's miniature cars
Sylvester's miniature cars = 35 cars
To find out how many miniature cars Alice has, multiply the number of Sylvester's miniature cars by 1/5:
35 cars x 1/5 = 7 cars
Therefore, Alice has 7 miniature cars.
The human population doubles approximately every 50 years. If there were 2.5 million people in 1950, how many people are forecasted to populate the earth in 2050?
Answers
2.5 x 2 = 5
5 x 2 = 10
Tell what each of the residual plots below indicates about the appropriateness of the linear model
Answers
Residual plots can indicate the appropriateness of a linear model by examining patterns and deviations of the residuals.
Explanation:A residual plot is a graph that shows the difference between the observed and predicted values in a linear regression model. It helps to assess the appropriateness of the linear model by examining the patterns and deviations of the residuals. In the first graph, there seems to be a systematic pattern and non-randomness in the residuals, indicating that the linear model may not be appropriate. However, in the second graph, the residuals are randomly scattered around zero with no evident pattern, suggesting that the linear model is more appropriate.
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a sheep breeding farm counted a total of 40 sheep on their grounds after one year the number of sheep doubled then in the next year the number of sheep doubled again if this trend continues which of the following options represents the number of sheep on the farm by then end of each year
Answers
graph (b)
Explanation:
The farm started with 40 sheep and the number doubled each year.
So, the equation modeling this situation would be:
N(x) = 40*(2)^2
By getting the equation, we can notice that we already excluded the third and fourth choices as they have the wrong equations.
Now, we will need to select the right graph which is either graph a or graph b.
To do this, we will get the value of N(x) for different values of x as follows:
At x = 0: N(0) = 40*(2)^0 = 40
At x = 1: N(1) = 40*(2)^1 = 80
At x = 1: N(2) = 40*(2)^2 = 160
Now, taking a look at graph a, we will find that:
N(1) = 120
N(2) = 360
These numbers are not the same as the numbers we calculated, therefore, this graph is wrong
Taking a look at graph b, we will find that:
N(1) = 80
N(2) = 160
These numbers are exactly the same as the ones calculated, therefore, this graph is the correct one.
Hope this helps :)
which set of three numbers could be the side lengths of a triangle A.5,5,14 B.3,3,2 C.3,3,8 D. 5,5,10
Answers
Answer:
B. 3, 3, 2
Step-by-step explanation:
The triangle inequality requires the sum of the lengths of the two shortest sides exceed the length of the longest side. That is the case only for the lengths of selection B:
2 + 3 > 3
it rained 3/8 of a inch each day for 3 days straight how much rain fell altogether
Answers
It rained the same amount on each of the 3 days, so the denominator will remain the same. Multiply the fraction by the amount of days:
3/8 × 3 = 1 1/8
ANSWER:
1 1/8 (or 9/8) inches of rain fell altogether on the 3 days.
HELP ME PLEASEEEEEEEEEEEEEEEEEE
Answers
First, let's give the variable a name:
Let
x = gallons of water to be added
For the 10% solution we have:
0.1 * 8 = 0.8
Then, for 5% we have:
(0.8 / x + 8) = 0.05
Rewriting:
(0.8 / x + 8) = (5/100)
Answer:
An equation can be used to find x, the humber of gallons of water he should add is:
(0.8 / x + 8) = (5/100) (option 2).
Solve the system of equations using the substitution method.
{y=−3x+7
x=−2y−16
Enter your answers in the boxes.
x=
y=
Answers
ANSWER
[tex]x = 6[/tex]
[tex]y = - 11[/tex]
EXPLANATION
The given system of equations is
[tex]y = - 3x + 7...(1)[/tex]
and
[tex]x = - 2y - 16...(2)[/tex]
We substitute equation (1) into equation (2) to get;
[tex]x = - 2( - 3x + 7) - 16[/tex]
[tex]x = 6x - 14- 16[/tex]
We group similar terms
[tex]x - 6x = - 14 - 16[/tex]
[tex] - 5x = - 30[/tex]
Divide both sides by -5.
[tex]x =6[/tex]
Put x=6 into equation (1).
[tex]y = - 3(6) + 7[/tex]
[tex]y = - 18 + 7[/tex]
[tex]y = - 11[/tex]
Answer:
x = 6 and y = -11
Step-by-step explanation:
Given : System of linear equation
y=−3x+7
x=−2y−16
We have to solve the system of equations using the substitution method.
In substitution method, we substitute the value of one variable in term of other and solve for it.
Consider the given system of linear equation
y = −3x + 7 ...(1)
x = −2y − 16 .....(2)
Substitute, (2) in (1), we get,
y = -3(-2y - 16) + 7
Simplify , we get,
y = 6y + 48 + 7
6y - y = - 55
5y = -55
y = -11
Substitute y = -11 in (2), we get,
x = −2(-11) − 16 = 22 - 16 = 6
thus, x = 6
Thus , x = 6 and y = -11
how do you solve x^2+4x-5=0
Answers
1. root1*root2=-5; root1+root2=-4.
2. root1=-5; root2=1.
answer:1;-5.
Actually the answer is (-1,5)
x^2 – 4x – 5 = 0
x^2 – 4x = 5
x^2 – 4x + 4 = 5 + 4
(x – 2)^2 = 9
x – 2 = ± 3
x = 2 + 3 and x = 2 – 3
x = 5 and x = –1
{–1, 5}
7+11v=9v-9 how do you solve by steps
Answers
7 + 11v = 9v - 9 Subtract 7 from both sides
7 - 7 + 11v = 9v - 9 - 7 Simplify
11v = 9v - 16 Subtract 9v from both sides
11v - 9v = 9v - 9v - 16 Simplify
2v = -16 Divide both sides by 2
[tex] \frac{2v}{2} [/tex] = -[tex] \frac{16}{2} [/tex] Simplify
v = -8
Check your answer by plugging the value (-8) into the original equation.
7 + 11(-8) = 9(-8) - 9 Simplify the mulitiplication steps
7 + (-88) = -72 - 9 Rewrite 7 + (-88) as 7 - 88
7 - 88 = -72 - 9 Simplify both sides
-81 = -81
The check worked out, so your answer is v = -8 .
£850 is invested for 2 years at 6% per annum compound interest. a) Work out the total interest earned over the first 2 years.
Answers
Answer:
6% annum for 850 would be 955
Measure the length of the top of your desk in centimeters.describe how you found the length
Answers
Find a ⋅ b.
a = 7i - 4j, b = 4i + 3j
A) <28, -12>
B) 16
C) -40
D) <11, -1>
Answers
Answer:
B) 16
Step-by-step explanation:
The dot product of a pair of vectors is the sum of the products of their corresponding parts. It is a scalar.
... a · b = (7i -4j) · (4i +3j) = 7·4 + (-4)·3
... = 28 -12 = 16
if the circumference of a circle measures 3π cm, what is the area of the circle in terms of π?
Answers
with that info, we can find out the area of the circle which is pi r squared.
1.5*1.5=2.25
AREA=2.25pi
The area of the given circle, in terms of pi, is:
A = (9/4)pi cm^2
How to find the area of the circle?We know that for a circle of radius R, the circumference is:
C = 2*pi*R
And the area is:
A = pi*R^2
In this case, we know that:
C = 3pi cm = 2pi*R
Then we must have:
3cm = 2R
(3/2)cm = R
Now we can replace this on the area equation:
A = pi*((3/2)cm)^2 = pi*(9/4) cm^2
If you want to learn more about circles, you can read:
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Can you please help me ?
Answers
Tan (x) = a / b
Where,
a: opposite side of the triangle.
h: adjacent side of the triangle.
Clearing x:
x = Atan (a / b)
Substituting:
x = Atan (a / b)
x = Atan (5.74 / 4)
x = 55.12874356
Whole degree
x = 55
Answer:
x = 55 (option 3)
If the newspaper plans to select an ad at random each week to be published free, what is the probability that the ad for a specific week will be a help dash wanted help-wanted ad
Answers
1 divided by 7
0.14285714285%
But to round..
0.14%
Answer:Theres a article about that ont he internet
Step-by-step explanation:
Maritza is buying a multipack of 3 pairs of socks for $25.98. She will save $6.24 by buying the multipack instead of buying 3 individual pairs of the same socks.
If each pair of socks costs the same amount, how much does each pair of socks cost when bought individually?
Answers
25.98-6.24=19.74
19.74/3=6.58
On the map of a town, 1 cm represents 6 miles. Find the distance represented by 4.5 cm. A) 4.5 miles B) 6 miles C) 17 miles D) 27 miles
Answers
I hope this helps you out!! <3
4.5 cm.................................................? miles
(6*4.5)/1=27 miles
the choice is D
rebekah's baby brother wights 7.71 pounds. Her newborn kitten weights 0.24 pound. How much more does tebekah's baby brother weight that her kitten?
Answers
what is 5/10 + 25/100
Answers
An employee has an annual salary of $51,300. They receive $2,830 in health insurance and $4,600 in paid time off per year. They drive their personal vehicle for work which costs them $600 per month, but the company reimburses them $0.54 per mile for the total work miles driven. If the employee drives 36,000 miles for work for the year, what will be their total employment compensation?
a.
$70,740
b.
$70,970
c.
$77,570
d.
$78,170
Answers
The total employment compensation of the employee is b. $70,970.
What are Arithmetic operations?Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.
Given that,
Annual salary of the employee = $51,300
Health insurance per year = $2,830
Paid time off per year = $4,600
Monthly expense for personal vehicle = $600
Yearly expense = 12 × $600 = $7200
Reimbursement for the vehicle = $0.54 per work mile
Reimbursement for vehicle for 36,000 miles for work for the year = $0.54 × 36,000 miles = $19,440
Total employment compensation = ($51,300 + $2,830 + $4,600 + $19,440) - $7200
= $70,970
Hence the employment compensation is $70,970.
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One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.
Answers
Final answer:
The two numbers in question are 8 and 41.
Explanation:
Step-by-Step Solution to Find the Two Numbers
Let the smaller number be x. Thus, the larger number would be x + 33. According to the problem, the larger number divided by the smaller number gives a quotient of 5 and a remainder of 1. We can represent this information using the following equation:
(x + 33) = 5x + 1
This equation states that when the larger number is divided by the smaller number, we obtain a quotient of 5 and a remainder of 1.
Now, let's solve the equation for x:
Subtract 5x from both sides of the equation: (x + 33) - 5x = 1Simplify the equation: -4x + 33 = 1Subtract 33 from both sides: -4x = -32Divide both sides by -4: x = 8Since we have found the smaller number to be 8, the larger number is:
8 + 33 = 41
Therefore, the two numbers are 8 and 41.
The modulus operator would confirm our solution since 41 % 8 does indeed yield a remainder of 1, as stated in the problem.
which of the following is important in a 2 column proof?
A list of all theorems
Staircase LOgic
Order
Detailed explanations for each step
Answers
Answer:
Order.Step-by-step explanation:
When we are proving a proposition, it's important to have order in our 2-column proof.
So, we must have a left colum for Statements and a right colum for Reasons, that's the order we need to have.
In the statements colum we write our deductions. In the reasons column, we write the justification or reason about our deduction.
Therefore, the right answer is the third choice: Order.
What are the zeros of the function f(x)=3x^2-3x-6
Answers
y = 3(x^2 - x - 2) Now it is much easier.
y = 3(x - 2)(x + 1)
Is the quotient of 5 and 1 / 2 greater than or less than 5? Explain your answer.
Answers
The quotient of 5 divided by 1/2 is greater than 5 because dividing by a number less than 1 results in a larger number. In this case, it is equivalent to multiplying 5 by 2, yielding 10.
To determine if the quotient of 5 and 1/2 is greater than or less than 5, we consider the operation of division. Dividing by a number less than 1 will result in a larger number, while dividing by a number greater than 1 will result in a smaller number. The number 1/2 is less than 1, so when 5 is divided by 1/2, the quotient is greater than 5. It is equivalent to multiplying 5 by 2 (since dividing by a fraction is the same as multiplying by its reciprocal), which is 10. Therefore, 5 divided by 1/2 equals 10, which is greater than 5.