Answer:
There are 13 quarters, 5 nickels and 20 dimes.Step-by-step explanation:
Givens
Max has $5.50.He has eight more quarters than he does nickels.He had four times as many dimes as he has nickels.From these statements, we can deduce algebraical expressions to solve the problem. Let's call [tex]q[/tex] quarters, [tex]n[/tex] nickels and [tex]d[/tex] dimes.
[tex]q=n+8[/tex] (8 more quarters than nickels)
[tex]d=4n[/tex] (he has four times as many dimes as he has nickels).
[tex]0.25q+0.05n+0.10d=5.50[/tex] (Max has a total of $5.50, one quartes is $0.25, one nickel is $0.05 and one dime is $0.10).
Let's replace the first two expressions into the third equation
[tex]0.25(n+8)+0.05n+0.10(4n)=5.50\\0.25n+2+0.05n+0.40n=5.50\\0.70n=5.50-2\\n=\frac{3.50}{0.70}\\ n=5[/tex]
There are 5 nickels.
Now, we use this value to find the number of quarters
[tex]q=5+8=13[/tex]
There are 13 quarters.
Also, [tex]d=4(5)=20[/tex]
There are 20 dimes.
Therefore, there are 13 quarters, 5 nickels and 20 dimes.
What is the Volume and surface area of a cone with a diameter of 18ft and a slant height of 30ft
Answer:
A cone with a diameter of 18ft and a slant height of 30ft
Using Pythagorean theorem, the height is calculated by:
H = sqrt(18^2 - (30/2)^2) = 9.95
The surface area:
A = lateral surface area + base
A = pi x radius x slant height + pi x radius^2
A = pi x (30/2) x 18 + pi x (30/2)^2 = ~1555.1 (ft2)
The volume:
V = base x height x (1/3)
V = pi x radius^2 x height
V = pi x (30/2)^2 x 9.95 = 7033.2 (ft3)
Hope this helps!
:)
How do you simplify [tex]\frac{\sqrt{2} +\sqrt{6} }{\sqrt{8} + \sqrt{6} }[/tex]?
The trick is to exploit the difference of squares formula,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:
[tex](\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2[/tex]
Whatever you do to the denominator, you have to do to the numerator too. So
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2[/tex]
Expand the numerator:
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}[/tex]
So we have
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2[/tex]
But √12 = √(3•4) = 2√3, so
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}[/tex]
I need help with this question please.
Answer:
work is shown and pictured
2 mil 20 yd = ____ yd
Answer:
3540
Step-by-step explanation:
There are 3520 yards in two miles and 1760 in one mile you multiply 1760 by 2 then add 20
Evaluate sin^2Θ, for Θ=45°
Answer:
sin^2(45) = (√2/2)^2 = 1/2
Step-by-step explanation:
sin2x = sin2 * x = 0.909x
sin(2(45)) = sin90 = 1
Hope this helps.
Answer:
The answer to this is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I did the assignment, hope it helps! :)
Rewrite the following equation in logarithmic form.
0.25 = 2^-2
Rewrite the following equation in exponential form.
log8 (512) = 3
Answer:
log2(0.25) = -2
512 = 8^3
Step-by-step explanation:
Use of formula: loga (b) = c ⇔ b = a^cRewrite the following equation in logarithmic form. 0.25 = 2^-2
log2(0.25) = -2Rewrite the following equation in exponential form. log8 (512) = 3
512 = 8^320,30,40,50,60,70,80 the mean of the number set is
Answer:
Mean is 50
Step-by-step explanation:
20 + 30 + 40 + 50 + 60 + 70 + 80 = 350
350 / 7 = 50
Answer:
50
Step-by-step explanation:
Mean means average number which sum of all numbers divided how many numbers we are investigating
We are investigating 7 numbers
The total sum of these numbers are:
20 + 30 + 40 +50+ 60+70+80= 350
Mean = 350/7= 50
How do I do Radicals?
Answer:
For online calculators you can type sqrt() or just sqrt and it will do it for you
Answer:
See belowStep-by-step explanation:
To simplify radicals that are not perfect squares, we need a new method.
Example: [tex]\sqrt{27}[/tex]
27 is not a perfect square square the square root cannot be used.
[tex]\sqrt{27} = 5.19615242271[/tex]
To solve this, we need to break down the radical into simpler parts.
[tex]\sqrt{27} = \sqrt{3} * \sqrt{9}[/tex]
[tex]\sqrt{9} = 3[/tex]
[tex]\sqrt{3}[/tex] cannot be simplified
[tex]\sqrt{27}[/tex] = 3[tex]\sqrt{3}[/tex]
Good luck on your test!
I'm always happy to help :)
What value of z makes the following equation true?
−3z+3=35
Answer:
-10 2/3Step-by-step explanation:
Given
−3z+3=35Solving for z:
-3z = 35 - 3-3z = 32z = 32/-3z = -10 2/3What numbers would make 4a ≤ 16 true?
Answer: a ≤ 4 or (-∞, 4]
Step-by-step explanation:
Here we have the inequality:
4a ≤ 16
this means that the left sides is less or equal than the right side.
First, find the equal part:
4*a = 16
a = 16/4 = 4
So the maximum possible value of a is 4.
Now, all the values of a smaller than 4 also make the inequality true (even the negative values) so the possible values of a are:
a ≤ 4 or (-∞, 4]
Answer:
Any number that is less or equal to 4 makes this inequality true.
Step-by-step explanation:
In order to calculate the numbers that make this inequality valid, we need to solve it for "a". This can be done in the same manner as we would solve an equation, although we must pay attention to the inequality. This is done below:
[tex]4*a \leq 16\\a \leq 16/4\\a \leq 4[/tex]
Any number that is less or equal to 4 makes this inequality true.
Tina loves to read. Before breakfast, she read 21/2 pages, at lunch she read 31⁄5 pages, and after dinner she read 11⁄3 pages. How much did Tina read in total?
Answer: 7 1/30
Step-by-step explanation:
Tina loves to read. Before breakfast, she read 2 1/2 pages, at lunch she read 3 1/5 pages, and after dinner she read 1 1/3 pages. To find the total, we add all the pages together. This will be:
2 1/2 + 3 1/5 + 1 1/3
The LCM of 2, 5 and 3 is 30.
= 2 15/30 + 3 6/30 + 1 10/30
= 6 31/30
= 7 1/30.
What is the probability that I will choose a cat owner and a bird owner. Please help. Thanks
Answer:
The probability is 1/36.
Step-by-step explanation:
2/3 are dog owners
1/6 are cat owners
1/6 are bird owners
If you choose two owners, there is a 1/6 chance that you will choose a cat owner and a 1/6 chance you will choose a bird owner. Each of these are independent, so you simply multiply 1/6 by 1/6.
1/6 * 1/6= 1/36
Bryna has $300 to open a checking account. She wants an account with the least amount of fees. She does not plan on using an ATM and her employer offers direct deposit.
A 6-column table with 3 rows. Column 1 has entries A, B, C. Column 2 is labeled Minimum Balance with entries 500 dollars, 250 dollars, 50 dollars. Column 3 is labeled Interest with entries 0.1 percent, 0 percent, 0 percent. Column 4 is labeled Overdraft protection with entries yes, no, no. Column 5 is labeled A T M Fees with entries 0 dollars for all A T M s, 0 dollars for A B C banks A T M s, 2 dollars per transaction. Column 6 is labeled Monthly Fee with entries 5 dollars, 10 dollars, 0 dollars with direct deposit.
Bryna should choose account
.
Answer:
Its C On Edge Just Took The Quiz
Step-by-step
Answer:
c
Step-by-step explanation:
took quiz 100%
Write this number in scientific notation.
0.0000071=
Answer:
7,1 × 10-⁶
Step-by-step explanation:
Once you move the comma 1 time by right (,) you have -1, so by moving it six times, you have 7,1 × 10-⁶
The graph of f(x) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1.75, 4), has a vertex of (negative 0.25, negative 3), and goes through (1.4, 4). Solid circles appear on the parabola at (negative 1.6, 3.1), (negative 1.2, 0), (negative 0.25, negative 3), (0.8, 0), (1.2, 3.1).
Over which interval on the x-axis is there a negative rate of change in the function?
–2 to –1
–1.5 to 0.5
0 to 1
0.5 to 1.5
Answer:
The answer to this question is A, or -2 to -1.
Hope this helps.
Answer: A
Step-by-step explanation:
which of the binomials below is a factor of this trinomial? x^2+6x-40
Answer:
C
Step-by-step explanation:
(x-4)(x+10)=x^2+6x-40
Answer:
C. X-4
Step-by-step explanation:
A P E X
I’m just confused on how to find the equation with the quadratic function given.
option b is the correct answer
What is the solution set to the equation x^2=-1
Answer:
Step-by-step explanation:
For example, if your money earns an 8 percent interest rate, it will triple in 14 years and 5 months (115 divided by 8 equals 14.4). If your money earns a 5 percent interest rate, it will triple in 23 years (115 divided by 5 equals 23).
Five 12s is equal to how many 48s?
Answer:
1 1/4 48's.
Step-by-step explanation:
5 * 12 = 60
60 / 48 = 1 12/48
= 1 1/4.
Answer:
1 48
Step-by-step explanation:
if 2 twelve is equal to 24 and 24+24= 48 then 4 12s would equal one 48 with 12 still remaining
please help 50 points and brainliest!!!!!!!!
Answer:
To do this you need to fill in the equation: 1/2 height*sidelength *width. So, height = 8 ft, side length = 4 ft, and width = 24 ft. So, plugging in the numbers you get:
1/2(8) * 4 * 24 =
4*4*24 = 384 ft
Step-by-step explanation:
Answer:
345 ft^3
Step-by-step explanation:
B=1/2(5)(6)=15
V=15(23)=345
5x + 7 + 2x anwer plz
Answer:
The final answer is [tex]7x +7[/tex] .
Step-by-step explanation:
-Solve equation:
[tex]5x + 7 + 2x[/tex]
-Combine like terms:
[tex]5x + 7 + 2x[/tex]
[tex]7x +7[/tex]
-Result:
[tex]7x +7[/tex]
Please help me ASAP and I have more so PLEASE
The answer is B part
As the requirement for the student is either a senior or one who studies maths or both.
So, just add the values within the two venn circles divide it by total no of values.
=> 240+40+110/240+40+110+840
=> 360/1200
Answer:
B
Step-by-step explanation:
840 people aren't senior or don't takes math.
210 + 40 = 250 are seniors
110 + 40 = 150 people take math
In this class has 840 + 210 + 40 + 110 = 1200 people => All
210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)
Probabilty that a randomly selected student is a senior or takes math =>[tex]\frac{P(S U M)}{All}[/tex]
[tex]\frac{P(S U M)}{All} = \frac{360}{1200}[/tex]
Hope this helps ^-^
The quadratic equation x^2−8x+16=0 can be rewritten as (x−4)(x−4)=0.
What is the multiplicity of the root x=4?
The multiplicity of the root is 4.
The multiplicity of the root is 2.
The multiplicity of the root is 1.
The multiplicity of the root is 3.
Answer:
The multiplicity of the root is 2Step-by-step explanation:
Multiplicity of a number is the number of times the factor of a given function appears in the factor form of such given equation. For us to know the multiplicity of the root of the function, first we must know its root.
Factorizing the given quadratic function x²−8x+16=0
[tex]x^{2} -4x-4x+16 = 0\\x(x-4)-4(x-4)=0\\(x-4)(x-4) = 0\\x-4 = 0 and x-4 = 0\\x = 4\ twice[/tex]
Since the root of the function which is 4 appears twice then the multiplicity of the root is 2
correct expression equivalent to 9-(3-6x)
Answer:
6 + 6x
Step-by-step explanation:
9 - (3-6x) = 9 - 3 - (-6x)
= (9-3) +6x
= 6 + 6x
1) expand the bracket
2) group like terms together
3) simplify to form expression
the decimal expansion of 131 upon 120 will terminate after how many places of decimal A)1 b)2c) 3D) will not terminate
Answer:
c) 3
Step-by-step explanation:
Given that events A and B are independent with P(A)=0.24P(A)=0.24 and P(B|A)=0.85P(B∣A)=0.85, determine the value of P(B)P(B), rounding to the nearest thousandth, if necessary.
Answer:
P(B) = 0.85
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
[tex]P(A) = 0.24, P(B|A) = 0.85[/tex]
These events are independent.
This means that [tex]P(A \cap B) = P(A)*P(B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(B|A) = \frac{P(A)*P(B)}{P(A)}[/tex]
[tex]P(B|A) = P(B)[/tex]
So
[tex]P(B) = 0.85[/tex]
The exterior angle of a regular polygon is 30°. What is the measure of an interior angle of the polygon.
B. How many sides does this polygon have.
C. What is the sum of all the interior angels.
This is all the same polygon.
Answer:
A) Measure of an interior angle of polygon = 150°
B) No of sides = 12
C) Sum of all interior angles = 1800°
Step-by-step explanation:
Measure of interior angle of polygon = 180°- measure of exterior angle of polygon
= 180°-30°
= 150°
B.
[tex]No.\: of \: sides = \frac{360\degree}{30\degree} = 12\\\\C.\\Sum\:of\: all \:interior\: angles \\= (n-2)\times 180\degree\\= (12-2) \times 180\degree\\= 10\times 180\degree\\= 1800\degree[/tex]
An irregular figure was broken into a triangle and rectangle. The area of the triangle is in2. The area of the rectangle is in2. The area of the irregular figure is in2.
Answer:
the anser is 24,32,56
Step-by-step explanation:
i did it got it wrong and then it gave me the right anser witch is that
Answer:
24,32,and 56 is right. trust me
Step-by-step explanation:
One of the solutions to x^2 – 2x – 15 = 0 is x = -3. What is the other solution?
x = -5
x = -1
x = 1
x = 5
Answer:
work is shown and pictured
3x + 5 = 2x + 8 =
help me plz
Answer:
x=3
Step-by-step explanation:
Answer:
The answer would be 3.
Step-by-step explanation: