Answer:
81y^4 - 16x^2, difference of squares.
Step-by-step explanation:
So we need to expand the following product:
(9y2-4x)(9y2+4x) = 9y2*9y2 + 4x*9y2 - 4x*9y2 -4x*4x = 81y^4 - 16x^2
And this type of product is the difference of squares.
Answer:
Step-by-step explanation:
The given expression is ( 9y² - 4x) (9y² + 4x)
We will simplify the given expression
(9y² - 4x) (9y² + 4x) = 9y² (9y² + 4x) - 4x (9y² + 4x) [Distributive property]
= 81y⁴ + 36xy² - 36xy² - 16x²
= (81y⁴ - 16x²)
This simplified form is the difference of squares of terms (9y²) and (4x)
For a certain spinner, if we expect to win a prize four times in sixty tries, what is the theoretical probability of winning a prize?
A) 1/30
B) 1/20
C) 1/15
D) 1/5
Answer:
C
Step-by-step explanation:
60 divided by 4, is fifteen, and 1/15 is 4/60 simplified.
Answer: A is maybe the answer.
Step-by-step explanation:
You are to demonstrate that you understand what represents a function and what does not represent a function. You may do this by either writing a paragraph using complete sentences or drawing pictures with labels.
we are required to demonstrate that we understand what represents a function and what does not represent a function by writing a paragraph which can be given as:
We know that functions are mathematical entities that assign unique outputs to given inputs. In other words, a function can't have repeated values in the input repeated x-value.
For example consider the relation {(1,4), (1,5), (2,6), (3,7), (4,8), (5,9)}.
We see that above relation has repeated x-value "1" which is assigned to two different output values 4 and 5. So by definition of function, above relation can't be a function.
Suppose that 7% of the general population has a disease and that the test for the disease is accurate 70% of the time. What is the probability of testing positive for the disease.
Answer:
0.049
4.9 % of probability
Step-by-step explanation:
The probability of having the disease is equal to 7%
The probability of testing positive, having the disease is equal to 70%
We are looking for the probability of testing positive.
For that, we need to multiply the probabilities to find the result
P = (0.07)*(0.7)
P = 0.049
P = 4.9%
A can contains 24 fluid ounces of juice. How many pints of fruit juice does the can contain?
Answer:
The can contains 1.5 pints of fruit juice.
Step-by-step explanation:
A can contains 24 fluid ounces of juice.
We have to convert the amount of juice from ounce to pints.
As we know that 1 fluid ounces = [tex]\frac{1}{16}[/tex] pints or 0.0624 pints.
So 24 fluid ounces = 0.0625 × 24 = 1.5 pints.
Therefore, The can contains 1.5 pints of fruit juice.
The can contain 1.5 pints of fruit juice
How many pints of fruit juice does the can contain?A pint is equal to 16 fluid ounces. That is:
1 pint = 16 fluid ounces
To find out how many pints of juice the can contains, we need to divide the number of fluid ounces by the number of fluid ounces in a pint.
Thus, 24 fluid ounces of juice in pint will be:
24/ 16 = 1.5 pints
Therefore, the can contains 1.5 pints of fruit juice.
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Six less than what number is eighteen?
3
12
24
108
Answer:
24
Step-by-step explanation:
X - 6 = 18
Add 6 to both sides
x = 24
Answer:
the answer is 24
Step-by-step explanation:
find the value of x 5x+6-2=9
A.1
B.5
C.3/7 fraction
D. 5/7 fraction
Answer:
A
Step-by-step explanation:
Given
5x + 6 - 2 = 9, that is
5x + 4 = 9 ( subtract 4 from both sides )
5x = 5 ( divide both sides by 5 )
x = 1 → A
solve for x
x=
the graph shown below
Answer:
x=27
Step-by-step explanation:
Without the arrow crossing through that right angle, it would equal 90 degrees. Since it's cut in half, each part equals 45 degrees. A straight line equals 180 degrees. 3×27=81 and 81+9=90. 90+90=180 :)
7x+6(x+10)>5 (-3-3x)+3x
Answer:
[tex]\large\boxed{x>-3\to x\in(-3,\ \infty)}[/tex]
Step-by-step explanation:
[tex]7x+6(x+10)>5(-3-3x)+3x\qquad\text{use the distributive property}\\\\7x+(6)(x)+(6)(10)>(5)(-3)+(5)(-3x)+3x\\\\7x+6x+60>-15-15x+3x\qquad\text{combine like terms}\\\\(7x+6x)+60>(-15x+3x)-15\\\\13x+60>-12x-15\qquad\text{subtract 60 from both sides}\\\\13x>-12x-75\qquad\text{add 12x to both sides}\\\\25x>-75\qquad\text{divide both sides by 25}\\\\x>-3[/tex]
What is the probability of flipping a coin 10 times and getting tails 7 times ? Round your answer to the nearest tenth of a percent.
Answer:
Option C: 11.7%
Step-by-step explanation:
The number of elements in sample space when a coin is flipped 10 times will be:
[tex]n(S) = 2^{10} \\= 1024[/tex]
Let A be the event that the tails appear 7 times:
Then,
[tex]C_{(n,k)}=\frac{n!}{(k!)(n-k)!} \\where\\n=population\\k=picks\\In our case, k =7\\and\\n=10\\C_{(10,7)}= \frac{10!}{(7!)(10-3)!}\\= 120\\So, \\P(A) = \frac{n(A)}{n(S)} \\P(A) = \frac{120}{1024} \\= 0.1171\\[/tex]
Converting into percentage:
[tex]P(A) = 0.1171*100=11.7%[/tex]
So, option C is correct ..
Answer:4.4%
Step-by-step explanation:just took it
(6-3(cube root of 6)/(cube root of 9)
For this case we must simplify the following expression:
[tex]\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}}[/tex]
Multiplying the numerator and denominator by[tex](\sqrt [3] {9}) ^ 2[/tex]
[tex]\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}} * \frac {(\sqrt [3] {9}) ^ 2} {(\sqrt [3] { 9}) ^ 2} =[/tex]
We rewrite:
[tex]\frac {\frac {6-3 \sqrt [3] {6}} * (\sqrt [3] {9}) ^ 2} {\sqrt [3] {9} * (\sqrt [3] {9 }) ^ 2} =[/tex]
By properties of powers we have that:
[tex]a ^ m * a ^ n = a ^ {m + n}\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {(\sqrt [3] {9}) ^ 3} =\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {9} =[/tex]
We rewrite, moving the exponent within the radical:
[tex]\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {9 ^ 2}} {9} =\\\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {81}} {9} =[/tex]
We can rewrite[tex]3 * 3 ^ 3 = 81[/tex]
[tex]\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {3 * 3 ^ 3}} {9} =[/tex]
We simplify:
[tex]\frac {(6-3 \sqrt [3] {6}) * 3 \sqrt [3] {3}} {9} =[/tex]
We apply distributive property:
[tex]\frac {18 \sqrt [3] {3} -9 \sqrt [3] {18}} {9} =[/tex]
Simplifying we finally have:
[tex]2 \sqrt [3] {3} - \sqrt [3] {18}[/tex]
Answer:
[tex]2 \sqrt [3] {3} - \sqrt [3] {18}[/tex]
A state park had a population of 330 rabbits. The population grew, with continuous compounding at a rate of 15% per year for 12years. How many rabbits were in the park after the 12 years?
330(1.15)^12=1765.58
The population of rabbits grew continuous compounding so formula for continuously compounded will apply.
The rabbits were in the park after 12 years is 1,996 rabbits.
Given:
The population of rabbit is [tex]P=330[/tex].
The rabbit increasing rate is [tex]r=15\%[/tex].
Time is [tex]t=12\:\rm year[/tex].
Apply the formula for continuously compounded to calculate the number of rabbit after 12 year.
[tex]A=Pe^{rt}[/tex]
Substitute the value.
[tex]A=330.00(2.71828)^{(0.15)(12)}\\A=1,996.38 \\A\approx1996[/tex]
Thus, the rabbits were in the park after 12 years is 1,996 rabbits.
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Destiny bought 10 1/2 yards of material for costumes for the city pageant she will use one and 140 yards of the material to make each costume how many costumes can destiny complete
Answer:
She can complete 8 costumes
Step-by-step explanation:
Answer:
8 costumes
Step-by-step explanation:
What is 9 +[(4.2- 3.3)+(6.4/0.8)] x 3
answer. 35.7
explanation: bedmas is important in this question. subtract and divide in the brackets first. add the two numbers in the brackets second. multiply the 8.9 by the 3. then add the 9 to the 26.7
Answer:
35.7
Step-by-step explanation:
9 +[(4.2- 3.3)+(6.4/0.8)] x 3
(4.2- 3.3) = 0.9
(6.4/0.8) = 8
9 + (0.9 +80) × 3 = 9 + 8.9 × 3
= 9+26.7
= 35.7
Which of the following equations corresponds to the graph below
the answer would be d because it goes down 2 and over 1
The answer is d because of the y intercept is -1 and the slope is -2 according to y=mx+b
Which is the best estimate for the percent that is represented by the shaded portion of the diagram? 30% 36% 38% 40%
Answer:
Three of the boxes out of the eight are shaded.
So, 3/8 is .375 which is around 38%.
Hello there!
In this diagram, there are a total of 8 squares, and 3 of them are shaded. This means that 3/8 of them are shaded, and to find what percent this is, divide 3 by 8 and multiply what you get by 100.
3 divided by 8 = 0.375
0.375 x 100 = 37.5%.
37.5% is closest to 38%, so that is your answer!
I hope this helps and have a great rest of your day!
The circumference of a circle with a radius of 1 is 2π. Set up a proportion to find the circumference of a circle with a radius of 6.
Answer:
6 radius = 2π x 6
= 12π
Step-by-step explanation:
Circumference of a circle
C = 2πr
here r is radius of circle and 2π is constant is we can say that circumference of a circle is directly proportional to it's radius.
C ∡ r
Given in the question that circumference of a circle with a radius of 1 is 2π.
1 radius = 2π
6 radius = 2π x 6
= 12π
Which of the functions have period pi?
A.) y = tan x
B.) y = csc x
C.) y = cot x
D.) y = sec x
ANSWER
A.) y = tan x
C.) y = cot x
EXPLANATION
The period refers to the interval over which the graph completes one cycle
The trigonometric functions
[tex]y = \tan(x) [/tex]
and
[tex]y = \cot(x) [/tex]
are reciprocals of each other.
They have the same period, which is π
Also y=cscx and y=secx are reciprocals of the sine and the cosine functions respectively.
They have periods of 2π
If a car can go 200 miles in 6hours how far can it go in 7 hours
Answer:
If a car can go 200 miles in 6 hours at a constant rate, in 7 hours it will have gone 233.33 (0.33 repeating) miles.
Step-by-step explanation:
If a car can go 200 miles in 6 hours, then we know it can go about 33.33 miles per hour (found by dividing 200 by 6).
If the car is going at this constant rate we can then multiply 33.33 by 7, which would give us 233.33.
The car can go 233.33 miles in 7 hours
What is Ratio and proportion ?A comparison of two entities by dividing them is called Proportion and when two ratios are equated to one another , they are said to be in proportion.
It is given in the question that
a car can go 200 miles in 6 hours
Distance covered in 7 hours
In the given question the ratio of Distance covered and time is
200/6 = 100/3 = 100:3
Let the distance covered in 7 hours is x
therefore the ratio will be x : 7
These two ratios will be in proportion
100:3 = x: 7
100/3 = x / 7
x = 100 * 7 / 3
x = 700 / 3
x = 233.33 miles
Therefore The car can go 233.33 miles in 7 hours .
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What is the main purpose of the reproductive system in organisms on Earth?
A.
to enable an organism to make more of its kind
B.
to control the level of various hormones in the organism
C.
to allow an organism to move through contractile forces
D.
to provide leverage for movement and organ protection
Answer:
A.
Step-by-step explanation:
That's what I would say, at least.
A linear function includes the ordered pairs (2,5), (6,7) and (k,11). What is the value of k?
A)8
B)10
C)12
D)14
ANSWER
D)14
EXPLANATION
The linear function includes the ordered pairs (2,5), (6,7) and (k,11).
The slope of this line is the same for any two given points:
[tex] \frac{7 - 5}{6 - 2} = \frac{11 - 7}{k - 6} [/tex]
[tex]\frac{2}{4} = \frac{4}{k - 6} [/tex]
Cross multiply,.
2(k-6)=4×4
2(k-6)=16
Divide both sides by 2
k-6=8
k=8+6
k=14
Answer:
Option D will be the answer.
Step-by-step explanation:
y intercept form of a line is represented by y = mx + c
Where m = slope of the line and c = y- intercept of the line.
A line passing through two points (2, 5) and ( 6, 7) has the slope
m = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{7-5}{6-2}[/tex]
= [tex]\frac{2}{4}[/tex]
= [tex]\frac{1}{2}[/tex]
Equation will be y = [tex]\frac{x}{2}+c[/tex]
This line passes through (2, 5)
5 = [tex]\frac{1}{2}\times 2+c[/tex]
c = 5 - 1
c = 4
And the equation will be y = [tex]\frac{1}{2}x+4[/tex]
Since a point (k 11) passes through the line then we will plug in these values in the equation to find the value of k.
11 = [tex]\frac{1}{2}\times k+4[/tex]
11 - 4 = [tex]\frac{k}{2}[/tex]
7 = [tex]\frac{k}{2}[/tex]
k = 2×7
= 14
Option D will be the answer.
The equation of a parabola is given. y=1/4x^2−3x+18 What are the coordinates of the focus of the parabola?
Answer:
(6,10)
Step-by-step explanation:
Used a calculator
please help drag and drop
FCH - NPM
PNM - CFH
HF - MN
NP - FC
Complete the table, and make a graph showing the relationship between quarts and pints
Step-by-step explanation:
One quart equals to Two pints.
As a result to find the number of quarts that equal a certain number of pints you multiply number of quarts by 2
FORMULA= (P=Q×2)
1Q=2P
2Q=4P
3Q=6P
4Q=8P
if amanda got on the bus at 2:40 and got off the bus at 3:15. how long was amanda on the bus
Answer:
35 minutes
Step-by-step explanation:
Answer:
35 minutes
Step-by-step explanation:
She was on the bus for :20 before 3:00 and for :15 after 3:00, for a total of ...
:20 +:15 = :35
That is, 35 minutes.
___
There are 60 minutes in an hour. If you like, you can change an hour to 60 minutes and write the exit time as 3:15 = 2:75. Then you can perform the subtraction
2:75 -2:40 = 0:35
The expression -3m - [2m + (5 - m)] + 7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified correctly.
Answer: It is correctly simplified form.
Step-by-step explanation:
Since we have given that
[tex]-3m-[2x+(5-m)]+7[/tex]
We need to simplify the above expression:
[tex]-3m-2m-5+m+7\\\\=-5m+m+2(\text{gather the like terms})\\\\=-4m+2\\\\=2-4m[/tex]
So, [tex]-3m-[2x+(5-m)]+7=2-4m[/tex]
Hence, it is correctly simplified form.
Which best explains or justifies step 2
Answer B
Step-by-step explanation:
Choose the function whose graph is given by:
[tex]y=3sec\left(\frac{1}{2}x\right)[/tex]
Step-by-step explanation:The graphs of [tex]sec(x)[/tex] can be obtained from the graph of the cosine function using the reciprocal identity, so:
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
But in this problem, the graph stands for the function:
[tex]y=3sec\left(\frac{1}{2}x\right)[/tex]
Because the period is now 4π as indicated and for [tex]x=0[/tex] in the figure and this can be proven as follows:
[tex]Period=\frac{2\pi}{\frac{1}{2}}=4\pi[/tex]
Also, [tex]for \ x=1 \ then \ y=3[/tex] as indicated in the figure and this can be proven as:
[tex]y=3sec\left(\frac{1}{2}x\right) \\ \\ y=\frac{3}{cos(0.5x)} \\ \\ y=\frac{3}{cos(0.5(0))} \\ \\ y=\frac{3}{1}=3[/tex]
8 less than the product of a number n and 1/5 is no more than 95
Answer:
(n/5)-8≤95
Step-by-step explanation:
The solution for the given problem is : [tex]\( n \leq 515 \)[/tex].
Sure, let's solve the problem step by step.
Given: [tex]\( \frac{1}{5}n - 8 \leq 95 \)[/tex]
To solve for [tex]\( n \),[/tex] we'll first add 8 to both sides of the inequality:
[tex]\( \frac{1}{5}n \leq 95 + 8 \)[/tex]
[tex]\( \frac{1}{5}n \leq 103 \)[/tex]
Now, we'll multiply both sides by 5 to isolate[tex]\( n \)[/tex]:
[tex]\( 5 \times \frac{1}{5}n \leq 5 \times 103 \)[/tex]
[tex]\( n \leq 515 \)[/tex]
So, the solution is[tex]\( n \leq 515 \)[/tex]
In conclusion, the solution to the problem is [tex]\( n \leq 515 \)[/tex]. We reached this conclusion by carefully manipulating the inequality step by step to isolate [tex]\( n \).[/tex] This process ensures that our solution is accurate and follows the rules of algebra.
Complete question:
8 less than the product of a number n and 1/5 is no more than 95
What is the hypothesis of the given statement? If pigs had wings, you could fly.
The hypothesis of the given statement is that if pigs had wings, you could fly.
Explanation:The hypothesis of the given statement is that if pigs had wings, you could fly.
This statement is an example of a hypothetical scenario, as pigs do not actually have wings. The hypothesis implies that if pigs did have wings, it would enable flight for humans.
It is important to note that this statement is purely hypothetical and does not reflect the reality of pigs having wings.
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PLEASE HELP ME i'm struggling in math what is x? if i carry the 3 over does that mean i add or multiply? Brainliest answer!!!! 30 points
Answer:
carry over the three means to add i hope you are happy
Step-by-step explanation:
Answer: Usually you have to find the value of X, for example if 9 - x = 5, then you have to subtract 5 from the nine and you get 4, and when you carry three over that means you have to regroup, for example
902 +
459
so 9+2=11, so you put 1 right there
902 +
459
.....1
and you carry the other 1 next to the 0, then it will become 10 + 5,
hope this helps, if you still don't get it tell me
Step-by-step explanation:
+