Answer:
t = 2
Step-by-step explanation:
5(6t-3)=5t+35
Step 1 distribute the 5 by multiplying 5 to what is inside of the parenthesis
5(6t) - 5(3) = 5t + 35
Outcome: 30t - 15 = 5t + 35
Step 2 add 15 to both sides
30t - 15 + 15 = 5t + 35 + 15
Outcome: 30t = 5t + 50
Step 3 subtract 5t from both sides
30t - 5t = 5t - 5t + 50
Outcome: 25t = 50
Step 4 divide both sides by 25
25t/25 = 50 we're left with t = 2
While walking in the country, you count 39 heads and 116 feet in a field of cows and chickens. How many of each animal are there?
Answer: 58
Step-by-step explanation:
its 58 because chickens have two feet each so divide 2 % 166 and its 58
because each chicken has 2 legs count the 2 legs up to 116 then u get ur answer
(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)
Answer:
A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2
Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5
B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle
A) The length of each side of the square is (2x + 5).
B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.
Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.
A) Now the length of each side of the square is calculated by factoring the area expression completely,
[tex](4x^2 + 20x + 25)[/tex]
[tex]4x^2 + (10 + 10)x + 25[/tex]
[tex]4x^2 + 10x + 10x + 25[/tex]
[tex]2x (x + 5) + 5(2x + 5)[/tex]
[tex](2x + 5) (2x+5)[/tex]
Hence the length of each side of the square is (2x + 5).
B) the dimensions of the rectangle are calculated by factoring the area expression completely,
[tex](4x^2 - 9y^2)[/tex]
[tex](2x)^2 - (3y)^2[/tex]
[tex](2x - 3y) (2x + 3y)[/tex]
Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).
To learn more about the rectangle visit:
https://brainly.com/question/2607596
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Factor 64a^3 -8b^3 Explain all steps.
Answer:
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
Step-by-step explanation:
factor out the 8
then you have the sum/difference of cubes..
look that up SOAP: same opposite, always a plus
[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?
Answer:
hi amki nai patajjdkfkejd
Suppose Event A is taking 15 or more minutes to get to work tomorrow and Event B is taking less than 15 minutes to get to work tomorrow. Events A and B are said to be complementary events.
a. True
b. False
Answer:
Hence the answer is TRUE.
Step-by-step explanation:
If event A is taking 15 or more minutes to urge to figure tomorrow and event B is taking but a quarter-hour to urge to figure tomorrow, then events A and B must be complimentary events. this is often because the occurring of 1 is going to be precisely the opposite of the occurring of the opposite event and that they cannot occur simultaneously. In other words, events A and B are mutually exclusive and exhaustive.
Mathematically,
P(A) + P(B) = 1.
Can someone help me out plz
Volume = πr²h
Radius = 3yd
Height = 12yd
Take π = 22/7
Volume = 22/7×3×3×12
= 2376/7
= 339.4285714yd³
Rounding off to nearest tenth
= 339.43yd³
Answered by Gauthmath must click thanks and mark brainliest
I need help ASAP please
Answer:
5:10
6 (-2,0)
7 (-5,6)
8 (5,3)
9 No, ab=8 CD=6
Step-by-step explanation:
identify the roots of the equation and the multiplicities of the roots 8(x - 2)³ = 0
Answer:
The root of the equation is 2 with multiplicity 3
Step-by-step explanation:
8(x-2)^3=0
(x-2)^3=0
The root of the equation is 2 with multiplicity 3
which of these figures has rotational symmetry
9514 1404 393
Answer:
A
Step-by-step explanation:
The parallelogram has rotational symmetry of degree 2. It looks the same after rotation by 180°.
_____
Additional comment
When a figure only looks like itself after a full rotation of 360°, it is said to have rotational symmetry of degree 1. All of the figures here will return to their original appearance after one 360° rotation. So, we assume the intent of the question is to identify figures with a rotational symmetry of degree greater than 1.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
9514 1404 393
Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
Find the measures of angles S and T in the triangle below.
May I get some help with this question?
Question with last attempt is displayed for your review only
Amanda rented a bike from Ted's Bikes.
It costs $9 for the helmet plus $5.25 per hour.
If Amanda paid about $43.13, how many hours did she rent the bike?
Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
[tex]43.13 = 5.25h + 9[/tex]
Step-by-step explanation:
Let's solve this by making an equation.
$9 for the helmet, and $5.25 per hour.
h will stand for hours, C will stand for Amanda's cost.
[tex]C = 5.25h + 9[/tex]
Now, substitute in what we learned from the problem.
[tex]43.13 = 5.25h + 9[/tex]
This is an equation you can use to solve for the hours.
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n=12, p=0.35, x=2
Answer:
0.1088 or 10.88%
Step-by-step explanation:
q = 1 - 0.35 = 0.65
P(X=2) = 12C2 × (0.35)² × (0.65)¹⁰
= 0.1088
please help this is due right now
Answer:
108.82
Step-by-step explanation:
what is the least common multiple between 25 and 8
Answer:
200
Step-by-step explanation:
Break down 25 = 5*5
Break down 8 = 2*2*2
They have no common factors
The least common multiple is
5*5*2*2*2 = 25*8 = 200
Answer:
200
Step-by-step explanation:
list the factors of 25: 5,5
factors of 8:2,2,2,
Karissa purchased a set of LED lights online that normally sells for $72.00 but was marked down to $48.96. What is the discount rate Karissa received? (2 points)
32%
47%
68%
help
What is 5 added to 3 4?
6. 12
Answer:
8.4
Step-by-step explanation:
jjdijendjndoendidnie
The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576
Use the table above for the z-score, and be sure to round up to the nearest integer.
========================================================
Explanation:
At 95% confidence, the z critical value is roughly z = 1.960
The population standard deviation is given to be sigma = 3.7
The error is E = 2 since we want to be within 2 inches of the population mean mu
The min sample size needed is:
n = (z*sigma/E)^2
n = (1.960*3.7/2)^2
n = 13.147876
n = 14
We always round up to the nearest whole number to ensure that we clear the hurdle (otherwise, the sample is too small). It doesn't matter that we're closer to 13 than to 14.
Help please ….. help
Answer:
Step-by-step explanation:
a) categorical
b) add all of the numbers and divide by how many numbers there were.
c) outliers means any that were far away from the rest of the data
d) not entirely, you can make an estimate based on it, but nat an exact answer.
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
2y-3x=10
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Hey there! I'm happy to help!
Here is our equation.
[tex]2y-3x=10[/tex]
Let's add 3x to both sides.
[tex]2y=3x+10[/tex]
Divide both sides by 2.
[tex]y=\frac{3}{2}x+5[/tex]
Here is slope intercept form.
[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]
So, we can just find those two things in the equation, and here are our answers.
[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]
The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.
[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]
Have a wonderful day and keep on learning! :D
Shaun is planting trees along his driveway, and he has 66 redwoods and 66 pine trees to plant in one row. What is the probability that he randomly plants the trees so that all 66 redwoods are next to each other and all 66 pine trees are next to each other
Answer:
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
Step-by-step explanation:
The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
Desired outcomes:
Two cases:
6 redwoods(6! ways) then the 6 pine trees(6! ways)
6 pine trees(6! ways) then the 6 redwoods(6! ways)
So
[tex]D = 2*6!*6![/tex]
Total outcomes:
12 trees, so:
[tex]D = 12![/tex]
What is the probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other?
[tex]p = \frac{D}{T} = \frac{2*6!*6!}{12!} = 0.0022[/tex]
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample? Make sure to give a whole number answer.
Answer:
The administrator should sample 968 students.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.88}{2} = 0.06[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.06 = 0.94[/tex], so Z = 1.555.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 300.
This means that [tex]n = 300[/tex]
If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 1.555\frac{300}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 300*1.555[/tex]
Dividing both sides by 15
[tex]\sqrt{n} = 20*1.555[/tex]
[tex](\sqrt{n})^2 = (20*1.555)^2[/tex]
[tex]n = 967.2[/tex]
Rounding up:
The administrator should sample 968 students.
b) Use Greens theorem to find∫x^2 ydx-xy^2 dy where ‘C’ is the circle x2 + y2 = 4 going counter clock wise.
It looks like the integral you want to find is
[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy[/tex]
where C is the circle x ² + y ² = 4. By Green's theorem, the line integral is equivalent to a double integral over the disk x ² + y ² ≤ 4, namely
[tex]\displaystyle \iint\limits_{x^2+y^2\le4}\frac{\partial(-xy^2)}{\partial x}-\frac{\partial(x^2y)}{\partial y}\,\mathrm dx\,\mathrm dy = -\iint\limits_{x^2+y^2\le4}(x^2+y^2)\,\mathrm dx\,\mathrm dy[/tex]
To compute the remaining integral, convert to polar coordinates. We take
x = r cos(t )
y = r sin(t )
x ² + y ² = r ²
dx dy = r dr dt
Then
[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy = -\int_0^{2\pi}\int_0^2 r^3\,\mathrm dr\,\mathrm dt \\\\ = -2\pi\int_0^2 r^3\,\mathrm dr \\\\ = -\frac\pi2 r^4\bigg|_{r=0}^{r=2} \\\\ = \boxed{-8\pi}[/tex]
in how many ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies?
Answer:
5880 ways
Step-by-step explanation:
For selections like this, we solve using the combination theory. Recall that
nCr = n!/(n-r)!r!
Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,
= 10C6 * 8C4
= 10!/(10-6)!6! * 8!/(8-6)!6!
= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!
= 210 * 28
= 5880 ways
The arrangement can be done in 5880 ways
Find the first five terms of the sequence..
Answer:
The Next fiver tems are - 2, -2,-8,-12,-16
Step-by-step explanation:
Answer:
2,-6,2,-6,2
Step-by-step explanation:
a1 = 2
an = -an-1 -4
Let n =2
a2 = -a1 -4 = -2-4 = -6
Let n=3
a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2
Let n = 4
a4 = -a3 -4 = -2 -4 = -6
Let n=5
a5 = -a4 -4 = -(-6) -4 = +6-4 = 2
Which equation can be used to find the length of Line segment A C?
Answer:
I don't see the problem.
Step-by-step explanation:
find the missing length indicated
explainion:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.
write the greatest and smallest four digit number by using 7,8,0,9 digit
Assume that the matrices below are partitioned conformably for block multiplication. Compute the product.
[I 0] [W X]
[K I] [Y Z]
Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
(I assume I is the identity matrix and 0 is the zero matrix.)