Square both sides:
x^2+2sqrt3+3=0
x^2=-2sqrt(3)-3
x=sqrt(2sqrt(3)+3)i
or
x=-sqrt(2sqrt(3)+3)i
A(3, 7), B(5, 7), C(3-7), D(5, -7)
what is the area ?
Answer:
28 square units.
Step-by-step explanation:
This is a rectangle with sides (7 - (-7) and (5 - 3)
= 14 by 2
= 28 unit^2.
Write 3^7/2 in surd form.
Answer:
[tex]\sqrt[2]{3^7}[/tex]
Step-by-step explanation:
[tex]\sqrt[2]{3^7}[/tex]
The top number is the power and the bottom of the fraction is the root
Please help out explanation need it
For this you just look at the sides.
Soh cah toa
This is good to remember.
Sin = opposite/ hypotenuse
Cos= adjacent/ hypotenuse
Tan = opposite/ adjacent
In this case you have TanZ, the side adjacent to the angle is 10 and the opposite to the angle is 24. So tanZ is 24/10 which simplifies to 12/5.
The hypotenuse is always the longest side, but the opposite and adjacent sides can change depending on the angle.
Answer:90 = ... 42 + 48) - 360
Step-by-step explanation:
An item is regularly priced at $70. Keiko bought it on sale for 80% off the regular price. How much did Keiko pay? $
Answer:
$14
Step-by-step explanation:
80% of $70 is $14, saving him $56
The other person has a great answer. Here's another approach.
If the discount is 80%, then you have to pay the remaining 20% (the two percentages add to 100%)
20% of 70 = 0.20*70 = 14
The sale price is $14 which is the amount Keiko pays
We see that Keiko saves 70-14 = 56 dollars.
Ken needs a total of $410 to buy a new bicycle. He has $35 saved. He earns $15 each week delivering newspapers. How many weeks will Ken have to deliver papers to have enough money to buy the bicycle?
Thanks so much! :D
Answer:
25 weeks
Step-by-step explanation:
Since we already know that he has $35 buck-a-roons saved, we can just subtract that from the cost of the bicycle to find the actual price—which would be 375. Then, we know that for every week, he gains $15 bucks. Therefore we know that 15 would be our variable so we can create the following equation:
15x + 35 = 410
15x = 375
15x/15 = 375/15
x = 25
After 25 weeks, Ken will have enough money to buy the bicycle.
Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.
Answer:
Step-by-step explanation:
The remainder when f(x) is divided by x + 3 would be 76.
What is remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x).
We have been given a function;
[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]
We need to find the remainder when f(x) is divided by x + 3.
So, Let p(x) = x + 3
p(x) = 0
x + 3 = 0
x = -3
Substitute in the given function f(x);
[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]
Thus, the remainder when f(x) is divided by x + 3 would be 76.
Learn more about remainder;
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10 times as much as 9
Answer:
90
Step-by-step explanation:
10 x 9
=> 90
10 times 9 is 90.
1. Which of these sentences are propositions? What are the
truth values of those that are propositions?
a) Boston is the capital of Massachusetts.
b) Miami is the capital of Florida.
c) 2 + 3 = 5. d) 5 + 7 = 10.
e) x + 2 = 11. 1) Answer this question.
Answer:I have the same problem
Step-by-step explanation
Solve for y 2y+1>-9/5y-6
Answer: All real numbers
Step-by-step explanation:
Let's find the critical points of the inequality.
2y2+1=
−9
5
y−6
2y2+1−(
−9
5
y−6)=
−9
5
y−6−(
−9
5
y−6)(Subtract (-9)/5y-6 from both sides)
2y2+
9
5
y+7=0
For this equation: a=2, b=1.8, c=7
2y2+1.8y+7=0
y=
−b±√b2−4ac
2a
(Use quadratic formula with a=2, b=1.8, c=7)
y=
−(1.8)±√(1.8)2−4(2)(7)
2(2)
y=
−1.8±√−52.76
4
What is the domain of the function in the graph?
Answer:
C
Step-by-step explanation:
You are looking at the domain which is on the K axis. It starts at 6 and ends at 11. The range J is 80 to 120
Which expression is equivalent to sqrt of (6x^5 z)^3/ 4x^4 z^2
Answer:
[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]
I hope I helped you^_^
a test has 10 multiple-choice questions with 6 choices each, followed by 35 true/false questions. if a student guesses on each equation, how many ways can he answer the questions on the test
Answer:
6¹⁰×2³⁵
Step-by-step explanation:
he has 6 choices for the first multiple choice question.
and for each of those he had again 6 more choices to answer the second question. 6×6 = 36
so, for all 10 multiple choice questions he answer in
6¹⁰ different ways = 60466176 ways
then there are 35 true/false questions, which are Bausch again multiple choice questions but with only 2 options instead of 6.
so we get 2³⁵ different possibilities. a huge number.
and they're possible for each of the 60466176 ways of the multiple choice part.
so, in total we have
6¹⁰×2³⁵ different answer possibilities.
Mr. Howe ate 1/3 of a pizza and then Mr. Kurt ate 1/8 of the same pizza. How
much of the pizza has been eaten? *
12/24
Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.
Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24
Step Three: Add our new fractions: 3/24+8/24= 12/24
Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten
I hope I've help!
Complete the equation describing how
x and y are related.
X
-2
-1
D
у
12
8
0
-8
E 12
y = [? ]x
Enter the answer that belongs in [?]
Answer:
y= -(4x)
Step-by-step explanation:
A telephone call arrived at a switchboard at random within a one-minute interval. The switch board was fully busy for 10 seconds into this one-minute period. What is the probability that the call arrived when the switchboard was not fully busy
Answer:
50/60 = .8333= 83.33%
Step-by-step explanation:
The probability that the call arrived when the switchboard was not fully busy is 0.75.
What is Normal Distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Given:
Here X follows uniform distribution with parameter a and b.
Where,
a = 0 and b = 1.
Then,
The density function of Y is given by:
P( 15 < Y ≤ 60)
or, P( 0.25 < Y ≤ 1)
So, P( 0.25 < Y ≤ 1) = [tex]\int\limits^{1}_{0.25}{f(y) \, dy[/tex]
= [tex][y]^1 _ {0.25}[/tex]
= (1- 0.25)
= 0.75
Hence, The probability that the call arrived when the switchboard was not fully busy is 0.75.
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Express 18 hours to 2 days in its lowest term
Answer:
1 : 3
Step-by-step explanation:
We know that 1 days is 24 hours
2 days = 2*24 = 48 hours
16 hours : 48 hours
Divide each by 16
16/16 : 48/16
1 : 3
Answer:
[tex]3 : 8[/tex]
Step-by-step explanation:
[tex]18h : 2d \\ 18h : 2 \times 24h \\ 18 :48 \\ 3 : 8[/tex]
Suppose that appearances of a foe to battle (that is, a random encounter) in a role-playing game occur according to a Poisson process, and the average rate equals one appearance per two minutes. Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
Answer:
Rate parameter of [tex]\mu = 0.5[/tex]
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
One appearance per two minutes.
This means that [tex]m = 2[/tex]
Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
[tex]\mu = \frac{1}{m} = \frac{1}{2} = 0.5[/tex]
So
Rate parameter of [tex]\mu = 0.5[/tex]
A data set includes data from student evaluations of courses. The summary statistics are n=89, x=3.44, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
H0: μ=3.50
H1: μ>3.50
B.
H0: μ=3.50
H1: μ<3.50
C.
H0: μ≠3.50
H1: μ=3.50
D.
H0: μ=3.50
H1: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)
We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0
The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.
We go with answer choice D to form the null and alternative hypotheses.
The sign ≠ in the alternative hypothesis tell us that we have a two tail test.
---------------------------------------
Let's compute the test statistic
z = (xbar - mu)/(s/sqrt(n))
z = (3.44 - 3.50)/(0.67/sqrt(89))
z = -0.84483413122896
z = -0.84
The test statistic is roughly -0.84
---------------------------------------
Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.
Use a calculator or a Z table to determine that
P(Z < -0.84) = 0.2005
which is approximate
Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401
The p-value is roughly 0.401
-----------------------------------------
Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.
The conclusion based on that means that μ=3.50 must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50
A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,124 people. If this rate continues, what will be the number of infected people in another 9 months? Round your answer to the nearest whole number.
Answer:
About 6,785 people will be infected about nine months.
Step-by-step explanation:
We can write an exponential function to represent the situation. The standard exponential function is given by:
[tex]\displaystyle f(x) = a(r)^x[/tex]
Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.
3,124 people have already been infected. Thus, our initial value a = 3124.
And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.
Hence, our function is:
[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]
Then after nine months, the total amount of infected people will be f(9):
[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]
Use a calculator:
[tex]\displaystyle f(9) \approx 6785[/tex]
About 6,785 people will be infected about nine months.
Answer:
7,022
Step-by-step explanation:
Working at home: According to the U.S Census Bureau, 34% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 170 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .
Answer:
The answer is "0.340".
Step-by-step explanation:
[tex]n = 500\\\\x = 170[/tex]
Using formula:
[tex]\to \hat{p} = \frac{x}{n} = \frac{170}{500}=\frac{17}{50} =0.340[/tex]
please help me with this question!
HURRY PLEASE!!
2 •(3(5+2)-1)
Answer:
hopei help you
Step-by-step explanation:
mark i brainliest answer
Answer: 40
Concept:
When encountering questions that ask for simplifying expressions, the easiest way is to follow the PEMDAS method:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionSolve:
Given
2 · (3 (5 + 2) - 1)
Simplify parentheses by addition
=2 · (3 × 7 - 1)
Simpify multiplication first, then subraction
= 2 · (21 - 1)
= 2 · 20
Simplify multiplication
= 40
Hope this helps!! :)
Please let me know if you have any questions
on a 25 square grid how many squares need to be shaded to make 60% shaded
Answer:
15 squares
Step-by-step explanation:
60/100 * 25 = 15
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
8192
Step-by-step explanation:
2 cells at beginning, so the equation is (2)*(2^(4t)) where t is in hours. At the end of 3 hours, the cells will be 2*(2)^(12)=8192
17. what is the value of x?
18. what is the value of z?
please help me fast!!
for x ,
8x + 10x = 180°
[sum of linear pair is equal to 180°]
or, 18x = 180°
or, x = 180/18
therefore, x = 10°……
for z,
10z =8x
[ being corresponding angles are equal ]
or, 10z = 8 × 10°
( replacing x by 10°)
or, 10z = 80°
or, z = 80/10
thus z = 8°…………
Process control and acceptance sampling procedures are most closely related to _____. a. analysis of variance procedures b. hypothesis testing procedures c. interval estimation procedures d. linear regression procedures
find the two intersection points
(x+1)^2 +(y+2)^2 = 16
3x+ 4y = 1
Show your steps please
Answer:
Our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Step-by-step explanation:
We want to find where the two graphs given by the equations:
[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]
Intersect.
When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.
Since the linear equation is easier to solve, solve it for y:
[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]
Substitute this into the first equation:
[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]
Simplify:
[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]
Square. We can use the perfect square trinomial pattern:
[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]
Multiply both sides by 16:
[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]
Combine like terms:
[tex]25x^2+-22x+97=256[/tex]
Isolate the equation:
[tex]\displaystyle 25x^2 - 22x -159=0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 25, b = -22, and c = -159. Substitute:
[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]
Hence, our two solutions are:
[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]
We have our two x-coordinates.
To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:
[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]
And:
[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]
Thus, our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
True or false? The polynomial 3xy + 4z - 8 is a trinomial.
Answer:
False is the answer.Step-by-step explanation:
answer is False.Answer:
True.
Step-by-step explanation:
A trinomial is an algebraic expression consisting of 3 terms. The terms in this instance are: 3xy, 4z, and -8.
Multiply:
2 × (–21) × 7
A)
294
B)
–273
C)
–7
D)
–294
Answer:
[tex]2\times \left(-21\right)\times \:7[/tex]
PEMDAS order of operations:
[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]
[tex]=-42\times \:7[/tex]
[tex]=-294[/tex]
D) -294 is your answer
OAmalOHopeO
For an ordered pair left parenthesis x comma y right parenthesis in a relation, the x element represents the
Answer:
the x éléments représente the domain
x represents the value on the x-axis and the coordinate is also known as abscissa.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
For an ordered pair left parenthesis x comma y right parenthesis in a relation that is (x, y).
Here x represents the value on the x-axis and the coordinate is also known as abscissa.
More about the coordinate geometry link is given below.
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