Answer:
[tex] \sqrt{3} - 1[/tex]
Step-by-step explanation:
[tex](1 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2 - \sqrt{3} + 2 \sqrt{3} - 3 \\ = \sqrt{3} - 1[/tex]
A particular extension cord can support up to 8 amps. Mo has an iron whose label states 1,200 watts and wonders if the iron can be plugged into the extension cord. If watts are converted to amps by dividing by 120, how many amps does the iron use?
Answer:
10 AStep-by-step explanation:
Given data
Current in cord is I = 8 a m p
Power of iron is P = 1200 W
Voltage converted is
V = 120 V
The power can be expressed as
[tex]P=IV=\\I=\frac{P}{V}[/tex]
Substitute the given value in above we get,
I = [tex]\frac{1200}{120}= 10amps[/tex]
Thus, the current use by iron is
10 A
If you found that the 95% confidence interval to estimate the true proportion of visitors to Niagara Falls that are from the United States was (0.5216, 0.6784), does this provide evidence that a majority of visitors to Niagara Falls are from the United States
Answer:
The lower end of the interval is above 0.5, which means that it provides evidence that a majority of visitors to Niagara Falls are from the United States
Step-by-step explanation:
We want to see if the majority of Niagara Falls visitors are from the United States.
Looking at the confidence interval
We have to see if the lower end of the interval is higher than 0.5.
In this question:
The 95% confidence interval to estimate the true proportion of visitors to Niagara Falls that are from the United States was (0.5216, 0.6784).
The lower end of the interval is above 0.5, which means that it provides evidence that a majority of visitors to Niagara Falls are from the United States
What is 2/3 divided 1/6 ?
Answer: 4
Step-by-step explanation:
in order to divide one fraction by another, you must multiply by the reciprocal(the reverse of a certain fraction). the reciprocal of 1/6 is 6/1. so:
[tex]\frac{2}{3} / \frac{1}{6}[/tex] = multiply by the reciprocal of 1/6
[tex]\frac{2}{3} * \frac{6}{1}[/tex] = cross out
[tex]\frac{2}{1} * \frac{2}{1}[/tex] = multiply
[tex]\frac{4}{1}[/tex] = simplify
4
Answer:
4
Step-by-step explanation:
(2/3)/(1/6)
Eleminate the denominator by multiplying numerator and denominator with whatever is the reciprocal of the denominator. In this case the denominator is 1/6 so the reciprocal is 6/1 or "just" 6.
So, multiply numerator and denominator by 6. The next three (bold) steps, have been written down for explanatory purposes only, and normally are not nessasary.
(2/3)*6 / (1/6)*6
(2/3)*6 / (6/6)
(2/3)*6 / 1
(2/3)*6
12/3
4
Based on historical data, your manager believes that 39% of the company's orders come from first-time customers. A random sample of 171 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.32
Answer:
[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]
[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]
And we can find the probability with this difference:
[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n = 171[/tex] represent the sample size
[tex]p =0.39[/tex] the proportion of interest
We want to find the following probability:
[tex] P( 0.21 < \hat p < 0.32)[/tex]
We can use the normal approximation for this case since np >10 and n (1-p) >10
For this case we know that the distribution for the sample proportion is given by:
[tex]\hat p \sim N( p , \sqrt{\frac{p (1-p)}{n}} )[/tex]
And we can use the following parameters:
[tex] \mu_{\hat p}= 0.39[/tex]
[tex] \sigma_{\hat p} =\sqrt{\frac{0.39*(1-0.39)}{171}}= 0.0373[/tex]
And we can apply the z score formula given by:
[tex] z = \frac{p \\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And using this formula we got:
[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]
[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]
And we can find the probability with this difference:
[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]
Simplify (4.5)(5)(-2)
Answer:
[tex] - 45[/tex]
[tex]2.25( - 2) = - 45 \\ - 45[/tex]
At the kennel, the ratio of cats to dogs is 4:5. There are 27 animals in all. How many cats are in the kennel?
Answer:
Step-by-step explanation:
4x+5x=27
9x=27
x=27/9
x=3
4x3=12
5x3=15
The total number of cats were 12.
Based on the ratio of dogs to cats in the shelter, we know that out of 27 animals, there are 12 cats.
The ratio of cats to dogs is 4:5 which means that there are 5 dogs for every 4 cats.
This means that out of 9 animals, 4 would be cats and 5 would be dogs. If there was 27 animals therefore:
= 4 / 9 x 27
= 108 / 9
= 12 cats
In conclusion, there are 12 cats.
Find out more at https://brainly.com/question/9723361.
Ben scores 56 out of 79 marks in a maths test.
what is his score as a percentage to one decimal place
WILL MARK BRAINLIEST !!!
In the given point(-4,b) -4 is the x value.
Locate -4 on the graph and find the y value where the line is located. The y value would be b.
B = 1
1+1 i will make you brainliest lol
Answer:
2
Step-by-step explanation:
1 + 1 = 2
Answer:
1 + 1
= 2
1+1
= THIS THING
Express the following in simplest a + bi form.
V9+1-36
O
-91
O
3 - 61
3 + 6
91
Answer:
3+6i
Step-by-step explanation:
I did it
Answer:3+6i
Step-by-step explanation:
Multiply 6.7 x 104 times 4.8 x 106 by using scientific notation. Round your answer to one decimal place in scientific notation with no spaces.
Answer:
3.216×[tex]10^{11}[/tex]
Step-by-step explanation:
I'm assuming 104 is [tex]10^{4}[/tex] and 106 is [tex]10^{6}[/tex].
6.7×[tex]10^{4}[/tex]×4.8×[tex]10^{6}[/tex]=
32.16×[tex]10^{10}[/tex]=
3.216×[tex]10^{11}[/tex]
Our answer is 3.216×[tex]10^{11}[/tex].
Banking fees have received much attention during the recent economic recession as banks look for ways to recover from the crisis. A sample of 41 customers paid an average fee of $12.22 per month on their interest-bearing checking accounts. Assume the population standard deviation is $1.86. Complete parts a and b below.
a. Construct a 95% confidence interval to estimate the average fee for the population.
b. What is the margin of error for this interval?
Answer:
a) The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79
b) $0.57
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
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.
[tex]M = 1.96*\frac{1.86}{\sqrt{41}} = 0.57[/tex]
So the answer for b) is $0.57.
The lower end of the interval is the sample mean subtracted by M. So it is 12.22 - 0.57 = $11.65
The upper end of the interval is the sample mean added to M. So it is 12.22 + 0.57 = $12.79
The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79
what is the answer to -9x = -27
Answer:
x = 3
Step-by-step explanation:
9x = 27
Divide both sides by 9,
x = 27/9 which on factorization of the numerator is written as
x = 9 x 3/9 = 3
Calculation 2: Exponent Or Index Method
9x = 27
Since 9 = 3² and 27 = 3³, the given equation takes the form
3² x = 3³
This gives
x = 3³ ÷ 3² = 3³¯² [using the formula a^m ÷ a^n = a^(m-n)]
= 3¹ = 3 (since the first power of a number is the number itself)
9 x 1 = 9
9 x 2 = 16
9 x 3 = 279 x 4 = 36
We stop here because we have already got the answer 27, the right-side of the equality, when 9 is multiplied by 3 . So,
x = 3
hope this helped!
What value of b will cause the system to have an infinite number of solutions?
A system of equations. y equals 6 x plus b. negative 3 x plus StartFraction one-half EndFraction y equals negative 3.
A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes through the points (1, 0) and (0, negative 6).
-6
-3
3
6
Answer:
-6 on edge
Step-by-step explanation:
The value of b that causes the system of equations to have infinite solutions will be: b = -6
System with infinite solutions:A system of linear equations will have infinite solutions only when both equations represent the same line.
In this case our equations are:
y = 6x + b
-3x + (1/2)*y = -3
So the value of b needs to be such that these two equations are equal
Let's isolate y in the second equation:
(1/2)*y = -3 + 3x
y = -3*2 + 3x*2 = -6 + 6x
Then we must have:
6x - 6 = 6x + b
-6 = b
Thus, the value of b that causes the system to have infinite solutions is b = -6.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
find the common difference of the arithmetic sequence 4, 10, 16,...
4+6=10+6=16+6=22+6=28...
I hope it is helpful for everyone
Choose the slope and y-intercept that
correspond with the graph.
Answer:
slope = -3, y intercept = 3
Step-by-step explanation:
The y intercept is where it crosses the y axis
y intercept is 3
The slope is found by taking two points (0,3) and (1,0) and using the slope formula
m = (y2-y1)/(x2-x1)
= (0-3)/(1-0)
-3/1
=-3
Which inequality is represented by this graph?
Answer:
its probably a. x>-53
my appolgies if it's wrong
A manufacturing machine has a 40% defect rate. If 131 items are chosen at random, answer the following. a) Which is the correct wording for the random variable? rv X = the number of 131 randomly selected items that are defective Correct b) Pick the correct symbol: n Correct = 131 c) Pick the correct symbol: p Correct = 0.4
Answer:
A manufacturing machine has a 40% defect rate. If 131 items are chosen at random, then:
The random variable, X=Number of 131 randomly selected items that are defective.Number of Items, n=131The point estimate of defective items, p=40%=0.4Which numbers are solutions of the inequality below? (Select all that apply.)
x − 2 < −8
a) 6
b) −6
c) 4
d) −8
Answer:
d) −8
Step-by-step explanation:
x − 2+2 < −8+2
x < -6
The only number less than -6 is -8
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
If we rotate the 3-D figure around y-axis, we'll obtain a cylinder with a radius of 1 unit.
A large western state consist of 4341 million acres of land. Approximately 83% of this land is federally owned. Find the number of acres that are not federally owned
Answer:
737.97 acres
Step-by-step explanation:
Given
Approximately 83% of a large western state land is federally owned.
Total land in percentage will be 100%
% of land not federally owned = Total land in percentage - % of land federally owned = 100% - 83% = 17%
Thus, percentage of land not federally owned = 17% of total land
Also given "A large western state consist of 4341 million acres of land"
Therefore,
number of acres that are not federally owned = 17% of total western state land
number of acres that are not federally owned = 17/100 * 4341 = 737.97
Thus, 737.97 acres of western state land are not federally owned.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. (f + g)(x) = x - 7
Step-by-step explanation:
→Set it up, like so:
-3x - 5 + 4x - 2
→Add like terms (-3x and 4x, -5 and -2):
x - 7
A potter made 4080 diyas in the month of September. If he made the same number of diyas each day, how many diyas did he make in a week?
Which graph has a slope of 1/4?
Answer:Please include images of the graphs!
Step-by-step explanation:
Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.
Use the following equation to get the slope:
m (slope) = (y₂ - y₁)/(x₂ - x₁)
Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:
(x₁ , y₁) & (x₂ , y₂)
In this equation, make sure that the slope (m) will equal 1/4 (given).
The full equation that you will use is:
1/4 = (y₂ - y₁)/(x₂ - x₁)
Find the graph that will satisfy this equation.
Can someone help me with this?
x^2-4x+4
I understand -2 x 2=-4, but I’m not seeing how to add the factors to get +4, because -2+2=0. I’ve got the first half of the solution, but not the second.
Answer:
(x-2)(x-2)
Step-by-step explanation:
You should be trying to find two numbers that add to make the coefficient of x (in this case, -4), and two numbers that multiply to make the constant term (in this case, +4). The two numbers that work for both of those criteria are -2 and -2.
-2 x -2 = +4 (satisfies the constant term)
-2 + -2 = -4 (satisfies the coefficient of x)
Simplify
6x^-2. ....
Answer:
6/x^2
Step-by-step explanation:
6x^-2
6*x^-2
6*(1/x^2)
6/x^2
Please answer this correctly
Answer:
41-60 => 5
Step-by-step explanation:
41-50 => 2
51-60 => 3
So 2+3 =5
Answer:
5
Step-by-step explanation:
Add up the number of children between 41 and 60
41-50: 2
51-60: 3
------------
total 5
A hose fills a hot tub at a rate of 3.84 gallons per minute. How many hours will it take to fill a 305-gallon hot tub?
Answer:
1.56 hours
Step-by-step explanation:
300 gal × 1 min 3.2 gal × 1 hr 60 min = 1.56 hr.
Answer:
i thought the question said a 'HORSE' fills a hot tub...
Step-by-step explanation:
lol dont mind me i just want points :D
what is tan B enter your answer as a simplified fraction in the box
Answer:
7/24
Step-by-step explanation:
Tangent is opposite over adjacent. You know that the opposite leg is 14 but you don't know the adjacent.
To find the unknown leg, use Pythagorean theorem so that 50^2-14^2= leg. The length is 48.
14/48= tan B
7/24= tan B
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
It's a football ....=> So ... A sphere !!
