Answer:
The 90% confidence interval is (-1.987, -1.320).
Step-by-step explanation:
The data provided is:
Sleep without Sleep using
the drug the drug d=without-with
2.5 4.3 -1.8
2.7 4.2 -1.5
3.8 5.0 -1.2
3.8 6.2 -2.4
1.8 2.5 -0.7
4.7 7.1 -2.4
4.8 7.1 -2.3
2.7 3.3 -0.6
1.8 3.5 -1.7
2.2 4.3 -2.1
3.6 4.3 -0.7
5.3 7.0 -1.7
5.2 7.6 -2.4
Compute the sample mean and sample standard deviation:
[tex]\bar d=\frac{1}{n}\sum d=\frac{1}{13}\times [(-1.8)+(-1.5)+(-1.2)+...+(-2.4)]=-1.654\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum [d-\bar d]^{2}}=0.6753[/tex]
The degrees of freedom of the test is:
df = n - 1 = 13 - 1 = 12
Compute the critical value of t for 90% confidence level and 12 degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.10/2, 12}=1.782[/tex]
Compute the 90% confidence interval as follows:
[tex]\bar d-t_{\alpha/2, (n-1)}\cdot\frac{S_{d}}{\sqrt{n}}<\mu_{d}<\bar d+t_{\alpha/2, (n-1)}\cdot\frac{S_{d}}{\sqrt{n}}[/tex]
[tex]-1.645-[1.782\cdot\frac{0.6753}{\sqrt{13}}]<\mu_{d}<-1.645+[1.782\cdot\frac{0.6753}{\sqrt{13}}]\\\\-1.645-0.334<\mu_{d}<-1.654+0.334\\\\-1.988<\mu_{d}<-1.320[/tex]
Thus, the 90% confidence interval is (-1.987, -1.320).
Which graph represents this system of inequalities? y > x + 3 y ≤ 5x − 1
Answer:
it should be the second one
Step-by-step explanation:
the only reason i kno this is because one side always has to be white
hope this helps
sorry if its wrong
the last graph i personally think this because of answer i got using desmos when i put in this problem. ( make sure the answer you click matches the last graph on this question i don't want you to get an incorrect answer because you didn't pay attention)
Need help giving 13 points
Simplifying Square Roots of negative numbers
Answer:
0+10i
Step-by-step explanation:
First, the square root of 100 is 10 because 10*10 is 100.
i=-1
Therefore, to get rid of the minus, it would be 10i
Since there is nothing else to solve,
the answer is 0+10i
What is the value of x?
O 30
O 45
O 55
O 60
Which of the following functions is not quadratic?
Answer:
f ( x ) = 5x - 5 is not a quadratic function.
The degree of the equation f(x) = 5x – 5 is one, then it is not a quadratic equation. Then the correct option is B.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have
If the degree of the equation is not 2, then the function is not a quadratic.
f(x) = 5x – 5, the degree of the equation is one, then it is not a quadratic equation.
Then the correct option is B.
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Louise Gaines is paid a bi-weekly salary of $6,000. To date, she has earned $96,000. Her filing
status is Head of Household.
What is her Social Security tax withholding for this pay period?
Answer:
$5952
Step-by-step explanation:
By the Federal Insurance Contributions Act which is a U.S. payroll tax meant to fund Medicare and Social Security, the FICA tax is shared among the employer and the employee whereby the employers share is 7.65% of the employees gross income and the employees share is also 7.65% of their gross income with 6.2% being for social security and 1.45% being for Medicare.
Louise Gaines, therefore will have 6.2% of $96,000 or $96,000 × 0.062 = $5952 withheld for the period.
How do you know if two line segments are parallel?
A. The slope of one is the negative of the slope of the other.
OB. Their slopes are equal.
C. Their slopes are reciprocals.
D. Their slopes are negative reciprocals.
Answer: B Their slopes are equal.
Step-by-step explanation:
Two line segments are parallel if and only if their slopes are equal.
Option B is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Two line segments are parallel if and only if their slopes are equal.
If the slopes of two lines are equal, then they have the same steepness and will never intersect.
However, if the slopes are different, the lines will intersect at some point, and they will not be parallel.
Thus,
Two line segments are parallel if and only if their slopes are equal.
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Need help with 2,4,6!!!!!!!!!!!!!!
Answer:
m+22=30m+22-22=30-22
m=8
7y=287/7 y=28/7
y=4
12+3p=-312-12+3p=-3-12
3p=-15
3/3 p=-15/3
p=-5
Two less than a number and five is 12 less than the number itself
Answer: x - 2 + 5 = x - 12
Step-by-step explanation:
At first I was confused. Then I read the question again and translated it.
Less than translated means - 2.
A number, aka X.
and means plus(+).
when you put that together you get,
x - 2 + 5.
The next step is to translate to second part of the equation.
Is means equals(=).
So far we have: X - 2 + 5 = 12.
This is where I got confused...
After solving that peice, we have the words; " 12 less than the number it's self. I wasn't sure if 2 x's could be in the same equation. Now I know they can.
Above, we established that 'a number' is x.
Now, it's talking about that number again because it says; "The number itself." At first, I thought it was talking about 12 - 12! Then I realized that it's not.
The new equation, after understanding that in the second piece isn't 12 - 12, would be none other than,
x - 2 + 5 = 12 - x
I hope this helps!!
Answer:
Step-by-step explanation:
Twelve less than the one-fifth of a number is-7
easy 10 points and brainliest :)
Answer:
quadrant 1
Step-by-step explanation:
both of them are positive
Answer:
Quadrant I
Step-by-step explanation:
Since x is greater than zero and y is greater than zero, that means the point (x, y) is to the right and above the origin. Hence, the first quadrant.
Cheers.
The number of peanuts in bags is normally distributed with a mean of 184.7 peanuts and a standard deviation of 3.3 peanuts. What is the z-score of a bag containing 178 peanuts? Question 6 options: negative 1.42 negative 2.03 negative 2.49 negative 1.65
Answer:
The z-score of a bag containing 178 peanuts is -2.03.
Step-by-step explanation:
A z-score is a normally distributed value with mean 0 and standard deviation 1. The distribution of these z-scores is known as the standard normal distribution.
The formula to compute z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The information provided is:
x = 178
μ = 184.7
σ = 3.3
Compute the z-score of a bag containing 178 peanuts as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\frac{178-184.7}{3.3}\\\\=-2.03[/tex]
Thus, the z-score of a bag containing 178 peanuts is -2.03.
Solve the Equation. 20x + 12 ≥ 14x + 30 A. x ≥ 7 B. x ≤ 7 C. x ≥ 3 D. x ≤ 3
Answer:
x≥3
Step-by-step explanation:
Treat the ≥ symbol like it is an equals sign. First, subtract 14x from each side to get 6x+12≥30. Then, Subtract 12 from each side to get 6x≥18. I will let you solve the rest :)
Answer:
[tex]\huge\boxed{C.\ x\geq3}[/tex]
Step-by-step explanation:
[tex]20x+12\geq14x+30\qquad\text{subtract 12 from both sides}\\\\20x+12-12\geq14x+30-12\\\\20x\geq14x+18\qquad\text{subtract}\ 14x\ \text{from both sides}\\\\20x-14x\geq14x-14x+18\\\\6x\geq18\qquad\text{divide both sides by 6}\\\\\dfrac{6x}{6}\geq\dfrac{18}{6}\\\\\boxed{x\geq3}[/tex]
PLEASE HELP ME QUICKLY In ΔABC,
if m∠CAD = 29°, the m∠DAB is _______
Answer:
it will also be 29°
Step-by-step explanation:
LDAB will be also 29° cuz D is the bisector and at the top the two lines resembles that. So if CAD is 29° then DAB will be also 29°
I hope so it will help ✨
The angle ∠DAB will be equal to 29 degrees.
What is an angle bisector?The line or line segment that divides an angle into two equal halves is known as the internal angle bisector or (interior) bisector. An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Given that in triangle ABC the angle ∠CAD is 29°. Then the angle will be calculated as below:-
The line AD is an angle bisector at point A of the triangle. Then the two angles ∠CAD and ∠DAB will be equal to each other.
∠CAD = ∠DAB
∠CAD = 29°
Therefore, the angle ∠DAB will be equal to 29 degrees.
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Nikki works at a store that sells consumer electronics. She earns $12 per hour, plus a commission of 5% of her total sales amount each day. Nikki worked 8 hours on Saturday. Including her commission, Nikki earned a total of $139 on Saturday. Which equation can be solved for x, Nikki’s total sales amount in dollars on Saturday?
Answer:
See below.
Step-by-step explanation:
So, Nikki earns $12 per hour.
And she also earns a 5% or 0.05 commission of her total sales each day.
On Saturday, she worked eight hours and she earned $139. In other words, she earned 8(12) or $96 from working her hours and another $43 (139-96) from her commission.
Thus:
[tex]139=96+0.05x[/tex]
Where x represents Nikki's total sales on Saturday.
Further notes:
To solve, subtract 96 from both sides and divide by 0.05:
[tex]139=96+0.05x\\43=0.05x\\x=\$860[/tex]
Thus, her total sales that day were $860.
how to solve 2|4-3x|-2 <10?
━━━━━━━☆☆━━━━━━━
▹ Answer
(-2/3, 10/3)
▹ Step-by-Step Explanation
2|4 - 3x| - 2 < 10
2|-3x + 4| - 2 < 10
2|-3x + 4| < 12
= (-2/3, 10/3)
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
4.89 x 2.2 find the product
Answer: Hi!
4.89 * 2.2 = 10.758 (rounded is 10.76 or 10.8)
Tip: Line up the terms vertically and multiply.
Hope this helps!
what is x? please answer asap!!
Answer:
Hey there!
Angle x is equal to 148 degrees because it is supplementary with the angle of 32 degrees.
Let me know if this helps :)
4.89 gallons of milk is sold for $12.79. If you have $21.44 in your wallet. How many
gallons of milk you can buy?
Answer:
You can buy 8.18 gallons of milk.
Step-by-step explanation:
12.79/4.89 = 2.62
21.44/2.62 = 8.18
(12y2
+ 17y - 4) + (9y2
- 13y + 3) =
Answer:
[tex]21y^{2} +4y-1[/tex]
Step-by-step explanation:
Hello!
[tex](12y^{2} +17y-4)+(9y^{2} -13y+3)[/tex]
For this, we can combine like terms
[tex]12y^{2} +9y^{2}=21y^{2}[/tex]
17y - 13y = 4y
-4 + 3 = -1
Combine the answers and we get
[tex]21y^{2} +4y-1[/tex]
Hope this Helps!
Answer:
21y² + 4y -1
Step-by-step explanation:
(12y² + 17y - 4) + (9y² - 13y + 3) ---- remove parentheses
= 12y² + 17y - 4y + 9y² - 13y + 3
= 12y² + 9y² + 17y - 13y - 4 + 3 -----grouped like terms
= 21y² + 17y - 13y - 4 + 3
= 21y² + 4y - 4 + 3
= 21y² + 4y - 1
A train starts at Omaha at 2 pm and heads for Reedley, 750 km away. At the same time, a train leaves Reedley and heads for Omaha at 85 km per hour. If the trains meet at 5 pm, what is the rate of the first train
Answer:
250 km per hour
Step-by-step explanation:
In order to find the rate of the first train, we need to know that the distance between Omaha and Reedly is 750 km away and that it will move at 2 pm and arrive at the location at 5 pm. So, first subtract the hours from 5 to 2. 5 - 2 = 3
The train would arrive in 3 hours.. so we substitute 3 into the number of hours.
Distance = 750
km (kilometers per hour) = ?
Hours = 3
Now we should substitute the number values into the equation, it should look like this: 750 = km(3)
3 multiplied by the varible will be 3km because there is no coefficient for km.
750 = 3km
Then, we divide 3 by both sides to make the 3 into a one for km.
750 ÷ 3 = 3km ÷ 3
250 = km
The rate of first train is 165 mph.
What is Speed- Distance?Speed = Distance/Time Distance = Speed X Time, Time = Distance / Speed.We can frame the situation as
Distance Rate Time
First train x 3
Second train 85 3
Now, using Distance= Speed x time
Distance Rate Time
First train 3x x 3
Second train 255 85 3
So, the equation is
3x+ 255 = 750
3x = 750 -255
3x =495
x= 165
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Point A is at -7, -3. There are 12 points between A and B. What are possible coordinates for point B?
Answer:
(5,9)
(-19, - 15)
(5, - 15)
(-19, 9)
Step-by-step explanation:
Given that :
Coordinate of point A = - 7, - 3
Number of points between point A and B = 12
Possible coordinate of point B
Possible coordinates of point B:
(-7, - 3) + 12 = (5, 9)
(-7, - 3) - 12 = (-19, - 15)
(-7, - 3) = (-7 +12, -3 - 12) = (5, - 15)
(-7, - 3) = (-7 - 12, - 3 + 12) = (-19, 9)
Hence possible coordinates of be are :
(5,9)
(-19, - 15)
(5, - 15)
(-19, 9)
Does this equation have one, many, or no solutions? [tex]2+4(3-4x)=5x+9[/tex] If one, what is the value of 'x'? Show work please.
Answer: This equation has one solution.
Steps:
2+4(3-4x) = 5x +9
First, we need to distribute to the terms inside the parentheses.
4 * 3 = 12 and 4 * -4= -16x
Our equation now looks like this:
2 + 12 - 16x = 5x + 9
We can now combine like terms. We have 2 like terms that we can combine:
2 + 12 + = 14
Our equation now looks like this:
-16x + 14 = 5x + 9
We can now use inverse operations to get rid of 5x. The inverse operation for addition is subtraction; so we subtract 5x on both sides. Remember, our goal is to isolate the x.
-16x + 14 = 5x + 9
-5x -5x
The fives cancel out. Our equation now looks like this:
-21x + 14 = 9
We can now use inverse operations to get rid of the 14:
-21x + 14 = 9
- 14 -14
The fourteens cancel out. Our equation now looks like this:
-21x = -5
Last step! Now we use inverse operations to isolate the x. -21 is being multiplied by x; the inverse operation for multiplication is division.
-21x/-21 = and -5/-21 = 5/21
x is equal to 5/21.
Hope this helps!
Answer:
-5x + -5 + 5x-.1
Step-by-step explanation:
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)? Determine the gear ratio for a bike with 45 front teeth and 18 rear sprocket teeth.
Answer:
The answer is 660.4 millimeters in diameter.
Step-by-step explanation:
The wheel is 26 inches in diameter. An inch is 25.4 millimeters. 26 * 25.4 = 660.4
please help on 9 to be marked the brainliest
OA) 30°
O B) 60°
D) 50°
OC) 90°
Answer:
A) 30°
Step-by-step explanation:
Sum of three angles of a triangle = 180°
75° +75° + ∠WYZ = 180°
Add like terms
150° + ∠WYZ = 180°
Subtract 150°from both sides
∠WYZ = 180 - 150
∠WYZ = 30°
Approximate √18 to the nearest whole number.
Answer:
4 is the answer
Step-by-step explanation:
Answer:
hey
√18 = 4.242
Step-by-step explanation:
rounded = 4
what is the sum and product of x^2+12x+32=0? pls help me
Answer:
Sum= -12
Product=32
Step-by-step explanation:
[tex]x^2+12x+32=0[/tex]
By factorization, we get
[tex]x^2+4x+8x+32=0\\x(x+4)+8(x+4)=0\\(x+4)(x+8)=0\\[/tex]
Therefore, the roots of the equation are = -4,-8
Sum of the roots =[tex]\alpha+\beta =\frac{-b}{a}[/tex]
[tex]\alpha +\beta[/tex]=[tex]-8-4=-12[/tex]
Product of the roots=[tex]\alpha \beta =\frac{c}{a}[/tex]
[tex]\alpha \beta =8*4=32[/tex]
-4.75 = x/2 what is x
Answer:
x= -9.5
Step-by-step explanation:
We want to find out what the variable, x, is equal to. Therefore, we must isolate the variable on one side of the equation.
-4.75 = x/2
x is being divided by 2. The inverse of division is multiplication. Multiply both sides of the equation by 2.
2*(-4.75) = (x/2)*2
2*(-4.75)=x
2* -4.75=x
Multiply 2 and -4.75
-9.5=x
Let's check our solution. Plug -9.5 back in for x and solve.
-4.75= x/2
-4.75= -9.5/2
-4.75= -4.75
This checks out, so we know our solution is correct.
x is equal to -9.5
Answer:
[tex]x = \frac{19}{2} [/tex]
Step-by-step explanation:
[tex] \frac{x}{2} = - 4.75[/tex]
First convert the decimal to an improper fraction
That's
[tex] - 4.75 = - \frac{19}{4} [/tex]
So we have
[tex] \frac{x}{2} = - \frac{19}{4} [/tex]
Cross multiply
4x = - 38
Divide both sides by 4
We have the final answer as
[tex]x = \frac{19}{2} [/tex]
Hope this helps you
Eighty percent of adults drink coffee and seventy percent drink tea. What is the smallest possible percent of adults who drink both coffee and tea?
Answer:
50%
Step-by-step explanation:
Given that Eighty percent ( 80%) of adults drink coffee and seventy ( 70%) percent drink tea.
Let the percent of the adults that drink coffee and tea be y
The total percentage of adults = 100
80 - y + y + 70 - y = 100
150 - y = 100
- y = 100 - 150
Y = 50.
Therefore, the smallest possible percent of adults who drink both coffee and tea is 50 %
A Simpler Answer:
Add together the probabilities.
80%+70%=150%
Therefore we overcounted 50 percent, so the least amount possible is [tex]\boxed{50\%}[/tex]
Solve for u.
4u²+3=-8u
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution."
Answer:
u = [tex]-\frac{1}{2}[/tex] ; u = [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
4u² + 3 = -8u
4u² + 3 + 8u = -8u + 8u (add 8u both sides)
4u² + 8u + 3 = 0 simplify
using quadratic equation:
- 8 ± √ (8² - 4 * 4 *3)
u = ------------------------------
2 * 4
u = [tex]-\frac{1}{2}[/tex] ; u = [tex]-\frac{3}{2}[/tex]