Step-by-step explanation:
Step 1: 12x-6= 1
step 2:12x=7
What is the chance of getting 3 of the same cards in a row in a 52 cards deck?
Answer:
1/425
Step-by-step explanation:
The first card can be any card, so we don’t have to evaluate the probability.
Now we can suppose that the exit card is a two
- For the second card we have 3/51 of possibilities that is a 2 = 1/17
- For the third card we have 2/50 of possibilities that is a 2 = 1/25
1/17 * 1/25 = 1/425
Angles are not necessarily drawn to scale.
X=?
Answer:
x = 76
Step-by-step explanation:
A line has an angle measurement of 180 degrees.
Knowing that, let's first find the angle measurement of DIJ:
180 - 107 = 73
Angle DIJ has an angle measurement of 73
To find the angle measurement of DJI, we have to apply knowledge of angles in a triangle. When you add all the angles in a triangle, they ALWAYS equal to 180 degrees.
Using that knowledge, we can add 73 and 31 and subtract that value from 180:
73 + 31 = 104
180 - 104 = 76
The angle measurement of Angle DJI is 76.
Because vertical angles are ALWAYS going to have the same angle measurement, Angle AJF is going to have an angle measurement of 76 as well.
So x = 76
Hope that helps (●'◡'●)
Factor the trinomial x^2-8x-65
Step-by-step explanation:
here's the answer to your question
Create a sample of 10 numbers that has a mean of 8.6.
Answer:
10 + 8 + 10 + 10 + 10 + 10 + 8 + 8 + 6 + 6
I really need help big time thank you
A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line? Question 26 options: a) y = x b) y = –x – 7 c) y = x + 3 d)y = –x + 2
Answer:
sorry my bad bro I have no clue
The restrictions for f(x)=2x+3/x^2−4 are ±2
True
False
Answer: True
=========================================================
Explanation:
If you meant to say [tex]f(x) = \frac{2x+3}{x^2-4}[/tex], then we cannot have x^2-4 equal to 0
We can never have 0 in the denominator.
Set the expression equal to 0 and solve for x
x^2 - 4 = 0
(x-2)(x+2) = 0 .... difference of squares rule
x-2 = 0 or x+2 = 0
x = 2 or x = -2
So if either x = 2 or x = -2, then we have x^2-4 equal to zero.
So these are the values we must kick out of the domain to avoid a division by zero error.
In short, the restrictions for x are 2 and -2. That's why the statement is true.
x^{2}-7x-25=0 to the nearest tenth
Answer:
x = 9.6
x = - 2.6
Step-by-step explanation:
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
Ignore the before the ± it wouldn't let me type it correctly.
x² - 7x - 25 = 0
a = 1
b = - 7
c = - 25
[tex]x=\frac{-(-7)±\sqrt{-7^{2}-4((1)(-25)) } }{2(1)}[/tex]
[tex]x=\frac{7±\sqrt{49-4((1)(-25)) } }{2(1)}[/tex]
[tex]x=\frac{7±\sqrt{49+100 } }{2(1)}[/tex]
[tex]x=\frac{7±\sqrt{149 } }{2}[/tex]
[tex]x=\frac{7±12.2}{2}[/tex]
Two separate equations
[tex]x=\frac{7+12.2}{2}[/tex]
[tex]x=\frac{7-12.2}{2}[/tex]
[tex]x=\frac{7+12.2}{2}[/tex]
[tex]x=\frac{19.2}{2}[/tex]
x = 9.6
[tex]x=\frac{7-12.2}{2}[/tex]
[tex]x=\frac{-5.2}{2}[/tex]
x = - 2.6
For this just use the quadratic formula to find the zeros. In this case, you get 7 +/- square root 149 over 2. Which gives you -2.6 and 9.6.
A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 614 babies born in New York. The mean weight was 3398 grams with a standard deviation of 892 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1614 grams and 5182 grams. Round to the nearest whole number.
Answer:
The number of newborns who weighed between 1614 grams and 5182 grams was of 586.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean weight was 3398 grams with a standard deviation of 892 grams.
This means that [tex]\mu = 3398, \sigma = 892[/tex]
Proportion that weighed between 1614 and 5182 grams:
p-value of Z when X = 5182 subtracted by the p-value of Z when X = 1614.
X = 5182
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5182 - 3398}{892}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
X = 1614
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1614 - 3398}{892}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228
0.9772 - 0.0228 = 0.9544.
Out of 614 babies:
0.9544*614 = 586
The number of newborns who weighed between 1614 grams and 5182 grams was of 586.
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 If they hope that the prep course is effective in improving the exam scores, what is the alternative hypothesis?
Solution :
Group Before After
Mean 693.75 743.75
Sd 155.37 143.92
SEM 54.93 50.88
n 8 8
Null hypothesis : The preparation course not effective.
[tex]$H_0: \mu_d = 0$[/tex]
Alternative hypothesis : The preparation course is effective in improving the exam scores.
[tex]$H_a : \mu_d>0$[/tex] (after - before)
help please! i'm in class and i have 10 mins left. :)
Answer:
3:8
Step-by-step explanation:
i will gadit
that only
What is this can someone help
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[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
see this attachment ☝
PLEASE HELPPPPP ASAPPPPPPPPPPPPP PLEASEEEE
Answer:
0.5679
Step-by-step explanation:
From. The table Given above :
The probability of female Given an advanced degree ;
P(F|A) = p(FnA) / p(A)
From the table, p(FnA) = 322
P(Advanced degree), P(A) = (245 + 322) = 567
Hence,
P(F|A) = p(FnA) / p(A) = 322 / 567 = 0.5679
Please help
4. The equation of a curve is y = (3 - 2x)^3 + 24x.
(a) Find an expression for dy/dx
5. The equation of a curve is y = 54x - (2x - 7)^3.
(a) Find dy/dx
(4) y = (3 - 2x)³ + 24x
Use the power and chain rules:
dy/dx = 3 (3 - 2x)² d/dx [3 - 2x] + 24
dy/dx = 3 (3 - 2x)² (-2) + 24
dy/dx = -24x ² + 72x - 30
(5) y = 54x - (2x - 7)³
Same basic procedure:
dy/dx = 54 - 3 (2x - 7)² d/dx [2x - 7]
dy/dx = 54 - 3 (2x - 7)² (2)
dy/dx = -24x ² + 168x - 240
Simplificar expresiones algebraicas
Find the midpoint of the line segment with end coordinates of: (-2,-2) and (2,8)
Answer:
(0 ; 3)
Step-by-step explanation:
hello :
the midpoint of the line segment is : ((-2+2)/2 ;(-2+8)/2 )
(0 ; 3)
PLEASE HELP AND BE RIGHT BEFORE ANSWERING
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Since point P is the center of dilation, it doesn't move. (It is "invariant.") The other points on the figure move to 1/4 of their original distance from P. On this diagram, it is convenient that the distances are all multiples of 4 units, so dividing by 4 is made easy.
solve the equation
r²-4s+s²=8r+2s=28
Answer:
[tex] {r}^{2} - 4s + {s}^{2} = 8r + 2s = 28 \\ \\ r = \frac{24}{5 } - i \frac{ \sqrt[4]{129} }{5} \\ \: s = \frac{58}{5} + i \frac{ \sqrt[2]{129} }{5 } \\ \\ r = \frac{24}{5} + i \frac{ \sqrt[4]{129} }{5} \\ s = \frac{58}{5} - i \frac{ \sqrt[2]{129} }{5} [/tex]
Write down the turning point of the graph y=x^2 - 8x + 22
Answer:
y=6
Step-by-step explanation:
Differentiate the equation
dy/dx=2x-8
Find the value of x in equation form
2x-8=0
x=8/2=4
Now x=4 is the line of symmetry or the parabola of the quadratic equation.
Plug back x=4 into the equation to find the turning point(minimum value)
y=(4)²-8(4)+22
y=16-32+22
y=6
Answer:
(4 , 6) is the vertex. I guess that can be called the "turning point"
Step-by-step explanation:
Use vertex formula : x = [tex]\frac{-b}{2a}[/tex]
x = [tex]\frac{-(-8)}{(2)(1)}[/tex] = [tex]\frac{8}{2}[/tex] = 4
Substitute x in original equation and solve for y:
y = [tex]4^{2}[/tex] - 8(4) + 22
y = 16 - 32 + 22
y = 6
A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inches thick: The figure shows a cylinder of height 14 inches and diameter 8 inches What is the approximate inside volume of the pipe?
332 cubic inches
69 cubic inches
703 cubic inches
99 cubic inches
Answer: 332 cubic inches
Step-by-step explanation:
You can eliminate 69 and 99 as those answers don't make any sense. This leaves you with 703 and 332.
It says the wall of the pipe is 1.25 inches thick so you multiply that by 2 and subtract it by the diameter to get the insider diameter of 5.5
Now you just use the equation V = (3.14)(r^2)(14) where the radius is half of 5.5.
So to finalize the equation you get V = (3.14)(5.5)^2(14) which comes out to 332 cubic inches
The best choice is 332 cubic inches.
69 cubic inches and 99 cubic inches are less and 703 cubic inches is a large approximation.
Diameter = d= 8 inches
Height= Length = l= 14 inches
Thickness= 1.25 inches
Outer Radius= R= diameter/2= 8/2=4 inches
Inner radius = r= Radius - thickness
= 4- 1.25= 2.75 inches
Volume of the cylinder = Area × length
= π r²× l
= 22/7 × (2.75)² × 14
= 332. 616 inches cube
So the best answer is 332 cubic inches
https://brainly.com/question/21067083
Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43
(x ,y), (x, y) (x, y) (x, y)
Answer:
(-3,5),(-3,-5),(3,5),(3,-5)
Step-by-step explanation:
i changed my answer :)
A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?
Answer:
10:3
Step-by-step explanation:
Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.
For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.
So make 5/2 to a 10/4.
Take the numerator 10 & 3.
Your answer will be 10:3
No problem.
(07.05A)
Which statement best explains whether y = 4x + 8 is a linear function or a nonlinear function?
Answer:
Step-by-step explanation:
There are no statements provided, but since it is modeled after the linear function y = mx + b, it is a line. m is the slope or rate of change (which is constant; that's what makes this a line!), and b is the y-intercept (the value of y when x is equal to 0). Its slope is 4 (the function raises 4 units for every 1 unit it moves to the right). Its y-intercept is 8, having the coordinate (0, 8).
Answer:
y = 4x + 8 is a linear function.
Step-by-step explanation:
No statements are given, but here's why:
- It's in slope-intercept form, y = mx + b.
- It has a constant slope.
- A non-linear function does not have a constant slope, and this one does.
Find the equation, in slope-intercept form, of the line passing through the point (2,5) and perpendicular to the line 2x + y = 7
Answer:
[tex]y=\displaystyle\frac{1}{2}x+4[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-interceptPerpendicular lines always have slopes that are negative reciprocals (examples: 1/2 and -2, 3/4 and -4/3)1) Determine the slope (m)
[tex]2x + y = 7[/tex]
Reorganize the given equation into slope-intercept form; subtract 2x from both sides to isolate y:
[tex]2x + y-2x = -2x+7\\y= -2x+7[/tex]
Now, we can easily identify the slope of the line to be -2. Because perpendicular lines always have slopes that are negative reciprocals, the slope of a perpendicular line would be [tex]\displaystyle\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle\frac{1}{2}x+b[/tex]
Plug in the given point (2,5) and solve for b:
[tex]5=\displaystyle\frac{1}{2}(2)+b\\\\5=1+b[/tex]
Subtract 1 from both sides to isolate b:
[tex]5-1=\displaystyle\frac{1}{2}(2)+b-1\\4=b[/tex]
Therefore, the y-intercept of the line is 4. Plug this back into [tex]y=\displaystyle\frac{1}{2}x+b[/tex]:
[tex]y=\displaystyle\frac{1}{2}x+4[/tex]
I hope this helps!
A strawberry and banana juice blend is made with a ratio of strawberry to banana of 2:3. Fill in the table to show different proportional amounts
Answer:
See Explanation
Step-by-step explanation:
Given
Let
[tex]s \to Strawberry[/tex]
[tex]b \to Banana[/tex]
So:
[tex]s:b = 2:3[/tex]
Required
Complete the table
The table, to be complete, is not given; so, I will generate one myself.
The table is generated as follows:
Multiply by 1.5
[tex]s : b = 3 : 4.5[/tex]
Multiply by 2
[tex]s : b = 2*2 : 2 * 3[/tex]
[tex]s : b = 4 : 6[/tex]
And so on....
In summary, whatever factor is multiplied to S must be multiplied to B
I need help with this
Answer:
below
Step-by-step explanation:
A AND C is the right option
congruent angles are angles with exactly the same measure
1+4=5
2+3=10
10+5=25
4+1?
Answer:
8
Step-by-step explanation:
Consider A Triangle ABC. Suppose That A= 119 Degrees, B=53, And C=57. Solve The Traingle
9514 1404 393
Answer:
a = 94.8, B = 29.3°, C = 31.7°
Step-by-step explanation:
Side 'a' can be found using the Law of Cosines:
a² = b² +c² -2bc·cos(A)
a = √(2809 +3249 -6042·cos(119°)) ≈ √8987.22 ≈ 94.8
Then one of the other angles can be found from the Law of Sines.
sin(C)/c = sin(A)/a
C = arcsin(c/a·sin(A)) ≈ arcsin(0.525874) ≈ 31.7°
Then the remaining angle can be found to be ...
B = 180° -A -C = 180° -119° -31.7° = 29.3°
__
The solution is a ≈ 94.8, B ≈ 29.3°, C ≈ 31.7°.
Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are needed? Round to the nearest tenth.
Answer:
3.1 gallons
Step-by-step explanation:
To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that
miles of gas / gallons = miles of gas / gallons
23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house
If we write the gallons needed to go to Bob's mother's house as g, we can say
23 miles / 1 gallon = 72 miles/g
multiply both sides by 1 gallon to remove a denominator
23 miles = 72 miles * 1 gallon /g
multiply both sides by g to remove the other denominator
23 miles * g = 72 miles * 1 gallon
divide both sides by 23 miles to isolate the g
g = 72 miles * 1 gallon/23 miles
= 72 / 23 gallons
≈ 3.1 gallons
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1=50 n2=35
x¯1=13.6 x¯2=11.6
σ1=2.2 σ2=3.0
Required:
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
Answer:
a. 2
b. The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
[tex]\mu_1 = 13.6, s_1 = \frac{2.2}{\sqrt{50}} = 0.3111[/tex]
Sample 2:
[tex]\mu_2 = 11.6, s_2 = \frac{3}{\sqrt{35}} = 0.5071[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 13.6 - 11.6 = 2[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.3111^2+0.5071^2} = 0.595[/tex]
a. What is the point estimate of the difference between the two population means?
Sample difference, so [tex]\mu = 2[/tex]
b. Provide a 90% confidence interval for the difference between the two population means.
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 - 0.9}{2} = 0.05[/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 pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
The margin of error is:
[tex]M = zs = 1.645(0.595) = 0.98[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 0.98 = 1.02
The upper end of the interval is the sample mean added to M. So it is 2 + 0.98 = 2.98
The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. Provide a 95% confidence interval for the difference between the two population means.
Following the same logic as b., we have that [tex]Z = 1.96[/tex]. So
[tex]M = zs = 1.96(0.595) = 1.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 1.17 = 0.83
The upper end of the interval is the sample mean added to M. So it is 2 + 1.17 = 3.17
The 95% confidence interval for the difference between the two population means is (0.83, 3.17).