[tex] {a}^{m} \times {b}^{m} = ( {ab)}^{m} [/tex]
(2×3×7)⁴=(2×3)⁴×7⁴(2×3×7)⁴=(2×3×7)⁴RHS=LHSplease mark this answer as brainlist
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = x2 − 4x y = 3x
Answer:
Hello your question is incomplete attached is the missing part the second curve ; y = 3x is incomplete so i would solve the problem taking the second curve as ; y = 3x + 8 ( giving you the general methodology )
answer : y = ( 5,32) , x = ( -1,8 )
area of shaded region = 90.673
Step-by-step explanation:
The given curves ; [tex]y = x^2 - 4x\\y = 3x +8[/tex]
solving the above curves simultaneously
[tex]x^2-4x = 3x + 8[/tex]
x^2 - 7x - 8 = 0
( x + 1 )(x - 8 ) = 0
hence X = ( -1 , 8 )
Therefore y = 3x + 8
when x = -1 , y = -3 + 8 = 5
when x = 8 , y = 24 + 8 = 32
hence y = ( 5, 32 )
attached below is the sketched region
Integrating the curves to determine the shaded area in respect to x = ( -1, 8)
∫ [( 3x +8 ) - ( x^2 - 4x ) ] dx
∫ ( -x^2 +7x + 8 ) dx
= { - x^3/3 + 3x^2 + 8x }
= { - 8^3/3 + 3(64) + 64} - { -1^3/3 + 3 - 8 }
= {-170.66 + 192 + 64 } - { -1/3 - 5 }
= -170.66 + 192 + 64 + 5.333 = 90.673 ( area of the shaded region )
A jar contains 8 pennies, 5 nickels and 7 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Be very precise with your answers.
a. Find the probability x = 2 cents.
b. Find the probability x = 6 cents.
c. Find the probability x = 10 cents.
d. Find the probability x = 11 cents.
e. Find the probability x = 15 cents.
f. Find the probability x = 20 cents.
g. Find the expected value of x.
Answer:
a. The probability x = 2 cents = 7/22
b. The probability x = 6 cents = 35/66
c. The probability x = 10 cents = 5/33
d. The probability x = 11 cents= 28/33
e. The probability x = 15 cents = 20/33
f. The probability x = 20 cents = 14/33
g. The expected value of x = 5.9
Step-by-step explanation:
This is a binomial probability distribution. The number of trials is known .
a. The probability x = 2 cents.
Probability ( X=2) P( selecting 2 dimes)= 7C2 / 12c2
= 21 / 66 = 7/22
b. The probability x = 6 cents.
Probability ( X=6) P( selecting a nickel and a dime)= 5C1 * 7C1/ 12c2
= 5*7 / 66 = 35/66
c. The probability x = 10 cents.
Probability ( X=10) P( selecting two nickels )= 5C2 / 12c2)
= 10/ 66 = 5/33
d. The probability x = 11 cents.
Probability ( X=11) P( selecting a penny and a dime)= 8C1 * 7C1/ 12c2)
= 8*7 / 66 = 56/66= 28/33
e. The probability x = 15 cents.
Probability ( X=15) P( selecting a penny and a nickel)= 8C1 * 5C1/ 12c2)
= 8*5 / 66 = 40/66= 20/33
f. The probability x = 20 cents.
Probability ( X=20) P( selecting 2 pennies )= 8C2 / 12c2)
= 28 / 66 = 14/33
g. The expected value of x.
E(X) = np
E(X) = 2 * (8C2+ 5C2+ 7C2)/(8+5+7) = 2( 28+10+21)/20
=2(59)/20= 5.9
Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).
Answer:
Step-by-step explanation:
Sin tita= 0.6892.find the value Of tita correct to two decimal places
Answer:
[tex]\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}[/tex]
or
[tex]\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}[/tex]
Considering [tex]\theta \in (0, 2\pi][/tex]
[tex]\theta \approx 2.38[/tex]
or
[tex]\theta \approx 0.76[/tex]
Step-by-step explanation:
[tex]\sin(\theta)=0.6892[/tex]
We have:
[tex]\sin (x)=a \Longrightarrow x=\arcsin (a)+2\pi n \text{ or } x=\pi -\arcsin (a)+2\pi n \text{ as } n\in \mathbb{Z}[/tex]
Therefore,
[tex]\theta= \arcsin (0.6892)+2\pi n, \quad n \in \mathbb{Z}[/tex]
or
[tex]\theta = \pi -\arcsin (0.6892)+2\pi n, \quad n\in \mathbb{Z}[/tex]
---------------------------------
[tex]\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}[/tex]
or
[tex]\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}[/tex]
A height is labeled on the triangle below.
Which line segment shows the base that corresponds to the given height of the triangle
Option A,B,C
Answer:
A
Step-by-step explanation:
The height is always perpinducular to the base. The height here is perpendicular to line segment A.
Answer:
A
Step-by-step explanation:
If there are 25 students in a class in which 5 of the 11 guys wear glasses and 6 out of the 14 girls wear glasses- what is the probability that one of the students in the class is a guy that he wears glasses?
Answer:
6 out of 25
Step-by-step explanation:
The length of the hypotenuse of a 30 -60 -90 triangle is 32. What are the lengths of the legs?
Answer:
16, 16(sqrt3)
Step-by-step explanation:
30-60-90 triangles follow a rule where the hypotenuse is 2 times the shortest leg, and the longer leg is sqrt3 times the shorter leg.
So, the sides are x, 2x, and (sqrt3)x.
If 2x = 32, then x = 16.
Therefore the two legs are 16 and 16(sqrt3)
you can search up 30-60-90 triangle for more information
Which expression defines the given series for seven terms?
–4 + (–5) + (–6) + . . .
Answer: -n+(-n-1)
Step-by-step explanation:
Expression will be -n + (-1)
Series
-4 +(-5)+(-6)+(-7)+(-8)+(-9)+(-10)+(-11)+(-12)+(-13) and so on
Here number -n has + (-n-1) being added to it
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Michael records the height of 1000 people. This data is a normal distribution and the sample mean was 0.75. Identify the margin of error for this data set.
Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
Find the value of x and y is (3x_6) (12,y-1)
Answer:
x=4
y=7
Step-by-step explanation:
12=3x
x=4
6=y-1
y=6+1
y=7
Answer:
x=4
Step-by-step explanation:
8. Point Mis 6 units away from the origin. Circle the letter by each pair of possible coordinates. A. (3.0) B. (4.2) C. (5,3) D. (0.6) E. (4.4) F. (1,5)
9514 1404 393
Answer:
D. (0, 6)
Step-by-step explanation:
The origin is where the axes cross. The coordinates of that point are (0, 0). The distance of a point (x2, y2) from point (x1, y1) is given by the distance formula ...
d = √((x2 -x1)² +(y2 -y1)²)
When (x1, y1) = (0, 0), this reduces to ...
d = √(x² +y²)
We want to find (x, y) such that d=6. This can be a little easier if we square both sides of the equation to eliminate the radical.
x² +y² = 6² = 36
This is the equation of a circle of radius 6 centered at the origin: all points that are distance 6 from the origin. So, any point on the circle will be at a distance of 6 from the origin.
__
The sum of squares in each case is ...
A. 3² +0² = 9 . . . inside the circle
B. 4² +2² = 20 . . . inside the circle
C. 5² +3² = 34 . . . inside the circle
D. 0² +6² = 36 . . . on the circle at a distance of 6 from the origin
E. 4² +4² = 32 . . . inside the circle
F. 1² +5² = 26 . . . inside the circle
what is the maximum number of students among whom 100 orange ,150 cirtrus, and 250 guavas can be equally distirbuted ? what is the share of each fruits for a student?
Answer:
Hello,
Step-by-step explanation:
HCF(100,150,250)=50*HCF(2,3,5)=50*1=50
Part of each fruits for a student:
2 oranges, 3 cirtrus and 5 guavas.
What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25
Complete Question
What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is 7.5
Answer:
The minimum sample size is [tex]n =97[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 1.25[/tex]
The standard deviation is [tex]s = 7.5[/tex]
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha =10\%[/tex]
[tex]\alpha =0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]
The minimum sample size is mathematically evaluated as
[tex]n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }[/tex]
=> [tex]n = \frac{1.645^2 * 7.5^2 }{1.25^2 }[/tex]
=> [tex]n =97[/tex]
20
#1. Which statement is the converse to: If a polygon is a triangle, then it
has 3 sides. *
O A polygon is a triangle, if and only if, it has 3 sides.
If a polygon has 3 sides, then the polygon is a triangle.
If the polygon does not have 3 sides, then it is not a triangle
If a polygon is not a triangle, then it does not have 3 sides
Answer:
If a polygon has 3 sides, then the polygon is a triangle.
Step-by-step explanation:
Bold = hypothesis
Italic = conclusion
Statement:
If p, then q.
Converse: If q, then p.
To find the converse, switch the hypothesis and conclusion.
Statement:
If a polygon is a triangle, then it has 3 sides.
Now we switch the hypothesis and the conclusion to write the converse of the statement.
If it has 3 sides, then a polygon is a triangle.
We fix a little the wording:
If a polygon has 3 sides, then it is a triangle.
Answer: If a polygon has 3 sides, then the polygon is a triangle.
The converse statement will be;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
Now,
Since, The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
We know that;
The converse of statement for p → q will be q → p.
Thus, The converse statement is find as;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
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cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 6 instead, she subtracted 6 and then divided the result by 3 giving an answer of 25 what would her answer have been if she had worked the problem correctly?
Answer:
13
Step-by-step explanation:
let the number be x
how Cindy worked it out :
(x -6) ÷ 3 = 25
x -6 = 75
x = 81
How she should have worked it out:
(x - 3) ÷ 6
(81 - 3) ÷ 6
78 ÷ 6 = 13
Assume that the following confidence interval for the difference in the mean length of male babies (sample 1) and female babies (sample 2) at birth was constructed using independent simple random samples:0.2 in2.7 in. What does the confidence interval suggest about the difference in length between male babies and female babies?
Answer:
The confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.
Step-by-step explanation:
Consider the hypothesis for testing the difference in the mean length of male babies and female babies at birth:
H₀: There is no significant difference between the mean length of male babies and female babies at birth, i.e. μ₁ - μ₂ = 0.
Hₐ: There is a significant difference between the mean length of male babies and female babies at birth, i.e. μ₁ - μ₂ ≠ 0.
The decision rule based on the confidence interval is:
If the (1 - α)% confidence interval does not consist of the null value, i.e. 0 then the null hypothesis will be rejected.
The confidence interval for the difference in the mean length of male babies and female babies at birth is:
CI = (0.2 in, 2.7 in)
The confidence interval does not consist of the null value, i.e. 0.
Thus, the null hypothesis will be rejected.
Hence, concluding that there is a significant difference between the mean length of male babies and female babies at birth.
Since the confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.
-40=-8(x+2) solve the equation
Answer:
x = 3
Step-by-step explanation:
-40 = -8 (x + 2)
-8 (x + 2) = -40 --- divide both sides by - 8
-8 (x + 2) -40
-------------- = ----------
-8 -8
x + 2 = 5 --- subtract 2 from both sides
x + 2 - 2 = 5 - 2 then simplify
x = 3
Answer:
x=3
Step-by-step explanation:
First, write out the equation as you have been given it:
[tex]-40=-8(x+2)[/tex]
Then distribute the -8 to the terms inside the parenthesis:
[tex]-40=-8x-16[/tex]
Next, add 16 to both sides:
[tex]-40+16=-8x-16+16\\-24=-8x[/tex]
Finally, divide both sides by -8:
[tex]\frac{-24}{-8}=\frac{-8x}{-8}\\3=x[/tex]
Therefore, x=3.
simplify radical -50
Answer:
[tex]5i\sqrt{2}[/tex]
Step-by-step explanation:
If we want to convert [tex]\sqrt{-50}[/tex] into a radical simplified, we need to find two numbers that multiply to be -50 and one of them can be squared.
[tex]\sqrt{-50} = \sqrt{-25 \cdot 2}[/tex]
The square root of -25 is 5i.
So:
[tex]5i\sqrt{2}[/tex]
Hope this helped!
Answer: [tex]=5i\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{-50}=\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{5^2\cdot \:2}[/tex]
[tex]=\sqrt{2}\sqrt{5^2}[/tex]
[tex]\sqrt{5^2}=5[/tex]
[tex]=5\sqrt{2}[/tex]
forty-six times y is no more than 276.
Answer:
yip that's all
Step-by-step explanation:
not more than 276 means less or equal to 276,
46 × y ≤ 276
y ≤ 6
Answer:
46y<276
Step-by-step explanation:
no more than means less than or equal to.
Help!!! Make brainliest
Answer:
b=(2a-1)/(3a-1)
Step-by-step explanation:
a=(b-1)/(3b-2)
3ab-2a=b-1
3ab-b=2a-1
b(3a-1)=2a-1
b=(2a-1)/(3a-1)
PLEASE HELP ME ASAP On a test, the average score of 25 boys and 15 girls is 68 points. The average test score of the boys is 62 points. What is the average score of the girls? SHOW YOUR WORK
Answer:
74
Step-by-step explanation:
The average score of boys and girls is 68 and boys is 62
Think of it as an equation (62 + x)/2 = 68, where x is the average score of girls
First multiply each side by 2 making the equation 62 + x = 136
Now subtract each side by 62, which will make the average score for girls 74
(x = 74)
Each wagon in the Parley
Company of Travelers wagon
train was about 3.65 meters long.
If 12 wagons traveled end to
end, how long would the wagon
train be?
Answer:
43.8 meters
Step-by-step explanation:
12 x 3.65
Please answer this correctly without making mistakes
Answer:
[tex]\large \boxed{\mathrm{1/2 \ boxes}}[/tex]
Step-by-step explanation:
Subtract the fractions.
[tex]\frac{9}{16}-\frac{1}{16}=\frac{8}{16} =\frac{1}{2}[/tex]
Vicky had 1/2 of a box more baking powder yesterday.
If x = -1 then how much is 2x - 1
a) 1
b) -3
c) -2
hurry please need to turn in 10 min
Answer: -3
Step-by-step explanation: 2x = -2 then you subtract 1 from that which is the same as adding negative one so -2 - 1 or -2 + -1 = -3
IV. Round to the nearest ten thousand
31. 41,876
32. 260,098
33. 91,975
34. 207,865
35. 462,876
AB is dilated from the origin to create A'B' at A' (0, 8) and B' (8, 12). What scale factor was AB dilated by?
Answer:
4
Step-by-step explanation:
Original coordinates:
A (0, 2)
B (2, 3)
The scale is what number the original coordinates was multiplied by to reach the new coordinates
1. Divide
(0, 8) ÷ (0, 2) = 4
(8, 12) ÷ (2, 3) = 4
AB was dilated by a scale factor of 4.
Mr. Lock bought 6 quarts of oil for his car. He spent $16.02. How much was each quart of oil?
Answer:
2.67
Step-by-step explanation:
To solve this problem do 16.02 / 6.
I hope this answer helps you out! Brainliest woudl be appreciated.make a box-and-whisker plot for the data. numbers of colors in a country's flag :3,2,2,4,4,3,6,3,5,3,4,1
Answer: see attachment
Step-by-step explanation:
Put the numbers in order from smallest to biggest:
1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 6
↓ ∨ ↓
Q1 Median Q3
Q1 median = (2+3)/2 = 2.5 <---- left side of box plot
Median = (3+3)/2 = 3 <---- Vertical Line of box plot
Q3 median = (4+4)/2 = 4 <---- right side of box plot
What number must be added to the expression below to complete the square? x2-5x
Answer:
6.25
Step-by-step explanation:
(x-a)^2=x^2-2ax+a^2
2a=5
a=2.5
2.5 ^ 2 = 6.25
Which of the following graphs accurately displays a parabola with its directrix and focus?
Answer:
Hey there!
The first graph is the correct answer. A point on the parabola is equally far from the focus as it is to the directrix.
Let me know if this helps :)
The graph that accurately displays a parabola with its directrix and focus is the first graph.
How do we make graph of a function?Suppose the considered function whose graph is to be made is f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
They are together plotted on the point (x,y) = (x, f(x))
This is why we usually write the functions as: y = f(x)
A point shown in the graphs on the parabola is equally far from the focus as it is to the directrix.
Therefore, The first graph is the correct answer.
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