Answer:
Following are the answer to this question:
Step-by-step explanation:
In the given equation there is mistyping so, correct equation and its calculation can be defined as follows:
Given:
[tex]f(x) =\left\begin{array}{cc} 0&x< 1\\0.5& 1 < x<3\\ 1&3 < x\end{array}\right[/tex]
Calculated value:
[tex]1) \ \ P(x < 3) =1\\\\2) \ \ P(x < 2) = 1-0.5 \\[/tex]
[tex]= 0.5[/tex]
[tex]3) P(1 < x < 2) = P( x< 2) -p(x< 1)\\\\[/tex]
[tex]=0.5-0\\=0.5\\[/tex]
[tex]4) \ \ P(x> 2)= 1-P(x<2)[/tex]
[tex]=1-0.5\\=0.5\\[/tex]
That's why the given equation is true.
The probabilities are:
[tex]1. \:P(x < 3) =1\\2.\: P(x < 2) = 0.5\\3.\: P(1 < x < 2) = 0.5\\4.\: P(x > 2) = 0.5[/tex]
Given function is:
[tex]\[ f(x)= \begin{cases} 0, \: \text{x}< 1\\ 0.5, \: 1 < x < 3\\1, \: x \geq 3\end{cases}\][/tex]
Verification that f(x) is Cumulative distribution function:
1. Since for x > 3, f(x) = 1, thus we have [tex]\lim_{x \to \infty} f(x) = 1[/tex]
2. Since for x < 1, f(x) = 0, thus we have [tex]\lim_{x \to -\infty} f(x) = 0[/tex]
3. Since values of f(x) are not decreasing as x is increasing, thus f(x) is non decreasing.
4. f(x) is right continuous too.
Thus f(x) is a cumulative distribution function.
The Probabilities are calculated as follows:
[tex]1. \:P(x < 3) = f(3) =1\\2.\: P(x < 2) = f(2) = 0.5\\3.\: P(1 < x < 2) = P(x < 2) - P(x < 1)= 0.5 - 0 = 0.5\\4. \: P(x > 2) = 1 - P(x < 2 \: and \: x = 2) = 1 - 0.5 = 0.5[/tex]
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A study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed. The sample average age was 24.2 with a standard deviation of 3.7. The p-value is
Answer:
The p-value is 2.1%.
Step-by-step explanation:
We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.
The sample average age was 24.2 with a standard deviation of 3.7.
Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average age = 24.2
s = sample standard deviation =3.7
n = sample of U.S. Adults = 43
So, the test statistics = [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex] ~ [tex]t_4_2[/tex]
= 2.127
The value of t-test statistics is 2.127.
Now, the p-value of the test statistics is given by;
P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%
Find the solution(s) of the system of equations: x2 + y2 = 8 y = x – 4 options: (–2,–6) (2,–2) and (–2,–6) (2,–2) No solutions
Answer: x=2 y=-2
(2,-2) one solution
Step-by-step explanation:
Solve by substitution
[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=x-4[/tex]
[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]
[tex]2x^2-8x+16=8[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]
[tex]\mathrm{For\:}y=x-4[/tex]
[tex]\mathrm{Subsititute\:}x=2[/tex]
[tex]y=2-4[/tex] [tex]2-4=-2[/tex]
[tex]y=-2[/tex]
[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]
[tex]x=2,\:y=-2[/tex]
A rectangular garden is 20 ft longer than it is wide. Its area is 3500 ft?. What are its dimensions?
Its width equals
Preview
and its length equals
Answer:
width of the garden is 50 ft and the length is 70 ft
Step-by-step explanation:
Solution:-
- We will denote the width and and the length of the rectangular garden as:
Width: x
Length: x + 20
- We are given the area ( A ) of the garden is 3500 ft^2. We are to determine for what dimensions is the area A = 3500 ft^2.
- Recall that the area ( A ) of a rectangle is the product of length and width as follows:
A = Length * width
A = x*( x + 20 )
3500 = x^2 + 20x
x^2 + 20x - 3500 = 0
- Use the quadratic formula to determine the value of ( x ):
[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-20 +/- \sqrt{20^2 - 4*-3500} }{2}\\\\x = \frac{-20 +/- 120 }{2} = -10 +/- 60\\\\x = -70 , 50[/tex]
- Ignore the negative value of ( - 70 ft ). Physical impractical to have a negative value. Hence, the width of the garden is 50 ft and the length is 70 ft
Please help. What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
Answer:
y = 3x + 4
Step-by-step explanation:
We can use the equation y = mx + b to find the equation:
Plug in the slope and the point into the equation, and we can find b:
-5 = 3(-3) + b
-5 = -9 + b
4 = b
Now, we can plug in the slope and y-intercept into the equation:
y = 3x + 4 will be our equation
If the payment is not made on the credit card by the end of the grace period,
which of the following will occur?
Answer: C. Interest will be charged
Step-by-step explanation:
Answer:
Step-by-step explanation:
Interest will be charged is your answer!
Farid is baking muffins, The recipe calls for 3/4 cup of sugar for a full batch. Farid is making 1/2 of a batch. Write an expression for the amount of sugar Farid needs to make 1/2 of a batch of muffins. WILL GIVE BRAINLIEST, THANKS, AND FIVE STARS PLZ HELP ME
Answer:
y = 3/8x
or
3/8 cups of sugar for every 1/2 batch of muffins
Step-by-step explanation:
Since we are only making 1/2 of the full batch of muffins, we only need to use 1/2 the cups of sugar:
[tex]\frac{3}{4} (\frac{1}{2} )= \frac{3}{8}[/tex] cups of sugar.
Answer:
[tex]\frac{x}{2} = \frac{3y}{8}[/tex]
Step-by-step explanation:
Let the batch be x and the amount of sugar be y
Condition:
x = [tex]\frac{3}{4} y[/tex]
Multiplying both sides by 1/2
[tex]\frac{1}{2} x = \frac{3}{4}y * \frac{1}{2}[/tex]
[tex]\frac{x}{2} = \frac{3y*1}{4*2}[/tex]
[tex]\frac{x}{2} = \frac{3y}{8}[/tex]
So, For 1/2 batch of muffins, Farid need 3/8 cups of sugar.
In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day.
How much meat would seven Siberian tigers need for the month of April?
Select one:
a. 750 pounds
b. 175 pounds
c. 5425 pounds
d. 5250 pounds
Answer:
the answer is 750 because there are 30 days in the month of april and you just need to multiply it by how much meat they need to have per day.
Step-by-step explanation:
30 x 25 = 750
A fair die is rolled two times. What is the probability that both rolls are 6?
Answer:
1/36
Step-by-step explanation:
the fair die has 6 equal parts which means its the total
the probability of rolling a 6 is 1/6
the probability of rolling another 6 is 1/6
so u multiply 1/6 times 1/6 which is 1/36
hope this helps
Hey there
To make it perfectly clear, consider the sample space for rolling a die twice. There are 36 equally likely possible outcomes, 6 of which define the event "rolling the same number two times in a row". Then, the probability of this event occurring is 636, which is equal to 16.Hope this hopeFill in the blanks.
(x+_)^2=x^2+14x+_
Step-by-step explanation:
(ax + b)² = a²x² + 2abx + b²
In this case, a = 1, so:
14 = 2b
b = 7
(x + 7)² = x² + 14x + 49
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (f o g)(-5)
15. A manufacturer of electronic calculators is interested in estimating the fraction of defective units produced. A random sample of 800 calculators contains 10 defectives. a. Formulate and test the hypothesis to determine if the fraction defective exceeds 0.01. Use 0.05 significance level. b. Calculate a 95% CI for this problem. Does the CI agreed with your result on (a) explain.
Answer:
a
The Null hypothesis is [tex]H_o : p = 0.01[/tex]
The defect did not exceed 0.01
b
The 95% confidence interval is [tex]0.004801 < p < 0.020199[/tex]
Yes the CI agrees with the result in a because the value 0.01 fall within the CI
Step-by-step explanation:
From the question we are told that
The sample size is n = 800
The number of defective calculators is k = 10
The population is [tex]p = 0.01[/tex]
The Null hypothesis is [tex]H_o : p = 0.01[/tex]
The Alternative hypothesis is [tex]H_a : P> 0.01[/tex]
Generally the proportion of defective calculators is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
substituting values
[tex]\r p = \frac{10}{800}[/tex]
[tex]\r p = 0.0125[/tex]
Next is to obtain the critical value of [tex]\alpha[/tex] from the z-table.The value is
[tex]Z_{\alpha } = 1.645[/tex]
Now the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p (1- p )}{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.0125 - 0.01 }{ \sqrt{ \frac{0.01 (1- 0.01 )}{800} } }[/tex]
[tex]t = 0.71067[/tex]
Now comparing the values of t to the value of [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1-\r p )}{n} }[/tex]
where [tex]Z_{\frac{\alpha }{2} }[/tex] is the critical value of [tex]\frac{\alpha }{2}[/tex] which is obtained from the z-table.The value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval ( [tex]1- \alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error .
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
So
[tex]E = 1.96 * \sqrt{\frac{ 0.0125 (1-0.0125 )}{800} }[/tex]
[tex]E = 0.007699[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < p < \r p - E[/tex]
substituting values
[tex]0.0125 - 0.007699 < p < 0.0125 + 0.007699[/tex]
[tex]0.004801 < p < 0.020199[/tex]
Now given the p = 0.01 is within this interval then the CI agrees with answer gotten in a
a scale drawing of a rectangular playground has a length of 20 inches and a width of 10 inches as shown below. the scale is 1 inch = 4 feet. what is the area of the actual playground? *
Answer:
3200ft^2
Step-by-step explanation:
1 inch = 4ft
so 20 inches = 80ft
and 10 inches = 40ft
Area = 80ft*40ft
Area = 3200ft^2
You are looking to invest in several different real estate deals. You have received ceconomic reports that explain the probability of good economic conditions will be .6 and .4 for bad economic conditions. Below is the Payoff Table, and after calculating the expected value for each decision, you determine the best "payoff deal is:
Good Economic Bad Economic
Conditions Condition (.60) Conditions (.40)
Apartment Building 50,000 30,000
Office Building $100,000 $-40,000
Warehouse 30,000 $10,000
A. Apartment Building
B. Office Building
C. Warehouse
D. None of the above.
Answer:
Real Estate Deals
The best "payoff deal:"
B. Office Building
Step-by-step explanation:
A) Payoff Table
Good Economic Bad Economic
Conditions Conditions
Probability (.60) (.40)
Apartment Building $50,000 $30,000
Office Building $100,000 $-40,000
Warehouse $30,000 $10,000
B) Calculation of Expected Values:
Good Economic Bad Economic Expected Values
Conditions Conditions
Probability (.60) (.40)
Apartment Building $30,000 $12,000 $42,000
Office Building $60,000 $-16,000 $44,000
Warehouse $18,000 $4,000 $22,000
b) The expected value for these real estate deals can be derived as the sum of the payoffs under the two economic conditions after they have been weighed with their odds of occurrence. The office building, in this example, showed the best payoff deal as the expected payoff from it results to a payoff of $44,000, which is higher than the expected payoff from the Apartment and Warehouse. However, it is also the riskiest, especially when bad economic conditions occur. This also accords with the general economic risk-return pattern that higher risky investments attract higher returns.
Use the given conditions to write an equation for the line in point-slope form
Passing through (7,3) and (4,4)
OA
1
1.
y-3 = - =(x-
5(x-4) or y-4 = - 3(x - 7)
B.
1
1
y-3= - 3(x-7) or y- 4= - 3(x - 4)
O C. y - 3 = 7(x + 7) or y-4= 4(x-3).
OD
1
1
y + 3 = - 3(x+7) or y+4= - 3(x+4)
Answer:
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
Steb by step explanation:
The condition for the line is (7,3) and (4,4).
Point slope form of equation is in this format below.
(Y-y1)= m(x-x1)
We have the given parameters in the above format except the m
M = gradient
Gradient= (y2-y1)/(x2-x1)
Gradient=(4-3)/(4-7)
Gradient= 1/-3
Gradient= -1/3
So
(Y-y1)= m(x-x1)
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
How many odd 2 digit positive odd integers geater than 50 are there?
Answer:
25
Step-by-step explanation:
Let's break this down step by step:
"2 digit positive odd integers greater than 50"
So we start at 50
Don't exceed 99 since 2-digit limit
Any 2-digit integer greater than 50 will be positive (So that's a redundant statement)
Well...we know that from 50-99, is 50 integers counting by ones.
We know that half will be even and half will be odd.
With this we can say 50/2 == 25
Hence, there are 25 2 digit positive odd integers greater than 50.
Cheers.
Solve the equation and give the solution 6x – 3y = 3 –2x + 6y = 14
Answer:
x=3.9 or 39/10 and y=3.13333 or 47/15
Step-by-step explanation:
Since both expressions (6x-3y) and (3-2x+6y) are equal to 14, separate the equations:
6x-3y=14 and 3-2x+6y=14
Simplify the equations
6x-3y=14 and -2x+6y=11
Now, line the equations up and pick a variable (either x or y) to eliminate
6x-3y=14
-2x+6y=11
In this case, let's eliminate y first. To do so make the y values in both equations the same but with opposite signs. Make both be 6y but one is +6y and the other -6y
Multiply (6x-3y=14) by 2 to get:
12x-6y=28
Line the equations up and add or subtract the terms accordingly
12x-6y=28
-2x+6y=11
This becomes:
10x+0y=39
Isolate for x
x= 39/10 or x= 3.9
Now substitute the x value into either of the original equations
6x-3y=14
6(3.9)- 3y=14
Isolate for y
23.4-14=3y
3y= 9.4
y= 3.1333 (repeating) or y= 47/15
Answer: x = 39/10, y = 94/30
Step-by-step explanation:
6x - 3y = 3 - 2x + 6y,
Now solving this becomes
6x + 2x -3y - 6y = 3
8x - 9y = 3 ------------------- 1
3 - 2x + 6y. = 14
-2x + 6y = 14 - 3
-2x. + 6y = 11
Now multiply both side by -1
2x. - 6y = -11 ----------------- 2
Solve equations 1 & 2 together
8x - 9y. = 3
2x - 6y = -11
Using elimination method
Multiply equation 1 through by 2 ,and equation 2 be multiplied by 8
16x - 18y = 6
-16x - 48y = -88 ------------------------- n, now subtract
30y = 94
Therefore. y = 94/30.
Now substitute for y in equation 2
2x - 6y = -11
2x - 6(94/30) = -11
2x - 94/5 = -11
Now multiply through by 5
10x - 94 = -55
10x = -55 + 94
10x = 39
x = 39/10
Point C is on the graph of the function y = x2 – 3. Its x-coordinate is 4. Which ordered pair gives the location of point C? A.(4, 42 – 3) B.(4, 2 + 3) C.(42, 42 – 3) D.(4, 42)
Answer:
B (4, 2+3)
Step-by-step explanation:
To do this you fill in x with 4 so the equation becomes y = (4)2 - 3
You then solve to y = 8 - 3
then 8 - 3 is 5.
Making the coordinates (4, 5) and in this case with the answers (4, 2+3)
Answer:
A. (4, 4^2 – 3)
3 = 1/2x + 1/2x + 1/2x.
Answer:
x =2
Step-by-step explanation:
3 = 1/2x + 1/2x + 1/2x
Combine like terms
3 = 3/2 x
Multiply each side by 2/3 to isolate x
3 * 2/3 = 2/3 * 3/2 x
2 =x
Let A = {H, T} be the set of outcomes when a coin is tossed, and let B = {1, 2, 3, 4, 5, 6} be the set of outcomes when a die is rolled. The set of outcomes when a coin is tossed twice. Write the set in terms of A and/or B. A ∩ B A × A A × B A ∪ B List the elements of the set.
Answer:it is 6 trust
Step-by-step explanation:yah know
PLZ IM ON THE CLOCK!!!!! A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month? $457.50 $460.00 $462.50 $572.50
Answer:
460
Step-by-step explanation:
Answer:
460
Step-by-step explanation:
Fill in the blank. A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
Answer:
Random variable
Step-by-step explanation:
The reason it is a random variable is because a, the definition fits, and b you can use context clues as well, such as 'determined by chance' which is another example of random! So, the answer is random, because random variables are determined by chance. Hope this helped.
Answer:
"A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure."
A random variable is distinct on the off chance that it takes on a countable number of quantities.
At an assembly, 180 students sit in 9 equal rows. How many students sit in each row?
Answer:
20 students per row
Step-by-step explanation:
person per each row=180/9=20
Answer:
20
Step-by-step explanation:
Take the number of students and divide by the number of students
180/9
20
There are 20 students in each row
Solve the equation 1/3 (x + 1) +2x =2
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]\frac{1}{3} (x+1)+2x=2[/tex]
Step 1: Simplify both sides of the equation.
[tex]\frac{1}{3} (x+1)+2x=2[/tex]
[tex](\frac{1}{3}) (x) + (\frac{1}{3} ) (1) + 2x = 2[/tex] (Distribute)
[tex]\frac{1}{3} x + \frac{1}{3} + 2x = 2[/tex]
[tex]( \frac{1}{3} x + 2x ) + (\frac{1}{3}) = 2[/tex] (Combine Like Terms)
[tex]\frac {7}{3} x + \frac{1}{3} = 2\\\frac{7}{3} x + \frac{1}{3} = 2[/tex]
Step 2: Subtract 1/3 from both sides.
[tex]\frac{7}{3} x + \frac{1}{3} - \frac{1}{3} = 2 - \frac{1}{3} \\\\\frac{7}{3} x = \frac{5}{3}[/tex]
Step 3: Multiply both sides by 3/7.
[tex]( \frac{3}{7} ) * (\frac{7}{3}x) = ( \frac{3}{7}) * \frac{5}{3} \\\\x = \frac{5}{7}[/tex]
So the answer is : [tex]x = \frac{5}{7}[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
3.01)Which statement best describes the area of the triangle shown below?
9
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
O It is one-half the area of a square of side length 4 units.
Ont is twice the area of a square of side length 4 units.
Answer:
C. It is one-half the area of a square of side length 4 units.
Step-by-step explanation:
Hey there!
Well if a square has side lengths of 4 units,
the area would be 16 because of l*w.
Now the formula for the area of a triangle is,
b*h/2
b = 4
h = 4
4*4=16
16 ÷ 2 = 8
So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,
meaning the area of a triangle is one-half the area of a square.
Hope this helps :)
find the exact value of sin 0
Answer:
12/13
Step-by-step explanation:
First we must calculate the hypotenus using the pythagoran theorem
5²+12² = (MO)² MO = [tex]\sqrt{5^{2}+12^{2} }[/tex] MO = 13Now let's calculate sin0
sin O = 12/13So the exact value is 12/13
Answer:
C.) 12/13
Step-by-step explanation:
In a right angle triangle MN = 12, ON = 5 and; angle N = 90°
Now,
For hypotenuse we will use Pythagorean Theorem
(MO)² = (MN)² + (ON)²
(MO)² = (12)² + (5)²
(MO)² = 144 + 25
(MO)² = 169
MO = √169
MO = 13
now,
Sin O = opp÷hyp = 12÷13
A graph shows an x- and y-axis. The data line is in the shape of a "vee." The begins above the x-axis and to the left of the y-axis, extends below the x-axis to a point on the y-axis, and ascends above the x-axis to the right of the y-axis. Which statement describes the relationship between x and y? As x increases, y decreases. As x increases, y increases. As x increases, y increases and then decreases. As x increases, y decreases and then increases.
Answer:
As x increases, y decreases and then increases
Step-by-step explanation:
You need only understand your own description of the graph:
begins above the x-axis, extends below the x-axis, and ascends above the x-axis
This is a description of decreasing, then increasing:
As x increases, y decreases and then increases
Answer:
C. As x increases, y increases and then decreases.
Step-by-step explanation:
Just took the Unit Test and got it correct on Edge.
Answer question 18 or 19 in the image thank you and please help
Answer:
19)
[tex]\frac{1}{2}*\frac{1}{4}*\frac{1}{8}*\frac{1}{16} = 2^n[/tex]
Notice that in the left side, all the numbers are powers of 2.
2 = 2^1
4 = 2^2
8 = 2^3
16 = 2^4
remember that:
(a^x)*(a^y) = a^(x+y)
then the denominator in the left is:
(2*4*8*16) = 2*(2^2)*(2^3)*(2^4) = 2^(1 + 2 + 3+ 4) = 2^8
Then we have:
[tex]\frac{1}{2}*\frac{1}{4}*\frac{1}{8}*\frac{1}{16} = \frac{1}{2^8} = 2^n[/tex]
[tex]1 = 2^8*2^n = 2^{8 + n}[/tex]
then 8 + n = 0
then n = -8.
18)
here we have:
x = (x/9) + (x/6) + (x/2) + 4 + (x/12) + 2
now in the left side we can use the common factor x and write it as:
x = x*( 1/12 + 1/9 + 1/6 + 1/2) + 6
x = x*(0.861) + 6
x - x*(0.861) = 6
x*(1 - 0.861) = 6
x = 6/(1 - 0.861) = 43.2
Find the measures of the angles in the figure.
Answer:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
which agrees with the first answer in the list of possible options.
Step-by-step explanation:
We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":
[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]
Therefore the angles of this quadrilateral are:
[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]
Answer:60,60,120,120
Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360
You take one ball randomly from a bag with 10 yellow, 5 orange and 5 green balls. What is the probability that you take a yellow ball.
1
1/4
10/15
1/2
Answer:
1/2
Step-by-step explanation:
The probability of taking a yellow ball can be found by dividing the number of yellow balls over the total number of balls.
P(yellow ball)= yellow balls / total balls
There are 10 yellow balls. There are a total of 20 balls. There are 20 because there are 10 yellow, 5 orange, and 5 green. When 10, 5, and 5 are added, the result is 20.
yellow balls = 10
total balls= 20
P(yellow ball)= yellow balls / total balls
P(yellow ball)= 10/20
The fraction 10/20 can be simplified. Both the numerator( top number) and denominator (bottom number) can be evenly divided by 10.
P(yellow ball)= (10/10) / (20/10)
P(yellow ball)= 1/(20/10)
P(yellow ball)= 1/2
The probability of taking a yellow ball is 1/2.
A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces?
Answer:
P = 0.0714
Step-by-step explanation:
If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.
Additionally, from the 28 cubes painted only 4 have exactly two painted faces.
Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:
[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]
Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.