Answer:
Vanessa is 60 and the other person is 12
Step-by-step explanation:
X + 5x = 72
6x = 72
x = 12
12 x 5 = 60
vanessa is 60
the other person is 12
60 + 12 = 72
Answer:
18
Step-by-step explanation:
Let's say x is Oscar's age, and y is Vanessa's age.
When Oscar was Vanessa's age, Vanessa was y−(x−y) = 2y−x years old. Oscar is five times older than this:
x = 5 (2y − x)
x = 10y − 5x
6x = 10y
3x = 5y
When Vanessa is Oscar's age, Oscar will be x+(x−y) = 2x−y years old. The sum of their ages will by 72.
2x−y + x = 72
3x − y = 72
Substituting:
5y − y = 72
4y = 72
y = 18
Vanessa is 18. Which means Oscar is 30.
Let's check our answer. When Oscar was 18, Vanessa was 6. Oscar is 5 times older than that (30). When Vanessa is 30, Oscar will be 42, and their ages will add up to 72.
What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minus 9 x EndFraction minus StartFraction x + 1 Over x squared minus 9 EndFraction StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction StartFraction (x + 5) (x + 4) Over x cubed minus 9 x EndFraction StartFraction negative 2 x + 11 Over x cubed minus 12 x minus 9 EndFraction StartFraction 3 (x + 2) Over x squared minus 3 x EndFraction
Answer:
[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]First option is the correct option.
Step-by-step explanation:
[tex] \frac{2x + 5}{ {x}^{2} - 3x } - \frac{3x + 5}{ {x}^{3} - 9x } - \frac{x + 1}{ {x}^{2} - 9 } [/tex]
Factor out X from the expression
[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x( {x}^{2} - 9)} - \frac{x + 1}{ {x}^{2} - 9} [/tex]
Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression
[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x(x - 3)(x + 3) } - \frac{x + 1}{(x - 3)(x + 3)} [/tex]
Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )
[tex] \frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]
Multiply the parentheses
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)} [/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]
Distribute -x through the parentheses
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x }{x(x - 3)(x + 3)} [/tex]
Using [tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex] , simplify the product
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x}{x( {x}^{2} - 9)} [/tex]
Collect like terms
[tex] \frac{ {x}^{2} + 7x + 15 - 5}{x( {x}^{2} - 9)} [/tex]
Subtract the numbers
[tex] \frac{ {x}^{2} + 7x + 10}{ x({x}^{2} - 9)} [/tex]
Distribute x through the parentheses
[tex] \frac{ {x}^{2} + 7x + 10}{ {x}^{3} - 9x} [/tex]
Write 7x as a sum
[tex] \frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x } [/tex]
Factor out X from the expression
[tex] \frac{x(x + 5) + 2x + 10}{ {x}^{3} - 9x} [/tex]
Factor out 2 from the expression
[tex] \frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x } [/tex]
Factor out x + 5 from the expression
[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]
Hope this helps...
Best regards!!
The difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]
The expression is given as:
[tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex]
Factorize the denominators
[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x^2 - 9)} - \frac{x + 1}{x^2 - 9}[/tex]
Apply the difference of two squares to the denominators
[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x - 3)(x + 3)} - \frac{x + 1}{(x - 3)(x + 3)}[/tex]
Take LCM
[tex]\frac{(2x + 5)(x + 3) - 3x - 5 -x(x + 1) }{x(x - 3)(x + 3)}[/tex]
Expand the numerator
[tex]\frac{2x^2 +6x + 5x + 15 - 3x - 5 -x^2 - x }{x(x - 3)(x + 3)}[/tex]
Collect like terms
[tex]\frac{2x^2 -x^2 - x +6x + 5x - 3x+ 15 - 5 }{x(x - 3)(x + 3)}[/tex]
Simplify
[tex]\frac{x^2+7x+ 10 }{x(x - 3)(x + 3)}[/tex]
Factorize the numerator
[tex]\frac{(x+5)(x+ 2) }{x(x - 3)(x + 3)}[/tex]
Expand the denominator
[tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]
Hence, the difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
Can someone help me?
Answer:
sq. root(330)
Step-by-step explanation:
[tex] \sqrt{-55 \sqrt[3]{-216} } = \sqrt{-55(-6)} = \sqrt{330} [/tex]
[Cube root of -216 = -6]
A certain animated movie earned $1.1⋅109\$1.1 \cdot 10^9 $1.1⋅10 9 dollar sign, 1, point, 1, dot, 10, start superscript, 9, end superscript in revenues at the box office. The movie lasts 9.1⋅1019.1\cdot10^1 9.1⋅10 1 9, point, 1, dot, 10, start superscript, 1, end superscript minutes. How much revenue was earned per minute of the movie? Write your final answer in scientific notation, and round to two decimal places.
$ 1.21 * 10⁷ per minute
Step-by-step explanation:Movie Earning = $ 1.1 * 10⁹
Movie lasted for = 9.1 * 10¹ minutes
Money earned in 9.1 * 10¹ minutes = $ 1.1 * 10⁹
Money earned in 1 minutes = $ 1.1 * 10⁹ / (9.1 * 10¹)
= $ 110 * 10⁷ / (9.1 * 10¹)
= $ 12.09 * 10⁶
= $ 1.209 * 10⁷
= $ 1.21 * 10⁷
Movie earning = $ 1.21 * 10⁷ per minute
Answer:
$ 1.21 * 10⁷ per minute
Step-by-step explanation:
What is the perimeter of a triangle that has two sides measuring 7 centimeters and a third side measuring 9 centimeters?
The perimeter is the sum of all of the lengths of the sides. To find the perimeter, add together the length of each side.
For this triangle, our side lengths are 7, 7, and 9.
7 + 7 = 14
14 + 9 = 23
The perimeter of a triangle that has two sides measuring 7 centimeters and a third side measuring 9 centimeters is 23 centimeters.
Hope this helps!! :)
Find the angle between the given vectors to the nearest tenth of a degree. u = , v = (2 points)
Answer:
3.6°Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the angle between the given vectors to the nearest tenth of a degree.
u = <8, 7>, v = <9, 7>
we will be using the formula below to calculate the angle between the two vectors;
[tex]u*v = |u||v| cos \theta[/tex]
[tex]\theta[/tex] is the angle between the two vectors.
u = 8i + 7j and v = 9i+7j
u*v = (8i + 7j )*(9i + 7j )
u*v = 8(9) + 7(7)
u*v = 72+49
u*v = 121
|u| = √8²+7²
|u| = √64+49
|u| = √113
|v| = √9²+7²
|v| = √81+49
|v| = √130
Substituting the values into the formula;
121= √113*√130 cos θ
cos θ = 121/121.20
cos θ = 0.998
θ = cos⁻¹0.998
θ = 3.6° (to nearest tenth)
Hence, the angle between the given vectors is 3.6°
In an examination 1/3 of the total student used unfair means and out of which 1/4 caught red handed while cheating. If 5 student caught red handed then find the total number of student appeared in exam
Answer:
total number of students =60
Step-by-step explanation:
total number of students 60
used unfair means 1/3= 20
1/4 caught red handed 1/4 of 20= 5
Solve this linear equation for x: 7 + 4 (5/4x - 1) = 18
Answer:
x=3
Step-by-step explanation:
7+4(5/4x-1)=18
7+5x-4=18
3+5x=18
5x=15
x=3
Answer:
x = 3
Step-by-step explanation:
18 = 7 + 4([tex]\frac{5}{4}[/tex]x - 1)
18 = 7 + 5x - 4
18 = 3 + 5x
15 = 5x
x = 3
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99.9% confident that you estimate is within 1% of the true population proportion. How large of a sample size is required
Answer: 27061
Step-by-step explanation:
given that Р = 0.5
so
1 - P = 1 - 0.5 = 0.5
ERROR OF MARGIN E = 0.01
SIGNIFICANCE LEVEL α = 1 - confidence level
α = [(1 - (99.9/100)] = 0.0010
α / 2 = 0.001 / 2 = 0.0005
Zα/2 = Z0.0005 = 3.29 (using the Z table )
therefore
Sample size n = ((Zα/2) / E)² * P * (1 - P )
Sample size n = (3.29 / 0.01)² * 0.5 * 0.5
Sample size n = 108,241 * 0.5 * 0.5
Sample size n = 27,060.25 ≈ 27,061
Answer:
sample size should be atleast n= 27069
Step-by-step explanation:
Given that,
confident level(CI) = 99%= 0.999
desired marginal error=1%= 0.01
note: marginal error = length of CL/2
significant level α = 1 - confident level = 1 - 0.999= 0.001
critical value = Zα/2 = Z(0.001/2) = Z0.0005( value of from z table) = 3.2905267
since we don't have preliminary estimate, p' = 0.5, which is require for maximum value
n = p' × (1 - p')(critical value/desired marginal)²
n= 0.5 × 0.5(3.2905267/0.01)²
n = 27068.91
the value of n has to be an integer = 27069
solve a+1= √b+1 for b
Answer: The Third one is correct
Step-by-step explanation:
Solve for x. 3 1 2 140
Answer:
Hey there!
Angle QRS is 70, and since it is located on the circle, we have a useful formula. If 141x-1 is called y, then 70 is half of that.
Thus, we have 141x-1=140
141x=141
x=1
Hope this helps :)
verify the trigonometric identity: tan(2π - x) = tan(-x)
Answer:
See Below
Step-by-step explanation:
Taking Right Hand Side to verify the identity:
tan ( 2π - x)
Resolving Parenthesis
tan 2π + tan (-x)
We know that tan 2π = 0
0 + tan (-x)
=> tan(-x) = Left Hand Side
Hence Proved
Answer:
[tex]\boxed{ \sf {view \: explanation}}[/tex]
Step-by-step explanation:
[tex]\Rightarrow \sf tan ( 2\pi - x)=tan(-x)[/tex]
[tex]\sf Apply \ distributive \ law.[/tex]
[tex]\Rightarrow \sf tan (2\pi) + tan (-x) =tan(-x)[/tex]
[tex]\sf Apply : tan(2\pi) =0[/tex]
[tex]\Rightarrow \sf 0 + tan (-x) =tan(-x)[/tex]
[tex]\Rightarrow \sf tan (-x) =tan(-x)[/tex]
[tex]\sf Hence \ verified.[/tex]
A survey asks "would you like to see more or less government spending on natural disasters?" Of the 1496 respondents, 723 responded "more" or "much more". The population of interest consists of
A) the proportion of American adults who would respond "more" or "much more"
B) the 723 respondents who responded "more" or "much more"
C) the 1496 respondents
D) all American adults
E) the proportion of respondents who responded "more" or "much more"
Answer:
D) all American adults
Step-by-step explanation:
The 1496 respondents are the sample of the survey that was used to represent the population of interest, which is the total population from which the sample was drawn and the population from which the researchers want to find conclusions.
Looking at the alternatives, the only one that fits the description is alternative D) all American adults .
please Evaluate 27 times ( 1/3) to the 3 power. A). 1 B). 3 C). 9 D). 27
Answer:
you want to follow PEMDAS so you would multiply 27 by 1/3 to get 81.003, which you would round to 81, then you would multiply 8 to the third power and you would get 512.
Step-by-step explanation:
27(1/3)^3
81^3
512
Graph this compound inequality: 2.5 < x < 4.5
-5 4
-3
-2
-1 0
+ ++ +
1 2 3 4 5
o
Drag a point to the number line.
Answer:
Please find the attached the required inequality graph
Step-by-step explanation:
Given that inequality is 2.5 ≤ x ≤ 4.5, we have;
The region in the given inequality is the region between 2.5 and 4.5 inclusive
Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;
A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.
Quadrilateral ABCD is a kite. A kite. Angle A is 90 degrees, angle B is unknown, angle C is 130 degrees, angle D is unknown. What is the measure of angle B? degrees
Answer:
70 degrees
Step-by-step explanation:
(360 - 90 - 130)/2=70
Equivalent equation to 19-6(-k+4)=
Answer:
-5+6k
Step-by-step explanation:
19-6(-k+4)=16+6k-24=6k-5
Answer:
6k-5
Step-by-step explanation:
19-6(-k+4)=
19+6k-24=
6k-5
Can someone help me ASAP???!!
Answer:
25x ²−49y ²
Step-by-step explanation:
We need to find product of (5x+7)(5x−7y)
By using identity (a+b)(a−b)=a −b ²
We have a=5x,b=7y
Thus (5x+7y)(5x−7y)=(5x) ²−(7y)
let me know if it was helpful
25x² - 49y²
Step-by-step explanation:
To Find:
The product of (5x - 7y)(5 x + 7)
How to solve:
Just need to use the formula of a² - b² = (a+b)(a-b)
let's assume a = 5x and b = 7x
Solution:
(5x - 7y)(5 x + 7) = (5x)² - (7y)²
= 25x² - 49y²
Hence required answer is 25x² - 49y².
evaluate 1/2^-2x^-3y^5 for x=2 and y=-4
Answer:
[tex] - \frac{1}{32} [/tex]Step-by-step explanation:
Given,
x = 2
y = - 4
Now, let's solve:
[tex] \frac{1}{ {2}^{ - 2} \: {x}^{ - 3} \: {y}^{5} } [/tex]
plug the values
[tex] \frac{1}{ {2}^{ - 2} \: {(2)}^{ - 3} \: {( - 4)}^{5} } [/tex]
A negative base raised to an odd power equals a negative
[tex] \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {( - 4}^{5}) } [/tex]
Determine the sign of the fraction
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {4}^{5} } [/tex]
Write the expression in exponential form with a base of 2
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {2}^{10} } [/tex]
Calculate the product
[tex] - \frac{1}{ {2}^{5} } [/tex]
Evaluate the power
[tex] - \frac{1}{32} [/tex]
Hope this helps...
Best regards!!
how many digits are in the decimal expansion of 2^34
Answer:
2^34 = 17179869184
I hope this helps :)
hurry please!! The equation cos35°=a/25. What is the length of the line BC? Round to the nearest 10th
Answer:
25 is the same lenghth rounded
Step-by-step explanation:
aproximitly it rounded to the 10
4. A number m is such that when it is divided by 30, 36, and 45 the remainder is always 7,
find the smallest possible value of m
Answer:
187
Step-by-step explanation:
A number m is such that when it is divided by 30, 36 and 45 the remainder is always 7.
We should first find the LCM of 30, 36 and 45
We get that the LCM of the three numbers is 280 (working attached).
So now;
[tex]\frac{180}{30}[/tex] = 6
[tex]\frac{180}{36}[/tex] = 5
[tex]\frac{180}{45}[/tex] = 4
But we need a number that leaves a remainder of 7 so we add 7 to 180 to get; 180 + 7 = 187.
A magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. Describe what is meant by the statement that "the margin of error was given as percentage points.
Which one would be a true statement?
A. The statement indicates that the study is 100%−3%=97% confident that the true population percentage of people that prefer chocolate pie is 11%
B. The statement indicates that the interval 11%+3% is likely to contain the true population percentage of people that prefer chocolate pie.
C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11%±3%.
D. The statement indicates that the study is only 3% confident that the true population percentage of people that prefer chocolate pie is exactly 11%.
Answer:
C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11%±3%.
Step-by-step explanation:
Data provided in the questions
Number of respondents = 1,000
Choose chocolate pie = 11%
margin of error = ±3 percentage points
Based on the above information,
The lower limit is
= 0.11 - 0.03
= 0.08
And, the upper limit is
= 0.11 + 0.03
= 0.14
So based on the above computation, the option c is correct as it represents the true population percentage of people with respect to the chocolate pie preference
A school has 6 3/4 kg of detergent in stock. During ' Use Your Hands ' campaign, each class will be given 3/8 kg of detergent. There are 28 classes in the school.
(a) What fraction of the school will be supplied with the detergent in stock?
(b) How much detergent will be required altogether for the whole school?
(c) How much more detergent does the school need to order?
(d) If the school gives out the detergent in stock to the 15 lower secondary classes first,
(i) how much detergent will be given out;
(ii) how much detergent in stock will be left?
Answer:
Step-by-step explanation:
Total stock available = 6 x 3/4 = 18/4
Detergent given to each class=3/8
Total number of classes in the school = 28
Total detergent required by the school=3/8*28
=42/4
a. Fraction if the school who will get the detergent=18/42
b. Total required detergent for the whole school= 42/4
c. School needs to order = 42/4 - 18/4
= 24/4
= 6
d. i. Detergent given out to 15 classes = 15 x 3/8
= 45/8
ii. There will be no detergent left in stock
Solve the following equation for x . 9=x2+2
Answer:
X=3.5
Step-by-step explanation:
9=x2+2
9-2=x2
(9-2)÷2=x
Complete the equation: x2+10x+__=(__)^2 A. 25; x+5 B. 25; x−5 C. 10; x+10 D. 10; x−10
Answer:
Answer A) 25, and x+5
Step-by-step explanation:
You need to complete the square by adding a constant that makes the quadratic expression a perfect square of a binomial. So base your analysis on the fact that the coefficient accompanying the square term of x is one, and the fact that the middle term has coefficient 10 which is twice "5" so 5 is the likely candidate for the binomial that goes squared: (x + 5) and the square of 5 (25) is what you need to add as constant term to get the perfect square of a binomial:
[tex]x^2+10x+25=(x+5)^2[/tex]
heLp would be appreciated for the image below :))
Answer:
A
Step-by-step explanation:
The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles.
Using Pythagoras' identity in either of the 2 right triangles, then
([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²
[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides )
[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12 → A
Large samples of women and men are obtained, and the hemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2:
negative 1.76 g divided by dL less than mu 1 minus mu 2 less than minus 1.62 g divided by dL
−1.76 g/dL<μ1−μ2<−1.62 g/dL. Complete parts (a) through (c) below.
a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?
Answer:
a) Because the confidence interval does not include 0 it appears that there
is a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.
b)There is 95% confidence that the interval from −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2
c) 1.62 < μ1−μ2< 1.76
Step-by-step explanation:
a) What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?
Given:
95% confidence interval for the difference between the two population means:
−1.76g/dL< μ1−μ2 < −1.62g/dL
population 1 = measures from women
population 2 = measures from men
Solution:
a)
The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in men is not equal and that the women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in men.
b)
There is 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.
c)
If we interchange men and women then
confidence interval range sign will become positive.μ1 becomes the population mean of the hemoglobin level in menμ2 becomes the population mean of the hemoglobin level in women So confidence interval becomes:1.62 g/dL<μ1−μ2<1.76 g/dL.
There is a significant difference between the mean level of hemoglobin in women and in men.
How to interpret the confidence intervalThe confidence interval of the mean is given as:
[tex]-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL[/tex]
The above confidence interval shows that the confidence interval is exclusive of 0.
This means that 0 is not part of the confidence interval
Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.
Read more about confidence intervals at:
https://brainly.com/question/17097944
A 10-sided die numbered 1 to 10 is rolled once. Find these probabilities.
A. Pr(8)
B. Pr(odd)
C. Pr(even)
D. Pr(less than 6)
E. Pr(prime) (remember that 1 is not prime)
F. Pr(3 or 8)
G. Pr(8, 9 or 10)
H. Pr(greater than 9)
^please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?
^and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you
Answer:
A. Pr(8) = 1/10
B. Pr(odd) = 1/2
C. Pr(even) = 1/2
D. Pr(less than 6) = 1/2
E. Pr(prime) = 2/5
F. Pr(3 or 8) = 1 / 5
G. Pr(8, 9 or 10) = 3/10
H. Pr(greater than 9) = P(10) = 1/10
Step-by-step explanation:
We assume a FAIR 10-faced die, meaning there is an equal probability of throwing any one of the ten numbers.
With 10 possible outcomes each with equal probability, the probability of throwing any number is 1/10.
(It is preferable to work with fractions in probability because fractions are exact numbers, while decimals can often be rounded, or truncated).
A. Pr(8) means probability of throwing an 8, therefore Pr(8) = 1/10
B. Pr(odd) there are 5 odd number from 1 to 10, so Pr(odd) = 5/10 = 1/2
C. Pr(even) there are 5 even number from 1 to 10, so Pr(even) = 5/10 = 1/2
D. Pr(less than 6) there are 5 numbers less than 6 (between1 to 10),
so Pr(less than 6) = 5/10 = 1/2
E. Pr(prime) (remember that 1 is not prime)
A prime number is an integer not divisible by any number except one and itself.
Between 1 to 10, the four prime numbers are 2,3,5,7
therefore Pr(prime) = 4/10 = 2/5
F. Pr(3 or 8)
(3 or 8) make 2 successful outcomes out of 10, so Pr(3 or 8) = 2/10 = 1 / 5
G. Pr(8, 9 or 10)
similarly, (8,9 or 10) make three successful possible outcomes out of 10, so
P(8,9 or 10) = 3/10
H. Pr(greater than 9)
there is only one successful outcome, namely "10" out of 10 possible outcomes. So
P(greater than 9) = P(10) = 1/10
1. please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?
A die is singular for dice, which can take up any number of faces. With a 10-faced solid, we can make a 10-faced die numbered 1 to 10.
2. and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you
See solutions above.
Answer:
Remember that standard probabilities are defined as the ratio between the number of favorable cases, and the total number of possible events.
In this case, we have a 10-sided die, which means its faces are numbered from 1 to 10, which gives us 10 total number of possible events. In other words, the denominator of the ratio is going to be 10.
Now we're able to find each probability.
(A) Probability of getting an 8:[tex]P_{8} =\frac{1}{10}=0.10[/tex]
The numerator is 1 because there's only one number 8 in the die, that means the number of favorable cases is 1, and, as we said before, the total number of possible events is 10.
(B) Probability of getting an odd number:[tex]P_{odd} =\frac{5}{10}=0.5[/tex]
The numerator is 5 because there are 5 odd numbers from 1 to 10. In other words, there are 5 favorable cases to this probability.
(C) Probability of getting an even number:[tex]P_{even}=\frac{5}{10}=0.5[/tex]
There are 5 even numbers from 1 to 10, that's why we had the same probability.
(D) Probability of getting a number less than 6:We know that there are only 5 numbers less than 6 for this die.
[tex]P_{<6}=\frac{5}{10}=0.5[/tex]
(E) Probability of getting a prime number:A prime number is such that it can be divided only by itself and the unit. So, there are four prime numbers from 1 to 10, which are 2, 3, 5, 7.
[tex]P_{prime}=\frac{4}{10}=0.4[/tex]
(F) Probability of getting 3 or 8:When we are going to find the probability of an event "or" another, we must sum those favorable cases.
[tex]P_{3 \ or \ 8} =\frac{1+1}{10}=\frac{2}{10}=0.2[/tex]
(G) Probability of getting 8, 9, or 10:In this case, we need to some all three favorable cases. The die has only one 8, one 9 and one 10. So, the probability is
[tex]P_{8,9,10}=\frac{1+1+1}{10}=\frac{3}{10} =0.3[/tex]
(H) Probability of getting a number greater than 9:We know that there's only one number greater than 10 on such die.
[tex]P_{>10}=\frac{1}{10}=0.1[/tex]
Lastly, "die" refers to this special 10-sided dice. In other problems, you can find "a die" with more faces even. But, in general, "die" refers to a dice.
If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
Answer:
Step-by-step explanation:
REcall that f(x) is a polynomial whose one of its roots is -3+i. The fundamental algebra theorem states that any polynomial of degree n has n complex roots. In the real case, it can be also interpreted as any polynomial can be factored in factors of degree at most 2.
Consider that given a polynomial of degree 2 of the form [tex]ax^2+bx+c[/tex] the solutions are given by
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In this case, the fact that x is real or complex depends on the number [tex]b^2-4ac[/tex] which is called the discriminant. When this number is negative, we have that x is a complex root. Let say that [tex]b^4-4ac<0[/tex] and that [tex]\sqrt[]{b^4-4ac}=di[/tex], so the roots are given by
[tex] x_1 = \frac{-b + di}{2a}, x_2 = x_1 = \frac{-b - di}{2a}[/tex]
this means that, whenever we have a complex root, the other root is the complex conjugate. Recall that the complex conjugate of a complex number of the form a+bi is obtained by changing the sign of the imaginary part, that is a-bi.
So, in our case since -3+i is a root, then -3-i necessarily is another root.
If -3 + i is a root then -3 - i is too.
Therefore, the answer is -3 - i
In a school, half of the 300 students saw Zootopia, 180 students saw Finding Dory, and 45 students did not see either movie. How many students saw both movies?
Answer:
150
Step-by-step explanation:
Answer:
150 = half of 300
± 180
230
soooo 230 students
Step-by-step explanation: