Answer:
(B)Rocco wrote the equivalent fraction in Step 1 incorrectly.
Step-by-step explanation:
In trying to find the fraction equivalent of 0.012, Rocco's work is shown below:
Step 1: 0.012 = [tex]\dfrac{12}{100}[/tex]
Step 2: [tex]\dfrac{12}{100}=\dfrac{3}{25}[/tex]
Step 3: Therefore 0.012 [tex]=\dfrac{3}{25}[/tex]
Observe that in Step 1, Rocco wrote the equivalent fraction incorrectly.
Correctly: 0.012 = [tex]\dfrac{12}{1000}[/tex]
The correct answer is B.
Answer:
The correct answer would be number B. Hope this helps!
Step-by-step explanation:
Given the probability density function f(x) = 1/5 over the interval [4, 9], find the expected value, the
mean, the variance and the standard deviation.
Expected value:
Mean:
Variance:
Standard Deviation:
Answer:
Step-by-step explanation:
Assume that f(x) = 0 for x outside the interval [4,9]. We will use the following
[tex]E[X^k] = \int_{4}^{9}x^k f(x) dx[/tex]
[tex]Var(X) = E[X^2}- (E[X])^2[/tex]
Standard deviation = [tex] \sqrt[]{Var(X)}[/tex]
Mean = [tex]E[X][/tex]
Then,
[tex]E[X] = \int_{4}^{9}\frac{1}{5}dx = \frac{9^2-4^2}{2\cdot 5} = \frac{13}{2}[/tex]
[tex]E[X^2] = \int_{4}^{9}\frac{x^2}{5}dx = \frac{9^3-4^3}{3\cdot 5} = \frac{133}{3}[/tex]
Then, [tex]Var(x) = \frac{133}{3}-(\frac{13}{2})^2 = \frac{25}{12}[/tex]
Then the standard deviation is [tex]\frac{5}{2\sqrt[]{3}}[/tex]
Possibilities Density Functions are a set of data measures that can be used to anticipate that a discontinuous value will turn out as the following calculation:
Density function calculated value:Given function= [tex]\frac{1}{5}[/tex]
interval= [4,9]
Assuming that the given function that is [tex]fx) = 0[/tex] .
For this, the x outside the interval is [4,9].
Equation:
[tex]E[X^k] = \int^{9}_{4} x^k\ f(x) \ dx\\\\[/tex]
[tex]Var(X) = E(X)^2 - (E[X])^2[/tex]
The values are:
Standard deviation [tex]= \sqrt{Var(X)}[/tex]
Mean [tex]= E[X][/tex]
Solving the equation then:
[tex]E[X] =\int^{9}_{4} \frac{1}{5}\ dx[/tex]
[tex]= \frac{9^2-4^2}{2\cdot 5} \\\\ = \frac{81-16}{10} \\\\ = \frac{65}{10} \\\\=\frac{13}{2} \\\\[/tex]
[tex]E[X^2] =\int^{9}_{4} \frac{x^2}{5}\ dx[/tex]
[tex]= \frac{9^3-4^3}{3\cdot 5} \\\\= \frac{729-64}{15} \\\\ = \frac{665}{15}\\ \\=\frac{133}{3} \\\\[/tex]
[tex]\to Var(x) = \frac{133}{3} - (\frac{13}{2})^2 = \frac{25}{12}\\\\[/tex]
Therefore the standard deviation value is [tex]\frac{5}{2\sqrt{3}}[/tex]
Find out more about the probability here:
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The figure below is made of 2 rectangular prisms. What is the volume of this figure?
_____ cubic units.
Answer:
100
Step-by-step explanation:
The Volume of the Rectangular prism on the left is 60
The Volume of the Rectangular prism on the right is 40
Answer:
Your correct answer is 40
Step-by-step explanation:
Multiply 8 x 5.
8 x 5 = 40
MUltiply 40 x 1.
40 x 1 = 40
So, it stays the same. Anything multiplied by 1 stays the same.
Therefore, your correct answer is 40.
What angle is included by AB and BC ?
B
A
O A. ZB
OB. ZA
O c. Zc
Answer:
[tex] \angle B[/tex]
Step-by-step explanation:
[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,
A new soft drink is being market tested. a sample of 400 individuals participated in the taste test and 80 indicated they like the taste.
A. At a 5% significant level, test to determine if at least 22% of the population will like the new soft drink.
B. Determine the p-value
Answer:
Step-by-step explanation:
p/100* 400=80
*100 *100
400p=8000
:400 :400
p=20
With 5% significant level I think we consider that 22% likes the drink
0.006772 to 1 significant number
Answer:
0.006772
If the last dropping digit is less than 5 then it will be ignored
0.00677
if the last dropping digit is greater than 5 than the the last retained digit increases by 1
0.0068
if the last dropping digit is greater than 5 than the the last retained digit increases by 1
0.007
if the last dropping digit is greater than 5 than the the last retained digit increases by 1
0.01
if the last digit is less than 5 so it will be ignored
0.0 is significant figure because zero to the right of decimal point are significant
Step-by-step explanation:
i hope this will help you :)
Answer:
0.007
Step-by-step explanation:
Rounding off 0.006772 to 1 significant figures:
=> 0.007
There is only 1 significant figure in this , since the zeroes on the left are not counted as significant figures.
Identify the glide reflection rule in the given figure
Answer:
Option (3)
Step-by-step explanation:
Glide reflection of a figure is defined by the translation and reflection across a line.
To understand the glide rule in the figure attached we will take a point A.
Coordinates of the points A and A' are (2, -1) and (-2, 4).
Translation of pint A by 5 units upwards,
Rule to be followed,
A(x, y) → A"[x, (y + 5)]
A(2, -1) → A"(2, 4)
Followed by the reflection across y-axis,
Rule to be followed,
A"(x, y) → A'(-x, y)
A"(2, 4) → A'(-2, 4)
Therefore, by combining these rules in this glide reflections of point A we get the coordinates of the point point A'.
Option (3) will be the answer.
Answer:Reflection along the line y= -1
Step-by-step explanation:
took test
What is the value of y?
Answer:
B. 65°
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
180 - 130 = 50
Angles in a triangle add up to 180 degrees.
y + y + 50 = 180
2y + 50 = 180
2y = 180 -50
2y = 130
y = 130/2
y = 65
Find the first, fourth, and eighth terms of the sequence A(n)=-3 X 2^n-1
1; –216; –279,936
–6; –48; –768
–12; –96; –1,536
–3; –24; –384
Answer:
The answer is
3, 24, 384Step-by-step explanation:
Usng the formula
[tex]A(n) = 3(2) ^{n - 1} [/tex]
Where n is the number of terms
For the first term
[tex]A(1) = 3(2)^{1 - 1} \\ = 3(2) ^{0} \\ = 3(1) \\ \\ = 3[/tex]
For the fourth term
[tex]A(4) = 3(2)^{4 - 1} \\ = 3 ({2})^{3} \\ = 3 \times 8 \\ \\ = 24[/tex]
For the eighth term
[tex]A(8) = 3 ({2})^{8 - 1} \\ = 3 ({2})^{7} \\ = 3(128) \\ \\ = 384[/tex]
Hope this helps you
Answer: –3; –24; –384
Step-by-step explanation:
The mean amount spent by a family of four on food is $500 per month with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $425 per month?
Answer:
[tex] z=\frac{x- \mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{425-500}{75}= -1[/tex]
And we can calculate this probabilit using the normal standard distribution or excel and we got:
[tex] P(z<-1)= 0.159[/tex]
Step-by-step explanation:
If we define the random variable of interest "the amount spent by a family of four of food per month" and we know the following parameter:
[tex] \mu = 500, \sigma = 75[/tex]
And we want to find the following probability:
[tex] P(X<425)[/tex]
And we can use the z score formula given by:
[tex] z=\frac{x- \mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{425-500}{75}= -1[/tex]
And we can calculate this probabilit using the normal standard distribution or excel and we got:
[tex] P(z<-1)= 0.159[/tex]
The given function is analytic at a = 0. Use appropriate series in (2) and long division to find the first four nonzero terms of the Maclaurin series of the given function.
Sec x.
Answer:
[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]
Step-by-step explanation:
From the given information:
we are to find the first four nonzero terms of the Maclaurin series of the given function.
Sec x.
If we recall ; we will realize that the derivative of sec x = [tex]\dfrac{1 }{cos \ x}[/tex]
Also; for cos x ; the first four terms of its Maclaurin Series can be expressed as ;
=[tex]1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}+...[/tex]
However, using the long division method: we have;
[tex]\dfrac{1}{1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}}[/tex]
the rule of the long division method is to first use the 1 from the denominator to divide the 1 from the numerator. the multiply it with the answer we get which is (1) before subtracting it from that answer (1).
i.e
1/1 = 1
1 × 1 = 1
1 - 1 = 0
Afterwards; we will subtract the remaining integers from this numerator.
So, we have:
[tex]\dfrac{-(1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!} )}{0+ \dfrac{x^2}{2!}-\dfrac{x^4}{4!}+ \dfrac{x^6}{6!}}[/tex]
We are going to apply the same process to the remainder [tex]\dfrac{x^2}{2!}[/tex];
which is to divide the second integer with 1
[tex]\dfrac{\dfrac{x^2}{2!}}{1}= \dfrac{x^2}{2!}[/tex]
Then we will multiply the numerator with [tex]\dfrac{x^2}{2!}[/tex] ; the result will then be subtracted from the polynomial.
[tex]= \dfrac{-( \dfrac{x^2}{2!} - \dfrac{x^4}{2! 2!} + \dfrac{x^6}{2! 4!}- \dfrac{x^8}{2! 6!}) }{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }[/tex]
Repeating the same process for remainder [tex]\dfrac{5}{24}x^4[/tex]; we have:
[tex]\dfrac{ \dfrac{5}{24}x^4 }{1}= \dfrac{5}{24}x^4[/tex]
so; we will need to multiply 1 with [tex]\dfrac{5}{24}x^4[/tex] and subtract it from the rest of the polynomial
[tex]=\dfrac{{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }}{ 1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]
[tex]= \dfrac {- ( \dfrac{5}{24}x^4 -\dfrac{5}{2!4!}x^6 - \dfrac{5x^8}{4!4!} - \dfrac{5x^{10}}{6!4!} } {0+ \dfrac{61}{720}x^6}[/tex]
Here ; the final remainder is [tex]\dfrac{61}{720}x^6}[/tex]; repeating the usual process for long division method; we have:
[tex]\dfrac{\dfrac{61}{720}x^6}{1}= \dfrac{61}{720}x^6}[/tex]
So;
[tex]= \dfrac{0+ \dfrac{61}{720}x^6}{1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]
[tex]= \dfrac{-( \dfrac{61}{720}x^6)}{0 }[/tex]
Now the first four nonzero terms of the Maclaurin series is the addition of all the integers used as remainders ; i.e
[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]
Please answer this question fast in two muintues
Answer:
W
Step-by-step explanation:
W is the vertex, you can see the letter above the angle
Answer:
W
Step-by-step explanation:
The vertex is where the 2 rays meet, or the corner of the angle
The vertex is W
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 38; p = 2/5 Group of answer choices σ = 13.55 σ = 14.40 σ = 7.87 σ = 10.28
Answer:
[tex] X \sim Binom (n=38, p=2/5)[/tex]
By properties the mean is given by:
[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]
Step-by-step explanation:
For this case we know that the random variable follows a binomial distribution given by:
[tex] X \sim Binom (n=38, p=2/5)[/tex]
By properties the mean is given by:
[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Work Shown:
A = area of bottom rectangular face = 10*5 = 50
B = area of back rectangular face = 12*10 = 120
C = area of slanted front rectangular face = 13*10 = 130
D = area of left triangle = 0.5*base*height = 0.5*5*12 = 30
E = area of triangle on right = 0.5*base*height = 0.5*5*12 = 30
S = total surface area
S = A+B+C+D+E
S = 50+120+130+30+30
S = 360
Nathan has a $75 budget to rent a car for a day. The daily rental charge is $29.50 and then he will also have to pay $0.55 per mile. How many miles can he drive the car without exceeding his budget? (All partial miles are counted as full miles.)
Answer:
82 miles
Step-by-step explanation:
Since Nathan only needs the car for a day and he has 75$ then we can set that as are maximum to build the equation to find the amount of miles he can drive.
75 = 29.5 + 0.55x
45.5 = 0.55x
x = 82.73
The problem states that partial miles will count as full miles, so Nathan can only afford to drive 82 miles on the rental car.
Cheers.
Nathan can drive a number of miles would be 82.73 the without exceeding his budget.
What is a numerical expression?A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
We have been given that Nathan only needs the car for a day and has $75, we can use it as the maximum to develop the equation to determine how many kilometers he can drive.
⇒ 75 = 29.5 + 0.55x
⇒ 45.5 = 0.55x
⇒ x = 82.73
Thus, the partial miles are counted as full miles, Nathan can only afford to travel 82 miles in the rented car.
Therefore, he can drive a number of miles would be 82.73 the without exceeding his budget.
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PLEASE help, thanks will give 5 stars
Answer:
x=4/3
Step-by-step explanation:
By using the formula =
MQ/QP=MN/NO
4/x=6/2
Cross multiply
6x=8
x=4/3
10.
AA'B'C' is a dilation image of AABC. Which is the correct description of the dilation?
12
of a
А)
6
B' =B
С
Answer:
Option (2)
Step-by-step explanation:
In the figure attached,
ΔA'B'C' is a dilation image of ΔABC or both the triangle are similar.
Therefore, by the property of similarity of two similar triangles, corresponding sides these similar triangles will be proportional.
Scale factor = [tex]\frac{\text{Side of image triangle}}{\text{Side of the pre-image}}[/tex]
= [tex]\frac{\text{B'A'}}{\text{B'A}}[/tex]
= [tex]\frac{\text{(B'A+AA')}}{\text{B'A}}[/tex]
= [tex]\frac{(6+12)}{6}[/tex]
= 3
Therefore, scale factor is 3 when center of dilation is B.
Option (2) will be the answer.
A population has a known standard deviation of 1.27 and a sample space contains 85 values find the margin of error needed to create a 99% confidence interval estimate of the mean of the population
Answer:
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
Step-by-step explanation:
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{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]\sigma = 1.27, n = 85[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 2.575*\frac{1.27}{\sqrt{85}}[/tex]
[tex]M = 0.3547[/tex]
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
Find the value of X.
Answer:
x=√30Given,
CB=X
CD=3
CA=3+7=10
HERE,
[tex] {(cb)}^{2} = cd \times ca \\ {x}^{2} = 3 \times 10 \\ {x}^{2} = 30 \\ x = \sqrt{30} [/tex]
Hope this helps...
Good luck on your assignment..
The value of x is: x= √30.
Here, we have,
from the given figure, we get,
let, angle C = Ф
then, from triangle BCD,
cos Ф = 3/x
and, from triangle ABC,
cos Ф = x/10
so, we have,
3/x = x/10
=> x² = 10×3
=> x² = 30
=> x= √30
Hence, The value of x is: x= √30.
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pls help i give brainliest
Answer:
Step-by-step explanation:
Area of triangle = 1/2 × b × h
69.3 = 8.4 × h
h = 69.3 / 8.4
h = 8.25 mm
hope this helps
plz mark as brainliest!!!!!!
Answer:
16.5mm
Step-by-step explanation:
1. 69.3 x 2
2. 138.6 divided by 8.4
3. solve which equals 16.5mm
Hope this helps you:)
A rocket is stopped 34 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 18 feet per second per second. The distance between the rocket and the satellite is given by the polynomial P(t) = 9t2 + 34. Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.
Answer:
The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.
Step-by-step explanation:
The distance between the rocket and the satellite, in feet, after t seconds, is given by the following equation:
[tex]P(t) = 9t^{2} + 34[/tex]
Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.
This is P(10).
[tex]P(t) = 9t^{2} + 34[/tex]
[tex]P(10) = 9*(10)^{2} + 34 = 934[/tex]
The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.
Solve 6 + 5 √ 2 4 9 − 2 x = 7
[tex]
6+5\sqrt{249}-2x=7 \\
-2x=7-6-5\sqrt{249} \\
-2x\approx-77.9 \\
x\approx\frac{-77.9}{2}\approx38.95
[/tex]
Hope this helps.
HELP PLS!!! ITS DUE ASAP AND I NEED HELP ITS THE LAST QUESTION
Answer:
See below.
Step-by-step explanation:
Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]
We know that the diameter is 14, so the radius is 7.
Plug it into the equation:
[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]
PLEASE HELP Kelly wants to join an aerobics class. The initial membership fee is $25.00, and each clas costs $10.00. She pays a total of $115.00 to register for a certain number of classes. Create an equation to find the number of classes Kelly registered for.
Answer:
$25.00 + $10x = $115.00
Step-by-step explanation:
We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.
Use the 4 step process to find the f'(x) of the function f(x)=x^2-3/2
Answer:
see below
Step-by-step explanation:
Modified problem
(x)^2-3/x
Step 1: Find f(x+h)
(x+h)^2-3/(x+h)
x^2 +2hx + h^2 -3/(x+h)
Step 2: Find f(x + h) − f(x)
x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)
Distribute the minus sign
x^2 +2hx + h^2 -3/(x+h) - x^2+3/x
Combine like terms and get a common denominator
2hx + h^2 -3x/(x(x+h)) +3(x+h)/(x(x+h)
2hx + h^2 +3h/(x(x+h))
Step 3: Find (f(x + h) − f(x))/h
(2hx + h^2+3h/(x(x+h)) )/h
2hx/h + h^2/h+3h/(x(x+h)) /h
2x +h +3/(x(x+h))
Step 4: Find lim h→0 (f(x + h) − f(x))/h
2x+0 +3/(x(x+0))
2x +3/x^2
Consider it this cone with a diameter of 19 cm use the drop-down menus to describe the con measurements
Answer:
1) Radius of the cone = 9.5 cm
2) BA = 90.25 π cm²
3) SA = 384.7 π cm²
Step-by-step explanation:
1) Radius of the cone = 9.5 cm
2) Base Area of the cone = [tex]\pi r^2[/tex]
BA = (π)(9.5)²
BA = 90.25 π cm²
3) Surface Area of Cone = [tex]\pi r(r+\sqrt{h^2+r^2)}[/tex]
SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)
SA = 9.5π(9.5 + 31)
SA = 9.5π(40.5)
SA = 384.7 π cm²
A theater group made appearances in two cities. The hotel charge before tax in the second city was $ 1500 higher than in the first. The tax in the first city was 5 % , and the tax in the second city was 8.5 % . The total hotel tax paid for the two cities was $ 836.25 . How much was the hotel charge in each city before tax?
Answer:
In city one, the hotel charges before taxes were $5,250.
In city two, the hotel charges before taxes were $6,750.
Step-by-step explanation:
Let the hotel charge in the first city be x and in the second city be y.
Given that the hotel charge before tax in the second city was $ 1500 higher than in the first. That can be written as:
[tex]y - x = \$1500[/tex] ...[1]
The tax in the first city was 5 %, and the tax in the second city was 8.5 %.
The total hotel tax paid for the two cities was $ 836.25
5% of x + 8.5% of y = $836.25
[tex]0.05x+0.085y=\$836.25[/tex]...[2]
Now putting value of y from [1] in to [2]:
[tex]y = \$1500+x[/tex]
[tex]0.05x+0.085\times (\$1500+x)=\$836.25[/tex]
On solving we get :
x = $5,250
Using vakue of x in [1] to find y:
[tex]y=\$1500+\$5,250=\$ 6,750[/tex]
In city one, the hotel charges before taxes were $5,250.
In city two, the hotel charges before taxes were $6,750.
Bob's mom is 3 times older than Bob. In 12 years, Bob's mom's age will be twice of
her son's. How old are Bob and Bob's mom now?
I would use a chart to solve this problem.
This is a good wya to organize your information.
Down the left side, list the people involved.
I put Bob first and the mom second but the order doesn't matter.
Since Bob's mom is 3 times older than Bob, we can represent
Bob's age now as x and Bob's mom's age now as 3x.
Bob's age in 12 years will be x + 12 and Bob's mom's
age in 12 years will simply be 3x + 12.
Since the second sentence starts with in 12 years,
we will be using the information from our second column.
In 12 years, Bob's mom's age, 3x + 12, will be,
equals, twice of her son's age, 2(x + 12).
Solving from here, we find that x = 12.
This means that Bob's age now is 12 and his mom is 36.
The chart is attached below.
Answer:
12 and 36 = bob is 12 and bob's mother is 36
Which equation can be used to solve for x in the following diagram?
Answer:
x + (4x-85) = 90
Step-by-step explanation:
The two angles are complementary which means they add to 90 degrees
x + (4x-85) = 90
Answer: A
Step-by-step explanation:
Both angles are makes a right angle which adds up to 90 degrees so they both have to add up to 90 degrees.
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 6 or 9? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
1/4
Step-by-step explanation:
There are 36 possible combinations. Of those 36, the ones that add up to either 6 or 9 are:
1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3
There are 9 combinations that add up to either 6 or 9. So the probability is 9/36, or 1/4.
The probability that the sum of the numbers rolled is either 6 or 9 is [tex]\frac{1}{4}[/tex] . In rounded to the nearest millionth, the probability is 0.25.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Possible outcomes are
1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3.
The number of possible outcomes is 9.
Each dice has 6 possible outcomes.
Total number of outcomes = 6 × 6 =36
The probability is the ratio of total number of outcomes to possible outcomes.
The probability is 9/ 36 = 1/4 = 0.25
Hence, required probability is 1/4 or 0.25.
Learn more about probability from the given link.
https://brainly.com/question/251701
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A LINE PASSES THROUGH THE POINTS. what is the EQUATION OF THE LINE? (2,-4) and (6,10)?
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Answer:
y = 7/2x - 11
Step-by-step explanation:
Use the slope formula to calculate the slope:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates:
[tex]m = \frac{10-(-4)}{6-2}[/tex]
Simplify:
[tex]m= \frac{14}{4}[/tex]
[tex]m = \frac{7}{2}[/tex]
Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:
10 = 7/2(6) + b
10 = 42/2 + b
10 = 21 + b
10 - 21 = b
b = -11.
Write the equation:
y = 7/2x - 11