Given:Three dice are tossed.
To find: Probability of rolling 3 different numbers.
Let E be the event of getting same number on three dice.
So,the favorable cases for E will be
(1,1,1) , (2,2,2) , (3,3,3), (4,4,4), (5,5,5) , (6,6,6).
So, the number of favorable cases=6
Now,the total number of cases for E will be
[tex]6\times6\times6[/tex]Since each dice has 6 numbers so three dice will have these number of cases.
Now, the probability to have a same number on 3 dice will be
[tex]P(E)=\frac{\text{Number of favorable cases}}{\text{Number of cases}}\text{ }[/tex][tex]\begin{gathered} P(E)=\frac{6}{6\times6\times6} \\ =\frac{1}{36} \end{gathered}[/tex]Now, probability of rolling 3 different numbers is
[tex]P(nu\text{mbers are different on thr}ee\text{ dice)}=1-P(E)[/tex][tex]\begin{gathered} =1-\frac{1}{36} \\ =\frac{30}{36} \\ =\frac{15}{18} \end{gathered}[/tex]Hence, the probability of rolling three different numbers is
[tex]\frac{15}{18}[/tex]Write a function to model the geometric sequence in the table. n: (1 2 3 4 5)a: (75 15 3 3/5 3/25)a) f(n) = 75 (1/5) nb) f(n) = 75 (1/5) n-1c) f(n) = 1/5 (75) nd) f(n) = 1/5 (75) n-1
First let's find the ratio of the sequence, by dividing one term by the term before:
[tex]\begin{gathered} \text{second term: 15} \\ \text{first term: 75} \\ ratio=\frac{15}{75}=\frac{1}{5} \end{gathered}[/tex]So the ratio is 1/5 and the first term is 75.
Now, we can use the following formula for the nth term of a geometric sequence:
[tex]a_n=a_1\cdot q^{n-1}[/tex]Where q is the ratio and a1 is the first term. So we have:
[tex]a_n=75(\frac{1}{5})^{n-1}[/tex]Substituting an by the function f(n), we have:
[tex]f(n)=75(\frac{1}{5})^{n-1}[/tex]So the correct option is b)
What is the place value of the 6-digit in the number 205.876?
The place value of 6 in 205.876 is 6 thousandth
One weekend 5,780 people saw a new movie at (7 different theaters. Each theater sold tickets at ($7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?
Each theater sold tickets at ($7.50 a piece, if each theater received the same number of moviegoers, each theater make $6192.85 using arithmetic operations.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or more quantities. They cover topics like the study of numbers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry. Without applying the laws of arithmetic operations, we are unable to solve the issue. The four fundamental rules of mathematics are addition, subtraction, multiplication, and division.
Let the amount of each theater get be x,
No. of theaters are = 7
Cost of each ticket = $7.50
No. of people = 5780
Then we can say,
7x = 5780 ×7.50
x = [tex]\frac{5780\times7.50}{7}[/tex]
= $6192.85
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Can you please also give all forms of the end behavior such as ups/downs, as_,_ , and limits #25
The given function is a rational function
We will find the zeros of the denominator
[tex]\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=\frac{-1}{2} \end{gathered}[/tex]The end behavior of the function will be as follows:
[tex]\begin{gathered} x\rightarrow(-\frac{1}{2})^-;f(x)\rightarrow\infty \\ x\rightarrow(-\frac{1}{2})^+;f(x)\rightarrow-\infty \\ x\rightarrow\infty;f(x)\rightarrow\frac{1}{2} \\ x\rightarrow-\infty;f(x)\rightarrow\frac{1}{2} \end{gathered}[/tex]The graph of the function is as follows:
The probability of a student eating at the cafeteria and a student living off campus is 0.07, and the probability of a student eating at the cafeteria given that the student lives off campus is 0.20, what is the probability of a student living off campus?
The probability of a student living off campus is 0.35.
What is the probability?It should be noted that probability simply means the likelihood that something will occur.
Remember the multiplication rule for conditional probability: P(B AND A)=P(B/A)P(A)
Rearranging, we find that P(A)=P(B AND A)P(B/A)
So if we think of A= the event a student lives off campus and B = event a student eats at the cafeteria, then we can plug in the known information to find:
P(A)=0.07 / 0.20
= 0.35
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Help me asp please!!
It is an ongoing function. A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
What is function?In mathematics, a function is an expression, rule, or law that defines a connection between one variable (the independent variable) and another variable (the dependent variable).A function is defined as a relationship between a set of inputs and one output for each. A function is an input-output relationship in which each input corresponds to exactly one output.Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this.To learn more about function, refer to:
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Hi, can you help me answer this question please, thank you!
Given that
[tex]\begin{gathered} \mu_d=\mu_2-\mu_1=21.1 \\ s_d=14.9 \\ n=8 \end{gathered}[/tex]a) The formula for the test statistics for this sample is,
[tex]t=\frac{\mu_d}{s_d\sqrt[]{n}}[/tex]Therefore,
[tex]\begin{gathered} t=\frac{21.1}{14.9\times\sqrt[]{8}}=0.50067 \\ t=0.50067\approx0.501(3\text{ decimal places)} \\ \therefore t=0.501 \end{gathered}[/tex]Hence, the test statistic for this sample is
[tex]t=0.501[/tex]b)
1936 divided by 8 in long division
The value of 1936 divided by 8 in long division is 242.
What is long division?Long Division is a method for dividing large numbers that divides the task into numerous phases that follow a sequence. Just like in conventional division problems, the dividend is divided by the divisor, yielding the quotient and, in some cases, a remainder.
The steps are:
Step 1: Take the first digit of the dividend from the left.
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend
Using the above step the division is 242.
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A cone has a volume of 3014.4 cubic inches and a radius of 12 inches.what is the height?
h = 20inches
Explanations:The formula for calculating the volume of a cone is expressed as:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where:
r is the radius
h is the height
Given the following
r = 12 inches
V = 3014.4 cubic inches
Substitute to determine the height
[tex]\begin{gathered} 3014.4=\frac{1}{3}\times3.14\times12^2\times h \\ 3014.4\times3=452.16h \\ h=\frac{9043.2}{452.16} \\ h=20inches \end{gathered}[/tex]Hence the height of the cone will be 20inches
What would be the first step when solving using the substitution method?
2x + 3y = -12
x = 3y + 3
The first step of substitution method for given system is put x = 3y +3 in place of x into the equation 2x+3y=-12 .
What is the method of substitution for system of equation in two variables ?The system of the equations in two variables x and y consists of two equation of the form a₁ x + b₁ y = c₁
and a₂ x + b₂ y = c₂
where a₁, a₂, b₁, b₂ , c₁, c₂ are constants
For substitution method, first expression of one variable is found from one equation and then put this expression in another equation to create a linear equation in second variable. Solve the linear equation in one variable for second variable and then put the value of second variable in first equation to solve for first variable
Given system of equations is :
2x + 3y = -12 .....(1)
x = 3y + 3 .....(2)
So the first step will be take expression for one variable from one equation and put it into another equation.
Take x = 3y +3 which is an expression for x from equation (2),
Then put it into equation (1)
⇒ 2 (3y +3 ) + 3 y = -12 , This is the first step of substitution method for this variable
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this. this is sucking my soul away.
Check the picture below.
let's recall that twin sides stemming from a common vertex, make twin angles at the base.
7TH GRADE MATH, BRAINLIEST WILL BE AWARDED
Answers:
Q1.a: 11g
Q1.b: 3m
Q1.3: [tex]-k^{2}[/tex]
Q2.a: 8x + 11y
Q2.b: 2a + b - 2c
Q3.a: 5q + 7
Q3.b: 6r + 3s + 7t
Step-by-step explanation:
Q1) simplify each of these expressions:
a. [tex]4g + 6g + g[/tex]
= g(4 + 6 + 1)
= 11g
____________
b. [tex]4m - m[/tex]
= m(4 - 1)
= 3m
____________
c. [tex]5k^{2} -4k^{2} -2k^{2}[/tex]
= [tex]k^{2} (5 - 4 - 2)\\[/tex]
= [tex]-1k^{2}[/tex]
= [tex]-k^{2}[/tex]
__________________________________
Q2) copy and complete the workings to simplify these expressions:
a. [tex]5x + 3x+6y+5y\\[/tex]
= x(5 + 3) + y(6 + 5)
= 8x + 11y
____________
b.[tex]2a+4b+6c-3b-8c[/tex]
combine terms b:
2a + b + 6c - 8c
combine terms c:
= 2a + b - 2c
__________________________________
Q3) simplify these expressions by collecting like terms:
a.[tex]9q-4q+15-8[/tex]
combine terms q:
5q + 15 - 8
combine numbers:
= 5q + 7
____________
b. [tex]8r+2s+4t-2r+s+3t[/tex]
combine terms r:
6r + 2s + 4t + s + 3t
combine terms s:
6r + 3s + 4t + 3t
combine terms t:
= 6r + 3s + 7t
A line contains points F, G, H, I, J. The space between F G is 2. The space between H and I is 1. The space between F and I is 7.
If FG = 2 units, FI = 7 units, and HI = 1 unit, what is GH?
3 units
4 units
5 units
6 units
The measure of GH is 4 units.
The correct option is (B)
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
FG = 2 units, FI = 7 units, and HI = 1 unit
Now,
FI = FG+ GH +HI
7= 2 + GH + 1
7= 3 + GH
GH = 7-3
GH = 4 units
Hence, the measure of GH is 4 units.
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Create a data set that has 4 values with a mode of 3, a median of 6, and a meanof 10
We are to create a data set of 4
that is a, b, c, d
mode means a number that occur the most
Median means the middle number
Mean means the average number
in the set, we must have a mode of 3
3, 3,
to get a median of 6, we need a number when we add to three and divide by 2 will give us 6
the number is 9
3 + 9 / 2
12/ 2 =
3, 3 , 9, d
the last number is d and it is unknown
since means is 10
mean = summation of all the numbers in the data set / the total number
the total number is 4
mean = 10
10 = 3 + 3 + 9 + d / 4
cross multiplication
10 x 4 = 3 + 3 + 9 + d
40 = 6 + 9 + d
40 = 15 + d
isolate d
d = 40 - 15
d = 25
therefore, the data set with a mode of 3, median of 6 and a mean of 10 are
3 , 3 , 9, 25
the store bought a bike from the factory for 90$ and sold it to Andre for 117 what percentage was the markup?
The markup percentage was
[tex]\begin{gathered} P=\frac{117-90}{90}\cdot100 \\ P=\frac{27}{90}\cdot100 \\ P=30 \end{gathered}[/tex]The markup percentage was 30%.
Use the table to find the products od the two polynomials. Write your answer in descending order l.
Answer:
To use the given table to find product of the two polynomials.
Given that,
[tex](x^2+x-2)(4x^2-8x)[/tex]Explanation:
Using the table, we get it as,
we get,
[tex](x^2+x-2)(4x^2-8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x[/tex][tex]=4x^4-4x^3-16x^2+16[/tex]we get,
[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]Answer is:
[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]Find the opposite of –15.
Answer:15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
If there is a negative sign just add a positive sign or remove the sign. And if it's a positive number add a negative sign.
Easy There we go!
Write the domain and range of g as intervals or unions of intervals
It's important to know that empty circles refer to open intervals or parenthesis.
In this case, we observe that the first interval of the domain is (-1, 1) and the second interval of the domain is (2, 5), so the whole domain would be the union of these two intervals.
[tex]\text{Domain}=(-1,1)\cup(2,5)[/tex]To obtain the range, let's observe the y-values. The function goes from y = -5 to y = 3, so the range would be
[tex]Range=(-5,3)[/tex]The mean Exam score on the SOC 15 Exam 2 is 84.28 with a standard deviation of 6.71Your friend scored an 86 on the exam. What percentage of students scored lower than your friendon the exam?
First, find the z-score of 86
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{86-84.28}{6.71} \\ z=\frac{1.72}{6.71} \\ z=0.2563 \end{gathered}[/tex]Rounding to the nearest hundredth, that is 0.26
Next, find z = 0.26 to the left of z in the z-table and we have the following
Multiply by 100%, and we have
[tex]\begin{gathered} P(z<0.26)=0.60257 \\ \\ 0.60257\cdot100\%=60.257\% \end{gathered}[/tex]Therefore, the percentage of students who scored lower than 86 is 60.257%.
Solve for brainliest and 20 points please
Answer:
C.
Step-by-step explanation:
540
Answer:
540
Step-by-step explanation:
you can use this equation to find the sum of angles for a shape
(n-2)180 with n being the number of sides. Since a pentagon has 5,
its 5-2= 3 then times 180 is 540
A recipe that makes 10 pancakes calls for 13/4 cups of milk. If you want to scale down the recipe so that it makes only 2 pancakes, about how much milk should you use? A. 3/4 cup B. 1/2 cupC. 7/20 cup D. 3/10 cup E. 7/12 cup
13/20 cups
Explanations:The recipe makes 10 Pancakes with 13/4 cups of milk
The recipe will make 1 pancake with x cups of milk
[tex]\begin{gathered} x\text{ = }\frac{13}{4}\div10 \\ x\text{ = }\frac{13}{4}\times\frac{1}{10} \\ x\text{ = }\frac{13}{40} \\ \end{gathered}[/tex]The recipe will make 1 pancake with 13/40 cups of milk
The recipe will make 2 pancakes with (2 x 13/40) cups of milk
= 26 / 40
= 13 / 20
The recipe will make 2 pancakes with 13/20 cups of milk
Writing out and solving inequalities a number divided by three less two is at most two
The inequlaity is ;
[tex]\begin{gathered} \frac{x}{3\text{ }}\text{ - 2}\leq2 \\ \end{gathered}[/tex]
And the solution is;
[tex]x\text{ }\leq\text{ 12}[/tex]
Let the number be x
The number divided by 3
That is x/3
less two means minus 2
x/3 - 2
Is at most 2 means it is less than or equal to 2
so the inequality is;
[tex]\begin{gathered} \frac{x}{3}\text{ - 2}\leq\text{ 2} \\ \\ \text{Solving the inequality, we have} \\ \\ \frac{x}{3}\text{ }\leq\text{ 2 + 2} \\ \\ \frac{x}{3}\text{ }\leq\text{ 4} \\ \\ x\text{ }\leq\text{ 3 }\times\text{ 4 } \\ x\text{ }\leq\text{ 12} \end{gathered}[/tex]what is the arc measure of ct in radians? what is the arc length in feet?
We will determine the arch lenght (In radians) as follows:
*First: We transform the measure of the angle from degrees to radians, that is:
[tex]\theta=80\cdot\frac{\pi}{180}\Rightarrow\theta=\frac{4\pi}{9}[/tex]*Second: We find the arc length:
[tex]s=r\theta\Rightarrow s=(13.2)(\frac{4\pi}{9})[/tex][tex]\Rightarrow s=\frac{88}{15}\pi[/tex]So, the arc length for CT is 88pi/15 radians.
*Third: We find its measure in feet:
[tex]s\approx18.43[/tex]So, the arch length for CT in feet is approximately 18.43 feet.
A space shuttle is moving in a straight line and is traveling at a constant speed. It takes 3 hours to get from A to B and 1 hour to get from B to C. Relative to a suitable set of axes, A is the point (4,-1,7) and B is the point (16,-10,10). Find the coordinates of C.
We will solve as follows:
First: We will use the i, j, k vector notation to describe each point as a vector:
[tex]A=4i-j+7k[/tex][tex]B=16i-10j+10k[/tex]Now, we have that the time it takes to get from A to B is 3 hours (t1). And the time it takes from B to C is 1 hour (t2).
Second: We determine the speed from A to B:
[tex]v=\frac{B-A}{t_1}\Rightarrow v=\frac{(16-4)i+(-10+1)j+(10-7)k}{3}[/tex][tex]\Rightarrow v=\frac{12i-9j+3k}{3}\Rightarrow v=4i-3j+k[/tex]Third: We now determine the value of C:
[tex]C=B+vt_2\Rightarrow C=(16+4)i+(-10-3)j+(10+1)k[/tex][tex]\Rightarrow C=20i-13j+11k[/tex]So, we would have that the coordinates of C are:
[tex]C=(20,-13,11)[/tex]How many positive real zeroes does f(x) = x⁵ - 4x³ + 7x² + 3x - 5 have?
Given -
f(x) = x⁵ - 4x³ + 7x² + 3x - 5
To Find -
How many positive real zeroes does f(x) have =?
Step-by-Step Explanation -
We have
f(x) = x⁵ - 4x³ + 7x² + 3x - 5
where the signs of coefficients are:
+ - + + -
We can see there are three changes in the sign in f(x).
So, from
Descarte's rule,
there are either 3 0r 1 positive real roots
Now,
f(-x) = -x⁵ + 4x³ + 7x² - 3x - 5
Signs: - + + - -
So, here f(-x) has two sign changes.
From this we can conclude there is at least 1 real root and either 4, 2 or 0 imaginary roots.
Final Answer -
Positive real zeroes f(x) have =
Minimum = 1
Maximum = 3
4. Find and interpret theaverage rate of change forthe interval. Show your work.1
Average rate of change = -2 celcius / hour
Interpretation: For every unit change in the time (x), there is a change of -2 celcius in the temperature
Explanations:The average rate of change is to be found for the interval:
[tex]1\text{ }\leq x\leq3[/tex]From the interval, we can deduce that:
[tex]x_1=1,x_2=3[/tex]Know the corresponding value of y for each value of x shown above:
[tex]\begin{gathered} \text{When x}_1=1,y_1=\text{ 6} \\ \text{When x}_2=3,y_2=\text{ 0} \end{gathered}[/tex]The average rate of cgange is given by the formula:
[tex]\begin{gathered} \frac{\delta y}{\delta x}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \frac{\delta y}{\delta x}=\text{ }\frac{0-6}{3-1} \\ \frac{\delta y}{\delta x}=\frac{-6}{3} \\ \frac{\delta y}{\delta x}=-2 \end{gathered}[/tex]The rate of change for the interval is -2 celcius/hour
This can be interpreted as for every unit change in the time (x), there is a change of -2 celcius in the temperature
After making your 20th payment of $524.50 on your car loan, you wanted to find out how much is left of your original 5 years loan at 6.2% compounded monthly of $27,000.00. What is the amount of the remaining balance of your car loan?
The amount of the remaining balance of the car loan is $26293.1103.
Given,
The initial loan amount, P = 27000
The rate of interest, r = 6.2%
Time period, t = 5 years
Interest is compounded monthly.
The 20th payment of the loan = $524.50
We have to find the remaining balance of the car loan.
Here,
Amount, A = P[1 + r/n]^nt
Where,
A is the total amount = principal amount + compound interest
P is the principal amount
r is the rate of interest
n is the number of times compounded
t is the time period
So,
A = P[1 + r/n]^nt
A = 27000 × [1 + 6.2/100/12]^12 × 5
A = 27000 × [12.062/12]^60
A = 27000 × [1.005166]^60
A = 27000 × 1.362
A = 36783.1103
The total amount should be paid after 60 months is $36783.1103
Now,
The 20th payment = $524.50
That is,
524.20 × 20 = 10490
$10490 is paid and the balance amount;
36783.1103 - 10490 = 26293.1103
Therefore,
The amount of the remaining balance of the car loan is $26293.1103.
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6.25 ft7.25 cm11 cm8.921.6 m
The area of the shaded region can determined by substracting the area of rectangle from the area of triangle,
[tex]\begin{gathered} A=A_r-A_t \\ =14\operatorname{cm}\times25\operatorname{cm}-(\frac{1}{2}\times11\operatorname{cm}\times25) \\ =212.5cm^2 \end{gathered}[/tex]Thus, the area of the shaded region is 212.5 square centimeters.
Calculate the mean height of five men whose weight in kg are 60, 65, 71, 75 and 80
Answer:
Given the data set of height (inches) for 12 students, calculate the mean: 60, 64, 66, 68, 70, 71, 72, 73, 78, 71, 65, 69
Keisha is making potato casserole for a party. she needs 3/2 of a potato per guest. how many potatoes will she need for 15 guest
Keisha needs 3/2 of potato per guest ( i.e one guest is equivalent to 3/2 potato)
Thus, for 15 guests
she needs;
[tex]\begin{gathered} 15\text{ }\times\frac{3}{2} \\ \frac{15\times3}{2}=\frac{45}{2} \\ 22\frac{1}{2} \end{gathered}[/tex]Keisha needs 45/2 potatoes for 15 guests