Answer:
b. 504
Step-by-step explanation:
In this case, we have to apply the permutation formula, since the order is important and it cannot be repeated. The formula is as follows:
nPr = n! / (n-r)!
From 0 to 9, there are 10 digits, but we must remember that the number 7 has already been used and cannot be repeated, therefore n = 9. And they are 4 digits but only 3 are needed, therefore r = 3.
Replacing:
9P3 = 9! / (9-3)!
nPr = 504
Therefore the answer is b.
Mrs. Anderson surveyed her class and asked each student, "How many hours do you spend
playing sports per week?" The results are below.
0,0,0,0.2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,8,12
Part A: Construct a dot plot of the data and choose the best graph from the choices below.
Part B: What observations can you make about the shape of the distribution?
Part C: Are there any values that don't seem to fit? Justify your answer.
Answer: Part A is the graph with 4 dots for 0, 2 dots for 2, 10 dots for 4, 9 dots for 6, 2 for 7(in between 6 and 8) 1 dot for 8, and 1 dot for 12.
Part B: Answer: Most are clumped together and smaller than 8, with one data point far away from the others.
Part C: Answer; 12 hours seems to much higher than the other data values.
Step-by-step explanation: Hope that helped:) I just did it and checked and it’s correct. Have a good day!
When a movie is released to theaters, production companies monitor revenues from individual cities for that movie on its release date. Below is a scatter plot that shows 10 different movie revenues from opening night in both Tallahassee and Gainesville. Revenue is reported in millions of dollars.
Part B: According to the model found in Part A, if a movie brought in $32.2 million in total revenue in Tallahassee, what would the expected revenue be for Gainesville? (Round your answer to the nearest thousandths *three decimal places*)
Answer:
$13.299 million
Step-by-step explanation:
We need the model from Part A to answer Part B to three decimal places,
The point marked by the blue arrow is clearly an outlier. I ignored it in "eyeballing" the best-fit line.
My line has four points above and five points below the line,
You probably had to use a statistical calculator to get the equation for the line of best fit.
Assume it was
y = 38.9016 - 0.7951x
You would use that equation to predict y when x = 32.2.
y = 38.9016 - 0.7951 × 32.2 = 39.1588 - 25.6022 = 13.299
If a movie brought in $32.2 million on opening night in Tallahassee, it should bring in $13.299 million in Gainesville.
The expected revenue be for Gainesville is $13.299 million.
Calculation of the expected value:here we assume that
y = 38.9016 - 0.7951x
Here that equation to predict y
when x = 32.2.
So,
y = 38.9016 - 0.7951 × 32.2
= 39.1588 - 25.6022
= 13.299
hence, The expected revenue be for Gainesville is $13.299 million.
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The baseball coach bought 2 new baseballs for $1 each. The basketball coach bought 6 new basketballs for $15 each. How much more did the basketball coach spend than the baseball coach?
Answer:
2
Step-by-step explanation:
2 for $1
6 for $15
15/6 = 2.5
1/2 = 0.5
Baseball = 1 for $0.5
Basketball = 1 for $2.5
2.5 - 0.5 = 2
Please answer this question, I will give 5 stars and thanks, even if it is incorrect. If you have any questions, go to "Ask For Details".
Answer:
the theoretical probability is 1/5.
the experimental probability is 3/10.
chances are the experimental probobility will approach the theoretical probobility.
Step-by-step explanation:
since blue is one of five equal sizes, the probobility that it will land on blue is 1/5.
the expiromental probobility is the number of times it landed on blue devided by the number of spins. 15/50. this can be simplified by pulling out a 5, leaving us with 3/10.
last it stands to reason that the more times the spinner is spun the closer the experimental probability will model the theoretical probability.
What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)? y minus 4 = 3 (x minus 1) 1 minus y = 3 (x minus 4) y 1 minus 4 = 3 (1 minus x 1) 1 minus y 1 = 3 (4 minus x 1) I NEED IT NOW PLEASEEEE!!!!
Answer:
y - 4 = 3(x - 1)
Step-by-step explanation:
It looks like you have slope 3 and a point (1, 4)
so it should be y - 4 = 3(x - 1)
which is your first choice: y minus 4 = 3 (x minus 1)
The point-slope form of a line is y - 4 = 3(x-1) which is correct option(A).
What is linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
GIven equation,
Slope of line (m) = 3
Slope form of a line is y-y₁ = m(x-x₁)
Line passes through point (1, 4)
⇒ y - 4 = 3(x-1)
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A car can average 140 miles on 5 gallons of gasoline. Write an equation for the distance d in miles the car can travel on g gallons of gas.
The distance between home and school is 4.5 miles. On a map it shows the distance to be 9 cm. What is the scale?
The scale factor for the measurements on the map would be 11 x 10 ⁻⁵.
What is scale factor?Scale factor is used to compare the size of two objects. Mathematically, we can write -
{K} = S{O1}/S{O2}
Given is that the distance between home and school is 4.5 miles. On a map it shows the distance to be 9 cm.
The distance between home and school : 4.5 miles.
On the map the distance between home and school is 9 cm.
We can write the scale factor as -
{K} = (9 x 5.5 x 10 ⁻⁵)/4.5
{K} = 11 x 10 ⁻⁵
Therefore, the scale factor for the measurements on the map would be 11 x 10 ⁻⁵.
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Is y = x 2 – 1 a linear equation?
Answer:
No
Step-by-step explanation:
Step 1: Determine if linear
It is not linear because it has the x variable to the second power which makes the line bend and turns into a parabola. A linear line would have the x to the first power or just x.
Answer: No
Graph Below
Water flows at a constant rate out of a faucet. Suppose the volume of water that comes out in three minutes is 10.5 gallons. How many gallons of water come out of the faucet in any number of minutes?
Answer:
3.5 Gallons Per Minute or 3.5m
Step-by-step explanation:
Since there is 10.5 Gallons in 3 minutes, do
10.5/3 = 3.5
(please mark brainliest if this helps!)
Final answer:
The flow rate from the faucet is 3.5 gallons per minute. To determine the amount of water that comes out in any number of minutes, we multiply the flow rate by the number of minutes desired.
Explanation:
Given that 10.5 gallons of water are dispensed in three minutes, we can calculate the rate of flow, which will allow us to determine how many gallons of water would come out of the faucet in any other number of minutes.
We start by finding the flow rate per minute by simply dividing the volume of water dispensed by the number of minutes it took. So, the flow rate is 10.5 gallons / 3 minutes = 3.5 gallons per minute. Now, to find out how many gallons flow in any number of minutes, we multiply the flow rate (3.5 gallons per minute) by the number of minutes.
For example, if we want to know how much water comes out in 5 minutes, we calculate it as follows: Flow rate x Time = 3.5 gallons/minute x 5 minutes = 17.5 gallons. Therefore, 17.5 gallons of water would come out of the faucet in 5 minutes.
What is 1 3/4 divided by 1/3 equal
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+5 x+4
The area of a rectangle is represented by the multiplication of its length and width. For a rectangle with dimensions 'x + 5' and 'x + 4', the area is given by the standard form polynomial ' [tex]x^2 + 9x + 20[/tex]'.
Explanation:The area of a rectangle is calculated by multiplying the length by the width of the rectangle. Here, the length and width of the rectangle are given by the expressions 'x + 5' and 'x + 4'. Therefore, to find the area, you multiply those two expressions together:
(x + 5) * (x + 4)
When you multiply these two expressions, you get:
[tex]x\times x + 4\times x + 5\times x + 5\times 4 = x^2 + 9x + 20[/tex]
This is the polynomial in standard form that represents the area of the rectangle,
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47% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four
Answer:
[tex]a. \ P(X=5)=0.2417\\\\b. \ P(X\geq 6)=0.3056\\\\c. \ P(X<3)=0.2255[/tex]
Step-by-step explanation:
a. This is a binomial probability distribution problem expressed as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]
Where:
[tex]p[/tex] is the probability a successful event.[tex]x[/tex] the number of successful events.[tex]n[/tex] is the total number of events.Given n=10, p=0.47 the probability of exactly 5 is calculated as:
[tex]P(X=5)={n\choose x}p^x(1-p)^{n-x}\\\\={10\choose 5}0.47^5(1-0.47)^5\\\\=0.2417[/tex]
Hence, the probability that exactly 5 adults have very little confidence is 0.2417
b. Given n=10, p=0.47,
-We substitute our values in formula and the probability of at least 6 is calculated as:
[tex]P(X\geq 6)={n\choose x}p^x(1-p)^{n-x}\\\\\\\ \ \ \ \ \ ={10\choose 6}0.47^6(0.53)^4+{10\choose 7}0.47^7(0.53)^3+{10\choose 8}0.47^8(0.53)^2+{10\choose 9}0.47^9(0.53)^1+{10\choose 10}0.47^{10}(0.53)^0\\\\\\=0.1786+0.0905+0.0301+0.0059+0.0005\\\\\\=0.3056[/tex]
Hence, the probability of at least 6 adults is 0.3056
c. The probability of of less that four adults is calculated as:
[tex]P(X<4)={n\choose x}p^x(1-p)^{n-x}\\\\\\\ \ \ \ \ \ ={10\choose 0}0.47^0(0.53)^{10}+{10\choose 1}0.47^1(0.53)^9+{10\choose 2}0.47^2(0.53)^8+{10\choose 3}0.47^3(0.53)^7\\\\\\=0.0017+0.0155+0.0619+0.1464\\\\\\=0.2255[/tex]
Hence, the probability that less that 4 adults have confidence in the newspapers is 0.2255
The correct probabilities for the given scenarios are:
(a) The probability that exactly five U.S. adults have very little confidence in newspapers is approximately 0.205 or 20.5%. (b) The probability that at least six U.S. adults have very little confidence in newspapers is approximately 0.254 or 25.4%. (c) The probability that less than four U.S. adults have very little confidence in newspapers is approximately 0.347 or 34.7%.
To solve this problem, we can use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]
(a) For exactly five adults:
[tex]\[ P(X = 5) = \binom{10}{5} (0.47)^5 (0.53)^5 \][/tex]
[tex]\[ P(X = 5) \approx 0.205 \][/tex]
(b) For at least six adults, we sum the probabilities of having six, seven, eight, nine, and ten adults with very little confidence:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
[tex]\[ P(X \geq 6) \approx 0.254 \][/tex]
(c) For less than four adults, we sum the probabilities of having zero, one, two, and three adults with very little confidence:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
[tex]\[ P(X < 4) \approx 0.347 \][/tex]
Use the multiplier method to increase £258 by 43%
You must show your working.
Answer:£368.94
Step-by-step explanation:
258*1.43= 368.94
A bag contains white marbles and red marbles, 90 in total. The number of white marbles is 6 less than 5 times the number of red marbles. How many white marbles are there?
Answer:
W = 72
Step by step explanation:
White = W
Red = R
W + R = 90
Write an equation
W = 5R - 6
Substitute
5R - 6 = 90
Add 6 to both sides of the equation
5R = 90
Simplify
90 ÷ 5 = 18
R = 18
90 - 18 = W
W = 72
Hope this was useful to you!
Final answer:
By setting up an algebraic equation, we determine that there are 74 white marbles in the bag when the total number of marbles is 90 and the white marbles count is 5 times the number of red marbles minus 6.
Explanation:
Calculating the Number of Marbles
To figure out how many white marbles are in the bag, we can set up a simple algebraic equation. Let's define the number of red marbles as x. According to the problem, the number of white marbles is 5 times the number of red marbles minus 6. We can represent this as 5x - 6. Since we know the total number of marbles is 90, we can write the equation as:
x + (5x - 6) = 90.
Combining like terms results in:
6x - 6 = 90.
Adding 6 to both sides gives us:
6x = 96.
Dividing both sides by 6, we get:
x = 16.
So, there are 16 red marbles. Now, to find the number of white marbles, we plug this back into the equation for white marbles:
5(16) - 6 = 80 - 6 = 74.
There are thus 74 white marbles in the bag.
What is 0.5 in as hundredths in fraction form
The decimal 0.5 is equal to the fraction 1/2. To find this answer, you first look at the place value of the decimal. 0.5 is read as 'five tenths'
Answer:
50/100
Step-by-step explanation:
.5 is also known as 1/2 so if you think about 100 50 is half of 1 hundred.
what is the correct first step to solving the equation x^2=10-3x
Answer:
take the square root of both sides
Step-by-step explanation:
Answer:
The correct first step is to factor x^2-10+3x.
Step-by-step explanation:
x^2−10+3x=0 (move all the terms to one side)
(x−2)(x+5)=0 (factor)
x=2,−5 (solve for x)
4x + 3y = 6
-4x + 2y = 14
Solve the system of equations.
Answer:
Systems of equations equals (-1.5, 4)
Step-by-step explanation:
1. isolate the y in both equations
2. a. 4x+3y=6
3y=-4x+6
y=-4/3x+2
b.
2y=4x+14
y=2x+7
3. Solve the system of equations
-4/3x+2=2x+7
2=3 1/3x+7
-5=3 1/3x
-1.5=x
4. Solve for y by plugging x into one equation
y=2x+7
y=2(-1.5) + 7
y= -3+7
y=4
5. Systems of equations equals (-1.5, 4)
6. If this was helpful for you, it would mean a lot if you could click the braniest button on my answer so I could move up in the ranks. Good luck!
Answer:
your answer would be x= -3/2
Convert the equation you found, T = A 3/2, into a
form without any rational exponents.
Answer:
C
Step-by-step explanation:
i got it right
Answer:
C
Step-by-step explanation:
Edge 2021 assignment:)
HELP!!!! Due today!!!!
The congruent relationship between the triangles are;
10. ΔABC ≅ ΔDBC, SSS congruence rule
11. ΔABD ≅ ΔDBC, ASA congruence rule
12. ΔABC ≅ ΔDCB, SSS congruence rule
13. ΔABC ≅ ΔEDC, SAS congruence rule
14. ΔABC ≅ ΔDCB, SAS congruence rule
15. ΔABC ≅ ΔDCB, SAS congruence rule
16. ΔABC ≅ ΔDBC, ASA congruence rule
17. ΔABC ≅ ΔEDC, LH congruence rule
18. ΔBAC ≅ ΔCDB, SSS, congruence rule
What are congruent triangles?Congruent triangles have the same size and shape.
10. [tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex] by the reflexive property, [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CD}[/tex] by the definition of midpoint of [tex]\overline{AD}[/tex], therefore;
ΔABC is congruent to ΔDBC by the Side Side Side, SSS, congruence rule
11. ∠ABC is congruent to ∠DBC (definition of bisected angle)
ΔABD is congruent to ΔDBC by the Angle Side Angle, ASA congruence rule
12. The reflexive property indicates that line segment [tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex], therefore; ΔABC is congruent to ΔDCB by the Side Side Side, SSS congruence rule
13. The definition of bisected line segments indicates; [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CE}[/tex] and [tex]\overline{BC}[/tex] is congruent to [tex]\overline{CD}[/tex]
∠ECD is congruent to ∠BCA (Vertical angles theorem)
Therefore, ΔABC is congruent to ΔEDC by the Side Angle Side SAS congruence rule
14. [tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex] reflexive property, therefore;
ΔABC is congruent to ΔDCB by the Side Angle Side, SAS, congruence rule
15. The alternate interior angles and a facing side of the quadrilateral ABCD are congruent, the location of the angles and the sides indicates that ABCD is a parallelogram
[tex]\overline{BD}[/tex] is congruent to [tex]\overline{AC}[/tex] (Properties of the facing sides of a parallelogram)
ΔABC is congruent to ΔDCB by the Side Angle Side, SAS, congruence rule
16. [tex]\overline{CB}[/tex] is congruent to [tex]\overline{CB}[/tex] (reflexive property)
∠ACB is congruent to ∠DCB and ∠CBA is congruent to ∠CBD (Definition of bisected angles ∠DCA and ∠DBA)
ΔABC is congruent to ΔDBC by the Angle Side Angle, ASA congruence rule
17. [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CE}[/tex], definition of bisected line segment [tex]\overline{AE}[/tex]
ΔABC is congruent to ΔEDC by the Leg Hypotenuse, LH, congruence rule
18. Quadrilateral ABCD is a parallelogram (Definition of a parallelogram)
[tex]\overline{AC}[/tex] is congruent to [tex]\overline{BD}[/tex] and [tex]\overline{AB}[/tex] is congruent to [tex]\overline{CD}[/tex] (Properties of a parallelogram)
[tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex] (Reflexive property)
ΔBAC is congruent to ΔCDB by the Side Side Side, SSS, congruence rule
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A study of college business majors included 150 sophomores and 200 juniors. The study showed that 80 sophomores and 150 juniors had summer internships. One person from the study is selected at random. What is the probability that the person is a sophomore given that the person had a summer internship? Please help i need asap!!!!!!!!!!!!!!!!!!
Answer:
0.3478
Step-by-step explanation:
Given:-
- The number of sophomore, S = 150
- The sophomore and had summer internship, x = 80
- The number of juniors, J = 200
- The junior and had summer internship, y = 150
Find:-
What is the probability that the person is a sophomore given that the person had a summer internship?
Solution:-
- The total sum of sophomore and junior students is N:
N = S + J
N = 150 + 200
N = 350 students.
- We will denote event A as random selection of sophomore from total.
- We will denote event B as random selection of student who had summer internship.
- We are to determine the conditional probability that a person selected is sophomore given that the person had a summer internship. That is the probability of event A given that event B has already occured.
- The conditional probability can be written as:
P ( A / B ) = P ( A & B ) / P ( B )
Where,
P ( A & B ) : The probability the person is a sophomore and had a summer internship.
P ( B ): The probability that the person selected had a summer internship.
P ( A & B ) = x / N
= 80 / 350
= 0.22857143
P ( B ) = ( x + y ) / N
= ( 80 + 150 ) / 350 = 230/350
= 0.65714286
Therefore the required probability is:
P ( A / B ) = 0.22857143 / 0.65714286
= 0.3478 ... Answer
Answer:
8/23
Step-by-step explanation:
Kerry bought a conical tent to put on the back porch. The tent instructions reveal the height at the tallest point to be
4.5 feet and the space inside to be 10.5 cubic feet. About how many square feet of the back porch will be covered by
the tent?
Which measure of the cone needs to be calculated to answer the problem?
A. diameter
B. Radius
C. Base area
D. Volume
Which equation represents the scenario?
A. V= (1/3)(10.5)(4.5)
B. 4.5 = (1/3)(10.5)(h)
C. 10.5 = (1/3)(4.5)(h)
D. 10.5= (1/3)B (4.5)
How many square feet of the back porch will the tent cover?
A. 2.33 square feet
B. 6 square feet
C. 7 square feet
D. 15.75 square feet
1) The measure needed is the C. Base area, 2) the scenario represents the equation D. 10.5= (1/3)B (4.5)
and 3) the tent will cover C. 7 square feet of the back porch.
Use the appropriate formulas to solve it step-by-step.
We know the height (h) of the conical tent is 4.5 feet.The volume (V) of the tent is given as 10.5 cubic feet.The formula for the volume of a cone is:
[tex]V = \frac{1}{3} \pi r^2 h[/tex]
We need to find the base area of the cone (which is a circle) to determine the area covered by the tent on the back porch. The base area (A) of the cone is:
[tex]A = \pi r^2[/tex]
To calculate this, we must first determine the radius (r) of the cone. Let's rearrange the volume formula to solve for the radius (r):
[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]
Simplifying this equation, we get:
[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]
Multiply both sides by 3 to get rid of the fraction:
[tex]31.5 = \pi r^2 4.5[/tex]
Divide both sides by 4.5:
[tex]\frac{31.5}{4.5} = \pi r^2[/tex]
[tex]7 = \pi r^2[/tex]
Divide both sides by π:
[tex]r^2 = \frac{7}{\pi}[/tex]
Taking the square root of both sides, we find the radius (r):
[tex]r = \sqrt{\frac{7}{\pi}}[/tex]
Now we can calculate the base area (A) of the cone:
[tex]A = \pi r^2[/tex]
Substitute r^2 back into the equation:
[tex]A = \pi \left( \frac{7}{\pi} \right) = 7 \text{ square feet}[/tex]
What is 5 log 3 + log 4 written as a single logarithm?
Is this a piecewise graph function? Check using vertical line test.
HELP!
PLEASE help me it is about rate tables.
Answer:
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
you take 18-12 wich gives you 6, then you do 18+6 wich equals 24. hope this helps. good luck in the future :)
Please answer this quickkkkkkk
Answer:
A = 12 units^2
Step-by-step explanation:
The area of a trapezoid is
A = 1/2 (b1+b2)* h where b1 and b2 are the bases (which are parallel)
b1 = AT = 4 units
b2 = SR = 2 units
The heights is along the x axis which is 4 units
A = 1/2 ( 2+4) *4
A = 1/2 (6)*4
A = 12 units^2
What is the area of the following rectangle?
A) 18 sq ft
B) 36 sq ft
C) 80 sq ft
D) 100 sq ft
Answer:
C
Step-by-step explanation:
Because area = L x w
8 x 10 = 80
C
Answer:
A=80
Step-by-step explanation:
You find the area of rectangle using Length times width. 8 times 10 =80
What is the pattern in the sequence below? 2, 5, 10, 17, 26, …
Answer:
It goes in order of odds.
Step-by-step explanation:
2+3=5
5+5=10
10+7=17
17+9=26
and so on.
Answer:
D) Add 1 to the term number squared
Step-by-step explanation:
i got it right on edg2021
What is the order of the quadratic functions f(x)=−0.5x2,f(x)=14x2, and f(x)=x2 from the widest graph to the narrowest graph?
Answer:
[tex]f(x) = - 0.5 {x}^{2} \to \: f(x) = {x}^{2} \to \: f(x) = 14 {x}^{2} [/tex]
Step-by-step explanation:
The given quadratic functions are:
[tex]f(x) = - 0.5 {x}^{2} [/tex]
[tex]f(x) = 14 {x}^{2} [/tex]
[tex]f(x) = {x}^{2} [/tex]
We want to order these functions, from the widest to the narrowest.
How wide the graph will open depends on the absolute value of the coefficient of the function.
The smaller the absolute value of the coefficient, the wider the graph.
Since
[tex] | - 0.5| \: < \: |1| \: < \: |4| [/tex]
Therefore from the widest graph to the narrowest graph, we have:
[tex]f(x) = - 0.5 {x}^{2} \to \: f(x) = {x}^{2} \to \: f(x) = 14 {x}^{2} [/tex]
Use the data in the table to complete the sentence.
The function has an average rate of change of....
The Average of rate is -1.
Step-by-step explanation:
Everytime it goes up by one the y goes down by 1 so it would be -1.
The function has an average rate of change of -1. It is denoted by R.
What is the average rate?The single rate applies to property in several locations and is a weighted average of the separate rates that apply to each place.
The function has an average rate of change of -1.
[tex]\rm R = \frac{4-5}{1-0} \\\\ R=-1[/tex]
Hence, the function has an average rate of change of -1.
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Select ALL of the correct names for you the give angle.
Answer:
1. ∠ O
2. ∠ QOP
3. ∠ POQ
Step-by-step explanation: