Ross forms all two-digit whole numbers using digits 1, 2, and 3. He allows digits to repeat. Select statement(s) that are CORRECT. *
probability of both digits being the same is a likely outcome
the probability that a number includes the digit 2 only once is 5/9
first digit greater than the second digit is equally likely as the first digit less than the second digit
23 is an unlikely outcome
Answers
Answer:
Probability of both digits being the same is a likely outcome (A) and;
The first digit is greater than the second digit is equally likely as the first digit less than the second digit (C)
Step-by-step explanation:
Question:
Ross forms all two-digit whole numbers using digits 1, 2, and 3. He allows digits to repeat. Select statement(s) that are CORRECT. *
a) probability of both digits being the same is a likely outcome
b) the probability that a number includes the digit 2 only once is 5/9
c) The first digit is greater than the second digit is equally likely as the first digit less than the second digit
d) 23 is an unlikely outcome
SOLUTION
Find attached how I got the value combination.
Forming a two-digit whole number with digit 1,2 and 3 where repetition is allowed:
11, 12, 13, 21, 22, 23, 31, 32, 33
Let's check which of the options are correct.
a) Is probability of both digits being the same is a likely outcome?
From the numbers we got: 11, 22 and 33 have both digits the same.
Yes, the probability is a likely outcome
Option A is correct
b) Let the probability that a number includes the digit 2 only once = Pr( 2 only once)
Pr( 2 only once) = (digits which have number 2 once / total number)
12, 21, 23, 32
Digits which have number 2 once = 4
Total = 9
Pr( 2 only once) = 4/9
4/9 is not same as 5/9
So option B is wrong
c)The first digit is greater than the second digit = 21, 31, 32 = 3 in total
the first digit less than the second digit = 12, 13, 23 = 3 in total
Yes, they are equal in number
Option C is correct
d) 23 is a likely outcome
Option D is wrong
Related Questions
Find the equation of the line that is perpendicular to y = – 1 3 x + 2 and passes though the point (–5, 2)
A) y = 3x + 13
B) y = 3x + 17
C) y = –3x + 13
D) y = –3x + 17
Answers
Answer:
y = 3x + 17
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4. Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction. Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4. Who is correct and why? Nadine is incorrect because she should have applied the quotient of powers rule first. Nadine is correct because she correctly applied the power of a product rule. Calvin is incorrect because he should have applied the power of a product rule first. Calvin is correct because he correctly applied the quotient of powers rule.
Answers
Answer:
what is the question
Step-by-step explanation:
plsss give brainliest
The correct answer is Calvin is correct because he correctly applied the quotient of powers rule.
The correct option is (D).
Calvin is correct because he correctly applied the quotient of powers rule.
According to the quotient of powers rule, [tex]\( \frac{a^m}{a^n} = a^{m - n} \).[/tex]
So, in this case:
[tex]\[ \frac{r^{-5}s^{-3}}{r^8s^{-2}} = r^{-5 - 8}s^{-3 - (-2)} = r^{-13}s^{-1} \][/tex]
Then, when you raise this expression to the power of -4:
[tex]\[ (r^{-13}s^{-1})^{-4} = r^{-13 \times -4}s^{-1 \times -4} = r^{52}s^4 \][/tex]
Nadine's approach would result in:
[tex]\[ \left( \frac{r^{-5}s^{-3}}{r^8s^{-2}} \right)^{-4} = \left( \frac{e^{-20}s^{-12}}{r^{32}s^8} \right) \][/tex]
Which is incorrect.
So, the correct answer is D. Calvin is correct because he correctly applied the quotient of powers rule.
complete question given below:
Nadine and Calvin are simplifying the expression ( (r^(-5)s^(-3))/r^8s^(-2) ). Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power (e^(-20)s^(-12))/r^(32)s^8 . Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r^(-13)s^(-1))^-4.
Who is correct and why?
A.Nadine is incorrect because she should have applied the quotient of powers rule first.
B.Nadine is correct because she correctly applied the power of a product rule.
C.Calvin is incorrect because he should have applied the power of a product rule first.
D.Calvin is correct because he correctly applied the quotient of powers rule
1. Without solving, identify whether this equation has a solution that is positive, negative, or zero:
3x – 5 = -3
2. Solve the equation.
x - 5(x - 1) = x - (2x - 3)
Answers
Answer:
3
Step-by-step explanation:
The equation will have a positive solution and the value of x will be 2/3.
What is an equation?A mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, x - 5(x - 1) = x - (2x - 3)
On solving,
x-5x+5 = x-2x+3
3x = 2
x = 2/3
Hence, The equation will have a positive solution and the value of x will be 2/3.
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Which expression represents the volume, in cubic units, of the composite figure?
Answers
Answer:
11.17
Step-by-step explanation:
Two angles in a triangle measure 1020 and 670. What is the measure of the third angle?
O 110
O 78°
1130
1699
Answers
Answer:
A) 110°
Step-by-step explanation:
All triangles equal 180, so:
102 + 67 + x = 180
169 + x = 180
x = 11
Find the surface area of the pyramid shown below. The base is a rectangle and the opposite
triangular faces are the same size and shape.
Answers
Answer:
SA = 397
Step-by-step explanation:
The area of the rectangle is L x W = 18 x 7 = 126
The area of the triangle[tex]\frac{1}{3}[/tex] face is
A = [tex]\frac{1}{2}[/tex]bh
A = [tex]\frac{1}{2}[/tex] 18 x 10
A = [tex]\frac{1}{2}[/tex] 180
A = 90
Since there are two triangles the same size we times by 2
90 x 2 = 180
The triangles on the left and right sides are two other sizes compared to the other two triangles
A = [tex]\frac{1}{2}[/tex]bh
A = [tex]\frac{1}{2}[/tex] 7 x 13
A = [tex]\frac{1}{2}[/tex] 91
A = 45.5
Since there are two triangles the same size we times by 2 again so it will be 91
Than we add them up
91 + 126 + 180 = 397
Sorry if its wrong
2/7> b+5/7 what is “B”
Answers
Answer:
-3/7 > b
Step-by-step explanation:
2/7> b+5/7
Subtract 5/7 from each side
2/7-5/7> b+5/7-5/7
-3/7 > b
Mila has 7 stamps. Dante has 84 stamps.
Dante has how many times as many stamps as Mila? Enter the answer in the box.
Answers
Answer:
Dante has 12 times more stamps as Mila
Step-by-step explanation:
7 x 12 = 84
Answer:
12
Step-by-step explanation:
84 divided by 7 is 12
a triangular metal plate with a triangular metal plate placed in a box with a regular triangular prism with all the side edges 3 dm. It rests on the edge of the base and is inclined to the bottom of the box at an angle of 60 °. Calculate the area of the plate 0.01 dm2 accuracy. Take a look at how the spacing between planes is measured.
Answers
Answer:
6.75 dm²
Step-by-step explanation:
All the side edges in the regular triangular prism are 3 dm long. Then, the base of the triangular plate is 3 dm long, and the other two sides are: √[3² + 3²] = 4.24 dm long (a right triangle is made and Pythagorean theorem is applied).
The height of the triangular plate is: √[4.24² + 1.5²] = 4.5 dm long (again Pythagorean theorem is applied)
Area of the triangular plate is: base*height/2 = 3*4.5/2 = 6.75 dm²
Philip shoots an arrow from the top of a hill into the ground. the flight of the arrow can be modeled with the quadratic function y=-5x^2+15x+90, where y represents the vertical height of the arrow, in meters, and x represents the time, in seconds. use factoring to find the positive zero of the function. what does this zero represent? then find the maximum value of the function by completing the square. what does the maximum value represent? explain each step in your answer.
Answers
Answer:
(a)Time taken to reach the ground, x=6 seconds
(b)Maximum height of the arrow during its flight =101.25 feet
Step-by-step explanation:
Given the quadratic function which models the flight of the arrow:
[tex]y=-5x^2+15x+90[/tex]
Where:
y represents the vertical height of the arrow, in meters; and x represents the time, in seconds.(a)Positive Zero
[tex]-5x^2+15x+90=0\\-5(x^2-3x-18)=0\\-5(x^2-6x+3x-18)=0\\-5(x(x-6)+3(x-6))=0\\-5(x+3)(x-6)=0\\x+3=0\:or\:x-6=0\\x=-3,x=6[/tex]
In 6 seconds, the arrow will hit the horizontal plane, i.e. the ground.
(b)
[tex]y=-5x^2+15x+90\\y-90=-5(x^2-3x)\\y-90-5(\frac{9}{4}) =-5(x^2-3x+(\frac{3}{2} )^2)\\y-101.25=-5(x-\frac{3}{2} )^2\\y=-5(x-\frac{3}{2} )^2+101.25[/tex]
Comparing with the vertex form:
[tex]y=a(x-h)^2+k[/tex]
Our vertex, (h,k)=(1.5, 101.25)
Maximum Value of y=101.25
The maximum value of y represents the maximum height of the arrow during its flight, which is 101.25 feet.
To make fruit punch, Tyrone needs 3 3/8 quarts of orange juice and 3 3/4 quarts of cranberry juice.
How many quarts of juice does he need in all?
Answers
- Identify the outlier in the data set {12, 15, 20,
44, 18, 20}, and determine how the outlier
affects the mean, median, mode, and range of
the data.
Answers
The outlier in the data set {12, 15, 20, 44, 18, 20} is 44. It significantly increases the mean and range of the data set, but the median and mode are less affected. The outlier highlights sampling variability and induced variability.
The student has asked to identify the outlier in the data set {12, 15, 20, 44, 18, 20} and assess how it affects the mean, median, mode, and range of the data. Considering the provided data, it's apparent that the number 44 is the outlier since it is significantly higher than the rest of the numbers in the set. To confirm, we can calculate the interquartile range (IQR) and use it to detect outliers, but since the data set is small, a visual inspection is sufficient.
Without the outlier (44), the data set is {12, 15, 18, 20, 20}. The mean (or average) is calculated by adding all the numbers and dividing by the count of numbers, which results in a mean of (12 + 15 + 18 + 20 + 20) / 5 = 17. The median, which is the middle number when the data is sorted, is 18. The mode, the number that appears most often, is 20 in this case. As for the range, which is the difference between the largest and smallest number, it's 20 - 12 = 8.
With the outlier included, the mean becomes (12 + 15 + 18 + 20 + 20 + 44) / 6 = 21.5, the median remains 18, the mode is still 20, and the range expands to 44 - 12 = 32. Clearly, the outlier has a significant effect on the mean and range, causing them to increase, while the median and mode are less impacted due to their nature of being more resistant to extreme values. The presence of an outlier shows some degree of sampling variability and may introduce induced variability in the analysis of data.
Question 12 (Multiple Choice Worth 5 points)
(05.02 MC)
What is the slope-intercept form equation of the line that passes through (5, 7) and (8, 22)?
Oy= -5x + 18
Oy=5x - 18
Oy=-5x - 18
O y = 5x + 18
Answers
Answer:
y = 5x - 18
Step-by-step explanation:
Points:
Equation of the line:
y = ax + b
(5; 7) and (8; 22)
(5; 7)
7 = 5a + b
(8; 22)
22 = 8a + b
a and b are the same values:
{- 5a - b = - 7
{8a + b = 22
3a = 15
a = 5
5a + b = 7
5.5 + b = 7
25 + b = 7
b = 7 - 25
b = - 18
Equation:
y = 5x - 18
I Hope I've helped you.
Final answer:
The slope-intercept form equation of the line that passes through the points (5, 7) and (8, 22) is y = 5x + 18, found by first calculating the slope and then using the point-slope form to solve for y.
Explanation:
To find the slope-intercept form of the equation of the line that passes through the points (5, 7) and (8, 22), we first need to calculate the slope (m). The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using our points, this becomes:
m = (22 - 7) / (8 - 5) = 15 / 3 = 5
Now, we use one point and the slope in the point-slope form of the equation, y - y1 = m(x - x1), which becomes:
y - 7 = 5(x - 5) => y - 7 = 5x - 25
Solving for y to get the slope-intercept form, y = mx + b:
y = 5x + (25 - 7) = 5x + 18
So, the correct slope-intercept form equation of the line is y = 5x + 18.
Triangle ABC is similar to triangle DEF. What is EF?
Answers
Answer:
24
Step-by-step explanation:
First, divide 30.4 by 19 to get your factor.
You get 1.6
Then times 1.6 by 15 to get 24 for EF.
In June, Cory begins to save money for a video game and a TV he wants to buy in December.
He starts with $22. Each month he plans to save 10% more than the previous month. How
much money will he have at the end of December?
A) 186.72
B) 208.72
C) 188.56
D) 204.56
Answers
Answer: B
Step-by-step explanation:
The answer is 32.2102.
In June, Cory begins to save money for a video game and a TV he wants to buy in December.
He starts with $22. Each month he plans to save 10% more than the previous month.
How to find how much money will he have at the end of December?
the given scenario is an application of a geometric sequence with
a1=$20 and r= 22/2 *100 = 1.1
. Since December is 6 months from June, then to find out the 6th term.
As, a2 = a1 * r = 20 × 1.1 = 22
a3= a2 *r = 22 * 1.1 = 24.2
a4= a3 * r = 24.2 * 1.1 = 26.62
a5=a3 * r = 26.62 *1.1 = 29.282
a6= a4*r = 29.282 * 1.1 = 32.2102.
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NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Betsy's high school is putting on a production of a play as a fundraiser for the school's music programs. A local bank has agreed to allow the school to use a line of credit from which they can withdraw money to pay for the play. Then, any deposits they make at the bank will be applied to the negative balance of the credit account.
The play cost $3,200.00 to produce, and they intend to sell tickets for $10 each. After the play, Betsy will take the ticket proceeds and deposit them with the bank. If 1,007 people attend the play's opening night, what will the balance of the bank account be?
A.
$13,270
B.
$6,870
C.
$10,070
D.
- $3,099
Answers
Answer:
B. $6,870
Step-by-step explanation:
Calculate how much money they earned from tickets then subtract the cost of making and that's their balance:
(1007×10)-3200=
10070-3200=
$6,870
B. $6,870
Final answer:
After calculating the total proceeds from selling tickets to 1,007 attendees at $10 each, the balance of the line of credit used to fund the play's production ($3,200) will be a positive $6,870.
Explanation:
The question pertains to a fundraiser calculation for Betsy's high school play. To determine the balance of the bank account after ticket sales, we must calculate the total proceeds from selling tickets to the attendees and then adjust the balance of the line of credit that was originally used to fund the production.
The production cost is $3,200.00, and tickets are sold at $10 each. With 1,007 people attending, the total ticket proceeds will be 1,007 imes $10 = $10,070. Since the school used a line of credit to pay for the play, the proceeds will pay off this balance. Hence, after depositing the ticket sales, the balance is:
Balance after deposit = Ticket proceeds - Production costs
= $10,070 - $3,200
= $6,870 (Credit balance)
The correct balance of the bank account after the play's opening night is therefore $6,870 (Option B).
PLEASE HELP!! WILL GIVE BRAINLIEST !!!
Which of the following is true of the data represented by the box plot?
box plot with point at 15, min at 17, Q1 at 51, median at 65, Q3 at 74, max at 90
A) If the outlier is included in the data, the median would not significantly change.
B) If the outlier is included in the data, the mean would increase.
C) If the outlier is included in the data, the box plot would be significantly skewed.
D) If the outlier is included in the data, the length of the tails would change significantly.
Answers
Answer:
the outlier is the point at 15
the data is skewed to the bottom because the values below the median are far more spread out; there are more extreme values that are far below the median than above the median.
Step-by-step explanation:
A) If the outlier is included in the data, the median would not significantly change.
Box Plot is a pictorial way of denoting data's distribution on the basis of Quartile 1, Quartile 3, Minimum, Median and Maximum
Outliers are the data observations or points, lying at huge significant difference (distance) from other concentrated data observation points.
A data value below the Box Plot Minimum, or above the Box Plot Maximum is an Outlier.Median is a Positional average, the mid point of data. It divides the data into two equal halves, 50% below it & 50% above it.
Median is not effected by extreme values like Outliers. So, inclusion of outliers doesn't significantly change Median.Mean is an Arithmetic Average. It is effected by extreme values like outliers. However, in this case of presence of Lower Outlier, the mean would decrease rather than increasing.
Skewness or Tail in the data denotes concentration of values in either (lower or higher side). It is not related to outliers.
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Will mark brainliest! Need help (50 points)
Answers
Answer:
(-4y,+12y), (z,19z)
Step-by-step explanation:
i got the same question.
Calculate the area of the shaded region
Answers
Answer:
48π or 150.72
Step-by-step explanation:
The radius of the big circle is 8.
We can use that to find the area of the big circle.
Area is πr^2
π(8)^2
64π
Now, we can find the area of the small circle.
The diameter of that is 8, meaning the radius is 4.
πr^2
π(4)^2
16π
Now we subtract the area of the small circle from the area of the big circle to get the area of the shaded region.
64π-16π=48π
As a decimal: 48*3.14=150.72
If y=-16 when x=4 find x when y=48
Answers
Answer:
x= -12
Step-by-step explanation:
Assuming this is a direct variation
y = kx
When y = -16 x =4 we can find k
-16 = k*4
Divide each side by 4
-16/4 = 4k/4
-4 =k
So
y = -4k
Y = 48
48 = -4x
Divide each side by -4
48/-4 = -4x/-4
-12 =x
9. Find the vertex of f(x) = –2x2 - 4x – 8
a. Vertex: (-1,-6) b. Vertex: (-6,-1) C. Vertex: (2,1)
d. Vertex: (1,6)
e. Vertex: (1,-6)
Answers
Answer:
A is the answer, (-1,-6) is the vertex.
Step-by-step explanation:
With any quadratic, the formula for the x coordinate of the vertex is -b/2a.
In this case it is -(-4) / 2(-2) = 4 / -4 = -1.
To find the y, simply substitute the x.
f(-1) = -2(-1)² – 4(-1) – 8 = -2 + 4 – 8 = 2 – 8 = -6
what is -3+1/3=?
what is 5+6+7x+3=
Answers
Answer:
-3+1/3=-8/3 or-2.6, 5+6+7x+3=7x+14
Step-by-step explanation:
Answer:
-3+1/3= -2.66666666667
Step-by-step explanation:
Describe how the area of a rectangle will change if its width remains
constant but its length is doubled.
Answers
Answer:
its the 2nd one
Step-by-step explanation:
PLZZZZZ HELP ME HELP A DUMB CHILD OUT
Answers
Answer:
80 inches
Step-by-step explanation:
Pythagorean theorem
2(b+c) (use the distributive property)
Answers
Answer:
2b + 2c
Step-by-step explanation:
when distributed, the 2 get multiplied by the b and the c, so you'd have 2b + 2c.
Answer:
Answer is 2b + 2c
Step-by-step explanation:
2(b+c) you multiply 2 with b and then with c
Ahmed is riding the elevator in a building. The building has floors above and below ground level. Ahmed uses the expression below to describe his movement.
6 + (negative 8)
Which statement could describe Ahmed’s movement?
Answers
Final answer:
Ahmed's movement described by the expression 6 + (negative 8) suggests he moves from the sixth floor above ground level down to the second floor below ground level.
Explanation:
The expression Ahmed uses to describe his movement in the elevator is 6 + (negative 8). To understand this expression in the context of elevator movement, 6 could represent Ahmed starting on the sixth floor above ground level. The addition of negative 8 would signify moving 8 floors downward. Thus, the expression indicates that Ahmed moves from the sixth floor down to the second floor below ground level (since 6 - 8 equals -2). The negative result corresponds to floors below ground level. Therefore, the statement that could describe Ahmed's movement is: Ahmed moves from the sixth floor above ground level down to the second floor below ground level.
x^2 – 3x – 7 = 0
Solve the quadratic equation using the quadratic formula.
Answers
Answer:
x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0.
Step-by-step explanation:
x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0. Use the quadratic formula to find the solutions. −b±√b2−4(ac)2a - b ± b 2 - 4 ( a c ) 2 ...
Answer:
x=3/2 ± √37/2
Step-by-step explanation: the answer
What is the probability Jane gets a cone with any ice cream and any topping?
1/12
1/4
1/2
2/3
Answers
A triangle is reduced. A triangle has a base of 16 inches, a height of 12 inches, and a side length of 20 inches. A smaller triangle has a base of 12 inches, a height of 9 inches, and a side length of the blank. Not drawn to scale What is the perimeter of the reduced triangle, in inches?
A.) 15
B.) 21
C.) 36
D.) 48
Answers
Answer:
A
Step-by-step explanation:
Answer:
The answer is 15
Step-by-step explanation:
i took the test
Someone please help
Answers
1.20 Euro
BruhBruhBruh
Answer:
£1.20
Step-by-step explanation:
2/5 on magazine and 1/3 on dance lesson then we need to add these together by converting them to same fraction multiples.
2/5 x 3 = 6/15
1/3 x 5 = 5/15
6/15 +5/15 = 11/15
11/15 of 4.50 is found by division of the multiplier (the denominator)= 15
4.50/15 = 0.3 nb/ 0.3 = 1/15 of the whole 11 we search for
We then can multiply 0.3 x 11 as we have 1/15 and want 11/15
0.3 x 11 = 3.3
£3.30 = value of spending on dance lesson and magazine
0.3 x 4 = 1.2 = value of left over money
£1.20 converted to monetary