Answers
The probability that the card has a multiple of 3 is 5/16. We use the concept of probability and multiples to get the answer.
Define Probability.Probability of an event = (no of possible ways it can happen) / (total number of outcomes)
Define Multiples.For instance, 20 is a multiple of 4 and 5 if we declare that 4 + 5 = 20. The remaining multiples of four can be written as follows: 4, 8, 12, and so on. Four times one equals four. Numerous other mathematical ideas can be explored with the aid of multiples knowledge.
Given, total number of the cards in the bag is from 1 to 16.
So, total number of cards = 16.
Multiples of 3 below 16 = 3,6,9,12,15.
Number of cards below 16 which are multiples of 3 = 5
Therefore P(E) = No. of possible ways/Total no. of ways
=5/16
To know more about Multiples visit:
https://brainly.com/question/17779641
#SPJ1
Related Questions
Angad and Nick win some money and share it in the ratio 2:1. Angad gets £32. How much did Nick get Sushil, Alex and Peter share some sweets in the ratio 1:1:4. Sushil gets 15 sweets. How many did Peter get?
Answers
Answer:
Nick will get £16; Peter will get 60 sweets
Step-by-step explanation:
Angad and Nick win some money and share it in the ratio 2:1. The total ratio is:
2 + 1 = 3
Let the total amount shared be x.
Angad gets £32. This implies that:
2/3 * x = 32
=> 2x = 32 * 3 = 96
x = 96 / 2 = £48
Therefore, Nick will get:
1/3 * 48 = £16
Sushil, Alex and Peter share some sweets in the ratio 1:1:4. The total ratio is:
1 + 1 + 4 = 6
Let the total sweets shared be x.
Sushil gets 15 sweets. This means that:
1/6 * x = 15
x = 15 * 6 = 90 sweets
Therefore, Peter will get:
4/6 * 90 = 60 sweets
This question is pretty simple and easy so please answer it.
Determine if the table represents a linear function, exponential function or quadratic function.
The pattern value that identifies part of the equation is_______
Answers
Answer:
Quadratic
Step-by-step explanation:
if the null space of a 7 × 9 matrix is 3-dimensional, find rank a, dim row a, and dim col a.
Answers
The rank of matrix A = 6, dim row A = 6 and dim col A = 6.
Given a 7 × 9 matrix, if the null space of the matrix is 3-dimensional, then to find the rank of matrix A, dimension of row space and dimension of column space. Let us use rank-nullity theorem which states that the dimension of the null space added to the rank of a matrix equals the number of columns of the matrix.Let N(A) be the null space of matrix A.
ThenNullity (A) + Rank (A) = number of columns of A => Nullity (A) + Rank (A) = 9Nullity (A) = 3Dim N(A) = 3We know that dim Row (A) = Rank (A)Thus, Rank (A) = 9 - Nullity (A) = 9 - 3 = 6Dim Row (A) = Rank (A) = 6To find dimension of column space we know that dim Column (A) = number of non-zero columns in Row Echelon Form of AThus, 3 columns are zero. Therefore, 9 - 3 = 6 columns are non-zeroHence, dim Col (A) = 6Therefore, rank of matrix A = 6, dim row A = 6 and dim col A = 6.
To know more about matrix visit :-
https://brainly.com/question/29132693
#SPJ11
Given the following information, what is the least squares estimate of the y-intercept?
x y 2 50 5 70 4 75 3 80 6 94
a)3.8 b)5 c) 7.8 d) 42.6
2) A least squares regression line
a) can only be determined if a good linear relationship exists between x and y.
b) ensures that the predictions of y outside the range of the values of x are valid.
c) implies a cause-and-effect relationship between x and y.
d) can be used to predict a value of y if the corresponding x value is given.
3) Regression analysis was applied between sales (in $1,000s) and advertising (in $100s) and the following regression function was obtained.
ŷ = 900 + 6x
Based on the above estimated regression line, if advertising is $10,000, find the point estimate for sales (in dollars).
a) $1,500 b) $60,900 c) $907,000 d) $1,500,000
Answers
Answer:
Step-by-step explanation:
Using the least squares regression method, we obtain the equation of the regression line: y = 22.4x + 26.2. The y-intercept is the value of y when x = 0, which is 26.2. Therefore, the answer is d) 26.2.
The correct answer is d) can be used to predict a value of y if the corresponding x value is given. A least squares regression line is a statistical method used to find the equation of a line that best fits the data points. It can be used to predict the value of the dependent variable (y) for a given value of the independent variable (x).
The regression function is ŷ = 900 + 6x, where x is the advertising in $100s and ŷ is the sales in $1,000s. To find the point estimate for sales when advertising is $10,000, we substitute x = 100 in the regression function: ŷ = 900 + 6(100) = 1,500. Therefore, the answer is a) $1,500.
The least squares estimate of the y-intercept is 42.6.
What is a y-intercept?An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Given that,
x y
2 50
5 70
4 75
3 80
6 94
Calculate the means of x and y values:
x_mean = (2 + 5 + 4 + 3 + 6) / 5 = 20 / 5 = 4
y_mean = (50 + 70 + 75 + 80 + 94) / 5 = 369 / 5 = 73.8
Calculate the differences from the means for x and y:
x_diff = [2-4, 5-4, 4-4, 3-4, 6-4] = [-2, 1, 0, -1, 2]
y_diff = [50-73.8, 70-73.8, 75-73.8, 80-73.8, 94-73.8] = [-23.8, -3.8, 1.2, 6.2, 20.2]
Calculate the product of the x and y differences and the square of x differences:
xy_diff = [-2×(-23.8), 1×(-3.8), 0×1.2, -1×6.2, 2×20.2] = [47.6, -3.8, 0, -6.2, 40.4]
x_squared_diff = [-2², 1², 0², -1², 2²] = [4, 1, 0, 1, 4]
4. Sum up the product of the x and y differences and the square of x differences:
sum_xy_diff = 47.6 - 3.8 + 0 - 6.2 + 40.4 = 78
sum_x_squared_diff = 4 + 1 + 0 + 1 + 4 = 10
Calculate the slope (m):
m = 78 / 10 = 7.8
Use the slope (m) to find the least squares estimate of y-intercept (b) using the equation
b = 73.8 - 7.8 × 4 = 73.8 - 31.2
= 42.6
Therefore, the least squares estimate of the y-intercept is 42.6.
To learn more about the y-intercept visit:
brainly.com/question/14180189.
#SPJ2
Find the hypotenuse.
Answers
Answer:
Step-by-step explanation
b/sin(102°) =27/sin(28°)
⇔b ≈56,2548
Using sine rule of triangles, the length of the hypotenuse is 56.3 rounded to the nearest tenth
Solving Triangles using sine RuleSine rule of triangles is related using the formula :
b/sinB = a/sinAInputting values into the relation
b/sin(102) = 27/sin(28)
cross multiply
b * sin(28) = 27 * sin(102)
divide both sides by sin(28)
b = 26.40998/sin(28)
b = 56.254
Therefore, the length of b in the figure given is 56.3
Learn more on sine rule:https://brainly.com/question/23720007
#SPJ2
-6m - 1 = -31
m = ___
please show work
Answers
ANSWER:
M = 5
Step 1: Add 1 to both sides of the equal sign
-6m-1+1=31+1
-6m=-30
Step 2: Divide both sides by -6
-6m/6 = -30/-6
(Note: Both -6 values (The denominators) will cancel each other out, which is why the end result is 5 so, again, M=5)
The graph below represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10, and the vertical axis shows Distance (yards) numbered 4 to 40. The line shows an increase, then decrease, then constant distance.
Which statement could describe the dog’s movement at 5 seconds once the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer to receive a treat.
The dog was running away from the trainer to chase a squirrel.
The dog was stopped but began running towards the trainer.
Answers
The statement dog was running towards the trainer to receive a treat.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that graph represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10,
The vertical axis shows Distance (yards) numbered 4 to 40.
The line shows an increase, then decrease, then constant distance.
At the point on the graph where time is 5 seconds, the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer.
The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.
Hence, the statement dog was running towards the trainer to receive a treat.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
Use the digits 0 - 9 to write five decimal numbers that arranged in ascending order.use each digit once in each decimal number.
Answers
Answer:
0.1, 2.3, 4.5, 6.7, 8.9
or
1.0, 3.2, 5.4, 7.6, 9.8
Is 14.3729 rational or irrational
Answers
Answer: Rational
Step-by-step explanation:
Answer:
Irrational
Step-by-step explanation:
A derivative is available with premium W(0)=1.34 when its underlying asset has value S(0)=36. This derivative will have expiry values W(1,↑)=0.64 and W(1,↓)=4.55, when the underlying asset has values S(1,↑)=57 and S(1,↓)=26, respectively. A writer sells 100 of these derivative and wants to set up a portfolio which will have zero cash flow, both at the time the derivative is sold and at the time the derivative expires. The portfolio will include 100 derivatives, borrowed or lent cash, and bought or short sold underlying assets. To ensure a zero cash flow, how many underlying assets should the writer have in the portfolio (with positive meaning bought assets and negative meaning short sold assets)? Give your answer to the nearest integer.
Answers
To ensure a zero cash flow in the portfolio, the writer needs to set up a portfolio that offsets the cash flow from selling the derivatives. The writer should have -3 underlying assets in the portfolio (meaning short sold assets)
The cash flow from selling 100 derivatives can be calculated as:
Cash Flow from selling derivatives = 100 * (Premium at time 0 - Expiry value)
Cash Flow from selling derivatives = 100 * (1.34 - 0.64) = 70
To offset this cash flow, the writer needs to include an equal and opposite cash flow from the underlying assets. Let's assume the writer buys ""x"" underlying assets.
Cash Flow from underlying assets = x * (Value at time 0 - Value at time 1)
Cash Flow from underlying assets = x * (36 - 57) = -21x
To make the cash flow from underlying assets equal to the cash flow from selling derivatives, we set up the equation:
-21x = 70
Solving this equation, we find:
x ≈ -3.33
Since the number of underlying assets must be an integer, we round -3.33 to the nearest integer, which is -3.
Therefore, the writer should have -3 underlying assets in the portfolio (meaning short sold assets).
To know more about derivative, click here: brainly.com/question/25324584
#SPJ11
pls answer. On a coordinate plane, a line with a 90-degree angle crosses the x-axis at (negative 4, 0), turns at (negative 1, 3), crosses the y-axis at (0, 2) and the x-axis at (2, 0). What is the range of the function on the graph? all real numbers all real numbers less than or equal to –1 all real numbers less than or equal to 3 all real numbers less than or equal to 0
Answers
Range: All real numbers greater than or equal to 3. The Option C.
What is the range of the function on the graph formed by the line?To find the range of the function, we need to determine the set of all possible y-values that the function takes.
Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.
Therefore, the range of the function is all real numbers greater than or equal to 3.
Read more about Range
brainly.com/question/14209611
#SPJ1
$3000 principal earning 6% compounded annually, 5 years
Answers
Hope this helps ;)
what volume of n2, measured at 17 °c and 720 mm hg, will be produced by the decomposition of 10.7 g nan3? 2 NaN3 (s) = 2 Na(s) + 3N2 (g)
Answers
1.74 L of N₂ will be produced by the decomposition of 10.7 g of NaN₃ at 17°C and 720 mmHg.
To solve this problem, we need to use the ideal gas law which states that PV = nRT where P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin by adding 273.15. Thus, 17°C + 273.15 = 290.15 K.
Next, we need to convert the pressure from mmHg to atm by dividing by 760.
Thus, 720 mmHg / 760 mmHg/atm = 0.947 atm.
We can then use stoichiometry to find the number of moles of N₂ produced.
2 moles of NaN₃ produces 3 moles of N₂.
Thus, 10.7 g NaN₃ x (1 mol NaN₃/65.01 g NaN₃) x (3 mol N₂/2 mol NaN₃) = 0.0830 mol N₂.
Finally, we can use the ideal gas law to find the volume of N₂ produced.
V = (nRT)/P = (0.0830 mol x 0.0821 L x atm/K x mol x 290.15 K)/0.947 atm = 1.74 L.
Learn more about ideal gas law at
https://brainly.com/question/30458409
#SPJ11
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (3, StartFraction 108 Over 5 EndFraction), (2, 36), (1, 60), (0, 100).
Which function represents the given graph?
f(x) = 100 · (Three-fifths)x
f(x) = (100 · Three-fifths)x
f(x) = 100 + Three-fifthsx
f(x) = 100 · (Two-fifths)x
Answers
Answer:
the answer is A
Step-by-step explanation:
Who is father of maths?
Answers
if f(x) is \(cos x sin 3x\) then f' at (π/6) is
a) 1/2
b) - √3 / 2
c) 0
d) 1
e) - 1/2
Answers
Answer:
A) 1/2
Step-by-step explanation:
Mr. Nunez opened an account with a deposit of $3,000.
- The account earned annual simple interest.
- He did not make any additional deposits or withdrawals.
- At the end of 5 years, the balance of the account was $3,765.
What is the annual Interest rate on this account?
A. 6.6
B. 5.1
C. 4.5
D. 5.7
Answers
x-y=8 write it in slope-intercept form
Answers
The equation y = x - 8 is expressed as a slope-intercept form.
What is slope-intercept form?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
The slope-intercept form is y = mx+c, where the slope is m and the y-intercept is c.
The equation is given in the question, as follows:
x - y = 8
We have to write it in the slope-intercept form,
As per the question, we have
x - y = 8
Rearrange the variables in the above equation, and we get
y = x - 8
This equation is in the slope-intercept form.
Learn more about the slope-intercept here:
https://brainly.com/question/26290667
#SPJ9
this one alsooooooooo
Answers
Answer:
the answer is cd
Step-by-step explanation:
Jozef works in a factory and is paid £352 a week. He works 40 hours a week. What is his hourly rate?
Answers
Jozef's hourly rate, we need to divide his weekly pay by the number of hours he works in a week. Therefore, Jozef's hourly rate is £8.80.
Simply said, an hourly rate is the amount of money you get paid for each hour of labour. If you want to be successful in business, you must grasp how to calculate your time using this hourly salary rate.
By dividing the weekly hours worked by the number of weeks in a year, 52, you can first calculate the overall number of hours worked. Divide this amount by the yearly salary next.
Jozef's weekly pay = £352
Jozef's number of working hours per week = 40
Jozef's hourly rate = weekly pay / number of hours per week
Jozef's hourly rate = £352 / 40
Jozef's hourly rate = £8.80
Learn more about hourly rate visit: brainly.com/question/28645441
#SPJ4
-5x <2
true false
x=-2 x=-2
x=1 x=1
x=2 x=2
x=-1 x= -1
Answers
The inputs that are solutions for the inequality are:
x = 2
x= 1
For which inputs is the inequality true?Here we have the following inequality:
-5x < 2
We want to see which of the given inputs is a solution for this.
First we can isolate the variable in our inequality, so we get:
-5x < 2
-2 < 5x
-2/5 < x
-0.4 < x
So any value larger than -0.4 is a solution, from the given options, the two that are solutions are:
x = 1
x = 2.
Learn more about inequalities at:
https://brainly.com/question/24372553
#SPJ1
Each pair of figures is similar find the missing sie
Answers
Answer:
x = 3
Step-by-step explanation:
since they are similar use these ratios
x/9 = 1/3
do cross multiplication
9*1 = 3*x
9/3 = x
3 = x
The equation of the line of best fit is y = 0.677x + 1.77.
Based on the line of best fit, approximately how many students are predicted to be in the marching band at a school with 35 students in the concert band?
Answers
There are 25 students in the marching band
How to determine the number of students?The equation of the line of best fit is
y = 0.677x + 1.77
The number of students in the concert band is given as
Students =35
This means that
x = 35
Substitute 35 for x in the equation y = 0.677x + 1.77
So, we have
y = 0.677 x 35 + 1.77
Evaluate the products in the above equation
This gives
y = 23.695+ 1.77
Add the numbers
y = 25.465
Approximate
y = 25
Hence, the students are 25
Read more about linear regression at
https://brainly.com/question/10209928
#SPJ1
what does the circled section represent? one child solved the rubik's cube in 21.7 seconds. one child took 72 seconds to solve the rubik's cube, while another took 71 seconds to solve it. 21 children completed the rubik's cube in 7 seconds. 21 children completed the rubik's cube in 7 minutes.
Answers
The circled section represents the outliers in the data.
In the context of the given information, the circled section represents data points that deviate significantly from the majority of the data. Outliers are observations that lie far away from the central tendency of the dataset, and they can have a notable impact on statistical analysis.
In this case, the child who solved the Rubik's Cube in 21.7 seconds is an outlier as their time is significantly lower than the other children. Similarly, the child who took 72 seconds to solve the cube is also an outlier, as their time is much higher than the majority of the children who completed it in around 7 seconds. Outliers can provide valuable insights into the distribution and behavior of the data, and they are often examined separately due to their unique characteristics.
learn more about "outliers":- https://brainly.com/question/3631910
#SPJ11
There were 96 members in a club. The ratio of the number of female members to male members was 7:5. When 58 new members joined the club, the ratio became 5:6. How many of the new members were males?
Answers
Answer:
dihdvsjhvbsuhdsvubhjvdhbdsvhbdsvhbkvdshbds
Step-by-step explanation:
DJ CUCRACH AAE SLAHTI8AOS
The table below gives the dimensions of a sculpture and a scale model of the sculpture.
Find the scale factor of the model to the real sculpture.
Write your answer as a fraction in simplest form.
Answers
Based on the information provided in the chart, the scale factor of the model to the real sculpture is 1/6 (one-sixth).
What is a scale?This is a ratio or proportion used to create a model from an original figure. This can be used to make a smaller or bigger model.
What is the scale in this case?While the sculpture measures 42x35x49, the model measures 6x5x7. This means the model is seven times smaller than the original sculpture. For example length - 42/7 = 6. Based on this the scale factor is 1/6.
Learn more about the scale in https://brainly.com/question/30215119
#SPJ1
What is the value of 2x - 3y, if x = 2 and y=-1?
Answers
Answer:
7
Step-by-step explanation:
I) Construct an expression to find the answer:
2(2) - 3(-1)
II) Simplify/Solve:
2(2) - 3(-1)
= 4 - (-3)
= 7
Answer:
7
Step-by-step explanation:
Substitute 2 for x and -2 for y
2(2) - 3(-1)
4 - -3 = 7
If you need 4 eggs to make 12 Yorkshire puddings. How many do you need to make 18
Yorkshire puddings?
Answers
6
Answer:
54
Step-by-step explanation:
First of all,
Cross multiplication
4 = 12
18 = x
Let the value of the number of eggs be represented by x
4x = 12×18
4x = 216
4. 4
(Same as 216÷4)
x = 54
T/F: it is best to plan future activities for the group during the middle of the group
Answers
Answer:
False.
Step-by-step explanation:
It's ok to plan future activities for the group, but it's best to plan in the beginning of the group.
Which expressions are equivalent to -56z+28−56z+28minus, 56, z, plus, 28?
Answers
Answer: B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
i just got the biggest brain ever