The probability of rolling a number less than 12 is 91.6%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.
We can have the number 12, the probality will be 1/12
So the probability of rolling a number less than 12 is = (1 - probability of 12)
=1-1/12
=11/12
=0.916
Hence the probability of rolling a number less than 12 is 91.6%.
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NEED to know today please
Game Station 4: Spinner of 4 equal parts: Red, Purple, Green and Orange - Rules: If the arrow lands in the red quadrant, "Team Y" gets 7 points. If it lands in the other quadrants, both teams lose 1 point
A. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red exactly 3 times and on purple exactly 2 times?
B. "Team Z" spins 4 times. How many of the possible outcomes could have landed in Red
C. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red at least once?
use combinations, not probability.
The number of outcomes, using the Fundamental Counting Theorem, is given as follows:
A. Red exactly 3 times and Purple exactly 2: 10.
B. Red at least ounce in 4 spins: 175.
C. Red at least ounce in 5 spins: 781.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Item a is used with the combination formula, as it is an arrangement of five elements with 3 and 2 repetitions, hence the number of outcomes is:
[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]
What is the Fundamental Counting Theorem?The Fundamental Counting Principle states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item b, in four spins, each with four outcomes, the parameters are given as follows:
[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex]
Hence the number of outcomes is:
N = 4^4 = 256.
For no red results, the parameters are as follows:
[tex]n_1 = n_2 = n_3 = n_4 = 3[/tex]
Hence:
N = 3^4 = 81.
Hence the number of outcomes with at least one red is:
256 - 81 = 175.
For item 3, the lone difference is that there are five trials, hence:
Total outcomes: 4^5 = 1024.None red: 3^5 = 243.At least one red: 1024 - 243 = 781.More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
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Evaluate the expression when m = -7. m2+4m−4
If our equation is as follows;
[tex]f(m)=m^2+4m-4[/tex]We are given an initial condition. We replace the unknown by [tex]-7[/tex] to get the result.
[tex]f(-7)=(-7)^2+4(-7)-4[/tex][tex]f(-7)=49-28-4[/tex][tex]f(-7)=17[/tex]a teacher gives a test with 15 questions that is worth 35 points It includes multiple choice questions worth 1 point each and short response questions worth 5 points each how many short responses and multiple choice questions are there
There are 10 multiple choice questions and 5 short response.
How to calculate the value?The following can be deduced:
The teacher gives a test with 15 questions that is worth 35 points.
Multiple choice questions = m = 1 point each
Short response questions = s = 5 points
The equation will be:
a + s = 15
a + 5s = 35
Subtract
4s = 20
Divide
s = 20/4
s = 5
Number of short response questions = 5
Number of multiple choice will be:
a + s = 15
a + 5 = 15
a = 15 - 5
a = 10
Multiple choice = 10
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Assume that a simple random sample has been selected from a normally distributed
population. Find the test statistic t.
A local newspaper reported that for the adult population of a town, the mean annual salary is $30,000.
Test the claim that for the adult population of this town, the mean annual salary is greater than
$30,000. Sample data are summarized as n = 17, sample mean = $22,298, and s = $14,200. Use a
significance level of alpha = 0.05.
Find the test statistic t.
a) -2.24
b) -1.57
c) 1.57
d) 2.24
e) 0.05
The test statistic when the a simple random sample has been selected from a normally distributed population is a) -2.24
What is test statistic?The test statistic is a number derived from a statistical test that is used to determine whether your data could have occurred under the null hypothesis.
u = 30000
x = 22298
s = 14200
n = 17
Test statistic = = (x - u) / s / ✓n
x = mean
u = theoretical value
s = standard deviation
{n} = variable set size
= (x - u) / s / ✓n
= (22298 - 30000) / 14200 / ✓17
= -2.24
Test statistic = -2.24
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a truck costs 40,000. it depreciates in value 5000 dollars per year write a linear model in the form v(t)=mt+b where v(t) represents the current value of the truck after t years of owning it
Which set is infinite?
Answer:
Q
Step-by-step explanation:
The size P of a certain insect population at time t (in days) obeys the function P(t) = 700e^0.04t
(a) Determine the number of insects at t = 0 days.
(b) What is the growth rate of the insect population?
(c) Graph the function using a graphing utility.
(d) What is the population after 10 days?
(e) When will the insect population reach 1190?
(f) When will the insect population double?
The number of insects at t=0 is 700, the growth rate is 28e^0.04, population of insects after 10 days is 1044, and the graph of the function is attached.
What is function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
a) Number of insects at time (t) = 0 days,
Putting t = 0 in given function:
P(t) = 700e^0.04(0) = 700e^0 = 700
Hence, the number of insects at t = 0 days is 700.
b) Growth rate of insect population,
In order to find growth we need to differentiate the given function with respect to t.
So, dP(t)/dt = 700(0.04)e^0.04(0)
= 28e^0.04
Hence, the growth rate is 28e^0.04.
c) Graph the function is attached in the question.
d) The population of the insects after 10 days,
putting t = 10,
= 700e^0.04(10) = 1044
Hence, population of insects after 10 days is 1044.
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An ordinary fair die is a cube with the numbers 1 through 6 on the sides. Imagine that such a die is rolled twice in succession and that the faces of the 2 rolls are added together. This sum is recorded of single trial of a random experiment. Event A: The sum is greater than 8. Event B: the sum is not divisible by 5
The probability of event A is 5/18.
The probability of event B is 29/36.
What are the probabilities?Probability is used to determine how likely it is that a random event would happen. The probability that the random event would happen would lie between 0 and 1.
The probability that the sum is greater than 8 = sample space that have a sum greater than 8 / total number of sample space
sample space that have a sum greater than 8 = (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6, 4) (6,5) (6,6) = 10
Total number of sample space = 36
The probability that the sum is greater than 8 = 10 / 36 = 5/18
The probability that the number is not divisible by 5 = sample spaces that is not divisible by 5 / total number of sample spaces
= 29 / 36
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Here is the rest of the question:
Write your answers as exact fractions.
P(a)
P(b)
Find the perimeter of the rectangle. length 7 inches and area 35 square inches.
pls help!!!
Step-by-step explanation:
Find the perimeter of the rectangle. length 7 inches and area 35 square inches.
P = 2W + 2L
A = LW
because you know that L = 7:
A = LW
35 = 7W
divide both sides by 7:
35/7 = 7W/7
W = 5
substitute into first equation:
P = 2W + 2L
P = 2(5) + 2(7)
P = 10 + 14
P = 24
the anwer is 5
35 divied by 7 is 5
7 times 5 is 35
Fill in the blanks
Suppose a person gained three pounds (a negative weight loss). Then z =__. This z-score tells you that x = -3 is__ standard deviations to the (right or left) of the mean.
Suppose a person gained three pounds (a negative weight loss). Then z = -1. This z-score tells you that x = -3 is 1 standard deviation to the left of the mean.
A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values in terms of standard deviations. It is calculated using the formula:
[tex]\\\mathrm {z = \frac{x - \mu}{\sigma} }[/tex]
Where:
z = z-score
x = individual data point (in this case, the weight change in pounds)
μ = mean of the data set (average weight change in pounds)
σ = standard deviation of the data set (a measure of how spread out the data is)
If the person gained three pounds (a negative weight loss), it means the value of x is -3 pounds (x = -3).
To calculate the z-score, we need to know the mean and standard deviation of the weight changes in pounds for the entire group of people.
Let's assume the mean (μ) is 0 pounds (no weight change on average), and the standard deviation (σ) is 3 pounds (for example).
z = (-3 - 0) / 3
z = -1
So, the z-score (z) is -1.
A negative z-score indicates that the data point (in this case, the weight change of -3 pounds) is below the mean.
Since the z-score is -1, this tells us that the weight change of -3 pounds is 1 standard deviation to the left of the mean.
The negative sign indicates it is below the mean, and the absolute value of the z-score (1) indicates it is 1 standard deviation away from the mean.
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Which event has a theoretical probability of exactly Three-fourths? Select three options. not picking a square picking a square picking a triangle picking a shape that has only straight edges not picking a circle
The event that has a theoretical probability of exactly Three-fourths include:
A. not picking a square
D. picking a shape that has only straight edges
E. not picking a circle
What is a theoretical probability?The theoretical probability is defined as the proportion of favorable outcomes to possible outcomes. The theory of probability is the science of probability.
The sample space of an object determines theoretical probability. The probability of rolling a 3 on a fair die, for example, is 1/6. This is because the number 3 represents one of the six possible outcomes of rolling a fair die
Therefore, based on the information given, it should be noted that the correct options are A, D and E.
This equation is written as follows: Theoretical Probability = the number of favorable outcomes divided by the total number of possible outcomes.
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Jack has 32 quarters on his desk and Molly has q quarters in her purse
Answer:
32+q
Step-by-step explanation:
it doesn't ask for money
Adriana just won $500 000 in a lottery. She plans to invest the money in an
account from which regular withdrawals can be made every month for 25 years.
How much is each withdrawal if the interest rate is 5% per year, compounded
monthly?
a. $2549.31 c. $11 079.06
b. $2922.95 d. $5539.53
$5539.53 is each withdrawal if the interest rate is 5% per year, compounded monthly.
What is compounded interest?
Compound interest is the interest earned on savings that are calculated on both the initial principal and the interest earned in previous periods.
We have,
Initial amount - le 5,00,000
Interest = l = 5/100 = 0.05/12 = 0.004167
Time period T = 25 x 12 = 300
[tex]A = P(1 + r)^t[/tex]
where A = total balance after t years,
P = principal amount (the amount invested),
r = interest rate (decimal form), and
t = time in years.
How much money will Jack have after 25 years?
[tex]A = 5,00,000 (1+ 0.05)^{25}[/tex]
A = 1661859
A / 300 = 5643
Therefore, $5539.53 is each withdrawal if the interest rate is 5% per year, compounded monthly.
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(b) Tickets for a raffle are placed in a box. The box contains 25 blue tickets and 20 red
tickets. Tickets are drawn at random from the box, one at a time and are not replaced.
What is the probability that:
(i) the first ticket drawn is red and the second ticket drawn is blue?
2
The probability that a red ticket is drawn first and then the second ticket drawn is blue is 0.253.
What is the probability?Probability determines the odds that a random event would occur. The odds that the random event occurs has a probability value that lies between 0 and 1.
The more likely it is that the event would occur, the closer the probability value would be to 1. The more unlikely it is that the event would not happen, the closer the probability value would be to 0.
The probability that a red ticket is drawn first and then the second ticket drawn is blue = (number of red tickets / total number of tickets) x (number of blue tickets / total number of tickets)
Total number of tickets = number of blue tickets + number of red tickets
25 + 20 = 45
The probability that a red ticket is drawn first and then the second ticket drawn is blue = (20 / 45) x (25 / 44) = 0.253
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Solve for b.
b - 14 = -10
A. b = -4
B. b = 4
C. b = -24
D. b = 24
The value of b after solution of the expression, b-14 = -10, is 4.
According to the question,
We have the following expression:
b-14 = -10
Now, we will first add 14 on both sides of the above equation:
b = -10+14
We know that when two integers are of different signs then the smaller number is subtracted from the larger number but the sign in the result is of the larger number.
So, in this case, 14 is larger than 10 then the result will be positive.
So, we have the following expression:
b = 4
Hence, the correct option is B.
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The Old Farmer’s Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
The probability that the mean of the sample is between 120 and 126 gallons is 0.4176
How to determine the probability that the mean is between 120 and 126 gallons?The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation
Given: population mean (µ) = 123, standard deviation(σ) =21 and number of sample (n) = 15
Let X represent the gallons of water: We want to find:
P(120 ≤ X ≤ 126)
Z-score(Z) = (X-µ) / (σ/√n)
Z₁ = (120-123)/ (21/√15) = -0.55
Z₂ = 126-123/ (21/√15)= 0.55
P(-0.55≤ Z ≤ 0.55) = = 0.7088 - 0.2912 = 0.4176
(Check the image of the table attached)
Therefore, the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons is 0.4176
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someone help tyyyyy its due soon
For which pair of triangles could the Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ ? I only have an hour pls help.
The pair that support Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ is option B
What are congruent triangles?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
examples of these rules are
Angle - Side - Angle = ASASide - Side - Side = SSSSide - Angle - Side = SASAngle - Angle - Side = AASHypotenuse and one leg = HLThe problem requires the prove by Angle - Side- Angle = ASA to ensure that the the triangles are congruent
The Angle - Side - Angle = ASA have it that the two triangles being compared should have their two angles and the included side being equal
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WRITE AS A SIMPLE LOGARITHM.. 2logx-3log(x+2)+3logy
Answer:
log(x^2 y^3/(x+2)^3)
Step-by-step explanation:
The quadrilateral below is a parallelogram. Solve for x.
Answer:
x = 16 units
Step-by-step explanation:
supplementary angles = 180°
so
3x + 5 + 9x - 17 = 180
12x - 12 = 180
12x = 180 + 12
12x = 192
x = 192 : 12
x = 16 units
--------------------------------
check
3 * 16 + 5 + 9 * 16 - 17 = 180
180 = 180
the answer is good
How much longer is a stick insect measuring 12 cm than a fly which is 2.5 mm long? Give your answer in millimeters.
The required answer would be the stick insect is 117.5 millimeters long.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
The stick insect measures 12 cm then a fly which is 2.5 mm long.
According to the given question, the required solution would be as:
⇒ 12 cm - 2.5 mm
Convert the centimeters into millimeters
⇒ 10 × 12 mm - 2.5 mm
⇒ 120 - 2.5
Apply the subtraction operation,
⇒ 117.5 millimeters
Thus, the required answer would be the stick insect is 117.5 millimeters long.
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Find the value of x.
f(x)= (1/3)x + 5
Has the output value of -15
Answer:
-60
Step-by-step explanation:
-15 = 1/3x + 5 Multiply all the way through by 3
-45 = x + 15 Subtract 15 from both sides of the equation
-60 = x
Answer: -60 = x
Step-by-step explanation:
If the output value is -15, we need to do this equation.
-15 = (1/3)x + 5.
-5 -5
-20 = (1/3)x
x3 x 3
-60 = x.
Now, let's double-check our answer.
f(60) = (1/3)(-60) + 5
f(-60) = -20 + 5
f(-60) = -15.
This means that x = -60 is our correct answer.
Name an angle vertical to LEGH.
Answer:
IGF
Step-by-step explanation:
the two angles have the same vertex and lie on the same lines
PLEASE HELP I HAVE TO SUBMIT IN 10 MINUTES
Carl began his hike at feet 1,482 above sea level. He then hiked down 2,173 feet, increased his altitude by another 663 feet and then decreased his altitude by 345 feet. What is Carl's final altitude?
The final altitude of Carl is -373 feet
What is an 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.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Carl began his hike at an altitude = 1482 feet
And , Carl hiked down an altitude = 2173 feet
Now , Carl is at an altitude of = 1482 - 2173 feet
= -691 feet
And , Carl increased his altitude by = 663 feet
Now , Carl is at an altitude of = -691 + 663 feet
= -28 feet
And , Carl decreased his altitude by = 345 feet
Now , Carl is at an altitude of = -28 - 345
= -373 feet
The final altitude of Carl is -373 feet
Hence , the final altitude is -373 feet
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If A=(x | x is an even integer), B=(x | x is an odd integer), C=(2, 3, 4, 5), and D=(13, 14, 15, 16), list the element(s) of the following set.
←
A ∩ D
A ∩ D= (Use a comma to separate elements in the set.)
Answer:
A ∩ D = { 14; 16 }======================
A ∩ D means intersection of the two sets or the common elements of A and D.
We observe that:
Set A has all even integers,Set B has even integers 14 and 16.It means the common elements of the two sets are 14 and 16:
A ∩ D = { 14; 16 }Answer:
A ∩ D = {14, 16}
Step-by-step explanation:
Given sets are,
→ A = {x | x is an even integer}
→ D = {13, 14, 15, 16}
Now we have to,
→ find required set of A ∩ D.
Then the answer will be,
→ A ∩ D = {2, 4, 6, 8, ... n} ∩ {13, 14, 15, 16}
→ A ∩ D = {14, 16}
Hence, the required set is {14, 16}.
how many times smaller is 4 than 400?( Hint -4 does not have any zeros, 2-0=2.
Answer:
396
Step-by-step explanation:
400-4=396
Answer:
396
Step-by-step explanation:
Assume that females have pulse rates that are normally distributed with a mean of =76.0 beats per minute and a standard deviation of o=12.5 beats per minute. Complete parts (a) through (c) below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 83 beats per minute.
The probability is
The required probability for 1 adult female is randomly selected, find the probability that her pulse rate is less than 83 beats per minute is 0.5948.
In statistics, what does a probability mean?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.Statistics is the study of events that follow a probability distribution.Let, X= The female have pulse rate
μ = 7.60 bpm , σ² = 12.5²
a) We find
P[ 1 adult female is randomly selected, her pulse rate is less than 79 bpm]
= P [ X < 79]
= P [ X - μ/ σ < 79 - μ/ σ ]
= P[ X - 76/12.5 < 79 - 76/ 12.5 ]
= P[Z < 0.24]
= 0.5948 (From standard normal cumulative probability table)
Hence, the required probability of 1 adult female is randomly selected, find the probability that her pulse rate is less than 83 beats per minute.is 0.5948.
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Solve the equation for exact solutions. 6 cos^(-1) x = pi
I got √3/2
The exact solutions for the equation cos⁻¹x = π will be x=√3/2.
What is the equation?
An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation to be solved,
cos⁻¹x = π
[tex]6\arccos \left(x\right)=\pi \quad :\quad x=\frac{\sqrt{3}}{2}[/tex]
Divide by 6 on both the side,
[tex]\frac{6\arccos \left(x\right)}{6}=\frac{\pi }{6}[/tex][tex]\frac{6\arccos \left(x\right)}{6}=\frac{\pi }{6}[/tex]
Simplify,
[tex]\arccos \left(x\right)=\frac{\pi }{6}[/tex]
From the trigonometric inverse principle,
[tex]x=\frac{\sqrt{3}}{2}[/tex]
Thus, the exact solution for the equation cos⁻¹x = π will be x=√3/2.
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Find the compound interest and the total amount after an hour if the interest is compounded
every ten minutes.
Principal = 512
Rate of interest = 5% per minute
The compound interest = $5320
and the total amount = $5832
In this question, we need to find the compound interest and the total amount after an hour if the interest is compounded every ten minutes.
Here, principal P= $512
rate of interest R = 5% per minute
= 5 x 10 (interest for every 10 min)
= 50
Now n = 60 / 10
n = 6
So using compound interest formula the total amount would be,
A = P(1 + R / 100)^n
A = 512 (1 + 50/100)^6
A = 512 (3/2)^6
A = 5.2 (1.5)^6
A= $5832
Now the Compound Interest = A – P
= 5832 – 512
= $5320
Therefore, the compound interest = $5320
and the total amount = $5832
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Magan went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of sodium. Magan purchased a total of 11 cans of soup and frozen dinners which collectively contain 4750 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Magan bought 8 cans of soup and 3 cans of frozen dinners.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x represent the number of cans of soup purchased and y the number of frozen dinners purchased.
Magan purchased a total of 11 cans of soup and frozen dinners.
As per the given information, we can write the equations would be as
x + y = 11 ....(i)
Also:
350x + 650y = 4750
7x +13y =95 ....(ii)
Solving equations (i) and (ii) simultaneously gives the values are:
x = 8, and y = 3
Thus, Magan bought 8 cans of soup and 3 cans of frozen dinners.
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