The probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6
How to find the probability?To find the probability, we need to start by identifying the event or situation for which we want to calculate the probability.
Since Karmen has three choices for the exterior color, two choices for the interior color, and two choices for the transmission, the total number of possible car configurations is:
3 x 2 x 2 = 12
This means there are 12 different cars to choose from.
To find the probability of picking a car that has a black exterior and a belge interior, we need to determine how many cars meet these criteria. There is only one car that has a black exterior and a belge interior, so the probability of picking this car is:
1/12
Therefore, the probability of Karmen picking a car with a black exterior and a belge interior is 1/12.
To find the probability of picking a car with a belge interior and an automatic transmission, we need to determine how many cars meet these criteria. There are two cars that have a belge interior and an automatic transmission, so the probability of picking one of these cars is:
2/12
Simplifying this fraction gives:
1/6
Therefore, the probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6.
Learn more about probability
brainly.com/question/11234923
#SPJ11
Using the probability distribution represented by the graph
below, find the probability that the random variable, X, falls
in the shaded region.
Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.
Define probability?Probability is the ratio of favourable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.
Positive Outcomes/Total Results = x/n = Probability(Event)
Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.
Here in the question,
Total region = 8.
Shaded region = 5
So, probability of falling in the shaded region = 5/8
To know more about probability, visit:
https://brainly.com/question/29251004
#SPJ1
i need help with this
Answer:
[tex]x = \$2.06[/tex]
Step-by-step explanation:
Representing the price of one juice bottle as x, we can construct the equation:
[tex]15x + \$1.93 = \$32.83[/tex]
From here, we can solve for x.
↓ subtracting $1.93 from both sides
[tex]15x = \$32.83 - \$1.93[/tex]
[tex]15x = \$30.90[/tex]
↓ dividing both sides by 15
[tex]\boxed{x = \$2.06}[/tex]
In the figure, quadrilateral GERA is inscribed in circle P. TA is tangent to circle P at A, m∠REG = 78°, m AR ≅ 46°, and ER = GA. Find each measure
Someone please help will give brainliest
The measure of in quadrilateral GERA ∠GAR = 102° , ∠TAR = 23°, ∠GAN = 55° , m AG = 110° , m RE = 110° , m GE = 94°
∠REG = 78° , m AR = 46
The sum of the opposite angle of the quadrilateral is equal to 180°
∠REG + ∠GAR = 180°
∠GAR = 180 - ∠REG
∠GAR = 180 - 78
∠GAR = 102°
The tangent chord angle is half the intercept arc
∠TAR = 1/2 m AR
∠TAR = 1/2 ×46
∠TAR = 23°
The sum of straight angles is 180
m ∠GAN = 180 - (m ∠TAR + m ∠GAR )
m ∠GAN = 180 - (23 + 120)
m ∠GAN = 55°
The tangent chord angle is half the intercept arc
m AG = 2 m ∠GAN
m AG = 2(55)
m AG = 110°
as EG = GA
m RE = m GA
m RE = 110°
Complete angle sum = 360°
m GE = 360 - (m AG + m AR + m RE)
m GE = 360 - (110 + 46 + 110 )
m GE = 94°
To know more about quadrilateral click here :
https://brainly.com/question/29934440
#SPJ4
Shapes A and B are similar.
a) Calculate the scale factor from shape A to shape B.
b) Find the value of w.
Give each answer as an integer or as a fraction in its simplest form.
4 cm
7 cm
A
12 cm
3 cm
w cm
B
9 cm
Algebra 2 question need help.
Answer:
c
Step-by-step explanation:
The student council set a goal of raising at least $500 in flower sales. So far it
has raised $415.
Part A
Write an inequality to show how many more dollars, d, the student council needs
to reach its goal.
Answer
Part B
How many solutions does the inequality have? Explain your reasoning by giving
some examples of solutions to the inequality.
In both cases, the inequality holds true. The inequality is 415 + d ≥ 500.
Part A:
To write an inequality that represents the situation, we can use the following format: money raised so far + additional money needed ≥ goal. In this case, the money raised so far is $415, and the goal is $500. Let d represent the additional money needed. So the inequality would be:
415 + d ≥ 500
Part B:
The inequality 415 + d ≥ 500 has infinitely many solutions, as there are countless values of d that can satisfy the inequality. This is because as long as the total amount raised is equal to or greater than $500, the student council meets its goal. For example, if d is 85, then the council would exactly meet its goal (415 + 85 = 500). If d is 100, the council would exceed its goal (415 + 100 = 515). In both cases, the inequality holds true.
More on inequalities: https://brainly.com/question/14192797
#SPJ11
solve the equation
i will give brainliest
Answer:
5.09
Step-by-step explanation:
You eliminate the decimal by multiplying both sides by 10:
10(.25x+0.5)=10(0.61+0.14x)
Then you get your new equation and combine like terms:
25x+5=61+14x
-14x -14x
11x+5=61
11x+5=61
-5 -5
11x=61
Then finally you do 61/11 which gets you around 5.09 if you round to 2 decimal places.
The National Vital Statistics Reports for November 2011 states that U. S. Cesarean delivery rate for 2010 was about 32. 8%. Cesarean delivery is also called a "C-section. " It means the baby is not delivered in the normal way. The baby is surgically removed through an incision in the mother’s abdomen and uterus. Suppose this year a random sample of 100 births has 41 that are C-sections. Use the estimate from the NVS Report for 2011 as the population proportion, p, and the result from this year’s random sample to estimate the U. S. Cesarean delivery rate for this year with 95% confidence. (Be sure to check that a normal model is appropriate. )
The 95% confidence interval for the U.S. Cesarean delivery rate for this year is approximately (0.3314, 0.4886) or 33.14% to 48.86%.
How to find the delivery rate for a particular year using a sample and a population proportion estimate from a previous report?To estimate the U.S. Cesarean delivery rate for this year with 95% confidence using the provided information, we can construct a confidence interval for the population proportion.
Given:
Population proportion estimates from the NVS Report for 2011: p = 0.328 (32.8%)
Sample size: n = 100
Number of C-sections in the sample: x = 41
First, we need to check if a normal model is appropriate for the sample proportion. For this, we can verify if the sample size is sufficiently large and if both np and n(1-p) are greater than 10.
np = 100 * 0.328 = 32.8
n(1-p) = 100 * (1 - 0.328) ≈ 67.2
Since both np and n(1-p) are greater than 10, we can assume that the conditions for a normal model are met.
Now, we can calculate the confidence interval using the sample proportion and the critical value corresponding to a 95% confidence level.
Sample proportion (p-hat) = [tex]\frac{x }{ n}[/tex] =[tex]\frac{ 41 }{ 100 }[/tex]= 0.41
The critical value for a 95% confidence level can be obtained from a standard normal distribution or a Z-table. In this case, the critical value is approximately 1.96.
The margin of error (E) can be calculated as:
E = Z * [tex]\sqrt((\frac{p-hat * (1 - p-hat))} { n})[/tex]
E = 1.96 * [tex]\sqrt((\frac{0.41 * (1 - 0.41))}{ 100)}[/tex]
E ≈ 0.0786
Finally, we can construct the confidence interval by subtracting and adding the margin of error from the sample proportion.
Confidence interval = p-hat ± E
Confidence interval = 0.41 ± 0.0786
Therefore, the 95% confidence interval for the U.S. Cesarean delivery rate for this year is approximately (0.3314, 0.4886) or 33.14% to 48.86%.
Note: It's important to consider that this calculation assumes the sample is representative of the U.S. population and that the conditions for a normal model are satisfied. Additionally, the estimate from the NVS Report for 2011 is used as the population proportion.
Learn more about the delivery rate for this year.
brainly.com/question/11805232
#SPJ11
solve this trigonometric equation cos²x =3sin²x
Answer:
Step-by-step explanation:
cos²x =3sin²x subtract both sides by 3sin²x
cos²x - 3sin²x = 0 use identity cos²x+sin²x=1 => cos²x = 1-sin²x
substitute in
(1-sin²x)-3sin²x = 0 combine like terms
1-4sin²x=0 factor using difference of squares rule
(1-2sin x)(1+2sin x)=0 set each equal to 0
(1-2sin x)=0 (1+2sin x)=0
-2sinx = -1 2sinx= -1
sinx=1/2 sinx =-1/2
Think of the unit circle. When is sin x = ±1/2
at [tex]\pi /6, 5\pi /6, 7\pi /6, 11\pi /6[/tex]
This is from 0<x<2[tex]\pi[/tex]
Camila empieza a jugar un video juego que tiene 840 niveles. La primera semana, supera 16
parte de los niveles; la segunda semana, 14
de lo que le hace falta y la tercera, 45
de los niveles que le hacían falta por superar.
Si en la cuarta semana Camila pretende terminar el juego, ¿cuántos niveles debe superar?
A.
95
B.
105
C.
182
D.
420
The amount of levels left at the end is 105.
How many levels Camila needs to complete?There is a total of 840 levels in the game.
On the first day she completes 1/6 of the total, so she completes:
840/6 = 140
The remaining is 840 - 140 = 700
Then she completes 1/4 of that, which is:
(1/4)*700 = 175
So now she has left 700 - 175 = 525
Then she completes 4/5, so she does:
(4/5)*525 = 420
The amount left is: 525 - 420 = 105
The correct option is B.
Learn more about fractions at:
https://brainly.com/question/11562149
#SPJ1
2. an insurance salesman sells policies to 10 men, all of identical age and all of whom are in good health. according to his company's records, the probability that a man of this particular age will be alive in 20 years is 0.69. find the probability that in 20 years the number of the men that are still alive will be: a) exactly five b )more than 8 c)at least two
a) The probability that exactly five men will still be alive in 20 years is approximately 0.024.
b) The probability that more than eight men will still be alive in 20 years is approximately 0.057.
c) The probability that at least two men will still be alive in 20 years is approximately 0.999.
To calculate the probabilities, we can use the binomial distribution formula, where n is the number of trials, p is the probability of success, and x is the number of successes. Therefore,
a) P(X = 5) = (10 choose 5) * (0.69)⁵ * (0.31)⁵ ≈ 0.024
b) P(X > 8) = P(X = 9) + P(X = 10) = [(10 choose 9) * (0.69)⁹ * (0.31)¹] + [(10 choose 10) * (0.69)¹⁰ * (0.31)⁰] ≈ 0.057
c) P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) = 1 - [(10 choose 0) * (0.69)⁰ * (0.31)¹⁰] - [(10 choose 1) * (0.69)¹ * (0.31)⁹] ≈ 0.999
In summary, we have used the binomial distribution formula to calculate the probability that exactly five men, more than eight men, and at least two men will still be alive in 20 years, given that the probability that a man of this particular age will be alive in 20 years is 0.69.
Learn more about probability
https://brainly.com/question/24756209
#SPJ4
Furnace repair bills are normally distributed with a mean of 264 dollars and a standard deviation of 30 dollars. if 144 of these repair bills are randomly selected, find the probability that they have a mean cost between 264 dollars and 266 dollars.
Answer is the probability that 144 furnace repair bills have a mean cost between 264 dollars and 266 dollars is approximately 0.2881 or 28.81%
The distribution of the sample mean of furnace repair bills will also be normally distributed with a mean of 264 dollars and a standard deviation of 30/sqrt(144) = 2.5 dollars (by the Central Limit Theorem).
We need to find the probability that the sample mean falls between 264 and 266 dollars:
z1 = (264 - 264) / 2.5 = 0
z2 = (266 - 264) / 2.5 = 0.8
Using a standard normal distribution table or calculator, we can find the area under the curve between z1 and z2:
P(0 ≤ Z ≤ 0.8) = 0.2881
Therefore, the probability that 144 furnace repair bills have a mean cost between 264 dollars and 266 dollars is approximately 0.2881 or 28.81%.
To know more about standard deviations:
https://brainly.com/question/475676
#SPJ11
Giving away a lot of points please don't put something random, no explanation is needed only the answer.
Thank you
The theoretical probability is: 12.5%. After 100 trials, the experimental probability is of: 20%. After 400 trials, the experimental probability is of: 11%. After more trials, the experimental probability is closer to the theoretical probability.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:
1/8 = 0.125 = 12.5%.
(eight sides, each of them is equally as likely).
The experimental probabilities are obtained considering the trials, hence:
100 trials: 20/100 = 0.2 = 20%. -> results given in the text.400 trials: 44/400 = 0.11 = 11%.The more trials, the closer the experimental probability should be to the theoretical probability.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
What technique is happening to this object?
Step-by-step explanation:
Looks as though it has been cropped.....picture is only a PART of the original...it has been 'cut off' or 'cropped' on both sides .
Garden plots in the Portland Community Garden are rectangles
limited to 45 square meters. Christopher and his friends want a plot
that has a width of 7.5 meters. What length will give a plot that has
the maximum area allowed?
The length should be less than or equal to 6 meters in order to have a plot with the maximum area allowed (45 square meters) when the width is 7.5 meters.
To find the length that will give a plot with the maximum area allowed, we can use the formula for the area of a rectangle:
Area = Length × Width
The width is given as 7.5 meters, and the area should not exceed 45 square meters.
Let's denote the length as L.
We want to maximize the area, so we need to find the value of L that satisfies the condition Area ≤ 45 and gives the largest possible area.
Substituting the given values into the area formula, we have:
Area = L × 7.5
Since the area should not exceed 45 square meters, we can write the inequality:
L × 7.5 ≤ 45
To find the maximum value of L, we can divide both sides of the inequality by 7.5:
L ≤ 45 / 7.5
Simplifying the right side:
L ≤ 6
Therefore, the length should be less than or equal to 6 meters in order to have a plot with the maximum area allowed (45 square meters) when the width is 7.5 meters.
To learn more on Area click:
https://brainly.com/question/20693059
#SPJ1
15. It is given that X~B(5,p) and P(X=3) = P(X=4)
Find the value of p, given that 0 < p < 1
[3 marks]
Given that 0 < p < 1 for X~B(5,p) and P(X=3) = P(X=4), so the value of p is 2/3.
We know that X~B(5,p) and P(X=3) = P(X=4).
Using the probability mass function of a binomial distribution, we can write:
P(X=3) = (5 choose 3) * p³ * (1-p)²
P(X=4) = (5 choose 4) * p⁴ * (1-p)¹
Since P(X=3) = P(X=4), we can set these two expressions equal to each other and simplify:
(5 choose 3) * p^3 * (1-p)² = (5 choose 4) * p⁴ * (1-p)¹
10p^3(1-p)^2 = 5p^4(1-p)
Dividing both sides by [tex]p^{3(1-p)[/tex] and simplifying, we get:
10(1-p) = 5p
10 - 10p = 5p
10 = 15p
p = 2/3
Therefore, the value of p is 2/3, given that 0 < p < 1.
To know more about probability mass function, refer to the link below:
https://brainly.com/question/30765833#
#SPJ11
Use the method of Lagrange multipliers to find the points on the
curve x2 + y2 −6x + 7 = 0 that are closest to and furthest from the
point P = (0, 3).
Using the value of λ = (18 + √130)/18, we get: x = 3λ ≈ 4.895 y = 3λ - 3 ≈ 5.316 So the point on the curve that is furthest from P is approximately (4.895, 5.316).
To use the method of Lagrange multipliers, we first need to define our objective function and our constraint. Our objective function is the distance between the point P and a point on the curve, which can be expressed as:
f(x, y) = (x - 0)^2 + (y - 3)^2 = x^2 + (y - 3)^2
Our constraint is the equation of the curve:
g(x, y) = x^2 + y^2 - 6x + 7 = 0
To use the method of Lagrange multipliers, we need to introduce a new variable λ and solve the following system of equations:
∇f = λ∇g
g(x, y) = 0
where ∇f and ∇g are the gradients of f and g, respectively.
Taking the partial derivatives of f and g with respect to x and y, we have:
∂f/∂x = 2x
∂f/∂y = 2(y - 3)
∂g/∂x = 2x - 6
∂g/∂y = 2y
Setting ∇f equal to λ∇g, we have:
2x = λ(2x - 6)
2(y - 3) = λ(2y)
Simplifying these equations, we get:
x = 3λ
y = 3λ - 3
Substituting these expressions into the equation of the curve, we get:
(3λ)^2 + (3λ - 3)^2 - 6(3λ) + 7 = 0
Simplifying this equation, we get:
18λ^2 - 36λ + 13 = 0
Solving for λ, we get:
λ = (18 ± √130)/18
Substituting these values of λ into our expressions for x and y, we get the coordinates of the points on the curve that are closest to and furthest from the point P.
To find the point that is closest to P, we need to minimize the objective function f(x, y). Using the value of λ = (18 - √130)/18, we get:
x = 3λ ≈ 1.105
y = 3λ - 3 ≈ -0.316
So the point on the curve that is closest to P is approximately (1.105, -0.316).
To find the point that is furthest from P, we need to maximize the objective function f(x, y). Using the value of λ = (18 + √130)/18, we get:
x = 3λ ≈ 4.895
y = 3λ - 3 ≈ 5.316
So the point on the curve that is furthest from P is approximately (4.895, 5.316).
Learn more about point here:
brainly.com/question/30423121
#SPJ11
I’m giving 10 points.
Answer:
12
Step-by-step explanation:
-3(b - 5) + 7a - (9 - a) ^6 a = 7 and b = -4
-3(-4 - 5) + 7(7) - (9 - 7)^6
= -3(-9) + 49 - (2)^6
= 27 + 49 - (64)
= 27 + 49 - 64
= 76 - 64
= 12
Suppose M and C each represent the position number of a letter in the alphabet, but M represents the letters in the original message and C represents the letters in a secret code. The equation c=m+2 is used to encode a message.
The equation that can be used to decode the secret code is m = c - 2
How so you find the equation to decode the secret code?For you to decode the secret message, you need to turn the the encoding process around. Find the inverse.
Since the encoding process uses the equation c = m + 2, to decode the message, all that need to be found is the value of m. This can be done by rearranging the encoding equation to solve for m
move 2 to c side. it becomes m = c-2
The above answer is in response to the full question below;
Suppose M and C each represent the position number of a letter in the alphabet, but M represents the letters in the original message and C represents the letters in a secret code. The equation c=m+2 is used to encode a message.
Write an equation that can be used to decode the secret code into the original message.
Find more exercises on decoding;
https://brainly.com/question/29976739
#SPJ1
If y, p and q vary jointly and p is 14 when y and q are equal to 2, determine q when p and y are equal to 7
In the given question, if y, p and q vary jointly and p is 14 when y and q are equal to 2 and p and y are equal to 7, we get q is equal to 14 using the joint variation formula.
To solve this problem, we need to use the formula for joint variation, which states that y, p, and q vary jointly if there exists a constant k such that ypk = kq.
In this case, we know that when y=2 and q=2, p=14. So we can set up the equation: 2*14*k = 2kq
Simplifying this, we get: 28k = 2kq
Dividing both sides by 2k, we get: 14 = q
So when p=7 and y=7, we can use the same equation: 7*14*k = 7kq
Simplifying this, we get: 98k = 7kq
Dividing both sides by 7k, we get: q = 14
Therefore, when p and y are equal to 7, q is equal to 14.
To know more about joint variation refer here:
https://brainly.com/question/29181669#
#SPJ11
Will mark brainliest (to whoever explains this clearly)
Lizzie came up with a divisibility test for a certain number m that doesn't equal 1:
-Break a positive integer n into two-digit chunks, starting from the ones place. (For example, the number 354764 would break into the two-digit chunks 64, 47, 35. )
- Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be 64-47+35=52. )
- Find m, and show that this is indeed a divisibility test for m (by showing that n is divisible by m if and only if the result of this process is divisible by m)
Lizzie's divisibility test states that a number n is divisible by a certain number m if and only if the alternating sum of its two-digit chunks is divisible by m.
How does Lizzie's divisibility test work?Lizzie's divisibility test involves breaking a positive integer into two-digit chunks, finding the alternating sum of these chunks, and then determining if the result is divisible by a certain number m.
To apply the test:
Break the positive integer n into two-digit chunks from right to left.Calculate the alternating sum of these two-digit numbers, adding the first number, subtracting the second, adding the third, and so on.Find m, the divisor for which you want to test divisibility.If the result of the alternating sum is divisible by m, then n is also divisible by m.To prove that this is a divisibility test for m, you need to show that n is divisible by m if and only if the result of the alternating sum is divisible by m.
Learn more about alternating
brainly.com/question/19718027
#SPJ11
Find the volume of the cone to the nearest whole number. Use 3. 14
for it.
Cone
Radius Height
Volume
varrh
Worms
3in.
6in.
Tree
Gum
The volume of the cone is 57 cubic inches. To find the volume of the cone, we use the formula: V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius of the cone, h is the height of the cone, and π is approximately 3.14.
Given that the radius of the cone is 3 inches and the height is 6 inches, we can substitute these values into the formula and solve for V: V = (1/3)π([tex]3^{2}[/tex])(6), V = (1/3)π(9)(6), V = (1/3)(3.14)(54), V = 56.52 cubic inches
Rounding to the nearest whole number, the volume of the cone is 57 cubic inches.
To know more about volume of cone, refer here:
https://brainly.com/question/29767724#
#SPJ11
Need HELP ASAP!! please
Answer :
D. XY = 5 , YZ = 2Step-by-step explanation :
As We Know that Opposite sides of the Parallelogram are equal.
SO,
(i) YZ = XW (opposite sides)
YZ = 2bXW = b + 1=> 2b = b + 1
=> 2b - b = 1
=> b = 1
Since, YZ = 2b
=> YZ = 2 × 1
=> YZ = 2.
Also,
(ii) XY = WZ (opposite sides)
XY = 3a - 4 WZ = a + 2=> 3a - 4 = a + 2
=> 3a - a = 2 + 4
=> 2a = 6
=> a = 6/2
=> a = 3 .
Since, XY = 3a - 4
putting the value of a = 3.
=> 3(3) - 4
=> 9 - 4
=> 5
XY = 5.
Therefore, Option D is the required answer.
Let's use Priya as an example again. The number of hairs per square cm varies from person to person, but Priya has approximately 150 hairs per square cm.
She measures the diameter of her scalp from front to back and ear to ear and she finds that it is about 28cm in both directions. Her head is round so that makes her think that she could use the area of a circle to estimate how many total hairs she has on her head.
a. What is the area of Priya's scalp?≈
≈
cm2
b. About how many strands of hair are on Priya's head? ≈
≈
strands of hair
a. The area of Priya's scalp is ≈ [tex]615.75 cm^2[/tex]. b. Priya has approximately 92,363 strands of hair on her head.
a. The area of Priya's scalp can be estimated using the formula for the area of a circle, which is A = π[tex]r^2[/tex] ,where r is the radius (half the diameter) of the circle. Since Priya's diameter is 28cm, her radius would be 14cm. So, the area of her scalp would be:
A = π[tex](14cm)^2[/tex]
A ≈[tex]615.75 cm^2[/tex]
b. To estimate how many strands of hair Priya has on her head, we can multiply the number of hairs per square cm by the total area of her scalp. So, if Priya has approximately 150 hairs per square cm and her scalp has an estimated area of 615.75 cm^2, then:
Total number of hairs ≈ [tex]150 hairs/cm^2 * 615.75 cm^2[/tex]
Total number of hairs ≈ 92,362.5 hairs
Therefore, we can estimate that Priya has approximately 92,363 strands of hair on her head.
Know more about area here:
https://brainly.com/question/25292087
#SPJ11
The diameter of a circle measures 10m. What is the circumference of the circle?
Use for 3. 14 and do not round your answer. Be sure to include the correct unit in your answer
The circumference of the circle with a diameter of 10m is 31.4m, using 3.14 as the value of pi and including the correct unit in the answer.
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Substituting the given value of the diameter, we get C = 3.14 x 10m = 31.4m as the circumference of the circle.
Since the value of pi is irrational, it cannot be expressed as a finite decimal or fraction, so we use an approximation, such as 3.14, to calculate the circumference. It is important to include the correct unit, which is meters in this case, in the answer to indicate the quantity being measured. Therefore, the circumference of the circle is 31.4m.
For more questions like Circumference click the link below:
https://brainly.com/question/28757341
#SPJ11
roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax what was the total for rogers purchased
After the discount and the tax, the amount that Roger pays is $45.41
How to find the final price?We know that Roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax, then the total cost before the discount and tax is:
C = 12.00 + 34.50 = 46.50
Now we apply the discount and the tax (as factors in a product) to get:
C' = 46.50*(1 - 0.1)*(1 + 0.085) = 45.41
That is the amouint that Roger pays for the two items.
Learn moer about taxes at.
https://brainly.com/question/1775528
#SPJ1
12
select the correct number from each drop-down menu to complete the equation
7
2 +
+ b
a
2
-2
The completed equation is:
2 + 7 = a - 2
a = 11.
We are given the following equation:
2 + b = a - 2
We need to select the correct number from the drop-down menu to complete the equation.
From the first drop-down menu, we select 7.
2 + 7 = 9
From the second drop-down menu, we select 2.
2 + b = 9 - 2
2 + b = 7
Subtracting 2 from both sides, we get:
b = 5
Therefore, from the third drop-down menu, we select 5.
So, the completed equation is:
2 + 7 = 5 - 2
9 = 3
This is not a true statement, so there must be an error in one of our selections. Upon closer inspection, we can see that the correct number to select from the first drop-down menu is 5, not 7.
2 + 5 = 7
Now, substituting 5 for b in the original equation, we get:
2 + 5 = a - 2
7 + 2 = a
a = 9
Therefore, from the third drop-down menu, we select 9.
So, the completed equation is:
2 + 5 = 9 - 2
7 = 7
This is a true statement, so we have selected the correct numbers to complete the equation.
To know more about equation refer here:
https://brainly.com/question/29657983
#SPJ11
BRANLIEST!!
Three coins are tossed. Let the event H = all Heads and the event K = at least one Heads.
1. 7/8 P(K) =
2. 1/7 The probability that the outcome is all heads if at least one coin shows a head
3. 1/8 P(H∩K) =
The probability that the outcome is all heads if at least one coin shows a head is 8/49.
How to find the probability?To solve these problems, we'll use the basic principles of probability.
The probability of an event K (at least one head) can be calculated by subtracting the probability of the complement of K (no heads) from 1.
Since the coins can either show all heads or not, the complement of K is the event of no heads, which is denoted as T (tails for all coins). Therefore, we have:
P(K) = 1 - P(T)
Each coin toss is independent, and the probability of getting tails on a single toss is 1/2. Since there are three coins tossed independently, we multiply the probabilities together:
P(T) = ([tex]\frac{1}{2}[/tex]) * ([tex]\frac{1}{2}[/tex]) * ([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{8}[/tex]
Substituting this into the equation for P(K):
P(K) = 1 - P(T) = 1 - [tex]\frac{1}{8}[/tex] = [tex]\frac{7}{8}[/tex]
So, the probability of event K (at least one head) is [tex]\frac{7}{8}[/tex].
The probability that the outcome is all heads if at least one coin shows a head can be calculated using conditional probability. We want to find P(H | K), which represents the probability of event H (all heads) given event K (at least one head).
The formula for conditional probability is:
P(H | K) = [tex]\frac{P(H \∩ K) }{ P(K)}[/tex]
To find P(H∩K), we need to determine the probability of the intersection of events H and K (i.e., the probability of getting all heads and at least one head).
Since H is a subset of K (if all coins show heads, then at least one head is shown), we have:
P(H∩K) = P(H)
Therefore, P(H∩K) is the same as P(H). According to the problem, P(H) = [tex]\frac{1}{7}[/tex].
Now, substituting P(H∩K) = P(H) and P(K) = [tex]\frac{7}{8}[/tex] into the conditional probability formula:
P(H | K) = [tex]\frac{P(H\∩K) }{ P(K)}[/tex] = ([tex]\frac{1}{7}[/tex]) / ([tex]\frac{7}{8}[/tex]) = ([tex]\frac{1}{7}[/tex]) * ([tex]\frac{8}{7}[/tex]) = [tex]\frac{8}{49}[/tex]
So, the probability that the outcome is all heads if at least one coin shows a head is [tex]\frac{8}{49}[/tex].
To summarize:
P(K) = [tex]\frac{7}{8}[/tex]
P(H | K) = [tex]\frac{8}{49}[/tex]
P(H∩K) = [tex]\frac{1}{7}[/tex]
Learn more about probability.
brainly.com/question/30034780
#SPJ11
Max's niece pushed a playground merry-go-round so that it travels 4. 5 feet along the
curve. The radius of the merry-go-round is 5 feet. Find, to the nearest degree, the
central angle.
The central angle is approximately 51.6 degrees.
How to find the Arc length of a central angle?To solve this problem, we can use the formula for arc length of a circle:
arc length = θ × r
where θ is the central angle in radians, and r is the radius of the circle.
We know that the arc length is 4.5 feet and the radius is 5 feet. So we can rearrange the formula to solve for θ:
θ = arc length / r
θ = 4.5 / 5
θ = 0.9 radians
To find the central angle in degrees, we can convert radians to degrees by multiplying by 180/π:
θ = 0.9 × (180/π)
θ ≈ 51.6 degrees
Therefore, the central angle is approximately 51.6 degrees.
Learn more about Length
brainly.com/question/2497593
#SPJ11
find the extremum of each function using the symmetry of its graph. Classify the etremum of the function as maximum or a minimum and state the of x at which it occurs k(x)(300+10x)(5-0.2x)
The extremum of the function is a minimum at x = -2.5
The given function is k(x)(300+10x)(5-0.2x).
To check for symmetry about the y-axis, we replace x with -x in the given function and simplify as follows:
k(-x)(300-10x)(5+0.2x)
To check for symmetry about the x-axis, we replace y with -y in the given function and simplify as follows:
k(x)(300+10x)(5-0.2x) = -k(x)(-300-10x)(5+0.2x)
To find these points, we set the function equal to zero and solve for x:
k(x)(300+10x)(5-0.2x) = 0
This equation has three solutions:
x = 0
x = -30
x = 25.
The midpoint of the line segment connecting these points is
(x1+x2) ÷ 2 = (-30+25) ÷ 2 = -2.5.
To determine the type of extremum at this point, we need to check the sign of the second derivative. The second derivative of the function is:
k(x)(-1200+x)(0.2x+15)
Since the function is symmetric about the x-axis, the second derivative will be negative at the extremum if it is maximum and positive if it is a minimum.
When x = -2.5, the second derivative is positive, which means that the function has a minimum at x = -2.5.
To learn more about extremum follow the link:
https://brainly.com/question/31343270
#SPJ1