Answer:
1/1001%I hope this helps...
Please mark me brainliest
Answer:
Step-by-step explanation:
1 out of 100 is 1 percent. This is because percentage is always out of 100 so you don’t have to change anything. That means 1 is always 1 percent of 100. It is also 1 part of 100.
2. A life insurance company will pay out $30,000 if a client dies, $10,000 if they are disabled, and $0 otherwise. The company's databases suggest that 1 out of 1,000 of its clients will die and 1 out of 250 of its clients will become disabled within the next year. To figure out how much to charge customers for each policy, they must figure out how much money they expect to lose per policy. Find the mean and standard deviation of the amount of money the insurance company can expect to lose on each policy.
The mean amount of money the insurance company can expect to lose on each policy is $142.00 with a standard deviation of $1,243.67.
What is an insurance?
Let X be the random variable representing the amount of money the insurance company will lose on a policy. Then we can calculate the expected value (mean) of X and the standard deviation of X as follows:
Expected value:
E(X) = 30,000(1/1,000) + 10,000(1/250) + 0(1 - 1/1,000 - 1/250) = $142.00
The first term in the sum corresponds to the probability of a client dying (1/1,000) multiplied by the payout ($30,000), the second term corresponds to the probability of a client becoming disabled (1/250) multiplied by the payout ($10,000), and the third term corresponds to the probability of neither event occurring (1 - 1/1,000 - 1/250).
Standard deviation:
To calculate the standard deviation, we need to find the variance of X first:
Var(X) = [30,000 - E(X)]²(1/1,000) + [10,000 - E(X)]²(1/250) + [0 - E(X)]²(1 - 1/1,000 - 1/250)
= $1,547,797.56
The first term in the sum corresponds to the squared difference between the payout for a client dying and the expected payout, multiplied by the probability of a client dying, and so on for the second and third terms.
Then, we can take the square root of the variance to find the standard deviation:
SD(X) = √[Var(X)] = $1,243.67
Therefore, the mean amount of money the insurance company can expect to lose on each policy is $142.00 with a standard deviation of $1,243.67.
To know more about insurance, visit:
https://brainly.com/question/28015669
#SPJ1
Two points on a circle of radius 1 are chosen at random. Find the probability that the distance between the two points is at most 1.5.
The probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%, which corresponds to the range of central angles less than or equal to 3 radians out of the total central angle of 2π radians.
Let's consider two points on a circle of radius 1, labeled A and B. The distance between A and B is given by the length of the arc AB on the circle, which is a fraction of the circumference of the circle. The circumference of a circle of radius 1 is 2π, so the length of the arc AB is given by
d = θ/2π * 2πr = θ
where d is the distance between A and B, θ is the central angle between A and B (in radians), and r is the radius of the circle (which is 1 in this case).
To find the probability that the distance between A and B is at most 1.5, we need to find the range of central angles that correspond to arc lengths less than or equal to 1.5. Let's call this range of angles θ₁. We have
θ₁ = 2d/r = 2(1.5)/1 = 3
This means that the central angle between A and B must be less than or equal to 3 radians for the distance between A and B to be at most 1.5. Since the total central angle of the circle is 2π radians, the probability of selecting two points with a central angle less than or equal to 3 radians is
P(θ ≤ 3) = θ/2π = 3/2π ≈ 0.477
Therefore, the probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%.
To know more about Probability:
https://brainly.com/question/11234923
#SPJ1
There are four boards measuring 3 feet 4 inches, 27 inches, 1 1/2 yards, and 2 3/4 feet. What is the total length of all four boards?
On adding the measurement of "4-boards", the total length of the 'four-boards" is 154 inches.
In order to add the lengths of these four boards, we first need to convert all the measurements to the same units.
So, Let us convert all the measurements to inches:
(i) 3 feet 4 inches = (3×12) + 4 = 40 inches, ...because 1 feet = 12 inch;
(ii) 27 inches = 27 inches;
(iii) 1(1/2) yards = (1.5 × 3 × 12) = 54 inches;
(iv) 2(3/4) feet = (2.75 × 12) = 33 inches;
Now, we can add the lengths of the four-boards:
⇒ 40 + 27 + 54 + 33 = 154 inches,
Therefore, the total length of all four boards is 154 inches.
Learn more about Length here
https://brainly.com/question/30200619
#SPJ1
A single letter from the word SLEEPLESS is chosen. What is the probability of choosing a P or an S? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
If a single letter from the word SLEEPLESS is chosen, the probability of choosing a P or an S as a fraction in lowest terms is 5/8.
To find the probability of choosing a P or an S from the word SLEEPLESS, we need to first determine the total number of letters in the word and then count how many of those letters are P's or S's.
There are 8 letters in the word SLEEPLESS, so there are 8 possible outcomes when selecting a single letter at random. Of these 8 letters, 2 are P's and 3 are S's.
Therefore, the probability of choosing a P or an S is the sum of the probabilities of choosing a P and choosing an S:
P(P or S) = P(P) + P(S)
P(P) = 2/8 = 1/4, since there are 2 P's out of 8 total letters.
P(S) = 3/8, since there are 3 S's out of 8 total letters.
P(P or S) = 1/4 + 3/8
P(P or S) = 5/8, which is the final probability expressed as a fraction in lowest terms.
Alternatively, we can convert the fraction to a decimal and round to the nearest millionth:
P(P or S) = 0.625
To learn more about probability click on,
https://brainly.com/question/29142178
#SPJ1
How many radians are in a full circle?
Answer: 2 Radians
Step-by-step explanation:
A full circle is 2 full radians, also known as 2π. Half of a circle is equal to 180 degrees, which is equal to one radian, π.
I have attached a picture of the unit circle below, this picture comes form www.remind.com, but you can find many online.
Determine if each of the following relationships represents a proportional relationship or not.
SELECT ALL situations that represent a proportional relationship.
A). Natalia is selling fresh eggs at the local farmer's market. She sells 6 eggs for $3.12, a dozen eggs for $6.24, and eighteen eggs for $9.36.
B). Joey is training for a bicycle race and has been completing his longer training rides on Saturdays. Over the past month, Joey has ridden his bicycle 36 miles in 3 hours, 46 miles in 4 hours, and 22 miles in 2 hours.
C). graph 1 provided in the pictures
D). graph 2 provided in the pictures
E). Azul bought several different packages of 8-inch by 10-inch art canvases for craft project at her family reunion. The number of canvases in a package and the cost of the package is shown in the table. (TABLE PROVIDED IN PICTURES)
F). Kareem is comparing the cost of regular unleaded gasoline at three different gas stations near his home. Instead of filling up his car's gas tank at one station, he puts a few gallons in at each of the three different stations. The number of gallons of gasoline and the cost of the gasoline is shown in the table. (TABLE PROVIDED IN PICTURES)
The situations that represent a proportional relationship are:
A). Natalia is selling fresh eggs at the local farmer's market. She sells 6 eggs for $3.12, a dozen eggs for $6.24, and eighteen eggs for $9.36.
C). Graph 1 provided in the pictures. This graph shows a straight line passing through the origin, which indicates a proportional relationship.
D). Graph 2 provided in the pictures. This graph also shows a straight line passing through the origin, which indicates a proportional relationship.
E). Azul bought several different packages of 8-inch by 10-inch art canvases for a craft project at her family reunion. The number of canvases in a package and the cost of the package is shown in the table.
Therefore, the situations A, C, D, and E represent proportional relationships.
What is Proportional Relationship?A proportional relationship is a relationship between two quantities where one quantity is a constant multiple of the other quantity. In other words, if one quantity increases or decreases by a certain factor, then the other quantity will increase or decrease by the same factor. This relationship can be represented by a straight line passing through the origin on a graph.
For example, if the price of gasoline is proportional to the number of gallons purchased, then buying twice as many gallons would cost twice as much money. Similarly, if the distance traveled is proportional to the time taken, then traveling twice as long would cover twice the distance.
Learn more about proportional relationship here: https://brainly.com/question/12242745
#SPJ1
A set of data items is normally distributed with a mean of 600 and a standard deviation of 30. Find the data item in this distribution that corresponds
to the given z-score.
Z=-3
The data item that corresponds to z= -3 is
s(Type an integer or a decimal.)
The data item in this distribution corresponding to a z-score of -7 will be 290.
Here, we have,
The standard score in statistics is the number of standard deviations that a raw score's value is above or below the mean value of what is being observed or measured.
Raw scores that are higher than the mean have positive standard scores, whereas those that are lower than the mean have negative standard scores.
The Z-score measures how much a particular value deviates from the standard deviation.
The Z-score, also known as the standard score, is the number of standard deviations above or below the mean for a given data point.
The standard deviation reflects the level of variability within a particular data collection.
Here,
z=(X-μ)/σ
-7=(X-500)/30
-210=X-500
X=290
The data item in this distribution that corresponds to we given z-score
z equals to -7 will be 290.
To know more about z-score,
brainly.com/question/25819936
#SPJ1
Toggle navigation
Logout
139 days until renewal
Ratio
Return to Assigned Work
Overview
«
1
2
3
4
5
6
7
8
9
10
11
»
Question Progress
0 / 5 Marks
Homework Progress
20 / 33 Marks
23%
The profit for one small cake is £1.31.
How to calculate the profitLet's first determine the overall count of parts demonstrated in the ratio 5:7:12, which is equal to 24. Subsequently, each part would hence correspond to a quantity of nine cakes as per the equation below:
216 cakes / 24 = 9 cakes
5 parts x 9 cakes/part = 45 cakes
Likewise, similarly calculating the number of medium cakes leads us to 63 cakes, while that of large cakes sums up to 108 cakes:
7 parts x 9 cakes/part = 63 cakes
12 parts x 9 cakes/part = 108 cakes
Considering what the profit for one small cake is denoted by "x", and similarly, the profit for one medium cake is "2x" and the profit for one large cake is "3x", we can express the total gain as follows:
45x + 63(2x) + 108(3x) = 648.45
After similifying and solving for "x", we obtain an answer of £1.31 after rounding it off to two decimal places:
495x = 648.45
x = 1.31 (rounded to two decimal places)
Thus, the income earned from selling one single small cake is estimated at £1.31.
Learn more about profit on
https://brainly.com/question/1078746
#SPJ1
Activity 3
A
Write in increasing order according to their capacity:
In increasing order according to their capacity:
C, A, B A, B, CB, C, A B, C, AA, B, C C, A, BB, C, A A, C, BWhat is capacity?The capacity of a container, such as a cup, bottle, or tank, is the amount of fluid or material it can hold. It is usually stated in volume quantities such as liters, milliliters, gallons, or ounces.
Capacity is a necessary concept in engineering, manufacturing, and transportation, where it is used to design and run systems involving the storage, movement, and processing of fluids or materials.
Find out more on capacity here: https://brainly.com/question/17120212
#SPJ1
-3+8n=-5 for 7th grade math equation algebra
Answer: -0.25
Step-by-step explanation:
Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)
+3 on both sides of equal sign, which gives you
8n=-2
then divide by 8 on both sides (undo the times 8)
n=-0.25
Answer: -0.25
Step-by-step explanation:
Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)
+3 on both sides of equal sign, which gives you
8n=-2
then divide by 8 on both sides (undo the times 8)
n=-0.25
Can’t solve this please help urgent.
The value of the derivative of variable x with respect to parameter t is equal to dx / dt = - 1 / 2.
How to find the derivative of a parametric function
In this problem we need to find the derivative of variable x with respect to parameter t. This can be done by the following expression:
dy / dx = (dy / dt) / (dx / dt)
If we know that y = 4 · x² + 4, x = - 1 and dy / dt = 4, then the exact value of dy / dt is:
dy / dx = 8 · x
[8 · (- 1)] = 4 / (dx / dt)
- 8 = 4 / (dx / dt)
dx / dt = - 1 / 2
To learn more on derivatives of parametric equations: https://brainly.com/question/31388182
#SPJ1
The image of a trapezoid is shown. What is the area of a trapezoid?
The area of a trapezoid =1/2× (sum of the parallel sides)×h
=1/2×(a + b)×h=1/2×(3+6)×4=9×2= 18 square units.
What is a trapezoid?A trapezoid is a geometric shape with four sides, where two of the sides are parallel and the other two sides are not parallel. The parallel sides are called bases, and the non-parallel sides are called legs. The height or altitude of the trapezoid is the distance separating the two bases.
There are two main types of trapezoids: isosceles and non-isosceles. In an isosceles trapezoid, the legs are congruent, and the base angles (the angles formed between each base and a leg) are also congruent. In a non-isosceles trapezoid, the legs and base angles are not congruent.
To know more about trapezoids, visit:
https://brainly.com/question/8643562
#SPJ1
In Bridget's class, 35% of the students chose pizza as their favorite food. If 14 of the students chose pizza as their favorite food, how many students are in the class?
Answer:
40 students are in the class :)
Step-by-step explanation:
35%=14
1%=14/35=0.4
0.4*100=40=100%
According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 94 beat estimates, 29 matched estimates, and 39 fell short.
(a) What is the point estimate of the proportion that fell short of estimates? If required, round your answer to four decimal places.
pshort = .2407
(b) Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. If required, round your answer to four decimal places.
ME =
(c) How large a sample is needed if the desired margin of error is 0.05? If required, round your answer to the next integer.
n* =
a)0.2407 is the point estimate of the proportion.
b) The 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).
c) A sample size of 754 is needed to achieve a desired margin of error of 0.05.
(a) What is the point estimate of the proportion?
The point estimate of the proportion that fell short of estimates is 39/162 = 0.2407. Rounded to four decimal places, this is pshort = 0.2407.
(b) How to determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates?
To determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates, we need to first find the point estimate and standard error of the proportion that beat estimates.
The point estimate of the proportion that beat estimates is 94/162 = 0.5802.
The standard error can be calculated as:
SE = √(p×(1-p)/n)
where p is the point estimate of the proportion that beat estimates and n is the sample size. Substituting the values we get:
SE = √(0.5802×(1-0.5802)/162) = 0.0482
To calculate the margin of error, we use the formula:
ME = zSE
where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z* = 1.96 (from the standard normal distribution table).
Substituting the values we get:
ME = 1.96×0.0482 = 0.0944
Therefore, the margin of error is 0.0944. To find the 95% confidence interval, we add and subtract the margin of error from the point estimate of the proportion that beat estimates:
CI = 0.5802 ± 0.0944
CI = (0.4858, 0.6746)
Therefore, the 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).
(c) How large a sample is needed if the desired margin of error is 0.05?
To find the sample size needed for a desired margin of error of 0.05, we use the formula:
n* = (z*/ME)² × p×(1-p)
where z* is the z-score corresponding to the desired confidence level (we use 1.96 for a 95% confidence level), ME is the desired margin of error (0.05), and p is an estimate of the proportion (we use the point estimate of 0.5802 for the proportion that beat estimates).
Substituting the values we get:
n* = (1.96/0.05)² × 0.5802×(1-0.5802) = 753.16
Rounding up to the next integer, we get n* = 754. Therefore, a sample size of 754 is needed to achieve a desired margin of error of 0.05.
Learn more about estimate of proportion here,
https://brainly.com/question/29436481
#SPJ1
Joseph bought a T-shirt for $10.30 and another T-shirt for $18.90. what is the total amount spent
Answer:
29.2
Step-by-step explanation:
10.30+18.90=29.2
Answer:
$29.20
Step-by-step explanation:
$10.30
+$18.90
=$29.20
angles of a triangle
Answer:
x=70°
Step-by-step explanation:
angles on straight line add to 180 so...
180-120=60°
angles in triangle add to 180° so...
180°-50°-60°=70°
so x=70°
Find the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1).
Answer:
The standard form of the equation of a circle with center at (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
We are given that the center of the circle is (4, -1), so h = 4 and k = -1. We also know that the circle passes through the point (-4, 1), which means that the distance from the center of the circle to (-4, 1) is the radius of the circle.
The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So the radius of the circle is:
r = sqrt((-4 - 4)^2 + (1 - (-1))^2) = sqrt(100) = 10
Now we can substitute the values of h, k, and r into the standard form equation of a circle:
(x - 4)^2 + (y + 1)^2 = 10^2
Expanding the equation gives:
x^2 - 8x + 16 + y^2 + 2y + 1 = 100
Simplifying and putting the equation in standard form, we get:
x^2 + y^2 - 8x + 2y - 83 = 0
Therefore, the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1) is:
x^2 + y^2 - 8x + 2y - 83 = 0
i need help with this one, thank you
Answer: 288.62
Step-by-step explanation:
10.4^2 + 15.3^2 = 342.25,
c^2 = 342.25
c (hypotenuse of the right triangle & length of rectangle) = 18.5
7(8) + 10.4(15.3) = 288.62
Three pipes in a school building are
leaking. After 30 minutes, pipe A has leaked 3/4 gallon of water. After 45 minutes, pipe B has leaked 1 1/4 gallons of water. After 20 minutes, pipe C has leaked 1/2 gallon of water.
Which sentence is true?
A. Pipe A is leaking at the fastest rate
B. Pipe C is leaking at the slowest rate.
C. Pipe A and C are leaking at the same rate.
D. Pipes A and B are leaking at a faster rate than Pipe C.
Answer: Option C
Step-by-step explanation: To compare the rates at which the pipes are leaking, we can find the amount of water each pipe leaks per minute.
For Pipe A:
3/4 gallon ÷ 30 minutes = 1/40 gallon per minute
For Pipe B:
1 1/4 gallon ÷ 45 minutes = 5/36 gallon per minute
For Pipe C:
1/2 gallon ÷ 20 minutes = 1/40 gallon per minute
Therefore, Pipes A and C are leaking at the same rate, which means option C is true. Option A and D are false, as Pipe B has the fastest leak rate. Option B is false, as both Pipe A and Pipe C are leaking at the same rate.
what is an equation of the line that passes through the points (0,8) and (-6,-2)?
Points are (0,-8) and (-6,-3) Slope m = rise/run = Δy/Δx. [(-3 - (-8)]/[-6 - 0] = 5/-6 = -5/6
y = mx + b Using the (0,-8) point: -8 = 0x + b, so b = -8
The line is y = -5x/6 - 8 or (-5/6)x - 8. You can check via the Desmos Graphing Calculator site
I used the slope-intercept form, but you could also use the point-slope form (y2 - y1) = m(x2 - x1)
A party company is designing a new line of individualized bubbles for various celebrations such as birthday parties, weddings, and anniversaries. The bubbles will be sold in various-sized packs. The individual container of bubbles will be a plastic cylindrical tube with a diameter 2 cm and a height of 8 cm.
How many square centimeters of plastic are needed for one tube of bubbles?
Round your answer to the nearest whole number.
A. 50 cm^2
B. 57 cm^2
C. 63 cm^2
D. 53 cm^2
Answer:
The formula for the surface area of a cylinder is:
SA = 2πr^2 + 2πrh
where r is the radius and h is the height.
Since the diameter of the tube is 2 cm, the radius is 1 cm.
Substituting the given values, we get:
SA = 2π(1^2) + 2π(1)(8)
SA = 2π + 16π
SA = 18π
To find the surface area in square centimeters, we need to multiply by the conversion factor (1 cm)^2/(1 π) = 1 cm^2/3.14.
SA = 18π × (1 cm^2/3.14)
SA ≈ 18 × 0.3185
SA ≈ 5.73 cm^2
Rounding to the nearest whole number, we get:
SA ≈ 6 cm^2
Therefore, the answer is B. 57 cm^2.
Step-by-step explanation:
Create a list of steps, in order, that will solve the following equation.
(x - 5)² = 25
Solution steps:
Add 5 to both sides
Multiply both sides by 5
Square both sides
Take the square root of both
sides
The solutions to the equation (x - 5)² = 25 are x = 10 and x = 0.
Define equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). Each side of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
What is Square?It is a shape with four sides of equal length and four right angles. It is also a number multiplied by itself.
Solve the equation (x - 5)² = 25:
1. Take the square root of both sides of the equation to remove the exponent of 2 on the left side.
√[(x - 5)²] = √25
2. Simplify the left side by removing the exponent of 2 and keeping the absolute value.
|x - 5| = 5
3. Write two separate equations to account for both possible values of x when taking the absolute value.
x - 5 = 5 or x - 5 = -5
4. Solve for x in each equation.
x = 10 or x = 0
So the solutions to the equation (x - 5)² = 25 are x = 10 and x = 0.
Learn more about square root here:
https://brainly.com/question/29286039
#SPJ1
A construction worker throws a water bottle out of the basement to his friend, who did not catch it. The equation below can be used to determine h, the height of the bottle in feet, base on t, the time in seconds since the bottle was thrown. h=-16t^2+56t-24
When is the height of the thrown bottle equal to 0?
The height of the thrown bottle becomes zero at the t = 1/2 that is half a second and at t = 3 seconds
How do you form an equation?An equation is formed by expressing the relationship between two or more mathematical expressions. It can be formed by using mathematical symbols, operations, and variables. Typically, equations are used to solve problems or find unknown quantities by setting up an equation that represents the problem and then manipulating the equation using algebraic operations until the solution is obtained. For example, to solve the equation 2x + 3 = 7, you would use algebraic operations to isolate the variable x on one side of the equation, giving you the solution x = 2.
To find when the height of the thrown bottle is equal to 0, we need to solve the given equation:
h = -16t² + 56t - 24 = 0
Takin -8 common out we get,
-8(2t² - 7t + 3) = 0
Now we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:
-8 = 0 or 2t² - 7t + 3 = 0
But -8 ≠ 0, so we only possible one is,
2t² - 7t + 3 = 0
(2t - 1)(t - 3) = 0
Using the zero product property, we get,
2t - 1 = 0 or t - 3 = 0
Solving for t we get,
t = 1/2 or t = 3
Therefore, the height of the thrown bottle is equal to 0 at t = 1/2 seconds and t = 3 seconds.
To know more about equations visit:
brainly.com/question/29538993
#SPJ1
The height of the thrown bottle becomes zero at the t = 1/2 that is half a second and at t = 3 seconds
How do you form an equation?An equation is formed by expressing the relationship between two or more mathematical expressions. It can be formed by using mathematical symbols, operations, and variables. Typically, equations are used to solve problems or find unknown quantities by setting up an equation that represents the problem and then manipulating the equation using algebraic operations until the solution is obtained. For example, to solve the equation 2x + 3 = 7, you would use algebraic operations to isolate the variable x on one side of the equation, giving you the solution x = 2.
To find when the height of the thrown bottle is equal to 0, we need to solve the given equation:
h = -16t² + 56t - 24 = 0
Takin -8 common out we get,
-8(2t² - 7t + 3) = 0
Now we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:
-8 = 0 or 2t² - 7t + 3 = 0
But -8 ≠ 0, so we only possible one is,
2t² - 7t + 3 = 0
(2t - 1)(t - 3) = 0
Using the zero product property, we get,
2t - 1 = 0 or t - 3 = 0
Solving for t we get,
t = 1/2 or t = 3
Therefore, the height of the thrown bottle is equal to 0 at t = 1/2 seconds and t = 3 seconds.
To know more about equations visit:
brainly.com/question/29538993
#SPJ1
Janelys has a bag of candy full of 15 strawberry chews and 5 cherry chews that
she eats one at a time. Which word or phrase describes the probability that
she reaches in without looking and pulls out a strawberry chew?
The word that describes the probability that Janelys reaches in without looking and pulls out a strawberry chew is "the probability of selecting a strawberry chew randomly from the bag".
Calculating the phrase of the probabilityThe word or phrase that describes the probability of pulling out a strawberry chew without looking is "the probability of selecting a strawberry chew at random" or "the probability of picking a strawberry chew by chance".
This probability is calculated by dividing the number of strawberry chews in the bag by the total number of chews in the bag, since each chew is equally likely to be selected.
In this case, there are 15 strawberry chews and 5 cherry chews, so the probability of selecting a strawberry chew at random is 15/(15+5) or 3/4, which is approximately 0.75 or 75%.
Read more about probability at
https://brainly.com/question/251701
#SPJ1
Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
- The distance from their home to Yellowstone National Park is 1,701 miles.
- On average the RV gets 10.5 miles per gallon.
- On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
A. $1,166.40
B. $2,480.63
C. $583.20
D. $64,297.80
Answer:
The answer is A. $1,166.40
Step-by-step explanation:
The figure below shows the transformation A to become rectangle B.
Which steps describe the transformation shown in figure?
A. a dilation with a factor of 1 1/2 followed by a translation to the left
B. a dilation with a factor of 2/3 followed by a translation to the left
C. a translation with a factor of 1 1/2 followed by a dilation to the left
D. a translation with a factor of 2/3 followed by a dilation to the left
Answer:
Step-by-step explanation:
A is correct
A particle moves along the x-axis so that at any time t >= 0 its position is given by x(t)= 1/2(a - t)^2, where a is a positive constant. For what values of t is the particle moving to the right?
If will be positive if:
-24(a-t) > 0
-(a-t) > 0
-a + t > 0
t > a
How to solveUsing derivatives, it is found that the particle is moving to the right for t > a , that is, values of t in the interval (a, ∞)
A particle is moving to the right if its velocity is positive.
The position of the particle is given by:
x(t) = 12(a -t)^2
The velocity is the derivative of the position, hence:
v(t) = -24(a-t)
If will be positive if:
-24(a-t) > 0
-(a-t) > 0
-a + t > 0
t > a
Read more about derivatives here:
https://brainly.com/question/28376218
#SPJ1
csc²x+cot²x/csc⁴x-cot⁴x=1
By putting the value it proved that csc²x+cot²x/csc⁴x-cot⁴x=1
What is Trigonometry mean ?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles.There are six type of Trigonometry
According to question,
we have prove that
(csc²x + cot²x) / (csc⁴x - cot⁴x) = 1
Now by manipulating the left-hand side of the equation using trigonometric identities.
Then, we can simplify the denominator using the identity:
a² - b² = (a + b)(a - b)
In this case we get , a = csc²x and b = cot²x, so:
csc⁴x - cot⁴x = (csc²x + cot²x)(csc²x - cot²x)
By substituting this expression into the given equation, we get:
(csc²x + cot²x) / [(csc²x + cot²x)(csc²x - cot²x)] = 1
By solving the numerator, we get:
1 / (csc²x - cot²x) = 1
Now, we can use the identity:
csc²x - cot²x = 1 / sin²x - cos²x / sin²x
= (1 - cos²x) / sin²x
= sin²x / sin²x
= 1
Substituting this expression back into the equation, we get:
1 / 1 = 1
Hence, we have proved that:
(csc²x + cot²x) / (csc⁴x - cot⁴x) = 1.
Learn more about Types of Trigonometry here
https://brainly.com/question/30283045
#SPJ1
61) If an ellipse has vertices at (-7.0). (7.0), (0.4), and (0-4), what is its domain? What is its range?
The domain of the ellipse is [-7, 7].
The range of the ellipse is [-4, 4].
What is a domain?In mathematics, the domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all values of the independent variable (usually denoted by x) for which the function produces a valid output (usually denoted by y).
What is the range?In mathematics, the range of a function is the set of all possible output values that the function can produce for a given set of input values. In other words, it is the set of all values of the dependent variable (usually denoted by y) that can be obtained from the function.
According to the given informationTo find the domain and range of an ellipse, we need to identify the minimum and maximum x-coordinates and y-coordinates of the points on the ellipse.
The center of the ellipse is the midpoint of its major axis, which is the line segment connecting its vertices (-7,0) and (7,0). The midpoint is ((-7+7)/2, (0+0)/2), or (0,0). This means the center of the ellipse is at (0,0).
The semi-major axis is the distance from the center of the ellipse to one of its vertices, which is 7. The semi-minor axis is the distance from the center of the ellipse to one of its co-vertices, which is 4.
So, the equation of the ellipse can be written in standard form as:
(x - 0)²/7² + (y - 0)²/4² = 1
Simplifying, we get:
x²/49 + y²/16 = 1
To find the domain and range, we need to consider the x-coordinates and y-coordinates separately.
For the x-coordinates, we can rearrange the equation as:
x² = 49 - 49y²/16
This tells us that the minimum and maximum values of x occur when y is at its extremes, which are -4 and 4. Substituting these values, we get:
x² = 0 and x² = 49
Taking the square root, we get:
x = 0 and x = ±7
So, the domain of the ellipse is [-7, 7].
For the y-coordinates, we can rearrange the equation as:
y² = 16 - 16x²/49
This tells us that the minimum and maximum values of y occur when x is at its extremes, which are -7 and 7. Substituting these values, we get:
y² = 0 and y² = 16
Taking the square root, we get:
y = 0 and y = ±4
So, the range of the ellipse is [-4, 4].
Therefore, the domain of the ellipse is [-7, 7], and the range of the ellipse is [-4, 4].
To know more about the domain and range visit:
brainly.com/question/28135761
#SPJ1
When Jace runs the 400 meter dash, his finishing times are normally distributed with a mean of 87 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 95% of his finishing times in the 400 meter race.
The middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.
Approximately 68% of the data falls within 1 standard deviation of the mean (i.e., between μ - σ and μ + σ).
Approximately 95% of the data falls within 2 standard deviations of the mean (i.e., between μ - 2σ and μ + 2σ).
Approximately 99.7% of the data falls within 3 standard deviations of the mean (i.e., between μ - 3σ and μ + 3σ).
We want to find the interval of times that represents the middle 95% of Jace's finishing times, which means we want to find the interval that falls between μ - 2σ and μ + 2σ.
Substituting the given values, we get:
μ - 2σ = 87 - 2(2.5) = 82
μ + 2σ = 87 + 2(2.5) = 92
Therefore, the middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ1