To find the inverse of a function, you can follow these steps:
Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.
Solve the equation for y. In this case, you would get:
x = √y + 8
y = x - 8
Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:
f^-1(x) = x - 8
This is the inverse function of y = √x + 8.
Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.
the american veterinary association claims.. what is the probabilty that your anual cost will ve within 5 of the mean
The probability that the annual cost will be 5 of the mean is 0.0912.
How does probability analysis work?A method used by risk managers to predict upcoming events, like accidental and commercial losses. In order to determine a probability distribution that can be applied to forecast future losses, this procedure involves reviewing historical loss data.
X = Annual cost of medical care for dogs.
X~ Normal (μ = 200, σ = 60)
Sample size n = 16
We know that the sample mean Xbar has a normal distribution with mean = μ and sd = σ/√n
Xbar ~ Normal (μ’ = 200, σ’ = 60/√16 = 15)
Required probability -
P[Average cost of medical care for 16 sampled dogs is > 220]
= P[Xbar > 220]
= P[(Xbar-μ’)/σ’ > (220-200)/15]
= P[Z > 1.3333], Z is a standard normal variable.
= 1 - P[Z < 1.3333]
= 1 - 0.9087, from standard normal table.
= 0.0912
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The complete question is:
A veterinary association claims that the annual cost of medical care for dogs averages $200 with a standard deviation of $60, and for cats averages $240 with a standard deviation of $70. Assume the costs follow a normal distribution. What is the probability the average annual cost of medical care for 16 randomly chosen dogs is greater than $220.
Do you remember all 4 ways to solve a quadratic equation?
The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.
what is quadratic equation ?A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.
given
Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.
Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)
Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.
The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.
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Find the distance between point k and point L.
The distance between points L and K is 4 units.
What is the distance formula between two points?The distance formula between two points (x₁, y₁) and (x₂, y₂) is gien by,
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].
Given, Are two points L and K.
The coordinate points of L(- 2, 6) and K(- 2, 2).
Therefore, The distance between points L and K is,
[tex]|LK| = \sqrt{(- 2 + 2)^2 + (2 - 6)^2}[/tex].
[tex]|LK| = \sqrt{16}[/tex].
[tex]|LK| = 4[/tex].
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16 quarts of soil are used to completely fill 5 flower pots. If each pot holds the same amount of soil, how many quarts will each pot hold?
How many quarts of soil are used to fill 3 flower pots?
9.6 quarts
First, find the unit rate, which is that when you divide 16 and 5 and you will get 3.2, then you multiply it with 3 for the 3 flower pots, and that's how you end up with the answer
The distance that an object falls varies directly as the square of the time the object is in motion. If an object falls for 3 seconds, it will fall 144. 9 feet. To estimate the height of a cliff, a person drops a stone at the edge of the cliff and measures how long it takes for the stone to reach the base. If it takes 3. 5 seconds, what is the height of the cliff?
As per the given equation the height of the cliff is 196.225 feet.
How to calculate the distance of an object in motion?We know that the distance an object falls varies directly as the square of the time it is in motion, meaning that the distance is proportional to the square of the time. If we let d be the distance fallen and t be the time, we can write this relationship as [tex]d = kt^2[/tex] for some constant of proportionality k.
We also know that when an object falls for 3 seconds, it falls 144.9 feet. We can use this information to find the value of k:
[tex]144.9 = k(3^2)[/tex]
k = 16.1
Now that we know the value of k, we can use it to find the distance fallen when the time is 3.5 seconds:
[tex]d = kt^2\\d = 16.1(3.5^2)\\d = 16.1(12.25)\\d = 196.225[/tex]
So, the height of the cliff is 196.225 feet.
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Find the Average Rate of Change of the table below for the interval 2 < x < 5
The AROC is 3 for the interval 2 < x < 5, which is the correct answer that would be option (A).
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
The table is given in the question as follows:
x y
0 -2
1 -3
2 0
3 3
4 6
5 9
We have to determine the Average Rate of Change in the table below for the interval 2 < x < 5
As per the given table, the required AROC would be as:
⇒ (9 - 3)/(5-3)
⇒ 6/2
Apply the division operation, and we get
⇒ 3
Hence, the correct answer would be option (A).
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What are the properties of addition and subtraction?
Answer:
Step-by-step explanation:
In addition and subtraction, the identity is 0. In multiplication and division, the identity is 1. That means that if 0 is added to or subtracted from n, then n remains the same. Also, if n is multiplied or divided by 1, then n remains the same
ORRRRRRRRR
Five Properties of Addition
Closure property of Addition.
Commutative property of Addition.
Associative property of Addition.
Additive identity property of Addition.
Additive inverse property of Addition.
The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
8:20 =
Ponies
3
Write the ratio of ponies to goats.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio,
possible.
T
123 f() ∞*E ABC αβγ
Rabbits
8
21
7
8
O
1.
Sheep
6
a
DG
Answer: 1:1
Step-by-step explanation:
We will write a ratio of ponies to goats;
ponies : goats
3 : 3
Next, 3:3 can be simplified to 1:1. This gives us our fully reduced ratio.
Q4 ABC is an isosceles triangle with AB=AC and AD is one of its altitudes. i) State the three pairs of equal pairs in ADB and ADC.
ii) Is ADB = ADC? Why or why not?
iii) Is B=C? Why or why not?
iv) Is BD=CD? Why or why not?
Answer:
d
Step-by-step explanation:
Brad has a cylindrical barrel with radius 10 inches and height 15 inches. He wants to fill it from a well, using a bucket in the shape of a hemisphere with a radius of 10 inches. How many trips must Brad make to the well in order to fill the barrel
He needs to make 1 and a half trips to the well to fill the barrel which has a height of 15 inches and radius 10 inches.
What are cuboid?A cuboid is a three-dimensional geometric shape that has six rectangular faces, three of which meet at each corner. A cuboid has three dimensions: length, width, and height. It is also commonly referred to as a rectangular prism. The formula for the volume of cuboid is [tex]V = l *w * h[/tex], where l is the length, w is the width, and h is the height. The formula for the surface area of a cuboid is [tex]2lw + 2lh + 2wh[/tex]. Cuboids are used in everyday life such as building blocks and package boxes.
The cylindrical barrel has a volume of [tex]\pi * r^2 * h = \pi * 10^2 * 15 = 1500\pi[/tex] cubic inches.
The hemisphere has a volume of [tex](2/3) * \pi * r^3 = (2/3) * \pi * 10^3 = (2000/3)\pi[/tex] cubic inches.
So, to fill the barrel, Brad must make [tex]1500\pi / (2000/3)\pi = 3/2 = 1.5[/tex] trips to the well.
In other words, he needs to make 1 and a half trips to the well to fill the barrel.
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Convert one three fifths to a percent find that percent of 30 Divide your answer by 25% of 16
Answer:
40%
Step-by-step explanation:
1 and 3/5 as a fraction is 8/5 which as a percent is 160%.
25% of 16 is 4
160%/4 = 40%
1. The population average fuel efficiency of U.S. light vehicles for 2005 was 21 mpg. If the standard deviation of the population was 2.9 and the gas ratings were normally distributed, what is the probability that the mean for a random sample of 25 light vehicles is under 20 mpg
The probability that the mean mpg for a random sample of 25 light vehicles is 0.042341
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
z = (x-μ)/σ/n, where
x is the raw score = 20 mpg
μ is the population mean = 21 mpg
σ is the population standard deviation = 2.9
n = random number of samples [tex]x < 20[/tex]
[tex]= z = 20 - 21/2.9/\sqrt{25} \\= z = -1/2.9/5\\= z = -1.72414\\[/tex]
P-value from Z-Table:
[tex]P(x < 20) = 0.042341[/tex]
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hello please help i’ll give brainliest
Answer:
ocean crust is thinner
Step-by-step explanation:
Answer:
Oceanic crust is thinner
hope this helped
Step-by-step explanation:
How do i convert £10 to dollar? and what calculation do i ue
(it' on exchange rate)
We convert 10 pounds to Dollars and get 12.2 United states Dollars.
What does currency convert and exchange rate?Exchange rate is the rate at which one currency can be exchanged to another currency. The rate represents the relative value of one currency against the currency from another country. Currency conversion means convert one currency to another at an exchange rate.
How do we convert 10-pound sterling to dollar?We can convert pound to dollar by using currency exchange rate determined by the world market. The exchange rate is vary depending on the current situation of two country in which currency is converted between. The rate may be differed from one day to another.
1 pound sterling = 1.22 United States Dollar
10-pound sterling = 12.2 US Dollars
1 pound sterling = 1.76 Australian Dollar
10-pound sterling = 17.6 Australian Dollars
1 pound sterling = 1.64 Canadian Dollar
10-pound sterling = 16.4 Canadian Dollars
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When the solution of x2 - 9x - 6 is expressed as 9
vr, what is the value of r?
x= -bb2 - 4ac
2a
06
42.
57
105
The value of r is 105 in this equation.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
In the quadratic formula, √r =[tex]\sqrt{b^{2}-4ac }[/tex]
Where a = 1, b = -9, and c = -6.
So √r = √(-9)² - 4(1)(-6)
√r = √81 -4(-6)
√r = √81 + 24
√r = √105
Hence, the value of r is 105 in this equation.
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Please help I will give 15 points
Answer:
THE FIRST ONE
Step-by-step explanation:
In a circle with radius 5.1, an angle intercepts an arc of length 30.3. Find the angle in
radians to the nearest 10th.
Answer:
5.9 radian
Step-by-step explanation:
Applying,
S = 2πrФ/360°................. Equation 1
Where s = length of the arc, r = radius, Ф = angle.
make Ф the subject of the equation
Ф = 360S/(2πr)........... Equation 2
From the question,
Given: S = 30.3, r = 5.1
Constant: π = 3.14
Substitute into equation 2
Ф = (360×30.3)/(2×5.1×3.14)
Ф = 340.58°
Ф = (340.58×2×3.14)/360
Ф = 5.9 radian
the question in the picture below
Answer:
answer is option A
Step-by-step explanation:
2x+6≤10or2x+8>20
2x≤10-6 or 2x>12
x≤4/2 or x>2/12
x≤2 or x>6
On a negatively skewed curve, which is true?
a.The median is lower than the mode which is lower than the mean. b.The mean, median, and mode are the same. c.The mean is lower than the median which is lower than the mode. d.The mode is lower than the mean which is lower than the median. e.The mean is lower than the mode which is lower than the median.
The mean is lower than the mode which is lower than the median.
What is skewed?A skewed curve is a type of statistical distribution in which the data is unevenly distributed. It is often referred to as an asymmetric distribution, meaning that the two halves of the curve look different. Skewed curves can be either positively or negatively skewed, depending on which direction the data points are shifted. Positively skewed curves tend to have a long tail to the right, while negatively skewed curves have a long tail to the left. This type of distribution is commonly seen in real-world data, such as income or wealth distributions.
A negatively skewed curve is characterized by a tail on the negative side of the graph. This means that the data points have a higher probability of being lower than the mean. As such, the mean is lower than the mode, which is lower than the median. The mean is the arithmetic average of all of the data points, the mode is the most frequent value, and the median is the midpoint of the data points.
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Jak starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2.1% interest, compounded annually. What is the future value of the investment, rounded to the nearest dollar, when jak is ready to purchase the vacation home?
Answer:
[tex]P=\$40840[/tex]
Step-by-step explanation:[tex]I=840[/tex]
From the question we are told that:
Time interval [tex]t=50-40=>10years[/tex]
Annual contribution [tex]X= 4*1000=>\$4000[/tex]
Annual interest rate [tex]r=2.1\%[/tex]
Generally the 10 years interest I is mathematically given by
[tex]I=X*t*r[/tex]
[tex]I=4000*0.021*10[/tex]
[tex]I=840[/tex]
Generally the equation for the future value of the investment [tex]P[/tex] is mathematically given by
[tex]P=X*t+840[/tex]
[tex]P=(4000*10)+840[/tex]
[tex]P=\$40840[/tex]
Find the value of x.
x+16
9
Answer:
x = - 7
Step-by-step explanation:
given that the 3 angles in the triangle are congruent, then the triangle is equilateral with the 3 sides congruent , then
x + 16 = 9 ( subtract 16 from both sides )
x = - 7
Answer:
x=-7
Step-by-step explanation:
The triangles sides are all the same in length, therefore, you need all the sides to be equal to 9.
-12+16=4 This addition problem does not equal to 9 so it is not correct.
-7+16=9 This is correct because -7+16 or 16-7 = 9.
-9+16=7 This addition problem does not equal to 9 so it is not correct.
-11+16=5 This addition problem does not equal to 9 so it is not correct.
So, x = -7.
please help me!!10points
Answer:
167 feet
Step-by-step explanation:
Please see the attached image.
(90-42)°=48°
The tangent of an angle is the opposite side relative to that angle divided by the adjacent side.
tan(48°)=x/150
x=tan(48°)*150
x≈167
Answer: 167 feet
b) Sita had.50 sweets. She ate 10 sweets and gave 8 sweets to her brother. If she divided the rest of them among her 8 friends equally, how many sweets would each friend get?
Answer:
4 sweets each
Step-by-step explanation:
50 sweets to begin with and eats 10 , so 50 - 10 = 40 left
she then gives 8 to her brother , leaving 40 - 8 = 32 sweets
she then shares 32 equally among her 8 friends , so
32 ÷ 8 = 4
that is each friend got 4 sweets
Work out the area of this shape. Give your answer
in cm².
4 cm
4 cm
10 cm
Answer:
48cm^2
Step-by-step explanation:
Rectangle=LxW
Triangle=bh/2
Rectangle: 10x4=40cm^2
Triangle: 4x4=16/2=8cm^2
40+8=48cm^2
Hope this helps :)
he cost per pound of chicken is $2. Each serving of chicken is about 4 oz. What will be the portion cost of the chicken
The unit price of the portion of the chicken will be $0.50.
To find the portion cost of the chicken, we need to know how much it costs per ounce, and then multiply that by the number of ounces in a serving.
We can begin by calculating the cost per ounce of chicken by dividing the cost per pound by the number of ounces in a pound:
$2 (cost per pound) ÷ 16 (ounces per pound) = $0.125 (cost per ounce)
Now that we know the cost per ounce, we can find the portion cost of the chicken by multiplying it by the number of ounces in a serving:
$0.125 (cost per ounce) × 4 (ounces per serving) = $0.50
So the portion cost of the chicken is $0.50 . So the answer is
C. $0.50.
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The complete question is-
The cost per pound of chicken is $2. Each serving of chicken is about 4 oz. What will be the portion cost of the chicken?
A. $0.75
B. $2
C. $0.50
D. $0.60
E. $1
Jaylen has a fun-size bag SweetTarts. Inside the bag are 4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts. What is the probability of drawing a yellow SweetTart three time in a row if each SweetTart selected is eaten before the next SweetTart is drawn?
The probability of picking a yellow sweet tart three times in a row is 0
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, There are 4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts. P(yellow ball three times in a row) = 2/12 ×1/11 ×0/10
= 0
Hence, The probability of picking a yellow sweet tart three times in a row is 0
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How I find a area of triangle when 3 equation of sides are given?
The area of a triangle when three side lengths are calculated by Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c)
To calculate the area of a triangle when three side lengths are given, we can use Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c) where s is half the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.
To calculate the area of the triangle given three side lengths, we first need to calculate the perimeter (p) of the triangle. The formula for the perimeter is p=a+b+c.
Then, use this formula to calculate s, which is half the perimeter.
s = p/2
Once s is calculated, plug it into Heron's Formula to calculate the area of the triangle.
Area = √s(s-a)(s-b)(s-c)
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The piggy bank in the video was filled with pennies and
quarters worth a total of $62. 0.
What are three possible combinations of pennies and
quarters that are worth $62. 00?
Enter your combinations in the table.
Number of Pennies
Number of Quarters
I
The three combinations of pennies and quarters are:
A. 1,560 Pennies and 124 Quarters
B. 2,600 Pennies and 49 Quarters
C. 3,120 Pennies and 24 Quarters
The total value of the pennies and quarters is $62.00. This can be achieved with either 1,560 pennies and 124 quarters (1,560 x 0.01 + 124 x 0.25 = 62.00), 2,600 pennies and 49 quarters (2,600 x 0.01 + 49 x 0.25 = 62.00) or 3,120 pennies and 24 quarters (3,120 x 0.01 + 24 x 0.25 = 62.00).
To find the combinations of pennies and quarters that are worth $62.00, begin by finding the number of pennies that equal $
62.00. 62.00/0.01 = 6,200 pennies.
Next, subtract the value of the pennies from the total to find the value of the quarters.
62.00 - (6,200 x 0.01) = 24.00.
Divide the value of the quarters by 0.25 to find the number of quarters. 24.00/0.25 = 96 quarters.
To arrive at the three combinations
, 1,560 pennies and 124 quarters
(1,560 + 96 = 1,656, 1,656 x 0.01 + 124 x 0.25 = 62.00),
2,600 pennies and 49 quarters
(2,600 + 49 = 2,649, 2,649 x 0.01 + 49 x 0.25 = 62.00)
and
3,120 pennies and 24 quarters
(3,120 + 24 = 3,144, 3,144 x 0.01 + 24 x 0.25 = 62.00).
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What is dual expression?
The Dual of Boolean Expression is defined as an expression that is obtained by interchanging the addition and multiplication and interchanging the 0's and 1's .
What is a Boolean Expression ?
The Boolean Expression is defined as an logical statement which results in the Boolean value which can either be True or False.
Sometimes, the synonyms is used to express statement such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’. and also, 1 and 0 are used for digital circuits for True , False .
If in the Boolean expression , the addition and multiplication are interchanged and the binary 0 and 1 are also interchanged then the resulting expression will be called as a Dual Of Boolean Expression .
The given question is incomplete , the complete question is
What is Dual Boolean Expression ?
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Jeris Shoppe marks up every item 75% over the wholesome price. If a sweater costs $16.00 from the wholesaler, how much will the sweater retail for at Jeris?
Answer:
$28
Step-by-step explanation:
175%*16.00 = 175/100 * 16.00
Put it int he calculator to get 28 dollars