A container of low fat yogurt has 13 grams of protein, which is 26% of the
daily amount. What is the recommended daily amount of
recommended
protein?

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

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Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

Answer:

6cm

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

because it has 3 parts. tri.

Null hypothesis: The mean number of points scored by the taller team is not significantly different from the population mean of 72.

Alternative hypothesis: The mean number of points scored by the taller team is significantly greater than the population mean of 72.

Since the population variance is unknown, we will use a t-test. The degrees of freedom for this test will be 9 (n-1), where n is the sample size of the taller team (10).

Using an alpha level of 0.05 and 9 degrees of freedom, the critical t-value is 1.833.

To calculate the test statistic, we first need to find the sample mean and standard deviation of the taller team's scores. The sample mean is 82, and the sample standard deviation is 9.89. Using these values, we can calculate the t-value:

t = (82-72) / (9.89 / sqrt(10)) = 3.19

Since the calculated t-value (3.19) is greater than the critical t-value (1.833), we reject the null hypothesis and conclude that there is a significant difference between the mean number of points scored by the taller team and the population mean of 72. The coach can therefore conclude that having a taller team does result in a greater number of points scored.

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(a) The population density in people per square mile is 6.7million (b) the population density in animals per square mile is 1.53million

Population density is defined as a measurement of population per unit land arear.

The given parameters are:

Length and Width of the land:

L=590 miles

W=250 miles

Area of land= Length *width

Area =590*250

Area=147500 m²

Population of people = 990,000 people

Population density = \(\frac{Number of people}{Land area}\)

Population density=\(\frac{990000}{147500}\)

Population Density=6.71million

(b) Population density for animals

population of animals=225,000

Population density = \(\frac{Number of people}{Land area}\)

Population density=225000/147500

population density of animals =1.53million

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Answer:

Gracias por favor

Step-by-step explanation:

Answer:

√52

Step-by-step explanation:

6^2 = 36

4^2 = 16

   a.       b

√36 + √16 = c

c = √52

Step-by-step explanation:

2

\(2 \sqrt{13 } \)

Answer:

AUB=(1,2,5,6,7,8,12,13,15, 18,20)

AnB={1,2,6,7,8}

Answer:

Hello,

Step-by-step explanation:

\(A =\{1,2,6,7,8,13,15\} \\B= \{1,2,5,6,8,12,15, 18, 20\}\\\\A\ \bigcup\ B=\{1,2,5,6,7,8,12,13,15,18,20\}\\\\A\ \bigcap\ B=\{ 1,2,6,8,15\}\\\)

Answer:

B

Step-by-step explanation:

i took da test

The value of x is 1.6 or 8/5 which makes the order 8/7, 1 2/5, x, 1 2/3, and 2 from least to greatest option (B) 8/5 is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

These fractions are in order from least to greatest:

8/7, 1 2/5, x, 1 2/3, 2

As we know the number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, 1/2, 4/5, 3/7, etc are the numbers.

The fractions number are: 8/7, 1 2/5, x, 1 2/3, 2

The fraction can be written as a decimal:

8/7, 7/5, x, 5/3, 2

or

1.14, 1.4, x, 1.66, 2,

x will be 8/5 = 1.6

Thus, the value of x is 1.6 or 8/5 which makes the order 8/7, 1 2/5, x, 1 2/3, and 2 from least to greatest option (B) 8/5 is correct.

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Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

.66 are in each bag.

Step-by-step explanation:

14/3 = 4.66666666667

then you grab the answer for 14/3 and divide by 7

this in turn will get you .66 repeated

so .66 of a pound is in each 7 bags.

Answer:

  (x, y) = {(-2, -3), (2, 5)}

Step-by-step explanation:

You want to solve the system of equations y=x²+2x-3 and y=2x+1.

The two expressions for y can be equated, and the resulting equation put in standard form.

  x² +2x -3 = 2x +1

  x² -4 = 0 . . . . . . . . . . subtract (2x+1)

  (x -2)(x +2) = 0 . . . . . factor

Values of x that make the factors zero are 2 and -2.

Corresponding values of y are ...

  y = 2x +1 = 2(2) +1 = 5

  y = 2(-2) +1 = -3

Solutions are ...

Answer:

20%

Step-by-step explanation:

If we think of the circle as 1, and each piece 1/5, and since we know that 1/5 = 20%, we can conclude that each piece takes up 20% of the circle.

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

A graph of the resulting triangle after a rotation of -180° about the origin is shown below.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of triangle TOP 180° counterclockwise or -180° about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point T (6, 0)  →  Coordinates of point T' = (-6, 0)

Coordinates of point O (-2, -5)  →  Coordinates of point O' = (2, 5)

Coordinates of point P (-2, 5)  →  Coordinates of point P' = (2, -5).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

9514 1404 393

Answer:

   4x^2 +5x -6

Step-by-step explanation:

The remaining empty space is the difference between the original amount of empty space and the volume that was filled.

  (8x^2 +2x -4) -(4x^2 -3x +2) = 8x^2 +2x -4 -4x^2 +3x -2

  = (8 -4)x^2 +(2 +3)x +(-4 -2)

  = 4x^2 +5x -6

The jar could hold 4x^2 +5x -6 more cubic inches.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

-1.031 m/s or  \(\frac{-\sqrt{17} }{4}\)

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is \(\frac{dy}{dt}\) = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =  \(\frac{dx}{dt}\) = ?

for x = 4

Applying Pythagorean Theorem we have

\(1^{2} +x^{2} =y^{2}\)    .... equ 1

solving, where x = 4, we have

\(1^{2} +4^{2} =y^{2}\)

\(y^{2} = 17\)

\(y = \sqrt{17}\)

Differentiating equ 1 implicitly with respect to t, we have

\(2x\frac{dx}{dt} = 2y\frac{dy}{dt}\)

substituting values of

x = 4

y = \(\sqrt{17}\)

\(\frac{dy}{dt}\) = -1

into the equation, we get

\(2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)\)

\(\frac{dx}{dt} = \frac{-\sqrt{17} }{4}\) = -1.031 m/s

To determine the magnitude and direction of the resultant force applied at b, we can use vector addition of the tensions in cables AB and BC. Let's assume that the positive x-direction is to the right, and the positive y-direction is upwards.

We can represent the tension in cable AB as a vector T1 = 4500 lb in the direction of AB, and the tension in cable BC as a vector T2 = 2000 lb in the direction of BC.

The magnitude of the resultant force applied at b is given by:

R = √(T1^2 + T2^2) = √(4500^2 + 2000^2) = 5000 lb

The direction of the resultant force can be found using the arctangent function:

θ = tan^-1 (T2/T1) = tan^-1 (2000/4500) = approximately 39.2 degrees

Therefore, the magnitude and direction of the resultant force applied at b are 5000 lb and 39.2 degrees, respectively.

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Answer:

the 2nd one

Step-by-step explanation:

i took the test

The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

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The third quartile of the data set is 20, and option C  is correct.

A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it. Data can be arranged for our study in the form of graphs, charts, or tables.

Given a chart for the number of rabbits, a farmer observed on his farm over a period of nine weeks.

week         1     2    3     4       5     6     7      8      9

rabbits       2    3     5     7     11    15     18    22    27

the formula of quartiles is

Lower Quartile (Q1) = (N+1) * 1 / 4

Middle Quartile (Q2) = (N+1) * 2 / 4

Upper Quartile (Q3 )= (N+1) * 3 / 4

here N = 9

third quartile(Q3) = (N+1) * 3 / 4

third quartile(Q3) = (9 + 1)3/4

third quartile(Q3) = 7.5 term

third quartile(Q3) is the term between 7th and 8th week

third quartile(Q3) = (7th term + 8th term)/2

7th term = 18

8th term = 22

third quartile(Q3) = (18 + 22)/2

third quartile(Q3) = 20

Hence option C is correct.

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Answer:

13, 11, 4, 16, 6, 22

Step-by-step explanation:

Let the second digit be x and the last digit be y

Given:

The mean of the data is the average. The average can be calculated by determining the sum of the terms and dividing it by the total digits.

\(\implies \text{Mean of data:} \ \dfrac{13 + x + 4 + 16 + 6 + y}{6} = 12\)

Let us substitute the value of y (2x) in the data.

\(\implies \dfrac{13 + x + 4 + 16 + 6 + 2x}{6} = 12\)

Now, add all the terms in the data and simplify.

\(\implies \dfrac{39 + x +2x}{6} = 12\)

\(\implies \dfrac{39 + 3x}{6} = 12\)

Distribute the denominators and simplify.

\(\implies \dfrac{39}{6} + \dfrac{3x}{6} = 12\)

\(\implies \dfrac{13}{2} + \dfrac{x}{2} = 12\)

\(\implies 6.5 + \dfrac{x}{2} = 12\)

Subtract 6.5 both sides and simplify.

\(\implies 6.5 + \dfrac{x}{2} - 6.5 = 12 - 6.5\)

\(\implies \dfrac{x}{2} = 5.5\)

Use cross multiplication and simplify.

\(\implies x= 5.5 \times 2\)

\(\implies x= 11\)

To determine the value of "y", simply substitute the value of "x" into the expression that represents the value of "y".

\(\implies y = 2x\)

\(\implies y = 2(11)\)

\(\implies y = 22\)

When the x and y values are substituted in the data, we get;

Therefore, the data is 13, 11, 4, 16, 6, 22.

Answer: The second option would be the answer

Step-by-step explanation:

Factoring the number is just listing all the whole numbers it can be divided by, and in this case it includes the variable. 16a is dividable by 1, 2, 4, 8, 16, and a; since 16a / a = 16. Apply this to 18b, and 1, 2, 3, 6, 9, 18, and b.

Student 1's answer is the correct answer: (x+2)(x+12).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Expression is a mathematical phrase which combines, numbers, variables and operators to show the value of something. An equation is a mathematical statement wherein two expressions are set equal to each other.

Student 2's answer, 3(x+2)(x+12), is incorrect because they multiplied the factors by 3, which is not necessary and changes the value of the expression.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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The answer choice which correctly draws a comparison between the end behaviors of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.

As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).

It therefore follows that as; x reduces (approaches -∞), the y value increases.

And, as x -increases (approaches +∞), the y-value decreases.

For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).

Consequently, as x reduces (approaches -∞), the y- values decrease.

And, as x increases (approaches +∞), the y-values decrease.

Ultimately, the two functions in discuss can be concluded to have; Choice C.

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Answer:

♥Love You♥ DUDE

Step-by-step explanation:

Answer:

The diagonals are perpendicular.

The diagonals are congruent to each other.

The diagonals bisect the vertex angles.

The statements that are true of squares include:

It should be noted that a square simply means a shape that has four sides equal. The angles are also 360° since they're 90° each.

In squares, the diagonals are perpendicular and the diagonals are congruent to each other.

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True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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