According to the statistical Abstract of the United State, the mean consumption of fruits in 2003 was 98.4 pounds. A dietician believes more people are becoming health conscious and that fruit consumption has risen since then. A survey of randomly selected 125 people revealed an average fruit consumption of 102.1 pounds with a standard deviation of 9 pounds. 6. The null and alternate hypotheses are:

When x is a uniformly distributed random variable on [0,1], it divides the interval [0,1] into two subintervals: [0,x] and [x,1]. This division exhibits symmetry, as explained in the following paragraphs.

Consider a uniformly distributed random variable x on the interval [0,1]. The probability density function of x is constant within this interval. When x takes a particular value, it acts as a dividing point that splits [0,1] into two subintervals.

The first subinterval, [0,x], represents all the values less than or equal to x. Since x is randomly distributed, any value within [0,1] is equally likely to be chosen. Therefore, the probability of x falling within the subinterval [0,x] is equal to the length of [0,x] divided by the length of [0,1]. This probability is simply x.

By symmetry, the second subinterval, [x,1], represents all the values greater than x. The probability of x falling within the subinterval [x,1] can be calculated as the length of [x,1] divided by the length of [0,1], which is equal to 1 - x.

The symmetry arises because the probability of x falling within [0,x] is the same as the probability of x falling within [x,1]. This symmetry is a consequence of the uniform distribution of x on the interval [0,1].

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Answer:

♡ hi there! madeline here. ♡

- your answer is 10001

also, since I answered first, can I get the brainliest?

thank you, have a great day sandra!

✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧

Step-by-step explanation:

Calculating the cost of 4.25 kilogram(kg) is £2.38, by multiplying it by 4.25 kg by 1 kg.

Costs are the expenses incurred in the manufacture, marketing, or preparation of a good or asset for regular use. In other terms, it's the cost incurred to produce a good, buy inventories, sell goods, or prepare equipment for use in a commercial activity.

Given,

2.5 kg cost  £1.40 i.e,

2.5 kg = £1.40

For 1 kg= \(\frac{1.40}{2.5}\)

= £0.56

To find the cost of 4.25 kg:

Then,

1 kg = £0.56

4.25 kg = 0.56 x 4.25

= £2.38

£2.38 is the cost of 4.25kg after calculating it.

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Answer:

\((\frac{12}{-4n^{2}})\)

Step-by-step explanation:

\((\frac{3}{-2n})(\frac{4}{2n})=(\frac{3*4}{-2n*2n})=(\frac{12}{-4n^{2}})\)

Answer:

\( -\dfrac{3}{n^2} \)

Step-by-step explanation:

\( \dfrac{3}{-2n} \times \dfrac{4}{+2n} = \)

\( = \dfrac{3 \times 4}{-2n \times 2n} \)

\( = \dfrac{12}{-4n^2} \)

\( = -\dfrac{3}{n^2} \)

Answer:

V = 4.187 ft³

Step-by-step explanation:

Volume of sphere is given by the equation:

\(V=\frac{4}{3}\pi r^3\)

you're given r=1ft and they ask you to use 3.14 for pi, so lets plug those in and solve on the calculator.

\(V=\frac{4}{3}\pi r^3\)

\(V=\frac{4}{3}(3.14) (1)^3\)

\(V = 4.1866666666\)

To find the tangential and normal components of the acceleration for the position function r(t) = 3cos(t), we first differentiate the position function twice to obtain the velocity and acceleration functions. Then, we can decompose the acceleration vector into its tangential and normal components.

The position function r(t) = 3cos(t) represents the motion of an object along a circular path with radius 3. To find the tangential and normal components of the acceleration, we need to differentiate the position function twice with respect to time.

First, we find the velocity function by taking the first derivative of r(t):

v(t) = dr/dt = -3sin(t)

Next, we find the acceleration function by taking the second derivative of r(t):

a(t) = d²r/dt² = -3cos(t)

The acceleration vector a(t) = -3cos(t) can be decomposed into its tangential and normal components. The tangential component, at, represents the rate of change of speed and is given by:

at = a(t) • T

where T is the unit tangent vector, which is the normalized velocity vector v(t)/|v(t)|.

The normal component, an, represents the change in direction of the velocity vector and is given by:

an = a(t) • N

where N is the unit normal vector, which is perpendicular to the unit tangent vector T.

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Answer: A

Step-by-step explanation:

Answer:

136

Step-by-step explanation:

multiply 4 times 6, divide by two to get the area of the front side, then multiply that by two to get eh area of the two triangles.

Then multiply each side, two sides of 5 time 7 and one side of 6 times 7

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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The time exactly halfway between 42.60 seconds and 49.24 seconds is 45.92 seconds.

Halfway simply means the midpoint between two values. It is the distance between two values divided by two. It can also mean the average of the two values.

If the women's 400m world record is 42.60 seconds and the 16th fastest women's 400m runner ran it in 49.24 seconds, to find the exact halfway of these two records means to find the average of these two records of time. Add the two records of time and divide by two.

n = (42.60 + 49.24)/2

n = 91.84/2

n = 45.92 seconds

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The value of x for the two angles (5y + 10)° and (3x + 7)° on a straight line is equal to 21.

Angles that are on a straight line involves the sum of angles that can be arranged together so that they form a straight line. Angles on a straight line when added together sum up to 180°.

From the question, we observe;

y + 90° + 3x + 7 = 180° and also,

5y + 10 + 3x + 7 = 180°

so;

5y + 10 + 3x + 7 = y + 90° + 3x + 7

5y - y + 3x - 3x = 90 + 7 - 10 - 7 {collect like terms}

4y = 80 {divide through by 4}

y = 80/4

y = 20

substituting 20 for y in y + 90° + 3x + 7 = 180°, we get;

20 + 90° + 3x + 7 = 180°

3x + 117° = 180°

3x = 180° - 117° {subtract 117° from both sides}

3x = 63°

x = 63°/3 {divide through by 3}

x = 21

I'm conclusion, we have that x have its value as 21 for the angle (3x + 7)° which lie on a straight line with (5y + 10)°

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f(x) =3x-8 and g(x) = √x+2 are the function and their inverses intersect.

A function is a mathematical representation that maps one set of values to another set of values. The inverse of a function is a reflection of the original function over the line y=x, where the input and output are reversed.

For the function f(x) = 3x - 8, the inverse can be found by switching the input and output values, then solving for x.

In this case, we have

=> y = 3x - 8 and x = (y + 8)/3.

The two functions will intersect when the input value is equal to the output value, or when

=> 3x - 8 = (y + 8)/3.

Solving for x, we find that x = 4. This is the only intersection point between the two functions.

For the function g(x) = √x + 2, the inverse can be found by switching the input and output values, then solving for x.

In this case, we have

=> y = √x + 2 and x = y² - 2.

The two functions will intersect when the input value is equal to the output value, or when

=> √x + 2 = y² - 2.

Solving for x, we find that x = 4. This is the only intersection point between the two functions.

Therefore option (a) and (b) is correct.

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Answer:

A and C

Step-by-step explanation:

Answer:

4×4×4=64

Step-by-step explanation:

The true statement is (b) Function 2 has the lowest average rate

We start by calculating the average rates of each function

The interval is given as [1, 2]

For Function 1

We have

f(1) = -3

f(2) = 3

The average rate is then calculated as

Average rate = [f(2) - f(1)]/[2 - 1]

Average rate = (3 + 3)/1

Average rate = 6

For Function 2

We have

f(1) = (1/4)^1 + 4 = 4.25

f(2) = (1/4)^2 + 4 = 4.0625

The average rate is then calculated as

Average rate = [f(2) - f(1)]/[2 - 1]

Average rate = (4.0625 - 4.25)/1

Average rate =-0.1875

For Function 2

We have

f(1) = -2

f(2) = 0

The average rate is then calculated as

Average rate = [f(2) - f(1)]/[2 - 1]

Average rate = (0 + 2)/1

Average rate = 2

The lowest average rate is -0.1875 for function 2

Hence, function 2 has the least rate

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The function f(x) = 8 - 2x equals its average value at x = 3.

To find the point(s) at which the function equals its average value on the interval [0,6], we need to determine the average value first. The average value of a function on a closed interval [a, b] can be calculated by integrating the function over that interval and dividing by the length of the interval (b - a). In this case, the interval is [0, 6], so the length of the interval is 6 - 0 = 6.

To find the average value, we integrate the function f(x) = 8 - 2x over the interval [0, 6]:

∫(0 to 6) (8 - 2x) dx = 8x - x^2 evaluated from 0 to 6

= (8 * 6 - 6^2) - (8 * 0 - 0^2)

= (48 - 36) - (0 - 0)

= 12

The average value of the function f(x) over the interval [0, 6] is 12/6 = 2.

Now, we set the function equal to its average value:

8 - 2x = 2

Solving for x, we get:

2x = 6

x = 3

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The name of the equation for the regression line is the Regression Equation.

Regression Line:

Regression is a statistical technique used in finance, investing, and other fields that attempts to determine the strength and nature of the relationship between one dependent variable (usually denoted Y) and several other variables (called independent variables).

Simple linear regression:

Y = a + bX+ u

​Multiple linear regression:

Y = a + b₁ X₁ + b₂ X₂ + b₃ X₃ +..... + bₙ Xₙ +u

where:

Y = The dependent variable that can be predicted.

X =The independent variables that are used to predict

a = The y-intercept

b (beta coefficient) = is the slope of the independent variable(s)

u = The error term

​Regression equation:

Regression equations are used in statistics to determine if there is any relationship between data sets. For example, if you measure a child's height every year, you'll find that they grow about 3 inches each year. This trend (growth of 3 inches per year) can be modeled using a regression equation. In fact, most things in the real world (from oil prices to hurricanes) can be modeled with a few equations. You can predict future events.

There are several types of regression equations. Some of the more common ones include exponential and simple linear regression (to fit data to an exponential or linear equation). The regression equation most likely to be encountered in elementary statistics takes the form of a linear one.

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A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

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The Answer is : 20/40

Answer:

The answer is B

Step-by-step explanation:

Its just B

The sequences that have a common difference of 2 are B and D, Option B and D both are correct.

Given that, determine the Which of the arithmetic sequence with common difference 2.

A. 1, −3, 5, −7, 9, …                B. 2, 4, 8, 16, 32, …
C. 10, 8, 6, 4, 2, …                 D. 13, 15, 17, 19, 21, …

Arithmetic progression is the series of numbers that have common differences between adjacent values.

Here,
A. 1, −3, 5, −7, 9, …

Common difference = -3 - 1 = -4

B. 2, 4, 8, 16, 32, …
Common difference = 4 - 2 = 2

C. 10, 8, 6, 4, 2, …
Common difference = 8 - 10 = -2

D. 13, 15, 17, 19, 21, …
Common difference = 15 - 13 = 2

Thus, the sequences that have a common difference of 2 are B and D, and Option B and D both are correct.

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Answer:

86 cm

Step-by-step explanation:

parameter of the Pentagon

= the parameter of the square + the parameter of the

triangle

= 48 + 38

= 86

Answer:

24/48 is the wer

Step-by-step explanation:

Answer:

the answer is

Step-by-step explanation:

\( \frac{6 }{ 12} = \frac{24}{n} \)

6*n=24*12

\(n = \frac{24 \times 12}{6} \)

n=48

Answer:

(x - 4)(x + 4)(x - 1)(x + 1)

Step-by-step explanation:

Given

\(x^{4}\) - 17x² + 16

Use the substitution u = x², then

u² - 17u + 16

Consider the factors of the constant term (+ 16) which sum to give the coefficient of the u- term (- 17)

The factors are - 16 and - 1, then

u² - 17u + 16

= (u - 16)(u - 1) ← replace u by x²

= (x² - 16)(x² - 1) ← both factors are difference of squares

= (x - 4)(x + 4)(x - 1)(x + 1)

Answer: -18

Step-by-step explanation: x4-17x2+16= -18

i am not completely sure but here. i hope this helps god bless

Answer:

Made $840 in commissions for the past month.

Step-by-step explanation:

sales = 70 * 150 = 10500

commission = .08 * 10500 = 840

Answer:

$840

Step-by-step explanation:

8% = 0.08

.08 * 150 = 12 per unit sold

12 * 70 = 840.00

Answer:

420 meters

Step-by-step explanation:

Perimeter = 2L+2W

80+60=140

Three times around

140x3=420meters

Step-by-step explanation:

t = 4

u = 6 + 2

Find t - u

solu

t - u

= 4 - ( 6 + 2 ) = 4 - 8

Answer is -4

The value of t-u is -2(1+i).

The complex number is basically the combination of a real number and an imaginary number.

For the subtraction of two complex numbers we subtract real part from the real and imaginary from imaginary.

According to the given question.

We have two complex numbers

t = 4 + 0i and u = 6 + 2i

Therefore,

\(t - u = 4+ 0i - ( 6 + 2i)\)

⇒\(t - u = 4 + 0i - 6 - 2i\)

⇒\(t - u = -2 -2i\)

⇒\(t - u = -2(1+i)\)

Hence, t - u = -2(1 + i).

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Answer:

1+(3×u-1÷2u)=1+(5u÷2)=(2+5y)÷1

Answer:

99 (I am not sure if this is correct)

Step-by-step explanation

75/4.75 so we can see how many miles per mile and then we would round the answer we got would be 16 and then muiltiply by 6.25 and round it to the nearest mile so i got 99. (unless I missed calculated)

Answer:

1 and 2nd congruent and 4th is similar

there are 33 pleasing ordered triples.

We are given a set {1, 2, 3, 4, 5, 6}. We need to count the number of pleasing ordered triples (a, b, c), where a < b < c, and a, b, c are elements of the set.

Condition (b) requires that both b and c be greater than a. Since a can take any value from 1 to 4, the number of possibilities for (a, b, c) is:

For a = 1, there are 4 choices for b (2, 3, 4, 5) and 5 choices for c (3, 4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 4 × 4 - 1 = 15 pleasing triples with a = 1.

For a = 2, there are 3 choices for b (3, 4, 5) and 4 choices for c (4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 3 × 4 - 1 = 11 pleasing triples with a = 2.

For a = 3, there are 2 choices for b (4, 5) and 3 choices for c (5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 2 × 3 - 1 = 5 pleasing triples with a = 3.

For a = 4, there is only 1 choice for b (5) and 2 choices for c (6, 5). Therefore, there is only 1 × 2 = 2 pleasing triples with a = 4.

The total number of pleasing ordered triples is:

15 + 11 + 5 + 2 = 33

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