a nursery employee wishes to plant $2$ identical golden delicious apple trees and $5$ identical bartlett pear trees in one row. how many distinct arrangements are possible?

If the Gasoline costs $3.58 per gallon and Karl paid $30.43 , the number of gallons Karl purchased is  8.5 gallons .

The Per unit cost of Gasoline is = $3.58  ;

the amount paid by Karl for gasoline is = $30.43   ;

we have to calculate the number of gallons of gasoline purchased by Karl,

the number of gallons can be calculated by the formula :

Number Of Gallons purchased = [tex]\frac{Total \; Amount }{Cost \; per \; Gallon}[/tex] ;

Substituting the values of amount and cost per gallon in the formula ,

we get ;

Number of gallons = [tex]\frac{30.43}{3.58}[/tex] ;

we get ; ⇒ 8.5 .

Therefore , Karl purchased 8.5 gallons of gasoline .

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Answer:

101

Step-by-step explanation:

f(1) = 5 = 4*1 +1

f(9) = 37 = 4*9+1

f(6) = 4*6+1 = 25

f(f(6)) = f(25) = 4*25+1 =101

Answer:

  101

Step-by-step explanation:

Given the values of a linear function f(1) = 5 and f(9) = 37, you want the value of f(f(6)).

The given ordered pairs are (1, 5) and (9, 37). Using these, we can find the slope of the function to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (37 -5)/(9 -1) = 32/8 = 4

The y-intercept is ...

  b = y -mx

  b = 5 -4(1) = 1

So the function in slope-intercept form is ...

  y = mx +b

  f(x) = 4x +1

The value of f(6) is ...

  f(6) = 4·6 +1 = 25

The value of f(f(6)) is ...

  f(f(6)) = f(25) = 4·25 +1 = 101

The value of f(f(6)) is 101.

Answer:

The communicative property does not apply to subtraction.

10 - 8 = 2

8 - 10 = -2

We do not get the same answer.  2 and -2 are not the same number.

Step-by-step explanation:

If a student in stat 121 wants to estimate the average score on the stat 121 final exam from last semester. The sample is: The 200 students interviewed.

Sample can be defined as the data or information that are randomly collected from a group of population so as to reach or drawn a conclusion.

Based on the scenario the sample will be the 200 students who took the class last semester  as the 200 students were randomly selected from a larger population so as to reach a conclusion.

Therefore we can conclude that the sample is the 200 students interviewed.

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Answer:

........

Step-by-step explanation:

Answer:

(7x + 5)(- x - 11)

Step-by-step explanation:

9(x - 1)² - 16(x + 2)² ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

9(x - 1)² - 16(x + 2)²

= [ 3(x - 1) ]² - [4(x + 2) ]² with a = 3(x - 1) and b = 4(x + 2)

= [ 3(x - 1) + 4(x + 2) ] [ 3(x - 1) - 4(x + 2) ] ← distribute parenthesis

= [ 3x - 3 + 4x + 8 ] [ 3x - 3 - 4x - 8 ]

= (7x + 5)(- x - 11 )

We can say that in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem.

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Other complex mathematical strategies were known to the Babylonians. For example, in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem long before Pythagoras.

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In order to have negative correlation between two variables the covariance must be negative.

What is correlation?

The degree to which two variables are linearly related is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It is a typical technique for outlining straightforward connections without stating cause and effect.

The correlation between two variables x and y is,

[tex]r = \frac{Cov(x, y)}{S_x*S_y}[/tex]

where,

Cov(x, y) is the covariance between x and y.

[tex]S_x[/tex] and [tex]S_y[/tex] respectively denotes the standard deviation of x and y.

If the correlation is negative then  r < 0.

Now r < 0

[tex]\frac{Cov(x, y)}{S_x*S_y} < 0\\Cov(x, y) < 0\\Sx > 0, S_y > 0[/tex]

If r < 0 the Cov(x, y) < 0.

In order to have negative correlation between two variables the covariance must be negative.

Hence, in order to have negative correlation between two variables the covariance must be negative.

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The total distance travelled on the cycle is 30.46m and the acceleration  is the last 8 seconds is 0.85 m/s².

"Acceleration is the measure of the speed at which velocity changes."

OR "Acceleration depends upon the velocity if the velocity continously increases or decreases the acceleration will be produced."

Positive acceleration results from continuously increasing velocity.

Negative acceleration will be negative if the velocity is continuously decreasing.

FORMULA

Acceleration is defined as a change in velocity divided by time, or a = (Vf-Vi)/t UNIT.

Meter/second+square, or m/S², is the SI unit of velocity in the MKS system.

a. Total distance = Hypotenuse₁ + mid distance + Hypotenuse₂

Hypotenuse₁ = [tex]$ \sqrt{10^2 + 6^2} $[/tex]

Hypotenuse₁ = 11.66m

mid distance = 12 - 6

                      = 6m

Hypotenuse₂ = [tex]$ \sqrt{10^2 + (20-12)^2} $[/tex]

Hypotenuse₂ = [tex]$ \sqrt{10^2 + (8)^2} $[/tex]

Hypotenuse₂ = 12.80m

Total distance = 11.66m + 6m + 12.80m

Total distance = 30.46m

b. Acceleration  [tex]{\displaystyle ={\frac { \text{v - u} }{t}}[/tex]

[tex]\displaystyle = {\frac { \text{12.80 - 6} }{8}[/tex]

[tex]\displaystyle = {\frac { 6.80 }{8}[/tex]

0.85 m/s²

Thus, the total distance travelled on the cycle is 30.46m and the acceleration  is the last 8 seconds is 0.85 m/s².

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Esperanza is aware of Sally's desire to avoid having to return back to school so you would not need to fret about her father, rumors, or feeling out of place.

Monkeys are often undesirable pets. Yes, for a while, some may be extremely sweet. However, the truth is that monkeys cannot live in a human home because they are too dangerous and require too much care. These concerns pertain to apes and are just as significant (chimpanzees, orangutans, and gibbons).

People and monkeys are both considered primates. But neither monkeys or indeed any other current ape species are linked to people. Yes, chimpanzees and humans both descend from apes.

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Answer:

7/32

Step-by-step explanation:

First we need to make the mixed fraction an improper fraction

4*7=28

28+4=32

So, the improper fraction will be 32/7

a reciprocal is the opposite of a fraction

this means we will flip this fraction over, moving the 7 to the numerator and 32 to the denominator

7/32

These two points on the number line describe that she descended by 70 units.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
She started at –5 and descended to –75.
On the number line, the difference between  -75 and -5 is given as
= -5 - (-75)
= 70

Thus, these two points on the number line describe that she descended by 70 units.

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The equation of the line that passes through the points (-6,4) and (-2,2) is y - 4 = -1/2(x + 6)

What is the equation of the line?

To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

The slope of the line can be found by using the two points:

m = (y2 - y1) / (x2 - x1)

So,

m = (2 - 4) / (-2 - (-6)) = -2/4 = -1/2

We know that the line passes through the point (-6,4) so we can substitute the values into the equation:

y - 4 = -1/2(x + 6)

Hence, the equation of the line that passes through the points (-6,4) and (-2,2) is y - 4 = -1/2(x + 6)

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The smallest possible whole-number length for the third side is 12

Following the Pythagorean theorem which states that the hypotenuse square is equal to the sum of the squares of the other two sides in a triangle.

This is represented as;

a² = b² + c²

Given that;

From the information given, we have that;

14² = 6² + c²

Find the square values

196 = 36 + c²

collect like terms

c² = 196 - 36

subtract the values

c² = 160

Find the square root of both sides

c = √160

c = 12. 65

Thus, the value is 12

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The area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.

Area is a measure of the size of a surface or the amount of space it takes up. It can be measured in square units such as square feet, square meters, or acres. Area is used to describe the size of a two-dimensional object or shape, and is often used when discussing the size of a plot of land, a room, or other geographical area.

The first octant is defined as the area in the three-dimensional Cartesian coordinate system where all the coordinates are positive. In this case, the equation 5x + 3y + z = 15 can be rearranged to solve for z: z = 15 - 5x - 3y. This new equation can then be used to find the area of the plane that lies in the first octant by integrating the equation over the area of the octant.

To solve for the area, we must first find the boundaries of the octant. Since all coordinates must be positive, the boundaries of the octant are x = 0, y = 0, and z = 0. The area of the plane that lies in the first octant is then computed using the triple integral:

Area = ∫∫∫ 0 0 0 15-5x-3y dzdydx

= ∫∫ 0 0 (15x + 45y)dydx

= ∫ 0 (15x^2/2 + 45xy)dx

= 15x^3/6 + 45x^2y/2

Therefore, the area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.

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Answer:

Step-by-step explanation:

The mystery number is 9. The least common multiple of 3 and 36 is 36. When you pair 9 with 36, their least common multiple is still 36. 9 is greater than 6, but less than 12. Therefore, the mystery number is 9.

Answer:

[tex]g(5)=-75[/tex]

Step-by-step explanation:

[tex]g(x)=-3x^{2} \\g(5)=-3(5)^{2} \\g(5)=-75[/tex]

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The area of the region enclosed by the inner loop of the curve can be calculated by integrating the function r = 6 + 12 sin θ over the interval of θ.

The area of the inner loop is given by Area = 1/2 ∫r^2 dθ = 1/2 ∫(6 + 12 sin θ)^2 dθ

We can solve this integral by breaking it into two parts: Area = 1/2 (∫(6 + 12 sin θ)^2 dθ) = 1/2(∫36 + 72sin θ + 144sin^2 θ dθ)

The first integral is simple and equals to 36*θ and the second one is equal to 48θ - 48cos(2θ)

The limits of integration are [0, 2π]

So the area of the inner loop is 1/2(36*2π + 48(2π) - 48(2)) = 72π

So the area of the region enclosed by the inner loop of the curve is 72π square units.

Answer:

the equation for the product of 12 x 8 = 96

The distance Jon travels to work is 472.5 miles.

Let d be the distance Jon travels to work.

The time it takes to drive is 20 minutes and the time it takes to bike is 45 minutes.

The difference in speed between driving and biking is 14.5 mph.

We can set up the following equation:

20min * (14.5mph + x) = 45min * x

Solving for x gives us the average speed of Jon on the bike, which is 10.5 mph.

Now we can use the distance formula to solve for d:

d = rate * time

d = 10.5mph * 45min

d = 472.5 miles

Therefore, the distance Jon travels to work is 472.5 miles.

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P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are if we are unclear about how an event will turn out. Statistics refers to the study of occurrences subject to probability.

According to the question

a) Assuming that X is the random variable that takes the place of the number of defectives and has a normal distribution with a mean of 10 ounces and a standard deviation (σ) of 0.15.

The random variable's values deviate from the mean by 1, causing them to either exceed or fall short of (10 + 0.15) and (10-0.15)

= 10.15 or 9.85.

The following formula may be used to determine the likelihood that there will be either more or lesser defects than the range of 10.15 to 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P[tex](\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(1) - φ(-1)

Now we calculate the value of z for z = 1 and z = -1; we have: 0.841345 and 0.158655 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.841345 - 0.158655)

P( X < 9.85 or X > 10.15 ) = 0.31713

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

b) It is possible to lower the process standard deviation to 0.05 by making modifications to the process design.

The following formula may be used to determine the likelihood that the number of defectives is either larger than 10.15 or lesser than 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P[tex](\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(3) - φ(-3)

Now we calculate the value of z for z = 3 and z = -3; we have: 0.99865 and 0.00135 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.99865 - 0.00135)

P( X < 9.85 or X > 10.15 ) = 0.00271

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

(c) What is the benefit of increasing the number of standard deviations from the mean for process control limits by minimizing process variation?

As we can see from the reduction from a to b above, the key benefit of minimizing process variance is that it will decrease the likelihood of receiving a defective item.

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Answer:

76
This is because, when you exceed 76 copies, the cost will be greater than 11.50 and you will not be able to afford it.

Step-by-step explanation:

To solve this inequality, you can divide both sides by 0.15: x <= 76.67

Answer:

(1, 1 )

Step-by-step explanation:

choose any value of x to substitute into the equation and solve for y

choosing x = 1 , then

- 1 + 5y = 4 ( add 1 to both sides )

5y = 5 ( divide both sides by 5 )

y = 1

then (1, 1 ) is a solution to the equation

Answer:

- x + 5 y = 4                                     (x = 6)

- ( 6 ) + 5 × 2 = 4                             (y = 2)

- 6 + 10 = 4

 4 = 4

∴ (6, 2) is an ordered pair that is a solution to the given equation .

For the given data the mean is 180.28 and the modal class is 177 - 185.

First finding mean:

For the class of 150 - 158, the class boundaries are 149.5 - 158.5.

Middle value = (150 + 158)/2 = 154

Frequency = 5

mean= 154 × 5 = 770

For the class 159 - 167, the class boundaries are 158.5 - 167.5

Middle value  = (159 + 167)/2 = 163

Frequency = 16

middle value.  frequency = 163 × 16 = 2608

For the class 168 - 176, the class boundaries are 167.5 - 176.5

Middle value = (168 + 176)/2 = 172

Frequency = 20

middle value.  frequency = 172 × 20 = 3440

For the class 177 - 185, the class boundaries are 176.5 - 185.

Middle value = (177 + 185)/2 = 181

Frequency = 21

middle value.  frequency  = 181 × 21 = 3801

For the class 186 - 194, the class boundaries are 185.5 - 194.5

Middle value (x_m) = (186 + 194)/2 = 190

Frequency = 20

middle value.  frequency  = 190 × 20 = 3800

For the class 195 - 203, the class boundaries are 194.5 - 203.5

Middle value  = (195 + 203)/2 =199

Frequency = 15

middle value.  frequency  = 199 × 15 = 2985

For the class 204 - 212, the class boundaries are 203.5 - 212.5

Middle value  = (204 + 212)/2=208

Frequency = 3

middle value.  frequency  = 208 × 3 = 624

Now in order to determine the mean of this group data all values calculated separately through the product of middle value and frequency will be added together and divided by the total frequency count (i.e 100).

That is

Mean =  ( 770 + 2608 + 3440 + 3801 + 3800 + 2985 + 624 ) = 18028 / 100

Mean  =   180.28

Now determine the model class:

Model class refers to the with the highest occurring frequency. So this is the class "177 - 183" having the frequency 21.

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The inequality that describes this situation will be 6x + 2s ≤ 76

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x = number of group dance numbers

s = number of solo performances

The inequality will be 6x + 2s ≤ 76

This inequality can be read as "the total duration of the group dance numbers (6 minutes per group dance number) plus the total duration of the solo performances (2 minutes per solo performance) is less than or equal to 76 minutes."

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The distance between the two people is changing at a rate of 3.2 mi/hr.

The distance between the two people can be calculated by using the Pythagorean theorem.

Let one person be at the origin (0, 0) and the other person be at (x, y). After 15 minutes, the first person will be at (3*15, 0) and the second person will be at (2*15*cos45, 2*15*sin45).

Using the Pythagorean theorem, the distance between them can be calculated as:

d = sqrt((3*15 - 2*15*cos45)^2 + (2*15*sin45)^2) = sqrt(225 + 225) = sqrt(450) = 21.213

The rate of change of distance is given by the formula d/t, where d is the distance and t is the time.

Therefore, the rate of change of distance between the two people after 15 minutes is 21.213/15 = 3.2 mi/hr.

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119 pupils, according to a Venn diagram, prefer Snickers or Reese's Peanut Butter Cups but not Twix.

In the 1880s, John Venn popularized the Venn diagram, a common type of diagram illustrating logical links between sets. In probability, logic, statistics, linguistics, and computer science, diagrams are used to teach basic set theory and to illustrate straightforward set relationships. In a Venn diagram, overlapping circles and other shapes are used to represent the connections between two or more sets of elements. Highlighting similarities and differences between components when organizing information graphically frequently proves beneficial. A space in the middle of a Venn diagram is created by the intersection of two sizable circles.

The group of students that enjoy Snickers is represented by set A.

The students who enjoy Twix are represented by set B.

The students who enjoy Reese's Peanut Butter are represented by set C. All three types of chocolate candies are favorites among 19 students.

Snickers and Reese's Peanut Butter Cups are among the 31.

Reese's Peanut Butter Cups and Snickers alone = 31 - 19 = 12

82 like Twix and Reese's Peanut Butter Cups

149 like Snickers

149 − (51 + 12 + 19) = 67 for Snickers alone.

The number of students who prefer Snickers or Reese's Peanut Butter Cups but not Twix is equal to 67 + 40 + 12.

There are 119 pupils that enjoy Snickers or Reese's Peanut Butter Cups.

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Answer:

standard form:

4×100,000

400,000

Step-by-step explanation:

remember, to transform an equation we need to apply any operation to both sides of the equation. otherwise the equality relation is destroyed.

we want to get the equating to look like " x = ..."

so, the "+ 39" is in the way.

we need to subtract 39, but as mentioned, we need to do this on both sides.

x + 39 = 74

x + 39 - 39 = 74 - 39

x = 35 in

the fig tree is therefore 35 in. that is 39 in shorter than 74 in (the orange tree).