I need help with number 9, please.

Answer:

He sold 32 pounds of apples, 14 pounds of plums and 23 pounds of peaches.

Step-by-step explanation:

Let:

x = Mass of Apples (pounds)

y = Mass of plums (pounds)

z = Mass of peaches (pounds)

He sold 18 more pounds of apple than pounds of plums:         [tex]x = 18 + y[/tex]

He sold 9 less pounds of peaches than pounds of plums:         [tex]z - 9 = y[/tex]

He sold a total of 69 pounds of fruit:                                       [tex]x + y + z = 69[/tex]

We have 3 unknown variables, therefore a system of 3 linear simultaneous equations:

                                                [tex]x = 18 + y[/tex] ——- (equation i)

                                          [tex]z - 9 = y[/tex]

                                         ∴     [tex]z = 9 + y[/tex] ——— (equation ii)

                                   [tex]x + y + z = 69[/tex] ——- (equation iii)
The above linear simultaneous equations can be solved by Substitution Method:

Substitute (equation i) and (equation ii) into (equation iii) to solve for y. Expand the parenthesis and bring all the like terms together. y has to be made the subject of the equation:

[tex](18 + y) + y + (y + 9) = 69[/tex]

= [tex]18 + y + y + y + 9 = 69[/tex]

= [tex]y + y + y = 69 - 18 - 9[/tex]

= [tex]3y = 42[/tex]

= [tex]y = \frac{42}{3}[/tex]

∴ y = Mass of plums = 14 pounds

Substitute the calculated value of y into the other two equations to solve for x and for z:

                 [tex]x = 18 + (14)[/tex]

              ∴ x = Mass of apples = 32 pounds

                 [tex]z = 9 + (14)[/tex]

              ∴z = Mass of peaches = 23 pounds

Answer:

Step-by-step explanation:

Answer:

The number is -10.4

Explanation:

Assume that the number we are looking for is x.

Now, we want to get 10 times te sum of half the number and 6 and equate this expression to 8. Then we can solve for x

Let's take this step by step:

half the number is 0.5x

the sum of half the number and 6 is 0.5x + 6

10 times the sum of half the number and 6 is 10(0.5x +6)

10 times the sum of half the number and 6 equals 8 is 10(0.5x+6) = 8

Now we can solve for x as follows:

10(0.5x + 6) = 8

5x + 60 = 8

5x = 8 - 60

5x = -52

x = -52/5

x = -10.4

Hope this helps :)

Answer:

Step-by-step explanation:

Rational numbers are numbers that can be written in the form pq, where p and q are integers and q≠0. The difference between rational numbers and fractions lies in the fact that fractions cannot have negative numerator or denominator.

so, yes.

When t is any real number, the true statements will be:

A. -t < 0:

B. -t = 0

E. (-t)^2 = -t^2

If t is any real number, then the following statements are true:

A. -t < 0: This statement is true if t > 0, and false if t <= 0.

B. -t = 0: This statement is true if t = 0, and false if t ≠ 0.

C. -t = t: This statement is false for all real numbers t, since the negative of any non-zero real number is not equal to the original number.

D. t|-t: This statement is false for all real numbers t, since the absolute value of any real number is non-negative.

E. (-t)^2 = -t^2: This statement is true for all real numbers t, since squaring a real number gives a non-negative result. Note that the negative sign in front of the square is distributive and can be moved inside the square.

Learn more about numbers on:

https://brainly.com/question/27894163

#SPJ1

7200+80x = 3200+120x

Reason:

Canton starts off with 7200 people. Add on 80x to represent the fact the town grows 80 people per year. That's how we end up with the expression of 7200+80x

Similarly, the expression 3200+120x represents the idea Holly Springs started off with 3200 people and grows at 120 people per year.

The solution for x in the triangle is x = 52.5

The bisector of an angle in a triangle divides the opposite side in the ratio of the sides containing the angle. That is:

PQ/QR = PS/SR

PQ = x, QR = 35, PS = 42 and SR = 70 - 42 = 28.

Therefore, we have:

PQ/QR = PS/SR

x/35 = 42/28

28*x = 42*35

28x = 1470

x = 1470/28

x = 52.5

Learn more about bisector of an angle in a triangle on:

https://brainly.com/question/24334771

#SPJ1

This student would receive 10 bag of popcorns.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the quantity of popcorn, we would make use of the information provided about the unit price for one bag of popcorn by using the following mathematical expression;

Number of bag of popcorns = Cost of one bag of popcorn/Unit price

Substituting the given parameters into the mathematical expression above, we have the following;

Number of bag of popcorns = 5/0.50

Number of bag of popcorns = 10 bag of popcorns.

Read more on unit price here: brainly.com/question/25381934

#SPJ1

The mean of the data is given by the equation M = 679.3846 and the standard deviation σ = 34.1535

The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Standard Deviation is calculated by

Each number's deviation from the mean must be determined, and then squared.

Next, add up all of these values.

Divide the result by the quantity of numbers.

Then calculate its square root.

σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²

Given data ,

Let the data be represented as Set A

Now , the value of set A is

Set A = { 688 , 711 , 625 ,701 , 688 , 667 , 694, 630, 547, 703, 688, 697, 703, 656, 677, 700, 702, 688, 691, 664, 688, 679, 708, 699, 667, 703 }

The mean of the sample data = Sum of all the values / number of values

The mean M = 17664 / 26

The mean M = 679.3846

Now , the standard deviation is calculated by

σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²

Substituting the values in the equation , we get

The standard deviation σ = √ ( 30328.153846154 / 26 )

The standard deviation σ = √ ( 1166.4674556213 )

The standard deviation σ = 34.1535

Hence , the standard deviation is 34.1535

To learn more about standard deviation click :

https://brainly.com/question/28189061

#SPJ1

Serina is mistaken because Serina should have solved for x in the second equation because it has a coefficient of 1.

Serina is mistaken because solving for x in the first equation as her first step does not necessarily lead to the most efficient solution. While it is true that both 2 and 3 can be divided into 18, this approach may require additional steps to solve for the other variable, y, in the second equation.

In this case, it is actually more efficient to solve for x in the second equation because it has a coefficient of 1. This means that once we solve for x, we can substitute that value into the first equation and solve for y directly, without needing to perform any additional calculations.

Here's how we can solve the system of equations using this approach:

X + 7 y = 31 (solve for x)

x = 31 - 7y

Substitute x = 31 - 7y into the first equation:

2 x + 3 y = 18

2 (31 - 7y) + 3 y = 18

62 - 14 y + 3 y = 18

-11 y = -44

y = 4

Substitute y = 4 into the equation we used to solve for x:

x = 31 - 7y

x = 31 - 7(4)

x = 3

Therefore, the solution to the system of equations is x = 3, y = 4.

In summary, while it is important to consider which variable to solve for first when solving a system of equations, the most efficient approach may vary depending on the specific equations and coefficients involved. In this case, solving for x in the second equation was the most efficient approach.

To learn more about equation here:

https://brainly.com/question/29657983

#SPJ4

The value of length AC is,

⇒ AC = 31

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The lengths are,

AB = 12 and BC = 19

Now, If the points A, B and C are colinear.

Then, The value of length AC is,

⇒ AC = AB + BC

⇒ AC = 12 + 19

⇒ AC = 31

Thus, We get;

⇒ AC = 31

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ2

Answer:

2.64

Step-by-step explanation:

Answer: number 2 is A

Step-by-step explanation:

Answer:

The larger number is 100

The smaller number is 60

Step-by-step explanation:

x + (40 + x) = 160

2x + 40 = 160

x + 20 = 80

x = 60

60 + (40 + 60) = 160

160 = 160

Answer:

Step-by-step explanation:

perp.: -4/3

y - 1 = -4/3(x - 3)

y - 1 = -4/3x + 4

y = -4/3x + 5

y-int: (0, 5)

The number of adults and children in the group were 64 and 36 respectively by using an algebraic equation.

It is given that the entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056.

Let the number of adults in the group = x

number of adults in the group = y

Total number of  people paid an entry fee = 100

So the equation becomes : x + y = 100

 or x = 100 - y

Cost for adult ticket = $12

Cost for child ticket = $8

Total entry fee paid = $1,056

Second equation = 12x + 8y = 1056

putting value of x from equation 1

12(100 - y) + 8y = 1056

1200 - 12y + 8y = 1056

4y = 144

y = 36

x = 100 - 36 = 64

To know more about algebra

https://brainly.com/question/487274

#SPJ4

Answer:

Step-by-step explanation:

The formula for calculating the future value of a continuously compounded investment is:

FV = PV * e^(rt)

where PV is the present value, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.

Plugging in the given values, we get:

FV = 5100 * e^(0.08 * 13) = 5100 * e^1.04 = 5100 * 2.856116786 = 14536.86

So, the future value of the investment after 13 years at an 8% interest rate compounded continuously would be approximately $14,536.86. Rounded to 2 decimal places, this is $14,536.86.

Answer:

The solution is 13

Step-by-step explanation:

x+8/3 = 7

x+8 = 7×3

x+8 = 21

x = 21-8

x = 13

The pattern does not have a consistency to get the differences

The method of successive differences involves finding the difference between each consecutive term in a sequence, and then using those differences to find the next term.

Here's how the method would work for the sequence given:

7; 35; 173; 771; 2529; 6667; 15,095

Difference between terms:

28; 138; 598; 1758; 4138; 8428

Second difference between terms:

110; 460; 1160; 2380; 4290

Third difference between terms:

350; 700; 1220; 1910

Fourth difference between terms:

350; 520; 690

There is no consistency between the patterns.

Read more on successive differences here:https://brainly.com/question/3097135

#SPJ1

To make the concentration of 50% syrup,

she needs to add 0.5 lb of sugar.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

Emma has half a pound of sugar.

To make the concentration of 50% syrup:

Let n be the required amount.

In decimals, 50% is 0.5.

Applying the percentage formula;

we get,

[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]

Applying cross multiplication,

we get,

[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]

0.5 = 0.5(n + 0.5)

1 = n + 0.5

n = 1 - 0.5

n = 0.5 lb.

Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ9

The mean of the frequency distribution is 52 degrees. and option A is carrect  . A) The computed mean is close to the actual mean because the difference between the means is less than​ 5%

First, we calculate the class mid-points (x); This is the mean of the class intervals.

For 40 - 44, x = (40 + 44)/2 = 42. This is applied to all other classes.

40 −44 = 42

45 −49 = 47

50 −54 = 52

55 −59 =57

64 −64 = 62

So:

x  42    47     52       57     62

f    22    55    1212     77      11

mean = ∑f(x)/∑f

= (42*22+47*55+52*1212+57*77+62*11)/(22+55+1212+77+11)

= 71604/1377

=52

actual mean = 51.8

and now mean = 52

percentage difference = ((52-51.8)/51.8)*100

= 0.3861 percentage

know more about percentage difference click here; https://brainly.com/question/22226398

#SPJ4

Box plot, because the median can easily be determined from the large set of data.

What exactly is a median?

The median is defined as the value in the centre of a given set of numbers or statistics. There are three main measures in mathematics that are used to calculate the average value for a given group of integers. They are the mean, the median, and the mode. These three indicators are known as central tendency measures. Mean computes the average value of the provided data. A median defines the midway value of the provided data. Mode defines the repeating value of the input data.

Now,

As, A box plot is a very visual means of displaying a concise overview of one or more sets of data. It is especially handy for quickly summarising and comparing several sets of findings from various trials. A box plot, at a glance, gives a graphical representation of the distribution of findings as well as indicators of symmetry within the data.

and it can handle a large set of data.

Hence,

            Box plot, because the median can easily be determined from the large set of data.

To know more about median visit the link

https://brainly.com/question/21396105?referrer=searchResults

#SPJ1

Answer:box plots

Step-by-step explanation:

i did it

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is C = 2 * π * r, where r is the radius of the circle. We can find the radius of the circle by rearranging the formula to r = C / (2 * π).

Substituting the given values into the formula, we get:

r = 21.98 inches / (2 * 3.14) = 21.98 inches / 6.28 = 3.50 inches

The diameter of the circle is equal to twice the radius, so we can find the diameter by multiplying the radius by 2:

d = 2 * r = 2 * 3.50 inches = 7.00 inches.

To find the diameter of a circle with a given circumference, you can use the following steps:

Define the formula for the circumference of a circle: The circumference of a circle is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Substitute the given circumference into the formula: If the circumference of the circle is 21.98 inches, we can substitute that into the formula to get 21.98 = 2πr.

Solve for the radius: To solve for the radius, we can divide both sides of the equation by 2π: 21.98 / 2π = r. Using 3.14 for π, this gives us 21.98 / (2 * 3.14) = r, which can be simplified to r = 2.01 inches.

Calculate the diameter: The diameter of a circle is twice the radius, so the diameter can be calculated as 2 * r = 2 * 2.01 = 4.02 inches.

So, the diameter of the circle with a circumference of 21.98 inches is 4.02 inches.

The two integers are 5 and 10.

What do you mean by Integers?

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so it said to be positive integers

A number is negative if it is less than zero, so it said to be negative integers.

A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

Let x be the positive number

2x be the other positive number

Find the first integer

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{1}{2x} = \frac{1}{10}[/tex]

2x = 10

x = 5

Therefore, the first positive integer is 5.

Find the other integer

2x = 2(5) = 10

Therefore, the other integer is 10.

To check:

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{1}{10} = \frac{1}{10}[/tex]

To know more about Integers visit:

brainly.com/question/1768254

#SPJ1

Answer:

he division story will be that there are 16 boys who want to share 4 oranges. What fraction will each person get?

Number of boys = 16

Number of oranges = 4

Fraction that each person will get will be:

= Number of oranges / Number of boys

= 4/16

= 1/4

Each boy gets 1/4.

Step-by-step explanation:

Answer: To find the height of the embankment, we need to first find the volume of the well and then the volume of the embankment.

Volume of the well = πr^2h = π * (d/2)^2 * h = π * (5/2)^2 * 24 = 157.08 cubic meters

Volume of the embankment = π * (R^2 - r^2) * h, where R is the outer radius of the embankment and r is the inner radius.

Outer radius of the embankment = (5 + 3)/2 = 4 m

Inner radius of the embankment = (5 - 3)/2 = 1 m

Volume of the embankment = π * (4^2 - 1^2) * h = π * 15 * h

We know that the volume of the well is equal to the volume of the embankment, so we can write:

157.08 = π * 15 * h

Solving for h, we get:

h = 157.08 / (π * 15) = 157.08 / 47.12 ≈ 3.32 m

So, the height of the embankment is approximately 3.32 meters.

Step-by-step explanation:

Answer: 50 Cups

Step-by-step explanation:

16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48

Two cups in a pint so add 2 to 48 which is 50

Answer:

You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Step-by-step explanation:

To convert between gallons, quarts, and pints, we need to use the following conversions:

1 gallon = 4 quarts

1 quart = 2 pints

Here's the step-by-step process to convert the given volume to cups:

Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts

Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts

Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts

Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts

Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups

Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Step-by-step explanation:

This symbol is signma, which is the sub of all the X's after plugging them into the equation.

Just to show the pattern, the first 3 numbers on your table are 15, 13, and 13... doing those 3 with Sigma, and simplifying

[tex]( {1 5 - 2)}^{2} + ({13 - 2)}^{2} + {(13 - 2)}^{2} [/tex]

[tex]169 + 121 + 121[/tex]

You would pretty much do that all the way down the list.

After doing so, we wind up with

15, 13, 13, 4, 19, 12, 6, 5, 14

[tex]169 + 121 + 121 + 4 + 289 + 100 + 16 + 9 + 144[/tex]

Adding these together gets your answer of:

[tex]973[/tex]

Answer:

Below

Step-by-step explanation:

Slope = rise / run = change in y / change in x  = -30 / 6 = -5

Answer: -5

Step-by-step explanation:

Start with the slope formula

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

Substitute point values in the formula

m = (20 - 50) / (-4 - -10)

Simplify the fraction

m = (20 - 50) / (-4 - -10) = -30 / 6

Solve for slope (m)

m = -5

Answer:

{40.7,49.3}

Step-by-step explanation:

[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{80\%}=45\pm1.282\biggr(\frac{19}{\sqrt{32}}\biggr)\\ \\CI_{80\%}\approx45\pm 4.3\\\\CI_{80\%}=\{40.7,49.3\}[/tex]

Thus, we are 80% confident that the true sample mean amount spent is between $40.70 and $49.30