Bob bought 40 gumboils from a quarter machine. The number of each flavor he got is shown in the table. If there are 140 gumboils remaining in the machine. what is a reasonable prediction for the number of cola flavored gumboils left?

The sequence is an arithmetic sequence.

A rule for each term is t(n) = 7 - 4(n - 1).

Arithmetic sequence is a sequence of numbers where the numbers are arranged in a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence is 7, 3, –1, –5, –9, ....

First term = 7

Second term = 7 + -4 = 3

Third term = 7 + (-4 × 2) = -1

....................

Here each term is getting by adding -4 to the preceding term.

So -4 is the common difference.

nth term of the sequence is t(n) = 7 - 4(n - 1).

Hence the sequence is arithmetic sequence and any term of the sequence is t(n) = 7 - 4(n - 1).

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The equation is 16 + 2x = 3(x - 4) and the solution is x = 28

From the question, we have the following parameters that can be used in our computation:

Sixteen increased by twice a number is 3 times the number decreased by 4​

Let the variable be x

So, we have

16 + 2x = 3(x - 4)

Open the brackets

16 + 2x = 3x - 12

Evaluat the like terms

x = 28

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By using shipping volume, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift.

To solve this problem, we need to work backwards from the shipping volume and use the given processing rates to determine the required processing volumes for each stage of the process.

First, we can calculate the total number of hours of packing and shipping required to process 168,000 units:

168,000 units ÷ 175 units per person per hour = 960 hours

Next, we can determine the volume of items that need to be packed by Group B in order to ship this total volume. Since Group B processes 65% of the volume, we can set up the following equation:

0.65x = 168,000 units

where x is the total volume of items processed by all packing groups. Solving for x, we get:

x = 168,000 units ÷ 0.65 = 258,461.54 units

So the total volume of items processed by all packing groups is approximately 258,461.54 units. We can now use the given processing rates to determine the required processing volumes for each stage:

Picking: 100% of 258,461.54 units = 258,461.54 units

Packing Group A: 35% of 258,461.54 units = 90,461.54 units

Packing Group B: 65% of 258,461.54 units = 168,000 units

Therefore, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift. The answer is 168,000.

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____The given question is incorrect, the correct question is given below:

Team % of Volume Items processed per person per hour Picking 100% 150 Packing Group A 35% 105 Packing Group B 65% 70 Shipping 100% 175 How many items will be processed by Packing Group B in order to ship a total of 168,000 units for the shift?

46,  

70,  

84,000,  

109,200,  

168,000

Answer:

Step-by-step explanation:

Answer:

B.

The equation you can use to find the area of a sphere when given radius is:

V = 4/3πr 3

Fitting 5 into the equation:

V = 4/3π5 3

V = 523.598776

Therefore, B is the correct answer.

The transformation represents a horizontal of 2 units to the right and a vertical of 5 units up

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the initial coordinates of the point be represented as P

Now , the coordinates of P = P ( x , y )

And , the transformed point be represented as Q

Now , the coordinates of Q = Q ( x - 2 , y + 5 )

when x → ( x - 2 )

The graph is moved 2 units to the right

And , when y → ( y + 5 )

The graph is moved 5 units up

Substituting the values in the equation , we get

The transformation is 2 units to the right and 5 units up

Hence , the transformation is 2 units to the right and 5 units up

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Answer:

$10 / hour

Step-by-step explanation:

$40 ÷ 4 hours = 10/hour

Answer:  Part A: Zach is paid $10 per hour

Part B: The equation would be p = 10h

Step-by-step explanation: Part A :Zach worked 4 hours and was paid $40. The question asks How much is Zach's paid per hour? Per hour means to find the unit rate and in order to find the unit rate in this case, you have to divide the $40 by the 4 to get how much Zach got per hour.

1.$40/4=10

Therefore, Zach is paid $10 per hour.

Part B: In the question it says Which equation shows the relationship between , h, the number of hours worked. The number of hours Zach worked was 4 hours. So, h = 4. Then for the next part of the problem, and p the amount paid.  We know that Zach got paid $40. So p = 40. Now that we know our numbers, we could put the equation together.

1. P = 10h is the same as $40 = 10 x 4.

There's the answer, Hope it helps! Have a nice day!

It would be expected to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

The expected value, also known as the mathematical expectation, is a key concept in probability theory and statistics.

Here,
Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.

To find the expected number of correct predictions over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),

39% * 38 = 14.82

So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

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The value of x is given as follows:

x = 155º.

For the triangle at the left, considering that the sum of the measures of the internal angles of a triangle is of 180º, the angle measures are given as follows:

For the triangle at the right, considering the ray formed at the top, the measures are given as follows:

An angle is supplementary with it's external angle, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:

x = 180 - 25

x = 155º.

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Answer: Look below :)

Step-by-step explanation:

I graphed the inequality below:

from that we can see:

a. Points on the line are combinations of US/Mexico minutes he can do where all of his prepaid money will be used, For example, he could do 50 USA minutes and 80 Mexico minutes, and there would be no money left to spend

b. Points above the line are combinations of US/Mexico minutes that will cost him more than the prepaid $50.

c. Points below the line are combinations of US/Mexico minutes that will leave him with money left over from his $50.

I hope this makes sense! ask questions if you have any :)

The measurement closest to the number of miles between the two towns is 227.5 miles.

A method for finding the answer to linear equations in two variables is cross-multiplication. It turns out to be the quickest way to resolve two linear equations. To cross multiply two fractions, multiply the first fraction's numerator by the second's denominator and the second fraction's numerator by the first fraction's denominator.

Given that, distance between Dallas and Houston is about 364 kilometers.

The measurement of:

8 km = 5 miles

364 km = x miles

Using the method of cross multiplication, we have:

x = 364 (5) / 8

x = 227.5 miles

Hence, the measurement closest to the number of miles between the two towns is 227.5 miles.

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well, since we know that one root is 5, that is a factor of it is (x-5), so hmmm by the remainder theorem we also know that if we plug "5" as our argument in our f(x), that is, if we do f(5), it must result to 0. so f(5) = 0, if that's so then

[tex]2x^2+bx-10=f(x)\implies 2(5)^2+b(5)-10=f(5) \\\\\\ 2(5)^2+b(5)-10=0\implies 50+5b-10=0\implies 5b=-40 \\\\\\ b=\cfrac{-40}{5}\implies \boxed{b=-8} \\\\[-0.35em] ~\dotfill\\\\ 2x^2-8x-10=0\implies 2(x^2-4x-5)=0\implies 2\stackrel{ {\Large \begin{array}{llll} x=-1 \end{array}} }{(x+1)}(x-5)=0[/tex]

If so far the George's string is 44 inches long , then his string is not long enough , so he need to make it longer .

To find whether George's string is long enough, we first convert both measurements to same unit of measurement.

that means we convert length of the string in inches to feet by dividing it by 12 ; because  there are 12 inches in a feet  ;

⇒ (44 inches)/(12 inches/feet)  

⇒ 3.67 feet  ;

The George's string is currently 3.67 feet long and he needs a string that is 4 feet long  .

So , his current string is not long enough and he needs to make it longer. He needs to add another 0.33 feet to his string  .

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The given question is incomplete , the complete question i

George needs a string that is 4 feet long. So far his string is 44 inches. Is it long enough or does he need to make it longer ?

The Linear Equation for the line with slope as -1/3 and the point (-9,-1) is y = (-1/3)x - 4   .

We use the point slope form of a linear equation to write the equation of a line with its slope and a point on the line.

The point-slope form is ⇒ y - y₁ = m(x - x₁)  ;

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

The Slope (m) of line  is  = -1/3 and point on line (x₁, y₁) is = (-9, -1),

Now , we substitute  these values ;

we get ;

⇒ y - (-1) = (-1/3)(x - (-9)) ;

⇒ y + 1 = (-1/3)(x + 9)  ;

Simplifying further ,

we get ;

⇒ y + 1 = (-1/3)x - 9/3  ;

Subtracting 1 from both sides, we get:

⇒ y = (-1/3)x - 4

Therefore, the equation of the line is y = (-1/3)x - 4  .

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Answer:

I got 20 when calculating this

         a = amount given to the 1st share, ratio of 5.

a + 122 = amount given to the 2nd share, ratio of 7.

        T = total amount

so the total amount is really "T", and we'll be splitting that into a 7 : 5 ratio, that is, we'll be dividing "T" by (7 + 5) and distribute accordingly.

[tex]\stackrel{\textit{total split by 7 + 5}}{\cfrac{T}{7+5}\implies \cfrac{T}{12}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{we know the 1st share is}}{a= 5\cdot \cfrac{T}{12}}\implies a=\cfrac{5T}{12} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know the 2nd share is}}{a+122= 7\cdot \cfrac{T}{12}}\implies a+122=\cfrac{7T}{12}\implies \stackrel{\textit{substituting from above}}{\left( \cfrac{5T}{12} \right)+122=\cfrac{7T}{12}} \\\\\\ 122=\cfrac{7T}{12}-\cfrac{5T}{12}\implies 122=\cfrac{2T}{12}\implies 122=\cfrac{T}{6}\implies \boxed{732=T}[/tex]

Answer:

Step-by-step explanation: Sure! Here's a step-by-step solution to find the amount of red icing Ashley needs for one cake:

Divide the total amount of red icing by the number of cakes: 10 1/2 ÷ 3 1/2 = 3.

Simplify the result from step 1: 3 = 3 ounces of red icing per cake.

So Ashley needs 3 ounces of red icing to write a message on one cake.

By expression, x - y = x' - y' , Distance of 3rd and 4th obstacle is equal to distance of 7th and 9th obstacle.

Distance is a numerical measurement of how far apart objects or points are, it is the length along a line or line segment between two points on the line or line segment.

Given,

The distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine.

Distance of 7th obstacle = x

Let,

Distance of 9th obstacle = y

Distance of 3rd obstacle = x'

Distance of 4th obstacle = y'

Distance between obstacle 3 and 7 = x - x'

Distance between obstacle 4 and 9 = y - y'

Distance between obstacle three and obstacle four = x' - y'

Distance between obstacle seven and obstacle nine.= x - y

According to the question

x-x' = y-y'

⇒ x - y = x' - y'

Hence, Distance between third and fourth obstacle is same as distance between 7th and 9th obstacle.

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Answer: To find the father's and son's ages, we can set up two simultaneous equations:

Let's say the son's age is "x"

Then, the father's age would be x + 25

And the sum of their ages is x + (x + 25) = 53

So, 2x + 25 = 53

Solving for x, we get:

2x = 28

x = 14

Therefore, the son is 14 years old, and the father is 14 + 25 = 39 years old.

To use the elimination method, we can add the two equations:

x + (x + 25) = 53

2x + 25 = 53

Simplifying, we get:

2x = 28

x = 14

And the father's age would be x + 25 = 14 + 25 = 39 years old.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

First:

(-2 1/2)*(-1 3/5) = 2.5*1.6

Second:

2.5*1.6=5/2*8/5

Third:

5/2*8/5=

4

The average speed of Paul Revere's horse, assuming he rode straight to Lexington without stopping, would have been approximately 25.4 miles per hour.

To find the average speed of Paul Revere's horse, we can use the formula:

average speed = total distance / total time

In this case, the total distance is 11 miles, and the total time is 26 minutes, or 0.4333 hours (since there are 60 minutes in an hour).

So, the average speed of Paul Revere's horse would be:

average speed = 11 miles / 0.4333 hours

average speed ≈ 25.4 miles per hour

Therefore, the average speed of Paul Revere's horse, to the nearest tenth of a mile per hour, would have been 25.4 miles per hour.

Using the formula for average speed, we can calculate that Paul Revere's horse would have had to travel at an average speed of approximately 25.4 miles per hour to cover the 11-mile distance in 26 minutes. This assumes that he rode straight through without stopping.

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The complete question is:

On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

Answer:

75

Step-by-step explanation:

trust me bro

The equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number" is 3 – (n – 1) = 1/2(3n – 4)

Let the number be n.

Gven: "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"

So,

The expression "three minus the difference of a number and one" represent the equation is;  

3 – (n – 1)

Also,

The expression "one-half of the difference of three times the same number and four" represent the equation  is;

1/2(3n – 4)

Hence,

Complete expression represents the equation is

3 – (n – 1) = 1/2(3n – 4)

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(1 – n) – 3 = (4 – 3n)

3 – (1 – n) = (4 – 3n)

(n – 1) – 3 = (3n – 4)

3 – (n – 1) = (3n – 4)

We will prove that if we remove the root of a k-th order binomial tree, it results in k binomial trees of smaller orders.

Base case: If k = 1, the binomial tree consists of a single node. Removing the root node leaves an empty tree, which can be considered as a collection of 0 binomial trees of smaller orders.

Induction hypothesis: Assume that the statement is true for a k-th order binomial tree.

Induction step: We need to prove that the statement is true for a (k+1)-th order binomial tree, which is formed by joining two k-th order binomial trees.

Remove the root node of the (k+1)-th order binomial tree. This results in two trees, each of which is a k-th order binomial tree.

By the induction hypothesis, removing the root node of each of the two k-th order binomial trees results in k binomial trees of smaller orders.

Thus, removing the root node of the (k+1)-th order binomial tree results in a total of 2k binomial trees of smaller orders, which completes the proof.

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There are 10/4 ways ( [tex]\frac{10}{4}[/tex] ) to accomplish the given task by wearing the ties for a week according to the permutations and combinations.

Given if you wear tie for a week, where one need t wear 4 of his ties from the 10 of total. The number of ways to wear the ties will be equal to the value. So there are many ways to wear a tie of different types and also to remove the tie there are different ways. Now we will see the ways to wear a tie accordingly.

According to the permutations and combination rules the formula will be:

Number of ways: (Number of ties want to wear) / (Number of Total ties)

Therefore total number of ways to wear ties = 10/4

Number of ways this can be accomplished is 10/4

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Answer:

A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure,divide it into simple, nonoverlapping figures. Find the area of each simplerfigure, and then add the areas together to find the total area of the compositefigure

Step-by-step explanation:bc of the way u gave it im showing it to u

The cost per student for the app is $3, and can be found by dividing the total cost of $96 by the number of students, 32, which equals $3 per student.

Let x be the cost of the almonds Sophia bought and y be the cost of the app per student. Then, we have the subsequent two equations:

x + $5 = $15

32y = $96

To find the cost of the app per student, we can solve for y in the second equation:

y = $96 / 32 = $3

So the app costs $3 per student.

To find the cost of the app per student, we need to find the total cost of the app and then divide it by the number of students. Mr. Boone spent $96 on the app for 32 students, so the cost per student would be $96 / 32 = $3. This means that each student paid $3 for the app.

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