Answer:
1 solution
Step-by-step explanation:
Y = 4
Y = 4x - 1
Substitute value of Y here,
4 = 4x - 1
4 + 1 = 4x
5 = 4x
5/4 = x
1.25 = x
•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.
______
hope this helps!
A number added to twice another number is-8. The sum of the two numbers is-2. What is the lesser of these two numbers?
Answer:
-6
Step-by-step explanation:
a + 2b = -8 Eq. 1
a + b = -2 Eq. 2
From Eq. 1:
a = -8 -2b Eq. 3
From Eq. 2:
a = -2 -b Eq. 4
Equalizing Eq. 3 & Eq. 4:
-8 -2b = -2 -b
-2b + b = -2 + 8
-b = 6
b = -6
From Eq. 4
a = -2 - (-6)
a = -2 + 6
a = 4
Check:
From Eq. 1:
a + 2b = -8
4 + 2*-6 = -8
4 - 12 = -8
Answer:
-6<4
Then;
The lesser number is:
-6
In 1993, the life expectancy of males in a certain country was 65.2 years. In 1998, it was 67.7 years. Let E represent the
life expectancy in year t and let t represent the number of years since 1993. Determine the linear function E(t) that fits
the data. Use the function to predict the life expectancy of males in 2006.
The predicted Iife expectancy οf maIes in 2006 is 71.7 years.
What is Iinear equatiοn?A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.
Tο find the Iinear functiοn E(t) that fits the data, we need tο find the equatiοn οf the Iine that passes thrοugh the twο given pοints: (0, 65.2) and (5, 67.7), where t = 0 cοrrespοnds tο the year 1993 and t = 5 cοrrespοnds tο the year 1998.
Using the sIοpe-intercept fοrm οf a Iinear equatiοn, we have:
E(t) = mt + b
where m is the sIοpe οf the Iine and b is the y-intercept.
We can find the sIοpe by using the fοrmuIa:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (0, 65.2) and (x2, y2) = (5, 67.7):
m = (67.7 - 65.2)/(5 - 0) = 0.5
Sο the equatiοn οf the Iine is:
E(t) = 0.5t + b
Tο find the y-intercept, we can use οne οf the given pοints. Let's use (0, 65.2):
65.2 = 0.5(0) + b
b = 65.2
Therefοre, the Iinear functiοn E(t) that fits the data is:
E(t) = 0.5t + 65.2
Tο predict the Iife expectancy οf maIes in 2006, we need tο find t when the year is 2006:
t = 2006 - 1993 = 13
Sο we can use t = 13 in the equatiοn:
E(13) = 0.5(13) + 65.2
E(13) = 6.5 + 65.2
E(13) = 71.7
Therefοre, the predicted Iife expectancy οf maIes in 2006 is 71.7 years.
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72 inches = ______ feet 6 feet 144 feet 864 feet 5 feet
Step-by-step explanation:
72 inches = 6 feet
There are 12 inches in a foot, so to convert inches to feet, you divide the number of inches by 12.
72 inches / 12 inches/foot = 6 feet
14 points! PLEASE HELP!!!
Step-by-step explanation:
I just did in the other posting. how often did you post it ?
this is a trick question. the triangle at the top is not an isoceles triangle.
we use Pythagoras for an the steps.
so, the left part of the baseline (split by the height) is calculated by
12² = 10² + part²
144 = 100 + part²
part = sqrt(44) = 6.633249581... ft
the other part is then
20 - 6.633249581... = 13.36675042... ft
and the second leg of the large triangle is
leg² = 10² + 13.36675042...² = 278.6700168...
leg = 16.69341238... ft
P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈
≈ 64.69 ft
please see the answer to the other posting for more details.
What is the sum of 18+516+38 1 8 + 5 16 + 3 8 ?
Answer:
4906 that is the answer. also your welcome and sorry if I misunderstood the question
A student has $43 in total to buy books that cost $8.50 each and pens that cost $2.25 each. If
the student buys 4 more pens than books, which inequality represents the possible number of
books, k, the student can buy?
A 8.50k +2.25(k+ 4) ≤ 43
B 8.50k +2.25(k+ 4) < 43
C 10.75k + 4 ≤ 43
D 10.75k + 4 < 43
4
Go to the next page
The student can purchase no more than four books, or k. This can be represented so the correct answer option (A) is 8.50k +2.25(k+ 4) ≤ 43
In what way do numbers depict inequality?Symbol for inequality: Comparing two numbers that are not equal requires the use of an inequality symbol. (>) More Than: The larger number is always on the left when using this symbol, and the smaller number is always on the right.
First, let's define some variables. Let b be the quantity of books the student purchases, and p represent the quantity of pens. Since the student purchases four more pens than books, the total cost of the purchase is $43, and we know that p = b + four. This can be expressed as an equation:
8.50b + 2.25p = 43
By replacing p = b + 4, we obtain:
8.50b + 2.25(b + 4) = 43
If we simplify, we get:
10.75b + 9 = 43
9 is subtracted from either side, resulting in:
10.75b = 34
By multiplying both sides by 10.75, we obtain:
b ≈ 3.16
The student may purchase either 3 or 4 books because the total number of books must be a whole number. Let's use the initial equation to verify these values:
If the student purchases three books, then p = 3 + 4 = seven pens are needed. 8.50(3) + 2.25(7) = 38.25, or less than $43, is the total price.
If the student purchases four books, then p = four plus four equals eight pens. 8.50(4) + 2.25(8) = 43, or precisely $43, is the total price
As a result, the student can purchase no more than four books, or k. This can be represented as:
8.50k + 2.25(k + 4) ≤ 43
Answer (A) is the right selection.
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Professional baseball player Rusty Raspberry earns $1,715,000 a year playing baseball. Last
year, a biography that he had written sold 300,000 copies at a price of $24 each. Raspberry
received 10% in royalties on the book sales. What was his total salary last year from the book
and his baseball career?
Answer:
Rusty Raspberry's total earnings last year would be the sum of his earnings from playing baseball and his earnings from book royalties.
Earnings from playing baseball = $1,715,000
To calculate earnings from book royalties, we need to find out how much Rusty received in royalties for the 300,000 copies sold.
Royalties per book = 10% of $24 = $2.40
Total royalties for 300,000 books = $2.40 x 300,000 = $720,000
Therefore, Rusty Raspberry's earnings from book royalties last year = $720,000
Total earnings = Earnings from playing baseball + Earnings from book royalties
= $1,715,000 + $720,000
= $2,435,000
Therefore, Rusty Raspberry's total salary last year from the book and his baseball career was $2,435,000.
Use the standard normal table to find the z-score that corresponds to the cumulative area 0.3897. If the area is not in the table, use the entry closest to the are
between two entries, use the z-score halfway between the corresponding z-scores.
Click to view page 1 of the standard normal table) Click to view page 2 of the standard normal table.
Z= (Type an integer or decimal rounded to two decimal places as needed.)
The z-score that corresponds to a cumulative area of 0.3897 is 0.25.
What is the z-score:A Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution.
It is calculated by subtracting the mean of the distribution from the data point and then dividing the result by the standard deviation of the distribution.
Here we have
The cumulative area is 0.3897
Using the standard normal table, we can find the z-score that corresponds to a cumulative area of 0.3897 as follows:
1. Locate the entry in the body of the table that is closest to 0.3897. In this case, the closest entry is 0.3897 in the body of the table.
2. Identify the corresponding row and column headers for this entry. The row header is 0.0 and the column header is 0.08.
3. The z-score that corresponds to the area of 0.3897 is the value at the intersection of the row and column headers. In this case, the value is 0.25.
Therefore,
The z-score that corresponds to a cumulative area of 0.3897 is 0.25.
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Alan is going to sell eggs to a local market. Unfortunately, he dropped the box with the eggs and broke them all. He needs to figure out how many eggs he broke, but he forgot the exact number. This is what he does remember:
When he put all his eggs in groups of 2, one egg was left over.
When he put all his eggs in groups of 3, one egg was left over.
When he put all his eggs in groups of 4, one egg was left over.
When he put all his eggs in groups of 5, no eggs were left over.
How many eggs did he have before he broke them? Is there more than one answer? How do you know?
This is for extra credit and i need them. :) PLEASE
Step-by-step explanation:
It is an ODD number due to statement 1
it is a multiple of 5 due to the last statement
5 15 25 35 45 55 65 75 85 95 105 .....
When you divide by 3 there is a R 1
25 55 85 115 145
When you divide by 4 there is a R = 1
25 is the lowest number next possible number is 145 then another posssible is 265 etc
1111111111111111111111111111 friends?
Answer:
[tex]k = - 3[/tex]
Step-by-step explanation:
[tex]y = kx[/tex]
[tex]k \times ( - 1) = 3[/tex]
[tex] - k = 3[/tex]
[tex]k = - 3[/tex]
Answer:
[tex]k = -3[/tex]
Step-by-step explanation:
Step 1: Substitute
To solve this problem you are going to need to substitute the values of y and x into the problem y=kx. Which would give you the problem of 3=-1k or 3 = -k to make things easier.
Step 2: Using properties of equality
In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]
Step 3: Check
In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct
Roland’s family drove 4 and 6/10 km from their home they home to the gas what is the maximum number of days that Carl can feed his dog exactly 2 and 1/2 cups of dog food from one full bag
According to the question 560 cups divided by 20 cups per week equals 28 weeks.
What is divided?Division is a mathematical operation that involves splitting a number or quantity into equal parts. It is an essential process in mathematics, used to solve problems and find solutions. Division involves dividing a number, or a set of numbers, by another number. The result of the division is known as the quotient. Division can also be used to find fractions or ratios, as well as to divide a number into its parts.
Assuming the bag of dog food is a large bag and Carl is feeding his dog 2 1/2 cups daily, the maximum number of days Carl can feed his dog from one full bag is 28.
This is because 2 1/2 cups equals 20 cups per week, and a large bag typically contains approximately 560 cups.
Therefore, 560 cups divided by 20 cups per week equals 28 weeks.
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The entire number of kilometres driven by Roland's family can be determined by using the phrase [tex]=\frac{69}{10}[/tex]
How to calculate Distance?To determine the total number of kilometres driven by Roland's family, the distance from their home to the gas station and the distance from the gas station to the shop must be added.
There are [tex]4\times \frac{6}{10}[/tex] kilometres between their home and the gas station, which can also be stated incorrectly as follows:
[tex]4\times \frac{6}{10}=\frac{(4\times 10+6)}{10} \\\\=\frac{46}{10}[/tex]
The formula for expressing the distance between the gas stop and the store is 2 30/100 kilometers, which can be written as follows:
[tex]2\times\frac{30}{100} =\frac{(2\times100+30)}{100} \\\\=\frac{230}{100}[/tex]
To calculate the overall distance traveled, we add the two distances:
[tex]\frac{46}{10} +\frac{230}{100}[/tex]
To combine these fractions, we need to find a common denominator. Only one unique digit, 100, can be used to divide both 10 and 100. In light
of this, we can rewrite the equation as follows using 100 as the common denominator:
[tex](\frac{46}{10} )\times (\frac{10}{10} )+(\frac{230}{100} )\times (\frac{1}{1} )[/tex]
That amounts to:
[tex]\frac{46}{100} +\frac{230}{100} =\frac{690}{100}[/tex]
Therefore, we can reduce this fraction by multiplying the numerator and denominator by their ten largest common factor:
[tex]\frac{690}{100} =\frac{(69/10)}{(100/10)} \\\\=\frac{69}{10}[/tex]
Consequently, the phrase that follows may be used to determine the overall number of kilometres driven by Roland's family:
[tex]2\times\frac{30}{100} +4\times \frac{6}{10} =\frac{69}{10}\ km[/tex]
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Rest of the question is,
They drove 2 30/100 kilometers from the gas station to the store. Which expression can be used to determine the number of kilometer Ronald's family drove altogether.
What will be the result of substituting 2 for x in both expressions below?
Substituting for x in an expression means replacing the variable x with a specific value or expression. This is often done to evaluate the expression for that particular value or to simplify the expression.
What is the substituting for x in expressions?Substituting 2 for x in the first expression, we get:
[tex]1/2(2) + 4(2) + 6 - 1/2(2) - 2 = 1 + 8 + 6 - 1 - 2 = 12[/tex]
Substituting 2 for x in the second expression, we get:
[tex]2(2) + 2 - 1 = 5[/tex]
One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
Therefore, the first expression evaluated with x = 2 is 12, and the second expression evaluated with x = 2 is 5. Since they do not have the same value, the correct option is:
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The given question is incomplete. The complete question is given below:
What will be the result of substituting 2 for x in both expressions below? One-half x + 4 x + 6 minus one-half x minus 2 Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Both expressions equal 6 when substituting 2 for x because the expressions are equivalent. One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent. One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
Im stuck on these questions I need help
Answer:
Step-by-step explanation:
modal weight: the weight that appear most often
4.5 kg appears 3 times
6-sided polygon: even though it is an irregular polygon, the interior angles still add up to (6 - 2)180 = 720
therefore, angle f = 720 - 576 = 144 (the sum of a+b+c+d+e is very blurry in the image, it looks like 576--please double check that!)
modal score: read this right off the graph. The score with the highest frequency is the modal score: 14 (meaning, 9 contestants got this score)
What is the least common multiple of 3 and 16?
Cuántos meses son 44 semanas
Answer:
alrededor de 10 meses
Step-by-step explanation:
HELP PLEASE!!!!
What is.........
2+77+2+4+18+9/4+5+23+78+33-76-4+12=???????????????????
Answer:
We can solve this expression using the order of operations, also known as PEMDAS:
2 + 77 + 2 + 4 + 18 + (9/4) + 5 + 23 + 78 + 33 - 76 - 4 + 12
First, we can simplify the fraction by adding the whole number and fraction parts:
2 + 77 + 2 + 4 + 18 + 2.25 + 5 + 23 + 78 + 33 - 76 - 4 + 12
Next, we can perform addition and subtraction from left to right:
= 187 + 2.25 + 68
= 257.25
Therefore, the value of the expression 2+77+2+4+18+9/4+5+23+78+33-76-4+12 is 257.25.
LOL the answer is 176.25
Can you solve this question?
find dy/dx=?
We may conclude after answering the presented question that derivatives Therefore, the derivative of y = ln(cos(x)) with respect to x is: dy/dx = -tan(x)
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.
To find dy/dx when y = ln(cos(x)), we'll need to use the chain rule and the derivative of the natural logarithm.
[tex]dy/dx = (dy/du) * (du/dx)\\d/dx [ln(u)] = 1/u * du/dx\\dy/du = 1/u = 1/cos(x)\\dy/dx = (dy/du) * (du/dx) = (1/cos(x)) * (-sin(x)) = -tan(x)\\[/tex]
Therefore, the derivative of y = ln(cos(x)) with respect to x is:
dy/dx = -tan(x)
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Plot a point that best represents the value of square root 215 on the number line
Answer:
Put the point a tiny bit more than half way between 14 and 15.
Step-by-step explanation:
If you are allowed to use a calculator, put in sqrt215 and you get out 14.66, that goes a little bit more than halfway between 14 and 15.
If you are not allowed to use a calculator, think of the numbers on the numberline in terms of answers to *perfect square* questions.
So 12 is sqrt 144.
13 is sqrt 169.
14 is sqrt 196.
15 is sqrt 225.
So the 215 in your question is in between 196 and 225.
215 is closer to 225 (than to 196) so put the point closer to sqrt 225. That is, in between 14 and 15 and just a tad bit closer to 15.
a punch bowl has a capacity of 8 quarts. a recipe fills the bowl 3/4 full.how many quarts does the recipe make
Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.
Here,
The quantity of punch produced by the recipe is:
If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.
=> 6 pints = 8 * 3/4.
The formula yields 6 quarts of punch as a result.
Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.
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haya tres enteros pares consecutivos tales que 6 veces el primer entero sean 10 más que la suma del segundo y el tercero
So the three integers are 4, 6, and 8 such that 6 times the first integer is 10 more than the sum of the second and the third integers.
What is integer?An integer is a whole number that does not have any fractional or decimal parts. Integers include positive numbers (1, 2, 3, etc.), negative numbers (-1, -2, -3, etc.), and zero (0).
Here,
Let's call the first even integer x. Since the three integers are consecutive even integers, the second and third integers are x + 2 and x + 4, respectively.
From the problem statement, we know that:
6x = (x + 2) + (x + 4) + 10
Simplifying the right side of the equation:
6x = 2x + 16
Subtracting 2x from both sides:
4x = 16
Dividing both sides by 4:
x = 4
Therefore, the three consecutive even integers are:
x = 4
x + 2 = 6
x + 4 = 8
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Complete question:
"There are three consecutive even integers such that 6 times the first integer is 10 more than the sum of the second and the third integers." find the integers.
Use the drawing tool(s) to form the correct answers on the provided grid.
Draw all of the lines of reflection for the given figure.
Drawing Tools
Select
Line
Click on a tool to begin drawing
Reset
Next
Delete
Undo
Reset
As a text-based AI, I am unable to use drawing tools or interact with grids. However, I can still help you understand the terms you mentioned and provide guidance on how to approach the problem.
1. "Delete": This term typically refers to removing an element or a part of the content you're working on. When working with a grid, you may need to delete some lines, shapes, or text that are not needed.
2. "Reset": Resetting refers to reverting a grid or a drawing tool to its original state, essentially starting from scratch. This can be useful if you've made multiple changes and want to begin anew without having to manually undo each step.
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write the point-slope from the equation of the line with slope -7/4 that passes through the point (-9,2)
Answer:
y - 2 = - [tex]\frac{7}{4}[/tex] (x + 9)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{7}{4}[/tex] and (a, b ) = (- 9, 2 ) , then
y - 2 = - [tex]\frac{7}{4}[/tex] (x - (- 9) ) , that is
y - 2 = - [tex]\frac{7}{4}[/tex] (x + 9)
5. Elsa earns $150 more than Anna per week. Each girl spent $320 a week and saved the rest of their earning. When Anna had saved $2880, Elsa had saved $2400 more than Anna. How much did Elsa earn per week?
The amount Elsa earns per week, which is $150 more than Anna per week and Elsa had saved $2400 more than Anna when Anna had saved $2880, found by solving the simultaneous equations obtained is $650.
What are simultaneous equations?Simultaneous equations are equations that share the same variables.
Let x represent the amount Elsa earn per week, we get;
The amount Anna earns per week + 150 = The amount Elsa earns per week
Therefore; The amount Anna earns per week = x - 150
The amount each girl spent per week = $320
The amount saved per week = The rest of their weekly earning
The mount more Elsa add saved when Anna saved $2880 = $2400
Let n represent the number of weeks after which Anna had saved $2,880, we get the following equations;
n × (x - 150 - 320) = 2800
n × (x - 470) = 2800...(1)
n × (x - 320) = 2880 + 2400 = 5280
n × (x - 320) = 5280...(2)
The above simultaneous equations (1) and (2) indicates;
n × (x - 470) = 2800
x - 470 = 2880/n
x = 2880/n + 470
n × (x - 320) = 5280
x - 320 = 5280/n
x = 5280/n + 320
2800/n + 470 = 5280/n + 320
5280/n - 2880/n = 470 - 320 = 150
(5280 - 2880)/n = 150
n = (5280 - 2880)/150 = 16
n = 16
x = 5280/n + 320
Therefore;
x = 5280/16 + 320 = 650
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h (x) = (3x - 4) (x + 2)^2 (x - 5)
• (2, 0)
• (-3/4, 0)
• (4/3, 0)
• (5, 0)
The zeros of the function H(x) = (3x - 4)(x + 2)^2(x - 5) are (4/3, 0), (-2, 0), and (5, 0).
Calculating the zeros of the polynomial functionTo find the zeros of the function H(x), we need to find the values of x that make the function equal to zero.
H(x) = (3x - 4)(x + 2)^2(x - 5)
Setting H(x) equal to zero, we have:
(3x - 4)(x + 2)^2(x - 5) = 0
Using the zero product property, we can see that H(x) will be equal to zero when any of the factors are equal to zero.
So, the zeros of the function H(x) are:
3x - 4 = 0, which gives x = 4/3
x + 2 = 0, which gives x = -2
x - 5 = 0, which gives x = 5
Therefore, the zeros of the function H(x) are (4/3, 0), (-2, 0), and (5, 0).
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Zoe is 16 years old. Her brother, Luke, is 3 years more than half her age. Write a numerical expression for Luke’s age. Show your work.
Answer:
; Simplified =
Let "Zoe" = z
Let "Luke" = x
x = 16/2 + 3 is your equation
You're expression is
~
Step-by-step explanation:
i hope it's helpful for you
12000 x 5 = 9500 + 9500 + 10000 + x + y
Answer:
31000 - y = x
Step-by-step explanation:
Solve for x
[tex]12000\times5=9500+9500+10000+x+y[/tex]
Add and multiply the integers
[tex]60000=29000+x+y[/tex]
Subtract 29000 on both sides
[tex]31000=x+y[/tex]
Subtract y on both sides
[tex]31000-y=x[/tex]
Assume that the first term of a sequence is -3. Write the first four terms of the sequence if it is an arithmetic sequence with a common difference of -1/3.
Answer:
The first term of the sequence is -3 and the common difference is -1/3. Therefore, the second term of the sequence can be found by adding the common difference to the first term:
second term = first term + common difference
second term = -3 + (-1/3)
second term = -10/3
Similarly, we can find the third term by adding the common difference to the second term:
third term = second term + common difference
third term = -10/3 + (-1/3)
third term = -11/3
And we can find the fourth term by adding the common difference to the third term:
fourth term = third term + common difference
fourth term = -11/3 + (-1/3)
fourth term = -4
Therefore, the first four terms of the sequence are -3, -10/3, -11/3, and -4.
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle?
A. 13/20
B. 7/20
C. 1/4
D. 5/8
show all steps
Answer:
Sandra's curiosity led her to sift through recycling and trash bins, wearing gloves to keep her hands clean. She counted the plastic type of each bottle and noted which ones were properly disposed of. It's important to be mindful of our recycling behaviors and make sure we're doing our part to protect the environment. Let's all strive to recycle properly and reduce our waste!
Find the savings plan balance after
4
years with an APR of
8%
and monthly payments of
$150.
Question content area bottom
Part 1
The balance is
$enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The balance of the savings plan after 4 years with an APR of 8% and monthly payments of $150 is approximately $7,456.76.
What exactly is a savings plan formula?As a result, the savings plan formula for such challenges is as follows: final saving = number of periods * (first and last period savings) / 2.
To calculate the balance of the savings plan after four years, we can use the formula for the future value of an annuity with regular payments:
P * ((1 + r/n)(n*t) - 1) / (r/n)
Where P is the monthly payment amount, which is $150.
r = 8% annual interest rate
n = the number of times annual interest is compounded = 12 (since we have monthly payments)
4 t = the number of years
We get the following results when we plug these values into the formula:
FV = 150 * ((1 + 0.08/12)^(12*4) - 1) / (0.08/12) ≈ $7,456.76
As a result, the savings plan balance after four years with an APR of 8% and monthly payments of $150 is approximately $7,456.76.
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
A) The completed table is given as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
B) the graph is attached accordingly.
C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
What is the explanation for the above response?a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.
We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.
D(L) = ceil(L/6)
Using this formula, we can complete the table as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).
b) The graph is attached.
c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.
So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.
In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
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