Answer:
[tex]\sum\limits^{n=6}_{n=1} {(-4+8n)}[/tex] is the notation to represent the sum of first six terms of the sequence 4, 12, 20, ....
So, the option "the summation from n equals 1 to 6 of negative 4 plus 8 times n" is the correct option as: [tex] \sum\limits^{n=N}_{n=1} {(-4+8n)}[/tex].
Step-by-step explanation:
Let us consider the sequence
4, 12, 20, ....
As d = 12-4 = 20 - 12 = 8
Hence, the sequence is an arithmetic as the common difference between consecutive terms is same (constant).
So,
For the arithmetic sequence,
a, a + d, a + 2d, a + 3d.........a + (n - 1)d
The nth term = a + (n - 1)d
a = first term, d = common difference
For the given sequence 4, 12, 20,...
a = 4, d = 8
Lets put these values in Summation Formula.
Sigma notation to represent the sum of the first six terms of the following sequence: [tex] \sum\limits^{n=N}_{n=1} {a+(n-1)d}[/tex]
⇒ [tex] \sum\limits^{n=N}_{n=1} {4+(n-1)8}[/tex]
⇒ [tex] \sum\limits^{n=N}_{n=1} {(4+8n-8)}[/tex]
⇒ [tex] \sum\limits^{n=N}_{n=1} {(-4+8n)}[/tex]
Hence, [tex]\sum\limits^{n=6}_{n=1} {(-4+8n)}[/tex] is the notation to represent the sum of first six terms of the sequence 4, 12, 20, .....
So, the option "the summation from n equals 1 to 6 of negative 4 plus 8 times n" is the correct option as: [tex] \sum\limits^{n=N}_{n=1} {-4+8n}[/tex].
Keywords: sigma notation, arithmetic sequence, series
Learn more about sigma notation from brainly.com/question/14062962
#learnwithBrainly
Answer:
the summation from n equals 1 to 6 of negative 4 plus 8 times n
Alberto recently opened a barbecue restaurant in Midtown. He paid for seven large tables to be delivered to the restaurant. If Alberto paid a delivery fee of
$95.45 and each table cost $235.75, what is the total amount Alberto paid?
$1,650.25
$1,626.00
$1,745.70
$1,554.80
Option C
Total amount paid by Alberto is $ 1745.7
Solution:Given that Alberto paid for seven large tables to be delivered to the restaurant
Alberto paid a delivery fee of $95.45
Cost of 1 table = $ 235.75
To find: total amount Alberto paid
cost of seven tables = cost of 1 table x 7
[tex]\text {cost of seven tables }=235.75 \times 7=1650.25[/tex]
Total amount paid = cost of seven tables + delivery feeTotal amount paid = 1650.25 + 95.45
Total amount paid = 1745.7
Thus total amount paid by Alberto is $ 1745.7 Therefore option C is correct
When Steve woke up. His temperature was 102º F. Two hours later it was 3º lower. What was his temperature then?
Answer:
Steve's temperature now is 99 degrees.
Step-by-step explanation:
102 degrees- 3 degrees=
99 degrees.
Steve's temperature was 102º F when he woke up. Two hours later, his temperature had dropped by 3º F, thus making his temperature 99º F.
Explanation:The subject of this question is a real-life mathematics reasoning task about temperature change. Based on the given information, Steve's initial temperature when he woke up was 102º F.
According to the problem, Steve's temperature decreased by 3º after two hours.
To find Steve's temperature after the decrease, you simply have to subtract this decrease from the original temperature. So you calculate 102º F - 3º F, which equals 99º F. Therefore, Steve's temperature two hours later was 99º F.
Learn more about Temperature Change here:https://brainly.com/question/32089365
#SPJ3
What point is interected between 10x-3y=19 and 5x+4y=-7
Answer:
(1, -3)
Step-by-step explanation:
Solve the system of equations of the two lines:
10x-3y=19 ------> eq 1
5x+4y=-7 --------> eq 2
Solve by elimination:
eq 2 x 2
2( 5x+4y) = 2(-7 )
10x + 8y = - 14 ------> eq 3
eq3 - eq 1:
(10x + 8y) - (10x-3y) = - 14 - 19
10x + 8y - 10x + 3y = -33
8y + 3y = -33
11y = -33
y = -3 (substitute back into eq 1)
10x - 3y = 19
10x - 3(-3) = 19
10x + 9 = 19
10x = 19 - 9
10x = 10
x = 1
Hence the intersection point is (1, -3)
If half the positive difference between 4.81 and 2.25 is multiplied by 0.32, what is the result?
The distance between 4.81 and 2.25 is 2.56.
Divide 2.56 by 2.
2.56 / 2 = 1.28.
Then multiply 0.38 by 1.28.
128 x 32 = 4096, then move the decimal 4 times to the left.
4096.
The decimal is behind the 6, you need to move the decimal in front of the 4.
Therefore, your result is 0.4096.
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points) Group of answer choices No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answer:
No, because the bike order does not meet the restrictions of 6c + 4a ≤ 100Step-by-step explanation:
It is given that, each child bike requires 4 hours to build and each adult bike requires 6 hours to build.
Hence, c child bikes and a adult bikes require [tex](4c + 6a)[/tex] hours to build.
It is also given that, each child bike requires 4 hours to test and each adult bike requires 4 hours to test.
Total time to test, c child bikes and a adult bikes is [tex](4c + 4a)[/tex]
The company will be able to make c child bikes and a adult bikes if [tex](4c + 6a) \leq 120\\(4c + 4a)\leq 100[/tex]
If c = 20 and a = 6, then (4c + 6a) = 116 < 120.
and (4c + 4a) = 104 > 100.
A flour mill produces the same amount of flour every hour. At the end of 16 hours , the mill has produced 48,000 pounds of flour . How many pounds of flour does the mill produce in 1 hour ?
Answer: 3,000
Step-by-step explanation:
Divide 48,000 by 16
48,000 ÷ 16 = 3,000
Answer:
3000
Step-by-step explanation:
If they produce 48,000 in 16 hours, that means in one hour they produce 48,000 divided by 16.
48000 ÷ 16 = 3000
A pizza restaurant charges a flat fee for a plain cheese pizza. There is an extra charge for any additional toppings. The cost of a pizza can be I determined from the equation C = 0.5m + 5, where m is the number of
additional toppings and C is the cost of the pizza ordered. What are the
interpretations of slope and y-intercept in the equation?
A
slope: cost per additional topping
y-intercept: cost of the plain pizza
B. slope: cost per additional topping
y-intercept: cost of the first topping
C. slope: cost of the plain pizza
y-intercept: cost per additional topping
D. slope: ratio of cost of additional topping to the cost of the plain pizza
y-intercept: cost of an additional topping
The slope of 0.5 represents the cost per additional topping, while the y-intercept of 5 represents the cost of the plain pizza. Option A provides the correct interpretations.
To interpret the slope and y-intercept of the equation C = 0.5m + 5, where C represents the cost of the pizza and m represents the number of additional toppings:
A. The correct interpretation is:
- Slope: The slope of 0.5 represents the cost per additional topping. This means that for each additional topping added to the pizza, the cost increases by $0.5.
- Y-intercept: The y-intercept of 5 represents the cost of the plain pizza without any additional toppings. This is because when m = 0 (no additional toppings), the cost of the pizza is $5, which is the flat fee for the plain cheese pizza.
To confirm:
- When m = 0, the equation becomes C = 0.5(0) + 5 = 5 , which is the cost of the plain pizza without any additional toppings.
- When m = 1, the equation becomes C = 0.5(1) + 5 = 5.5, indicating that the cost increases by $0.5 when one additional topping is added.
Therefore, option A correctly interprets the slope and y-intercept of the equation.
Part A : How long will it take you to pay a $600000 loan at 3.7% yearly interest if you continue to make monthly payments of $2500 per month?
Part B : How much money will you have paid in total after you are done paying the above loan with its respective interest rate? AND, based on your answers, how much money did the bank make in profit?
DO ALGEBRAICALLY!!! PLEASE AND THANK YOU!!!
Answer:
Part A: 2.159 years.Part B: $647929.8. $47929.8Step-by-step explanation:
Part A:
Let, it will take x years to pay.
According to the question,
[tex]2500\times12x = $600000 + $600000 \times \frac{3.7x}{100} \\12x = 240(1 + \frac{3.7x}{100})\\x = 2(1 + \frac{3.7x}{100})\\0.926x = 2\\x = 2.159[/tex]
Part B:
Total money that needs to be paid is [tex]600000(1 + \frac{3.7\times 2.159}{100} )[/tex] = $647929.8.
The bank made $47929.8 in profit.
PLEASE HELP ME ASAP!!!! (I included the picture below with the question!!!)
I WILL GIVE BRAINLIEST! PLEASE SOLVE FAST!
Answer:
[tex]x=30^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle KNL
we know that
[tex]m\angle KNL+m\angle LNM+m\angle ONM=180^o[/tex]----> by straight angle
we have
[tex]m\angle LNM=45^o[/tex] ---> given problem
[tex]m\angle ONM=105^o[/tex] ---> given problem
substitute the given values
[tex]m\angle KNL+45^o+105^o=180^o[/tex]
[tex]m\angle KNL+150^o=180^o[/tex]
[tex]m\angle KNL=180^o-150^o[/tex]
[tex]m\angle KNL=30^o[/tex]
step 2
Find the value of x
In the right triangle KNL
we know that
[tex]m\angle KNL+m\angle NKL=90^o[/tex] ----> by complementary angles
we have
[tex]m\angle KNL=30^o[/tex]
[tex]m\angle NKL=2x[/tex]
substitute
[tex]30^o+2x=90^o[/tex]
[tex]2x=90^o-30^o[/tex]
[tex]2x=60^o[/tex]
[tex]x=30^o[/tex]
PLEASE HELP!!!
Nivyana and Ana are selling their apparel to earn money for a cruise. Knitted scarves are $50, and mittens are $25 per pair. They cannot make more than 30 scarves and mittens combined. They need to earn at least $1000 to pay for the cruise and souvenirs.
Part A:Write the inequalities that would represent the situation
Part B: GRAPH the system of linear inequalities and shade where the solutions are.
Part C: Identify two possible solutions to Nivyana and Ana's situation
--------- scarves ------------scarves
---------------mittens -----------mittens
Step-by-step explanation:
Part A:
Let [tex]m[/tex] be the number of mittens and [tex]s[/tex] be the number of scarves. Then we have the inequalities:
[tex]s+m\leq 30.[/tex] This says Nivyana and Ana cannot make more than 30 scarves
[tex]50s+25m\geq 1000.[/tex] This says that Nivyana and Ana have to earn at least $1000.
Part B:
The graph is attached.
Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.
The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.
Part C:
From the graph we get two possible solutions:
15 scarves & 10 mittens
25 scarves & 5 mittens.
These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)
What is the equation of the line graphed below?
Answer:
C
Step-by-step explanation:
The slope is 4/1, written as 4
The y int is 4
Write the equation in y = mx + b form
y = 4x + 4
if point A(-6,-2) of a trapezoid is moved through the translation (x+1, y-3) what will coordinates of A1 be?
Answer:
A1(-5,-5)
Step-by-step explanation:
given : A(-6,-2)
simply apply the translation to the coordinates above
A1 ( -6 + 1, -2-3) = A1(-5,-5)
using distributive property-2(n+9)
Answer: -2n + -18
Explanation: Let's simplify this problem using the distributive property.
The first thing we want to do is to distribute or multiply the -2 by each of the terms inside the set of parentheses.
So we get -2 (n) + -2 (9) and this simplifies to -2n + -18.
#18 i can't figure this out
Answer:
∠Q = 75 °
Step-by-step explanation:
Since PR = PQ then Δ PQR is isosceles and the base angles are congruent, that is
∠R = ∠Q = 2x + 15
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
2x + 15 + 2x + 15 + x = 180, that is
5x + 30 = 180 ( subtract 30 from both sides )
5x = 150 ( divide both sides by 5 )
x = 30
Hence
∠Q = 2x + 15 = (2 × 30) + 15 = 60 + 15 = 75°
two years ago, the howards bought a van for $27,500. today the value of the van has decreased 35%. what is the value of the van now?
Answer: $17,875
Step-by-step explanation:
take 27,500 and multiply it by 35% or .35
27500 x .35= 9625
take 9625 and subtract it from the initial value
27500 - 9625= 17875
Answer:
35 × $27500 = $9625
100 1
= $27500-$9625
=$17875
Elijah made 100 brownies this week. He baked 4 more than three times the total he made last week. How many brownies did he bake last week?
Answer:
32
Step-by-step explanation:
Subtract 4 from 100
96
Divide by 3
32
The solution to the equation is x = 32, so Elijah baked 32 brownies last week.
Explanation:To find out how many brownies Elijah baked last week, we need to solve the equation 100 = 4 + 3x, where x is the number of brownies he made last week. Here are the steps to solve the equation:
Subtract 4 from both sides of the equation: 100 - 4 = 3xSimplify: 96 = 3xDivide both sides of the equation by 3: 96 ÷ 3 = xCalculate the result: x = 32Therefore, Elijah baked 32 brownies last week.
Learn more about solving equations here:https://brainly.com/question/17595716
#SPJ2
If x =− 2 and x^2+y^2+3xy =-5 , then find y
Answer:
y = 3
Step-by-step explanation:
Given:
x²+y²+3xy =-5 and x = -2
Substituting x=-2 into the equation:
(-2)² + y² + 3y(-2) = -5
4 + y² - 6y = -5
y² - 6y +4 + 5 = 0
y² - 6y +9 = 0 (solve by factorization)
(y-3) (y-3) = 0
y = 3
All of the x values or inputs are called what?
For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the equation. Be sure to include at least two terms from the word bank. Word Bank sum difference product quotient equal variable solution inverse add subtract multiply divide more than less than greater than inequality greater than or equal to less than or equal to equation negative
x/2 + 3 = -5
Answer:
The solution for the equation is x equal to -16
Step-by-step explanation:
Let's find the solution for x in the equation given:
x/2 + 3 = -5
Multiplying by 2 at both sides of the equation, we have:
x + 6 = -10
Subtracting 6 at both sides of the equation, we have:
x + 6 - 6 = - 10 - 6
x = - 16
The solution for the equation is x equal to -16
Terms used: multiply, subtract, solution, equal to, equation
To solve the equation x/2 + 3 = -5 for x, subtract 3 from both sides to get x/2 = -8. Then multiply both sides by 2 to isolate x, giving the solution x = -16.
Explanation:To find the solution for the variable x in the given equation x/2 + 3 = -5, we need to use the inverse operations of addition and division. Firstly, we need to eliminate the +3 from the left-hand side of the equation. We apply the inverse operation to addition which is subtraction. Therefore, we subtract 3 from both sides of the equation. This calculates to: x/2 = -5 -3. This can be simplified to x/2 = -8.
Secondly, to solve for the variable x we then need to remove the division by 2 and to do this, we multiply each side of the equation by 2 (the inverse operation of division) because x divided by 2 multiplied by 2 is equal to x. Hence the new equation becomes: 2*(x/2) = 2*-8 and simplifying gives us x = -16.
This process shows that the solution to the equation x/2 + 3 = -5 is x = -16.
Learn more about Equation Solving here:https://brainly.com/question/18262581
#SPJ3
How many inches are in 15% of 1.2 feet?
Answer:
2.16 inches so ya
The number of inches in 15 percent of 1.2 foot is obtained as 216.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The number of inches in 1 feet = 12.
Then, in 1.2 foot the inches are 1.2 × 12 = 14.4.
Now, the percent value 15% of 1.2 foot is given as below,
15% × 1.2 foot
⇒ 15/100 × 14.4 inch
⇒ 216 inch
Hence, the number of inches are given as 216.
To know more about arithmetic operation click on,
https://brainly.com/question/25834626
#SPJ2
A state park is designed in a circular pattern as shown. Martha rides her bike along the circular path from the ranger station to the pool. How far does she ride to the nearest hundredth of a mile?
A) .79 miles
B) 1.6 miles
C) 2.3 miles
D) 3.7 miles
C. 2.3 miles
Step-by-step explanation:
The details of the image are as follows;
Ranger station to Nature Center = 90°
Nature center to petting zoo= 40°
Petting zoo to Tennis court =120°
Tennis court to Pool = 65°
Pool to Ranger station= 45°
The radius of the circular pattern = 1 mile
The formula to apply is;
Arc length = 2πr angle / 360° where r is radius and π=3.14
Finding arc length from Ranger Station to Nature Center will be;
Arc length = 2×3.14×1×90°/360°
Arc length=2×3.14×1×1/4 =1.57 miles
Finding distance from Nature Center to Petting Zoo
Arc length= 2×3.14×1×40°/360°
Arc length= 2×3.14×1×1/9 = 0.70 miles
Total =1.57+0.70 =2.27 miles
Answer to the nearest hundredth = 2.3 miles
Learn More
Arc length : https://brainly.com/question/11692709
Keywords : circular , pattern, path, hundredth
#LearnwithBrainly
tell whether the sequence is geometric 31, 213, 4459, 637, 91,....
Answer:
No.
Step-by-step explanation:
If it is geometric the quotient of the terms and the previous term will be a constant.
213 / 31 = 6.871
4459 / 213= 20.93
These are not equal so the sequence is not geometric.
what is a squar plus b squiar
Answer:
The theorem states that if a right triangle has two sides equal to a and b, and a hypotenuse equal to c, then a squared plus b squared equals c squared. The hypotenuse of a right triangle is the side opposite the right angle.
Step-by-step explanation:
EXPLAIN HOW 28*4/7 IS CORRECT AND (28 / 7) x 4 IS NOT. I'M GIVING 100 POINTS AND I NEED ANSWERS
Step-by-step explanation:
[tex]28\cdot\dfrac{4}{7}=\dfrac{28}{1}\cdot\dfrac{4}{7}=\dfrac{28\cdot4}{1\cdot7}\\\\\text{simplify 28 and 7 (divide both by 7)}\\\\=\dfrac{28\!\!\!\!\!\diagup^4\cdot4}{1\cdot7\!\!\!\!\diagup_1}=\dfrac{4\cdo4}{1\cdot1}=\dfrac{16}{1}=16[/tex]
[tex]\dfrac{28}{7}\cdot4=(28:7)\cdot4=4\cdot4=16[/tex]
[tex]\text{Both expressions give the same result.}[/tex]
[tex]28\cdot\dfrac{4}{7}=\dfrac{28}{7}\cdot4\\\\28\cdot\dfrac{4}{7}=\dfrac{28}{1}\cdot\dfrac{4}{7}=\dfrac{28\cdot4}{1\cdot7}=\dfrac{28\cdot4}{7\cdot1}=\dfrac{28}{7}\cdot\dfrac{4}{1}=\dfrac{28}{4}\cdot4[/tex]
Your question:
EXPLAIN HOW 28*4/7 IS CORRECT AND (28 / 7) x 4 IS NOT
It all depends on the content of the question for which these expressions are.
Qestion:
Mr. Chang’s class has 28 students, 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang’s class?
Correct is 28 * 4/7.
(You calculate a fraction of a number).
28/7 * 4 - gives the same result. But the expression does not match the content of the question.
Daniel is selecting a sock from his drawer.
He chooses a sock at random, does not
replace it, and then selects a second sock at
random. What is the probability that Daniel
selected a solid sock both times?
Answer:15/28
Step-by-step explanation: Ive had this question before That is the answer :)
Final answer:
To find the probability of selecting a solid sock both times from Daniel's drawer, multiply the probabilities at each step independently to get 1/105 or approximately 1% in total.
Explanation:
To calculate the probability of selecting a solid sock both times, you need to consider the independent probabilities at each step.
Probability of selecting a solid sock the first time is 1/7.
Probability of selecting a match for the second sock from the remaining socks would be 1/5.
Continuing this pattern, the total probability of selecting a solid sock both times is 1/105 or about 1%.
There are 128128128 ounces in a gallon. There are 444 quarts in a gallon.
How many ounces are in a quart?
Answer:
32 ounces
Step-by-step explanation:
128oz=1gal
4quarts=1gal
128÷4=32
32oz=1 quart
Answer:
1
Step-by-step explanation:
hope this helps some one
stay safe and pease still were a mask
Trina's car uses 10 gallons of gas to travel 120 miles. If she has 5 gallons of gas in the tank, how much more gas will she need to drive 204 miles?
Answer: 12 gallons
Step-by-step explanation:
Use proportion to estimate how much gas she needs for 204 miles.
10:120=x:204
204*10=120x
x=2040/120
x=17 gallons
For 204 mile trip Trina needs 17 gallons of gas. She has 5 gallons.
17-5=12
She will need 12 gallons of gas.
Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality:
y > one half x + 2 (5 points)
The origin is not included in the shaded region and the shaded area is above the line.
The origin is not included in the shaded region and the shaded area is below the line.
The origin is included in the shaded region and the shaded area is above the line.
The origin is included in the shaded region and the shaded area is below the line.
Answer:
The correct option is
The origin is included in the shaded region and the shaded area is below the line.
Step-by-step explanation:
Y>3/2x + 2
Put x=0
Y= 2
(0,2)
Put y=0
X= -4/3
(-4/3,0)
See attached picture for the sketch
Answer:
The origin is included in the shaded region and the shaded area is below the line.
Write the equation of the line with a slope of 5 and the point (2, 6) in slope-intercept form
Answer:
y = 5x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, thus
y = 5x + c ← is the partial equation
To find c substitute (2, 6) into the partial equation
6 = 10 + c ⇒ c = 6 - 10 = - 4
y = 5x - 4 ← equation of line
An employee earns $175 for 15 hours work.
Assuming he is paid by the hour, how much will this employee earn in 18 hours?
Answer:
$210
Explanation:
175/15 = 11.67
11.67x18 = 210
The amount of money that employees earn in 18 hours with the same rate of change will be $210.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
An employee earns $175 for 15 hours of work.
Per hour earning = $175/15
Earning in 18 hours will be, 175/15 x 18 = $210
Hence "The amount of money that employees earn in 18 hours with the same rate of change will be $210".
To learn more about the rate of change here,
brainly.com/question/12786410
#SPJ2