To get the interquartile range (IQR) of the data set, we must first determine the median [tex](Q2). 00 0 0 12\dfrac12 2 1 begin fraction,[/tex] divide by 2, end fraction.
[tex]00 0 011 1 1 12\dfrac12 2 1 begin fraction,[/tex]divide by 2, end fraction 22 2 2 11 1 1 14\dfrac14 4 1 begin fraction, divide by 4, end fraction 54\dfrac 5 4 5 end fraction, 5, divided by 4, start fractio When the data is sorted in order, the median is the middle value, thus we must locate the value that is exactly in the centre[tex]0 0 0 11] 1 12\dfrac12 2 1 begin fraction,[/tex] divide by 2, end fraction 22 2 11 1 1 14\dfrac14 4 1 begin fraction, divide by 4, end fraction 54\dfrac54 4 5 end fraction, 5, divided by 4, start fraction The median is (1 + 1)/2 = 1 since the middle two numbers are 1 and 1. The median of the lower half of the data (Q1) and the median of the upper half of the data (Q2) must then be determined (Q3) For the bottom half: 00 0 0 11 1 1 Q1 = 0 since the intermediate value is 0. For the top half: 12\dfrac12.
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Translate the triangle then enter the new coordinates (1,4) (-3,2) (2,-2)
Step-by-step explanation:
the given pair (3, 2) is the length of the translation ?
it is really totally simple : you need to add the x value of the translation to the x-cordinate of each point. the same for the y value and the y- coordinates.
A' = (1 + 3, 4 + 2) = (4, 6)
B' = (2 + 3, -2 + 2) = (5, 0)
C' = (-3 + 3, 2 + 2) = (0, 4)
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 51 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 4000 aspirin tablets actually has a 8% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is 0.1813 (Round to four decimal places as needed.) The company will accept% of the shipments and will reject % of the shipments, so (Round to two decimal places as needed.)
The probability that this whole shipment will be accepted is 0.1813. The company will accept 82.87% of the shipments and will reject 17.13% of the shipments, so the likelihood of a rejected shipment is relatively low.
Probability is essentially the likelihood that something will occur. The entire number of potential outcomes must first be known in order to calculate the likelihood of a particular event.
P(E) = Number of favorable outcomes / Number of total outcomes
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How many degrees is the sum of the measures of the interior angles of a regular polygon with 18 sides?
One x-intercept for a parabola is at the point
(1,0). Use the factor method to find the other
x-intercept for the parabola defined by this
equation:
y = 2x² + 8x - 10
Separate the values with a comma.
Enter the correct answer.
Needddd the answerrrrr plssss
The expοnential functiοn fοr the given table is y = 5(2)ˣ.
What is a Functiοn?A functiοn is relatiοn between set οf inputs (called dοmain) and set οf οutputs (called range), where each input is assοciated with exactly οne οutput. A functiοn is usually denοted by symbοl like f, and is written as f(x), where x is element οf dοmain.
we can use the general fοrm οf an expοnential functiοn, which is:
y = abˣ
where a and b are cοnstants that we need tο determine.
Using the given values οf x and y in the table, we can fοrm fοur equatiοns as fοllοws:
2.5 = ab⁽⁻¹⁾
5 = ab⁰
10 = ab¹
20 = ab²
Dividing the secοnd equatiοn by the first equatiοn, we get:
5/2.5 = (ab⁰)/(ab⁽⁻¹⁾ )
2 = b
Substituting this value οf b in the οther equatiοns, we get:
2.5 = a(2)⁽⁻¹⁾
a = 5
10 = 5(2)¹
10 = 10
20 = 5(2)²
20 = 20
Therefοre, the expοnential functiοn fοr the given table is:
y = 5(2)ˣ.
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You invest $3000 in an account at 3.5% per year simple interest. How much will you have in the account at the beginning of the 7th year? Round your answer to the whole dollar.
Answer: the answer is that you will have $3630 in the account at the beginning of the 7th year.
Step-by-step explanation:
I = Prt
Using this formula:
I = Prt
I = 3000 x 0.035 x 6
I = $630
Therefore, the total amount in the account at the beginning of the 7th year will be
Total = Principal + Interest
Total = $3000 + $630
Total = $3630
In September, Larson Inc. Sold 40,000 units of its only product for $383,000, and incurred a total cost of $325,000, of which $38,000 were fixed costs. The flexible budget for September showed total sales of $400,000. Among variances of the period were: total variable cost flexible-budget variance, $7,000U; total flexible-budget variance, $74,000U; and, sales volume variance, in terms of contribution margin, $45,000U. The total sales revenue in the master budget for September, to the nearest dollar, was:
Thus, to the closest dollar, the total sales revenue included in the master budget for September was as follows: master budget sales income = $11.71 multiplied by 40,000 Sales master budget.
Let's first get the precise variable cost per unit:
Real variable cost is $7.43 per unit.
Let's next determine the revenue from the flexible budget:
$400 000 in flexible budget revenue
Let's now determine the actual sales revenue:
$383,000 was the actual sales revenue.
Let's figure out the overall variance for the flexible budget:
Overall variance for the flexible budget is $17,000.
Given that the flexible-budget variance is unfavourable (U), we can infer that actual revenue was lower than anticipated.
a... a.. a.. a.. a
Variance in sales volume is 40,000 x ($9.58 - $10.00 + $7.43)
Variance in sales volume = 40,000 x $6.01
Variance in sales volume = $240,400
Let's figure out the overall flexible-budget variation for variable costs:
Variance in the flexible budget for all variable costs is $-106,800.
Let's now determine the precise number of units sold using the sales volume variance.
The budgeted amount of units sold that were sold:
With the actual number of units sold compared to the projected amount (34,132.94), we can determine the budgeted price per unit as follows:
$11.71 is the planned price per unit (rounded to nearest cent)
Thus, to the closest dollar, the total sales revenue included in the master budget for September was as follows:
master budget sales income = $11.71 multiplied by 40,000
Sales master budget
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Using the bag of marbles below, find the probability of pulling a blue marble two times in a row. After pulling the first blue marble, you do NOT replace it in the bag before pulling the second one. Each marble has an equally likely chance of being pulled. Answer as a simplified fraction.
The probability of picking two blue marbles is 1/21.
What is the probability?Probability is used to determine how likely it is that a random event would occur. The probability of a random event happening lies between 0 and 1. If it is certain the event would happen, the probability value is 1 and if it is certain that the event would not happen, the probability value is 0.
Probability of picking two blue marbles = (number of blue marbles / total number of marbles) x (number of blue marbles -1 / total number of marbles - 1)
Total number of marbles = 7
(2/7) x (2-1/7-1)
2/7 x 1/6 = 1/21
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$4, 700 is invested in an account earning 6.8% interest (APR), compounded continuously. Write a function showing the value of the account after t years, wher the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage o growth per year (APY), to the nearest hundredth of a percent.
The function for the value of the account after t years is:[tex]\rm V(t) = 4700 \times e^{(0.068t)[/tex].
The percentage growth per year (APY) is 7.03%.
What is formula for continuous compounding?The formula for the value of an account with continuous compounding is given by:
[tex]\rm V = Pe^{(rt)[/tex]
where:
V is the value of the account after t years
P is the initial principal amount invested (in this case, $4,700)
e is the mathematical constant (approximately equal to 2.71828)
r is the annual interest rate expressed as a decimal (in this case, 0.068)
t is the time period in years.
Therefore, the function for the value of the account after t years is:
[tex]\rm V(t) = 4700 \times e^{(0.068t)[/tex]
To find the annual percentage yield (APY), we use the formula:
[tex]APY = 100 \times (e^r - 1)[/tex]
where r is the annual interest rate expressed as a decimal (in this case, 0.068).
[tex]APY = 100 \times (e^{0.068} - 1)[/tex]
= 7.03%
Therefore, the percentage growth per year (APY) is 7.03%.
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If you place 37 foot ladder against the top of a 15 foot building
I you place the 37 foot ladder against the top of the 15 foot building, it will reach a height of 52 feet.
If you place a 37 foot ladder against the top of a 15 foot building, then the ladder will reach a height of 52 feet (37+15=52). To calculate this, you can use the formula for addition, which is x + y = z, where x is the height of the building, y is the height of the ladder, and z is the total height the ladder will reach. In this case, x = 15 and y = 37, so the total height the ladder will reach will be z = 15 + 37 = 52. This means that if you place the 37 foot ladder against the top of the 15 foot building, it will reach a height of 52 feet.
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The graph of y = 4sin(x + 3) - 2 is obtained by shifting the graph of y = 4sin x - 2 horizontally 3 units to the right.
True of false
Step-by-step explanation:
False, it is 3 units to the left
For any function,
[tex]f(x)[/tex]
the function transformation of
[tex]f(x - h)[/tex]
implies a transformation h units to the left
If h is the positive, this implies a transformation to the right
If h is negative, this implies a transformation to the left.
Here's since
[tex](x + 3[/tex]
can be written as
[tex](x - ( - 3))[/tex]
Our h is negative, therefore we move 3 units to the left
Lorie Reilly decides to go back to college. For transportation, she borrows money from her parents to buy a small car for $7,200. She plans to repay the loan in 7 months. What amount can she deposit today at 5.25% to have enough money to pay off the loan?
Lorie should deposit $6,986.05 today at 5.25% to have enough money to pay off the loan in 7 months.
What amount can Lorie Reilly deposit today at 5.25% to have enough money to pay off the loan?To determine the amount that Lorie should deposit today to have enough money to pay off the loan.
We use the simple interest formula for accrued amount.
A = P( 1 + rt )
Where A is total amount, P is initial amount, r is interest rate and t is elapsed time.
Given that;
Accrued amount A = $7,200Time = 7 monthsrate R = 5.25%Principal P = ?First, converting R percent to r a decimal
r = R/100
r = 5.25/100
r = 0.0525
Next, we put time into years for simplicity,
t = 7 months / 12 months
t = 7/12 year
Plug the values into the above formula.
A = P( 1 + rt )
P = A / ( 1 + rt )
P = $7,200 / ( 1 + ( 0.0525 × 7/12 ) )
P = $7,200 / ( 1 + 0.030625 )
P = $7,200 / 1.030625
P = $6,986.05
Therefore, the principal or initial amount is $6,986.05.
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The amount she should deposit today to have enough money to pay off the loan would be = $1,060
How to calculate the amount that should be deposited today?The cost of the small car that Lorie Reilly needs to buy for college = $7,200.(P)
The number of months that she plans to repay the money = 7 months = 0.58 yr.(T)
The rate at which the money needs to be deposited = 5.25%. (R)
The simple interest = Principal× Time × Rate /100
Simple interest = 7200× 0.58 × 5.25/100
= 21924/100
= $219.24
The amount she is expected to pay after 7 months = 7200+219.24 = 7419.24
The amount she should deposit today to have enough money to pay off the loan = 7419.24/7 = $1,060( approximately)
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24f(x)=−x2+1 g(x)=x
Exer. 21-34: Find (a) (f∘g)(x) and the domain of f∘g and (b) (g∘f)(x) and the domain of g∘f.
(a) (f∘g)(x) and the domain of f∘g are defined for real numbers and (b) (g∘f)(x) and the domain of g∘f is defined for real numbers.
The given functions are:f(x) = −x² + 1g(x) = x
Exer. 21-34: To Find
(a) (f ∘ g)(x) and the domain of f ∘ g and (b) (g ∘ f)(x) and the domain of g ∘ f.(a) (f ∘ g)(x) and the domain of f ∘ gTo find the composite of the two functions, substitute the value of g(x) into f(x). Now, (f ∘ g)(x) is given by:f(g(x)) = f(x) = f(x) = f(x) = -x² + 1. The domain of (f ∘ g)(x): Since g(x) is defined for all real numbers, the domain of (f ∘ g)(x) is also defined for all real numbers.
(b) (g ∘ f)(x) and the domain of g ∘ f
To find the composite of the two functions, substitute the value of f(x) with g(x). Now, (g ∘ f)(x) is given by:g(f(x)) = g(-x² + 1) = -x² + 1
The domain of (g ∘ f)(x): The domain of f(x) is defined for all real numbers. However, the domain of g(x) is also defined for all real numbers. Therefore, the domain of (g ∘ f)(x) is defined for all real numbers.
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A dilation has center (0,0). Find the image of the point L(-4,3) for the scale
factor 3.
Answer: To find the image of point L(-4,3) after a dilation with a scale factor of 3 and center at the origin, we need to multiply the coordinates of point L by the scale factor.
The formula for dilation is:
(x', y') = (kx, ky)
where (x, y) are the original coordinates, (x', y') are the coordinates of the image, and k is the scale factor.
In this case, k = 3 and the coordinates of point L are (-4, 3).
So,
x' = kx = 3(-4) = -12
y' = ky = 3(3) = 9
Therefore, the image of point L(-4, 3) after the dilation with a scale factor of 3 and center at the origin is (-12, 9).
Step-by-step explanation:
PLS HELP ASAP
!!!!!!!!!
Answer:
3x³- 8x² + 2x +3
Step-by-step explanation:
All you need to do is multiply everything in the second bracket with the first bracket like you would normally do with double brackets.
3x³-3x²-5x²+5x-3x+3=
3x³-8x²+2x+3
Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?
The slope of the linear function that represents the cost of plan B is $0.17.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Since Plan B has the same monthly base charge as plan A, we can logically deduce that the data points (0, 14.45) and (45, 22.10) lie on the linear function.
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (22.10 - 14.45)/(45 - 0)
Slope (m) = $0.17
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Complete Question:
Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table. Monthly Charge for Plan A Minutes used, x Monthly charge ($), y 0 14.45 3 14.84 6 15.23 9 15.62 12 16.01 Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?
Jaya spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7300 feet. Jaya initially measures an angle of elevation of 16^∘ to the plane at point A. At some later time, she measures an angle of elevation of 28^∘ to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest tenth of a foot if necessary
The distance the plane traveled from point A with measures an angle of elevation of 16°, to point B with measures an angle of elevation of 28°, is equals to the 11,728.6feet.
Jaya spots an airplane on radar that is currently approaching in a straight line start from point O in above figure, and that will fly directly overhead.
Altitude that plane maintain,h = 7300 feet
Initially, measure an angle of elevation to the plane at point A = 16°
Measure an angle of elevation to the plane at point B = 28°
Now, Let the distance between point A and point B be equal to 'x feet' and distance between point B and point C ( base) be equal to 'y feet'. So, distance between point A to point C = (x + y ) feet. We have to calculate the distance the plane traveled from point A to point B, i.e., x feet. See the above figure carefully, we see in right angled triangle BOC, tan 28° = 7300/y --(1)
In right angled triangle AOC,
tan 16° = 7300/(x + y) --(2)
Cross multiplication in equation (2)
=> tan 16° ( x + y ) = 7300
=> x + y = 7300/tan 16° --(3)
from equation (1), y = 7300/tan 28°
=> y = 7300/0.5317 = 13,729.55
so, x = 7300/tan 16° - y = 7300/0.287 - 13,729.55
= 25,458.12 - 13,729.55
= 11,728.58 ~ 11,728.6
Hence, required distance is 11,728.6feet.
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What does 100-20-20-30-30+20+30+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+20+10=.
100-30-30-20-20=0. 20+30=50. 50+5+1+1+1+1+1=60. 60+1+1+1+1+1+1+1+1+1+1=70.
70+20=90. 90+10=100. So 100 is our answer.
Answer: this equals 100
Step-by-step explanation:
At dominos, each pizza is cut into 8 slices. Chris ate 5 slices from a pizza with a diameter of 20inch pizza, what is the area of the slices Chris ate?
Answer: The area of each slice of pizza can be calculated by finding the area of the whole pizza and dividing it by the number of slices.
The radius of the pizza is half of the diameter, so the radius is 20/2 = 10 inches.
The area of the whole pizza can be calculated using the formula for the area of a circle:
Area = π × radius^2
Area = π × 10^2
Area = 100π square inches
Since there are 8 slices, each slice has an area of:
100π square inches / 8 = 12.5π square inches
Therefore, the area of the 5 slices that Chris ate is:
5 × 12.5π square inches = 62.5π square inches
This is approximately equal to 196.35 square inches, when rounded to two decimal places.
Step-by-step explanation:
there are 6 pure spectral colors: red,blue,orange,yellow,green and violet,Bees can only see 2/3 of these colors.how many of the pure spectral colors can bees see?
Answer:
Step-by-step explanation:
2/3*6
6*6
12
You rent an apartment that costs $1200 per month during the first year, but the rent is set to go up 11% per year. What would be the rent of the apartment during the 8th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 8th year would be approximately $2491.4.
To calculate the rent of the apartment during the 8th year, we need to apply the 11% increase per year for a total of 7 years (from the 2nd to the 8th year). Here's the calculation:
Rent for the 2nd year:
$1200 + (11% of $1200) = $1200 + ($132) = $1332
Rent for the 3rd year:
$1332 + (11% of $1332) = $1332 + ($146.52) = $1478.52
Rent for the 4th year:
$1478.52 + (11% of $1478.52) = $1478.52 + ($162.64) = $1641.16
Rent for the 5th year:
$1641.16 + (11% of $1641.16) = $1641.16 + ($180.53) = $1821.69
Rent for the 6th year:
$1821.69 + (11% of $1821.69) = $1821.69 + ($200.39) = $2022.08
Rent for the 7th year:
$2022.08 + (11% of $2022.08) = $2022.08 + ($222.43) = $2244.51
Rent for the 8th year:
$2244.51 + (11% of $2244.51) = $2244.51 + ($246.90) = $2491.41
Therefore, the rent of the apartment during the 8th year would be approximately $2491.4.
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The Picture and Sound electronics store has hired Trevor to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. There is a proportional relationship between the number of times Trevor turns the crank to lift a box, x, and the height the box has been lifted (in feet), y. He turns the crank 5 times to lift a box 3 feet. Write the equation for the relationship between x and y.
y =
The relationship between the number of times Trevor turns the crank, x, and the height the box has been lifted, y, is a linear equation y = (3/5)x.
What is a linear equation?
A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a variable raised to the first power (i.e., the variable is not squared or cubed). The general form of a linear equation with one variable, x, is:
ax + b = 0
Now,
We are given that there is a proportional relationship between the number of times Trevor turns the crank, x, and the height the box has been lifted, y. Let k = constant of proportionality.
Then, we can write the equation as:
y = kx
We also know that Trevor turns the crank 5 times to lift a box 3 feet.
Now
3 = k(5)
Solving for k, we get:
k = 3/5
Substituting this value of k in the equation, we get:
y = (3/5)x
Therefore, the equation for the relationship between the number of times Trevor turns the crank, x, and the height the box has been lifted, y, is y = (3/5)x.
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A model igloo has a scale of 1in: 2ft. If the model igloo is 7in wide then how wide is the real igloo???
The actual width of the real igloo is 14 feet.
How wide is the real igloo?A ratio scale is simply a quantitative scale where there is a true zero and equal intervals between neighboring points.
The given scale tells us that 1 inch on the model igloo represents 2 feet on the real igloo.
If the scale of the model igloo is 1 inch to 2 feet, then we can use this ratio to convert the width of the model igloo (7 inches) to the width of the real igloo:
= 7 inches × 2 feet/inch
= 14 feet
Therefore, the width is 14 feet
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The statement say a contractor contracted to supply water to three Altein ring road has decided to investigate the financial impact that the monthly installments, salaries and the price of fuel had to his business per month. The contractor will use one of his water tankers to conduct an investigation. The contractor was supplying water to the Altien village 5 km ring road construction site where the road had to be paved using the paving bricks. The paving of the road has started in January 2022 and ran for 10 months.
Questions
1.1 write down the loan term of the truck in years
1.2 determine the monthly repayments that were made towards the water tanker including the insurance cover amount
1.3 the contractor had already made half of the monthly installments towards the truck in June 2022. Determine the total amount of money that was owed to the finance excluding the insurance in June 2022
1.4 give an explanation on the significance of including an insurance cover when a contractor purchases the water tanker
Therefore , the solution of the given problem of unitary method comes out to be in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.
What is an unitary method?The task can be completed by multiplying the data gathered using this type of nanosection along with two variable individuals who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.
Here,
1.1. The statement omits details about the truck's loan term. Therefore, without more details, we are unable to respond to this query.
1.2. Assume that the truck's loan period is n years and that the contractor borrowed P dollars at an annual interest rate of r to buy the water tanker.
M is calculated as (r * P * (1 + r)n) / ((1 + r)n - 1)
5 years + 60 months Equals n
r = 5% / 12 = 0.004166667 (weekly interest rate) (monthly interest rate)
P = $100,000
=> M = (0.004166667 * $100,000 * (1 + 0.004166667)^60) / ((1 + 0.004166667)^60 - 1)
≈> $1,870.24
As a result, the total monthly payments made for the water tanker, including the insurance protection, came to about $1,870.24.
1.3
(Total Amount Borrowed - Amount Paid) / 2
=> ($100,000 - $1,870.24 * 6) / 2 = $47,259.52 is the sum that is owed.
Therefore, in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.
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For the equation y=8-2, complete the table and plot the ordered pairs on the graph.
Оо
Size
O
X
y
< Previous
-3
-2
-1
0
2
3
Step-by-step explanation:
For the equation y=8-2, complete the table and plot the ordered pairs on the graph.
Оо
Size
O
X
y
< Previous
-3
-2
-1
0
2
3
Show your work plssss
As a result, the Moon orbits the Earth roughly 2.8 billion times while the Sun revolves once around the Milky Way's nucleus.
How is earths rotation calculated?
One cycle of the Sun around the Milky Way's nucleus is thought to take between 225 and 250 million years to complete. The synodic month, or the length of time it takes the Moon to complete one orbit of the Earth, lasts roughly 29.5 days.
We must divide the total time of one orbit of the Sun around the Milky Way by the amount of time it takes for the Moon to orbit the Earth once in order to determine how many times the Moon orbits the Earth during one orbit of the Sun around the Milky Way's centre.
The result is (Total time for one orbit of the Sun around the centre of the Milky Way)/(Time for one orbit of the Moon around the Earth) = (225 million years x 365.25 days per year)/(29.5 days per orbit of the Moon) = around 2.8 billion orbits of the Moon around the Earth.
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i need help on this question
Option C is correct. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.
What is equations ?
An equation is a mathematical statement that shows the equality of two expressions. It usually contains one or more variables and is solved to find the value of the variable(s) that make the equation true. Equations are used extensively in mathematics, physics, engineering, and many other fields to describe relationships between quantities and to solve problems.
The given system of equations is:
System A:
x + y = 5
3x - 2y = -35
And the solution to this system is (-7, 2).
To obtain System B, we need to manipulate the equations in System A. Let's start by isolating y in the first equation:
y = 5 - x
Now we can substitute this expression for y into the second equation and simplify:
3x - 2(5 - x) = -35
3x - 10 + 2x = -35
5x = -25
x = -5
Now that we have x = -5, we can substitute it back into either of the original equations to solve for y:
x + y = 5
-5 + y = 5
y = 10
So the solution to System B is (-5, 10).
Comparing the two solutions, we see that they are not the same. Therefore, the correct answer is A. To get System B, the second equation in System A was replaced by the sum of that equation and the first equation multiplied by 3. The solution to System B will not be the same as the solution to System A.
Therefore, Option C is correct. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.
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4.02 Lesson check ! (1)
1. The sequence is an arithmetic sequence with a common difference of d = -200.
2. The sequence is not an arithmetic sequence.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
For item 1, each term is the previous term subtracted by 200, hence the sequence is in fact an arithmetic sequence with a common difference of -200.
For item 2, the difference between consecutive terms is difference, hence the sequence is not an arithmetic sequence.
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Do a dot plot for the data set:
3, 7, 6, 5, 3, 6, 5, 3, 7, 3, 6
Answer: So pretty much what you do is you put a dot on the positive 3 then move over one and put another on the 7 and you just keep doing that with all of them
Step-by-step explanation:
Write an explicit formula for an,the nth term of the sequence 23,19,15,
If sequence 23,19,15, the nth term of the sequence 23, 19, 15 is given by the formula aₙ = 23 - 4(n-1).
To find the explicit formula for the nth term of the sequence 23, 19, 15, we need to look for a pattern in the sequence. We can observe that each term in the sequence is obtained by subtracting 4 from the previous term. Therefore, we can write the recursive formula for this sequence as:
a₁ = 23
aₙ = aₙ-1 - 4, for n ≥ 2
To find the explicit formula, we need to use the recursive formula to eliminate the dependence on the previous term. We can do this by repeatedly substituting the recursive formula into itself, until we get an expression for an in terms of a1:
a₂ = a1 - 4 = 23 - 4 = 19
a₃ = a₂ - 4 = (a₁ - 4) - 4 = a1 - 8 = 23 - 8 = 15
a₄ = a₃ - 4 = (a₁ - 8) - 4 = a1 - 12 = 23 - 12 = 11
From this pattern, we can see that each term can be written as:
aₙ = a₁ - 4(n-1)
Substituting a1 = 23, we get the explicit formula:
aₙ = 23 - 4(n-1)
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