Answer: an=4n+5
Step-by-step explanation:
a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...
A formula for the nth term of the arithmetic sequence:
[tex]a_n=a_1+d(n-1)[/tex]
where: a₁ - is the first term of the arithmetic sequence
d - is the difference between the terms of the arithmetic sequence
d=a₂-a₁=a₃-a₂=a₄-a₃= ...
d=13-9=17-13=31-17= ...
d=4
n - is the number of the arithmetic sequence term
[tex]a_n=9+4(n-1)\\\\a_n=9+4n-4\\\\a_n=4n+5[/tex]
Use the difference of two squares to find each product.
17•7
The product of 17×7 using the difference of two squares is 119.
= 17×7
=(12+5)(12-5)
=12(12-5)+5(12-5)
=12×12-12×5+5×12-5×5
=12²-5²
=144-25
=119
The difference between two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the sum of the square roots and the other one is the difference of the square root.
I hope this answer helps.
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41% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
P(3)=
P(x >4)=
P(x<9)=
The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is;
(a) exactly three = 0.1314
(b) at least four = 0.7953
(c) less than eight = 0.93382
How to solve Binomial Probability Distribution Problems?The binomial probability distribution is the probability of exactly x successes on n repeated trials, with p probability. The formula is;
P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)
We are given;
p = 41% = 0.41
n = 12
Thus;
1) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is exactly three;
P(3) = ¹²C₃ * 0.41³ * (1 - 0.41)^(12 - 3)
P(3) = 0.1314
2) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is at least four;
P(x ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
P(x ≥ 4) = 0.7953
3) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is less than eight using binomial probability calculator is;
P(X < 8) = 0.93382
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Express 6 + √ − 81 as a simplified complex number
The given algebraic expression can be simplified as 6+9i.
Complex NumberA complex number is represented by the following form: a+bi, where a and b are real numbers. The variables: a is the real part and bi imaginary part. See an example: 7 + 14i , then:
7 real part14i imaginary partRegarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 2i² = 2*(-1)= -2.
When you subtract or sum complex numbers, you can only subtract or sum: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. Here, you can see examples:
(5 + 2i) + (5 + 2i) = 10+4i
(4 + 9i) - (1 + 5i) = 1+4i
Therefore, the result for the 6 + √− 81 will be:
6+ √81i²
6+9i
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in exercises 10-11, find the value of x so that the function has the given value.
10. m(x) = -3/5x - 4; m(x) = 2
11. w(x) = 5/6x - 3; w(x) = -18
The value of x so the the the function has the given value is as follows:
m(x) = 2; x = - 10w(x) = - 18; x = - 18How to find the value of the input of a function?A function relates an input to an output.
In other words, a function is a special relationship among the inputs and their outputs codomain) where each input has exactly one output value.
Therefore, let's find the value of x so that the function has the given values.
m(x) = -3/5x - 4; m(x) = 2
let's find the value of x when m(x) = 2
2 = - 3/5x - 4
2 + 4 = - 3/5x
6 = - 3/5 x
cross multiply
-3x = 30
x = 30 / - 3
Hence,
x = - 10
w(x) = 5/6x - 3; w(x) = -18
let's find the value of x when w(x) = -18
- 18 = 5/6x - 3
- 18 + 3 = 5 / 6 x
- 15 = 5 / 6 x
5x = - 90
x = -90 / 5
Hence,
x = - 18
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Contains the points (5, 3) and (8, 12); slope-intercept form
Answer:
y = 3x + 12
Step-by-step explanation:
y = mx + b
The m is the slope and the b is the y intercept.
Slope:
Change in y over the change in x. The ordered pair is written in the form (x,y)
[tex]\frac{12-3}{8-5}[/tex] = [tex]\frac{9}{3}[/tex] = 3
The slope is 3.
Use the slope of the 3 and the x and y from one of the ordered pairs given. I am going to use the point (5,3), but either point will work
slope 3
x = 5
y=3 Plug these all in and solve for b
y = mx + b
3 = (3)5 + b
3 = 15 + b Subtract 15 from both sides
-12 = b
This is the y intercept
y = 3x - 12
Answer:
Slope-intercept form,
→ y = 3x - 12
Step-by-step explanation:
Formula we use,
→ y = mx + b
The value of slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (12 - 3)/(8 - 5)
→ m = 9/3
→ [ m = 3 ]
Then the value of b will be,
→ y = mx + b
→ 12 = (3)8 + b
→ b + 24 = 12
→ b = 12 - 24
→ [ b = -12 ]
Now the slope-intercept form is,
→ y = mx + b
→ [ y = 3x - 12 ]
Hence, the answer is y = 3x - 12.
For each chart below, identify the output rule and classify the function as exponential, linear or neither.
The classification and the output rule for each function in this problem is given as follows:
1. Output rule: y = 5x + 11. Classification: Linear.
2. Output rule: y = 2^x. Classification: Exponential.
3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.
What defines a linear function?A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:
y = mx + b.
In which:
m is the addition to y when x increases by one.b is the value of y when x = 0.Hence, for the first table, as 5 is added to x when x increases by one, the rule is:
y = f(x) = 5x + 16.
What defines an exponential function?An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:
y = a(b)^x.
In which:
b is the addition to y when x increases by one.a is the value of y when x = 0.Hence, for the second table, the rule is:
y = 2^x.
For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.
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You buy 3 gallons of milk at $2.48/gallon, 2 gallons of
ice cream at $1.49/gallon, and 4 lbs of strawberries at
$0.58/1b. What is your total cost?
(1 point)
O$9.51
O$12.74
0$4.55
O$10.67
The total cost is $12.74
In this question, we have been given the cost of 1 gallon of milk, 1 gallon of ice-cream and 1 1b of strawberry.
1 gallon of milk costs $2.48,
1 gallon of ice-cream costs $1.49
and 1b of strawberry costs $0.58
You buy 3 gallons of milk, 2 gallons of ice cream, and 4 lbs of strawberries.
So by unitary method total cost would be,
(3 * 2.48) + (2 * 1.49) + (4 * 0.58) = $12.74
Therefore, the total cost is $12.74
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PLEASE HELP ASAP!!! Write the expression as a power and evaluate it.
8•2^7
Answer:
1024
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
, then
8 × [tex]2^{7}[/tex]
= 2³ × [tex]2^{7}[/tex]
= [tex]2^{(3+7)}[/tex]
= [tex]2^{10}[/tex]
= 1024
What is the sum -10 + (-9) + (-8) + ... + 9 + 10 +11 + 12?
Answer:
23
Step-by-step explanation:
the numbers from -10 to 10 cancel out, so all that is left is 11+12=23
Which relation is a function?
Answer:
The bottom right
Step-by-step explanation:
A relation is just a set of ordered pairs. A function is a special relation. In a function every input (x) has only one output (y).
You can use the vertical line test. If you took your pencil and vertical passed over the graph left to right. If there is any point that more than one point would be under the pencil, the relation is not a function.
if Julie average arts test score at 85 and what would you predict her average math test score would be
1. Her Average would be 80
2. Yes, there are more dots around points 80.
Frank raises cattle for livestock. Last year, he sold exactly 30% of his cattle to a local rancher. If Frank has not gained or lost any cattle since last year, which of the following could be the total number of cattle he currently owns?
A) 610
B)520
C)350
D)300
The total number of cattle Frank currently owned could be C)350
How to find the total number of cattle Frank currently ownedThe problem is asking multiples of 7.
Multiples of 7 come into play after working the the percentage as follows
Frank sold 30%, the percentage left is
= 100% - 30%
= 70%
= 0.7
The multiple of 7 that is a number 7 will divide without remainder here is 350 and this is the correct answer.
= 350 / 0.7
= 500
This means Frank had 500 cattle sold
0.3 * 500 = 150
currently having
= 500 * 0.7 = 350
= 500 - 150 = 350
Remember that a cattle will always be in whole number
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A person is selected at random. A is the event “the person selected earns more than $100,000 per year” and B is the event “the person selected earns more than $250,000 per year.”
The pairs of events, A and B, that are disjoint include option A and B.
What are disjoint events?It should be noted that disjoint events simony means the events that are mutually exclusive as they can't occur at the same time.
For option A, because a person can be either male or female but not both, events A and B are disjoint.
For B, because the person already earns more than $100,000, events A and B are not disjoint.
For C, because the sum of two dice cannot be three when one die is three, events A and B are disjoint.
Therefore, A and C are disjoint.
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Complete question
Which of the following pairs of events, A and B, are disjoint?
(a) A person is selected at random. A is the event "sex of the person selected is male" and B is the event "sex of the person selected is female."
disjoint / not disjoint
(b) A person is selected at random. A is the event "the person selected earns more than $100,000 per year" and B is the event "the person selected earns more than $250,000 per year."
disjoint / not disjoint
(c) A pair of dice are tossed. A is the event "one of the dice is a 3" and B is the event "the sum of the two dice is 3."
disjoint / not disjoint
we spent $82.96 at a restaurant this total amount including a tip of 22% what was the amount of the bill before the tip?
Answer:
82.96-22% = 67.83
Step-by-step explanation:
82.96-22% = 67.83
Solve the following facts. (Round to the nearest hundredth.) A. Current ratio _______________ B. Acid test __________________ C. Average day's collection ___________ D. Asset turnover _____________ E. Profit margin on sales _____________ Current Assets $ 18,000 Accounts Receivable 3,000 Current Liabilities 16,000 Inventory 2,000 Net Sales 41,000 Total Assets 29,000 Net Income 6,000
The solutions to the financial ratio requirements based on the supplied facts are:
A. Current ratio is 1.125.
B. Acid test is 1.
C. Average days' collection is 26.7 days.
D. Asset turnover is 1.4x.
E. Profit margin on sales is 14.63%.
What are financial ratios?Financial ratios are ratios that show the relative magnitude of one financial account to another.
Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.
Current Ratio = Current Assets ÷ Current Liabilities
= $18,000 ÷ $16,000
= 1.125
Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities
= ($18,000 - 2,000) ÷ $16,000
= $16,000 ÷ $16,000
= 1
Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days
= $3,000 ÷ $41,000 x 365
= 26.7 days
Asset Turnover = Net Sales ÷ Total Assets
= $41,000 ÷ $29,000
= 1.4x
Profit Margin on Sales = Net Income ÷ Net Sales x 100
= $6,000 ÷ $41,000 x 100
= 14.63%
Current Assets = $18,000
Accounts Receivable = $3,000
Current Liabilities = $16,000
Inventory = $2,000
Net Sales = $41,000
Total Assets = $29,000
Net Income = $6,000
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3, 5) and (1,−1)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~1 - (-3)~~)^2 + (~~-1 - 5~~)^2} \implies d=\sqrt{(1 +3)^2 + (-1 -5)^2} \\\\\\ d=\sqrt{( 4 )^2 + ( -6 )^2} \implies d=\sqrt{ 16 + 36 } \implies d=\sqrt{ 52 }\implies d\approx 7.2[/tex]
A cell phone plan costs $100 to start. Then there is a $25 charge each month. What is the total cost (start-up fee and monthly charge) to use the cell phone plan for 1 month? 6 months? Be sure to show your work. What is the total cost for months? Enter your first and last name below and then click start. If this is your second attempt, be sure to put a "2" after your name so I know it is your second attempt. Graph the cost of the cell phone plan over a period of two years, using months as the units of time. Be sure to label your axes and scale them by labeling each gridline with a number.
The $100 start-up fee and $25 monthly rental gives;
The cost of using the phone for 1 month = $125
The cost of using the phone for 6 months = $250
The cons of using the phone for n months = $(100 + 25·n)
Please find attached the graph of the cellphone plan over a period of two years (24 months)
What is a graph of a function?A graph is a visual representation of the variation of one variable of a function with respect to other variables of the function.
The start-up fee of the cell phone plan = $100
The amount charged each month = $25
First part;
The total cost for the start-up fee and monthly rental for 1 month = $100 + $25
The total cost for 1 month = $125
The total cost for 6 months = $100 + 6 × $25 = $250
The total cost for n months = 100 + n × 25 = $(100 + 25·n)
Please find the graph of the total cost to the number of months created with MS Excel
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Rewrite this number in appropriate scientific notation:
answer=
464, 400,000
You may use either X or to represent multiplication.
If <1 and <2 are supplementary and m <1 = 67 degrees , what is m<2?
Answer:
D
Step-by-step explanation:
supplementary angles sum to 180° , that is
∠ 1 + ∠ 2 = 180°
67° + ∠ 2 = 180° ( subtract 67° from both sides )
∠ 2 = 113°
The problem is sketch the graph of each line
The required sketch graph of given straight line is shown below in the image.
Explain the concept of equation of line.
The general equation of line is written as Y = mx + c where, m is the gradient of straight line, c is the point where the line cut y-axis.
According to the question:we have, line y = x - 1
So, slope of line is 1 and y-intercept is -1
Thus,required graph of straight line is
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find the missing value ratio inches :2 and years: 3,1,8
Answer: The missing values in the ratio table will be 0.666 and 5.33 inches.
Step-by-step explanation:
As the ratio of the terms is equal. The value of x and y is ,
2/3 = x/1
x=2/3
x=0.66 inches
In order to obtain y,
2/3 = y/8
y=2×8/3
y=16/3
y=5.33 inches.
please help meee :((
The system of conics has two solutions.
(x−4)2+(y+1)2=9
(x−4)29+(y+1)281=1
What are the solutions to this system of conics?
Answer:
(1, -1) and (7, -1)===============
Given system(x − 4)² + (y + 1)² = 9(x − 4)² / 9 + (y + 1)² / 81 = 1Solve it by eliminationMultiply the second equation by 9 and subtract from the first one:
(y + 1)² - (y + 1)² / 9 = 0(y + 1)²/8 = 0(y + 1)² = 0y + 1 = 0y = - 1Substitute y and solve for x(x − 4)² + (-1 + 1)² = 9(x - 4)² = 9x -4 = ± 3x = 4 ± 3x = 1 and x = 7Answer:
[tex]\left(\; \boxed{1}\:,\boxed{-1}\;\right)\; \textsf{and}\;\left(\; \boxed{7}\:,\boxed{-1}\;\right)[/tex]
Step-by-step explanation:
Given system of conics:
[tex]\begin{cases}(x-4)^2+(y+1)^2=9\\\\\dfrac{(x-4)^2}{9}+\dfrac{(y+1)^2}{81}=1\end{aligned}[/tex]
Multiply the second equation by 81:
[tex]\implies \dfrac{81(x-4)^2}{9}+\dfrac{81(y+1)^2}{81}=81[/tex]
[tex]\implies 9(x-4)^2+(y+1)^2=81[/tex]
Rearrange to make (y + 1)² the subject:
[tex]\implies (y+1)^2=81-9(x-4)^2[/tex]
Substitute into the first equation and simplify:
[tex]\implies (x-4)^2+81-9(x-4)^2=9[/tex]
[tex]\implies -8(x-4)^2=-72[/tex]
[tex]\implies (x-4)^2=9[/tex]
Solve for x:
[tex]\implies \sqrt{ (x-4)^2}=\sqrt{9}[/tex]
[tex]\implies x-4=\pm3[/tex]
[tex]\implies x=4\pm3[/tex]
[tex]\implies x=1, 7[/tex]
Substitute the found values of x into the first equation and solve for y:
[tex]\begin{aligned}x=1 \implies (1-4)^2+(y+1)^2&=9\\(-3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]
[tex]\begin{aligned}x=7 \implies (7-4)^2+(y+1)^2&=9\\(3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]
Therefore, the solution to the given system of conics is:
(1, -1) and (7, -1)What is the reason for each step in the solution of the equation?
18−2x=4x
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Given
Addition property of equality
Division property of equality
Step-by-step explanation:
The first line is given.
Next 2x was added to each side. The addition property of equality says that for an equation to stay in balance, it you add something to one side of the equation, you have to add that same thing to the other side of the equation.
The same is true for the division property.
A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. What is the probability of rolling a 6?
Answer:
the probability of rolling a 6 is 1/6
Step-by-step explanation:
because there are six possible outcomes and it is a fair die, each outcome must be equally as likely, therefore there is a 1/6 chance of rolling any number.
A footballb team lost the same number of yards on each of 3 consecutive plays.what is the total change in yards from where the team started? Someone pls help I dont understand.
The total change in yards where the team started is 3x
How to determine the total change in yards?The given parameters in the question are:
Yards per play = unknown
Number of plays = 3 consecutive plays
Represent the yards per play with x
So, we have
Yards per play = x
The total change in yards is the amount of yard per play multiplied by the number of plays
This is represented as
Total change = Yards per play * Number of plays
Substitute the known values in the above equation So, we have the following equation
Total change = x * 3
Evaluate
Total change = 3x
Hence, the total change is 36 yards
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Five students were looking at a large poster of the periodic table. They noticed the elements were arranged in rows and columns. They also noticed the elements were nged in order from 1-118. They had different ideas about the arrangement of the elements on the periodic table. This is what they said:
Damon: I think the elements are arranged by increasing mass.
Flo: I think the elements are arranged according to their properties.
Sienna: I think the elements are arranged by when they were discovered.
Kyle: I think the elements are arranged according to how common they are.
Glenda: I don't agree with any of you. I think there must be a different reason for the arrangement.
WHO DO YOU AGREE WITH?
The person that I agree with is Glenda I don't agree with any of you. I think there must be a different reason for the arrangement.
What is a periodic table?The periodic table, commonly known as the periodic table of (chemical) elements, is a table that displays the chemical elements in a tabular format.
The chemical elements are ordered from left to right and top to bottom by increasing atomic number, or the number of protons in an atom's nucleus, which generally corresponds to increasing atomic mass.
The elements in the periodic table are organized into rows, called periods, in ascending atomic number order. Vertical columns, referred to as groups, in which the elements have similar qualities.
I agree with Glenda because they're arranged in atomic number.
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développer l'expression suivante
3−3(−3x−5)(−3x+5)−4(3x−2)(2x+3)
3-3(9x²+15x-15x+25)-4(6x²+9x-4x+6)
3-27x²-75-24x²-20-24
3-51x²-119
-116-51x²
A school is arranging a field trip to the zoo. The school spends 862.68 dollars on passes for 40 students and 2 teachers. The school also spends 345.20 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answer:
0.150985
Step-by-step explanation:
You add the two decimals together which gives you 120788.
Then, you move the decimal 4 places which is 12.0788.
Then you divide 12.0788 by 2 which gives you 6.0394.
Finally, you divide 6.0394 by 40 which gives you 0.150985.
angle 2=angle 3
angle 1 + angle 2= 180
prove angle 1+angle 3=180
Answer:
supplementary angles
Step-by-step explanation:
1.) angle 1& angle 2 is supple. angle 2 & and angle 3 is supple.; given
2.) measure of angle 1+ measure of angle 2= 180, measure of angle 2+ measure of angle 3=180; Def. of Supple.
3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive
4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality
5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence
Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24. Find the percent tip.
The percentage of the tip will be equal to 24.81%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24.
The percentage tip will be calculated as,
P = ( (37.24 - 28 ) / 37.24
P = 9.24 / 37.24
P = 0.2481 x 100
P = 24.81%
Therefore, the percentage of the tip will be equal to 24.81%.
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