Answer:
a) The sequence of first three terms
5 , 8 , 13 ..
b) The [tex]10^{th}[/tex] of the sequence
a₁₀ = 104
Step-by-step explanation:
Step(i):-
Given [tex]n^{th}[/tex] term of the sequence
aₙ = n² + 4
put n=1
First term a₁ = 1² +4 = 1+5
put n =2
Second term a₂ = 2²+4 = 4+4 =8
Put n=3
Third term a₃ = 3² +4 = 9+4 =13
The sequence of first terms
5 , 8 , 13 ..
Step(ii):-
Given [tex]n^{th}[/tex] term of the sequence
aₙ = n² + 4
put n =10
a₁₀ = 10²+4 = 100+4 = 104
a₁₀ = 104
The [tex]10^{th}[/tex] of the sequence
a₁₀ = 104
Use synthetic division to solve (x3 + 1) = (x - 1). What is the quotient?
o x2+x+1+12
O x2 - X+1
O x2+x+1+421
x - x² + x
Answer:
x² + x + 1 and remainder 2Step-by-step explanation:
Given
(x³ + 1) ÷ (x - 1)Without using a synthetic division, we can use easier method to find the quotient.
We know the formula:
x³ - 1 = (x - 1)(x² + x + 1)Rewrite the given as:
x³ + 1 = x³ - 1 + 2 = (x - 1)(x² + x + 1) + 2This expression, when divided by (x - 1) leave the quotient (x² + x + 1) and a remainder of 2
The quotient of the equation is A = x³ + x + 1 + ( 2/x + 1 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the first equation be p = x³ + 1
Let the second equation be q = x - 1
A = p / q
On simplifying , we get
A = x³ + 1 / ( x - 1 )
On dividing , we get the quotient as
A = x² + ( x² + 1 ) / ( x - 1 )
A = x³ + x + 1 + ( 2/x + 1 )
Hence , the quotient is A = x³ + x + 1 + ( 2/x + 1 )
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describe and correct the error in writing an equation of the line with a slope of 2 and a y intercept of 7
Answer:
An equation of the line with a slope of 2 and a is inercept of 7
Step-by-step explanation:
I think this is what you are saying?
Consider the expression 5x-20. Write an expression that if set equal to 5x-20 would result in the equation having no solution.
Answer:
5x=5x-20 or -20=5x-20
Step-by-step explanation:
A scientist digs near an ancient city.
She finds a cup buried at -7 feet. She finds a plate buried at -4 feet.
Use absolute value to show which was buried farther from the surface.
A. The cup is farther from the surface, because |-7 is less than 1-4).
B. The cup is farther from the surface, because |-71 is greater than |-
4.
C. The plate is farther from the surface, because (-71 is greater than
1-41.
D. The plate is farther from the surface, because -7 is greater than -
4.
My
Answer:
c
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 102 parts are summarized as follows: edge finish excellent good surface finish excellent 84 4 good 5 9 Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish. If a part is selected at random, determine the following probabilities. Round your answers to three decimal places (e.g. 98.765). (a) Upper P left-parenthesis Upper A right-parenthesis equalsEntry field with correct answer .8627 (b) Upper P left-parenthesis Upper B right-parenthesis equalsEntry field with correct answer .8725 (c) Upper P left-parenthesis Upper A prime right-parenthesis equalsEntry field with correct answer .1372 (d) Upper P left-parenthesis Upper A intersection Upper B right-parenthesis equalsEntry field with correct answer .8235 (e) Upper P left-parenthesis Upper A union Upper B right-parenthesis equalsEntry field with correct answer .9117 (f) Upper P left-parenthesis Upper A prime union Upper B right-parenthesis equalsEntry field with incorrect answer .9214
Answer:
a) P (A)= 88/102= 0.8627
(b) P (B)= 89/102= 0.8725
c) P (A`) = 14/102 = 0.1372
(d) P (A∩B) = 84/102 =0.8235
(e) P(AUB)= 93/102 = 0.9117
(f)P (A`UB) = 98/102= 0.96078
Step-by-step explanation:
edge
finish excellent good Total
(A )surface finish excellent 84 4 88
good ( B) ⇵ 5 9 14
Total 89 13 102
a) Upper P left-parenthesis Upper A right-parenthesis equals
P (A)= 88/102= 0.8627
All the elements of set A = 84+4= 88
(b) Upper P left-parenthesis Upper B right-parenthesis equals
P (B)= 89/102= 0.8725
All the elements of set B = 84+5= 89
c) Upper P left-parenthesis Upper A prime right-parenthesis equal
P (A`) = 14/102 = 0.1372
All the elements of Universal set U which are not elements of set A = 102- 88= 14
(d) Upper P left-parenthesis Upper A intersection Upper B right-parenthesis equals
P (A∩B) = 84/102 =0.8235
Only those elements of set A and set B which are common
(e) Upper P left-parenthesis Upper A union Upper B right-parenthesis equals
P(AUB)= 93/102 = 0.9117
Totalling elements of set A and B= 88+5= 93
(f) Upper P left-parenthesis Upper A prime union Upper B right-parenthesis equals
P (A`UB) = 98/102= 0.96078
All the elements of Universal set U which are not elements of set A and the elements of Set B = 5+9+ 84= 98
Sarah buys 8 packages, each with 20 balloons, and uses 1/4 of them to decorate the hall.
Write and evaluate an expression to find how many balloons Sarah has left.
Answer:
(8 × 20) ÷ 4
40
Step-by-step explanation:
8 × 20 = 160
160/4 = 40
The fraction is defined as a number in the form of a/b where a nd b are integers and b is not equal to zero. Sarah has left with 120 balloons.
What is a Fraction?A fraction is used to represent a portion or part of anything. It consists of two parts a numerator and a denominator. For example 1/4 is a fraction where numerator is 1 and denominator is 4.
The total number of packages = 8
Number of balloons in each package = 20.
The portion of balloons use to decorate hall = 1/4.
Suppose the remaining balloons are x.
Thus the expression for remaining balloons can be written as,
x = 20 × 8 - 1/4×(20 × 8)
x = 160 - 40
= 120.
Hence, Sarah has left with 120 balloons and the expression for left balloons is x = 20 × 8 - 1/4×(20 × 8).
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FOR 20 points
Show your work neatly for each problem.
1. Michelle and Cameron are selling popcorn for a school fundraiser. Michelle sold 10 tins of cheese
popcorn and 8 tins of caramel popcorn for a total of $446. Cameron sold 22 tins of cheese popcorn and
11 tins of caramel popcorn for a total of $803. Write a system of equations to determine the cost one tin
of cheese popcorn and one tin of caramel popcorn. Show all your work.
Answer:
one tin of cheese $23
one tin of caramel $27
Step-by-step explanation:
let 'x' = cost of cheese tin
let 'y' = cost of caramel tin
10x + 8y = 446
22x + 11y = 803
i multiplied the first equation by -11 and the second by 8 to eliminate the 'y' terms
-110x - 88y = -4906
+ 176x + 88y = 6424
66x = 1518
x = 1518 / 66
x = 23
find 'y': 10(23) + 8y = 446
230 + 8y = 446
8y = 216
y = 27
What is the probability you will get one tail? Toss a coin three times
Answer:
3/8
Step-by-step explanation:
We want the probability of getting a tail in three trials.
We will use binomial distribution, given by the formula:
[tex]\displaystyle P(x)={n\choose x}p^xq^{n-x}[/tex]
We want one success out of three trials. So, n = 3 and x = 1.
The probability for success in one trial is 1/2. So, p = 1/2.
And the probability for failure in one trial is 1/2. q = 1/2.
Therefore, the probability of getting a tail is:
[tex]\displaystyle P(1)={3\choose 1}\Big(\frac{1}{2}\Big)\Big(\frac{1}{2}\Big)^2[/tex]
Evaluate:
[tex]\displaystyle P(1)=3\Big(\frac{1}{8}\Big)=\frac{3}{8}[/tex]
The probability of getting a tail by tossing a coin thrice is 3/8.
Edit:
My apologies. If you haven't learned the binomial distribution yet, below is another method.
Using the fundamental counting principle, we have a total of 2 times 2 times 2 or 8 total outcomes.
We want only one tail. This can be the first toss, the second toss, or the third toss.
So, out of 8 total outcomes, only 3 are favorable.
Hence, the probability of getting one tail by tossing a coin thrice is 3/8.
3 4/5 • 3 1/2 divide reduce to the lowest term
Answer:
133/10
Step-by-step explanation:
first turn into proper fraction
19/5 * 7/2 = 133/10
Delaney wants to start saving money to buy a 3-D printer. If she needs to save at least $300.00 to pay for it and has decided to save $15.00 per week from doing chores around the house. Which inequality can be used to find how many weeks will it be before she can purchase the 3-D printer?
15x\geq 30015x≥300
\frac{x}{300} \geq 15
300
x
≥15
15x \leq 30015x≤300
\frac{x}{300} \leq 15
300
x
≤15
Answer:
20 weeks
Step-by-step explanation:
30/15=2
300/15=20
20 weeks
Brian goes to school 6 hours per day, and sleeps for 9 hours per day. What is the ratio of hours Brian works to hours Brian sleeps?
Answer:
6:4:9 Yw❤️
Step-by-step explanation:
I need help... plssss :))
Answer:
(1, -1), (1, -2), (2, -3), (2, -4)
NO
Step-by-step explanation:
✔️Each ordered pair is written as (input, output).
Thus, we would have the following:
(1, -1), (1, -2), (2, -3), (2, -4)
✔️This cannot be a function because every input value do not have exactly one output value related to it. A function should not have an input value related to more than one output value.
So, the answer is NO. It is not a function.
HURRY i have 42:12 min left
Point A is located in which quadrant?
Quadrant l
Quadrant ll
Quadrant lll
Quadrant lV
Answer:
point a is located Quadrant11
Step-by-step explanation:
Answer:
Need picture to give correct quadrant
Step-by-step explanation:
Select the correct symbol
Answer:
The answer is <
when do you go to soccer 4:00 A.M. or 4:00 P.M.
Answer:
4:00 pm for me because its right after school
Step-by-step explanation:
Stella is saving money for a P750
.00 schoolbag. if she saved 25% of the money she needed,how many money did she save?
Answer:
Stella saved $187.5
Step-by-step explanation:
She needs $750.00 to buy the schoolbag.
She has saved 25% of the money she needs. So
0.25*750 = $187.5
Stella saved $187.5
Evaluate.
1 to the power of 3
Answer:
3
Step-by-step explanation:
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There are 7 trucks for every 5 cars . If there are 21 trucks, how many cars are there?
Answer:
15 cars
Step-by-step explanation:
If there are 7 trucks for every 5 cars, the ratio is 7:5. So if there are 21 trucks, that's 7 x 3, which means we also multiply 5 by 3 = 15
5. Mason's mom bought g games online. The games cost $12 each plus a $7 shipping fee. Write an expression to represent how much Mason's mom spent for the games.
Identify the terms. Then identify the coefficients of the variable terms of the expression. (Enter your answers as a comma-separated list.)
6x + 7
Suppose restaurant A's chicken salad contains 6more grams of fat than restaurant B's chicken salad. Find the number of grams of fat in each salad if there are 56grams of fat in the two salads by solving the equation x plus (x plus 6 )equals 56,where xrepresents the number of fat grams in the restaurant B's chicken salad and x plus 6represents the number of fat grams in restaurant A's chicken salad.
Answer:
Restaurant A: 31 grams of fat
Restaurant B: 25 grams of fat
Step-by-step explanation:
[tex]x + (x + 6) = 56\\2x + 6 = 56\\2x = 50\\x = 25[/tex]
Mary French uses gas to heat her home. She has accumulated the following information regarding her monthly gas bill and monthly heating degree-days. The heating degree-days value for a month is found by first subtracting the average temperature for each day from 65 degrees and then summing these daily amounts together for the month. Month Heating Degree-Days Gas Bill February 1,900 $195 April 600 $78 The equation representing the relationship between the gas bill (Y) and heating degree-days (X) is:
Answer:
[tex]Y=$24+0.09X[/tex]
Step-by-step explanation:
From the question we are told that
February Heat [tex]H_1=1900\textdegree[/tex]
February Gas [tex]G_1 =\$195[/tex]
April Heat [tex]H_2=600\textdegree[/tex]
April Gas [tex]G_2=\$78[/tex]
Generally equation for heating degree-days X is mathematically given by
[tex]X=\frac{\triangle gas\ bills}{\triangle Heating\ days}[/tex]
[tex]X=\frac{195-78}{1900-600}[/tex]
[tex]X=\$ 0.09[/tex]
Generally the equation for gas bill Y is mathematically represented by
[tex]Y=78-(600*0.09)\\Y=\$24[/tex]
The equation representing the relationship between the gas bill (Y) and heating degree-days (X) is
[tex]Y=$24+0.09X[/tex]
please help!! i’m stuck and i’ll give brainliest but i need an explanation for the answer
9514 1404 393
Answer:
-12
Step-by-step explanation:
The average rate of change of a function f(x) on an interval [a, b] is defined as ...
average rate of change = ((f(b) -f(a))/(b -a)
For the given function and interval, this is ...
average rate of change = (f(1.25) -f(0.75))/(1.25 -0.75)
= (4 -10)/(0.5) = -12
The average rate of change is -12 on the interval.
__
The calculator results for f(1.25) and f(0.75) are shown in the attachment, along with the computation of the average rate of change.
graph y < X- 2, Y > -4X-1
80.6 divided by 6 please answer
Answer:
13.433333333
Step-by-step explanation:
10. Find the rate of change in the table below.
Show all work.
х
18
20
22
24
y
4.5
5
5.5
6
Answer:
it's times 4 every time
Step-by-step explanation:
4.5 times 4 is 18 etc
Can someone help!!!!
Answer:
12.7=x
Step-by-step explanation:
y=mx+b
10=.65x+1.75
-1.75 -1.75
8.25=.65x
.65 .65
12.69=x round up
12.7=x
را آزرا
What is the value of x in the proportion?
Answer:
Step-by-step explanation:
Cross multiply on both sides
= (x + 1) (21) = 15(x + 3)
= 21x + 21 = 15x + 45
Bringing like terms on one side
21x - 15x = 45 - 21
= 6x = 24
x = 24/6 = 4
Option A is the correct answer
[tex] =\tt (a) \: 4[/tex]
Steps to derive correct option :[tex] = \frac{x + 1}{x + 3} = \frac{15}{21} [/tex]
[tex] =( x + 1 )\times 21 = (x + 3 )\times 15[/tex]
[tex] = 21x + 21 = 15x + 45[/tex]
[tex] = 21x + 21 - 15x = 45[/tex]
[tex] = 6x + 21 = 45[/tex]
[tex] = 6x = 45 - 21[/tex]
[tex] = 6x = 24[/tex]
[tex] = x = \frac{24}{6} [/tex]
[tex] =\color{plum} \bold{x = 4}[/tex]
Let us now place 4 in the place of x and see if the substitution is equivalent to [tex] \frac{15}{21} [/tex] :
[tex] = \frac{4 + 1}{4 + 3} = \frac{15}{21} [/tex]
[tex] = \frac{5}{7} = \frac{15}{21} [/tex]
[tex] = \frac{5}{7} = \frac{15÷3}{21÷3} [/tex]
[tex] = \frac{5}{7} = \frac{5}{7} [/tex]
Therefore, the value of x in this proportion = 4
Find the missing value in the ratio table.. Please help me
Please help me with these math problems! I have had so much going on lately and haven't had time to do them
Will give lots of points and make brainliest please help