If d is the common difference between consecutive terms, then
[tex]a_4 = a_3 + d = a_2 + 2d[/tex]
We have [tex]a_2 = 64[/tex] and [tex]a_4 = 100[/tex], so
[tex]a_4 - a_2 = 100 - 64 = 36 = 2d \implies d = 18[/tex]
Then the 1st term in the sequence is
[tex]a_2 = a_1 + d \implies 64 = a_1 + 18 \implies a_1 = 46[/tex]
and the n-th term would be
[tex]a_n = a_1 + (n-1) d \implies a_n = 46 + 18 (n-1) \implies \boxed{a_n = 18n + 28}[/tex]
What is the solution to the following question
Answer:
3
Step-by-step explanation:
2(x + 1) = 3(5 - x) + 2
Distribute,
2(x + 1) = 3(5 - x) + 2
2x + 2 = 3(5 - x) + 2
Rearrange terms,
2x + 2 = 3(5 - x) + 2
2x + 2 = 3(-x + 5) + 2
Distribute,
2x + 2 = 3(-x + 5) + 2
2x + 2 = -3x + 15 + 2
Add the numbers,
2x + 2 = -3x + 15 + 2
2x + 2 = -3x + 17
Subtract 2 from both sides,
2x + 2 = -3x + 17
2x + 2 - 2 = -3x + 17 - 2
2x = -3x + 17 - 2
2x = -3x + 15
Add 3x to both sides,
2x = -3x + 15
2x + 3x = -3x + 3x + 15
5x = -3x + 3x + 15
5x = 15
Divide both sides by the same factor (15),
5x = 15
5x/5 = 15/5
x = 15/5
x = 3
Hence, the answer is 3.
Monômios
[tex]2x^{3}+5x-3x^{2} +x-6+2x^{2}=[/tex]
THE METHOD TO SOLVE THIS 2 EQUATION IS SUBSTITTUION AND ALGERBRICALLY HERE'S THE EQUATION:
y = -5x -18
y = x
Answer:
x = 3, y = 3
Step-by-step explanation:
x = -5x -18
5x + 18 = -x
6x + 18 = 0
6x = 18
x = 3
A single card is drawn from a standard deck of cards. Find the probability of drawing a club or a diamond.
Answer:
1/10
Step-by-step explanation:
group of 100 students were asked if they study French or Spanish in school. The results are shown in this two-way table. A 4-column table with 3 rows. The first column has no label with entries Spanish, not Spanish, total. The second column is labeled French with entries 5, 30, 35. The third column is labeled not French with entries 63, 2, 65. The fourth column is labeled total with entries 68, 32, 100. Which statements are correct? Check all that apply. 5 students study both French and Spanish. 63 students study French. 2 students study neither French nor Spanish. 30 students study French, but not Spanish. 63 students study Spanish
The statements which are correct include the following:
5 students study both French and Spanish.2 students study neither French nor Spanish.30 students study French, but not Spanish.ParametersThe table given shows that:
5 students study both French and Spanish.63 students study Spanish but not French.68 students study Spanish.30 students study French, but not Spanish.2 students study neither French nor Spanish.35 students study French.This therefore results in the conclusion that option 1,3 and 4 are
the most appropriate options.
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Help me this pls as soon as possible this is due today!!!
Answer:
pls refer to given attachemnt
Pickup a weighs about 1.,500 pounds pickup b weighs 685 kilogram’s which pickup actually weighs more
Answer:
pickup b
Step-by-step explanation:
Unit conversion :
1 kilogram is about 2.20462262 pounds
Solving :
⇒ Let's convert pickup b's mass into pounds
⇒ mass (pickup b) = 685 × 2.20462262
⇒ mass (pickup b) = 1510 pounds (approximately)
Clearly :
⇒ 1500 < 1510
⇒ mass (pickup a) < mass (pickup b)
Hence, pickup b weighs more.
The ratio of pounds of vegetables to pounds of protein on the dinner plate is 5 to 2. IF
there are 25 pounds of vegetables, how many pounds of protein are on the dinner plate?
Answer:
10 lbs
Step-by-step explanation:
25 is to 5 as x is to 2
25/5 = x/2
2 * 25/5 = x = 10 lbs
Math question 10 question PLSSS HELP
Answer:
A
Step-by-step explanation:
if it is at least -27 it will be greater than or equal to -27
A square has an area of [tex]18x^{2}[/tex] what is the length of one of its sides
Answer:
≈4.24x
Step-by-step explanation:
[tex]\sqrt{18} = 4.24[/tex]
Have a nice day! :)
Answer:
18x
Step-by-step explanation:
because itś squared, and the area of a square is always squared, its 18x
what is the perimeter of the isosceles trapezoid
Answer:
The perimeter of this isosceles trapazoid is 49
Step-by-step explanation:
P = 11 + 14 + 2(12)
You invest $5000 in an account to save for college.
The account pays 5% annually and compounds continuously.
What would be the account balance after 4 years.
Answer:
5000 multiplied by 0.05 multiplied by 4
Step-by-step explanation:
you should get 1000. :D next you add 1000 to the orginal 5000 to get 6000!
The price of of a mathematical set. was Ugx 2400 a month ago,and now it is Ugx 3000 - Find The percentage increase
Step-by-step explanation:
[tex]Another example , when a straight wire is moved up and down rapidly between the two poles of a horseshoe magnet , then an electric current is produced in the wire. This is also an example of electromagnetic induction .
A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach. To estimate support for firing the current head coach, a television news station provides a link on its website where fans of the team can respond to the question: "Do you feel the current head coach should be fired?” After 2,367 votes on the website, 79% of those who responded felt the coach should be fired. Which of these describes the type of bias in this survey and a likely direction of the bias in estimating overall support for firing the coach?
This is nonresponse bias. The result overestimates true support for firing the coach.
This is nonresponse bias. The result underestimates true support for firing the coach.
This is voluntary response bias. The result overestimates true support for firing the coach.
This is voluntary response bias. The result underestimates true support for firing the coach.
The statement third, “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.
What is a survey?A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.
We have:
A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach.
Number of votes V(n) = 2367
After the value of V(n) 79% of those who responded felt the coach should be fired.
Based on the data given, we can say this is referred to as voluntary response bias. The outcome exaggerates the level of support for firing the coach.
Thus, the statement third “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.
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Please help i will give you 100 points
x = 50.5°
Explanation:In order to solve, get to know about the sine rule:
[tex]\bf Sine \ Rule = \dfrac{A}{sinA} = \dfrac{B}{sinB}= \dfrac{C}{sinC}[/tex]
Solve for BD:[tex]\sf \dfrac{BD}{sin(50)} = \dfrac{5.6}{sin(78)}[/tex]
[tex]\sf BD = \dfrac{5.6(sin(50))}{sin(78)}[/tex]
[tex]\sf BD = 4.385686657 \ cm[/tex]
Then find angle D = 180° - 78° = 102°
Solve for angle C[tex]\sf \dfrac{4.385686657}{sinC} = \dfrac{9.3}{sin(102)}[/tex]
[tex]\sf C = sin^{-1}(\dfrac{4.385686657sin(102)}{9.3} )[/tex]
[tex]\sf C = 27.37 ^{\circ \:}[/tex]
Total Sum of interior angles of a triangle is 180°[tex]\sf B + C + D = 180^\circ[/tex]
[tex]\sf x + 27.37^\circ + 102^\circ = 180^\circ[/tex]
[tex]\sf x = 180^\circ - 102^\circ - 27.37^\circ[/tex]
[tex]\sf x = 50.53^\circ[/tex]
[tex]\sf x = 50.5^\circ \ \ \ (rounded \ to \ nearest \ 3 \ significant \ figure)[/tex]
Answer:
x = 50.5° (3 sf)
Step-by-step explanation:
Sine Rule for side lengths
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Find BD:
[tex]\implies \sf \dfrac{BD}{\sin BAD}=\dfrac{AB}{\sin BDA}[/tex]
[tex]\implies \sf \dfrac{BD}{\sin 50^{\circ}}=\dfrac{5.6}{\sin 78^{\circ}}[/tex]
[tex]\implies \sf BD=\dfrac{5.6\:sin 50^{\circ}}{\sin 78^{\circ}}[/tex]
[tex]\implies \sf BD=4.385686657...cm[/tex]
Angles on a straight line sum to 180°
⇒ ∠ADB + ∠BDC = 180°
⇒ 78° + ∠BDC = 180°
⇒ ∠BDC = 102°
Sine Rule for angles
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Find ∠BCD:
[tex]\implies \sf \dfrac{\sin BCD}{BD}=\dfrac{\sin BDC}{BC}[/tex]
[tex]\implies \sf \dfrac{\sin BCD}{4.385...}=\dfrac{\sin 102^{\circ}}{9.3}[/tex]
[tex]\implies \sf BCD=\sin^{-1}\left(\dfrac{4.385...\sin 102^{\circ}}{9.3}\right)[/tex]
[tex]\implies \sf BCD=27.46935172...^{\circ}[/tex]
The interior angles of a triangle sum to 180°
⇒ ∠CBD + ∠BDC + ∠BCD = 180°
⇒ x + 102° + 27.469...° = 180°
⇒ x = 50.53064828...°
⇒ x = 50.5° (3 sf)
What is the equation 8x-3y=6-4x in Stanford form?
Answer:
[tex]12x - 3y = 6[/tex]
Step-by-step explanation:
Standard form is written this way: [tex]Ax+By=C[/tex]
However, in this case, we just have to simplify 8x-3y=6-4x, as it is already mostly in standard form.
So, to do this, we have to combine like terms.
The only like terms that can be combined are -4x and 8x.
So, we add 4x to both sides, and we get: [tex]12x - 3y = 6[/tex].
Find the probability of rolling factors of 24
Answer:
5/6
Step-by-step explanation:
The factors of 24 that are on a die are: 1,2,3,4 and 6. This only leaves 5 that isn't a factor of 24. Therefore, since there are 5 possibilities out of the 6 total numbers, the probability of rolling factors of 24 is 5/6.
What are the vertical asymptotes
Which answer choice shows the numbers ordered from least to greatest?
*
15 points
A) 1/3, 0.333, 3/10, 33%
B) 0.333, 1/3, 3/10, 33%
C) 3/10, 0.333, 1/3, 33%
D) 3/10, 33%, 0.333, 1/
Answer:
D
Step-by-step explanation:
[tex] \frac{3}{10} = 0.3[/tex]
[tex] \frac{1}{3} = 0.333333333[/tex]
[tex]0.333 = 0.333[/tex]
[tex]33\% = 0.33[/tex]
[tex]0.3 < 0.33 < 0.333 < 0.333333333[/tex]
If you roll two fair six sided dice, what is the probability that the sum is 5 or lower
Answer: P(sum is 5 or lower) = 10/36 (not simplified) = 5/18 (simplified)
Step-by-step explanation: The event is {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1)}
In the figure QU=ST
What is the length of QR?
Answer:
the answer is 80
Step-by-step explanation:
QR=ST: 7x+3=5x+25
2x=22
x=11
7(11)+3=80 5(11)+25=80
Consider the following polynomial function with irreducable quadratic factor, find an expression which gives the degree of the polynomial
An expression that gives the degree of the polynomial is [tex]\rm ax^2+bx+c=0[/tex].
What is an irreducible quadratic factor?An irreducible quadratic factor is an irreducible factor that is quadratic or has the highest exponent of 2.
An irreducible quadratic factor is an irreducible factor that is quadratic or has the highest exponent of 2.
A nonlinear equation is one in which the maximum degree of a term is two or more than two. When the polynomial equation is with degree two, then it is called a quadratic equation, and it is represented by a standard expression;
[tex]\rm ax^2+bx+c=0[/tex]
Where a is not equal to 0.
The degree of the polynomial is 2.
A quadratic polynomial can be further divided into linear factors. Now, simplify one of the quadratic expressions by completing the square method, which gives two linear factors.
Hence, an expression that gives the degree of the polynomial is [tex]\rm ax^2+bx+c=0[/tex].
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A recent study found that the average length of caterpillars was 2.8 centimeters with a
standard deviation of 0.7 centimeters. what is the probability that a randomly selected caterpillar will have a
length longer than (greater than) 4.0 centimeters?
Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 2.8, \sigma = 0.7[/tex].
The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is one subtracted by the p-value of Z when X = 4, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4 - 2.8}{0.7}[/tex]
Z = 1.71
Z = 1.71 has a p-value of 0.9564.
1 - 0.9564 = 0.0436.
0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
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A decimal number is multiplied by 10². Which statement describes the change in position of the decimal point in the decimal number as a result of the multiplication?
QUICK PLEASE AND THANK YOU
A. The decimal point moves 2 places to the left.
B. The decimal point moves 10 places to the left.
C. The decimal point moves 2 places to the right.
D. The decimal point moves 10 places to the right.
Answer:
C.
Step-by-step explanation:
10^2=100
100 shifts the decimal point 2 places to the right
Which algebraic expression is a polynomial with a degree of 4? 5x4 startroot 4 x endroot x5 – 6x4 14x3 x2 9x4 – x3 – startfraction x over 5 endfraction 2x4 – 6x4 startfraction 14 over x endfraction
The algebraic expression of a polynomial with a degree of 4 is 9x⁴ – x³ – x/5
How to determine the polynomial?For a polynomial to have a degree of 4, the following must be true:
All exponents must be whole numbersThe highest exponent must be 4Using the above highlight, the algebraic expression of a polynomial with a degree of 4 is 9x⁴ – x³ – x/5
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type the correct answer in the box use nummerals instead of words. if necessary use / for the faction bar
ill mark the brainliest if correct
Answer: f(y) x g(y) = 1
Step-by-step explanation:
[tex]\frac{2y^3-y^2+2y-1}{y^3-y^2+y-1}\cdot \frac{2y^2-3y+1}{4y^2-4y+1}\\\\= \frac{4y^5-8y^4+9y^3-9y^2+5y-1}{4y^5-8y^4+9y^3-9y^2+5y-1} \\\\= \frac{(y-1)(2y-1)(2y-1)(y^2+1)}{(y-1)(2y-1)(2y-1)(y^2+1)} \\\\= 1[/tex]
Solve two sevenths plus seven fourteenths (2 points)
1 eleven fourteenths
2twelve fourteenths
3 nine seventh
4 eleven sevenths
Answer:
2/7 + 7/14 = 11/14
Step-by-step explanation:
7 x -2 = -14 Each seventh is going to be worth 2 fourteenths!
This means 2/7 = 4/14
4/14 + 7/14 = 11/14
Answer:
eleven fourteenths
Step-by-step explanation:
which part of this graph shows a nonlinear relationship?
1. 4
2. 1
3. 3
4. 2
i want to know the answer
Answer: Heyaa!~
Your Answer is... 15/2 in its exact form!
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Hopefully this helps you! ~
Spencer surveyed five of his friends to find out how many pets they have. His results are shown in the table below. What is the mean number of pets?
Cody has 1 lara has 4 sam has 5 ella has 3 maria has 2
The mean of the number of pets which Spencer has surveyed for five of his friends is number 3.
What is mean of the data set?The mean of the data is the average value of the given data. The mean of the data is the ratio of sum of all the values of data to the total number of values of data.
Spencer has surveyed five of his friends to known that how many pets they have.
His results are shown in the table below. Cody has 1 Lara has 4 Sam has 5 Ella has 3 Maria has 2. There are total 5 friends. Thus the mean number of pets is:
[tex]\text{Mean}=\dfrac{1+4+5+3+2}{5}\\\text{Mean}=\dfrac{15}{5}\\\text{Mean}=3[/tex]
Thus, the mean of the number of pets which Spencer has surveyed for five of his friends is number 3.
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