An equation for the nth term of the arithmetic sequence: an = n - 6.
ad 10th term a10 = 4.
Define the term arithmetic sequence?A sequence of a form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.A common difference of the sequence is d, and the number an is the first term.The formula for the nth term of the
an = a + (n -1)d
In which,
a = initial termd = common differencen = total number of termsThe arithmetic sequence is given as-
−5,−4,−3,−2, ...
Then, the equation will be
d = a2 - a1
d = -4 - (-5) = 1
an = a + (n -1)d
an = -5 + n - 1
Put n = 10 in the equation.
a10 = 10 - 6
a10 = 4
Thus, the 10th term of the sequence is 4.
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The correct question is-
Write an equation for the nth term of the arithmetic sequence. Then find a10.
−5,−4,−3,−2, ...
What is the value of this expression when a = 4, b = -5, and c = -7?
a + 2bc
3a
Answer:
Step-by-step explanation:
a = 4, b = -5, and c = -7
for a + 2bc
4 + 2(-5)(-7)
4 + 70
74
for 3a
3(4)
12
I'm not sure if the 2 parts are connected but if you add them, the answer is 86. If you subtract them, the answer is 62. If you multiply them, the answer is 888. If you divide them, the answer is 7/6.
Could you please give me brainliest? Thank you!
The length of a rectangular pool is seven less than twice its width. If the
perimeter of the pool is 106 feet, find its dimensions.
Answer:
width = 20 ft; length = 33 ft
Step-by-step explanation:
The formula for perimeter of a rectangle is P = 2l + 2w
Given that the length is seven less than twice its width, we have
[tex]l=2w-7[/tex]
We need to have only one variable or we can't solve.
Thus, we have:
[tex]106=2(2w-7)+2w\\106=4w-14+2w\\106=-14+6w\\120=6w\\20=w\\\\l=2w-7\\l=2(20)-7\\l=40-7\\\\l=33[/tex]
what is the minimum number of students required in a school to be sure that at least 17 students will be in the same class, assuming the school only has grade 1 to grade 6 and each grade has only one class?
The minimum number of students required in a school are 102 , it can be calculated by multiplying the 2 quantities.
What is arithmetic?
Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main body:
Total grades = 1 to 6 = 6
minimum students in each grade required = 17
total students required = 6*17
= 102
hence total minimum number of students required in a school are 102.
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write the slope intercept form of the equation of the line through the given points with given slope
The equation of the line passing through the point (-1, -5) with slope = 6 is y = 6x - 1
The coordinates of the point = (-1, -5)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line m = 6
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Substitute the values in the slope intercept form
-5 = 6(-1) + b
-5 = -6 + b
b = -6+5
b = -1
The slope intercept form
y = 6x - 1
Therefore, the equation of the line is y = 6x - 1
I have answered the question in general, as the given question is incomplete
The complete question is:
Write the slope-intercept form of the equation of the line through the given point with the given slope. Through (-1,-5), slope =6
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Drag numbers to use a negative factor to factor the expression –5g + 15h – 25. Numbers may be used once, more than once, or not at all.
–1 –2 –3 –4 –5 1 2 3 4 5
(___-5__g –____3_ h +___5__)
The expression -5g + 15h - 25 can be simplified as -5(g + 3h - 5)
ExpressionExpressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
In the question given, the expression is -5g + 15h - 25;
We have to simplify this to by factoring the expression.
-5g + 15h - 25 = -5(g + 3h - 5)
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Layla is thinking of a positive single digit even number. Luis guesses it was 7. What is the sample space??
The sample space for the single digit even number = {2, 4, 6, 8}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space.
Events are the subset of possible experiment results. Depending on the experiment, a sample space could contain a variety of results.
Given that,
Layla thinks about a positive single digit even number.
There are four single digit even numbers 2, 4, 6 and 8.
The sample space for the single digit even number = {2, 4, 6, 8}
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Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum
of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and
children weigh about 80 pounds. For each session of bounce time, Natalie charges adults
$3 each and children $2 each. Natalie hopes to make at least $20 for each session.
The set of inequalities formed for the bounce house of Natalie are-
200x + 80y ≤ 1200 and 3x + 2y ≥ 20.
Explain the term set of inequalities?A group of two or even more inequalities for one or more variables is referred to as a system of inequalities. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems with inequalities are used.The data for the people enrolled for the bounce house.
Let 'x' be the number of adults.
Let 'y' be the number of children.
Then,
Weight of adult = 200 pounds.
Weight of children = 80 pounds.
maximum weight = 1200 pounds
Then, equation becomes-
200x + 80y ≤ 1200
For the price.
adults -$3 each and
children - $2 each
Minimum profit at least $20
3x + 2y ≥ 20.
Thus, the set of inequalities are-
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One equation in a linear system is x + y = 1. Is it possible for the system to have a
solution of (0, 0)? (100, -49)? Explain your reasoning.
answer:
no, because 0+0≠1 and 100+-49≠1 so the values are not a part of the system.
step-by-step explanation:
for this question, plug in the x & y values into the equation x+y=1. if the values add up to be 1, then it's possible for the system to have those solutions. hope that helps!
hat are the zeros of the function: (x) = -x(x+ 2) (x - 6) (x + 4)
Answer:
zero of the function =0,-2,6,-4Step-by-step explanation:
f(x)=-x(x+2)(x-6)(x+4)-x=0 x=0(x+2)=0x=-2(x-6)=0x=6(x+4)=0x=-4Yuma needs a singer. Singer A is offering her services for an initial $50 in addition to $10 per hour. Singer B is offering his services for an initial $95 in addition to $5 per hour. When will the two singers charge the same amount of money?
After 9 hours, Singer A and Singer B will both charge the same amount.
What is meant by an equation?An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.
Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.
The Singer A's initial fee is $50.
Singer A's hourly rate is $10.
Singer B's initial fee was $95
Singer B's hourly wage is $5.
Assume the duration after which both singers will charge the same amount = x.
Then 50 +10x =95+5x
10x-5x=95-50
5x=45
x=45/5
x=9 hours
So, after 9 hours, Singer A and Singer B will both charge the same amount.
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the number of disintegrations per minute (dsm) of a sample of iodine-133 is measured at 5.5 x 102 dsm. when the sample is measured 295 minutes later, the number of disintegrations has decreased to 4.7 x 102 dsm. what is the half-life of iodine-133
Half-life of iodine-133 is 21.7 hours .
FR = 0.5n (fraction remaining)
n = number of half lives that have elapsed.
FR = 4.7x102 / 5.5x102 = 0.8545
n = to find
0.8545 = 0.5n
log 0.8545 = n log 0.5
-0.0683 = -0.301 n
n = 0.227 half lives have elapsed
Since this is equal to 295 minutes, we can easily find what 1 half life is
0.227 / 295 = 1 / x
x = 1300 min = 21.7 hours
The amount of time it takes for the concentration of a given reactant to reach half of its initial concentration is known as the half-life of a chemical reaction (i.e. the time taken for the reactant concentration to reach half of its initial value).
It is commonly expressed in seconds and is represented by the sign t1/2 .
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a search committee is formed to find a new software engineer. there are 6666 applicants who applied for the position. 1) how many ways are there to select a subset of 1515 for a short list?
The number of ways would be 2.68367259e14 for selecting 15 candidates out of 66 candidates.
What is arrangements ?Generally speaking, an arrangement of objects is just a collection of them. The sequence of the n items has no bearing on the number of "arrangements" that can be made of them (order is significant).
Total Candidates for software engineer = 66
Total Short listed candidates = 15
To find:
Number of 15 Candidates set possible
⁶⁶C₁₅ = [tex]\frac{66!}{51! 15!}[/tex]
After Calculating from calculator we get,
2.68367259e14.
Hence the number of ways would be 2.68367259e14.
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a newsletter publisher believes that less than 49% of their readers own a personal computer. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.05 level of significance, the advertiser decides to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
The proportion should be sufficiently demonstrated to be lower than 49% at the 0.05 level.
Given,
Less than 49% of a newsletter publisher's subscribers, in their estimation, own a personal computer.
A potential advertiser wants to verify this claim for marketing purposes.
The marketer chooses to reject the null hypothesis after running a test with a 0.05 level of significance.
We have to determine the conclusion regarding the publisher's claim;
Here,
Null and Alternative hypothesis;
H₀ = P ≥ 0.49
H₁ = P < 0.49 (Left tailed test)
The significance level is 0.05
So,
0.05 < 0.49
Then,
At the defined meaning level, it is chosen to reject the null hypothesis.
Therefore,
There should be sufficient evidence that the proportion is lower than 49% at the 0.05 level.
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How do I find and interpret the residual?
(Elementary statistics)
Answer:
y value , r i = y i − y i ^
Step-by-step explanation:
Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low. The aim of a regression line is to minimise the sum of residuals.
Which number sentence shows the best way to estimate 64.12÷7.4 ? A. 60 ÷ 10 = 6 60÷10=6
B. 63 ÷ 7 = 9 63÷7=9
C. 56 ÷ 7 = 8 56÷7=8
D. 100 ÷ 10 = 10
Answer:
B
Step-by-step explanation:
Round 64.12 and 7.4 to whole numbers that divide nicely, and are CLOSE to the original numbers.
B
21
31
20
C
G
42
H
16
28
D
if the null hypothesis is rejected in hypothesis testing, no conclusions can be drawn from the test. the sample size has been too small. the alternative hypothesis is true. the data must have been accumulated incorrectly.
if the null hypothesis is rejected in hypothesis testing the alternative hypothesis is true.
The relationship between important factors of interest and any apparent connection, according to a competing theory, is most certainly not accidental. The opposite of a null hypothesis is an alternative hypothesis. If we are able to rule out the null hypothesis, it signifies that we have enough data to support the alternative hypothesis. In one test, we cannot rule out both possibilities.
If one is disproven, it indicates that there is evidence to support the other. The opposing view is that a study's potential conclusion will materialize. It claims there is no coincidence in the relationship between important components of interest and the observed connection. As a result, the alternative hypothesis is true if the null hypothesis is disproved during hypothesis testing.
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A park began with a population of 8 rabbits. Every year, the rabbit population triples. How long will it take for the population to reach 1,944 rabbits? choose the equation for the population of rabbits, r, in terms of the number of years that have passed, y, and the correct solution.
When the population starts out with 8 people and triples, it will take 5 years to reach 1,944.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Initial population=8
Final population=1944
Rate of increment=3ˣ
1944=8*3ˣ
1944/8=3ˣ
243=3ˣ
3ˣ=3⁵
x=5
It will take 5 years for the population to reach 1,944 when started with with the population of 8 and increase by 3ˣ.
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Please Help!!!! 50 pts
Answer:
This may not help but, If you have any notes try using notes to solve this.
Or you can maybe ask your teacher to go over it when you both have free time or maybe have your teacher do a practice problem before or after class! That is what I would do but I hope it helps you! Good luck!
Answer:
A.
Step-by-step explanation:
A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15°, from a height of 2. 2 feet. How far away does the ball land in feet?use x=(v * cos [theta])*ty=h+(v * sin [theta]t-16t^2Solve T in the second equation using the quadratic formula, then solve x
The ball will land 67.381 feet away.
Thus, option (B) is correct.
Given:
v = 62 feet / second
[tex]\theta[/tex] = 15
h = 2.2 feet
Using the formula
Horizontal range = [tex]\dfrac{v \;cos\; \theta\; [v \;sin\;\theta + \sqrt{v^2\;sin\;\theta + 2gh]}}{g}[/tex]
Substituting the value back into the formula as
Horizontal range = [tex]\dfrac{62 \;cos\; (15)\; [62 \;sin\;(15)+ \sqrt{(62\;sin\;(15))^2 + 2g*2.2]}}{g}[/tex]
= 67.381 feet
Therefore, the distance is 67.381 feet.
Thus, option (B) is correct.
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The question attached here seems to be incomplete, the complete question is:
A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15", from a height of 2.2 feet. How far away does the ball land in feet? (5 points)
56.372 feet
67.381 feet
60.646 feet
47.293 feet
a plane has a cruising speed of 200 miles per hour when there is no wind. at this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. find the speed of the wind. speedofthewind:miles/hour
The speed of wind is 380 miles per hour.
What is speed?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path.
Here, we have
The plane has a cruising speed of 200 miles per hour when there is no wind. at this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind.
We have to find the speed of the wind.
Time = Distance/speed
Time = 500/200 = 2.5hrs
When the plane moves against the wind its effective speed reduces as it has to overcome the opposing force of the wind since it is given that it cover's a distance of 300 miles at the same time we can write
2.5 = 300/ V(plane) - v(wind)
2.5 = 300/500- v(wind)
v(wind) =380mph
Hence, the speed of the wind is 380mph.
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Describe the relationship between the lines.
1. The lines intersect to form an angle that is 180°
2. The lines intersect to form an angle that is not 90°
3. The lines intersect to form an angle that is 90°
4. he lines do not intersect.
geoff is about to open a restaurant. he has found two possible locations for the restaurant; one closer to the central business district (cbd) and one in the suburbs. geoff is concerned that if he chooses the cbd location, he will have to charge higher prices for his food to cover the higher rent. geoff is uncertain of the affect that this will have on his annual revenue. to help with his decision, geoff will carry out a multiple regression analysis to predict the annual revenue earned by restaurants based on their distance from the cbd in miles and the average price in dollars charged for a dish. geoff has collected a sample of 50 restaurants that are randomly spread around the city. the proximity to the cbd (x1i), average price of a dish (x2i) and annual revenues (yi) were recorded for each of these restaurants (i = 1, 2, ..., 50). Geoff believes that a multiple linear regression is appropriate for this data. After carrying out some analysis, geoff has noticed that moving one mile away from the CBD (assuming that the average price of a dish is held constant) will result in a decrease of $60,000 in annual revenues. Geoff has also noticed that increasing the average price of a dish by $1 (assuming that the distance from the CBD is held constant) will result in an increase of $40,000 in annual revenues. The data shows that a restaurant at the center of the CBD that gave away its food for free would have an annual loss of $20,000. Select the multiple linear regression equation that corresponds to Geoff's analysis: o ĝi = -20,000 - 60,000x11 + 40,000x2i o ĝi = 20,000 + 60,000x11 - 40,000x2i O Vi = -20,000 + 40,000x11 - 60,000x2i © y = 20,000 - 40,000x13 + 60,000x2i
The multiple regression linear regression equation is:
i = -20000 + -60000*x1i + 40000*x2i
The multiple regression equation here will be of the form
i = a*x1i + b*x2i + c
Where i is the annual revenue
a is the coefficient of x1i which is distance from CBD
where b is the coefficient of x2i average price of a dish
C is the constant term.
Given that moving one mile away from the CBD x1i , the annual revenues will i will decrease by $60000. So, the coefficient of x1i, a is -60000
Given that increasing the average price of dish x2i by $1 , the annula revenue will i will increase by $40000. So the coefficient of x2i, b is 40000
The data shows that the restaurant at the center of the CBD which means, x1i = 0 and giving away its food for free which means x2i = 0 is resulting in a loss of $20000. so the value of the constant term is c=20000.
so the multiple regression linear regression equation is:
i = -20000 + -60000*x1i + 40000*x2i
hence option A is correct
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Cesar danced for 16 minutes on Saturday. On Sunday he danced for 28 minutes more than he did on Saturday. How long has he danced in total
Answer:
60 minutes
Step-by-step explanation:
Saturday = 16 minutes
Sunday = 28 minutes + 16 minutes = 44 minutes
Saturday + Sunday = 44 + 16 = 60 minutes
1.5(6t+2) i need help with problem let me know if one of yall ppl get the answer so i can finish my homework sheet pls and thank you!!!
The value of the expression illustrated as 1.5(6t+2) is 9t + 3.
What is the value of the expression?Expression is simply used in Mathematics to show the relationship between the variables that are illustrated. In this case, this depicts the information given.
Based on the information, the expression is illustrated as:
1.5(6t+2)
Open the parentheses
(1.5 × 6t) + (1.5 × 2)
= 9t + 3.
The value is 9t + 3.
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Complete question
Find the value of the expression given 1.5(6t+2) i
Leah runs 2000 meters in 5 minutes. How may meters can Leah run in one min
meters per minute
Answer:
Leah runs:
400 meters per minute
Step-by-step explanation:
2000 meters ⇒ 5 minutes
A meters ⇒ 1 minute
A = 2000 meters * 1 minute / 5 minute
A = 400 meters
instructor number of failures prof. a 13 prof. b 0 prof. c 11 prof. d 16 what is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?
The standard deviation of the sampling distribution is 0.03
Instructor number is calculated as - (failure /100)
Number of failures for instructor A = 13 = 0.13
Number of failures for instructor B = 0 = 0.
Number of failures for instructor C = 11 = 0.11
Number of failures for instructor D = 16 = 0.16
Calculating mean -
Mean(m)
= 0.13 + 0.11 + 0.16) / 3
= 0.4 / 3
= 0.13
Calculating the Standard deviation -
Σ(X - m)² / N - 1
Σ(0.13 - 0.1333)² + (0.11 × 0.1333)² + ( 0.16 - 0.1333)² = 0.001266
= 0.001266 / 2
= 0.00063343
= √0.00063343
= 0.025168
= 0.03
Complete question -
The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: Instructor Number of Failures Prof. A 13 Prof. B 0 Prof. C 11 Prof. D 16 What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?
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What is the measure of ZLMQ?
Answer:
97
Step-by-step explanation:
< LMN = 33
The sum of the interior angles equal 180
180 - 92 - 55 = 33
<QM (can't read the last letter 50
180 - 45 - 85 = 50
<LMQ This is a straight angle and straight angles are 180
180 - 33 -50 = 97
if z is a standard normal variable, find the probability. the probability that z lies between -0.56 and 0.56
The normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution.
The usual normal distribution is then followed by the z variable. A value of the x variable's z variable, also known as the z-score of the x variable, indicates how many standard deviations from the mean it is.
The area under the normal distribution curve must be calculated that lies between
z=−1.56 and z=1.56
Using the standard normal table, the area is calculated as:
P(−1.56<z<1.56)
=P(z<1.56)−P(z<−1.56)
=P(z<1.56)−(1−P(z<1.56))
=0.9406−(1−0.9406)
=0.8812
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The complete question is
if z is a standard normal variable, find the probability. the probability that z lies between -1.56 and 1.56 is
Please help need this done asap