Consecutive terms in this sequence are separated by a constant c, so if the 4th term is 15, then the next terms would be
5th: 15 + c
6th: (15 + c) + c = 15 + 2c
7th: (15 + 2c) + c = 15 + 3c
and so on. More generally, since any given number in the sequence depends on the number that came before it, we can write the n-th term in terms of the 4th term,
n-th: 15 + (n - 4) c
Then the 9th term in the sequence is
15 + (9 - 4) c = 35
and solving for c gives
15 + 5c = 35 ==> 5c = 20 ==> c = 4
Then the 15th term would be
15 + (15 - 4)×4 = 15 + 11×4 = 15 + 44 = 59
The weight of an object above the surface of the Earth varies inversely with the square of the
distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from
Earth's center, what would it weigh if it were 4,015 miles from Earth's center?
Answer:
weight =48.71228786pounds
Step-by-step explanation:
[tex]w = \frac{k}{ {d}^{2} } \\ 50 = \frac{k}{ {3960}^{2} } \\ \\ k = 50 \times {3960}^{2} \\ k = 50 \times 15681600 \\ k = 784080000 \\ \\ w = \frac{784080000}{ {d}^{2} } \\ w = \frac{784080000}{16120225} \\ \\ w = 48.71228786 \\ w = 48.7pounds[/tex]
If a body weighs 50 pounds when it is 3,960 miles from Earth's center, it would weigh approximately 48.547 pounds if it were 4,015 miles from Earth's center, according to the inverse square law formula.
We know the inverse square law formula:
W₁ / W₂ = D²₂ / D²₁
Where W₁ is the weight of the body at the initial distance D₁, and W₂ is the weight at the final distance D₂.
So we have,
W₁ = 50
D₁ = 3,960
D₂ = 4015
We know that the body weighs 50 pounds when it is 3,960 miles from Earth's center,
So we can plug in those values as follows:
50 / W₂ = (4,015)²/ (3,960)²
To solve for W₂, we can cross-multiply and simplify as follows:
W₂ = 50 x (3,960)² / (4,015)²
W₂ = 50 x 15,681,600 / 16,120,225
W₂ = 48.547 pounds (rounded to three decimal places)
Therefore, if the body were 4,015 miles from Earth's center, it would weigh approximately 48.547 pounds.
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Draw the line segment with endpoints (-5, 9) and (-1, -7) and find the value of y if x=-4;-2.5;-2;-1.5;0 plz answer asap
Answer:
5, - 1, - 3, - 5, - 11
Step-by-step explanation:
The equation of the line is y=-4x-11. The y values corresponding to x are 5, - 1, - 3, - 5, - 11
A pizza parlor has a choice of 10 toppings for its pizzas. From these 10 toppings, how many different 7-topping pizzas are possible?
Answer:
120
Step-by-step explanation:
There are 10 possible toppings to choose from, you choose 7.
Using combinatorics, it's 10!/(7! 3!), or 120.
The formula is (total amount to choose from )! divided by (amount you choose)!(amount you don't choose)!
Or search up combination formula
A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
The formula for combination.
= [tex]^nC_r[/tex]
= n! / r! (n -r)!
The number of possible 7-toppings for the pizza is 120.
What is a combination?A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
We have,
The total number of toppings = 10.
n = 10
The number of required toppings = 7.
r = 7
The formula for combination.
= [tex]^nC_r[/tex]
= n! / r! (n -r)!
The possible number of possible 7-toppings pizzas.
= [tex]^{10}C_7[/tex]
= (10 x 9 x 8) / (3 x 2)
= 120
Thus,
n = 10 and r = 7
[tex]^{10}C_7[/tex] = 120
The number of possible 7-toppings for the pizza is 120.
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Practice Exercise 3.1 Fill in the blanks: (i) The factors of 12 are (ii) The least non-zero multiples of any number is (iii) ......... is a factor of every number. ing with Numbers
Answer:
i.)1,2,3,4,6,12
ii).the number itself
iii.)1
y=4.5x+13.45 y=6x-4.55
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(
12
,
67.45
)
Equation Form:
x
=
12
,
y
=
67.45
A math professor is wondering if students today are better or worse than in the past. He has given the same final to this year's class that he gave ten years ago. Compute mean, median, and mode for both classes and write a paragraph summarizing the differences.
This Year
35 45 65 75 87
80 69 71 53 90
99 95 70 82 73
93 67 61 57 74
72 77 71 81 83
Ten Years Ago
56 77 75 76 59
74 51 89 55 79
67 77 69 91 68
90 65 79 69 79
87 86 98 91 95
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following data:
This year :
35, 45, 53, 57, 61, 65, 67, 69, 70, 71, 71, 72, 73, 74, 75, 77, 80, 81, 82, 83, 87, 90, 93, 95, 99
Mean = ΣX / n = 1825 / 25 = 73
The mode = 71 ( most frequently occurring)
Median = 1/2(n+1)th term = 1/(26) = 13th term
Median = 73
10 years ago :
51, 55, 56, 59, 65, 67, 68, 69, 69, 74, 75, 76, 77, 77, 79, 79, 79, 86, 87, 89, 90, 91, 91, 95, 98
Mean = ΣX / n = 1902 / 25 = 76.08
The mode = 79 ( most frequently occurring)
Median = 1/2(n+1)th term = 1/(26) = 13th term
Median = 77
According to the computed statistics, we can conclude that, today is worse than the past as the average score which is almost similar to the median value is higher 10 years ago and the modal score is better 10 years ago as well.
if x and y are linear pair of angel then x +y=
Answer: x + y = 180²
Step-by-step explanation:
A linear pair is a pair of adjacent, supplementary angles.
Adjacent means next to each other.
Supplementary means that the measures of the two angles add up to equal 180 degrees.
Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.
I need help plz!!
8.57396817...•5/8 is rational or irrational?
Answer:
Irrational
Step-by-step explanation:
Any non-zero rational number multiplied by an irrational number will be irrational. We can rewrite this as (8.57... * 5) / 8, but we have no idea how to make 8.57... * 5 rational, or expressed as the quotient of two integers.
∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]
Split up the integral:
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]
For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get
[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]
and
[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]
Then
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]
Which of the two functions below has the smallest minimum y-value?
f(x) = 4(x - 6)4 + 1
g(x) = 2x3 + 28
O A. g(x)
B. f(x).
C. The extreme minimum y-value for f(x) and g(x) is --
D. There is not enough information to determine
Answer:
Answer A
Step-by-step explanation:
[tex]\displaystyle \lim_{n \to -\infty} (3x^3+28)=-\infty\\\\minimum\ of \ f(x)=6\\\\Answer\ A[/tex]
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2
= 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance σ2 = 83.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Use the traditional method. Assume that a simple random sample is selected from a normally distributed population.
a. Check requirements.
b. Establish H0 and H1 and note the level of significance.
c. Find the sample test statistic.
d. Find Critical Value.
e. Conclude the test and interpret results.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
consider a study conducted to determine the average protein intake among an adult population. Suppose that a confidence level of 85% is required with an interval about 10 units wide. if a preliminary data indicates a standard deviation of 20g, what sample of adults should be selected for the study?
Answer:
made up of about 20 common amino acids. The proportion of these amino acids varies as a characteristic of a given protein, but all food proteins—with the exception of gelatin—contain some of each. Amino nitrogen accounts for approximately 16% of the weight of proteins. Amino acids are required for the synthesis of body protein and other important nitrogen-containing compounds, such as creatine, peptide hormones, and some neurotransmitters. Although allowances are expressed as protein, a the biological requirement is for amino acids.
Proteins and other nitrogenous compounds are being degraded and resynthesized continuously. Several times more protein is turned over daily within the body than is ordinarily consumed, indicating that reutilization of amino acids is a major feature of the economy of protein metabolism. This process of recapture is not completely efficient, and some amino acids are lost by oxidative catabolism. Metabolic products of amino acids (urea, creatinine, uric acid, and other nitrogenous products) are excreted in the urine; nitrogen is also lost in feces, sweat, and other body secretions and in sloughed skin, hair, and nails. A continuous supply of dietary amino acids is required to replace these losses, even after growth has ceased.
Amino acids consumed in excess of the amounts needed for the synthesis of nitrogenous tissue constituents are not stored but are degraded; the nitrogen is excreted as urea, and the keto acids left after removal of the amino groups are either utilized directly as sources of energy or are converted to carbohydrate or fat.
37. The trip between 2 towns is exactly 90 miles. You have gone 40% of this distance. How far have
you gone?
Answer:
36 miles
Step-by-step explanation:
We want to find 40% of 90 miles
40% * 90
.40 * 90
36 miles
We have to find travelled distance inorder to find this we have to find 40℅ of 90miles
[tex]\\ \Large\sf\longmapsto 90\times 40\℅[/tex]
[tex]\\ \Large\sf\longmapsto 90\times \dfrac{40}{100}[/tex]
[tex]\\ \Large\sf\longmapsto 9\times 4[/tex]
[tex]\\ \Large\sf\longmapsto 36miles [/tex]
Solve the inequality
Answer:
hope this helps buddy, please mark the brainliest.
Step-by-step explanation:
The correlation coefficient, r, between the prices of smartphones, x, and the number of sales of phones, y, equals −0.63.
Select the statement which best describes the relationship between the price and sales.
The value of r indicates that the number of sales decreases as the price decreases.
The value of r indicates that the number of sales decreases as the price stays the same.
The value of r indicates that the number of sales decreases as the price increases.
The value of r indicates that the number of sales is not related to the price.
I think its (C): The value of r indicates that the number of sales decreases as the price increases.
Answer:
(C) The value of r indicates that the number of sales decreases as the price increases.
ED2021.
The best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.
What is a Negative Correlation Coefficient?A negative correlation coefficient has a negative sign, and implies a negative relationship between two variables.
This means that, as one variable decreases, the other variable increases.
Thus, a correlation coefficient of -0.63 shows a negative relationship between prices of smartphones and the number of sales.
Therefore, the best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.
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Question 3 plz show ALL STEPS
Answer:
7,0, -1 and -2
Step-by-step explanation:
Just substitute the values,
a. f(g(7))=f(-1) [g(7)=-1 given]
=7 [f(-1)=7 given]
b.f(g(-1))=f(3)=0 [g(-1)=3 Given]
c.g(f(-1))=g(7)=-1 [f(-1)=7 given]
d.g(f(7))=g(5)=-2 [f(7)=g(5) given]
any equations that equal three?
Last year, Rob set up the Road Runner Race for his school.
The race was 1,200 meters long and 188 people signed up to
run the race. 38 people did not show up to run. This year,
there will be 3 times as many runners as last year. How
many people will run the race this year?
Answer:
450 runners
Step-by-step explanation:
write
the following numbers using Roman numerals 20
Step-by-step explanation:
xx is the Roman number of 20
N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to
N?
A) 1 1/2
B 1 1/3
C) 5/3
D) 3/2
Answer:
it should be letter c 5/3 I could be wrong but I hope this help
pLEASE help best and right answer gets brainliest
Step-by-step explanation:
| - 5 | + | - 4 |
5 + 4
= 9
| - 6| - 4
6 - 4
2
I hope this answers your question.
Which expression is equivalent to (b^n)m?
Step-by-step explanation:
By the law of exponent :
(a^n)^m=a^n×m
Option C
b^n×m is the correct answer...
hope it helps
Make mathematical expressions then, simplify ,50 is divided by 2 times one more than the difference of F and 3.
Answer:
F = 27
Step-by-step explanation:
50/2 = (F - 3) + 1
25 = F - 2
F = 27
prove that tan² theta + cot² theta = sec² theta cosec² theta- 2
Step-by-step explanation:
Tan² theta = sec² theta - 1
Cot² theta = cosec² theta - 1
Tan²+Cot² = sec²-1+cosec²-1
= sec²+cosec²-2
Please find attached herewith the solution of your question.
If you have any doubt, please comment.
Integers are sometimes whole numbers
true or false
Answer:
True
Step-by-step explanation:
Integers are always whole numbers
negative, 0, positive:: whole numbers
What is the slope-intercept equation of the line below?
Answer:
y=-5/4x+3
Step-by-step explanation:
y=mx+c
m = (y1-y2)/(x1-x2) =(-2-3)/(4-0) =-5/4
sub the values y=3, x=0 to find c,
3 =-5/4(0) + c
c = 3
Which of the following algebraic steps will solve the equation 5p= -35 and what is the solution
Answer:
p=-7
Step-by-step explanation:
5p=-35
Divide both sides by 5
5p/5 =-35/5
therefore p=-7
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{5p= -35}\\\\\underline{\huge\text{DIVIDE 5 BOTH SIDES}}\\\\\mathsf{\dfrac{5p}{5p}= \dfrac{-35}{5}}\\\\\large\text{CANCEL out: }\dfrac{5}{5}\large\text{ because that gives you 1}\\\large\text{KEEP: }\dfrac{-35}{5}\large\text{ because that gives you the value of p.}\\\\\large\textsf{p = }\mathsf{\dfrac{-35}{5}}\\\\\mathsf{-35\div5= p}\\\\\large\text{Simplify above and you have your result to the p-value.}\\\\\boxed{\boxed{\huge\text{Therefore your answer is: \textsf{p = -7}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PLS HELP I DONT KNOW THIS ONE
Answer:
x+3
---------------
(x-3)(x-2)(x-4)
Step-by-step explanation:
x+4 x^2 -16
---------------÷ -------------
x^2 - 5x+6 x+3
Copy dot flip
x+4 x+3
--------------- * -------------
x^2 - 5x+6 x^2 -16
Factor
x+4 x+3
--------------- * -------------
(x-3)(x-2) (x-4)(x+4)
Cancel like terms
1 x+3
--------------- * -------------
(x-3)(x-2) (x-4)1
x+3
--------------- x cannot equal 3,2,4 -4
(x-3)(x-2)(x-4)
Hello I'm new can anyone help me with this question?
Thank you so much! <3 xoxo
Please help! Question and answers are in the pic
So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.
22 hours x $8.50 = $187
Subtract that from the cost of the computer:
899-187 = $712
She needs $712 more.
Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75
Divide what she needs by amount per shift:
712 / 46.75 = 15.22 shifts
She needs to work 16 more shifts.
