Answer:
COPD
Step-by-step explanation:
COPD is a lung disease caused by tobacco use and other factors
what is 7x-6=22
A 4
B 5
C 16
D 11
Alice has seven times the amount of pens that Maurice has. Paul has two-thirds of the amount of pens as Alice and Suzy have combined. Dawn has a dozen more pens than Paul. Suzy has half the pens that Maurice has. If Suzy has 2 pens, how many does Dawn have?
Answer:
Dawn has 32 pens.
Step-by-step explanation:
Let No. of pens Alice has = ALet No. of pens Maurice has = M Let no of pens Paul has = P Let no. of pens Suzy has = S Let no of pens Dawn has = DGiven :
A = 7M P = 2/3 (A + S) D = P + 12 S = 1/2 MIf S = 2 {Given} M = 4 [∵ S = 1/2 M → M = 2S = 2X(2) ] A = 28 [ ∵ A = 7M → A = 7 x 4 ] P = 20 [∵ P = 2/3 (A+S) → P = 2/3 (28 + 2) = 2/3 (30) ] D = 32 [ ∵ D = P + 12 → D = 20 + 12 ]By following the relationships between the number of pens each person has, it is calculated that Dawn has 32 pens.
Explanation:This is a multi-step problem involving proportions and addition. First, we determine Maurice's number of pens based on Suzy's: because Suzy has half the pens Maurice does, and Suzy has 2 pens, Maurice therefore has 4 pens. Then, to find out how many pens Alice has, we multiply Maurice's number of pens by 7 (Alice having 7 times Maurice's number of pens), hence Alice has 28 pens. As Paul has two-thirds the number of all the pens that Alice and Suzy have (28 + 2 = 30 pens), Paul has 20 pens. Finally, as Dawn has a dozen more pens than Paul, Dawn has 32 pens (20 + 12).
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Jason drew a scale drawing of a city. He used the scale 1 inch : 4 yards. A neighborhood park is 68 yards wide in real life. How wide is the park in the drawing?
Answer:
17 inches
Step-by-step explanation:
The scale is the same at every distance, so ...
[tex]\dfrac{\text{1 in}}{\text{4 yd}}=\dfrac{w}{\text{68 yd}}\\\\\text{(1 in)}\dfrac{\text{68 yd}}{\text{4 yd}}=w \qquad\text{multiply by 68 yd}\\\\\text{17 in}=w[/tex]
The park is 17 inches wide on the drawing.
Answer:
17 in
Step-by-step explanation:
68 yds divided by 4 equals 17 in
While visiting a pet store, you notice that there are only birds and cats in the cages. You can't help but wonder how many of each animal there is in the yard. But when you ask the store manager how many of each animal he has, he refuses to give you a direct answer. He says there are 16 animal heads and 42 animal feet. How many birds and cats are there in the pet store?
Answer: there are 11 birds and 5 cats
Step-by-step explanation:
Let x represent the number of birds in the pet store.
Let y represent the number of cats in the pet store.
A bird has one head and a cat also has one head. The store manager says that there are 16 animal heads in the store. It means that
x + y = 16
A bird has 2 feet and a cat has 4 feet. The store manager says that there are 42 animal feet in the store. It means that
2x + 4y = 42 - - - - - - - - - - - - 1
Substituting x = 16 - y into equation 1, it becomes
2(16 - y) + 4y = 42
32 - 2y + 4y = 42
- 2y + 4y = 42 - 32
2y = 10
y = 10/2 = 5
x = 16 - y = 16 - 5
x = 11
Mary buys p peaches at the farmer's market for d dollars each. She spends a total of tdollars on peaches. Create an equation that represents the relationship between t and p.
An equation that represents the relationship between t and p is [tex]\rm Cost \ of \ each \ peaches = \dfrac{p \times d }{t}[/tex].
Given
Mary buys p peaches at the farmer's market for d dollars each.
She spends a total of t dollars on peaches.
The cost of each peach is;
[tex]\rm Cost \ of \ each \ peaches = \Total \ number \ of \ peaches \times Amount \ of \ each \ peaches\\\\Cost \ of \ each \ peaches= p \times d[/tex]
Therefore;
An equation that represents the relationship between t and p is;
[tex]\rm Cost \ of \ each \ peaches = \dfrac{Total \ number \ of \ peaches \times Amount \ of \ each \ peaches} {Total \ money\ spend \ on \ peaches}\\\\Cost \ of \ each \ peaches = \dfrac{p \times d }{t}[/tex]
Hence, An equation that represents the relationship between t and p is [tex]\rm Cost \ of \ each \ peaches = \dfrac{p \times d }{t}[/tex].
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If 64.7% 2017 college students attended a 4year program and u took a random 500students in 2017 how many college students would you expect to attend 4year program
Answer:
Around 337 students
Step-by-step explanation:
We are given the following in the question:
Percentage of student who attended a 4 year programme in 2017 = 64.7%
Sample size, n = 500
We have to find he expected number of students who would attend 4 year programme.
Formula:
[tex]67.4\% \times n\\=67.4\% \times 500\\\\=\dfrac{67.4}{100}\times 500\\\\=337[/tex]
Thus, around 337 students are expected to attend 4 year program.
Are these ratios equivalent?
18 professors : 5 students
36 professors : 10 students
yes/no
Answer:
yes
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
18 : 5
36 : 10
36/2 : 10/2
18 : 5
Scientific notation is ________.a. used to keep track of very small and very large numbers during mathematical calculations b. used to accurately measure volumes used to measure length with precision c. used to communicate the level of precision
Answer:
A. Used to keep track of very large and very small numbers during mathematical calculations.
Step-by-step explanation:
Some very large and small numbers are not easily represented in mathematical calculations. Using scientific notations help us to represent very large and small numbers to the power of 10.
Why is the answer A?
Step-by-step explanation:
F(x) is the antiderivative (or integral) of f(x).
F(x) = ∫ f(x) dx
F(x) = sin(1/(x² + 1))
∫₁² f(x) dx
= F(2) − F(1)
= sin(1/(2² + 1)) − sin(1/(1² + 1))
= sin(⅕) − sin(½)
= -0.281
Can someone please help me with this? will give you brainiest if correct
Thank you so much <3
Answer: The solution is [2, 1]
Step-by-step explanation:
The given system of simultaneous equations is expressed as
7x - 6y = - 20 - - - - - - - - - - 1
3x + 5y = - 1 - - - - - - - - - - - - -2
We would eliminate x by multiplying equation 1 by 3 and equation 2 by 7. It becomes
21x - 18y = - 60 - - - - - - - - - - 3
21x + 35y = - 7 - - - - - - - - - - 4
Subtracting equation 4 from equation 3, it becomes
- 53y = - 53
Dividing the left hand side and the right hand side of the equation by - 53, it becomes
- 53y/ - 53 = - 53/ - 53
y = 1
Substituting y = 1 into equation 2, it becomes
3x + 5 × 1 = - 1
3x + 5 = - 1
Subtracting 5 from the left hand side and the right hand side of the equation, it becomes
3x + 5 - 5 = - 1 - 5
3x = - 6
Dividing the left hand side and the right hand side of the equation by 3, it becomes
3x/3 = - 6/3
x = 2
In your class, you have scores of 66, 74, 71, and 81 on the first four of five tests. To get a grade of Upper C, the average of the first five tests scores must be greater than or equal to 70 and less than 80. a. Solve an inequality to find the least score you can get on the last test and still earn a Upper C. b. What score do you need if the fifth test counts as two tests?
Answer:
A score of greater than equal to 128 and less than 188 will get a grade of Upper C
Step-by-step explanation:
We are given the following in the question:
Scores:
66, 74, 71, 81
Let x be the score on fifth test.
[tex]\text{Average} = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
To get a grade of Upper C, the average of the first five tests scores must be greater than or equal to 70 and less than 80.
[tex]70 \leq \text{Average} < 80[/tex]
The fifth test counts as two tests.
Putting the values we get:
[tex]70 \leq \dfrac{66 +74+71 + 81+ x}{6} < 80\\\\420 \leq 292 + x < 480\\420 -292 \leq x < 480 - 292\\128 \leq x < 188[/tex]
Thus, a score of greater than equal to 128 and less than 188 will get a grade of Upper C
To earn an Upper C, solve an inequality with the average test scores. If the fifth test counts as two tests, the formula changes. Solve the new inequality to find the score needed.
Explanation:To find the least score you can get on the last test and still earn an Upper C, you need to solve the inequality:
(66 + 74 + 71 + 81 + x)/5 ≥ 70
(66 + 74 + 71 + 81 + x)/5 < 80
Solving this inequality will give you the range of scores you can get on the last test. If the fifth test counts as two tests, you can use the weighted average formula:
((66 + 74 + 71 + 81) + 2x)/7 ≥ 70
((66 + 74 + 71 + 81) + 2x)/7 < 80
Solving these inequalities will give you the score you need on the last test.
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Lailah earns $9 per week working at the aquarium. Write and solve an inequality that can be used to find how many hours she must work in a week to earn at least $135.
Answer:
$9 per hour (not week)
9x > or = 135
x > or = 45 hours she must work
Step-by-step explanation:
Answer: she must work for at least 15 hours in a week to earn at least $135
Step-by-step explanation:
Let x represent the number of hours that Lailah must work in a week to earn at least $135.
Lailah earns $9 per week working at the aquarium. This means that in a week in which she worked for x hours, the total amount of money that she would earn is 9x
Therefore, the inequality that can be used to find how many hours she must work in a week to earn at least $135 would be
9x ≥ 135
x ≥ 135/9
x ≥ 15
Please help, will mark brainliest if correct!!!
Answer:8.5
Step-by-step explanation:
Pythagorean Theorem
A
a^2 + b^2 = c^2
3^2 + 8^2 = c^2
9 + 64 = c^2
73 = c^2
C= Sqrt (73)
C = 8.5
Claudia scores 275 points on a video game. Hannah scores 268 points on the same video game. The high score for the same game is 306. How many points did the girls score in all?
Answer:
543
Step-by-step explanation:
Given: Claudia score= 275 points
Hannah score= 268 points
Now, finding the how many points girls scored in the game.
Total score by girls= [tex]Score\ of\ Claudia + score\ of\ Hannah[/tex]
⇒ Total score by girls= [tex]275+268[/tex]
Total score by girls= 543.
Hence, Total score by girls is 543.
ABCD is a rhombus. If AC = 8 cm and BC = 6 cm, what is the area of the rhombus?
Answer:24, it depend upon the picture
Step-by-step explanation:
if the ac and bc are diagonals the area of rhombus equal to 24.because area of the rhombuss = pq/2where p and q are the diagonals
You have just used the network planning model and found the critical path length is 30 days and the variance of the critical path is 25 days. The probability that the project will be completed in 33 days or less is equal to:_______.
Answer:
0.726 is the probability that the project will be completed in 33 days or less.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 30 days
Variance = 25 days
Standard Deviation,
[tex]\sigma = \sqrt{\text{Variance}} = \sqrt{25} = 5[/tex]
We assume that the distribution of path length is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(completed in 33 days or less)
[tex]P( x \leq 33) = P( z \leq \displaystyle\frac{33 - 30}{5}) = P(z \leq 0.6)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x \leq 33) = 0.726 = 72.6\%[/tex]
0.726 is the probability that the project will be completed in 33 days or less.
Two trained professionals observe the behavior of children in a classroom. They each rate observed behaviors using the same form and the number of items that were rated the same is calculated. This is an example of which type of reliability?
a. inter-rater reliability
b. test-retest reliability
c. none of the above
d. parallel reliability
Answer: a) inter rater
Step-by-step explanation:
Inter rater is a type of relativity that measures the degree of agreement between rates and judges.
It is used to ensure that the score gotten among rates are in consensus with one another.
Inter rater relativity reduces inconsistency in the application of data collected.
The scenario where two trained professionals rate observed children's behaviors using the same form and comparing their ratings exemplifies inter-rater reliability (option a), focusing on the consistency of measurements between different observers.
The type of reliability being described in the scenario is inter-rater reliability. This type of reliability is concerned with the level of agreement between two or more independent observers or raters when they assess the same behaviors using a standardized method or form. To ensure that a study's measures are consistently capturing the concepts of interest, researchers often assess inter-rater reliability.
Inter-rater reliability can involve qualitative categories (like behavioral observations in a classroom) where the agreement percentage reflects the reliability. Alternatively, for measurements on interval or ratio scales, the correlation between the raters' scores can be used. When two professionals observe children and rate their behavior on the same form, looking for agreement in items rated, they establish inter-rater reliability.
Let f(x) = -2x + 4 and g(x) = -6.0 – 7. Find f(x) – g(x).
Please show your work and explain steps! GIVING BRAINLIEST!!
Answer:
-2x + 3
Step-by-step explanation:
f(x) - g(x)
(-2x + 4) - (-6.0 - 7)
-2x + 4 - (-6.0) - 7
-2x + 4 + 6.0 - 7
-2x + 10 - 7
-2x + 3
The conference method estimates cost functions: A. Using quantitative methods that can be very time consuming and costly B. Based on analysis and opinions gathered from various departments C. Using time-and-motion studies D. By analyzing the relationship between inputs and outputs in physical terms
Answer:
B. Based on analysis and opinions gathered from various departments
Step-by-step explanation:
Conference method of cost estimation envisages a widespread process in which head of different unit of organisation is consulted and their skill in their area of operation is tapped to make estimation of cost of the operation of different department.
The price-to-earning ratio for firms in a given industry is distributed according to normal distribution. In this industry, a firm with a standard normal variable value of Z=1:_________
a. Has an above average price-to-earning ratio
b. Has a below average price-to-earning ratio
c. Has an average price-to-earning ratio
d. May have an average or below average price-to-earnings ratio
Answer:
Option a) Has an above average price-to-earning ratio
Step-by-step explanation:
We are given the following in the question:
The price-to-earning ratio for firms in a given industry is distributed according to normal distribution.
For a particular firm the ratio x has a standard normal variable has a value,
z = 1
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]1 = \dfrac{x - \mu}{\sigma}\\\\\sigma = x - \mu\\x = \mu + \sigma[/tex]
Thus, the firm has an above average price-to-earning ratio as the ratio is one standard deviation above the mean.
Option a) Has an above average price-to-earning ratio
If a firm in a given industry has a standard normal variable value of Z=1, it signifies that the firm has an above average price-to-earning ratio.
Explanation:A student has asked about the interpretation of a standard normal variable value, Z, in the context of a firm's price-to-earning (P/E) ratio in a given industry. If a firm has a Z-value of 1, it means that the firm's P/E ratio is one standard deviation above the mean for the industry. Since the standard normal distribution has a mean of 0 and a standard deviation of 1, a Z-value of 1 corresponds to performance that is better than average. Therefore, a correct interpretation of this scenario is a. Has an above average price-to-earning ratio.
The price-to-earning ratio for firms in a given industry is distributed according to a normal distribution. A firm with a standard normal variable value of Z=1 would have an above average price-to-earning ratio.
This is because the standard normal distribution has a mean of 0 and a standard deviation of 1. A Z-score of 1 corresponds to a value that is one standard deviation above the mean. Since the mean represents the average price-to-earning ratio in the industry, a firm with a Z-score of 1 would have a ratio that is above average.
1. Find X
A. 16.45
B. 15.92
C. 12
D. 11.5
Applying the tangent ratio, the value of x in the given image is calculated as B. x = 15.92
How to find x using the tangent ratio?The tangent ratio is a trigonometric ratio that represents the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle in a right-angled triangle. It is denoted as tan(θ), where θ is the angle. Mathematically, tan(θ) = opposite/adjacent.
Thus, using the tangent ratio, we have:
tan 53 = x/12
x = tan 53 * 12
x ≈ 15.92
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What is the rate of increase for the function f(x) = One-third (RootIndex 3 StartRoot 24 EndRoot) Superscript 2 x? One-third 2RootIndex 3 StartRoot 3 EndRoot 4 4RootIndex 3 StartRoot 9 EndRoot
Answer:
D, [tex]4^{3} \sqrt{9}[/tex]
Answer:
d
Step-by-step explanation:
Find the least-squares regression line: ŷ =b0+b1x, through the points (−1,0),(0,9), (4,13), (8,20), (10,23). For x=5, what is ŷ? For x=9, what is ŷ?
The value of y =14.45689 when x=5 and y= 21.74137 when x= 9.
What is Regression line?An estimate of the line that depicts the actual, but unidentified, linear relationship between the two variables is called a regression line. When the value of the explanatory variable is known, the regression line's equation is used to predict (or estimate) the value of the response variable.
Because it is the line that fits the points the best when drawn through them, the regression line is occasionally referred to as the "line of best fit." It is a line that minimises the difference between the projected and actual scores.
Given Data:
(−1,0),(0,9), (4,13), (8,20), (10,23).
Sum of X = 21
Sum of Y = 65
Mean X = 4.2
Mean Y = 13
Sum of squares (S[tex]S_x[/tex]) = 92.8
Sum of products (SP) = 169
Regression Equation = ŷ = bx + a
b = SP/S[tex]S_x[/tex] = 169/92.8 = 1.82112
a = [tex]M_y[/tex]- [tex]bM_x[/tex]= 13 - (1.82x4.2) = 5.35129
ŷ = 1.82112x + 5.35129
For x= 5
ŷ = 1.82112(5) + 5.35129
ŷ = 14.45689
and, when x= 9
ŷ = 1.82112(9) + 5.35129
ŷ = 21.74137
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Final answer:
The least-squares regression line equation is ŷ = -1.72 + 2.18x. For x = 5, ŷ is approximately 9.88. For x = 9, ŷ is approximately 18.62.
Explanation:
To find the least-squares regression line, we need to use the formula ŷ = b0 + b1x, where b0 is the y-intercept and b1 is the slope. Using the coordinates of the given points, we can calculate the values of b0 and b1. Substituting these values into the formula, we get ŷ = -1.72 + 2.18x. For x = 5, we can plug this value into the equation: ŷ = -1.72 + 2.18(5) = 9.88. Similarly, for x = 9, we can substitute x into the equation: ŷ = -1.72 + 2.18(9) = 18.62.
A card chosen at random from a deck of 52 cards. There are 4 queens and 4 kings in a deck of playing cards. What is the probability it is a queen or a king?
The cost of 3 boxes of envelopes and 4 boxes of notebook paper is $22.65. Two boxes of envelopes and 6 boxes of notebook paper cost $24.60. Find the cost of each.
Answer: the cost of one box of envelope is $3.75.
the cost of one box of notebook paper is $2.85
Step-by-step explanation:
Let x represent the cost of one box of envelope.
Let y represent the cost of one box of notebook paper.
The cost of 3 boxes of envelopes and 4 boxes of notebook paper is $22.65. This means that
3x + 4y = 22.65 - - - - - - - - - - -1
Two boxes of envelopes and 6 boxes of notebook paper cost $24.60. This means that
2x + 6y = 24.6 - - - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 8y = 45.3
6x + 18y = 73.8
Subtracting, it becomes
- 10y = - 28.5
y = - 28.5/-10
y = 2.85
Substituting y = 2.85 into equation 1, it becomes
3x + 4 × 2.85 = 22.65
3x + 11.4 = 22.65
3x = 22.65 - 11.4 = 11.25
x = 11.25/3 = 3.75
What is the momentum of each hockey player? Hockey player 1 has a mass of 65 kg and a velocity of 3.8 m/s
Hockey player 2 has a mass of 58 kg and a velocity of 4.3 m/s
Answer:
Momentum of hocking player [tex]1:[/tex] [tex]247\ kg\ m/s[/tex]
Hockey player [tex]2:[/tex] [tex]=249.4\ kg\ m/s[/tex]
Step-by-step explanation:
For first hockey player :
Given that
mass (m) [tex]=65\ kg[/tex]
Velocity (v) [tex]=3.8\ m/s[/tex]
[tex]p=mv\................(1)[/tex]
where [tex]p[/tex] is momentum
put the value in equation (1)
[tex]p=65\times3.8\\\\p=247kg\times m/s[/tex]
For second hockey player :
Given that
mass (m) [tex]=58\ kg[/tex]
velocity (v) [tex]=4.3\ m/s[/tex]
[tex]p=mv\ ...............(2)[/tex]
Where [tex]p[/tex] is momentum
put the value in equation (2)
[tex]p=58\times4.3\\p=249.4\ kg\times m/s[/tex]
Humberto evaluates the expression 4t2 for t=3. He correctly substitutes 3 for t in the expression, but then says that the value is 144. However, he is incorrect!
Answer:
36
Step-by-step explanation:
He multiplied the four and the three first when he multiplied the equation together. However, according to the order of the operations, he was supposed to square three first. 3^2 = 9. Then multiplied 9*4 = 36.
Show that the Fibonacci numbers satisfy the recurrence relation fn = 5fn−4 + 3fn−5 for n = 5, 6, 7, . . . , together with the initial conditions f0 = 0, f1 = 1, f2 = 1, f3 = 2, and f4 = 3. Use this recurrence relation to show that f5n is divisible by 5, for n = 1, 2, 3, . . . .
Answer with step-by-step explanation:
We are given that the recurrence relation
[tex]f_n=5f_{n-4}+3f_{n-5}[/tex]
for n=5,6,7,..
Initial condition
[tex]f_0=0,f_1=1,f_2=1,f_3=2,f_4=3[/tex]
We have to show that Fibonacci numbers satisfies the recurrence relation.
The recurrence relation of Fibonacci numbers
[tex]f_n=f_{n-1}+f_{n-2}[/tex],[tex]f_0=0,f_1=1[/tex]
Apply this
[tex]f_n=(f_{n-2}+f_{n-3})+f_{n-2}=2f_{n-2}+f_{n-3}[/tex]
[tex]f_n=2(f_{n-3}+f_{n-4})+f_{n-3}=3f_{n-3}+2f_{n-4}[/tex]
[tex]f_n=3(f_{n-4}+f_{n-5})+2f_{n-4}=5f_{n-4}+3f_{n-5}[/tex]
Substitute n=2
[tex]f_2=f_1+f_0=1+0=1[/tex]
[tex]f_3=f_2+f_1=1+1=2[/tex]
[tex]f_4=f_3+f_2=2+1=3[/tex]
Hence, the Fibonacci numbers satisfied the given recurrence relation .
Now, we have to show that [tex]f_{5n}[/tex] is divisible by 5 for n=1,2,3,..
Now replace n by 5n
[tex]f_{5n}=5f_{5n-4}+3f_{5n-5}[/tex]
Apply induction
Substitute n=1
[tex]f_5=5f_1+3f_0=5+0=5[/tex]
It is true for n=1
Suppose it is true for n=k
[tex]f_{5k}=5f_{5k-4}+3f_{5k-5}[/tex] is divisible 5
Let [tex]f_{5k}=5q[/tex]
Now, we shall prove that for n=k+1 is true
[tex]f_{5k+5}=5f_{5k+5-4}+3f_{5k+5-5}=5f_{5k+1}+3f_{5k}=5f_{5k+1}+3(5q)[/tex]
[tex]f_{5k+5}=5(f_{5k+1}+3q)[/tex]
It is multiple of 5 .Therefore, it is divisible by 5.
It is true for n=k+1
Hence, the [tex]f_{5n}[/tex] is divisible by 5 for n=1,2,3,..
The Fibonacci sequence with its initial conditions does satisfy the given recurrence relation. With this, it can also be demonstrated that f5n is divisible by 5 for all positive integers n.
Explanation:The problem involves a specific series in mathematics known as the Fibonacci series. We are given the Fibonacci numbers initial conditions: f0 = 0, f1 = 1, f2 = 1, f3 = 2, and f4 = 3. From these initial conditions, we can calculate the next values of the Fibonacci numbers.
Using the given Fibonacci numbers recurrence relation: fn = 5fn−4 + 3fn−5, we get:
f5 = 5f1 + 3f0 = 5 + 0 = 5f6 = 5f2 + 3f1 = 5 + 3 = 8f7 = 5f3 + 3f2 = 10 + 3 = 13So, fn = 5fn−4 + 3fn−5 is valid for n = 5, 6, 7, and presumably, for greater integers as well.
We then use this recurrence relation to show that f5n is divisible by 5, for n = 1, 2, 3, etc. This is immediately obvious for n = 1, because f5 = 5. But for n greater than 1, we can see that f5n = f(5*(n-1)+5) = 5f(5*(n-1)) + 3f(5*(n-1)-1), which will be divisible by 5 because 5 is a factor in the first term and the second term is also divisible by 5 according to our earlier results. This confirms that f5n is divisible by 5 for n = 1, 2, 3, and so on.
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Please help i need answer
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle,
BC represents the hypotenuse of the right angle triangle.
With m∠C as the reference angle,
AC represents the adjacent side of the right angle triangle.
AB represents the opposite side of the right angle triangle. if Sin C = 15/17, it means that
Opposite side = 15
Hypotenuse = 17
We would find the adjacent side by applying Pythagorean theorem. Therefore,
Adjacent side² = 17² - 15² = 64
Adjacent side √ 64 = 8
To determine the ratio of Cos C, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos C = 8/17
If Felicia lives 1 1/5 miles from the school and 9/10mile from the doctor field how much closer would she live if she lived 7/10 like from the doctor field