Answer:
[tex] \boxed{\huge{\sf f(x) = 1}} [/tex]
Given:
[tex] \sf f(x) = \frac{x}{2 + 8} [/tex]
To Find:
[tex] \sf f(x) \: when \: \bold{x} = 10[/tex]
Step-by-step explanation:
[tex] \sf Evaluate \: f(x) = \frac{x}{2 + 8} \: where \: \bold{x} = 10 : \\ \sf \implies f(x) = \frac{x}{2 + 8} = \frac{10}{2 + 8} \\ \\ \sf 2 + 8 = 10 : \\ \sf \implies f(x) = \frac{10}{ \boxed{\sf 10}} \\ \\ \sf \frac{ \cancel{\sf 10}}{ \cancel{\sf 10}} = 1 : \\ \sf \implies f(x) = 1[/tex]
The point A is shown on the unit grid below.
Answer:
Coordinates of point B are (3, 5) and (5, 3).
Step-by-step explanation:
Coordinates of point A → (1, 1)
Let the coordinates of point B are (x', y')
Formula for the distance between points (x, y) and (x', y') is,
d = [tex]\sqrt{(x-x')^+(y-y')^2}[/tex]
AB = [tex]\sqrt{(x-1)^+(y-1)^2}[/tex]
[tex]2\sqrt{5}=\sqrt{(x-1)^2+(y-1)^2}[/tex]
[tex](2\sqrt{5})^2=(x-1)^2+(y-1)^2[/tex]
20 = (x - 1)² + (y - 1)²
Since point A lies on the intersection of two grid lines in the 1st quadrant, x and y must be the positive whole number.
For x = 0,
20 = (0 - 1)² + (y - 1)²
(y - 1)² = 20 - 1
y = 1 + √19
But y can't be a decimal, therefore, x = 0 is not the answer.
For x = 1
20 = (1 - 1)² + (y - 1)²
20 - 1 = (y - 1)²
y = 1 + √19
Not a whole number, so can't be the solution.
For x = 2,
20 = (2 - 1)² + (y - 1)²
y = 1 + √19
Not a whole number, therefore, not the answer.
For x = 3,
20 = (3 - 1)² + (y - 1)²
20 - 4 = (y - 1)²
y = 1 + √16
y = 5
Therefore, (3, 5) are coordinates of the point B.
For x = 4,
20 = (4 - 1)² + (y - 1)²
20 = 9 + (y - 1)²
y = 1 + √11
For x = 5,
20 = (5 - 1)² + (y - 1)²
20 - 16 = (y - 1)²
4 = (y - 1)²
y = 3
Therefore, (5, 3) the coordinates of point B.
The coordinates of [tex]B, (x,y)=(3,5)\text{ or }(5,3)[/tex]
From the diagram, the coordinates of [tex]A[/tex] are [tex](1,1)[/tex]
the distance from [tex]A[/tex] to [tex]B[/tex] is [tex]2\sqrt{5}[/tex]
Since [tex]B(x, y)[/tex] also lies on the grid, [tex]x[/tex] and [tex]y[/tex] should be integers and should satisfy the distance relationship
[tex](x-1)^2+(y-1)^2=(2\sqrt{5})^2\implies (x-1)^2+(y-1)^2=20[/tex]
There is a way to get [tex]\sqrt{5}[/tex] from Pythagoras rule
[tex]1^2+2^2=(\sqrt{5})^2\\\\\implies2^2+4^2=(2\sqrt{5})^2[/tex]
Which means we can either say
[tex]x-1=2 \text{ and } y-1=4\\\implies x=3 \text{ and } y=5\\\\\text{OR}\\\\x-1=4 \text{ and } y-1=2\\\implies x=5 \text{ and } y=3[/tex]
Therefore B is either at location [tex](3,5)[/tex] or [tex](5,3)[/tex]
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The figure below shows a line graph and two shaded triangles that are similar:
-20-16-12-8-40
-1
4 8 12 16 20
Which statement about the slope of the line is true?
The slope from point o to point A is one-fourth times the slope of the line from point A to point B.
The slope from point o to point A is four times the slope of the line from point A to point B.
Olt is throughout the line
It is -4 throughout the line.
Answer:
It is - [tex]\frac{1}{4}[/tex] throughout the line
Step-by-step explanation:
The points O, A and B lie on the line and so the slope will be the same for OA, OB and AB
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B(- 12, 3) and (x₂, y₂ ) = O(0, 0)
m = [tex]\frac{0-3}{0+12}[/tex] = [tex]\frac{-3}{12}[/tex] = - [tex]\frac{1}{4}[/tex]
Thus the slope is - [tex]\frac{1}{4}[/tex] throughout the line.
3.27 Underage drinking, Part II. We learned in Exercise 3.25 that about 70% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds. (a) How many people would you expect to have consumed alcoholic beverages? And with what standard deviation? (b) Would you be surprised if there were 45 or more people who have consumed alcoholic beverages? (c) What is
Answer:
a) Number of people expected to have consumed alcoholic beverages in the sample = 35.
Standard deviation = 3.24
b) 45 or more people consuming alcoholic beverages in the sample is about 3 standard deviations from the mean (35), hence, it would be surprising if this happened since most of the possible values in a distribution stay well within a few standard deviations of the mean.
c) The probability that 45 or more people in this sample have consumed alcoholic beverages = 0.0017
The mathematical and statistical chances of 45 or more people who have consumed alcoholic beverages in the sample is very low (0.0017), hence, it will be very surprising if this happened.
Step-by-step explanation:
Concluding part of the question
What is the probability that 45 or more people in this sample have consumed alcoholic beverages? How does this probability relate to your answer to part (b)?
a) The expected number of people that take alcoholic beverages in a sample of people is the mean of a binomial distribution and it is given as
Mean = np
where n = sample size = 50
p = population proportion of youths that take alcoholic beverages = 70% = 0.70
Number of people expected to have consumed alcoholic beverages in the sample = 0.70 × 50 = 35
The standard deviation is given as
σ = √[np(1-p)] = √(50×0.70×0.30) = 3.24
b and c) To investigate whether one should be surprised if 45 or more people out of the sample take alcoholic beverages, we first find the probability of this happening.
If the probability is very small or minute.
Using the normal approximation to the binomial distribution,
μ = 35
σ = 3.24
If X denotes the number of people that will take alcoholic beverages in the sample.
And we need P(X ≥ 45)
we first introduce the continuity correction factor.
P(X ≥ 45) = P(x ≥ 44.5)
We normalize or standardize the number 44.5
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (44.5 - 35)/3.24 = 2.93
To determine the required probability
We'll use data from the normal distribution table for these probabilities
P(X ≥ 45) = P(x ≥ 44.5) = P(z ≥ 2.93)
= 1 - P(z < 2.93)
= 1 - 0.99831
= 0.00169 = 0.0017 to 4 d.p.
Hope this Helps!!!
Jason is playing a game. He has two sets of cards. One set has three red cards, numbered 1, 2 and 3. The other set has four green cards, numbered 4, 5, 6 and 8. Jason chooses a red card and a green card at random. He works out his score by adding the numbers on the two cards together. A sample space diagram is drawn below. Work out the probability that Jason gets a score of 9 or more.
Answer:
1/3
Step-by-step explanation:
There are 12 different sums.
4 of the sums are 9, 9, 10, 11.
All other sums are 8 or less.
p(9 or more) = 4/12 = 1/3
i need help with this i dont understand at all. find the 1st, 2nd, 3rd, 4th and 10th nTh term rule is n+5
The rule is n + 5
So we have that
an = n + 5
Where n is the term, that said we want the 1st, 2nd, 3rd, 4th and 10th term
a1 = 1 + 5 = 6
a2 = 2 + 5 = 7
a3 = 3 + 5 = 8
a4 = 4 + 5 = 9
a10 = 10 + 5 = 15
Simple question
please answer need asap
the answer is A. 1,073 ft
rationalize the denominator of
1/3+√2
Answer:
(-√2 + 3)/7
Step-by-step explanation:
To rationalize the denominator, we need to multiply by the conjugate:
1/(3 + √2)*(3 - √2)/(3 - √2)
(3 - √2)/(9 - √4)
(3 - √2)/(9 - 2)
(-√2 + 3)/7
A small grain silo is filled with wheat at the end of each season. If the silo is only half full, how many cubic meters of wheat have been stored? Group of answer choices 339.29 m³ 223.19 m³ 169.65 m³ 113.10 m³
Answer:
Volume of wheat = 147.26 m³ (check the explanation)
Step-by-step explanation:
The question still lacks some details such as the size of the silo. We will go forward by assuming the size of the silo to aid our calculation. Silos are cylindrical storage structures that range from 3 - 27 m in diameter and 10 - 90 m in height. For the purpose of this question, let's assume that the size of the silo is 5 m (diameter) by 15 m (height).
Let's list out the parameters to be used:
diameter (D) = 5 m; r = D ÷ 2 ⇒ r = 5/2 = 2.5 m,
height (h) = 15 m
Volume of silo = πr²h = π * 2.5² * 15
V (silo) = 294.52 m³
The silo is half full ⇒ ½ * V
Volume of wheat stored is given by half of the silo volume, since the silo is half-full
V (wheat) = ½ * 298.52
V (wheat) = 147.26 m³
Find the equation of a line through the coordinate (3,−2) and parallel to the line represented y=12x−2. A y=12x−2 B y=−2x+4 C y=12x−72 D y=12x−52
Answer:
Step-by-step explanation:
y=12x−2. parallel lines have the same slope 12
find b at point (3,-2)
y=12x+b
-2=12(3)+b
-2-36=b
b=-36
the equation has to be y=12x-38
when you input the point(3,-2)
-2=12(3)-38
-2=-2 correct
The equation of line is [tex]y=12x-38[/tex] which is parallel to given line [tex]y=12x-2[/tex]
Equation of parallel line given is, [tex]y=12x-2[/tex]
Compare above equation of line from [tex]y=mx+c[/tex]
Since, all parallel lines have same slope.
Equation of line become,
[tex]y=12x+c[/tex]
Since, line passing through point (3, -2).
[tex]-2=12(3)+c\\\\c=-2-36=-38[/tex]
Hence, equation of line is [tex]y=12x-38[/tex] which is parallel to line [tex]y=12x-2[/tex]
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Blaine says that the product of a positive integer and a negative integer is always less than either factor. Is he correct? Provide examples or counterexamples to support your answer.
Answer:
you go to th harris right cause u literally have the same summer schools answers
Step-by-step explanation:
Prices for a day-ticket entrance at the Day-ticket Disneyland Paris Resort are as follows Pric Entrance Adult 205 $45 E170 Children Work out the percentage discount offered with the family ticket option. 2 adults, 2 children)
Answer:
15%
Step-by-step explanation:
Price of daily tickets entrance
Adult=£55
Children=£45
Family (2 adults and 2children)=£170(discount price)
Let
price for adults=a
Price for Children=c
Price of tickets without discount for 2 adults and 2 children=2(a+c)
=2(55+45)
=2(100)
=£200
Percentage discount offered with the family tickets=difference in price/original price×100
=£200-£170/200×100
=30/200×100
=30/2
=15%
The Percentage discount offered with the family tickets=15%
Whats TWO expressions that are equal to 2(3j+ 5 + 6j). REMEMBER I NEED TWO. ANSWER GETS BRAINLEST, 10 POINTS, 5 STARS, AND A THANKS.
Answer: I hope this helps!!!
Step-by-step explanation:
Phrase 1: 18j+10
Phrase 2: 2(9j+5)
Answer:
see explanation
Step-by-step explanation:
Given
2(3j + 5 + 6j) ← distribute the parenthesis by 2
= 6j + 10 + 12j ← equivalent expression ( collect like terms )
= 10 + 18j ← equivalent expression ( factor out 2 from each term
= 2(5 + 9j) ← equivalent expression
What is the sign of the product (−4)(2)(−3)(6)? (5 points) Select one: a. Positive, because the products (−4)(2) and (−3)(6) are negative and the product of two negative numbers is positive b. Positive, because the products (−4)(2) and (−3)(6) are positive and the product of two positive numbers is positive c. Negative, because the products (−4)(2) and (−3)(6) are negative and the product of two negative numbers is negative d. Negative, because the products (−4)(2) and (−3)(6) are positive and the product of two positive numbers is negative
Answer: Option A
Step-by-step explanation:
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population
Answer:
Step-by-step explanation:
This is exponential, of the form
[tex]y=a(b)^x[/tex] where a is the initial amount and b is the growth/decay rate. If Ginny begins the study with 1200 frogs in the population, our a value is 1200.
If the population is decreasing 3% per year, it is decreasing 100% - 3% = 97% which, as a decimal, is .97. Our exponential function, then, is
[tex]y=1200(.97)^x[/tex]
Find the measure of angle C of a triangle ABC, if: d m∠A = 60°+α, m∠B = 60°−α???
Answer:
c= 60
Step-by-step explanation:
The value of measure of angle C of a triangle ABC is 60°.
Here,
Given that, in a triangle value of two angles is,
m∠A = 60°+α, m∠B = 60°−α
We have to find the angle C of a triangle ABC.
What is sum of angle in triangle?
In a triangle, The sum of angles of a triangle is 180°.
Now,
Given that, in a triangle value of two angles is,
m∠A = 60°+α, m∠B = 60°−α
Let measure of angle C is x°.
⇒ Sum of all angle of triangle = 180°
⇒( 60°+α )+ ( 60°−α ) + x° = 180°
⇒ 120° + x° = 180°
⇒ x° = 180° - 120°
⇒ x° = 60°
Hence, The value of measure of angle C of a triangle ABC is 60°.
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The graphs of the quadratic function y= 2x^2and the exponential function y= 2^x are shown below.
Considering only the domain shown on the graph over which interval is the value of the exponential function greater than the value of the quadratic function?
A. -2.5
B. 1
C.-0.5
D.1
Answer:
C
Step-by-step explanation:
Answer: C
Step-by-step explanation: yay :D
AB is included between
A. BC and AC
B. AB and BC
C. ZB and ZC
D.A and B
Answer:
BC and AC are the answers
How many many weeks are in 105 days?
Answer: 15 weeks
Step-by-step explanation:
Because there are 7 days in a week, simply divide 105/7 to get 15 weeks.
Hope it helps <3
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------
Answer: There are 15 weeks in 105 days.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since there are 7 days in a week, we need to divide the time value by 7 .
Like this:
105 / 7 = 15.
A polynomial function can be written as (x + 1)(x + 4)(x – 7). What are the x-intercepts of the graph of this function?
(1,0), (4,0), (7,0)
O(-1,0), (-4,0), (-7,0)
O (1,0), (4,0), (-7,0)
O(-1,0), (-4,0), (7,0)
Answer:
fourth option
Step-by-step explanation:
Given
f(x) = (x + 1)(x + 4)(x - 7)
To find the x- intercepts let f(x) = 0, that is
(x + 1)(x + 4)(x - 7) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 4 = 0 ⇒ x = - 4
x - 7 = 0 ⇒ x = 7
x- intercepts are (- 1, 0 ), (- 4, 0 ), (7, 0 )
Can u guys PLEASE answer this question ASAP. The line l has equation y=3x+5
1)what is the y intercept
2)what is the gradient
3)find the equation of the line that has the same y intercept as l but has a gradient of 1/2
4) find the equation of the line that has the same equation as l but has a y intercept of -2
Answer:
try to look in desmos graphic calculator
Step-by-step explanation:
Pls help me ima mark BRAINLIST
Answer:
24.5
Step-by-step explanation:
Year 2000 would be 1, so year 2016 would be 17
Your equation is 1.5x - 1, and since we have x = 17, we simply plug it in:
1.5(17) - 1
25.5 - 1
24.5 is our estimated population using the line of best fit.
Answer:
23
Step-by-step explanation:
Note that the horizontal axis notes the years since 2000. This means that each increase in the x axis increases the year by 1. Thus, it means that at x=1, it is 2001, at x=2, it is 2002. In other words, in 2016, x=16.
We can just put this number into the equation:
y=1.5(16)-1
y=24-1
y=23
Which shows the correct method for solving the equation below? One-third (y minus 9) = 3 A 2-column table with 3 rows. Column 1 is labeled Solution step with entries one-third y minus 3 = 3, one-third y = 6, y = 18. Column 2 is labeled property used with entries distributive property, addition property of equality, multiplication property of equality. A 2-column table with 3 rows. Column 1 is labeled Solution step with entries one-third y minus 27 = 3, one-third y = 30, y = 10. Column 2 is labeled property used with entries distributive property, subtraction property of equality, division property of equality. A 2-column table with 3 rows. Column 1 is labeled Solution step with entries one-third y minus 3 = 1, one-third y = 4, y = 12. Column 2 is labeled property used with entries distributive property, addition property of equality, division property of equality. A 2-column table with 3 rows. Column 1 is labeled Solution step with entries one-third y minus 3 = 3, one-third y = 0, y = 0. Column 2 is labeled property used with entries distributive property, subtraction property of equality, division property of equality.
Answer:
1st one 18
Step-by-step explanation:
you distribute the 1/3 then at 3 then multiply by 3
When I say multiply by 3 I mean 1/3=6 multiply both sides by 3
Answer:
Its A or 18
Step-by-step explanation:
thanks to the other guy
Dan is 8 years older than Fiona. Gavyn is 9 years younger than Fiona. If the total of their ages is 56, how old is the eldest of them?
Answer:
27
Step-by-step explanation:
If Fiona's age is x, Dan and Gavyn's ages respectively are x + 8 and x - 9. We can write:
x + x + 8 + x - 9 = 56
3x - 1 = 56
3x = 57
x = 19
The eldest is Dan (because x + 8 > x and x + 8 > x - 9). His age is x + 8 = 19 + 8 = 27.
Chip has some peaches. He wants to give 4 peaches each to 4 of his friends. But he needs 2 more peaches to do that. How many peaches does Chip have?
Answer:
He has 14 peaches
Step-by-step explanation:
He wants to give away 4 peaches to 4 friends
4*4 = 16
But he is 2 short
16-2 = 14
He has 14 peaches
So for math class they gave me this equation and it is 6 ÷ 3(1+2) it makes no sense, I just keep getting stumped
Answer:
The answer is 6.
Step-by-step explanation:
6 ÷ 3 = 2
2+4 = 6
In a study of pain relievers , 100 people were given product A , and all but 33 experienced relief . In the same study , 50 people were given product B , and all but 12 experienced relief
Answer:
Here we want to find the relative frequencies for both products.
for product A we have a sample of 100 people (our 100%) and all but 33 of them experienced relief.
Then, we can find the relative frequency as:
Pa = (33/100)*100% = 33%
this means that product A is not efficient in 33% of the cases.
For product B, the sample is 50 people (our 100%) and all but 12 of them experienced relief, then the relative frequency is:
Pb = (12/50)*100% = 24%.
This means that product B is not efficient in 24% of the cases.
We can see that, in percentage, the product B seems to be more efficient.
I'm struggling a lot please helpp :(
Answer: 180,000,000 people
Step-by-step explanation:
We are looking for how many people there are, not the percentage of wealth.
60% of Americans are the poorest, and there are 300 million Americans in total.
60% = 0.6
300,000,000 * 0.6 = 180,000,000
Answer:
The Third Choice; answer C.
Step-by-step explanation:
180,000,000 Hope this helps <3
Gracie has 5555 pet bunnies that love to eat whole carrots. She has 39393939 carrots to feed the bunnies. Gracie will use as many carrots as she can and give each bunny the same number. How many carrots will each bunny get?
Answer:
7,091.61
Step-by-step explanation:
If you have a number 1. (39393939) and you have another number 2. (5555) and you want the second number to get the same amount as the other numbers but evenly, you need to divided the first number with the second number.
Ex. 39393939/ 5555 = 7,091.61
So each bunny will get 7,091.61 carrots.
the magic dragon cigarette company claims that their cigarettes contain an average of only 10 mg of tar. a random sample of 100 magic dragon cigarettes shows the average tar content to be 11.5 mg with a known population standard deviation of 4.5 mg. construct a hypothesis test to determine whether the average tar content of magic dragon cigarettes exceeds 10 mg. use a 5% level of significance.
what is the critical value method and pvalue method
Answer:
[tex]t=\frac{11.5-10}{\frac{4.5}{\sqrt{100}}}=3.333[/tex]
Critical value
The significance is 5% so then [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] then the critical value for this case would be [tex] z_{\alpha/2}= 1.64[/tex]. Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is higher than 10 mg
P value
The p value would be given
[tex]p_v =P(z>3.333)=0.000434[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 10 mg
Step-by-step explanation:
Information given
[tex]\bar X=11.5[/tex] represent the sample mean
[tex]\sigma=4.5[/tex] represent the population standard deviation
[tex]n=100[/tex] sample size
[tex]\mu_o =10[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is higher than 10mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 10[/tex]
Alternative hypothesis:[tex]\mu > 10[/tex]
the statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{11.5-10}{\frac{4.5}{\sqrt{100}}}=3.333[/tex]
Critical value
The significance is 5% so then [tex]\alpha=0.05[/tex] and [tex]\alpha/2=0.025[/tex] then the critical value for this case would be [tex] z_{\alpha/2}= 1.64[/tex]. Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is higher than 10 mg
P value
The p value would be given
[tex]p_v =P(z>3.333)=0.000434[/tex]
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 10 mg
1. What is the exact circumference of a circle that has a radius of 10 cm?
Answer:
62.8318531
10 x 2 = 20 so 20 is the diameter
20 x pi = 62.8318531
Hope this helps
Step-by-step explanation:
The exact circumference of a circle that has a radius of 10 cm is 62.8318531
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
Given that circle that has a radius of 10 cm
The circumference is given by
C = 2πr
= 2π10
= 20π
10 x 2 = 20
Therefore, 20 is the diameter
So, 20 x π = 62.8318531
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