Answer:
5 \(\frac{1}{3}\), 10 \(\frac{2}{3}\)
Step-by-step explanation:
There is a common ratio r between consecutive terms, that is
\(\frac{2}{3}\) ÷ \(\frac{1}{3}\) = 1 \(\frac{1}{3}\) ÷ \(\frac{2}{3}\) = 2 \(\frac{2}{3}\) ÷ 1 \(\frac{1}{3}\) = 2
Thus to obtain a term in the sequence multiply the previous term by 2, thus
a₅ = \(\frac{8}{3}\) × 2 = \(\frac{16}{3}\) = 5 \(\frac{1}{3}\)
a₆ = \(\frac{16}{3}\) × 2 = \(\frac{32}{3}\) = 10 \(\frac{2}{3}\)
PLEASE HELP!
A poll is given, showing 45% are in favor of a new building project.
If 4 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?
The probability that exactly 3 out of 4 people chosen at random favor the new building project is 0.2904.
This problem can be solved using the binomial probability formula. Let X be the number of people who favor the new building project out of the 4 chosen at random. Then X follows a binomial distribution with parameters n = 4 and p = 0.45.
The probability of having exactly k people who favor the new building project out of 4 is given by:
P(X = k) = (4 choose k) * \(0.45^{k}\) * \(0.55^{4-k}\)
where (4 choose k) is the binomial coefficient.
To find the probability that exactly 3 of the 4 people favor the new building project, we substitute k = 3 in the above formula and evaluate:
P(X = 3) = (4 choose 3) * \(0.45^{3}\) * \(0.55^{1}\)
= 0.290384375
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David washes all 24 windows in his house he washed 6 windows each mr big and 2 windows each afternoon
How many days did it take him to wash all of his windows?
Answer:
3 days
Step-by-step explanation:
6 in the morning and 2 at the afternoon which mean David washed 8 windows a day.
24/8=3
So it took him 3 days
Hope this helps! :)
(pls mark brainliest)
Answer:
3 days
Step-by-step explanation:
when you divide 24 by 8 you get 3
A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $17. For 9 pounds of jelly beans and 7 pounds of trail mix, the total cost is $37. Find the cost for each pound of jelly beans and each pound of trail mix.
Answer:
1.75 trailmix
2.75 jellybeans
Step-by-step explanation:
you need to set up the problem like
x + y = _
and solve by elimination or subsitution
-3(3j + 5t = 17)
9j + 7t = 37
-9j + -15t = -51
9j + 7t = 37
-8t = -14
t = -14/-8
t = 1.75 is the cost of trail mix each pound
plug t into either equation to find the cost of jelly beans for each pound
9j + 7(1.75) = 37
9j + 12.25 = 37
9j = 24.75
j = 2.75 is the cost of jelly beans each pound
hope this helps
Help if you please! thanks!
Answer:
Step-by-step explanation:
What are the domain and range of the relation given in the table? x y −12 0 −8 12 0 0 1 8
Answer:
domain: {−12,−8,0,1}
range: {0,8,12}
The domain and range of the relation given in the table are:
The domain: {-12, -8, 0, 1}
And range: {0, 8, 12}
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
We have the relation,
x → y
-12 → 0
-8 → 12
0 → 0
1 → 8.
The range of the relation: All achievable values.
So, the domain: {-12, -8, 0, 1}
And range: {0, 8, 12}
Therefore, range and domain is given below.
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Can someone please help me thank you
The answers to the worksheet are in the included picture! :p
-------------------------------------------------------------------------------
This is just an example on how to simplify fractions: Write the simplified form of the fraction 12/24.
The given fraction is 12/24.
Step 1: Let us write the factors of 12 and 24.
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Step 2: Let us identify the common factors of 12 and 24.
Common factors are: 1, 2, 3, 4, 6, 12
Step 3: Keep dividing the numerator and denominator by the common factors.
(12 ÷ 2)/(24 ÷ 2) = 6/12
And
(6 ÷ 2)/(12 ÷ 2) = 3/6
Now divide by 3,
(3 ÷ 3)/(6 ÷ 3) = 1/2
Thus, 1/2 is the simplified fraction of 12/24.
-------------------------------------------------------
Have a great day and God bless! :D
Simplify the expression by combining like terms.
4/3a - 1/2b + 1/3a + 5/2b
Answer: 5/3a + 4/2b
Step-by-step explanation:
\(\dfrac{4}{3} a-\dfrac{1}{2} b+\dfrac{1}{3} a+\dfrac{5}{2} b\)
Rearrange:
\(\dfrac{4}{3} a+\dfrac{1}{3} a-\dfrac{1}{2} b+\dfrac{5}{2} b\)
Combine Like Terms:
\(\dfrac{4}{3} a+\dfrac{1}{3} a=\dfrac{5}{3} a\\-\dfrac{1}{2}b+\dfrac{5}{2} b=\dfrac{4}{2} b\)
\(\fbox{$\dfrac{5}{3}$a + $\dfrac{4}{2}$b}\)
Some factors need to be controlled to keep this test fair. name two of them….
Two factors that need to be controlled to keep this test fair are the temperature and the sample volume.
What are the control variables?The control variables are those variables that should be kept constant in order to avoid interfering with the free flow of the experiment.
For the provided test, it is important that the temperature of the environment where the test sample is kept is controlled throughout the duration of the experiment so that some results are not affected by this. Also, the sample volume should be controlled for fair outcomes.
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Find the critical value of x2 based on the given information H1 >3.5 n=14 a=0.05
Answer:
The degrees of freedom are given by:
\( df = n-1=14-1=13\)
The significance level is \(\alpha=0.05\) and then the critical value can be founded in th chi square table we need a quantile that accumulates 0.05 of the area in the right tail of the distribution and for this case is:
\( \chi^2_{\alpha}= 22.362\)
And if the chi square statistic is higher than the critical value we can reject the null hypothesis in favor of the alternative.
Step-by-step explanation:
We have the followign system of hypothesis:
Null hypothesis: \(\sigma^2 \leq 3.5\)
Alternative hypothesis: \( \sigma^2 >3.5\)
The degrees of freedom are given by:
\( df = n-1=14-1=13\)
The significance level is \(\alpha=0.05\) and then the critical value can be founded in th chi square table we need a quantile that accumulates 0.05 of the area in the right tail of the distribution and for this case is:
\( \chi^2_{\alpha}= 22.362\)
And if the chi square statistic is higher than the critical value we can reject the null hypothesis in favor of the alternative.
Help asap please!
What is sin(B)?
5
√61
sin(B):
6 [?]√[]
B
=
Answer:5SQRT61/
61
Step-by-step explanation:
You are renting a car. You can choose a compact, mid-size,
full-size, or sports utility vehicle. From those
categories you can choose a low, average, or high priced
model. How many different automobile choices do you have?
Answer:
I believe the answer is 4
Step-by-step explanation:
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.
How to find the ratio?To find the proportion in this problem we have to do the following procedure:
The first step is multiply both sides by 1500.The second step is to evaluate the expression on the right-hand side.The third step is multiply 10 by 1500 on the left-hand side.The fourth step is divide 15000 by 20 on the left-hand side.Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.
According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).
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Study these equations:
f(x) = 2x – 4
g(x) = 3x + 1
What is h(x) = f(x)g(x)?
h(x) = 6x2 – 10x – 4
h(x) = 6x2 – 12x – 4
h(x) = 6x2 + 2x – 4
h(x) = 6x2 + 14x + 4
Answer:
6x2-10x-4
Step-by-step explanation:
hx=(2x-4)(3x+1)
hx=2x(3x+1)-4(3x+1)
hx=6x2+2x-12x-4
hx=6x2-10x-4
Which of the following statements are true of this equation select all that apply. 5 1/6 ÷ 2 5/12 = 2 4/29
The left hand side of the equation is equal to right hand side.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a equation :
5 1/6 ÷ 2 5/12 = 2 4/29
We can write -
5 1/6 ÷ 2 5/12 = 2 4/29
31/6 ÷ 29/12 = 62/29
31/6 x 12/29 = 62/29
62/29 = 62/29
Therefore, the left hand side of the equation is equal to right hand side.
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What would be the equation for a line that is perpendicular to a line of Y = 3X +2
The equation of the perpendicular line is y = -1/3x
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 3x + 2
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 3
This means that the slope is 2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -1/3
The equation of the line is then calculated as
y = mx
Where
m = -1/3
So, we have
y = -1/3x
Hence, the line has an equation of y = -1/3x
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In the following equation, when x=3, what is the value of y? -4x + 3y = 12 A. 9 B. 3 C. 0 D. 8 PLZ HURRY IM TIMED WILL MARK BRAINLIEST
Answer:
\(\huge\boxed{y = 8}\)
Step-by-step explanation:
-4x + 3y = 12
Given that x = 3
-4 (3) + 3y = 12
-12 + 3y = 12
Adding 12 to both sides
3y = 12+12
3y = 24
Dividing both sides by 3
y = 8
Answer:
y =8
Step-by-step explanation:
-4x + 3y = 12
Let x = 3
-4(3) +3y = 12
-12+3y = 12
Add 12 to each side
-12+12+3y =12+12
3y =24
Divide each side by 3
3y/3 = 24/3
y =8
The chess club has 24 members, of which 13 are male and the rest are female. What is the ratio of males to all club members?
Answer:
13:24
that is it
male:all
NO LINKS!!! URGENT HELP PLEASE!!!!
Please help me with 23 and 25
Part 2: Using the information given in each diagram below, decide if any triangles are congruent, similar but not congruent, or not similar. If you claim the triangles are congruent or similar, create a flowchart justifying your answer
Answer:
23. Similar as well as congruent triangle
25. Conguent triangle
Step-by-step explanation:
Answers:
23. Not enough information
25. Congruent (by the HL theorem)
HL = hypotenuse leg
=============================================
Explanation for problem 23.
Check out figure 1 shown below.
I have marked the given diagram with light blue and light pink to show which angles are congruent.
Because lines UN and TC are parallel, we know the following alternate interior pairs are congruent.
angle UNC = angle TCN (light blue)angle UNL = angle TCH (light pink)Therefore, we can establish one link of paired congruent angles of the triangles LNU and TCH. However, we cannot determine any other angle pairings. Why not? Because we don't know if segment UL is parallel to segment TH. If they were parallel, then we could establish something like angle LUN = angle CHT as one alternate interior pairing.
But again, we don't know if UL is parallel to TH. The arrow markers aren't shown for these segments.
Therefore, we simply don't have enough information to determine if the triangles are similar or congruent.
----------------------------------------
Explanation for problem 25.
Luckily this problem will provide sufficient info to prove the triangles KSR and ISR are congruent.
We start with the given info that KR = SI due to the identical tickmarks. This represents one node in the flowchart (see figure 2).
Another node is angle RKS = angle RIS because both are right angles, aka 90 degree angles.
A third node is SR = SR because of the reflexive property.
Those three nodes then feed into the final conclusion node that triangle KSR = triangle ISR. The reasoning is "HL theorem" where HL = hypotenuse leg. This theorem works for right triangles only.
Take note how I structured the proof so that it flows from top to bottom. The three nodes side by side are related so they share the same row.
There are many other ways to make the flowchart, so don't feel obligated to use this format. Use whatever works best for you.
Please find the missing ? Explanation need it
Answer:
the answer is 3.162
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
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sometimes you have to divide the diamter by 2 to get the radius.
true
false
it is true
tbh am not sure
Will Give Brainliest :) <3
Reid Park Zoo in Tucson has the following Admission Rates:
$10.50 adults ages 15-61
$8.50 seniors ages 62+
$6.50 children ages 2-14
FREE for children age 0-1
Part a)
Using the information above, write an equation that represents the admission price to the zoo as a function of age. (Remember: Identify your input and output variables, and use proper notation
Answer:
Part AAs per the given information there are 4 different price intervals.
Let x be the age and y be the admission price, then we have following equations;
y = 10.50, if 15 ≤ x ≤ 61y = 8.50, if x ≥ 62y = 6.50, if 2 ≤ x ≤ 14y = 0, if 0 ≤ x ≤ 1a valley is 94 feet below sea level. what is the absolute value of the elevation difference between the valley and the sea level?
The absolute value of the elevation difference between the valley and sea level is 94 feet.
The absolute value of a number is the distance of that number from zero on the number line. It represents the magnitude or size of a quantity without considering its direction. In the given scenario, we are dealing with the elevation difference between a valley and sea level.
The valley is described as being 94 feet below sea level. To find the absolute value of the elevation difference, we need to ignore the negative sign and consider the magnitude of the difference.
In this case, since the valley is below sea level, the elevation difference is negative. However, when we take the absolute value, we disregard the negative sign and focus solely on the numerical value of the difference.
By applying the absolute value to the elevation difference of -94 feet, we remove the negative sign and consider only the magnitude. Thus, the absolute value of -94 is simply 94.
Therefore, the absolute value of the elevation difference between the valley and sea level is 94 feet. It indicates that the valley is 94 feet away from sea level in terms of elevation, regardless of the direction (above or below sea level). The absolute value provides a measure of the magnitude of the difference while disregarding the direction or sign associated with it.
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find the first derivative with respect to x of the following function: f(x)=(7x+3)(4-3x)
Answer:
19 - 42x
Step-by-step explanation:
To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x
NEED HELP ASAP!! 35 POINTS
Rob is a geologist. He is surveying a conical crater that was created by a meteor impact. From one end to another, the crater forms a V shape. The deepest part of the crater is 400 feet deep. The depth of the crater varies at a rate of 0.25 foot with the horizontal distance from the west end of the crater.
The equation that models the depth of the crater, d, in feet, with respect to the horizontal distance in feet from the west end of the crater, h, is d =
. The depth of the crater is 250 feet at horizontal distances of
and
feet from the west end.
Answer:
equation: d(h) = 0.25|h -1600| -400 depth is 250 ft at 1000 ft and 2200 ft from the west edgeStep-by-step explanation:
The crater shape can be modelled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.
d(h) = 0.25×|h -1600| -400
We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.
__
At a depth of 250 ft, the distance from the west edge can be found from ...
-250 = 0.25|h -1600| -400
150 = 0.25|h -1600| . . . . . . . . add 400
600 = |h -1600| . . . . . . . . . . . multiply by 4
This resolves to two equations:
-600 = h -1600 ⇒ h = 1000
600 = h -1600 ⇒ h = 2200
The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.
Answer:
0.25|x-1,600|-400 / 1,000 / 2,200
Step-by-step explanation:
99% sure
Eli has $640 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $356.89.
He buys 2 bicycle reflectors for $16.70 each and a pair of bike gloves for $27.47.
He plans to spend some or all of the money he has left to buy new biking outfits for $74.08 each.
Write and solve an inequality which can be used to determine o, the number of outfits Eli can purchase while staying within his budget.
(write the equation that you used to solve this )
Answer:
Step-by-step explanation:
First of all we have to discover how much he spent.
356.89 + 2(16.70) + 27.47 = $417.76
Now we have to find how much money he saved
640 - 417.76 = $222.24
the total cost of biking outfits must be eqaua or less than $222.24..
We know the price of a single outift so we can write this inequality:
74.08o ≤ 222.24
we can find o by dividing the two members of the inequality:
o ≤ 222.24/74.08 = 3
o≤ 3
this mean that he can buy 1, 2 or 3 outfits
if you made 5 free throws and 4 half-court shots and your friend made 6 free throws and 3 half-court shots, who scored the most points?
Answer:
5+4= 9, 6+3=9
Step-by-step explanation:
None, they both have equal scores
The heights of american adult men are normally distributed with a mean of 69.7 inches and a standard deviation of 2.7 inches what is the standard score for a height of 6 foot 2 inches
Answer:
1.5926
Step-by-step explanation:
-We need to first convert the height in feet to inches: Since there are 12 inches in a foot, that means there are 74 inches in a height of 6 foot 2 inches.
-Since the observed height is 74 inches and the mean height is 69.7 inches, we can find the z score by using the following formula:
z = (x-mean) / standard deviation
-We would fill this out like this:
z = (74-69.7) / 2.7
-This equals = 1.592592593
-Rounded to 4 decimal places, this equals 1.5926
PLEASE SOMEONE HELP ME
Answer:
X=22
Step-by-step explanation:
90-68=22
Find the length of the loan in months, if $600 is borrowed with an annual simple interest rate of 9% and with $681 repaid at the end of the loan.
Length of the loan =__________ months
The length of the loan in months is 151. 33 months
How to determine the length of timeThe formula for determining simple interest is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal amountR is the simple interest rateT is the time in yearsFrom the information given, we have that;
Principal interest = $600
Simple interest = $681
Rate = 9%
Substitute the values into the formula
$681 = $600 × 9 × T/100
Multiply the numerators
$681 = 5400T/100
cross multiply
68100 = 5400T
Divide both sides by 5400
T = 68100/5400
T = 12. 61 years
Convert the years to months
T = 12.61(12)
T = 151. 33 months
Hence, the value is 151. 33 months
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