There are 20 bicycles at the Main Street station.
According to question statement, A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the given two stations.
We are supposed to know the number of bicycles at the Main Street station.
Let us assume that the number of bicycles at the Park Avenue station is "x". Then, number of bicycles at the Main Street station will be "5x".
We will have to form a Linear Equation of single variable "x" as per the conditions based in the question statement, and solving for x, we will obtain our desired answer.
As there are 24 bicycles at the two stations therefore,
[tex]x + 5x = 24[/tex], will be our equation.
Solving the equation for x, we get
[tex]x + 5x = 24\\6x = 24\\x=\frac{24}{6} \\or x=4[/tex]
Therefore the number of bicycles at the Park Avenue station is 4.
And the number of bicycles at the Main Street station will be 5x i.e., [tex]5*4 = 20[/tex].
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HELP WITH MATH QUETSION PLEASE I WILL GIVE BRAINLYEST The first 5 terms arithmetic sequence are shown on the graph.
a. describe the sequence in words.
b. what is the value of the 6th term?
c. write an explicit formula to find the nth term of the sequence.
The sequence is an AP with a = 11 and d = - 4 , 6th term is - 9 and formula is a + ( n - 1 ) d .
First Term = 11
Second Term = 7
Third Te3rm = 3
Fourth Term = - 1
Fifth Term = - 5
a ) Sequence is 11 , 7 , 3 , - 1 , - 5
b ) a + ( n - 1 ) d
11 + ( 6 - 1 ) ( - 4 )
11 + 5 ( - 4 )
11 - 20 = - 9
c ) a + ( n - 1 ) d
where a is the first term , n is the tem no . and d is the common difference of an AP .
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A population of mold decays at a rate of 30 mold spores per day. If the initial population of mold spores is 1560 spores, how many days will it take for the population to be less than 1000 mold spores?
By using a linear equation, we can see that after the 19 day the population will be less than 1000 mold spores.
How many days will it take for the population to be less than 1000 mold spores?We know that the population decays at a rate of 30 spores per day, and we have an initial population of 1560 mold spores.
Then, the population of spores after x days is given by the linear equation:
P(x) = 1560 - 30*x
The population will be exactly 1000 spores when:
P(x) = 1000 = 1560 - 30*x
We need to solve that for x.
30x = 1560 - 1000 = 560
x = 560/30 = 18.67
So after 18.67 days the population is 1000, this means that after the 19 day the population will be less than 1000 mold spores.
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PLEASE ANSWERING THIS QUESTION!
By completing the square, the expression [tex]\sf{x^2-12x+101}[/tex] equals (x+A)^2+B
where A = (Blank)
and B = (Blank)
Show your work!
Do not spam answers!
Explain your answer!
Thanks!
The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65
A = -6 and B = 65
Completing the squareFrom the question, we are to express the given expression in the form (x + A)^2+B by completing the square
The given expression is
x² -12x + 101
Using the completing the square method
x² -12x + 101
Divide the coefficient of x by 2 and then square it
The coefficient of x is -12
Dividing by 2, we get
-12/2 = -6
Squaring
(-6)²
Now, add and subtract this value from the expression
x² -12x + (-6)² + 101 - (-6)²
Then, we can write that
(x - 6)² + 101 - (-6)²
(x - 6)² + 101 - 36
(x - 6)² + 65
Thus,
The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65
By comparison,
A = -6
and
B = 65
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Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression. Answer exactly.
(sin60∘+cos60∘)^2=
13. What value of b would make the function f (x)- Ibal stretch horizontally by a
factor of 4 and reflect across the y-axis?
Answer:
give me those points boy=o >:)
Step-by-step explanation:
While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function
f
(
x
)
=
b
x
by a constant
|
a
|
>
0
. For example, if we begin by graphing the parent function
f
(
x
)
=
2
x
, we can then graph the stretch, using
a
=
3
, to get
g
(
x
)
=
3
(
2
)
x
and the compression, using
a
=
1
3
, to get
h
(
x
)
=
1
3
(
2
)
x
.
Find the radius of a circle with the arc length of 69 cm and a central angle measure of 81°
convert 81°into radian
81°=(81×pie/180)=9pie/20 pie=22/7
now,
radius=arc length/θ in radian
then 69/(9pie/20)
=48.79
The total cost of an annual pass for admission to a national
park plus camping for x days can be modeled by the function
f(x) = 20x + 80. A senior citizen pays $20 less than half of
this price for x days. What is the total cost for a senior citizen to
go camping for three days in the park?
The total cost paid by the senior citizen for 3 days = $50
Function word problemsThe function representing the total cost of the annual pass is:
f(x) = 20x + 80
A senior citizen pays $20 less than half of this price for x days
The total cost paid by the senior citizen = [tex]\frac{f(x)}{2} -20[/tex]
The total cost paid by the senior citizen =[tex]\frac{20x+80}{2} -20[/tex]
Simplify the resulting expression:
The total cost paid by the senior citizen =10x + 40 - 20
The total cost paid by the senior citizen = 10x + 20
x represents the number of days
Substitute x = 3 into the resulting equation
The total cost paid by the senior citizen for 3 days =10(3)+20
The total cost paid by the senior citizen for 3 days = $50
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Three rational numbers between 1/3 and 1/5
Three rational numbers between
1/3 and 1/5 are 4/15, 3/10, and 7/30
Given:The two numbers are 1/3 and 1/5
To find:The rational number between two numbers
Solution:Now, to find the rational number, add the numbers and divide their sum by 2.
(i) First rational number between
1/3, 1/5 = 1/3+1/5=8/5
Divide 18/5 by 2------> 8/15 x 1/2= 8/30= 4/15
The series becomes, 1/3, 4/15, 1/5
(ii) Second rational number
= 4/15+1/5 = 7/15
Divide
7/15 by 2 ------> 7/15 x 1/2 = 7/30
Hope this helps!
Suppose that for a function g (x), g (4) = 7. Select all of the statements that are true.
A. 4 is in the range of g.
B. For a value a, it is possible that g (a) = 4.
C. For a value y, it is possible that g (4) = y.
D. The point (4,7) is on the graph of y = g (x).
E. The point (7,4) is on the graph y = g (x).
Answer:
B and D
Step-by-step explanation:
The wording in the answer choices make a huge difference. It is possible implies that there is a possibility
A is false. The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)
A good example is a constant function such as g(x) = 7. Here, whatever the value of x, the y value is always 7. This represents a horizontal line passing through y = 7. So the range is just a single number {7}
B can be true. It is possible but not a certainty that f(a) = 4 for some value of a. For example, consider the function g(x) = x + 3.
At x = 4, g(4) = 4 .1 + 3 = 7
At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output
C is false. A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.
D is true. Since at x =4, y = g(x) = 7, this corresponds to a point on the graph. The point will be (x=4, y =7) or (4,7)
E is false. The x, y coordinates have been interchanged in this answer choice
The true statements are B and D.
The wording in the answer choices make a huge difference.
It is possible implies that there is a possibility
A. 4 is in the range of g.
A is false.
The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)
A good example is a constant function such as g(x) = 7.
Here, whatever the value of x, the y value is always 7.
This represents a horizontal line passing through y = 7.
So the range is just a single number {7}
B. For a value a, it is possible that g (a) = 4.
B can be true.
It is possible but not a certainty that f(a) = 4 for some value of a.
For example, consider the function g(x) = x + 3.
At x = 4, g(4) = 4 .1 + 3 = 7
At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output.
C. For a value y, it is possible that g (4) = y.
C is false.
A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.
D. The point (4,7) is on the graph of y = g (x).
D is true.
Since at x =4, y = g(x) = 7, this corresponds to a point on the graph.
The point will be (x=4, y =7) or (4,7)
E. The point (7, 4) is on the graph y = g(x).
False. The statement doesn't provide any information about g(7), and we cannot determine whether the point (7, 4) lies on the graph of the function y = g(x) based solely on the given information.
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Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. Joy walked 15 steps forward, and Shaunte walked 6 steps backwards. Which expression correctly represents the distance between the friends?
Answer choices
|−15| + 6 = 21 steps
|−15| + |−6| = 21 steps
15 + 6 = 21 steps
15 + |−6| = 21 steps
Answer: 15 + |−6| = 21 steps
Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.
Angel owns 10 more DVDs than Philip. Choose an equation
that represents the number of DVDs Philip owns (p) as a
function of the number of DVDs Angel owns (a).
The function of the number of DVDs Angel owns (a) will be a = p + 10
How to calculate the value?From the information, Angel owns 10 more DVDs than Philip.
The number of DVD that Philip owns was represented asp.
Therefore, the function of the number of DVDs Angel owns (a) will be:
a = p + 10
Therefore the function is a = p + 10
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Get a similar question You can retry this question below
In your investment portfolio, 25% of your stocks are in Company A with a return rate of 6%, 40% of
your stocks are in Company B with a return rate of 2.5%, and the rest of your stocks are in Company
C with a return rate of 2%. Use a weighted mean to find your average return rate.
Average return rate=
The Average return rate for the investment will be 3.2%.
The Return Rate can be defined as a profit that is made on investment .
In the Question
let the investment be "x" .
25% stocks in Company A have return rate of 6%.
Investment in Company A = (25% of x)
Return is 6% of investment = (25% of x) + 6% of (25% of x)
Return from company A= (25% of x)(1+0.06) ...as 25%=0.25 & 6%=0.06
= 0.25*x*(1.06) ...(i)
40% stocks in Company B have return rate of 2.5%.
Investment in Company B = (40% of x)
Return is 2.5% of investment = (40% of x) + 2.5% of (40% of x)
Return from company A = (40% of x)(1+0.025) ...
= 0.40*x*(1.025) ...(ii)
Stocks in Company C = 100 - 25 - 40 = 35%
35% stocks in Company C have return rate of 2%.
Investment in Company C = (35% of x)
Return is 2.5% of investment = (35% of x) + 2% of (35% of x)
Return from company C = (35% of x)(1+0.02) ...
= 0.35*x*(1.02) ...(iii)
Total Return = Return from Company A + Return from Company B + Return from Company C .
From equation (i) ,(ii) and (iii) we get
Total Return = 0.25*x*(1.06) + 0.40*x*(1.025) + 0.35*x*(1.02)
= 0.265x + 0.41x + 0.357x
= 1.032x
The Average rate of return = [tex]\frac{return- investment }{investment } \times100[/tex]
Substituting the value we get,
= (1.032x - x ) / x *100
= 0.032x /x * 100
= 0.032*100
= 3.2%
Therefore , the Average return rate for the investment will be 3.2%.
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The ratio 4:5 is equivalent to
(i) 80%
(ii) 60%
(iii) 40%
(iv) 20%
If u ans i will give 40 points and mark brainlyest
Answer:
(i)
Step-by-step explanation:
express the ratio as a fraction, that is
4 : 5 = [tex]\frac{4}{5}[/tex]
to convert the fraction to a percentage multiply it by 100%
[tex]\frac{4}{5}[/tex] × 100% = 4 × 20% = 80%
The equation 3x2+2x−4=0 has two solutions. What are they?
Answer:
x =(2-√52)/6=(1-√ 13 )/3= -0.869
x =(2+√52)/6=(1+√ 13 )/3= 1.535
it has either 0.868 or -1,85
mr drew wants to build a square sandbox with an area of 100 square feet. What is the length of wood Mr.Drew needs to.make the sides of the sandbox
1. I am a number between 120 to 130 and I am divisible by 3, 6 and 9. Who am I?
Answer:
126
Step-by-step explanation:
A number is divisible by 3 if its sum of digits is divisible by 3 (you can do it over and over again until it's one digit!).
A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.
A number is divisible by 6 if it is divisible by 2 and by 3.
A number is divisible by 9 if its sum of digits is divisible by 9 (you can do it over and over again until it's one digit!).
So we need a number with last digit 0, 2, 4, 6, or 8 (because it's divisible by 6 hence by 2) and with a sum of digits divisible by 9 (because if it's divisible by 9 it's also divisible by 3).
130 is not divisible by 9, so the first digits must be 12X.
to get a number divisible by 9, we need to add a digit D so that 1+2+D is divisible by 9.
9 - 1 - 2 = 6
126 is divisible by 9 because it's sum of digits is 9. It's also divisible by 6, because it is divisible by 3 and its last digit is 6.
Estimate the quotient by first rounding each number.
0.0355 ÷ 2
Answer:
0.01775
Step-by-step explanation:
What is the relationship between the volume and surface area of the sphere shown?
V>SA
OV
OV=SA
Answer: mark as brainliest please
Step-by-step explanation:
V=4/3 x 3.14 x 3^3
V= 113.04
SA= 4 x 3.14 x 3^2
SA= 113.04
The harvest was cornucopian as it was 45 percent greater than last year. If the yield was 140795 bushels, how many bushels were harvested last year
After solving for x in the constructed equation, 97100 bushels were harvested last year.
What is an equation?
A mathematical statement known as an equation is consisting of two expressions joined together by an equal sign.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.The point-slope form, standard form, and slope-intercept type are the three main types of linear equations.Constructing equation to determine no. of bushels.
Bales from the previous year = x + 0.45 x
= 140795 1.45 x
= 140795 X
= 97100 bales
After solving for x in the constructed equation, 97100 bushels were harvested last year.
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Answer:97100
Step-by-step explanation:
Identify the pair(s) of congruent angles in the figure. Explain how you know they are congruent.
by the Congruent Complements Theorem
$\angle NSP\cong\angle QSR$ by the Congruent Complements Theorem
$\angle MSP\cong\angle PSR$ by the Right Angles Congruence Theorem
$\angle MSP\cong\angle PSR$ by the Right Angles Congruence Theorem
$\angle MSN\cong\angle PSQ$ because they have the same measure
$\angle MSN\cong\angle PSQ$ because they have the same measure
$\angle MSN\cong\angle QSR$ by the Vertical Angles Congruence Theorem
$\angle MSN\cong\angle QSR$ by the Vertical Angles Congruence Theorem
$\angle NSP\cong\angle PSQ$ because they have the same measure
$\angle NSP\cong\angle PSQ$ because they have the same measure
$\angle NSQ\cong\angle MSP$ by the Right Angles Congruence Theorem
$\angle NSQ\cong\angle MSP$ by the Right Angles Congruence Theorem
$\angle NSQ\cong\angle PSR$ by the Right Angles Congruence Theorem
∠NSP ≅ ∠QSR, ∠MSP ≅ ∠PSR, ∠MSN ≅ ∠PSQ, ∠NSQ ≅ ∠MSP, ∠NSQ ≅ ∠PSR are the congruent angles.
∠NSP ≅ ∠QSR by the Congruent Complements Theorem. Because both are complementary to ∠PSQ.
∠MSP ≅ ∠PSR by the Right Angles Congruence Theorem. Because both ∠MSP = ∠PSR = 90°.
∠MSN ≅ ∠PSQ because they have the same measure. ∠MSN = ∠PSQ = 50°. Angles with same measure are congruent to each other.
∠NSQ ≅ ∠MSP by the Right Angles Congruence Theorem. Because ∠NSQ = ∠MSP = 90°.
∠NSQ ≅ ∠PSR by the Right Angles Congruence Theorem. Because ∠NSQ = ∠PSR = 90°.
Congruent Complements theorem states that if two angles are complementary (sum = 90°) to the same angle, then they are congruent.
Right Angles Theorem states that two right angles(90° angles) are congruent to each other.
Vertical Angles Congruence theorem states that two opposite angles formed between intersection of two lines are congruent. Here, ∠MSN is not congruent to ∠QSR because they are not vertical opposite angles.
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The temperature fell 12 degrees over 4 hours. What was the average change in temperature per hour?
Expression:
Answer:
The average change is 3 degrees per hour.
To calculate the average of any data we have to divide the change by the time taken for that change.
let us suppose there is a data 4,5,6,7 and 8.
Average of the data will be the sum of data divided by the number of terms.
Average=[tex]\frac{4+5+6+7+8}{5}[/tex]
=[tex]\frac{30}{5}[/tex]
= 6
So now we will calculate the average change in temperature per hour,
Given that there is a fall of 12 degrees in 4 hours.
Average change per hour=[tex]\frac{12}{4}[/tex]
= 3 degrees per hour
So, the required change is 3 degrees per hour.
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(Multiplying and Dividing with Scientific Notation MC)
How many times smaller is 5 x 10-7 than 8.5 x 10-4? I NEED THIS ASAP
Answer:
38
Step-by-step explanation:
5 x 10 -7= 43
8.5 x 10 -4= 81
81-43= 38
Answer:
[tex] 1.7 \times 10^3 = 1700 [/tex]
Step-by-step explanation:
To find how many times x is smaller than y, divide y by x.
Here we want to find how many times 5 × 10^-7 is smaller than 8.5 × 10^-4, so we divide 8.5 × 10^-4 by 5 × 10^-7.
[tex] \dfrac{8.5 \times 10^{-4}}{5 \times 10^{-7}} = [/tex]
[tex] = \dfrac{8.5}{5} \times \dfrac{10^{-4}}{10^{-7}} [/tex]
[tex] = 1.7 \times 10^{-4 - (-7)} [/tex]
[tex] = 1.7 \times 10^{-4 + 7} [/tex]
[tex] = 1.7 \times 10^3 = 1700 [/tex]
(3 × 1,000) + (4 × 100) + (5 × 10) + (2 × 1)
Answer:
3452
Step-by-step explanation:
Simplify the expression, and add/muiltiply where necessary.
A ball thrown horizontally at v₁ = 30.0 m/s travels a horizontal distance of d = 57.0 m before hitting the
ground. From what height h was the ball thrown?
Answer:
17.7 m
Step-by-step explanation:
57 m / 30 m/s = time in the air = 1.9 s
vertical drop for 1.9 s
vertical d = 1/2 a t^2 = 17. 7 m
A crab moves at a speed of 0.14 kilometers per hour. How far can it travel for 0.25 hours?
Answer:
0.14×0.25= 0.035 KM
so it can travel 0.035KM in 0.25 hr
Answer:
0.035 kilometers
Step-by-step explanation:
Proportions:
0.14 kilometers ⇒ 1 hour
A kilometers ⇒ 0.25 hour
A = 0.14 kilometers * 0.25 hour / 1 hour
A = 0.035 kilometers
Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
The time it would take Shirley to mow the lawn alone is 3 hours
How to determine the value
From the information given;
Let Shirley's working hours be x
Let Pam's working hours be y
We have that;
Shirley and Pam work 6 hours together, this is expressed as;
x + y = 6
Given that Pam work 3 hours alone, we have;
y = 3
Substitute the value of y as 3 in the equation
x + 3 = 6
x = 6 - 3
x = 3
Thus, the time it would take Shirley to mow the lawn alone is 3 hours
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Kayla has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6.
What is the probability Kayla rolls an even number on the red cube and a multiple of 3 on the blue cube?
So probability that kayla rolls an even number on the red cube and a multiple of 3 on the blue cube is 16.66 ≈ 16%
Given that we have red number cube and blue number cube so as we all know that Probability is the ratio of the favourable number of outcomes to the total number of outcomes is known as Probability.
First, find the possible outcomes.
Kalya has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6
So, possible outcomes =6×6 =36
Let, S be the sample space.
Then, ⁿ(s) =36
Let, E = the event of getting an even number on the red cube and a multiple of on the blue cube.
E = (2,3),(2,6),(4,3),(6,3),(6,6)
Then, ⁿ(E)=6
Let, P is the probability of the event .
So, P(E)= [tex]\frac{n(E)}{n(S)}[/tex] = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex] = 16.67 percent or 16[tex]\frac{2}{3}[/tex] %
Thus, the probability Kayla rolls an even number on the red cube and a multiple of on the blue cube is 16.66 percent.
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Answer:
16%
Step-by-step explanation:
Simplify the expression.
(4 × 6)y=
Answer:
24y^2
Step-by-step explanation:
4y x 6y =
24y ^2
24y to the second power
The table below models a particular physical situation.
x −9, −3, 4 ,10
y 9, 1, −7, 10
Find the piecewise linear equation that models the data above. Round to three decimal places if needed.
y={
___ x + ___. −9 ≤ x ≤ −3
___ x + ___. −3 < x ≤ 4
___ x + ___. 4 < x ≤ 10
Answer:
Step-by-step explanation:4
Step-by-step explanation:
We do the ones that are in parenthesis first. Find out the exponent. 2 to the power of two is 4. 3-4=-1. Then we would add 5. 5+-1 would result of 4.
Find the domain and the range of the relation. Determine whether the relation is a function.
{(9/2,1/4),(4 1/2,-4),(0,5/6)}
It is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.
We are given a relation:
{(9 / 2, 1 / 4),(4 1 / 2, -4),(0, 5 / 6)}
We can also write it as:
{(9 / 2, 1 / 4),(9 / 2, -4),(0, 5 / 6)}
The domain of the relation will be:
Domain = { 9 / 2 , 0}
The range of the relation will be:
Range = {1 / 4, -4, 6}
We know that every function can be a relation but every relation cannot be a function.
A relation means the connection between the input and the output.
A function means that for every input there should only be one output.
Here, this relation is not a function because:
The input 9 / 2 has 2 outputs as 1 / 4 and -4 which is not possible in a function.
Therefore, we get that it is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.
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