The average rate of change in gas prices from 3 to 6 predicted storms is 0.04, indicating a consistent increase of $0.04 in gas price for each additional storm predicted during that period. (option A)
The average rate of change is calculated by finding the difference in gas prices divided by the difference in the number of predicted storms.
[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in Gas Price}}{\text{Change in Number of Storms}} \][/tex]
For the given data:
- Change in Gas Price from 3 to 6 storms: 2.56 - 2.44 = 0.12
- Change in Number of Storms: 6 - 3 = 3
[tex]\[ \text{Average Rate of Change} = \frac{0.12}{3} = 0.04 \][/tex]
Therefore, the correct answer is 0.04. (option A)
For more questions on rate of change:
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The complete question is:
The price of gas has been increasing over the last month. Renee believes there is a positive correlation between the number of predicted storms and the price of gas.
Number of Storms Predicted 1 3 4 6 7
Gas Price $2.34 $2.44 $2.49 $2.56 $2.61
Use the table to determine the average rate of change from 3 to 6 storms.
a. 0.04
b. 3
c. 0.12
d. 0.27
A 6-kilogram bag of rice costs $3.80. What is the unit price, rounded to the nearest cent?
Answer:
The unit price is 63 cent per kilogram bag of rice.
Step-by-step explanation:
Given:
A 6-kilogram bag of rice costs $3.80.
Now, to find the unit price.
So, to get the unit price we use unitary method:
If cost of 6 kilogram bag of rice = $3.80.
Then cost of 1 kilogram bag of rice = [tex]\frac{3.80}{6}[/tex] = [tex]\$0.633.[/tex]
Thus, the unit price is $0.633 per kilogram bag of rice.
Now, according to question we convert the unit price into cent by using conversion factor:
$1 = 100 cent
$0.633 = [tex]0.633\times 100=63.3\ cent.[/tex]
So, rounded to nearest cent = 63 cent.
Therefore, the unit price is 63 cent per kilogram bag of rice.
Wich expression represents 5/34 in rational exponent form
Option C:
[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]
Solution:
Given expression is [tex]\sqrt[5]{34}[/tex].
To write the given expression in rational exponent form.
Using rational exponent rule:
[tex]$\sqrt[n]{a^m} =a^{\frac{m}{n} }[/tex]
i. e. [tex]$\sqrt[\text{root}]{a^\text{power}} =a^{\frac{\text{power}}{\text{root}} }[/tex]
Given [tex]\sqrt[5]{34}[/tex]
Here, root is 5 and power is 1.
Write it using the rational exponent rule,
[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]
Therefore option C is the correct answer.
Hence [tex]$\sqrt[5]{34} =34^{\frac{1}{5} }.[/tex]
Answer: 34^1/5
Step-by-step explanation:
Examine this information carefully.
Angles Sides
30 degrees 4 cm
60 degrees 3 cm
90 degrees 5 cm
What kind of triangle would these measurements make?
A. acute scalene triangle
B. right scalene triangle
C. right isosceles triangle
D. acute isosceles triangle
Answer:
B. right scalene triangle
i am sure about this answer as 90 degree tells us that it is a right angle triangle and as all the measure of angles as well as sides are different it is a scalene triangle.
Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account that earns 4% per year and the rest into a CD account that earns 9% per year. How much money should he put into each account?
Jack should invest $8400 in the CD account and $3600 in the savings account.
Step-by-step explanation:
Jack wants to earn 7.5% interest per year. That implies he wants to earn
7.5/100*12000 per year i.e $900 per year.
Lets assume he invests X amount in the savings account. That leaves 12000-X to be invested in the CD account.
That implies,
[tex]4/100*X + 9/100*(12000-X) = 900[/tex]
=> [tex](4X+108000-9X)/100 = 900[/tex]
=> [tex]-5X = 90000-1080000 = -18000[/tex]
=> X = 3600
I am a fraction equivalent to 6/8 my numerator is 16 less than my denominator what fraction am i
Answer:
The answer is
[tex] \frac{48}{64} [/tex]
Step-by-step explanation:
Equivalent fractions are set of fractions which have the same value when simplified.
The equivalent fraction to 6/8 whose numerator is 16 less than its denominator can be obtained through two basic methods below.
Method 1
Multiply the numerator and denominator by 8 respectively.
[tex] \frac{6}{8} = \frac{6 \times 8}{8 \times 8} = \frac{48}{64} [/tex]
The numerator being 16 less than the denominator is:
[tex]48 - 64 = - 16[/tex]
Method 2
Find the equivalent fraction to 6/8 whose numerator is 16 less than its denominator by continuous multiplication approach. In other words, multiply 6/8 till you arrive at an equivalent fraction whose numerator is 16 less than its denominator. Simply multiply 6/8 by 2, 3, 4, 5, 6, 7, 8. Thus:
[tex] \frac{6}{8} = \frac{12}{16} = \frac{18}{24} = \frac{24}{32} = \frac{30}{40} = \frac{36}{48} = \frac{42}{56} = \frac{48}{64} [/tex]
The difference between the numerator and denominator of the equivalent fractions are: -2, -4, -6, -8, -10, -12, -14, -16
Hence, 48/64 is the equivalent fraction to 6/8 whose numerator and denominator difference is less than 16.
That is,
[tex] \frac{6}{8} = \frac{48}{64} [/tex]
Such that 48 - 64 = -16.
The fraction equivalent to 6/8 with a numerator 16 less than the denominator is 48/64, which simplifies to 3/4.
Explanation:To find an equivalent fraction to 6/8 where the numerator is 16 less than the denominator, we use an equation to represent the relationship between the numerator (N) and the denominator (D): N = D - 16. Since 6/8 can be simplified to 3/4 by dividing both the numerator and denominator by 2, we set up the following equation: N/D = 3/4.
By substituting N with (D - 16), we get (D - 16)/D = 3/4. To find the value of D, we cross multiply: 4(D - 16) = 3D. Solving for this, we have 4D - 64 = 3D, and therefore D = 64. Since N is 16 less than D, N = 64 - 16, which gives us N = 48. So, the fraction we are looking for is 48/64.
We can check that 48/64 is indeed equivalent to 3/4 by simplifying. Dividing both numerator and denominator by 16, we get 48/64 = 3/4. Thus, the student's fraction is 48/64 which simplifies to 3/4.
It takes you
3/8 of an hour to walk 9/10 of a mile.
How far can you walk in 1 hour?
a. 0.42
b. 0.3375
c. 2.4
d. 5.25
Answer:
C
Step-by-step explanation:
You can already walk 0.9 of a mile in 3/8 so it cannot be A or B
C is the most reliable because even if you multiple the 0.9 by 3 so it is a little bit over a mile it is still closer to 2.4
a triangle is reduced. What is the perimeter of the reduced triangle, in inches.
Answer:
the perimeter is 36
Step-by-step explanation:
Answer:
The correct answer is 36
Step-by-step explanation:
Edg. 2020
A boat costs $19300 and decreases in value by 5% per year. How much will the boat be worth after 6 years
Answer:
[tex]\$14,187.27[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential decay function of the form
[tex]y=a(1-r)^x[/tex]
where
y ----> is the value of the boat in dollars
x ---> is the number of years
r ---> is the percent rate of change
a ---> is the initial value or y-intercept
we have
[tex]a=\$19,300\\r=5\%=5/100=0.05[/tex]
substitute
[tex]y=19,300(1-0.05)^x[/tex]
[tex]y=19,300(0.95)^x[/tex]
For x=6 years
substitute the value of x in the exponential function
[tex]y=19,300(0.95)^6\\y=\$14,187.27[/tex]
Solve the following quadratic inequality 2x^2+3x-5>0
Answer:
x < -2.5 and x > 1
Step-by-step explanation:
Mike has baseball cards and football cards. The ratio of baseball cards to football cards is 5:7 He has 40 baseball cards. How many football cards does he have?
Answer:
56 football cards
Step-by-step explanation:
If 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.
7x8=56
Compute 5e^2 - 4g + 7 where e = 4 and g = 6 ? (Not sure how to type a squared number where e^2 = “e squared”)
Answer:
63
Step-by-step explanation:
The given expresion is
[tex]5 {e}^{2} - 4g + 7[/tex]
We want to find the value of this expression when e=4 and g=6.
We substitute these values to get:
[tex]5( {4}^{2} ) - 4(6) + 7[/tex]
We evaluate to obtain:
[tex]5(16) - 4(6) + 7[/tex]
Let us multiply out to get:
[tex]80 - 24 + 7[/tex]
This simplifies to 63
The sum of two numbers is 35. The greater
number is 1 less than 5 times the smaller number.
What are the two numbers
Answer:
x = 29
y = 6
Step-by-step explanation:
Let the two numbers be represented as x and y
x + y = 35
x = 5y - 1
Substitute x as 5y -1 in equation one
5y -1 + y = 35
5y + y -1 = 35
Add 1 to both sides
6y - 1 + 1 = 35 + 1
6y = 36
Divide both sides by 6
6y/6= 36/6
y = 6
Now substitute y as 6 in any of the equations to get x.
Using equation one ,
We have
x + y = 35
x +6 = 35
Subtract 6 from both sides
x + 6 - 6 = 35 - 6
x = 29
write 3.005 using words
first person is the brainliest
Answer:
three and five hundreths
Answer:
three and five thousandths
Step-by-step explanation:
3 counts as one and the decimal is said as "and" and the spaces after the decimal are tenths,hundredths and thousandths
Rosa is participating in a fun run to raise money for the West Side Children's Hospital. The run is held at Rosa's high school track. The more laps Rosa runs around the track, the more money she raises for the hospital.
There is a proportional relationship between the number of laps Rosa runs, x, and the amount of money she raises for the hospital (in dollars), y.
x (laps) y (dollars)
1 $5
2 $10
3 $15
4 $20
Write an equation for the relationship between x and y.
y=
The equation representing the proportional relationship between the number of laps Rosa runs and the amount of money she raises is y = 5x. This linear equation suggests that for every lap completed, $5 is earned for the hospital.
Explanation:The relationship between the number of laps Rosa runs (x) and the amount of money she raises for the hospital (y) can be described by a linear equation because there is a proportional relationship between x and y. We can see from the values given that each lap corresponds to $5. Therefore, the slope (change in y divided by the change in x) is $rac{$5}{1 lap} = $5$ per lap. Since there is no initial fee mentioned (y-intercept, b), the equation is simply the slope times the number of laps.
So, we can write the equation as y = 5x. This equation tells us that for every lap Rosa runs, she will raise $5. If we plot this relationship on a graph with x as the independent variable and y as the dependent variable, we would get a straight line that passes through the origin (0,0).
The circumference of a circle is about 37.7 cm and the diameter is about 12 cm. What expression best represents the value of π ? Question 3 options: 6/37.7 12/37.7 37.7/6 37.7/12
Answer:
Step-by-step explanation:
Circumference of a circle means the perimeter of a circle and it is given be
Perimeter=2πr
P=2πr
Though π is a constant
But this question want us to find π
Make π the subject of the formula
Then, divide both side by
π=P/2r
Given that P=37.7cm
And diameter =12
And radius is half of diameter.
Therefore, radius =12/2=6cm
Then
π=P/2r
π=37.7/2×6
π=37.7/12.
Then, the last option is the correct option
d = 23 in.
Find the circumference of the circle
Answer:
72.22in
Step-by-step explanation:
c=d*pie
23*3.14
Answer:
About 72 in.
Step-by-step explanation:
The circumference = π x the diameter of the circle (Pi multiplied by the diameter of the circle).
c = π·23
c= 72.2566310326
I hope this helps!
brainliest is appreciated... :}
Janelle ate 82% of the pie. What fraction of the pie remained?Janelle ate 82% of the pie. What fraction of the pie remained?
Answer:
It remained 9/50 of the pie
Step-by-step explanation:
If Janelle ate 82% of the pie, now it remains:
100 - 82 = 18%
Let's convert 18% to fraction:
18% = 0.18 = 18/100
Let's simplify 18/100:
18/100 = 9/50 (Dividing by 2 the original fraction)
It remained 9/50 of the pie
Pleaseeeeeeee help !
Answer:
answer is a
look at picture
Sorin chose a three-digit number and doubled it. Jiao chose a two-digit number. Carlos subtracted Jiao’s number from Sorin’s product. What is the greatest number Carlos can get?
HELP QUICK PLS
Answer:
The number is 1988.Step-by-step explanation:
Carlo's outcome will be the greatest if Sorin's number will be the highest and Jiao's number is the lowest.
Sorin choose a three digit number, the highest three digit number is 999.
After doubled the number, 999, the outcome will be 1998.
Jiao chooses two-digit number, the lowest two-digit number is 10.
Hence, the greatest number that Carlo can get is (1998 - 10) = 1988.
Final answer:
The greatest number Carlos can get is 1988, which is found by doubling the largest three-digit number, 999, to get 1998, and then subtracting the smallest two-digit number, 10.
Explanation:
To find the greatest number Carlos can get, we must consider the largest possible three-digit number that Sorin could double and the smallest possible two-digit number Jiao could choose.
The largest three-digit number is 999. When doubled, it becomes 1998. The smallest two-digit number is 10. Therefore, Carlos' greatest possible number is obtained by subtracting the smallest two-digit number from Sorin's doubled number:
1998 - 10 = 1988
Hence, the greatest number Carlos can get is 1988.
PLEASE HELP FAST!! VERY IMPORTANT!!
Answer: B, C, D
Step-by-step explanation:
A linear function is a straight line and is written as y=mx+b
A y = 10x is linear
B y = -5x-15 is linear
C y = 2x^2+10 is not linear (the x^2 makes it a parabola)
D y = 12x + 1 is a straight line
E y = -20 is straight line through -20 on the y-axis
F y = 7x^2 + 4 is not a straight line
Geometry 8.6.3 - Equations of Parallel and Perpendicular Lines and Proofs
Option B: [tex]\frac{1}{25}[/tex]
Solution:
Slope of the perpendicular lines:
If two lines are perpendicular then their slopes are negative reciprocals of each other.
[tex]$m_1=\frac{-1}{ m_2}[/tex]
Slope of the parallel lines:
If two lines are parallel then they have the same slope.
i.e their slopes are equal.
[tex]m_1=m_2[/tex]
Given line m and p are parallel.
Slope of the line m = [tex]\frac{1}{25}[/tex]
Using slope of the parallel lines definition,
Slope of the line p = slope of the line m
Slope of the line p = [tex]\frac{1}{25}[/tex]
Option B is the correct aswer.
Hence the slope of the of line p is [tex]\frac{1}{25}[/tex].
PLEASE HELP ME!!! there's an equation: y × 6 for y = 2/3. what the heck is the y?!
Answer:
y equals 2/3. u have to do 2/3 ×6 I'm pretty sure
Solve -2.5(4x - 4)=-6
Final answer:
To solve the equation -2.5(4x - 4) = -6, distribute -2.5 to the terms inside the parentheses, isolate the variable, and solve for x.
Explanation:
To solve the equation -2.5(4x - 4) = -6, we can start by distributing -2.5 to the terms inside the parentheses:
-10x + 10 = -6
Next, we can isolate the variable by subtracting 10 from both sides:
-10x = -16
Finally, we can solve for x by dividing both sides by -10:
x = -16/-10
Therefore, x = 1.6.
select the correct answer.
which expression gives the same result as
Answer:
b
Step-by-step explanation:
Your answer should be polynomial standard form polynomial in standard form (c+8)8c+2)=
Answer:
8c² + 66c + 16
Step-by-step explanation:
Given
(c + 8)(8c + 2)
Each term in the second factor is multiplied by each term in the first factor, that is
c(8c + 2) + 8(8c + 2) ← distribute both parenthesis
= 8c² + 2c + 64c + 16 ← collect like terms
= 8c² + 66c + 16
For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Dean purchased 14 shares in the software company and 14 shares in the biotech firm, which cost a total of $812. At the same time, Carrie invested a total of $5,767 in 100 shares in the software company and 99 shares in the biotech firm. How much did each share cost?
Each share in the software company costs approximately $5,195.14 and each share in the biotech firm costs approximately $5,137.15.
Explanation:To find out how much each share costs, we need to solve a system of equations. Let's call the cost of each share in the software company 'x' and the cost of each share in the biotech firm 'y'.
From the given information, we know that Dean purchased 14 shares in each company for a total cost of $812. This gives us the equation 14x + 14y = 812.
Similarly, Carrie invested a total of $5,767 in 100 shares in the software company and 99 shares in the biotech firm. This gives us the equation 100x + 99y = 5,767.
Now, we can solve this system of equations using either substitution or elimination method.
Using the elimination method, multiply the first equation by 99 and the second equation by 14 to make the coefficients of 'x' in both equations equal:
1386x + 1386y = 79861400x + 1386y = 80718Now subtract the first equation from the second equation:
(1400x + 1386y) - (1386x + 1386y) = 80718 - 798614x = 72732Divide by 14 on both sides to find the value of 'x':
x = 72732 / 14x = 5195.14Now substitute the value of 'x' back into one of the original equations to find the value of 'y'. Using the first equation:
14(5195.14) + 14y = 81272732.08 + 14y = 81214y = -71920.08y = -71920.08 / 14y = -5137.15Therefore, each share in the software company costs approximately $5,195.14 and each share in the biotech firm costs approximately $5,137.15.
Consider this function for cell duplication where the cells duplicate every minute.
f(x) = 75(2)x
Determine what each parameter in the function represents.
A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute.
B) The 75 is the initial number of cells, and the 2 indicates that the number of cells increases by 2 every minute.
C) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells doubles every minute.
D) The 75 is the number of cells at 1 minute, and the 2 indicates that the number of cells increases by 2 every minute.
Answer:
A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute
Step-by-step explanation:
When x=0 (no minutes have elapsed), the value of the function is ...
f(0) = 75(2^0) = 75(1) = 75 . . . . the initial number of cells
As x increases by 1 (minute), the number of cells is multiplied by 2, so the 2 is the multiplier each minute. It indicates the number doubles. ("double" = "multiply by 2")
x is not defined, but for the function to make any sense, it must represent elapsed minutes.
What is 7/`15 divided by 3/4?
Answer:
28/45
Step-by-step explanation:
Solve using cross multiplication.
(7/15) / (4/3) =
28/45
The fraction is already in simplest form
answer:
[tex] \frac{7}{20} [/tex]
explanation:
[tex] \frac{7}{15} \times \frac{3}{4} = \frac{7 \times 3}{15 \times 4} = \frac{21}{60} = \frac{7 \times 3}{20 \times 3} = \frac{7}{20} [/tex]
Fifty-five and one-half percent of shareholders in a fast food chain are under 40. If 91,00 shareholders, how many are 40 and over?
Final answer:
To determine the number of shareholders aged 40 and over, subtract the number of shareholders under 40 (55.5% of 91,000) from the total, resulting in 40,495 shareholders who are 40 and over.
Explanation:
The question asks how many shareholders are aged 40 and over in a fast food chain given that 55.5% are under 40 and there are a total of 91,000 shareholders.
First, we must find the number of shareholders under 40: 0.555 × 91,000 = 50,505 shareholders. Next, we subtract this from the total number of shareholders to find the number of shareholders aged 40 and over: 91,000 - 50,505 = 40,495 shareholders.
Therefore, 40,495 shareholders are aged 40 and over.
how do I write the sum of 6x and 2x is at least 39 ?
Step-by-step explanation:
We have,,
6x and 2x
To find, the value of x = ?
According to question,
The sum of 6x and 2x is at least 39
∴ 6x + 2x = 39
⇒ 8x = 39
⇒ x = [tex]\dfrac{39}{8}[/tex]
∴ The value of x = [tex]\dfrac{39}{8}[/tex]
Thus, put x = [tex]\dfrac{39}{8}[/tex] I write the sum of 6x and 2x is at least 39 .