SOLUTION
Step 1 :
In this question, we are meant to know the relationship between Growth factor and Growth Rate.
Growth factor is the factor by which a quantity multiplies itself over time.
Growth rate is the addend by which a quantity increases ( or decreases ) over time.
Step 2 :
From the question, if the growth factor is 1.2 which is also 120 %,
then the growth rate will be ( 120 - 100 ) % = 20 % = 0. 2
CONCLUSION:
The Growth Rate = 0. 2
A math book is 2.5 cm thick.
How many of these books can
be stored on a shelf that is
one meter long?
The number of books that can be stored on one meter-long shelf is (forty) = 40.
Given
a book is 2.5 cm thick
number of books required are
Convert meters into centimeters first 1m = 100 cm now, divide them:
= 100 cm ÷ 2.5 cm to remove the decimal point divide 2.5 by 10 = 2.5/10
= [tex]100 * \frac{10}{25}[/tex]
= 40
thus the total number of books that can be stored on a one-meter bookshelf is 40 books.
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A store is having a sale on jelly beans and trail mix today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
please refer to the image
The required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
What is the equation?the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
According to the question,
6x + 5y = 28 - - - - (1)
2x + 3y = 14 - - - - (2)
Solving equations 1 and 2 by substitution method we get,
x = 7/4 = and y = 7/2
Thus, the required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
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Speeding tickets provide a significant source of revenue for many American cities. For one city in South Florida, the average annual speeding ticket revenue per police officer is $300,000. The standard deviation for these annual speeding ticket revenues is $58,000. If these amounts have a normal distribution, find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue generating officers from the other ninety-five percent.
Explanation
To find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue-generating officers from the other ninety-five percent.
We will need to find
[tex]P\left(x>z\right)=0.05[/tex]Therefore; using a z score calculator, this gives;
[tex]z=1.645[/tex]We can then find the cutoff amount z using the formula below;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}[/tex]Therefore, we will have
[tex]\begin{gathered} 1.645=\frac{x-300000}{58000} \\ \mathrm{Switch\:sides} \\ \frac{x-300000}{58000}=1.645 \\ crossmutiply \\ x-300000=58000\times1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}[/tex]Answer: 395410
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
The derivative of the function f(x) = √x-5 is 1/2√(x-5)
Given f(x) = √x-5
from the formula d/dx (√x) = 1/2√x
hence d/dx √x-5 = 1/2√x-5
or
d/dx √x-5 = 1/2 (x-5)¹/²
The formula for the derivative of root x is d(x)/dx = (1/2) x-1/2 or 1/(2x). The exponential function with x as the variable and base equal to 1/2 is the root x provided by x. Utilizing the Power Rule and the First Principle of Derivatives, we can get the derivative of root x.
Hence we get the value as 1/2 (x-5)¹/²
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13 divided by 10 5/6
Answer:
the answer is 1 1/5
Which is the best interpretation of the averagerate of change of this function?
We can calculate the rate of change as the slope between two points, like (1,2) and (2,4).
The slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{2-1}=\frac{2}{1}=2[/tex]If this is a linear function, this slope m has to be constant.
We will calculate the slope between other points, like (3,8) and (4,16):
[tex]m=\frac{y_4-y_3}{x_4-x_3}=\frac{16-8}{4-3}=\frac{8}{1}=8[/tex]The slope is not constant, so this function is not a linear function.
If we look at how f(x) increases, we can prove that f(x) is:
[tex]f(x)=2^x[/tex]and this function is an exponential function.
Answer: Option B (exponential function).
5x+y=4x-y=2GRAPHINGI need The Two slopes and The Two y- intercepts pleaseeeee
Given the equations:
5x + y = 4
x - y = 2
Convert the standard from to the slope intercept from
The slope intercept form is : y = mx + c
Where m is the slope and c is y-intercept
So, for the equation 5x + y = 4
the slope intercept form will be:
[tex]y=-5x+4[/tex]so, the slope = m = -5
and y-intercept = c = 4
The graph of the line will be as following:
For the second equation: x - y = 2
The slope intercept form is :
[tex]y=x-2[/tex]The slope of the line = 1
and the y-intercept = -2
The graph of the line will be as following :
Do you see my messages ?
a
(1.2 x 10^7)(2.2 x 10^-3)
The value of the expression is:
2.64 x 10² or 26400
Step - by - Step Explanation
From the question;
(1.2 x 10⁷ )(2.2 x 10⁻³)
To sim plify the expression above, we will multiply the decimal part and then apply indices to the exponent.
That is;
[tex]1.2\times2.2\times10^{7-3}[/tex][tex]=2.64\times10^2[/tex]Or
=26400
Use four rectangles to estimate the area between the graph of the function f(x) = Ty and the taxis on the interval 12, 6) using the left endpointsof the subintervals as the sample points. Write the exact answer, Do not round,
To find the area using four rectangles, we will use the following equation:
[tex]Area\approx A_1_{}+A_2+A_3+A_4[/tex][tex]Area\approx f(x_1)\Delta x+f(x_2)\Delta x+f(x_3)\Delta x+f(x_4)\Delta x[/tex][tex]Area\approx f(3)\Delta x+f(4)\Delta x+f(5)\Delta x+f(6)\Delta x[/tex][tex]Area\approx(\frac{6}{7(3)})(1)+(\frac{6}{7(4)})(1)+(\frac{6}{7(5)})(1)+(\frac{6}{7(6)})(1)[/tex][tex]Area\approx\frac{57}{70}[/tex]helppppppppppppppppppp
What is the solution to the equation below ? 0.5x = 6 A . 3 B . 12 C . 60
Given the equation:
[tex]0.5x=6[/tex]Multiplying both sides by 2
[tex]\begin{gathered} 2\cdot0.5x=2\cdot6 \\ x=12 \end{gathered}[/tex]So, the answer will be option B) 12
A $300,000 property appreciated in value by 3%. What is its new value?
Answer:
The word "Appreciated" means "Increase" in value of something.
Here, The value of property is Appreciated by 3%
Therefore,
New price = Old price + 3% of Old price
New price = $300000 + 3% of $300000
New price = $300000 + $( 3/100 × 300000)
New price = $300000 + $9000
New price = $309000
I hope it's helpful
Answer:
$309 000.
Step-by-step explanation:
It is now worth 3% more than its original 100%
So 103% ( in decimal 1.03)
1.03 * 300 000 = 309 000 dollars
Let's find2. 1+5 3First write the addition with a common denominator.Then add.12— +51-4-13Х5
The given addition exercise is:
[tex]\frac{2}{5}+\frac{1}{3}[/tex]The LCM of the denominator (5 and 3) = 15
Multiply 2/5 by 3/3
[tex]\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}[/tex]Multiply 1/3 by 5/5
[tex]\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}[/tex]The addition becomes
[tex]\frac{6}{15}+\frac{5}{15}=\frac{11}{15}[/tex]Therefore, we can fill in the vacant boxes as shown below:
[tex]\frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}=\frac{11}{15}[/tex]Use the slope and y-intercept to graph the line whose equation is given. 2 y = -x + 5x+1
ok
y = -2/5 + 1
This is the graph
Kui Software tinite Algebra 2 Compound Inequalities Solve each compound inequality and graph its solution. Name Samanthace ballos Date valgan 1) n+15-3 or-in- Perut k 2) ohs- n2-3-1
n<4 or n>8
10) Let's solve that compound inequality:
12 + 4n> 44 or 10 -12n> -38
2) Solving each one separately
12 + 4n > 44 Subtracting 12 from both sides
4n > 44 -12
4n > 32 Divide both sides by 4
n> 8
10 -12n> -38 Subtracting 10 from both sides
-12n > -38 -10
-12n > -48 Divide both sides by -1 and flipping the sign
n < 4
3) Graphing the solution, we have:
Notice that for that, we'll use open dots since 4 and 8 are not included.
Find the value of k so that x-1 is a factor of x^2 - 2x^2 + 3x + k
The value of k so that x - 1 is a factor of the polynomial, x² - 2x² + 3x + k is -2.
How to find the factor of a polynomial?The polynomial given is x² - 2x² + 3x + k.
Let's find the value of k so that x - 1 is a factor of the polynomial x² - 2x² + 3x + k.
Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
Therefore, the value of k that will make x - 1 a factor is when the polynomial is equals to zero when we input the root of x - 1 in the polynomial.
Hence,
x - 1 = 0
x = 1
let's substitute the value of x in the polynomial. The polynomial must be equals to 0 for x - 1 to be a factor of the polynomial.
0 = x² - 2x² + 3x + k
0 = (1)² - 2(1)² + 3(1) + k
0 = 1 - 2 + 3 + k
0 = - 1 + 3 + k
0 = 2 + k
k = - 2
Therefore, the value of k is -2.
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2. The length of one side of the square is the square root ofits area. Use the table tofind the approximate length of one side of the square. Explain how you used thetable to find this information
we know that
the area of a square is equal to
A=b^2
where
b is the length side
Apply square root both sides of the formula we have
[tex]\sqrt{A}=b[/tex]To the right is the graph of f(x) = x^2. The second graph, to the left of f(x) = x^2 is a new function made by stretching f(x) vertically by a factor of 2 and then translating it three units to the left and one unit down. Write the equation of the new function.
This problem invloves the topic of curved lines in a graph, curved lines or more speccifically curve line which looks like letter C (parabola) all follows a certain standard form of equation, which is;
[tex]y=ax^2+b[/tex]For example you can see that the equation for the black curve line in our picture is y=x² and notice that this equation can also be written as y = (1)x² + 0. Which simillar to the standard form given above where a is just 1 (a=1) and b is just 0 (b=0).
Since our black curve line follows the same standard form of equation as stated above, we can conclude that the RED curve line follows the same form of equation.
To summarize the steps that we must do in order to find the equation of the RED line we will list them as,
1. Sample two(2) points in the graph to be used as reference points.
2. Use the sampled points in our standar eqation in order to find the variables "a" and "b".
3. When we have the variables "a" and "b", we can just directly substitute it into our standard equation to find the equation of our RED line.
Let's start.
1. Sample 2 points to be used as refernce points. (Note that we will find the easiest points
to determine)
Let us use the points (-3, -1) and (-2, 1) as shown in the picture.
2. Use the points (-3, -1) and (-2, 1) in our standard equation.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-3, -1)} \\ -1=a(-3)^2+b_{} \\ 9a+b=-1 \end{gathered}[/tex]
for our 1st point we have the equation 9a+b = -1, let us now proceed to our next point.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-2, 1)} \\ 1=a(-2)^2+b_{}_{} \\ 1=4a+b \\ 4a+b=1 \end{gathered}[/tex]and for our 2nd point we have the equation 4a+b = 1, and by the process of subtitution and elimination we can now find "a" and "b", because we have two equations with two unknowns.
[tex]\begin{gathered} 9a+b=-1\text{ and} \\ 4a+b=1 \end{gathered}[/tex]transforming eqatuin number 1 to
[tex]9a+b=-1\text{ is just the same as b = -1 -9a}[/tex]
then substitue b = -1 -9a to the 2nd equation we have.
[tex]\begin{gathered} 4a+b=1\text{ , where b = -1-9a} \\ 4a+(-1-9a)=1 \\ 4a-1-9a=1 \\ -5a=2 \\ a=-\frac{2}{5} \end{gathered}[/tex]
since a = -2/5, we can find b using,
[tex]\begin{gathered} 4a+b=1\text{ , where a=-}\frac{2}{5} \\ 4(-\frac{2}{5})+b=1 \\ b=1+\frac{8}{5} \\ b=\frac{5}{5}+\frac{8}{5} \\ b=\frac{13}{5} \end{gathered}[/tex]therefore our a and b are;
[tex]a=-\frac{2}{5}\text{ and b = }\frac{13}{5}[/tex]3. We can now proceed in substituting it in our standard equation;
[tex]\begin{gathered} y=ax^2+b\text{ , where a = -}\frac{2}{5}\text{ and b = }\frac{13}{5} \\ y=(-\frac{2}{5})x^2+(\frac{13}{5}) \\ y=-\frac{2}{5}x^2+\frac{13}{5} \end{gathered}[/tex]you can also simplify the final equation by multiplying all sides by 5,
[tex]\begin{gathered} 5y=(5)\lbrack-\frac{2}{5}x^2+\frac{13}{5}\rbrack \\ 5y=-2x^2+13 \end{gathered}[/tex]therefore our final answer can be,
[tex]\begin{gathered} f(x)=-\frac{2}{5}x^2+\frac{13}{5} \\ or \\ 5y=-2x^2+13 \end{gathered}[/tex]
ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
which number of pounds of bananas and total cost of the bananas could be used as the missing values in the table
Given :
The table show a proportional relationship between the number of pounds and the total cost
so,
NEED HELP FAST!!
For ΔABC, m∠A = 41.3° and m∠B = 103.4°. Determine m∠C.
144.7°
72.35°
54.7°
35.3°
Answer: The answer is D. 35.3
Step-by-step explanation: Because the triangle has to add up to 180 and 41.3 + 103.4 = 144.7. Then you could either do 180-144.7 = 35.3 or you could add 144.7 + 35.3. Hope this helps
The value of angle C based on the information is A. 35.3°
How to calculate the angle?It's important to know that the total sum of angles in a triangle is 180°.
In this case, the following can be deduced:
Angle A = 41.3°
Angle B = 103.4°
Therefore, Angie C will be:
= Total angle - {Angle A + Angle B}
= 180° - (41.3° + 103.4°)
= 180° - 144.7°
= 35.3°
Therefore, the correct option is D.
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students at a local school were asked about how many hours do you spend on homework each week? the table shows the results of the survey classify the statement below as a true or false more students study for 3 to 4 hours than for 5 to 6 hours the statement is (true or false) because.... students study for 3 to 4 hours and..... students study for 5 to 6 hours.
The total of students that study for 3 to 4 h is 147
The total of students that study for 5 to 6 h is 107
Then, the statement: "more students study for 3 to 4 hours than for 5 to 6 hours" is true because 147 students study for 3 to 4 hours and 107 students study for 5 to 6 hours.
Are they inverses?f(x) = 6x - 6, g(x) = 1/6x + 1
Given function,
f(x) = 6x - 6
or
y = 6x -6
The inverse of a function is calculated by replacing the values of x and y
therefore
Inverse (y = 6x - 6)
x = 6y - 6
x + 6 = 6y
6y = x + 6
y = x/6 + 6/6
y = 1/6*x + 1
or
g(x) = 1/6*x + 1
Hence, both are inverse of each other.
2.3x + 8 = - 1.7x - 8 solve for x
The value of x after solving (2.3x + 8) = (-1.7x-8) is -4.
According to the question,
We have the following expression:
(2.3x + 8) = (-1.7x-8)
Now, moving -1.7x from the right hand side to the left hand side will result in the change of its sign from minus to plus:
2.3x+1.7x +8 = -8
4x+8 = -8
Now, moving 8 from the left hand side to the right hand side will also result in the change of the sign from plus to minus:
4x = -8-8
4x = -16
x = -16/4 (4 was in multiplication on the left hand side. So, it is in division on the right hand side.)
x = -4
Hence, the value of x is -4.
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Given that 4 is a zero of the polynomial function f(x), find the remaining zeros.f(x) = x³ - 6x² + 25x - 68List the remaining zeros (other than 4).4(Simplify your answer. Type an exact answer, using radicals and i as needed. Use a cc
ANSWER
[tex]\begin{gathered} x=1+4i \\ x=1-4i \end{gathered}[/tex]EXPLANATION
Given:
[tex]\begin{gathered} f(x)=x^3-6x^2+25x-68 \\ \end{gathered}[/tex]Also,
One of the zeros: x = 4
Desired Outcome:
List the remaining zeros using radicals and i.
Simplify the polynomial using x - 4 = 0
Determine the remaining polynomials by simplifying x^2 - 2x + 17 = 0 using the quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where:
a = 1,
b = -2
c = 17
Substitute the values
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(17)}}{2(1)} \\ x=\frac{2\pm\sqrt{4-68}}{2} \\ x=\frac{2\pm\sqrt{-64}}{2} \\ x=\frac{2\pm\sqrt{64\times-1}}{2} \\ x=\frac{2\pm(\sqrt{64}\times\sqrt{-1})}{2} \\ x=\frac{2\pm8\sqrt{-1}}{2} \\ x=1\pm4\sqrt{-1} \\ \text{ Recall: }\sqrt{-1}\text{ = }i \\ x=1\pm4i \\ x=1+4i\text{ }or \\ x=1-4i \end{gathered}[/tex]
Which ratio table shows equlvalent ratios? O First Quantity 63 Second Quantity 8 5 o First Quantity Second Quantity 15 4 22 First Quantity Second Quantity 6 3 First Quantity 2.1 Second Quantity 4 2
we are asked to determine which ratios are equivalent. For ratios to be equivalent the quotient of the ratios must be the same. For the ratios:
[tex]\frac{2}{4},\frac{1}{2}[/tex]If we take 2/4 and divide the numerator and denominator by 2 we get:
[tex]\frac{\frac{2}{2}}{\frac{4}{2}}=\frac{1}{2}[/tex]Since we got the same fraction that means that the ratios are equivalent.
Owners of a recreation area are adding water to a pond. The graph below shows the amount of water in the pond (in liters) versus the amount of time that water is added (in hours).Use the graph to answer the questions.(a)How much does the amount of water increase for each hour that water is added?liters=(b)What is the slope of the line?
GIVEN:
We are given a graph showing the increase in the amount of water pumped into a pond for every passing hour.
Required;
To determine the amount of increase in the water level for each hour that water is added.
Also, to determine the slope of the line as shown in the graph.
Step-by-step solution;
(a) Notice that the graph shows an increase in the water level for every passing hour. Notice also the following relationship;
[tex]\begin{gathered} (hours,liter) \\ \\ (0,100) \\ \\ (1,400) \\ \\ (2,700) \\ \\ (3,1000) \end{gathered}[/tex]We can see that the rate of change for every hour is 300 liters increment.
Therefore, for each hour that water is added, there is an increase of 300 liters.
(b) To calculate the slope of the line shown in the graph, we shall take the change in liters and divide by the corresponding change in the hours.
We now have the following;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(0,100) \\ \\ (x_2,y_2)=(1,400) \end{gathered}[/tex]We now have the slope as follows;
[tex]\begin{gathered} m=\frac{400-100}{1-0} \\ \\ m=\frac{300}{1}=300 \end{gathered}[/tex]The slope therefore is 300.
ANSWER:
[tex]\begin{gathered} (a)\text{ }Liters=300 \\ \\ (b)\text{ }slope=300 \end{gathered}[/tex]you’re making desert, but your recipe needs adjustment. your oatmeal cookie recipe makes 2 dozen cookies, but you need 3 cookies. If the recipe requires 1 and 1/3 cups of sugar, 3/4 teaspoon of salt, and 1 and 1/4 cups of raisins, how much of each of these ingredients are for 3 dozen cookies? simply your answer
we know that
For 2 dozen cookies
we need
1 1/3 cups of sugar
3/4 teaspoon of salt
1 1/4 cups of raisins
To convert 2 dozens to 3 dozens------> multiply by 3/2
but first convert mixed number to improper fractions
1 1/3=1+1/3=4/3 ----> multiply by 3/2
(4/3)*(3/2)=2 cups of sugar
3/4*(3/2)=9/8 ----> convert to mixed number
9/8=8/8+1/8=1 1/8 teaspoon of salt
1 1/4=1+1/4=5/4
5/4*(3/2)=15/8
15/8=8/8+7/8=1 7/8 cups of raisins
What two variables can you define to write an equation to match this scenario?x = number of minutes for fruit cans and y = number of minutes for vegetable cansx = total number of minutes and y = total number of cansx = number of minutes for fruit and y = total number of cansx = total number of minutes and y = number of minutes for vegetables
An equation to correctly match this scenario would have to include both separate products. The current order which is 384 cans of food, includes both fruits and vegetables, and therefore any expression that does not include them both would give a wrong answer and the order would not be properly met.
The correct scenario is;
[tex]\begin{gathered} x=Number\text{ of minutes for fruit cans} \\ y=\text{Number of minutes for vegetable cans} \end{gathered}[/tex]This way you can produce both at a maximum without overproducing one and underproducing the other.
TRIGONOMETRY Find the length of the longer diagonal of this parallelogram round to the nearest tenth
Given the parallelogram ABCD
As shown: AB = 4 ft
m∠BAC = 30
m∠BDC = 104
We will find the length of the longer diagonal which will be AC
See the following figure:
The point of intersection of the diagonals = O
The opposite sides are parallel
AB || CD
m∠ABD = m∠BDC because the alternate angles are congruent
So, in the triangle AOB, the sum of the angles = 180
m∠AOB = 180 - (30+104) = 46
We will find the length of OA using the sine rule as follows:
[tex]\begin{gathered} \frac{OA}{\sin104}=\frac{AB}{\sin 46} \\ \\ OA=AB\cdot\frac{\sin104}{\sin46}=4\cdot\frac{\sin104}{\sin46}\approx5.3955 \end{gathered}[/tex]The diagonals bisect each other
So,
[tex]AC=2\cdot OA=10.79[/tex]The longer diagonal is AC
Rounding to the nearest tenth
So, the answer will be AC = 10.8 ft
