Answer: The average rate of change is 1.
Step-by-step explanation:
The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)
a=−2 , b=2, f(x)=4X^2+x+3.
(f(b)-f(a))/(b-a)= (3+(2)+4(2)^2-(3+(-2)+4(-2)^2)) / (2-(-2)) = 1
Write (2p^2)^3 without exponents.(2p^2)^3 = ??
We are required to write the expression:
[tex](2p^2)^3[/tex]Without exponents. First, we operate the parentheses:
[tex](2p^2)^3=2^3(p^2)^3=2^3p^6[/tex]This is the simplified expression. If we wanted to avoid the exponents, then we have to express the exponents as products:
[tex]2^3p^6=2\cdot2\cdot2\cdot p\cdot p\cdot p\cdot p\cdot p\cdot p[/tex]This is the required expression
Apollo Enterprises has been awarded an insurance settlement of $6,000 at the end of each 6 month period for the next 12 years. calculate how much (in $) the insurance company must set aside now at 6% interest compounded semiannually to pay this obligation to Apollo
$12180 the insurance company must set aside now at 6% interest compounded semiannually to pay this obligation to Apollo.
This is a problem from the compound interest system. We can solve this problem by following a few steps.
Apollo Enterprises has been awarded an insurance settlement of $6,000 at the end of each 6-month period for the next 12 years with a 6% interest rate. We have to calculate the total amount after 12 years.
To solve this problem we should know the formula for the compound interest method.
Formula:-
A = P {(1 + r/n)^(n.t)}
Here,
A denotes the final amount, we have to find this.P denotes the initial principal balance which is $6,000r denotes the interest rate which is 6%n denotes the number of times interest is applied per time period which is 12/6 = 2. t denotes the number of time periods elapsed which is 12 years.Now, we can calculate the value of A.
A = 6000 {( 1 + 6/200 )^2.12} = 6000 ( 1 + 6/200 )^24 = 6000 × 2.03 = 12180
Therefore, the total amount after 12 years is $12180
To learn more about compound interest visit,
https://brainly.com/question/26457073?referrer=searchResults
#SPJ9
which best describes the relationship between the two lines described below?
If two lines are perpendicular, then the product of their slopes is equal to -1.
If two lines are parallel, then their slopes are equal.
Write the equation of the lines P and Q in slope-intercept form by isolating y. Compare their slopes to see if they are either parallel or pependicular, or none.
The equation of a line with slope m and y-intercept b in slope-intercept form, is:
[tex]y=mx+b[/tex]Line P:
[tex]\begin{gathered} 6x+3y=12 \\ \Rightarrow3y=-6x+12 \\ \Rightarrow y=\frac{-6x+12}{3} \\ \therefore y=-2x+4 \end{gathered}[/tex]Then, the slope of the line P is -2.
Line Q:
[tex]\begin{gathered} -4x=2y-2 \\ \Rightarrow2y=-4x+2 \\ \Rightarrow y=\frac{-4x+2}{2} \\ \Rightarrow y=-2x+1 \end{gathered}[/tex]Then, the slope of the line Q is -2.
Since both lines have the same slope, then they are parallel.
I need help with 18 I need an answer and a explanation
Mark's height last year was 46 inches.
Mark definitely grows over the past year. Let the height he grew be x.
Then, Mark's new height will be
[tex](46+x)\text{ inches}[/tex]Let us represent Mark's height with M and Peter's height with P.
This means that
[tex]M=46+x\text{ -----------(a)}[/tex]and, from the question, Peter's height is
[tex]P=51\text{ ----------(b)}[/tex]The question says that Mark's height is 3 inches less than Peter's height. This we can write as
[tex]M=P-3\text{ -------------(c)}[/tex]Therefore, if we put Mark's and Peter's ages into equation c, we can find a value for x as follows:
[tex]\begin{gathered} 46+x=51-3 \\ 46+x=48 \end{gathered}[/tex]Since 46 + x = M, then Mark's height is 48 inches
Write and graph a direct variation equation that passes through the given point.(2, 5)Write the direct variation equation.y=
For direct variation, an increase or decrease in one variable leads to a proportional increase or decrease in the other variable
Given that y varies directly with x, we would introduce a constant of proportionality, k
The expresion becomes
y = kx
For x = 2 and y = 5,
5 = 2k
k = 5/2 = 2.5
The direct variation equation is
y = 2.5x
A random sample of 860 births in a state included 423 boys. Construct a 95%
confidence interval estimate of the proportion of boys in all births. It is believed that
among all births, the proportion of boys is 0.513. Do these sample results provide
strong evidence against that belief?
Construct a 95% confidence interval estimate of the proportion of boys in all births.
Using the z-distribution, it is found that the 95% confidence interval is (0.45 , 0.52), and it does not provide strong evidence against that belief.
A confidence interval of proportions is given by:
[tex]\pi[/tex] ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
where [tex]\pi[/tex] is the sample proportion, z is the critical value and n is the sample size.
In this problem, we have 95% confidence level, hence [tex]\alpha[/tex] = 0.95, z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2}[/tex] = 0.975, so the critical value is z = 1.96
We have that a random sample of 860 births in a state included 423 boys, hence the parameters are given by:
n = 864, [tex]\pi =\frac{423}{860}[/tex] = 0.49
Then the bounds of the interval are given by:
[tex]\pi[/tex] + [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex] = 0.49 + [tex]1.96\sqrt{\frac{0.49(0.513)}{860} }[/tex] = 0.52
[tex]\pi[/tex] - [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex] = 0.49 - [tex]1.96\sqrt{\frac{0.49(0.513)}{860} }[/tex] = 0.45
The 95% confidence interval estimate of the population of boys in all births is (0.45 , 0.52). Since the interval contains 0.513, it does not provide strong evidence against that belief.
Know more about z-score: - https://brainly.com/question/24213960
#SPJ9
14) Solve the following quadratic equations by using the quadratic formula a) 3x2 - 7x + 4 = 0 b) 5x2 + 3x = 9
Quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a is the coefficient of the first term, b the coefficient of the second term and c the coefficient of third term
a)
[tex]3x^2-7x+4=0[/tex]replacing on the quadratic formula
[tex]x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(3)(4)}}{2(3)}[/tex]simplify
[tex]\begin{gathered} x=\frac{7\pm\sqrt[]{49-48}}{6} \\ \\ x=\frac{7\pm\sqrt[]{1}}{6} \\ \\ x=\frac{7\pm1}{6} \end{gathered}[/tex]x has two solutions
[tex]\begin{gathered} x_1=\frac{7+1}{6}=\frac{4}{3} \\ \\ x_2=\frac{7-1}{6}=1 \end{gathered}[/tex]b)
[tex]5x^2+3x=9[/tex]rewrite on general form
[tex]5x^2+3x-9=0[/tex]raplace on quadratic formula
[tex]x=\frac{-(3)\pm\sqrt[]{(3)^2-4(5)(-9)}}{2(5)}[/tex]simplify
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{9+180}}{10} \\ \\ x=\frac{-3\pm\sqrt[]{189}}{10} \end{gathered}[/tex]x has two solutions
[tex]\begin{gathered} x_1=\frac{-3+\sqrt[]{189}}{10}\approx1.075 \\ \\ x_2=\frac{-3-\sqrt[]{189}}{10}\approx-1.67 \end{gathered}[/tex]answer f 1 half 25 y intercept equals 375--g slope 1 half 25 y intercept equal 15H slope equals 25 y intercept equal 375J slope equals negative 25 y intercept equals 15
Answer:
[tex]\begin{gathered} \text{Slope}=-\frac{1}{25} \\ y-\text{intercept}=15 \end{gathered}[/tex]Step-by-step explanation:
Linear functions are represented by the following expression:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]m is the constant rate of change of the function, and it's calculated as the change in y over the change in x:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{14.6-15}{10-0} \\ m=-\frac{1}{25} \end{gathered}[/tex]The y-intercept of a linear function is when the line crosses the y-axis, which means when x=0.
Therefore, the y-intercept of the line is 15.
Find the additive inverse. −31
Answer:
To get the additive inverse of a positive number you put a minus in front of it and to get the additive inverse of a negative number, you remove the minus to make it a positive number.
in point a the diameter is 12 C D equals 8 and MCD equals 90 find a measure round to the nearest hundred
Given that BE is diameter and CD is perpendicular, we can deduct that arcs CE and DE are equal.
[tex]\begin{gathered} arc(CD)=arc(CE)+arc(DE) \\ 90=2\cdot arc(CE) \\ \text{arc(CE)}=45=arc(DE) \end{gathered}[/tex]Therefore, arc DE is 45°.
Which of the following is equivalent to tanблOA. tan 3OB. tan 5OC. tanOD. tanВп3Reset Selection
Okay, here we have this:
Considering the provided expression, we are going to identify to which is equivalent, so we obtain the following:
We obtain that the correct answer is the option C, because:
A price p (in dollars) and demand x (in items) for a product are related by 2x²-5xp + 55p²-23,200.
If the price is increasing at a rate of 3 dollars per month when the price is 20 dollars, find the rate of change of the demand with respect to time. (Round your answer to four
decimal places.)
The monthly rate of change in demand is -$40.7.
How is the rate of change estimated from an equation?The slope of a graphed function is determined using the average rate of change formula. The method for finding the slope is differentiation.
A price-demand relation equation is given.
2x²-5xp + 55p²=23,200.
Differentiate the given equation with time
[tex]\begin{aligned}&4 x \frac{d x}{d t}-5\left(x \frac{d p}{d t}+p \frac{d x}{d t}\right)+110 p \frac{d p}{d t}=0 \\&4 x \frac{d x}{d t}-5 p \frac{d x}{d t}=5 x \frac{d p}{d t}-110 p \frac{d p}{d t} \\&(4 x-5 p) \frac{d x}{d t}=(5 x-110 p) \frac{d p}{d t} \\&\frac{d x}{d t}=\frac{(5x-110 p)}{(4 x-5p)} \frac{d p}{d t}\end{aligned}[/tex]
Put the value of p in the original equation.
For p=20
[tex]2x^{2} -5x\times 20+ 55\times20^{2}=23200\\2x^{2}-100x+22000=23200\\2x^{2}-100x-1200=0\\x^{2}-50x-600=0\\x=60 \text{ or }-10[/tex]
Since the price can not be negative, x=60.
Putting these values in the differential equation.
[tex]\frac{d x}{d t}=\frac{(5 x-110 p)}{(4 x-5 p)} \frac{d p}{d t}\\=\frac{(5\times60-110\times 20)}{(4\times60-5 \times20)} \times3\\=\frac{300-2200}{140}\times3\\ =-40.7[/tex]
So, the monthly rate of change in demand is -$40.7.
The minus sign indicates that demand is decreasing.
To know more about the rate of change:
https://brainly.com/question/19752248
#SPJ9
a waffle cone with a height of 6 inches has a volume of 56.52 cubic inches. What's the area
Answer:
28.26 square inches.
Explanation:
Given a waffle cone with the following properties:
• Height = 6 inches
,• Volume = 56.52 cubic inches.
[tex]\text{Volume of a cone}=\frac{1}{3}\pi r^2h[/tex]Note that the base of the cone is a circle and the area of a circle:
[tex]A=\pi r^2[/tex]Substitute the given values:
[tex]\begin{gathered} 56.52=\frac{1}{3}\times\pi\times r^2\times6 \\ 56.52=2\pi r^2 \\ \pi r^2=\frac{56.52}{2} \\ \pi r^2=28.26in^2 \end{gathered}[/tex]The area of the base is 28.26 square inches.
In July 1 2020 culver inc invested $635250 in a mine estimated to have 847000 tons of ore of uniform grade during the last 6 months of 2020 146000 tons of ore were mined calculate depletion cost per unit
Given:
culver inc invested $635250 in a mine estimated to have 847000 tons of ore of uniform grade
So, the estimated cost per unit =
[tex]\frac{635250}{847000}=0.75[/tex]This means the cost = $0.75 per ton
You paid $600 for a new guitar. Your guitar cost $40 more than twice the cost of your friends guitar. Wright an equation based on this information.
Answer: 600 divided by 2 + 40
Step-by-step explanation:
Answer:
2x + 40 = 600
2x = 560
x = 280.
Your friends guitar costs $280.
Step-by-step explanation:
Set the equation equal to $600, the cost of the new guitar. Let the variable, x, represent the cost of your friends guitar. Since your guitar was + 40 more than double the cost of your friend’s, this can be written as an equation:
2x + 40 = 600
In New York the mean salary for high school teachers in 2017 was 97010 with a standard deviation of 9540. Only Alaska’s mean salary was higher. Assume new York’s state salaries follow a normal distribution. (A) what percent of new York’s high school teachers earn between 83,000 and 88,000? (B) what percent of New York teachers earn between 88,000 and 103,000?
(C) what percent of new York’s state high school teachers earn less than 73,000?
a. 20.31% of New York's high school teachers earn between 83,000 and 88,000
b. 18.49% of New York teachers earn between 88,000 and 103,000
c. 1.19% of New York’s state high school teachers earn less than 73,000
Given,
The salary for high school teachers in 2017 = 97010
Standard deviation = 9540
Consider salaries as normal distribution.
Here,
Mean, μ = 97010, Standard deviation, σ = 9540
a. Percentage of New York's high school teachers earn between 83,000 and 88,000
The proportion is the p-value of Z when X = 88,000 subtracted by the p-value of Z when X = 83,000.
That is,
X = 88,000
Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944
The p value of z score - 0.944 is 0.3452
Next,
X = 83,000
Z = (X - μ) / σ = (83,000 - 97010) / 9540 = -14010/9540 = -1.468
The p value of z score - 1.468 is 0.1421
Then,
0.3452 - 0.1421 = 0.2031 = 20.31%
That is,
20.31% of New York's high school teachers earn between 83,000 and 88,000
b. Percentage of New York teachers earn between 88,000 and 103,000
The proportion is the p-value of Z when X = 103,000 subtracted by the p-value of Z when X = 88,000
X = 103,000
Z = (X - μ) / σ = (103,000 - 97010) / 9540 = 5990/9540 = 0.6279
The p value of z score 0.6279 is 0.5301
Next,
X = 88,000
Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944
The p value of z score - 0.944 is 0.3452
Then,
0.5301 - 0.3452 = 0.1849 = 18.49%
That is,
18.49% of New York teachers earn between 88,000 and 103,000
c. Percentage of new York’s state high school teachers earn less than 73,000
The proportion is the p-value of Z when X = 73000
X = 73,000
Z = (X - μ) / σ = (73,000 - 97010) / 9540 = -24010/9540 = -2.516
The p value of z score - 2.516 is 0.0119
That is,
1.19% of New York’s state high school teachers earn less than 73,000
Learn more about Normal Distribution here;
https://brainly.com/question/28407698
#SPJ1
Skills Find the new bank account balance Old balance: $500.00Withdrawal: $175.00Withdrawal: $60.00Deposit: $37.50
In order to find the new bank account balance, we can do a sum of all the deposits and subtraction of all withdrawals to the old balance account,
[tex]\begin{gathered} BA=500.00-175.00-60.00+37.50 \\ BA=302.50 \end{gathered}[/tex]Let theta equals 11 times pi over 12 periodPart A: Determine tan θ using the sum formula. Show all necessary work in the calculation.Part B: Determine cos θ using the difference formula. Show all necessary work in the calculation.
The fisrt part is the divide your angle into two angles, could be 6/12π and 5/12π
[tex]\begin{gathered} A=\frac{4\pi}{12}=\frac{\pi}{3} \\ B=\frac{7\pi}{12} \end{gathered}[/tex]For the sum formula:
[tex]\begin{gathered} \tan (\theta)=\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B} \\ \tan (A+B)=\frac{1.73-3.73}{1-1.73\cdot(-3.73)} \\ \tan (A+B)=\frac{-2}{7.45}=-0.27 \end{gathered}[/tex]For the difference formula:
[tex]\begin{gathered} A=\frac{1\pi}{12} \\ B=\pi \end{gathered}[/tex][tex]\begin{gathered} \tan (B-A)=\frac{\tan B-\tan A}{1+\tan A\cdot\tan B} \\ \tan (B-A)=\frac{0-0.268}{1+0\cdot0.267} \\ \tan (B-A)=-0.268 \end{gathered}[/tex]Both methods work and result in the same answeer
you and your family are taking a trip to Brazil. You are bringing $175 on the trip. The rate pf currency exchange is 4.65 Real (Brazilian money) per 1 United States dollar. How many Real will you have on the trip?
Answer:
813.75 can you have .75 of a real? if not, then 813
Step-by-step explanation:
175 x 4.65 = 813.75
Line BC Is a tangent to circle A at Point B. How would I find the measure of angle BCA? I need more explanation
SOLUTION
Notice that line BA is a radius of the circle.
Since line BC is a tangen then the measure of angle ABC is:
[tex]m\angle ABC=90^{\circ}[/tex]Using Triangle Angle-Sum Theorem, it follows:
[tex]m\angle ABC+m\angle BAC+m\angle BCA=180^{\circ}[/tex]This gives:
[tex]90^{\circ}+57^{\circ}+m\angle BCA=180^{\circ}[/tex]Solving the equation gives:
[tex]\begin{gathered} 147^{\circ}+m\angle BCA=180^{\circ} \\ m\angle BCA=180^{\circ}-147^{\circ} \\ m\angle BCA=33^{\circ} \end{gathered}[/tex]Therefore the required answer is:
[tex]m\angle BCA=33^{\circ}[/tex]8 if x ≤-1
2x if -1 < x <4
-4 - x + 6 if x ≥ 4)
2x=-1+6
2x=5
x=3
so the answer is 3
Given P(A) = 0.5, P(B) = 0.65 and P(AUB) = 0.75,find P(ANB).
P(A∪B) = P(A) + P(B) - P(A∩B)
where P(A) is the probability of A happening
P(B) is the probability of B happening
P(A∪B) is the probability of A or B happening
P(A∩B) is the probability of A and B happening
P(A) = 0.5, P(B) = 0.65 and P(AUB) = 0.75
.75 = .5+ .65 - P(A∩B)
.75 =1.15 - P(A∩B)
.75 - 1.15 = -P(A∩B)
-.4 = -P(A∩B)
.4 =P(A∩B)
P(A∩B) = .4
how to solve 4|x|+|-4|=|-6|
x = 1/2, x = -1/2
Simplify:
4|x| + |-4| = |-6|
4|x| + 4 = 6
4|x| = 2
|x| = 1/2
Solutions:
1) x = 1/2
2) x = -1/2
Please help I was sick today and I don’t understand
Answer:
4
Step-by-step explanation:
By the exterior angle theorem,
[tex]27x+2=65+10x+5 \\ \\ 27x+2=10x+70 \\ \\ 17x=68 \\ \\ x=4[/tex]
List the factors to find the GCF of 24 and 12
Given:
GCF of 24 and 12.
[tex]\begin{gathered} 24=2^3\times3 \\ 12=2^2\times3 \end{gathered}[/tex][tex]\begin{gathered} \text{GCF of 24 and 12=}3\times2^2 \\ \text{GCF of 24 and 12=}12 \end{gathered}[/tex]Please help me, I am happy to contribute and learn .
Explanation:
We are told that the rate at which the pump dumps the pollutant per day to be
[tex]\frac{\sqrt{t}}{15}[/tex]To solve the question, let us assume that t is the number of days
So, to find the amount dumped after 3 days, we will put t =3 into the equation
[tex]\frac{\sqrt{3}}{15}=\frac{1.732}{15}=0.11547[/tex]Therefore, the answer is 0.115
Find the midpoint of the segment with endpoints of (-1, 7) and (3,-3) andenter its coordinates as an ordered pair. If necessary, express coordinates asfractions, using the slash mark (/) for the fraction bar.
We are given the points (-1,7) and (3,-3) and we want to calculate the midpoint of the segment that joins this points. REcall that given points (a,b) and (c,d), the midpoint of the segment that joins the points is calculated by averaging each coordinate (that is,adding the coordinates and then dividing them by 2). So the midpoint would be
[tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]If ( a + 3 , b – 1 ) = ( - 2 , 4 ) , then a + b =
Answer: {(1,3),(1,4),(2,3),(2,4)}
Step-by-step explanation:
Step -1: Define the Cartesian product.
Cartesian product: If A and B are two non empty sets, then
Cartesian product A×B is set of all ordered pairs (a,b) such that a∈A and b∈B.
Step -2: Find the Cartesian product of given sets.
We have given,
A={1,2} and B={3,4}
So, A×B={(1,3),(1,4),(2,3),(2,4)}
Hence, option A. {(1,3),(1,4),(2,3),(2,4)} is correct answer.
Evaluate the correlation shown in this scatter plot and then answer the 2 questions below.
How would you describe the direction and strength of this scatter plot? Is it positive or negative? Is it weak, moderately strong, or perfect? (worth 1.5 points)
How did you decide what words to choose to describe this correlation? (worth 1.5 points) 30 POINTS FORR WHO AWNSERS
The given scatter plot points are increasing, indicating a rise in data points, direction oriented to the right and the strength of scatter plot points correlation is moderately strong.
A graph with dots is shown to indicate the relationship between two sets of data.
According to the given scatter plot, the scatter plot points are increasing, indicating a rise in data points, and we may conclude that the correlation is positive.
The scatter plots are now oriented to the right. As a result, we may claim that the correlation is moderately strong.
Thus. the given scatter plot points are increasing, indicating a rise in data points, direction oriented to the right and the strength of scatter plot points correlation is moderately strong.
To learn more about the scatter plot here:
https://brainly.com/question/10238639
#SPJ1
Given g(x) = 1/x^3Explain if the question cannot be solved
Given
[tex]g(x)=\frac{1}{x^3}[/tex]To find:
[tex]\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g(x)dx[/tex]Explanation:
It is given that,
[tex]g(x)=\frac{1}{x^3}[/tex]That implies,
[tex]\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g(x)dx[/tex]