Answer:
The cost of the paper book= $12
Step-by-step explanation:
Hardcover books costs $21
But paper book cost only a fraction of the hardcover book.
The paper book cost 4/7 of the hardcover book.
The cost of paper book= 4/7* paper book
The cost of paper book = 4/7*$21
The cost of the paper book= 4*3
The cost of the paper book= $12
Bryan invests $500 in an account earning 3.5% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:
After 10 years?
After 15 years?
After 20 years?
Answer:
$705.30, $837.67, $994.89 Respectively
Step-by-step explanation:
Given
P= $500
r= 3.5%= 3.5/100= 0.035
Applying the compound interest formula we have
[tex]A= P(1+r)^t[/tex]
where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
1. for t= 10 years[tex]A= 500(1+0.035)^1^0\\\ A= 500(1.035)^1^0\\\\ A= 500*1.410598\\\ A=705.299[/tex]
A= $705.30
2. for t= 15 years[tex]A= 500(1+0.035)^1^5\\\ A= 500(1.035)^15\\\\ A= 500*1.67534\\\ A=837.67[/tex]
A= $837.67
3. for t= 20 years[tex]A= 500(1+0.035)^2^0\\\ A= 500(1.035)^2^0\\\\ A= 500*1.98978\\\ A=994.89[/tex]A= $994.89
find the coordinates of Q' after a reflection across parallel lines; first across the line y= -2 and then across the x-axis
Answer: new Q = (-4, 5)
Step-by-step explanation:
Given: Q = (-4, 1)
Reflected across y = -2:
Q is 3 units above y = -2 so a reflection is 3 units below y = -2 --> Q' = (-4, -5)
Reflected across x-axis:
Q' is 5 units below x-axis so a reflection is 5 units above x-axis --> Q'' = (-4, 5)
If w'(t) is the rate of growth of a child in pounds per year, what does 7 w'(t)dt 4 represent? The change in the child's weight (in pounds) between the ages of 4 and 7. The change in the child's age (in years) between the ages of 4 and 7. The child's weight at age 7. The child's weight at age 4. The child's initial weight at birth.
Complete Question
If w'(t) is the rate of growth of a child in pounds per year, what does
[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] represent?
a) The change in the child's weight (in pounds) between the ages of 4 and 7.
b) The change in the child's age (in years) between the ages of 4 and 7.
c) The child's weight at age 7.
d) The child's weight at age 4. The child's initial weight at birth.
Answer:
The correct option is option a
Step-by-step explanation:
From the question we are told that
[tex]w'(t)[/tex] represents the rate of growth of a child in [tex]\frac{pounds}{year}[/tex]
So [tex]{w'(t)} \, dt[/tex] will be in [tex]pounds[/tex]
Which then mean that this [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] the change in the weight of the child between the ages of [tex]4 \to 7[/tex] years
If cot(x)=2/3, what is The value of csc(x)
Answer:
Step-by-step explanation:
cot (x)=2/3
we know csc^2(x)-cot^2(x)=1
csc^2(x)=1+cot^2(x)=1+4/9=13/9
csc (x)=±√13/3
Drag the labels to the correct locations
Answer:
Graph A
So it has two distinct real roots.
Graph B
It has one repeated real root
Graph C
So it has two complex roots.
Graph D
One real root and one complex root
Step-by-step explanation:
For graph A
The value of the roots is x= 1 and x= 3
And the minimum value = -3
It's a positive graph
So it has two distinct real roots.
For graph B
The value of the roots is x = 2 and x= 2
That is x= 2 twice
Has a maximum value of 0
It's an inverse graph
It has one repeated real root
For graph C
It's a positive graph but on the negative of x
Has a minimum value of 1
It didn't touch x at y = 0
And it's root will be negative
So it has two complex roots.
For Graph D
Value of the roots is x= 2 and x= -2
It's a positive graph
Minimum value of -4
One real root and one complex root
what is the length of a rectangle with width 12 inches and an area of 66 inches^2
Answer:
The length is 5.5 inches
Step-by-step explanation:
The area of a rectangle is
A = lw
66 = l * 12
Divide each side by 12
66/12 = l
5.5 = l
The length is 5.5 inches
Answer:
5.5 inches
Step-by-step explanation:
Length times width is the area so
12*width =66
same as
66/12=5.5 inches
Ask more questions in the comments if you are still confused.
A=63°
C = 7.75 inch
B = 47°
Oblique Triangle
13. Refer to the oblique triangle shown. What's the length of side a? Round to the nearest hundredth of an inch.
O A. 7.75 inches
O B. 7.35 inches
O C.4.72 inches
O D. 6.03 inches
Answer:
B. 7.35 inches
Step-by-step explanation:
In the triangle:
A=63° c = 7.75 inch B = 47°Now we know that:
[tex]\angle A+\angle B+\angle C=180^\circ$ (Sum of angles in a \triangle)\\63^\circ+47^\circ+\angle C=180^\circ\\\angle C=180^\circ-(63^\circ+47^\circ)\\\angle C=70^\circ[/tex]
Using the Law of Sines
[tex]\dfrac{a}{\sin A} =\dfrac{c}{\sin C}\\\\\dfrac{a}{\sin 63^\circ} =\dfrac{7.75}{\sin 70^\circ} \\\\a=\dfrac{7.75}{\sin 70^\circ} \times \sin 63^\circ\\\\a=7.35$ inches (to the nearest hundredth of an inch)[/tex]
Answer:
B. 7.35 inches
Step-by-step explanation:
just use the law of sines
The alpha level that a researcher sets at the beginning of the experiment is the level to which he wishes to limit the probability of making the error of____________
Answer:
not rejecting the null hypothesis when it is false.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.
For making the error, it should not reject the null hypothesis at the time when it should be false.
What is alpha level?It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.
Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.
Learn more about error here: https://brainly.com/question/18831983
HELP PLEASE The graph of an exponential function of the form y = f(x) = ax passes through the points ______ and _______. The graph lies_____ the x-axis.
Answer:
1). (0, 1)
2). (1, a)
3). Above
Step-by-step explanation:
This question is not complete; here is the complete question.
The graph of an exponential function of the form y = f(x) = [tex]a^{x}[/tex] passes through the points 1). and 2). . The graph lies 3). x-axis.
1). (0.a), (0,1), (0,2), (0,-1)
2). (1,0), (1,1), (1,a), (1,-2)
3). (above), (below), (on the)
Given exponential function is f(x) = [tex]a^{x}[/tex]
1). For x = 0,
f(0) = [tex]a^{0}[/tex] = 1
Therefore, the given exponential function passes through a point (0, 1).
2). For x = 1,
f(1) = [tex]a^{1}[/tex]
f(1) = a
Therefore, graph of the exponential function passes through (1, a)
3).For y = 0
0 = [tex]a^{x}[/tex]
But for any value of 'x', f(x) will never be zero. Therefore, there is no x-intercept.
The graph lies above the x-axis.
6th grade math , help me please :)
Answer:
a. 4.5 grams per cup
b. 3.2 ounces per week
c. 19.2 grams per cubic centimeters
d. $3.29 per gallon
Step-by-step explanation:
The unit rate is simply a ratio comparing 2 given quantities, whereby the denominator is 1.
The unit rate of the above given problems can be determined as shown below:
a. 18 grams of salt per 4 cups, to find the unit rate, calculate how many grams of salt you'd get in 1 cup by dividing 18 by 4
[tex] \frac{18}{4} = 4.5 [/tex]
Unit rate = 4.5 grams per cup
b. 19.2 ounces is gained by the baby in 6 weeks.
Unit rate is the amount of ounces gained in 1 week
Unit rate = [tex] \frac{19.2}{6} = 3.2 [/tex]
Unit rate = 3.2 ounces per week
c. Unit rate = [tex] \frac{76.8}{4} = 19.2 [/tex]
Unit rate = 19.2 grams per cubic centimeters
d. Unit rate = [tex] \frac{23.03}{7} = 3.23 [/tex]
Unit rate = $3.29 per gallon
A cable company must provide service for 6 houses in a particular neighborhood. They would like to wire the neighborhood in a way to minimize the wiring costs (or distance). What is the minimal length of the network required to span the entire neighborhood? House Distances (yards) 1 to 2 250 1 to 3 400 1 to 4 300 2 to 3 400 2 to 4 400 2 to 5 400 3 to 5 350 3 to 6 450 4 to 5 300 4 to 6 350
Answer:
1650 yards
Step-by-step explanation:
Here, we have to find the minimal spanning tree required to span the neighborhood.
We start from house 1. The minimum distance from house 1 to house 2 is 250 yards. Now from 2, we can go to house 3,4 or 5 all having the equal distances of 400 yard from house 2. So we go to from house 2 to house 3. Now from 3, we go to house 5 which is at a minimum distance of 350 yards. Now from house 5 we go to house 4 with 300 yards and then from house 4 we go to house 6 which is at 350 yards from 4.
Thus the network is complete and the total distance covered is
= 250 + 400 + 350 + 300 + 350
= 1650 yards
This is the minimum distance by which the neighborhood can be wired.
And the tree is
[tex]$1\rightarrow2\rightarrow3\rightarrow5\rightarrow4\rightarrow6$[/tex]
A train is booked to do the run between two places 55 km apart,in 1 hr 20 min. if it travels for the first 30 km at 36km per hour, at what speed must it travel for the rest of the distance in order to complete the journey in time
Answer:
The train must travel at 50 km/hr to make it on time.
Step-by-step explanation:
distance to be covered = 55 km
time to cover this distance = 1 hr 20 min
1 hr 20 min = 1.33 hrs (20 min = 20/60 hrs = 0.33 hrs)
The train travels the first 30 km distance at a speed of 36 km/hr
and we know that time taken = distance/speed
therefore the time taken to run this 30 km will be
time = 30/36 = 0.83 hr
The train still has 55 - 30 = 25 km to cover,
and the time left is 1.33 - 0.83 = 0.5 hrs left
to make it on time, the train must travel at
speed = distance/time = 25/0.5 = 50 km/hr
x varies directly as y, when x=4,y=3. find Y when x=5
Answer:
Y =4
Step-by-step explanation:
Hope it helps
A young Greek by the name of Zeno is riding his horse to his friends house which is two miles away. He travels half the distance in one hour. But his horse gets tired, and only travels half the remaining distance the second hour, and, again, only half the remaining distance in the third hour. How many miles did Zeno travel in those three hours?
Answer:
1.75 miles
Step-by-step explanation:
Zeno's friend's house is two miles away. He travels half the distance in one hour.
0.5 × 2 = 1
The second hour, his horse travels half the remaining distance.
0.5 × 1 = 0.5
The third hour, his horse travels half the remaining distance.
0.5 × 0.5 = 0.25
1 + 0.5 + 0.25 = 1.75
Zeno travels 1.75 miles in three hours.
Hope this helps.
The descriptive statistics listed below. These descriptive statistics were generated from a random sample of all USF students and contain information about the amount of time they exercise per week and the amount of student loan debt (in thousands of dollars) they expect upon graduating college.
Exercise Debt
N 200 200
Lo 95% CI 6.6061 11.380
Mean 7.5000 14.385
Up 95% Cl 8.4639 17.390
SD 6.0000 19.307
Minimum 0.0000 0.0000
Maximum 47.000 100.00
Which of the following graphical methods allows the individual data values to still be visible whil also allowing us to assess the shape of the exercise times?
A. Histogram.
B. Boxplot.
C. Stem and-Leaf Display.
D. All of these could do this.
Answer:
A. Histogram.
Step-by-step explanation:
Histogram is a graphical display in the form of bars. The numerical data is displayed through graph to understand easily. Skewness measure frequency distribution of histogram. The histogram is skewed in a way that its right side tail is greater than its left side tail. They are skewed to right. The histogram are positively skewed which means their most of data falls to right side. The mean of positively skewed histogram is greater than its median.
A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is
Answer:
Margin of error is 9.8
Step-by-step explanation:
Using the formular for the margin of error
The margin of error = z* (sd/√n)
Where z is the z score for the desired confidence level = 1.96, sd is the population standard deviation = 50 and n is the sample size = 100
Thus
Margin of error = 1.96 (50/√100)
= 1.96 (50/10)
= 1.96 (5)
= 9.8
Margin of error is 9.8
"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L). 1.92.45.75.51.98.23.96.9 (a) Find the mean, median, and mode. (Round your answers to two decimal places.) mean 4.55 median 4.7 mode 1.9 (b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.) s CV % range (c) Based on the data, would you recommend radon mitigation in this house
Answer:
a) Mean = 4.55
Median = 4.7
Mode = 1.9
b) S = 2.3952
CV = 52.64 %
Range = 6.3
c) Yes, since the average and median values are both over "acceptable" ranges.
Step-by-step explanation:
Explanation is provided in the attached document.
2| x-3| - 5 = 7 Helpp
Answer:
x = {9, -3}
Step-by-step explanation:
2| x-3| - 5 = 72| x-3| = 12| x-3| = 6x - 3 = ± 6 ⇒ x= 3+ 6= 9⇒ x= 3 - 6= -3Or it can be shown as:
x= {9, -3}Find factors of x³+12x²-19x= -20
Answer:
No Factors
Step-by-step explanation:
[tex]x^3-12x^2-19x+20 = 0\\Let \ p(x) = x^3-12x^2-19x+20[/tex]
Factors of 20 = ±1, ±2 , ±4 , ±5 , ±10 and ±20
±1, ±2 and ±3 are not the factors of given polynomial.
Putting x = 4 in the given polynomial
[tex]p(4) = (4)^3+12(4)^2-19(4)+20\\p(4) = 64+192-76+20\\p(4) = 200[/tex]
So, x = 4 is not a factor of p(x)
Putting x = -4 in the given equation
[tex]p(-4) = (-4)^3+12(-4)^2-19(4)+20\\p(-4) = -64+192-76+20\\p(-4) = 73[/tex]
So, x = -4 in the given equation
Putting x = 5 in the given equation
[tex]p(5) = (5)^3+12(5)^2-19(5)+20\\p(5) = 125+300-95+20\\p(5) = 350[/tex]
So, x = 5 is not a factor of p(x)
Putting x = -5 in the given equation
[tex]p(-5) = (-5)^3+12(-5)^2-19(-5)+20\\p(-5) = -125+300+95+20\\p(-5) = 290[/tex]
So, x = -5 is not a factor of p(x)
Putting x = 10 in the given equation
[tex]p(10) = (10)^3+12(10)^2-19(10)+20\\p(10) = 1000+1200-190+20\\p(10) = 2030[/tex]
So, x = 10 is not a factor of p(x)
Putting x = -10 in the given equation
[tex]p(-10) = (-10)^3+12(-10)^2-19(-10)+20\\p(-10) = -1000+1200+190+20\\p(-10) = 410[/tex]
So, x = -10 is not a factor of p(x)
Putting x = 20 in the given equation
[tex]p(20) = (20)^3+12(20)^2-19(20)+20\\p(20) = 8000+4800-380+20\\p(20) = 12440[/tex]
So, x = 20 is not a factor of p(x)
Putting x = -20 in the given equation
[tex]p(-20) = (-20)^3+12(-20)^2-19(-20)+20\\p(-20) = -8000+4800+380+20\\p(-20) = -2800[/tex]
So, x = -20 is not a factor of p(x)
From the above solution, we conclude that the given equation can not be factorized and thus, has no factors.
Answer:
[tex]\boxed{\mathrm{No \: factors}}[/tex]
Step-by-step explanation:
[tex]x^3 +12x^2 -19x= -20[/tex]
Add 20 on both sides.
[tex]x^3 +12x^2 -19x+20= 0[/tex]
Add 67x and 44 on both sides.
[tex]x^3 +12x^2 +48x+64= 67x + 44[/tex]
Factor left side of the equation.
[tex](x+4)(x+4)(x+4)= 67x + 44[/tex]
[tex](x+4)^3=67x+44[/tex]
Subtract 67x and 44 on both sides.
[tex](x+4)^3-67x-44=0[/tex]
Cannot be factored further.
This is a prime expression. A prime expression cannot be factored.
We cannot factor out x from the expression, there are no factors.
6th grade math, help me pleasee.
Answer:
a) 12 ft/s (12 feet per second is the rate at which she runs)
b) the tables is completed as follows:
for column 1: 12
for column 2: 24
for column 3: 36
for column 4: 48
Step-by-step explanation:
Notice that since she did 60 feet in 5 seconds, then her speed (which is defined as distance divided by the time it took to cover that distance) is: 60/5 feet/second = 12 ft/s
Now this means that for every second she runs, she covers 12 feet
Then in the first second running she covered 12 ft, after 2 seconds running, she covered 24 ft, after 3 seconds running, she covered 36 ft, after 4 seconds running, she covered 48 ft. And these values complete the requested table.
Please help. I’ll mark you as brainliest if correct!
Answer:
Since we are talking annual interest and, I assume a time period of 1 year:
The interest earned is the sum of the interest earned on the two loans separately
Let x = amount loaned at 14%
18,500-x = amount loaned at 12%
I = prt
p = x and 18500-x
r = 0.14 and 0.12
t = 1
2390 = 0.14x + 0.1(18500-x)
2390 = .14x + 1850 - 0.1x
x = 13500
x = $13,500 loaned at 14%
18500-x = $5,000 loaned at 12%
Answer:
$8,500 was loaned at 14%, and
$10,000 was loaned at 12%.
Step-by-step explanation:
Total loan: $18,500.
Part at 14%
Part at 12%
Let the part at 14% = x.
Let the part at 12% = y.
Equation of amount of loan:
x + y = 18500
x amount at 14% earns 14% of x = 0.14x interest.
y amount at 12% earns 12% of y = 0.12y interest.
Equation of interest charged:
0.14x + 0.12y = 2390
We have a system of equations.
x + y = 18500
0.14x + 0.12y = 2390
Multiply both sides of the first equation by -0.12. Write the second equation below it, and add the equations.
-0.12x - 0.12y = -2220
(+) 0.14x + 0.12x = 2390
-------------------------------------
0.02x = 170
x = 170/0.02
x = 8500
x + y = 18,500
8500 + y = 18,500
y = 10,000
Answer:
$8,500 was loaned at 14%, and
$10,000 was loaned at 12%.
A box contains 100 marbles, some of which are red and the rest blue. A sample of 10 marbles is taken randomly (with replacement) from the box and the statistic: number of red marbles in the sample is calculated. The probability model for this statistic is shown below. (Note: the probabilities should add to 1 - any difference from 1 is due to round-off errors.)
values probability
(%)
0 0.6047
1 4.0311
2 12.0932
3 21.4991
4 25.0823
5 20.0658
6 11.1477
7 4.2467
8 1.0617
9 0.1573
10 0.0105
a. Roughly, what is the shape of the probability model? Write the shape in a complete sentence
b. Calculate the center (mean) of the probability model. Use R as a calculator to calculate the mean. Write the mean in a complete sentence
c. Argue that 1.5 is a good guess for the standard deviation of the probability model. Write a brief answer
d. Suppose you repeat the experiment of sampling 10 randomly with replacement n times. Each time, you calculate the number of red marbles in your sample. Suppose you were to make a plot of the running means of the results, what would happen as n increases?
Step-by-step explanation:
a) The Roughly shape of the probability model is bell shaped or symmetric
( normal )
(b) Roughly, guess the center (mean) of the probability model
The mean is 5/10 =0.5
Because the symmetric distribution mean is middle bar and here we see using histogram 5/10 is mean .
(c) Argue that 1.5 is a good guess for the standard deviation of the probability model.
Yes 1.5 is very good guess because then it follow normal distribution it is exactly correct .
PLEASE HELP!! Write the proportion. 120 feet is to 150 feet as 8 feet is to 10 feet. (18 points!!)
Answer:
4 : 5
Step-by-step explanation:
you can divide 120 and 150 by 30 and 8 and 10 by 2.
120/30 = 4
150/30 = 5
8/2 = 4
10/2=5
Answer: 4:5
Step-by-step explanation:
can someone help me with these ones :(? (with full process)
1.) (3,2) and (4,j),m=1
2). (5,0) and (1,k),m=1/2
3).(x, 2) and (3, -4), m = 2
4). (12, -4) y (r, 2), m = -1/2
Answer:
The answers for:
j = 3k = -2x = 6r = 0Step-by-step explanation:
In order to find the value of expression, you have to apply gradient formula :
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
So for Question 1,
[tex]let \: (3,2) \: be \: (x1,y1) \\ let \: (4,j) \: be \: (x2,y2) \\ let \: m = 1[/tex]
[tex] \frac{j - 2}{4 - 3} = 1[/tex]
[tex] \frac{j - 2}{1} = 1[/tex]
[tex]j - 2 = 1[/tex]
[tex]j = 1 + 2 = 3[/tex]
Question 2,
[tex]let \: (5,0) \: be \: (x1,y1) \\ let \: (1,k) \: be \: (x2,y2) \\ let \: m = \frac{1}{2} [/tex]
[tex] \frac{k - 0}{1 - 5} = \frac{1}{2} [/tex]
[tex] \frac{k}{ - 4} = \frac{1}{2} [/tex]
[tex]k = \frac{1}{2} \times - 4 = - 2[/tex]
Question 3,
[tex]let \: (x,2) \: be \: (x1,y1) \\ let \: (3, - 4) \: be \: (x2,y2) \\ let \: m = 2[/tex]
[tex] \frac{ - 4 - 2}{3 - x} = 2[/tex]
[tex] \frac{ - 6}{3 - x } = 2[/tex]
[tex] - 6 = 2(3 - x)[/tex]
[tex] - 6 = 6 - 2x[/tex]
[tex] - 6 - 6 = - 2x[/tex]
[tex] - 2x = - 12[/tex]
[tex]x = - 12 \div - 2 = 6[/tex]
Question 4,
[tex]let \: (12, - 4) \: be \: (x1,y1) \\ let \: (r,2) \: be \: (x2,y2) \\ let \: m = - \frac{1}{2} [/tex]
[tex] \frac{2 - ( - 4)}{r - 12} = - \frac{1}{2} [/tex]
[tex] \frac{6}{r - 12} = - \frac{1}{2} [/tex]
[tex] - 1(r - 12) = 2(6)[/tex]
[tex] - r + 12 = 12[/tex]
[tex]r = (12 - 12) \div - 1 = 0[/tex]
What is the value of the fourth term in a geometric sequence for which a1 =
30 and r= 1/2
Answer:
3¾
Step-by-step explanation:
Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.
Formula for geometric sequence:
[tex] a^n = a ( n-1 ) * r [/tex]
Given:
First term, a1 = 30
ratio, r = ½
Required:
Find the fourth term
Where, the first term, a¹ = 30
Second term: a² = 30 * ½ = 15
Third term: a³ = 15 * ½ = 7.5
Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾
Therfore the fourth term of the geometric sequence is 3¾
Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = −1, g(1) = −2, and g'(1) = 3. Find h'(1). h(x) = (x2 + 8)g(x)
Answer:
[tex]h'(1) = 23[/tex]
Step-by-step explanation:
Let be [tex]h(x) = (x^{2}+8)\cdot g(x)[/tex], where [tex]r(x) = x^{2} + 8[/tex]. If both [tex]r(x)[/tex] and [tex]g(x)[/tex] are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:
[tex]h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)[/tex]
[tex]r'(x) = 2\cdot x[/tex]
[tex]h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)[/tex]
Given that [tex]x = 1[/tex], [tex]g (1) = -2[/tex] and [tex]g'(1) = 3[/tex], the derivative of [tex]h(x)[/tex] evaluated in [tex]x = 1[/tex] is:
[tex]h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)[/tex]
[tex]h'(1) = 23[/tex]
4x ≤12 dimplify solve for x
Answer:
x<3
Step-by-step explanation:
Answer:
[tex]\boxed{x\leq 3}[/tex]
Step-by-step explanation:
[tex]4x \leq 12[/tex]
[tex]\sf Divide \ both \ parts \ by \ 4.[/tex]
[tex]\displaystyle \frac{4x}{4} \leq \frac{12}{4}[/tex]
[tex]x\leq 3[/tex]
Rafael is putting money into a savings account. He starts with $350 in the savings account, and each week he adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Rafael has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 19 weeks.
Answer:
Equation: S(W) = 60W + 350
After 19 weeks, total accumulated = S(19) = 1490
Step-by-step explanation:
The interest rate is not indicated, so cannot take that into account.
Each week, he adds 60$, with initial value of 350$
So the equation is
S(W) = 60W + 350
for W = 19,
S = 60*19 + 350
S(19) = 1490
Answer:
$1490
Step-by-step explanation:
if 5 litres of water are drawn from a cylindrical container of internal diameter 56cm find the drop in the level of water in the container
Answer:
the drop in the level of water in the container is 2.03 cm
Step-by-step explanation:
The volume of a cylinder can be written as;
[tex]V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter[/tex]
the change in height when the volume changes can be derived by differentiating the equation.
[tex]dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}[/tex]
substituting the given values;
[tex]\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.[/tex]
[tex]dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm[/tex]
the drop in the level of water in the container is 2.03 cm
The sum of Jason’s age and his brother’s age is 55. Jason is 7 years younger than his brother. How old is Jason?
Answer:
Jason is 24 years old
Step-by-step explanation:
Lets say that Jason's age is X, and his brother's age is Y.
We know that X + Y = 55.
We also know that (X + 7) = Y.
This means (X + 7) + Y = 62 (We got the 62 by adding 55 and 7)
Anyway if X+7= Y, and X+7 + Y = 62, then X+7 = 62/2, right?
We divide the 62 by 2 and we get 31.
Alright, so X+7 = 31.
substract both sides by 7.
We get X = 24
Sorry if this seemed longer or more complicated than it should've been, I don't know how to explain it better.