The given expression is
[tex]x^{10}[/tex]The side of the square is the square root of the are
[tex]s=\sqrt[]{x^{10}}=x^{\frac{10}{2}}=x^5[/tex]Hence, the answer is B.Find the derivative of the function at the given numberf(x)=x^2 - 5 when x=3 using the difference quotient f(x+h) - f(x) over h
Derivative
Given a function f(x), the derivative of f(x) in a point x = a can be found by using the definition:
[tex]f^{\prime}(a)=\lim _{h\to0}\frac{f(a+h)-f(a)}{h}[/tex]Given:
[tex]\begin{gathered} f(x)=x^2-5 \\ a=3 \end{gathered}[/tex][tex]\begin{gathered} f^{\prime}(3)=\lim _{h\to0}\frac{f(3+h)-f(3)}{h} \\ f^{\prime}(3)=\lim _{h\to0}\frac{(3+h)^2-5-(3^2-5)}{h} \end{gathered}[/tex]Operating:
[tex]\begin{gathered} f^{\prime}(3)=\lim _{h\to0}\frac{9+6h+h^2-5-4}{h} \\ f^{\prime}(3)=\lim _{h\to0}\frac{6h+h^2}{h} \\ \text{Factoring:} \\ f^{\prime}(3)=\lim _{h\to0}\frac{h(6+h)}{h} \\ \text{Simplifying:} \\ f^{\prime}(3)=6 \end{gathered}[/tex]Pure sounds produce single sine waves on an oscilloscope. Find the amplitude and period of the sine wave graph. On the vertical scale, each square represents 0.5; on the horizontal scale, each square represents 30° or pi/6.
To solve the question, we will need to understand some definition
PERIOD: The period is the time it takes for one complete cycle of a harmonic oscillation
AMPLITUDE: The amplitude is the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
To find the amplitude, we will have to count how many boxes there are from the equilibrium or mean position on the vertical axis and then multiply by 0.5.
The number of boxes is 8
Therefore, the amplitude will be
[tex]\begin{gathered} 0.5\times8=4 \\ =4 \end{gathered}[/tex]Amplitude = 4 units
For the period, we will have to count the number of boxes within one period
There are four boxes within one period. Since we know that each box on the horizontal axis is 30 degrees
or pi/6
The period will be
[tex]\begin{gathered} 30^0\times4=120^0 \\ or \\ \frac{\pi}{6}\times4=\frac{2}{3}\pi \end{gathered}[/tex]The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 24 minutes of calls is $21.64, and the remaining credit after 55 minutes of calls is $17.30 . What is the remaining credit after 79 minutes of calls?
Given data:
The credit that remains after 24 minutes is $21.64.
The credit that remains after 55 minutes is $17.30.
The expression for the equation is,
[tex]\begin{gathered} y-21.64=(\frac{17.30-21.64}{55-24}(x-24) \\ y-21.64=-0.14x+3.36 \\ y=-0.14x+25 \end{gathered}[/tex]Substitute 79 for x in the above expression.
[tex]\begin{gathered} y=-0.14(79)+25 \\ =13.94 \end{gathered}[/tex]Thus, the credit that remains after 79 minutes is $13.94.
Tom wants to open a store that sells hats. He thinks he can sell them for $20 each. He estimates his monthly expenses to be $3000, and it will cost him $8 for each hat. Tom wants to analyze his estimated revenues and expenses to see how many hats he would need to sell each month in order to break even. He uses x to represent the number of hats and y to represent the total dollars. If Tom sells 250 hats, he will break even. How many hats does Tom need to sell each month to make a profit of $1,200?
We have to model the profit for his business.
The fixed cost is $3000.
The variable cost is $8 per hat and the price is $20 per hat.
Let x be the number of hats sold, then we can model the profit y as:
[tex]\begin{gathered} y=20x-8x-3000 \\ y=12x-3000 \end{gathered}[/tex]We have to calculate the number of hats x for a profit y = 1200.
We can do it as:
[tex]\begin{gathered} y=1200 \\ 12x-3000=1200 \\ 12x=1200+3000 \\ 12x=4200 \\ x=\frac{4200}{12} \\ x=350 \end{gathered}[/tex]Answer: to make a profit of $1200 he needs to sell 350 hats.
The function P(t) = 1001.05)×
we have the function
P(t)=100(1.05^t)
For the year 2010
t=2010-1992=18 years
substitute
P(t)=100(1.05^18)
P(t)=240.66 -------> is in thousands
so
P(t)=240,660
therefore
the answer is'option B (241,000)Priya and Mai used the diagram below to find the value of 1/3 ÷ 4
1) Examining both diagrams, we can state that both diagrams represent
The value of
Prya's:
1/3 : 4
Mai's
1/4 x 3
Fill in the blanks below with the correct units. (a) Lamar went skiing on a mountain that is about 3 ? (b) To wash his car, Omar used 20 ? of water. (c) Melissa ate an apple that had a mass of about 150 ?
Solution:
a) Lamar went skiing on a mountain that is about 3 kilometers high. This is because the other units are too small to measure the height of a mountain.
b) To wash his car, Omar used 20 liters of water. This is because 20 milliliters of water is too small to wash a car.
c) Melissa ate an apple that had a mass of about 150 grams. An apple can not be as heavy as 150kg.
Graph the line: 3/4y -2x=6
Given the equation of the line:
[tex]\frac{3}{4}y-2x=6[/tex]To graph the line, we need two points lying on the line
We will graph the line with the help of the intercepts
when x = 0
[tex]\begin{gathered} \frac{3}{4}y=6 \\ y=\frac{4\cdot6}{3}=\frac{24}{3}=8 \end{gathered}[/tex]so, the y-intercept = (0, 8)
When y = 0
[tex]\begin{gathered} -2x=6 \\ x=\frac{6}{-2}=-3 \end{gathered}[/tex]So, the x-intercept = (-3, 0)
The line passes through the points (-3, 0) and (0, 8)
The graph of the line will be as shown in the following picture:
Write each fraction in simplest form. Write simplified if the fraction is already in simplest form. 18/27 a. 6/9b. 2/3c. 1/3d. simplified
Answer:
b. 2/3
Explanation:
Given the fraction:
[tex]\frac{18}{27}[/tex]We can write each of the numbers as a product below:
[tex]\frac{18}{27}=\frac{2\times9}{3\times9}[/tex]Next, cancel the common number, 9:
[tex]\frac{18}{27}=\frac{2\times\cancel{9}}{3\times\cancel{9}}=\frac{2}{3}[/tex]The simplified form of the fraction is 2/3.
Option B is correct.
Hi, can you help me to solve this problem please!
Given,
The function is,
[tex]g(x)=x^2+10x+6[/tex]Taking x = a - 7 then,
[tex]\begin{gathered} g(a-7)=(a-7)^2+10(a-7)+6 \\ =(a^2-14a+49)+10a-70+6 \\ =a^2-14a+10a+49-70+6 \\ =a^2-4a-15 \end{gathered}[/tex]Hence, the function is f(a-7) = a^2-4a-15.
y=2log(x)-8find the inverse of this function
Replace the variable y with x and varaible with y.
[tex]x=2\log (y)-8[/tex]Simplify the equation for y.
[tex]\begin{gathered} x=2\log y-8 \\ x+8=2\log y \\ \log y=\frac{x+8}{2} \\ y=10^{\frac{x+8}{2}} \end{gathered}[/tex]So inverse of the function is,
[tex]y=10^{\frac{x+8}{2}}[/tex]The formula v= 42.5r can be used to estimate the maximum safe velocity, v, in miles per hour, at which a car can travel if it is driven along a curved roadius of curvature r in feet. Find the maximum safe speed to the nearest whole number if a cloverleaf exit on an expressway has a radius of curvature of 290
Given:
[tex]\begin{gathered} V\text{ = 42.5r} \\ where\text{ V = maximum safe velocity} \\ r\text{ = radius of curvature} \end{gathered}[/tex]To find:
the maximum safe speed when the radius of curvature is 290
To determine the velocity, we will substitute the values into the formula:
[tex]\begin{gathered} V\text{ = 42.5\lparen290\rparen} \\ \\ V=\text{ 12325 miles per hour} \end{gathered}[/tex]Using the unit rate of $996,596/min calculate how much money is spent:1. in one hour2. in one day3. in one month (use average of 30 days)4. in one year *The numbers have to be rounded
Given:
Unit rate = $996,596/min
Let's calculate how much money is spent.
1) In one hour:
Given:
60 minutes = 1 hour
Thus, the amount spent in one hour will be:
[tex]\frac{996596}{1\min }\ast60=59795760[/tex]Therefore, the amount spent in one hour is $59,795,760
2) In one day:
Given:
1 day = 24 hours
Convert 24 hours to minutes
24 hours = 60 x 24 = 1440 minutes
The amount spent in one day will be:
[tex]996596\ast1440=1435098240[/tex]Therefore, the amount spent in one day is $1,435,098,240
3) In one month (30 days):
Given:
30 days = 30 * 24 hours * 60 mins = 43200 minutes
The amount spend in one month will be:
[tex]996596\ast43200=43052947200[/tex]Therefore, the amount spent in one month is $43,052,947,200
4. In one year:
Given:
One year = 12 months * 30 days * 24 hours * 60 mins = 518,400 mins
The amount spent in one year will be:
[tex]996596\ast518400=516635366400[/tex]Therefore, the amount spent in one year is $516635,366,400
Microwave oven has a list price of $125.50. Chain discount is 40/20. What is the netprice?
From the statement, we know that a microwave oven:
• has a list price of $125.50,
• and a chain discount of 40/20.
The net price of the microwave with the chain discount is:
[tex]NP=LP\cdot(1-d_1)\cdot(1-d_2)\text{.}[/tex]Where:
• NP is the net price,
,• LP is the list price,
,• d_1 is the first discount in decimals,
,• d_2 is the second discount in decimals.
In this case, we have:
• LP = $125.50,
,• d_1 = 40/100 = 0.4,
,• d_2 = 20/100 = 0.2.
Replacing these data in the formula above, we get:
[tex]NP=\text{ \$125.50 }\cdot(1-0.4)\cdot(1-0.2)=\text{ \$125.50 }\cdot0.6\cdot0.8=\text{ \$60.24.}[/tex]Answer
The net price is $60.24.
Which expression can be placed on the left side of the equation so that thecompleted equation will have no solutions?____________=5x -3
Given:
RHS of equation
[tex]=5x-3[/tex]Required:
Which expression can be placed on the left side of the equation so that the
completed equation will have no solutions?
Explanation:
We will go lpyion 3
Now,
[tex]\begin{gathered} 5(x+2)=5x-3 \\ 5x+10=5x-3 \end{gathered}[/tex]Answer:
Hence, required solution is above.
hello, there can help me with this question.A grove of redwood tree has an estimated 3,400,000 board feet of lumber at thestart of 2022. If redwoods grow at an exponential rate of 9% each year, then whatwould be the growth formula? Within which year will the grove reach one billion boardfeet of lumber?
Answer:
Explanation:
a) Firstly, we want to write the growth formula
We have the general form as:
[tex]L\text{ = I\lparen1 + r\rparen}^t[/tex]where:
L is the estimated board feet of lumber
l is the is the initial estimated board feet of lumber (the initial estimated board feet of lumber in 2022)
r is the percentage rate of increase which is 9% (9/100 = 0.09)
t is the number of years to reach the estimated board feet of lumber
With respect to the question given, we have the formula as:
[tex]\begin{gathered} L\text{ = 3,400,00\lparen1 + 0.09\rparen}^t \\ L\text{ =3,400,000\lparen1.09\rparen}^t \end{gathered}[/tex]b) We want to get the value of t when L is 1 billion
Substituting the values, we have it that:
[tex]\begin{gathered} 1000000000\text{ = 3400000\lparen1.09\rparen}^t \\ divide\text{ both sides by 3,400,000} \\ 294.12\text{ = 1.09}^t \\ ln\text{ 294.12 = tln 1.09t } \\ t\text{ = }\frac{ln\text{ 249.12}}{ln\text{ 1.09}}\text{ = 66 years} \end{gathered}[/tex]In 66 years (2088) , the groove will reach one billion board feet of lumber
I need help with this problem. None of the above is a answer as well it just doesn’t pop up.
Given the following radical:
[tex]\sqrt{64}[/tex]We will find the principal square root which will be the positive value of the root
As we know, 64 = 8 x 8
So, the principal square root = 8
So, the answer will be: 3 only
if one face of a die has an area of 144 square centimeters. find the volume of the die
what is the midpoint of line segment EF if E (-5,-1) and F (17,-9)?
STEP 1:
The formula for the midpoint of a line segment
[tex]\text{midpoint =(}\frac{x_{1\text{ }}+x_2}{2}),\text{ (}\frac{y_1+y_2}{2})[/tex]STEP 2:
We substitute the following information in the formular.
[tex]\begin{gathered} x_1=\text{ -5} \\ x_2=\text{ 17} \\ y_1=\text{ -1} \\ y_2=\text{ -9} \end{gathered}[/tex][tex]\begin{gathered} \text{midpoint = (}\frac{-5+17}{2}\text{),(}\frac{-1+(-9)}{2}\text{)} \\ \text{midpoint =(}\frac{12}{2}\text{),(}\frac{-10}{2}\text{)} \\ \text{midpoint = 6,-5} \end{gathered}[/tex]In conclusion, midpoint is 6,-5
If n(A)=10, and n(B)=24, and n(A u B)=25, what do you know about n(A n B)?
Let's make a diagram to represent the situation
According to the problem, the union of A and B has 25 elements, which means there are 25 elements in total.
Then, we have 10 elements in A and 24 elements in B. Let's use the following formula
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]Let's replace the given values and solve for the intersection.
[tex]\begin{gathered} 25=10+24-n(A\cap B) \\ n(A\cap B)=10+24-25=9 \end{gathered}[/tex]Hence, the number of elements in the intersection is 9.Your chores for the week are to cut the grass, wash the car, clean your room, clean the garage, and shine your shoes. You are to do 1 chore each day from Monday through Friday. You can do each chore on whatever day you want, except that you must wash the car either Thursday or Friday. In how many different orders can you perform your chores?
The chores
cut the grass
wash the car -- Thursday or Friday
clean your room
clean the garage
shine your shoes
We have 5 days in the week to do the chores.
[tex]\begin{gathered} 2*\mleft(4*3*2*1\mright)=48 \\ \end{gathered}[/tex]You can perform the chores in 48 different orders
GPAs at CCSU are normally distributed with a mean of 2.27 and a standard deviation of 0.59. Find the z-score for a GPA of 3.
GIVEN:
We are given the following data and measures of central tendency;
[tex]\begin{gathered} Mean(\mu)=2.27 \\ \\ Standard\text{ }deviation(\sigma)=0.59 \\ \\ GPA(x)=3 \end{gathered}[/tex]Required;
To find the z-score for a GPA of 3.0
Step-by-step solution;
The z-score will be determined by the formula;
[tex]z-score=\frac{x-\mu}{\sigma}[/tex]We now substitute the values and we have;
[tex]\begin{gathered} z-score=\frac{3-2.27}{0.59} \\ \\ z-score=\frac{0.73}{0.59} \\ \\ z-score=1.23728813559 \\ \\ z-score\approx1.237 \end{gathered}[/tex]ANSWER:
The fourth option is the correct answer.
[tex]1.237[/tex]Round all answers to the nearest hundredth.Solve for the radius. r= Determine which value to use for the height.h= Solve for the Volume. V=
Given:
A figure of a cone
Required:
1. Find the radius and round it to the nearest hundredth
2. Determine which value to use for the height.
3. Volume of the cone.
Explanation:
Using Pythagoras Theorem
[tex]undefined[/tex]Determine whether the following sequence is arithmetic, geometric, or neither.1, 4, 9, 16, ...neithergeometricarithmetic
Answer : neither
Explanation:
There is no common ratio or common difference between the values.
Common difference
16-9 = 7
9-4= 5
4-1= 3
Common ratio
16/9 =16/9
9/4= 2.25
4/1 = 4
What is 16/12 reduced?16/121 2/61 1/31 4/12
Explanation
Step 1
numerator and denominator divided by 2
[tex]\begin{gathered} \frac{16}{12} \\ \frac{16}{12}\rightarrow\frac{16\colon2}{12\colon2}\rightarrow\frac{8}{6} \\ \text{again, divide by 2} \\ \frac{8}{6}\Rightarrow\frac{8\colon2}{6\colon2}\Rightarrow\frac{4}{3} \\ \frac{16}{12}=\frac{4}{3} \end{gathered}[/tex]and
so,the answer is
[tex]\frac{4}{3}=1\frac{1}{3}[/tex]I hope this helps you.
Evaluate each expression using the Order of Operations. 3. (122 – 48) x 2
The given expression is
[tex](122-48)\times2[/tex]First, we subtract.
[tex]74\times2[/tex]Then, we multiply.
[tex]148[/tex]Hence, the answer is 148.Which point does not lie on the circle with center (0,0) and radius 10? A. (6,8) B. (0, 10) C. (10,-8) O D. (-8, 6)
Answer:
C. (10, -8)
Explanation:
The equation of a circle is given as:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{Centre}=(h,k) \\ \text{Radius}=r \end{gathered}[/tex]Given a circle with centre (0,0) and radius 10, its equation is:
[tex]\begin{gathered} x^2+y^2=10^2 \\ x^2+y^2=100\ldots(1) \end{gathered}[/tex]To determine the point that does not lie on the circle, we check the point that does not satisfy the equation (1) derived above:
• Point (6,8)
[tex]\begin{gathered} x=6,y=8 \\ 6^2+8^2=100 \\ 36+64=100 \\ 100=100 \end{gathered}[/tex]• Point (0,10)
,•
• Point (10, -8)
[tex]\begin{gathered} x=10,y=-8 \\ 10^2+(-8)^2=100 \\ 100+64=100 \\ 164\neq100 \end{gathered}[/tex]It is clear that point (10,-8) does not lie on the circle since the outcome is False.
The correct choice is C.
The profit when selling 'x pairs of shoes is defined by the function P(x) = 6x2 – 60x + 126. How many pairs of shoes should be sold to maximize the profit? 04 pairs of shoes O 7 pairs of shoes 6 pairs of shoes O 5 pairs of shoes
Hello!
We have a quadratic equation:
[tex]P(x)=6x^2-60x+126[/tex]As the coefficient a is positive, the concavity of the parabola will face upwards (so it will have a minimum point).
Look at the graph below:
Now, let's analyze the graph and the alternatives:
• when x = 5, profit is as small as possible
when x = 4 or x = 6, the profit
The line through (2, -1) and parallel to x - 2y = 6 has the equation:
1) Parallel lines have the same slope. So our new slope has the slope m=1
Looking at the options, we have two options with the same slope. So let's test them x-2y=4 and x+2y=0 plugging in the point to verify
(2,-1)
x+2y=0
-1+2(2) = 0
3 = 0 False
x- 2y =4
2 -2(-1) =4
2+2=4
2) So x -2y =4 and x+2y=0 are parallel to x-2y=6
But only x -2y =4 passes through the point (2,-1)
x-2y=4 is the answer
What expression can be used to subtract 2/3 - 4/9A. 8/12 - 4/12B. 2/12 - 4/12C. 2/9 - 4/9D. 6/9 - 4/9
What expression can be used to subtract 2/3 - 4/9?
Lowest Common Mutiple of 3 and 9 = 9
6/9 - 4/9 (D)