Recalling the laws of exponents:
[tex]a^m\cdot a^n=a^{m+n}[/tex]So, for the number 3^5 times 3^4, we have:
[tex]3^5\cdot3^4=3^{5+4}=3^9[/tex]Therefore, the answer is the option b) 3^9.
solve the problem by defining a variable and writing an equation
Randy and Wade started riding a bike at noon. Noon is 12 pm. Both of them are heading towards each other and 60km.
let
speed of wade = x
speed of Randy = 4 + x
They met each other at 1:30 pm. 12 pm to 1:30 pm is 1 hour 30 minutes(1.5 hours). Both of them will cover a total distance of 60km.
[tex]\begin{gathered} \text{speed}=\frac{dis\tan ce}{\text{time}} \\ \text{speed}\times time=dis\tan ce \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 1.5x+1.5(4+x)=60 \\ 1.5x+6+1.5x=60 \\ 3x=60-6 \\ 3x=54 \\ x=\frac{54}{3} \\ x=18\text{ km/hr} \end{gathered}[/tex]speed of wade = 18km/hr
speed of Randy = 4 + 18 = 22km/hr
you own a pet store that sells fish tank you brought a fish tank for $35 and are going to mark it up 20% what is the selling price going to be on the fish tank
If you're marking the fish tank up by 20%, it means you're looking to sell it at 120% of its original value.
Now, let's use a rule of three to calculate such percentage:
Thereby,
[tex]x=\frac{120\cdot35}{100}\rightarrow x=42[/tex]The selling price would be $42
A rectangle is bounded by the x-axis and the semicircle
y = 49 − x2 What length and width should the rectangle have so that its area is a maximum?
The length and width of the rectangle are 4.04 and 32.67 respectively for which the area is a maximum.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The rectangle is bounded by the x - axis and the semicircle y = 49 - x².
Since,
The area of rectangle with sides x and y is,
Area = x × y
A = xy
Since, The equation of the semicircle is;
y = 49 - x².
Substitute the values of y in equation (i), we get;
A = x (49 - x²)
A = 49x - x³
Now, Find the derivative and equate into zero,
A' = 49 - 3x²
A' = 0
49 - 3x² = 0
49 = 3x²
x² = 49/3
x = 7/√3
x = 7/1.73
x = 4.04
Hence, y = 49 - x²
y = 49 - (4.04)²
y = 49 - 16.3
y = 32.67
Since, The area is maximum when we can multiply x by y as;
Maximum area = 4.04 x 32.67
Maximum area = 132
Hence, The length and width of the rectangle are 4.04 and 32.67 respectively for which the area is a maximum.
Learn more about the rectangle visit:
https://brainly.com/question/25292087
#SPJ1
Which of the following is a proportion?8/10=6/83/4=12/154/6=9/126/9=8/12
To be able to determine which among the choices is a proportion, you check if each side has the same common ratio.
A. 8/10 = 6/8
Ratio: 0.80 = 0.75 (Not Proportional)
B. 3/4 = 12/15
Ratio: 0.75 = 0.80 (Not Proportional)
C. 4/6 = 9/12
Ratio: 0.67 = 0.75 (Not Proportional)
D. 6/9 = 8/12
Ratio: 0.67 = 0.67 (Proportional)
Since the ratio of each side of letter D is equal, Letter D is the one that is in Proportion.
Help me out please I don’t understand what I’m doing
Since we have the value for selling each shirt, the earnings that came from the hats sold and the total earnings we can complete equation using a linear equation in which the cost of each shirt will represent the slope and the y-intercept will be the earnings that came from the hats, like this:
[tex]5x+40=125[/tex]then clear the equation for x in order to find how many shirts were sold
[tex]\begin{gathered} 5x=125-40 \\ 5x=85 \\ x=17 \end{gathered}[/tex]5|x +1| + 7 = 38
Solve for x
Answer: No solutions
Step-by-step explanation:
[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]
However, as absolute value is non-negative, there are no solutions.
help meeeeeeeeee pleaseee !!!!!
The values of the composition of the functions are:
(f o g)(x) = -x³ - x + 1
(g o f)(x) = -x³ - x - 1
How to Determine the Composition of a Function?To find the value of the composition of a given function, the inner function is first evaluated, then the output of the inner function is then replaced into the outer function and simplified.
Given the functions:
f(x) = x³ + x + 1g(x) = -x(f o g)(x) = f(g(x))
Substitute -x for x into the function f(x) = x³ + x + 1:
f(g(x) = (-x)³ + (-x) + 1
f(g(x) = -x³ - x + 1
(g o f)(x) = g(f(x))
Substitute x³ + x + 1 for x into the function g(x) = -x:
g(f(x)) = -(x³ + x + 1)
g(f(x)) = -x³ - x - 1
Learn more about composition of function on:
https://brainly.com/question/10687170
#SPJ1
Perform a DuPont analysis on Healthy Body Nursing Home, Inc. Assume that the industry average ratios are as follows: Total margin: 3.9%
Total asset turnover: 0.5
Equity multiplier: 2.8
Return on equity: %
Using the DuPont analysis the return on equity is 5.46%.
What is the return on equity?
Return on equity is the ratio of net income to average total equity. Return on equity is an example of a profitability ratio. Profitability ratios measure the ability of a firm to generate profits using available resources.
Return on equity = net income / average total equity
Using the Dupont formula, return on equity can be determined using:
Return on equity = total margin x asset turnover x equity multiplier
Return on equity = (Net income / Sales) x (Sales/Total Assets) x (total asset / common equity)
3.9% x 0.5 x 2.8 = 5.46%
To learn more about return on equity, please check: https://brainly.com/question/27821130
#SPJ1
9. ¿Cuál es el equivalente
fraccionario
de 0.2666 ...?
Answer:
4/15
Step-by-step explanation:
4/15 = 0.26666666...
Use the cross Products Property to solve the proportions.1. 3/4 = v/142. 5/n = 16/32
1) 3/4 = v/14
v = (3 x 14) / 4
v = 42/4
v = 10.5
2) 5/n = 16/32
5(32) = n(16)
n = 5(32) / 16
n = 160/16
n = 10
A recipe uses 6 cups of flour to 1 1/10 cups of milk. If you have 2 cups of flour, how much milk should you use?
We were told that the recipe uses 6 cups of flour to 1 1/10 cups of milk. Converting 1 1/10 to improper fraction, it becomes 11/10
Let x represent the number of cups of milk that would be used for 2 cups of flour. The equations would be as shown below
11/10 = 6
x = 2
By cross multiplying, we have
2 * 11/10 = 6 * x
6x = 22/10 = 11/5
x = (11/5) / 6
If we flip 6 such that it becomes 1/6, the division sign changes to multiplication. Thus, we have
x = 11/5 * 1/6 = 11/30
Thus, 11/30 cup of milk should be used
A circle has a diameter of 12 inches. Find its exact and approximate circumference and area.
STEP 1:
We write out the formulas and the necessary values
[tex]\begin{gathered} \text{Area of circle =}\pi r^2 \\ \text{circumference of circle = 2}\pi r \\ \text{radius =}\frac{diameter}{2}=\frac{12}{2}=6\text{ inches} \end{gathered}[/tex]STEP 2
We substitute the values into the formula
[tex]\begin{gathered} \text{Area of the circle = 3.14 x 6 x 6} \\ Exactvalue=113.04\text{ square inches and Approx}imate\text{ value =113} \\ \text{circumference of the circle= 2 x 3.14 x6} \\ Exactvalue=37.68\text{ inches and approx}imate\text{ value = 38inches} \\ \end{gathered}[/tex]The radius, R, of a sphere is 5.7 cm. Calculate the sphere's volume, V.Use the value 3.14 for r, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The volume formula of a sphere is :
[tex]V=\frac{4}{3}\pi r^3[/tex]From the problem, the radius of the sphere is r = 5.7 cm
Using the formula above :
[tex]\begin{gathered} V=\frac{4}{3}(3.14)(5.7)^3 \\ V=775.3 \end{gathered}[/tex]ANSWER :
775.3 cm^3
As people are living longer and the world's population is increasing, there are more and more people ages 65 or older. In 2000, approximately 419 million people were 65 or older. By 2017, that number increased to 656 million. On the two questions below, round to the nearest tenth when relevant a. What was the absolute change in the number of people 65 or older from 2000 to 2017? b. What was the relative change in the number of people 65 or older from 2000 to 2017?
In 2000 there were 419 million people 65 or older
In 2017 there were 656 million people 65 or older
a)
To calculate the absolute change in the number of people 65 and older you have to subtract the initial number (on year 2000) from the final number (in year 2017)
[tex]656000000-419000000=240000000[/tex]The absolute change is 240millions
b)
The relative change is the percentage of change. To calculate it you have to calculate the difference between the final number and the initial number, divide the result by the initial number and multiply it by 100
[tex]\frac{240000000}{419000000}\cdot100=57.279\cong57.30[/tex]The relative change is 57.30%
A single die is rolled twiceFind the probability of rolling a 6 the first time and a 1 the second time.
Answer:
1/36
Explanation:
In a single die, the total number of outcomes = 6
• The probability of rolling a 6 the first time = 1/6
,• The probability of rolling a 1 the second time = 1/6
Thus, the probability of rolling a 6 the first time and a 1 the second time is:
[tex]\begin{gathered} =\frac{1}{6}\times\frac{1}{6} \\ =\frac{1}{36} \end{gathered}[/tex]Hi. Been out due to medical issues trying to catch-up and learn my work. Thank you in advance
The break even point is where cost is equal to revenue
cost : y = 25.96x + 22752
Revenue : y = 57.56x
Set the two equations equal to determine x
25.96x + 22752 = 57.56x
Subtract 25.96x from each side
25.96x-25.96x + 22752 = 57.56x-25.96x
22752 = 31.6x
Divide each side by 31.6
22752/31.6 = 31.6x/31.6
720 =x
Now find the value of y
y = 57.56x
y = 57.56 (720)
y = 41443.20
( 720, 41443.20)
Answer: ( 720, 41443.20)
Write the equation for a parabola with a focus at (1,-4) and a directrix at x= 2.x=?
The basic form of the equation is;
4p (x- h)= (y - k)²
where (h, k) is the vertex and p is the distance from the vertex to either of its directrix or the focus
But, focus is = (1, -4) adn directrix = 2
So, the perpendicular point is :
(1.5 , -4)
p = -0.5
Putting all the values into the formula
4p (x- h)= (y - k)²
4(-0.5)(x - 1.5) = (y - (-4)²
simplify
-2(x - 1.5) = (y + 4)²
-2(x - 1.5) = y² + 8y + 16
Divide through the equation by -2
x - 1.5 = (-1/2) y² - 4y - 8
Add 1.5 to both-side of the equation
[tex]x\text{ = -}\frac{1}{2}y^2-4y\text{ - 8 + 1.5}[/tex][tex]x=-\frac{1}{2}y^2-4y\text{ - 6.5}[/tex]Kareem wants to attend a college that will cost $13.800 for the first year. His uncle gave him a special gift of 3000 to use toward the cost. Kareem plans to attend the college in 3 years. How much must Kareem save each month to have enough for the year cost?
Kareem needs to save $13,800 in total
He already got $3000 from his uncle.
Thus, he needs $13,800 - $3000 = $10,800 more
He will need to save up $10,800 in 3 years, that is 3 x 12 = 36 months
To find the amount he must save each month, we will divide $10,800 by 36:
[tex]\frac{10,800}{36}=\$300[/tex]Answer$300find the LCD of the list of fractions 7/20, 5/15
Explanation:
First we have to find multiples of each of the denominators:
[tex]\begin{cases}20\rightarrow20,40,60,80,100\ldots \\ 15\rightarrow15,30,45,60,75,90\ldots\end{cases}[/tex]From those multiples we have to find which one is the least that is in both lists. In this case, the least number that's in both lists is 60
Answer:
LCD = 60
Which of the following correctly represents the movement on the number line for the calculation 21 - (- 15) + (- 30) ?
a- left right left
b-right left left
c- right left right
d-right right left
It is the movement on the number line is right right left
The option (d) is correct .
Given,
The movement on the number line for the calculation
21 - (- 15) + (- 30)
To find the which of the following correctly represents the movement of calculation?
Now, According to the question:
21 - (- 15) + (- 30)
21 + 15 - 30 = 6
right right left
Hence, It is the movement on the number line is right right left
The option (d) is correct.
Learn more about Number line at:
https://brainly.com/question/13425491
#SPJ1
Solve these: state whether there is no solution, one solution specify it , or infinitely many Solutions.
Step 1:
Write the two systems of equations
y = 3x = 2
3x = y - 3
Step 2:
Substitute y from the first equation into the second equation
[tex]\begin{gathered} 3x\text{ = y - 3} \\ 3x\text{ = 3x + 2 - 3} \\ 3x\text{ - 3x = 2 - 3} \\ 0\text{ = 2 - 3} \\ 2\text{ = 3} \end{gathered}[/tex]Final answer
NO SOLUTION
#8 iOrder the figures described below according to their volumes from least (on top) to greatest (on bottom).= a cylinder with 2-inch radius and 6-inch height= a cube with side length 4 inches= a rectangular prism with a length of 2 inches, a width of 3 inches, and a height of 6 inches
step 1
Find out the volume of each figure
Cylinder
The volume of a cylinder is given by
[tex]\begin{gathered} V=\pi r^2h \\ V=(3.14)(2)^2(6) \\ V=75.36\text{ in}^3 \end{gathered}[/tex]Cube
The volume of the cube is given by
[tex]\begin{gathered} V=b^3 \\ V=4^3 \\ V=64\text{ in}^3 \end{gathered}[/tex]Rectangular prism
The volume of the prism is given by the formula
[tex]\begin{gathered} V=L*W*H \\ V=(2)(3)(6) \\ V=36\text{ in}^3 \end{gathered}[/tex]therefore
The answer is
rectangular prismcubecylinderWhat the answer to this to solve the problem
Answer:
25
Step-by-step explanation:
180-88=92
92+61=123
123+30+x=180
153+x=180
x=25
Evaluate theexpression belowwhen x = = 3.<54 : 2.3 - 22Enter your answer inthe box below.
The given expression is
[tex]54\frac{.}{.}2\times3-x^2[/tex]where x=3
the dot in the expression means multiplication
substitute into the expression above we have
[tex]\begin{gathered} 54\frac{.}{.}2\times3-3^2 \\ \end{gathered}[/tex]Applying BODMAS
[tex]27\times3-3^2[/tex][tex]\begin{gathered} 81-3^2 \\ 81-9 \\ 72 \end{gathered}[/tex]Therefore the value of the expression is 72
A movie aspect ratio of 2.15:1 is shown as a letterboxed image on a TV with a width of 62.72in and a height of 35.28in what is the % of image shown on the TV
You have that the movie aspect ratio is 2.15 : 1, that is, you have following relation between width and height:
2.15/1 = 2.15 = 215%
that is, the widht is 2.15 times the height, or the width is 215% longer than height.
In order to determine what is the percentage of the image shown, you calculate the percentage that widht is more longer than height. You have a TV of 62.72 width and 35.28 in height:
62.72/35.28 = 1.77 = 177%
that is, width of TV is 1.77 times longer than height, or width is 177% longer.
Hence, on TV will be not possible to watch the complete image. And the percentage shown is of 177%.
A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation y=53 + 2x. Answer the questions below. Note that a change can be increased or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the road’s length when the crew started working?What is the change per day in the road’s length?
Given the equation:
[tex]y=53+2x[/tex]Where y represents the total length of the road (in miles), and x represents the number of days the crew has worked.
(a) What was the road’s length when the crew started working?
When the crew started working we have x = 0. Then:
[tex]\begin{gathered} y=53+2\cdot0 \\ \therefore y=53\text{ miles} \end{gathered}[/tex]The road's length is 53 miles.
(b) What is the change per day in the road’s length?
The change per day in the road's length is 2 miles/day.
In the circle below, if AB is a diameter, find the measure of arc AB.
A circle has 360°
since the diameter cuts in half the circle
The measure of the arc of half the circle (semicircle) measure arcAB is
[tex]AB=\frac{360}{2}[/tex][tex]AB=180[/tex]AB=180°
Then correct answer is
option a
which statement is true and why? & why not the others?
For this problem, we have three circles with different radii. We need to determine which circles are similar and point out the reason for our statement.
Every circle has the same shape, the only thing that sets them apart is the radii. Since we can represent the relationship between the radii as fractions, then all circles are similar. Due to this, the only correct option is the second one. "Circle 1 is similar to both circle 2 and circle 3".
what is the minimum surface area that such a box can have
Given a rectangular box with an open top and square base, the dimensions of the box are:
[tex]a\times a\times b[/tex]The volume can be calculated as:
[tex]V=a\cdot a\cdot b=a^2\cdot b[/tex]The area of the sides is:
[tex]A_L=a\cdot b[/tex]The area of the base:
[tex]A_B=a^2[/tex]There are 4 lateral sides and 1 base (the top is open), so the total surface area is:
[tex]A_{\text{total}}=4\cdot A_L+A_B=4\cdot a\cdot b+a^2[/tex]We have a fixed volume of 2048 in³, then:
[tex]\begin{gathered} a^2\cdot b=2048 \\ b=\frac{2048}{a^2} \end{gathered}[/tex]Using this result on A_total:
[tex]A_{\text{total}}=4\cdot a\cdot\frac{2048}{a^2}+a^2=\frac{8192}{a}+a^2[/tex]To find the minimum surface area, we take the derivative:
[tex]\begin{gathered} \frac{dA_{total}}{da}=-\frac{8192}{a^2}+2a=0 \\ a^3=4096 \\ a=16 \end{gathered}[/tex]Now, we calculate the minimum total area using a:
[tex]A_{\text{total}}=\frac{8192}{16}+16^2=768in^2[/tex]Dylan invested $93,000 in an account paying an interest rate of 3% compoundedquarterly. Assuming no deposits or withdrawals are made, how much money, to thenearest cent, would be in the account after 17 years?
The formula to calculate compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
[tex]\begin{gathered} A=\text{ final amount} \\ P=\text{ initial amount (principal)} \\ r=\text{ interest rate} \\ n=\text{ number of times interest applied per time period} \\ t=\text{ number of time period elapsed} \end{gathered}[/tex]The following parameters are given in the question:
[tex]\begin{gathered} P=93000 \\ r=\frac{3}{100}=0.03 \\ n=4(quarterly) \\ t=17\text{ years} \end{gathered}[/tex]We can substitute these values into the formula to calculate the final amount as follows:
[tex]A=93000(1+\frac{0.03}{4})^{4\times17}[/tex]Solving, we get:
[tex]\begin{gathered} A=93000\times1.0075^{68} \\ A=154,577.64 \end{gathered}[/tex]The amount after 17 years is $154,577.64