Answer
(6/√2) = 3√2
Explanation
We are asked to simplify
6/√2
So, we will rationalize this by multiplying numerator and denominator by √2
[tex]\frac{6}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{6\sqrt[]{2}}{\sqrt[]{2}\times\sqrt[]{2}}=\frac{6\sqrt[]{2}}{2}=3\sqrt[]{2}[/tex]Hope this Helps!!!
Which of the following are true about a one-to-one function? Select all that apply.1. It graph will pass the horizontal line test2. It will always have an inverse 3. It’s graph is symmetric about the y-axis 4. It will always have either a local or maximum but not both 5. The graph will pass through point (1,1).
SOLUTION
Recall the definition of a one-to-one function
one to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets
There, the correct answers are
1. It graph will pass the horizontal line test
2. It will always have an inverse
Match each ratio of the volumes of two solids to the pair of solids it represents. 3 : 1 2r : 3h h : 4r 4r : h 4r : 3h 4 : 1
Solution
[tex]\begin{gathered} \text{ Volume of a cylinder }=\pi r^2h \\ \\ \text{ Volume of a cone =}\frac{1}{3}\pi r^2h \\ \\ \text{ Volume of a sphere }=\frac{4}{3}\pi r^3 \\ \\ \text{ Volume of hemisphere }=\frac{2}{3}\pi r^3 \end{gathered}[/tex]For 1.
[tex]\frac{\text{ Volume of a cylinder}}{\text{ Volume of a cone}}=\frac{\pi r^2h}{\frac{1}{3}\pi r^2h}=\frac{1}{\frac{1}{3}}=\frac{3}{1}=3:1[/tex]For 2.
[tex]\frac{\text{ Volume of a sphere}}{\text{ Volume of a cylinder}}=\frac{\frac{4}{3}\pi r^3}{\pi r^2h}=\frac{4r}{3h}=4r:3h[/tex]For 3.
[tex]undefined[/tex]Which statement(s) can be interpreted from the equation for an automobile cost, C(t)= 28,000(0.73) *where C(t) represents the costand t represents the time in years?Select all correct statements.A. $28,000 represents the initial cost of an automobile that appreciates 73% per year over the course of t years.B. The equation is an exponential decay equation.OC. The equation is an exponential growth equation.D. $28,000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.E. The equation is neither exponential decay nor exponential growthF. $28,000 represents the initial cost of an automobile that appreciates 27% per year over the course of years.OG $28,000 represents the initial cost of an automobile that depreciates 73% per year over the course of t years.
1) Since the value in the bracket is below 1, that indicates it is a decay exponential equation if it is greater than one, it is a growth equation
Therefore option b is correct.
2) Also, since the value in the bracket is 0.73 this implies the automobile that depreciates 27% per year over the course of t years.
Therefore option d is also correct.
Peyton go shopping she finds two shirts one cost $24.97 the other cost $13.75 she needs to know if she has enough money to buy both shirt using mental math she rounds $24.97 to $25 and add that to $13.75 to get $38.75 how does Peyton need to say to find the exact a total of 2 shirts
We know that Peyton wants to buy two shirts.
• First shirt cost $24.97.
,• Second shirt cost $13.75.
To do the mental math is ok to round $24.97 to $25, and them sum with $13.75.
However, to get the exact number, Peyton needs to subtract 3 pennies from the last amount $38.75, becuase she rounded before.
Therefore, to find the exact amount she needs to subtract 3 pennies.
A car traveled a distance of 195 miles in 390 minutes.What is the cars average rate in miles per minutes?A) 2 miles per minute b) 40 miles per minute c) 0.5 miles per minute d) 390 miles per minute
Given data
Distance = 195 miles
Time = 390 minutes
[tex]\begin{gathered} \text{Average sp}eed\text{ = }\frac{Dis\tan ce}{\text{Time}} \\ =\text{ }\frac{195}{390} \\ =0.5\text{ miles per minute} \end{gathered}[/tex]Let F(x) = f(f(x)) and G(x) = (F(x)) ^ 2 . You also know that f(3) = 2 , f(2)=3, f^ prime (2)=7 , f^ prime (3)=11
From the information given,
F(x) = f(f(x)
G(x) = (F(x))^2
F'(x) = f'(f(x)) * f'(x)
F'(3) = f'(f(3)) * f'(3)
f'(f(3)) = f'(2) = 7
f'(3) = 11
F'(3) = 7 * 11
F'(3) = 77
G'(x) = 2F(x) * F'(x) = 2f(f(x) * F'(x)
G'(3) = 2F(3) * F'(3) = 2f(f(3) * F'(3)
Given,
f(f(3) = f(2) = 3
G'(3) = 2 * 3 * 77
G'(3) = 462
Every day the ocean has two low tides and two high tides. Function g represents the height, in feet, of the water level in a cove relative to theaverage sea level. Let t represent the number of hours elapsed since the water height was equal to the average sea level after a low tide.s(e) = ssin(}t)Plot the points where s(4) is equal to the average sea level.
We can see from the question that we have the sine function, which is modeling the water level in a cove relative to the average sea level, and this function is given by:
[tex]g(t)=4sin(\frac{\pi}{6}t)[/tex]And we need to find the points where g(t) is equal to the average sea level.
1. To find it, we need to analyze the given function as follows:
2. Then we can say that the function has:
• An amplitude (the value from the ,midline of the function, in this case, x = 0,).
,• The period of the function is given by:
[tex]\begin{gathered} \text{ Period=}\frac{2\pi}{B} \\ \\ \text{ Period=}\frac{2\pi}{\frac{\pi}{6}}=2\pi(\frac{6}{\pi})=12 \\ \\ \text{ Period=}12 \end{gathered}[/tex]3. These values can be seen as follows:
4. To find the points where g(t) is equal to the average sea level, we can see that the average sea level is represented by the midline, x = 0, and from the graph, we can see that these points are points on the x-axis, and they are (6, 0), and (12, 0) for the given graph:
The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 5.9. What is the probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher? Round your percentage to 2 decimals.
Given data
*The given mean is
[tex]\mu=18.6[/tex]*The given standard deviation is
[tex]\sigma=5.9[/tex]The value of the z score is calculated as
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} z=\frac{21-18.6}{5.9} \\ =0.41 \end{gathered}[/tex]The probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher is given as
[tex]\begin{gathered} P(Z\ge21)=P(X\ge0.41) \\ =1-P(X<0.41) \end{gathered}[/tex]The corresponding probability is evaluated by the table.
Substitute the values in the above expression as
[tex]\begin{gathered} P(Z\ge21)=1-0.6591 \\ =0.34 \end{gathered}[/tex]wpn Learning. UIC 3. Solve by elimination. x + 2y = -7 x - 5y = 7 A. (-7,0) B. (-3, -2) C. (-2,-3) D. (0, -7)
x+2y=-7 ------> equation 1
x-5y=7 -------->equation 2
Change the signs in equation 2
x+2y=-7 ------> equation 1
-x+5y=-7 -------->equation 2
Add equation 1 and 2
x+2y=-7 ------> equation 1
-x+5y=-7 -------->equation 2
_________
7y=-14
y=-14/7
y=-2
Now substitute y=-2 in equation 1,
x+2(-2)=-7
x-4=-7
x=-7+4
x=-3
(x,y)=(-3,-2)
Option B is the correct answer.
ity is net ranges $% per ment plus a one time.
Answer
a) The equation that represents the amount to be paid to xinfinity for using the internet for m months is
f(m) = 75m + 50
b) If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.
Explanation
If the amount paid in total fir using the xinfinity internet for m months onths is f(m),
And xinfinity internet charges a $75 per month fee plus a one-time activation fee of $50.
a) So, if one really does use the xinfinity internet for m months, the total charge is
f(m) = (75 × m) + 50
f(m) = 75m + 50
b) If Jose uses the xinfinity internet for 10 months, we cam calculate how much he pays the xinfinity.
m = 10 months
f(m = 10) = 75 (10) + 50
= 750 + 50
= 800 dollars.
If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.
Hope this Helps!!!is f(m),
And
It is a Algebra problemSuppose an object is thrown upward with an initial velocity of 48 feet per second from a height of 120 feet. The height of the object t seconds after it is thrown is given by h(t)=-16t²+48t+120. Find the average velocity in the first two seconds after the object is thrown.
Answer
Average velocity in the first 2 seconds = 16 ft/s
Explanation
The average value of a function over an interval [a, b] is given as
[tex]\text{Average value of the function = }\frac{1}{b-a}\int ^b_af(x)dx[/tex]The integral is evaluated over the same interval [a, b]
Since we are asked to find the average velocity over the first 2 seconds, we need to first obtain the funcion for th object's velocity.
Velocity = (dh/dt)
h(t)= -16t² + 48t + 120
Velocity = (dh/dt) = -32t + 48
So, we can then find the average velocity over the first 2 seconds, that is, [0, 2]
[tex]\begin{gathered} \text{Average value of the function = }\frac{1}{b-a}\int ^b_af(t)dt \\ a=0,b=2,f(t)=-32t+48 \\ \text{Average Velocity = }\frac{1}{2-0}\int ^2_0(-32t+48)dt \\ =\frac{1}{2}\lbrack-16t^2+48t\rbrack^{2_{}}_0 \\ =\frac{1}{2}\lbrack-16(2^2)+48(2)\rbrack_{} \\ =0.5\lbrack-16(4)+96\rbrack \\ =0.5\lbrack-64+96\rbrack \\ =0.5\lbrack32\rbrack \\ =16\text{ ft/s} \end{gathered}[/tex]Hope this Helps!!!
I don't even get like what a mean and a median is can you explain?
The mean is an average of a set of numbers, where in order to calculate it, we sum all the numbers and divide by the amount of numbers.
For example, in the set {2, 5, 7, 10}, the mean is:
[tex]\frac{2+5+7+10}{4}=\frac{24}{4}=6[/tex]The median is the middle term of the set when it's put in the crescent order.
For example, in the set {4, 7, 2, 10, 5}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,4,5,7,10\mright\rbrace \\ \text{middle term}\to5 \end{gathered}[/tex]If the number of elements in the set is even, the median will be the average of the two middle terms. For example, in the set {4, 7, 2, 10, 5, 3}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,3,4,5,7,10\mright\rbrace \\ \text{middle terms}\to4\text{ and 5} \\ \operatorname{median}\to\frac{4+5}{2}=4.5 \end{gathered}[/tex]what digit is in the
Given:
[tex]\frac{13}{7}+\frac{9}{14}[/tex]Find LCM of the denominators.
LCM (7, 14)=14.
Multiply the numerator of each fraction by the LCM 14 and divide by 14.
[tex]\begin{gathered} \frac{1}{14}(\frac{14\times13}{7}+\frac{9\times14}{14}) \\ =\frac{1}{14}(2\times13+9) \\ =\frac{1}{14}(26+9) \\ =\frac{35}{14} \\ =\frac{5}{2} \end{gathered}[/tex]Therefore, the result of the sum is 5/2.
your dinner bill was $21.00 if you leave a 20% tip, how much will the tip be?
As given by the question,
There are given that the total bill was $21.00
Now,
If leave a 20% tip,
Then,
[tex]\begin{gathered} 21\times\frac{20}{100}=21\times\frac{1}{5} \\ =4.2 \end{gathered}[/tex]Hence, the tip
The survey found that women's Heights are normally distributed with a mean of 63.9 in and standard deviation 2.2 in the survey also found that men's Heights are normally distributed with mean 67.6 in. and standard deviation 3.5 in considered and executed jet that seats 6 with a doorway height of 56.4 in. a)what percentage of adult men can fit through the door without bending?b) what's a doorway height would allow 40% of men to fit without bending
Let's begin by listing out the information given to us:
Mean for women (w) = 63.9 in
standard deviation for women (sd) = 2.2 in
Mean for men (m) = 67.6 in
standard deviation for men (sd) = 3.5 in
What is (a+b) (a+b) =?What is (a+1) (a+1) = ?What is (a+3) (a+3)=?What is (x+5) ^2=?
SOLUTION:
Case: Expansion
Method:
[tex]\begin{gathered} a^2+b^2=(a+b)^2 \\ R.H.S\text{ }expansion \\ (a+b)^2 \\ (a+b)(a+b) \\ a(a+b)+b(a+b) \\ a^2+ab+ab+b^2 \\ a^2+2ab+b^2 \end{gathered}[/tex]Final answer:
FALSE
[tex]a^2+b^2\ne(a+b)^2[/tex]Write T for true or F for false. 6. The number 14 is a multiple of 4. 7. The Identity Property says that any number times 1 equals the number itself. 8. A bar diagram can be used to show 3 X 6.
In the number 6, it says the number 14 is a multiple of 4. It means there would be an integer number X which when multiplied by 4 would result in the number 14. To check it, we can perform the following calculation.
[tex]14=X\times4\to X=\frac{14}{4}=3.5[/tex]Because the value of X found is not an integer, 6. is FALSE
In the number 7, it says the Identity Property rays that any number times 1 equals the number itself. This property says that there is a number that, when multiplied by any number will always equal the number itself, and this is the number 1. From this, 7 is TRUE
Number 8 says a bar diagram can be used to show 3X6. This technique can be used to show any multiplication by an integer number. Because both. 3 and 6, are integer, 8 is TRUE
The question is in the image. Answer question 20 only.
To convert radians to degrees we use the formula:
[tex]\theta\cdot\frac{180}{\pi}[/tex]In this case the angle is 12 radians, then we have:
[tex]12\cdot\frac{180\degree}{\pi}=687.55[/tex]Therefore, the angle in degrees is 687.55°
Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence how can Mia figure out how much more she has left to paint
If Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence then she 1380 more she has left to paint
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Mia is painting a fence that is 1625 meters long
Morning she painted 245 meter of the fence
We need to find how much more she has left to paint
To find this we need to subtract 245 from 1625
1625-245
1380
Hence 1380 more she has left to paint
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there are 7 Red 3 blue and 5 green marbles in a bag what is the probability that the first three chosen will not be red?
Determine the total number of marble in the bag.
[tex]\begin{gathered} n(T)=7+3+5 \\ =15 \end{gathered}[/tex]Determine the probability for first three marbles be red.
[tex]\begin{gathered} P(R=3)=\frac{^7C_3^{}}{^{15}C_3} \\ =\frac{35}{455} \\ =\frac{7}{91} \end{gathered}[/tex]The probability for first three marble is not to be red is equal to one minus the probability for the first three marble be red.
[tex]\begin{gathered} P(R\ne3)=1-P(R=3) \\ =1-\frac{7}{91} \\ =\frac{91-7}{91} \\ =\frac{84}{91} \\ =\frac{12}{13} \end{gathered}[/tex]So answer is 12/13.
A=16xx-6use the given area to find the missing sides of the rectangle
The area of the rectangle is given as 16 units squared
The length = x
The width = x-6
The area of a rectangle is given by the formula;
A= l * w
A= x {x-6}
16 = x^2 -6x -----------form a quadratic equation as;
[tex]x^2-6x-16\text{ =0}[/tex]Find the factors of -16 that can add or subtract to give -6
The factors will be -8 and 2
Factorize the equation as ;
[tex]x^2+2x-8x-16=0[/tex][tex]x(x+2)-8(x+2)=0[/tex][tex](x+2)(x-8)=0[/tex]Finding the real values of x , take that which will result to a positive length
( x-8) = 0
x-8 = 0
x= 8 units
So ; Length = x = 8 units
Width = x- 6 = 8-6 = 2 units
Answers
Length = 8 units
Width = 2 units
Instructions: Find the missing side. Round your answer to the nearest tenth. х 38° 30 X =
Let us call the third angle in the triangle y
y = 180 - 90-38 = 52 degrees ( sum of angles in a triangle is 180 degrees)
using trigonometric ratio
[tex]\sin \text{ 52=}\frac{\text{opposite}}{\text{hypothenuse}}[/tex]opposite = x
hypothenuse = 30
[tex]\begin{gathered} \sin 52\text{ =}\frac{x}{30} \\ x=\text{ 23.64032261} \end{gathered}[/tex]To the nearest tenth x = 23.6
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
The smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
What are triangles?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.So, the measure of the smallest angle in the triangle is:
90 + 4x - 7 + 3x - 15 = 1807x + 68 = 1807x = 180 - 68x = 112/7x = 16Now,
4x - 7 = 4(16) - 7 = 57°3x - 15 = 3(16) - 15 = 33°Therefore, the smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
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please help me with this question and explain it so I can understand. thank you!
We can solve this question using trigonometric functions. Here, we use the tangent of the angle of elevation to find the height of the tree.
[tex]\begin{gathered} \tan 40^o=\frac{h}{35} \\ 0.839=\frac{h}{35} \\ 0.839\times35=h \\ 29.36=h \end{gathered}[/tex]Thus, the height of the tree is 29 feet (to the nearest foot).
The table shows the diameters in volume certain balls used for different sports. A bowling ball has an approximate volume of 5200 cm³ what is the best estimate for the diameter of a bowling ball
From the table, the value V = 5200 cm³ is between x = 21 cm and x = 22 cm.
Computing the average of the volumes associated to these x-values, we get:
V = (4,849.1 + 5,575.3)/2
V = 5212.2
which is near V = 5200 cm³. Then, the x-value related to V = 5200 cm³ is approximately the average between x = 21 and x = 22, that is:
x = (21 + 22)/2
x = 21.5 cm
please help i dont know to do it please help
Given:
0.5
Let's write the decimal in form of a fraction a/b using integers.
To write the number in fractional form, we have:
[tex]0.5=5\times10^{-1}[/tex]Since the exponent is the negative of 1, using the definition of negative exponent, we have:
[tex]5\times10^{-1}=\frac{5}{10^1}=\frac{5}{10}[/tex]Therefore, the correct fraction is:
[tex]\frac{5}{10}[/tex]ANSWER:
[tex]\frac{5}{10}[/tex]I need help to find the area of each sector. I will send the exercise
The area of the circular sector is given by:
[tex]\begin{gathered} A=\frac{r^2\theta}{2} \\ where\colon \\ r=radius=17mi \\ \theta=angle=\frac{2\pi}{3} \\ \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=\frac{(17^2)\frac{2\pi}{3}}{2} \\ A=\frac{289\pi}{3}\approx302.64 \end{gathered}[/tex]E Xº = MLLEN = 50° yº = LN = ܘ L +7cm → N
In this case, we have an isosceles triangle, in this kind of figures the height (segment that goes from the vertex E to the base) bisects the upper angle, then the angle
[tex]m=\frac{50}{2}=25[/tex]Then, the measure of the upper angle of the triangle formed to the left equals 25°, the height of the triangle forms a right angle with the base of the triangle, then the measure of the angle on the right (next to y°) equals 90°. The sum of the internal angles of a triangle always equals 180°, then we can formulate the following expression:
x° + 25° + 90° = 180°
x° + 115° = 180°
x° + 115° - 115° = 180° - 115°
x° = 65°
Then x° equals 65°
As mentioned, the height forms a right angle with the base of the triangle, then the measure of the angle y° equals 90°
The length of the side LN equals twice the length of the base of the left triangle, then we get:
LN = 2*7 = 14
Then, the length of LN equals 14 cm
Which of these describes the function graphed below? 6 2 8 6 2 8 -2 -6 -8 There is a nonlinear relationship between x and y when x is less than 1 and a linear relationship when x is greater than 1 O There is a linear relationship between x and y when x is less than 1 and a nonlinear relationship when x is greater than 1 There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0. There is a nonlinear relationship between x and y when x is less than 0 and a linear relationship when x is greater than 0
Answer
Option C is correct.
There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0.
Explanation
From the graph, we can see that at values of x less than 0, the graph indicates a very straight line that translates to a linear relationship.
But at values of x greater than 0, the graph begins to curve showing that the relationship is no longer linear.
So, option C is correct.
Hope this Helps!!!
4-Which turkey is the better deal? * Sarah Lee Turkey $6.58 per lb O Butterball Turkey $11.16 for 2 lbs 4b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
We will determine the best deal as follows:
We divide 11.16 by 2 to obtain the value per Lb, and we get that for each Lb the price is $ 5.58.
So, the best deal is Butterball Turkey at a price of $5.58 per Lb.