8241 ÷ 173
173 will go into 8241 47 times an we will have a remainder of 110
So, it will be written as;
8241 ÷ 173
[tex]=47\text{ }\frac{110}{173}[/tex]Graph the line that passes through the point: (-1,-4) and who's slope is -2
The equation of the line is y = -2x -6.
We have,
The line passes through the point (-1, -4)
The slope of the line is -2.
The equation of the line when it passes through the point [tex](x_{1} ,y_{1} )[/tex] and has slope m is given by
[tex]y -y_{1} =m(x -x_{1} )[/tex]
Now, putting these values in the general equation of the line, we get,
y - (-4) = -2[ x -(-1) ]
y +4 = -2 [ x +1 ]
y +4 = -2x -2
y +2x = -2 -4
y +2x = -6
y = -2x -6
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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.
Thaddeus models the number of hours of daylight in his townas
We have the following function
[tex]D(t)=2.5\sin\frac{\pi t}{6}+12[/tex]The maximum and minimum of that function happens when sin(x) = 1 or sin(x) = -1, respectively.
Then let's find the maximum, that happens when the sin value is 1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot1+12 \\ \\ D(t)=2.5+12 \\ \\ D(t)=14.5 \end{gathered}[/tex]And the minimum, when sin value is -1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot(-1)+12 \\ \\ D(t)=-2.5+12 \\ \\ D(t)=9.5 \end{gathered}[/tex]Then the least: 9.5 hours; greatest: 14.5 hours.
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
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
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]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]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.
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
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.
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.
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]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
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:
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
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!!!
Here is a linear equation: y=1/4x+5/41. Are (1, 1.5) and (12,4) solutions to the equation?A. Both (1, 1.5) and (12,4) are solutions to the equation.B. Neither (1, 1.5) and (12,4) are solutions to the equation.C. (1, 1.5) is a solution but (12,4) is not.D. (12,4) is a solution to the equation but (1, 1.5) is not.Explain your reasoning.3. Find the x-intercept of the graph of the equationExplain or show your reasoning.
To find if any given point is a solution for the linear equation, simply plug in the x and y values given and check if the equality stands, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (1,1.5) \\ \rightarrow1.5=\frac{1}{4}(1)+\frac{5}{4}\rightarrow1.5=\frac{6}{4}\rightarrow1.5=1.5✅ \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (12,4) \\ \rightarrow4=\frac{1}{4}(12)+\frac{5}{4}\rightarrow4=3+\frac{5}{4}\rightarrow4=4.25✘ \end{gathered}[/tex]Thereby the answer is:
C. (1, 1.5) is a solution but (12, 4) is not
Now, to find the x-intercept just make y = 0 and clear x, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ \rightarrow0=\frac{1}{4}x+\frac{5}{4}\rightarrow0=\frac{x+5}{4}\rightarrow0=x+5\rightarrow-5=x \\ \rightarrow x=-5 \end{gathered}[/tex]Therefore, the x-intercept is -5
Write 62° 21´ 47´´ as a decimal to the nearest thousandth. 62.413°62.366°62.363°62.373°
The given number is °:
[tex]62\degree21^{\prime}47^{\doubleprime}[/tex]To write it as a decimal, start by placing the integer part the same, now to find the decimal part, let's take the minutes 21' and divide it by 60 (because there are 60 minutes in 1°):
[tex]\frac{21^{\prime}}{60}=0.35[/tex]Now, let's divide the seconds 47" by 3600 (because there are 3600 seconds in 1°):
[tex]\frac{47^{\doubleprime}}{3600}=0.013[/tex]Thus, the number is:
[tex]62\degree+0.35\degree+0.013\degree=62.363\degree[/tex]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
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.
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
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).
Juan's office had already recycled 24 kilograms this year before starting the new recycling
plan, and the new plan will have the office recycling 1 kilogram of paper each week. After
16 weeks, how many kilograms of paper will Juan's office have recycled?
kilograms
Answer:
40kg
24+16=40kg
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]A rectangle has a width of 50 centimeters and a perimeter of 208 centimeters. What is the rectangle's length?The length is cm.
The perimeter of a plane figure is the distance around it.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the information given,
Perimeter = 208 cm, Width = 50 cm
Therefore,
208 = 2(length + 50)
By dividing both sides of the equation by 2, it becomes
104 = length + 50
length = 104 - 50
length = 54 cm
Length of rectangle is 54 cm
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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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]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 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
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°