For (1):
[tex]\begin{gathered} 6x-10<82 \\ \text{Add 10 to both sides:} \\ 6x<82+10 \\ 6x<92 \\ \text{Divide both sides by 6:} \\ x<\frac{92}{6} \\ x<\frac{46}{3} \\ \end{gathered}[/tex]For (2):
[tex]\begin{gathered} 6x-10>-82 \\ \text{Add 10 to both sides:} \\ 6x>-82+10 \\ 6x>-72 \\ \text{Divide both sides by 6:} \\ x>-\frac{72}{6} \\ x>-12 \end{gathered}[/tex]Therefore, the solution is:
[tex]-12I need help figuring out the answer to the m2
The area of the composite figure can be solved by separating the figure into 3 portions, which are 2 identical rectangles with one rectangle.
The image of the composite figure will be shown below
Let us sketch out the image of the two identical rectangles
The formula for the area(A) of a rectangle is,
[tex]A=length\times width[/tex]where,
[tex]\begin{gathered} l=length=5m \\ w=width=2m \end{gathered}[/tex]Therefore, the area(A1) of the two identical rectangles are
[tex]\begin{gathered} A_1=2\times(5\times2)=2\times5\times2=20m^2 \\ \therefore A_1=20m^2 \end{gathered}[/tex]Let me sketch the second rectangle
Therefore, the area(A2) will be
[tex]\begin{gathered} A_2=3\times2=6m^2 \\ \therefore A_2=6m^2 \end{gathered}[/tex]Hence, the area(A) of the composite figure is
[tex]\begin{gathered} A=A_1+A_2=20m^2+6m^2=26m^2 \\ \therefore A=26m^2 \end{gathered}[/tex]Therefore, the area is
[tex]26m^2[/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
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 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
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]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
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
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!!!
A pizza restaurant has found that the probability that a customer will order thin crust is 0.4. In a random sample of 5 customers who order a pizza, find the probability that at least three of them want thin crust.
In this type of exercises, the probability of x successes on n reapeted trials in an experiment is given by the next formula:
[tex]P=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Here the nCx indicates the number of different combinations of x objects selected from a set of n objects. With the given data we can solve it easily:
p = 0.4
n = 5
x = 3
[tex]\begin{gathered} P=5\text{C3}\cdot0.4^3\cdot(1-0.4)^{5-3} \\ P=10\cdot0.064\cdot0.36 \\ P=0.2304 \end{gathered}[/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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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.
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]If I can read 1,042 words in 5 minutes. What is my reading rate in words per minute?Round your answer to the nearest whole number.
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.
Drake prepared 50 kilograms of dough in 5 hours. How many hours did Drake work if he prepared 70 kilogramsof dough at the same rate
We will determine how many hours he took to prepare 70 Kg as follows:
[tex]h=\frac{70\cdot5}{50}\Rightarrow h=7[/tex]It took him 7 hours.
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
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.
A mover brings a box up the stairs in 10 seconds. If he applied a force of 20 N over a distance 10 m on the box, calculate the power required for him to complete this action
Total work done is calculated as
[tex]\begin{gathered} \text{work}=\text{force}\times dis\tan ce \\ \text{ =20N}\times10m \\ \text{ =200 J} \end{gathered}[/tex]The power is calculated as ,
[tex]\begin{gathered} \text{Power}=\frac{work}{\text{time}} \\ \text{ =}\frac{\text{200 J}}{10\text{ sec}} \\ \text{ =20 W} \end{gathered}[/tex]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]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
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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PLEASE ANSWER QUESTION 2(1.) The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. answer: 10 yards(2.)Is the value you just wrote for the total length of the walkway a rational or irrational number? Explain.
We need to compute the hypotenuse of 4 right triangles.
The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of the right triangle.
In one of the triangles, the length of the legs are: 6 and 8 yards. Then the length of the hypotenuse is:
[tex]\begin{gathered} c^2_1=6^2+8^2 \\ c^2_1=36+64 \\ c_1=\sqrt[]{100} \\ c_1=10yd_{} \end{gathered}[/tex]In another triangle, the length of the legs are: 12 and 8 yards. Then the length of the hypotenuse is:
[tex]\begin{gathered} c^2_2=12^2+8^2 \\ c^2_2=144+64 \\ c_2=\sqrt[]{208} \\ c_2=4\sqrt[]{13}\text{ yd} \end{gathered}[/tex]In the triangle whose hypotenuse (c3) is 15 yd and one of its legs is 12 yd, the unknown is one of the legs, b, which can be computed as follows:
[tex]\begin{gathered} 15^2=12^2+b^2 \\ 225=144+b^2 \\ 225-144=b^2 \\ \sqrt[]{81}=b \\ 9=b \end{gathered}[/tex]The last triangle has legs of 9 yd and 6 yd. Its hypotenuse is:
[tex]\begin{gathered} c^2_4=9^2+6^2 \\ c^2_4=81+36 \\ c_4=\sqrt[]{117} \\ c_4=3\sqrt[]{13} \end{gathered}[/tex]Finally, the length of the walkway is:
[tex]\begin{gathered} c_1+c_2+c_3+c_4=10+4\sqrt[]{13}+15+3\sqrt[]{13}= \\ =(10+25)+(4\sqrt[]{13}+3\sqrt[]{13})= \\ =35+7\sqrt[]{13} \end{gathered}[/tex]This value is irrational because it includes and square root
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
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 number is multiplied by 6 and the product is added to 4 the sum is equal to the product of 2 and 17 find the number
A number = x
Is multiplied by 6 = 6x
And the product is added to 4 = 6x + 4
The sum is equal to the product of 2 and 17 ; 6x + 4 = 2 * 17
Solve for x
6x + 4 = 2 * 17
Combine like terms
6x = 34 - 4
6x = 30
Divide both sides by 6
6x/6 = 30/6
x = 5
Answer:
5, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
the product of 2 and 17 is 34
34 - 4 is 30
30 devided by 6 is 5
therefore, by working backwords we can figure out that this math riddle would be equal to 5 ^^
47 Dominic used the equation below to find d, the amount in dollars he would spend on gasolineto drive a distance of m miles.d =(3.5)Based on this equation, how much would Dominic spend on gasoline to drive a distance of180 miles?A $25.203.628B $21.00 - 2.94C $24.50 -343: 3.02D $28.00
Answer
Explanation
The equation that
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
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