In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
100 ÷ 74
Step 02:
Find the range of allowable values based on the given information. round to the nearest tenth. 50; can vary by 30%
The allowable values are;
[tex]35\text{ to 65}[/tex]Here, we want to get the allowable values for the given information
To do this, we need to find the percentage value
That would be;
[tex]\frac{30}{100}\times50\text{ = 15}[/tex]Now, the allowable values can be in both direction
Greater than 50 or less than 50
When greater, we add; when lesser, we subtract
Thus, we have it as;
[tex]\begin{gathered} 50-15\text{ to 50+15} \\ 35\text{ to 65} \end{gathered}[/tex]Which undefined geometric term is described as an infinite set of points that has length but not width?distancelineplanesphere
A line (option B)
Explanation:
A line contains an infinite number of points. It has no width. It is one dimentional.
A plane has is two dimentional. Hence it has awidth and length.
The correct answer is a line
The sale price S (in dollars) of an item is given by the formula S=L-rL, where L is the list price (in dollars) and r is the discount rate (in decimal form).Solve the equation for r.
ANSWER
[tex]r=1-(\frac{S}{L})[/tex]EXPLANATION
Given;
[tex]S=L-rL[/tex]To make r the subject of formula, flip the equation
[tex]rL=L-S[/tex]Divide both sides by L;
[tex]\begin{gathered} \frac{rL}{L}=\frac{L-S}{L} \\ r=\frac{L-S}{L} \\ =\frac{L}{L}-\frac{S}{L} \\ =1-\frac{S}{L} \end{gathered}[/tex]You spin the spinner twice.5243What is the probability of landing on a number less than 3 and then landing on a 5?Simplify your answer and write it as a fraction or whole number.Submit
To get the probability of an event, we need two things:
1. The total number of possibilities
2. The total number of possibilities considered favorable
For the first event A which is landing on a number less than 3, we only have one favorable possible which is landing on 2.
For the second event B which is landing on a 5, we also only have one favorable possible which is landing a 5 itself.
Now, for both events, the total number of possibilities is 4.
So, the probability of landing on a number less than 3 is 1/4 while the probability of landing on a 5 is also 1/4.
So, the probability of landing on a number lesser than 3 AND landing on a 5 is:
[tex]P(A\text{ }and\text{ }B)=P(A)\times P(B)[/tex][tex]P(A\text{ }and\text{ }B)=\frac{1}{4}\times\frac{1}{4}[/tex][tex]P(A\text{ }and\text{ }B)=\frac{1}{16}[/tex]Answer:
The probability of landing on a number lesser than 3 AND landing on a 5 on the next spin is 1/16.
Graph the equation Y =7x
The graph of the equation y =7x is shown below.
To find the slope and y-intercept, use the slope-intercept form.
y = m x + b is the slope-intercept form, where m is the slope and b is the y-intercept.
We are given y = 7x.
Determine the values of m and b using the formula y = m x + b.
m = 7
b = 0
The value of m is the slope of the line, and the value of b is the y-intercept.
Slope: 7
y-intercept: (0, 0)
Also, other ordered pairs will be (1, 7), (-1, -7), etc.
Now let's draw the graph:
Thus, the graph of the equation y =7x is shown above.
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sean is given a solution in which the population of a family of rabbits grows according to he equation....
No, the problem is not asking for
Here, we simply want to check if the method used is correct to find the number of months it will take for the population of Rabbits to be 500
The method used in this case is wrong
What should have been done is to substitute the value of 500 for y
Afterwards, we can proceed to find the value of t which is the number of months using technology
So the correct answer is the second option
Multiply Polynomials. Find the product and write answers in standard form
Step 1
Given;
[tex]5m^3(n^6)(6n^5)[/tex]Required; To multiply the polynomials
Step 2
Write the answers in standard form.
Rearrange the question and write like terms close to each other
[tex]5\times6\times n^6\times n^5\times m^3[/tex]Simplify using the following law of indices
[tex]a^b\times a^n=a^{b+n}[/tex][tex]\begin{gathered} 5\times6=30 \\ n^6\times n^5=n^{6+5}=n^{11} \\ m^3=m^3 \end{gathered}[/tex]Hence the combined answer will be;
[tex]30m^3n^{11}[/tex][tex]5m^3(n^6)(6n^5)=30m^3n^{11}[/tex]Answer;
[tex]30m^3n^{11}[/tex]A car is traveling at a steady speed. It travels 1 1/2 miles in 2 1/4 minutes. How far will it travel in 47 Minutes ? In 1 hour ?The car will travel ( blank) miles in 47 minutes (Simplify your answer. Type an integer, proper fraction, or mixed number.)
1 1/2 miles ---> 2 1/4 minutes
x miles -------> 47 minutes
[tex]\begin{gathered} x\times2\frac{1}{4}=1\frac{1}{2}\times47 \\ x\times\frac{9}{4}=\frac{3}{2}\times47 \\ \frac{9}{4}x=70.5 \\ \frac{9}{4}x\times\frac{4}{9}=70.5\times\frac{4}{9} \\ x=\frac{94}{3}=31\frac{1}{3} \end{gathered}[/tex]answer: 31 1/3 miles in 47 minutes
for 1 hour = 60 minutes
[tex]\begin{gathered} \frac{9}{4}x=\frac{3}{2}\times60 \\ \frac{9}{4}x=90 \\ \frac{9}{4}x\times\frac{4}{9}=90\times\frac{4}{9} \\ x=40 \end{gathered}[/tex]answer: 40 miles in 1 hour
Answer:
1 1/2 miles ---> 2 1/4 minutes
x miles -------> 47 minutes
answer: 31 1/3 miles in 47 minutes
for 1 hour = 60 minutes
answer: 40 miles in 1 hour
Step-by-step explanation:
Graph the inequality.3x+4y>4
Given the inequality equation below:
[tex]3x+4y>4[/tex]Find the y-intercept
[tex]\begin{gathered} set\text{ x=0} \\ 3x+4y=4 \\ 3(0)+4y=4 \\ 4y=4 \\ y=\frac{4}{4}=1 \\ y-intercept\rightarrow(0,1) \end{gathered}[/tex]Find the x-intercept
[tex]\begin{gathered} set\text{ y=0} \\ 3x+4y=4 \\ 3x+4(0)=4 \\ 3x=4 \\ x=\frac{4}{3} \\ x-intercept\rightarrow(\frac{4}{3},0) \end{gathered}[/tex]Find the shaded area
[tex]\begin{gathered} set\text{ x=0, and y=0} \\ 3x+4y>4 \\ 3(0)+4(0)>4 \\ 0+0>4 \\ 0>4\rightarrow false \\ Shade\text{ the side of the line where \lparen0,0\rparen is not includedand use dot line} \end{gathered}[/tex]Hence, the graph is
A cart weighing 200 pounds rests on an incline at an angle of 40°. What is the required force to keep the cart at rest? Round to the thousandths place.
Given:
There are given that the car weighed 200 pounds on an incline at an angle of 40 degrees.
Explanation:
To find the required force, first we need to draw the triangle.
So,
Now,
We need to find the value for x:
So,
To find the value for x, we need to use the sine function.
Then,
[tex]sin40=\frac{x}{200}[/tex]Then,
[tex]\begin{gathered} s\imaginaryI n40=\frac{x}{200} \\ x=sin40^{\circ}\times200 \\ x=128.5575 \\ x=128.558 \\ \end{gathered}[/tex]Final answer:
Henc
Answer:
128.558
Step-by-step explanation:
1. 12,5); x+y=72x-3y = 1 What are the steps
As the given lines are:
[tex]\begin{gathered} x+y=7\ldots\ldots\ldots\ldots(1) \\ 2x-3y=-11\ldots\ldots\ldots.(2) \end{gathered}[/tex]To find the system of linear equation:
multiply equation (1)by 3 and then add in equation 2:
[tex]\begin{gathered} 3(x+y)+2x-3y=3(7)-11 \\ 3x+3y+2x-3y=21-11 \\ 5x=10 \\ x=2 \end{gathered}[/tex]Now put the value of x in equation 1:
[tex]\begin{gathered} 2+y=7 \\ y=5 \end{gathered}[/tex]Stephan owns a landscaping company. Today, he is mowing three lawns: one is of an acre, one is į of an acre, and oneis 14 acres. How many acres of lawn is Stephan going to mow today? Simplify your answer and write it as a mixedfraction if necessary.21 acres
The acres of lawn mowed by Stephen is the total of the fractions of each of the mowed lawns.
Thus, we have:
[tex]\frac{1}{4}+\frac{1}{2}+1\frac{1}{3}[/tex]Simplifying the fraction above, we have:
[tex]\begin{gathered} \frac{1}{4}+\frac{1}{2}+\frac{4}{3} \\ \text{The L.C.M of 4, 2 and 3 is 12} \\ \text{Thus, we have:} \\ \frac{3+6+16}{12}=\frac{25}{12} \\ 2\frac{1}{12} \end{gathered}[/tex]Hence, the correct option is Option A.
Write the equation of a perpendicular and parallel line to the following: (in picture)
anIf we have an equation of the form
[tex]y=mx+b[/tex]then the equation of the perpendicular will be
[tex]y=-\frac{1}{m}x+c[/tex]where c is any arbitrary constant determined by the point the line must pass through,
Now in our case, we have
[tex]y=-10x+20[/tex]Therefore, the equation of the perpendicular line will be
[tex]y=\frac{1}{10}x+c[/tex]We must choose c such that the above line passes through (-2,2).
Putting in y = 2 and x = 2 from (-2, 2) gives
[tex]2=\frac{1}{10}(-2)+c[/tex][tex]2=-\frac{1}{5}+c[/tex][tex]\therefore c=\frac{11}{5}.[/tex]Hence, the equation of a line perpendicular y = -10x + 20 and passing through (-2, 2) is
[tex]y=\frac{1}{10}+\frac{11}{5}[/tex]Now we find the equation of a line parallel to y = -10x+20 and passing through (-2,2).
Now, the slope of the parallel line is the same as that of the original equation; therefore the equation for the parallel line we have is
[tex]y=-10x+k[/tex]We find k by using the point (-2,2) and substituting x = -2 and y = 2 into the above equation to get
[tex]2=-10(-2)+k[/tex][tex]2=20+k[/tex][tex]\therefore k=-18.[/tex]Hence, the equation of the parallel line is
[tex]y=-10x-18[/tex]6-4x=6x-8x-8. what does x =
Start by balancing it out.
First +4x to both sides:
6=6x-4x-8
Then +8 to both sides:
14=6x-4x
As 6x-4x=2x
14=2x
Finally, divide both sides by 2:
7=x
So, the answer is x = 7
A projectile is launched upward with a velocity of 288 feet per second from the top of a 35-foot platform. What is the maximum height attained by the projectile?
The maximum height attained by the projectile is 403.79 meters = 1324.77 feet.
The height formula has the following formula:
h = h₀ + v₀t - gt²/2
In which h₀ is the initial height, v₀ is the initial speed and g = 9.8 m/s² is the gravity.
Given, We are working with the gravity in meters, so we must convert the feet measures to meters.
Each feet has 0.3048 meters.
So 288 feet per second = 87.78 meters per second.
35 foot = 10.66 meters.
This means that:
h₀ = 10.66, v = 87.78
so,
h(t) = 10.66 + 87.78 - 4.9t²
The maximum height is attained at the moment of time in which the velocity is 0. The velocity is the derivative of the height. So:
v(t) = h'(t) = -9.8t+87.78
v(t) = 0
9.8t = 87.78
t = 8.96
The maximum height is attained at 8.96s. This height is
h(t) = 10.66 + 87.78t - 4.9t²
h(8.96) = 10.66 + (87.78×8.96) - (4.9×(8.96)²)
= 10.66 + 786.50 - 393.37
= 403.79 m
The maximum height attained by the projectile is 403.79 meters = 1324.77 feet.
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Find the difference Colton of earth that is fine for the following function
GIven:
[tex]f(x)=-5x+7[/tex]Required:
To find the value of
[tex]\frac{f(x+h)-f(x)}{h},h\ne0[/tex]Explanation:
To find the value of f(x+h) we have to substitute (x+h) in the function f(x) instead of 'x'
The simplify with the given question.
[tex]\begin{gathered} f(x+h)=-5(x+h)+7_{} \\ =-5x-5h+7 \end{gathered}[/tex]Simplifying for the value,
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-5x-5h+7-(-5x+7)}{h} \\ =\frac{-5x-5h+7+5x-7}{h} \\ =\frac{-5h}{h} \\ =-5 \end{gathered}[/tex]Final Answer:
[tex]\frac{f(x+h)-f(x)}{h}=-5[/tex]Error Analysis A store is instructed by corporate headquarters to put a markup of 11% on all items. Anitem costing $18 is displayed by the store manager at a selling price of $2. As an employee, you noticethat this selling price is incorrect. Find the correct selling price. What was the manager's likely error?The correct selling price is $ ). (Round to the nearest dollar as needed)Enter your answer in the answer box and then click Check Answer
The item cost $18 and the selling prices must aim a markup os 11%
Therefore, the selling price of this item should be 1.11*18 = $19.98
Rounding to the nearest dollar, the price should be $20
Then, the manager's likely error was doesn't display the "0" algarism for the selling price.
Rita is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of English is Fun she sells. Suppose that x and y are related by the equation 1900+110x=Y.
, if she does not sell any of English,x = The number of copies of English is Fun she sells
y = Total pay
[tex]y=1900+110x[/tex]Therefore,
a.
Her change in total pay for each copy of English is fun can be computed below.
(0, 1900) (1, 2010)
[tex]m=\frac{2010-1900}{1-0}=110[/tex]Her change in total pay for each copy of English is fun she sells = $110
b.
Her total pay if she does not sell any of English is fun is the y-intercept. Therefore,
[tex]\begin{gathered} y=1900+110x \\ y=1900+110(0) \\ y=\text{ \$1900} \end{gathered}[/tex]Her total pay if she does not sell any of English is fun = $1900
Note you can model it to the slope-intercept equation.
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{change in total pay for each copy of English is fun she sells } \\ b=\text{Her total pay if she does not sell any of English is fun} \end{gathered}[/tex]
Solve the problem. Students in a math class took a final exam. They took equivalent forms of the exam in monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by 6) - 70-20In (t.1). *20. Find Slu). 20 OSTU - 70 STO OSD- t + 1 20 0 st) SO) = -20 In
Find the derivative of S(t)=70-20ln(t+1)
[tex]\begin{gathered} \frac{dS(t)}{dt}=0-20\cdot\frac{1}{t+1}\cdot1 \\ \frac{dS(t)}{dt}=\frac{-20}{t+1} \\ \end{gathered}[/tex]The derivative is -20/t+1
I need help can u help me?
Mark has ten pens.
Kate has 5 times as many pens as mark has
Number of pen kate has = 5 (number of pens of Mark)
y is the number of Kates pen
y = 5( Number of pens of Mark)
y=5(10)
y= 5 x 10
Answer : C) y = 5 x 10
Answer:
Where is the math question?
If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a black sock as a fraction in simplest form?1/103/91/33/13
The probability of getting a black sock out of the drawer is given by the ratio between the amount of black socks in the drawer by the total amount of socks in the drawer.
We know that we have 3 black socks, now we just need to calculate the total amount of socks. We have three black, four white, two blue, and four gray socks in a drawer, then, the total is given by
[tex]3+4+2+4=13[/tex]We have a total of 13 socks in the drawer, therefore, the probability of getting a black sock out of the drawer is given by
[tex]\frac{3}{13}[/tex]And this is the fraction in the most simplified version.
Graph the function for the given domain.-2x - 10y = 10 , D: (-5, 0, 5, 10)
In order to graph the function, we need first to find the coordinates of the points. To do so, we need to apply the values of x given in the domain and calculate the corresponding values of y. So we have that:
[tex]\begin{gathered} x=-5\colon \\ -2\cdot(-5)-10y=10 \\ 10-10y=10 \\ -10y=0 \\ y=0 \\ \\ x=0\colon \\ -2\cdot(0)-10y=10 \\ -10y=10 \\ y=-1 \\ \\ x=5\colon \\ -2\cdot(5)-10y=10 \\ -10-10y=10 \\ -10y=20 \\ y=-2 \\ \\ x=10\colon \\ -2\cdot(10)-10y=10 \\ -20-10y=10 \\ -10y=30 \\ y=-3 \end{gathered}[/tex]So the points are (-5, 0), (0, -1), (5, -2) and (10, -3).
Graphing these points, we have that:
Write in form y=mx+b-3y = -6x - 24
Let's solve the equation for y:
[tex]\begin{gathered} -3y=-6x-24 \\ y=\frac{-6x-24}{-3} \\ y=\frac{-6x}{-3}-\frac{24}{-3} \\ y=2x+8 \end{gathered}[/tex]Therefore we have:
[tex]y=2x+8[/tex]For this equation we have that the slope is 2 and the y-intercept is 8.
Find the slope intercept equation of the line that has the given characteristics. Slope 1.3 and y intercept (0,-6)
We want to find the equation of the line in slope intercept form with the following values.
Slope = 1.3 and y-intercept ( 0, -6)
The equation of a line with slope m and y intercept (0,c) is;
[tex]y=mx+c[/tex]Thus, the equation of the line is;
[tex]y=1.3x-6[/tex]I’m stuck I don’t know what I’m doing at all help me out??
Point: (x,y) = (-4,8)
We have to graph the point and set a vertical line.
Line equation:
x= -4
For any value of x, it always will be -4.
7. Quinn had 3 more than two times the number of marbles Rowan has. Together they have 77marbles. How many marbles does each child have?
Explanation:
Let the number of marbles Rowan has = x
Two times x = 2x
3 more than two times the number of marbles Rowan has = 2x + 3
Quinn = 2x + 3
Together they have = 77 marbles
Rowan marbles + Quinn marbles = 77
x + (2x + 3) = 77
x + 2x + 3 = 77
Collect like terms:
3x = 77-3
3x = 74
Divide through by 3:
x = 74/3
x = 24.7
Melissa and brain are at the base of a mountain.melissa hikes to a location 27 meters above sea level.brain hikes to a location 21 meters below sea level. what us the diffrence if the hikers altitudes?
The point at the base of the mountain is described as point zero, that is they are still at sea level. If Melissa now moves to a position 27 metres above sea level, that is positive 5, assuming we are now measuring along a vertical number line. Brian however moves to a location which is 21 metres below sea level, or negative 21 along the vertical number line. Since we are measuring distances, the distance from point zero to both hikers' new position will be measured in absolute values only, that is both distances will be measured as positive.
Hence the distance between Melissa and Brian is;
Distance = 27 + 21
Distance = 48
The difference in altitude between both hikers is 48 metres
A grain bin is in the combined shape of a right cylinder and right cone, both of which have diameters of 10 feet.(a) Find the volume of the cylindrical portion of the bin to the nearest cubic foot.(b) Find the volume of the conical portion of the bin to the nearest cubic foot.(c) The bin is to be filled completely with dry corn that weighs 45 lbs per cubic foot. Of there are 2,000 pounds per ton, how many total tons of corn can be placed in the bin?
ANSWER :
a. 628 cubic foot
b. 52 cubic foot
c. 1.17 ton
EXPLANATION :
The volume formula of a cylinder is :
[tex]V=\pi r^2h[/tex]The volume formula of a cone is :
[tex]V=\frac{1}{3}\pi r^2h[/tex]From the problem, we have a diameter of 10 ft, so the radius is r = 5 ft
Cylinder's height is 8 ft and cone's height is 2 ft
a. volume of cylinder part :
[tex]\begin{gathered} V=\pi(5)^2(8) \\ V=628ft^3 \end{gathered}[/tex]b. volume of cone part :
[tex]\begin{gathered} V=\frac{1}{3}\pi(5)^2(2) \\ V=52ft^3 \end{gathered}[/tex]c. The combine volume is 628 + 52 = 680 cubic foot
A dry corn weighs 45 lbs per cubic foot.
That will be :
[tex]52ft^3\times\frac{45lbs}{ft^3}=2340lbs[/tex]There are 2000 pounds per ton, so that will be :
[tex]2340lbs\times\frac{1ton}{2000lbs}=1.17ton[/tex]If four friends collected 9 1/3 bags of treats and shared them among themselves equally,how many bags of treats did each person get?
It is given that four friends collected 9 1/3 bags of treats.
[tex]9\frac{1}{3}=\frac{28}{3}\text{ bags}[/tex]Now 28/3 bags divided equally among 4 friends will be:
[tex]\frac{\frac{28}{3}}{4}=\frac{28}{12}=\frac{7}{3}=2\frac{1}{3}\text{ bags}[/tex]Hence the total number of bags that each person will receive is 7/3 bags or 2 1/3 bags.
You have 3 black cups, 10 Green cups, 9 purple cups, and 19 gray cups. what is the ratio between purple and green cups?
We chave 9 purple cups and 10 green cups, so we can write the ratio between purple and green cups as 9:10 or "9 to 10".
Answer: 9:10