If 36 identical motors are installed in a drying oven on blowers for that oven and the total current for all 36 motors is 85 amps, what is the approximate current for each motor? Round your answer to two decimal places.
Step 1:
Given data
Number of identical motors = 36
Total current for all 36 motors = 85 amps
Step 2: Calculate current for each motor
If the total current in all 36 motors = 85 amps
To find the current in 1 motor, you will divide the total number of current with the total number of motors.
Step 3: Final answer
[tex]\begin{gathered} \text{Current for each motor = }\frac{Total\text{ current}}{\text{Total number of motors}} \\ =\text{ }\frac{85}{36} \\ =\text{ 2.36 amps/motor} \end{gathered}[/tex]Current for each motor = 2.36 amps/motor
hello I was trying to do this question on my own for a while and haven't gotten the answer I need but hopefully you can help me and thank you for your time
given diameter (D) of wheel = 24 in rotation of wheel 455 rpm
circunference (C) = π⋅D
[tex]\begin{gathered} C=\pi\times24\text{ in } \\ C=\pi\times\frac{24}{12}=\pi2\text{ ft/r} \end{gathered}[/tex]455 rpm x 60 = 27300 r/h
27300 x 2π = 54600π ft/h
5280 ft = 1 mile
[tex]\frac{54600\pi}{5280}=10.34\pi[/tex]or 10.34 π mph
Is Rashida’s work correct? If not, what is the first step where Rashida made a mistake?- Her work is correct - First mistake was in Step 1- First mistake was in Step 2- First mistake was in Step 3*pls help!*
Answer:
First mistake was in Step 1
Explanation:
If f(x) = x² - |x| and we find f(-x), we get:
f(-x) = (-x)² - | - x |
f(-x) = x² - | x |
Therefore, her first mistake was in Step 1 because she changed the sign of |x| and
|x| = |-x|
So, the answer is:
First mistake was in Step 1
m =Y2-71x2-x1Find the slope of the line that passesthrough these two points,(3, 1) (4,9)m = [?]
1) Since, we've got already two points. Let's plug them into the slope formula so that we can find how steep is the line between those two points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{9-1}{4-3}=\frac{8}{1}=8[/tex]2) Thus, that's the slope.
Sasha drew a scale drawing of a restaurant. A countertop in the restaurant, which is 5 feet long in real life, is 10 inches long in the drawing. What scale factor does the drawing use?Simplify your answer and write it as a ratio, using a colon.
Answer:
Explanations:
Based on the given information, we are told that Sasha drew a scale drawing of a restaurant. If the countertop in the restaurant is 5 feet long in real life and 10 inches long in the drawing, this shows that the drawing of the building was reduced.
To deetermine the scale factor, we will
Show work and/or describe how the expression for the completing the square method and the expression associated with the quadratic formula are equivalent.
Given a general quadratic expression:
[tex]ax^2+bx+c=0[/tex]firs, lets divide both sides of the equation by 'a' :
[tex]\begin{gathered} (\frac{1}{a})(ax^2+bx+c=0)^{} \\ \Rightarrow\frac{a}{a}x^2+\frac{b}{a}x+\frac{c}{a}=0 \\ \Rightarrow x^2+\frac{b}{a}x+\frac{c}{a}=0 \end{gathered}[/tex]next, we can move the term c/a to the right side of the equation:
[tex]\begin{gathered} x^2+\frac{b}{a}x+\frac{c}{a}=0 \\ \Rightarrow x^2+\frac{b}{a}x=-\frac{c}{a} \end{gathered}[/tex]now we are ready to complete the square on the left side. What we have to do, is to take the constant that is multiplying x (in this case,b/a), and first, we divide it by 2, and then elevate to the square the result:
[tex]\begin{gathered} \frac{b}{a}\frac{\cdot}{\cdot}2=\frac{b}{2a} \\ \Rightarrow(\frac{b}{2a})^2=\frac{b^2}{4a^2} \end{gathered}[/tex]then, adding this number on both sides of the equation, we get:
[tex]x^2+\frac{b}{a}x+\frac{b^2}{4a}=-\frac{c}{a}+\frac{b^2}{4a^2}[/tex]which we can write like this:
[tex](x+\frac{b}{2a})^2=\frac{-4ac+b^2}{4a^2}_{}[/tex]applying the square root on both sides,we get the following:
[tex]\begin{gathered} \sqrt[]{(x+\frac{b}{2a})^2}=\sqrt[]{\frac{b^2-4ac}{4a^2}}=\pm\frac{\sqrt[]{b^2_{}-4ac}}{2a} \\ \Rightarrow x+\frac{b}{2a}=\pm\frac{\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]finally, we can solve for x:
[tex]\begin{gathered} x+\frac{b}{2a}=\pm\frac{\sqrt[]{b^2-4ac}}{2a} \\ \Rightarrow x=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]as we can see, if we have a general quadratic equation, we can us the completing the square method to deduce the quadratic formula
Can someone help me with these geometry questions sorry it’s a two parter.
In this problem, we are trying to choose between using a permutation and a combination.
The main difference between the two is the order.
In a combination, order doesn't matter, but it does matter in a permutation. Since the coach is choosing people based on how they performed, this will be a permutation.
For the first box on your screen, you should drag and drop the "P" variable for permutation.
Next, we need to apply the permutation formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]I'm assuming there are a total of 14 players on the team? So we will let
[tex]\begin{gathered} n=14 \\ r=3 \end{gathered}[/tex]Where n represents the total number of players, and r represents the number of people being chosen based on performance. Then we have:
[tex]\frac{14!}{(14-3)!}=\frac{14!}{11!}[/tex]You can drag the 14! to the numerator and the 11! to the denominator.
Finally, we need to simplify to get the final answer. We can always use a calculator, but I'll show the steps for simplifying here:
[tex]\begin{gathered} \text{ Rewrite}14! \\ \frac{14\cdot13\cdot12\cdot11!}{11!} \end{gathered}[/tex][tex]\begin{gathered} \text{ Cancel the }11! \\ \\ \frac{14\cdot13\cdot12\cdot\cancel{11!}}{\cancel{11!}} \end{gathered}[/tex]Multiply the remaining values:
[tex]14\cdot13\cdot12=2184[/tex]The coach has 2184 ways to choose a player.
A certain company recorded the number of employee absences each week over a period of 10 weeks. The result is the data list 3, 5, 1, 2, 2, 4, 7, 4, 5, 5. Find the mean and standard deviation of the number of absences per week. Round the standard deviation to two decimal places.
The table of the number of absences every week for 10 weeks:
3, 5, 1, 2, 2, 4, 7, 4, 5, 5
The mean can be calculated as:
Where xi is the ith element of the list and n is the number of elements.
Then, the mean is:
Mean = (3+5+1+2+2+4+7+4+5+5)/10
Mean = 3.8
Now, the standard deviation (std) is given by the formula:
Then, using the formula above, we obtain:
std = 1.72
Choose the correct table for the inverse of the relation below
GIVEN:
We are given a table of x and y values that defines a function.
Required;
To find the inverse of the relation as shown.
Step-by-step solution;
For a relation defined as an ordered pair in the form,
[tex](x,y)[/tex]then its inverse is a relation of the set of ordered pairs in the form;
[tex](y,x)[/tex]In other words, what we have is;
[tex]\begin{gathered} f(x)=(x,y) \\ \\ f^{-1}(x)=(y,x) \end{gathered}[/tex]The function given has the following ordered pairs;
[tex]\begin{gathered} For\text{ }f(x): \\ \\ (-4,-3),(-1,1),(1,2),(3,6) \end{gathered}[/tex]Therefore, the inverse would be;
[tex]\begin{gathered} For\text{ }f^{-1}(x): \\ \\ (-3,-4),(1,-1),(2,1),(6,3) \end{gathered}[/tex]ANSWER:
Therefore, option A is the correct answer
Please HelpWhich of the following is a continuous random variable?A. X= number of incoming flights at the local airportB. T=winning time in the man's 100 meter dash at the 2016 OlympicsC. P=number of points scored by Stephen curry in a game D.H=The number of hats sold on Tuesday
A continuous random variable must be a variable that can take decimal values.
In this case, the number of incoming flights at the local airport can not take decimal values, because you can not say 3 and a half flights.
In a basketball game you can not score half point, it means this variable can neither take decimal values.
You can not sell 5 and a quarter hats, it means this variable can not take decimal values.
The only variable that meets this condition is the winning time in the man's 100 meter dash at the 2016 Olympics.
The correct answer is B.
Given the pattern -36, 12, -4, ...(a) Write an explicit formula for the pattern.(b) Write a recursive formula for the pattern.(c) Does the pattern converge or diverge? If it converges, to what value does it converge?(d) If you added the terms in this pattern, would the sum converge or diverge? If it converges, to what value does it converge?
Answer:
[tex]\begin{gathered} a)a_n=-36\cdot\frac{1}{3}^{n-1} \\ b)\text{ }a_n=\frac{1}{3}\cdot a_{n-1} \\ c)\text{ converges to -54} \\ d)\text{ s=-54} \end{gathered}[/tex]Step-by-step explanation:
The explicit and recursive formula for a geometric sequence is represented by the following:
[tex]\begin{gathered} \text{ Explicit formula:} \\ a_n=a_1\cdot r^{n-1} \\ \text{ Recursive formula:} \\ a_n=r\cdot a_{n-1} \\ \text{where,} \\ r=\text{ common ratio} \end{gathered}[/tex]The common ratio of the pattern is:
[tex]\begin{gathered} \frac{-12}{-36}=\frac{1}{3} \\ \frac{-4}{-12}=\frac{1}{3} \end{gathered}[/tex]Then, for the explicit formula:
[tex]a_n=-36\cdot\frac{1}{3}^{n-1}[/tex]Recursive formula:
[tex]a_n=\frac{1}{3}\cdot a_{n-1}[/tex]Now, to determine if the pattern converge or diverge:
[tex]\begin{gathered} \lvert r\rvert<1,\text{ the series converge to }\frac{a_1}{1-r} \\ \lvert r\rvert\ge1,\text{ the series diverges} \end{gathered}[/tex]Since the common ratio is less than 1, the series converges to:
[tex]\text{converges to }\frac{-36}{1-\frac{1}{3}}=-54[/tex]A sum of an infinite geometric series can be determined if it converges since this pattern converges, the sum would converge to;
[tex]\begin{gathered} S=\frac{a_1}{1-r} \\ S=\frac{-36}{1-\frac{1}{3}}=-54 \end{gathered}[/tex]In the early afternoon, a tree casts a shadow that is 2 feet long. A 4.2-foot-tall boy standing nextto the tree casts a shadow that is 0.7 feet long. How tall is the tree?
In this drawing, the traingle on the left, has the height of the tree (T) and the size of the shadow 2 feet
The tringle on the right, has the height of the boy, 4.2 feet and the shadow is 0.7 feet
The angle a is the angle with respect to the sun light
The triangles are congruent, because therefore the proportion of their sides is equal, so we can write:
T/2 = 4.2/0.7
Solving for T:
T = 2(4.2/0.7) = 12
T = 12
Answer:
The tree is 12 feet tall
identify all expressions equivalent to the given expressions. 2/3 • 9 ÷ 3 - 1 ANWSER: 6 ÷ 2 - 1 + 2 3 • 2/3 -12/3 • 9 ÷ 1
Simplify each expression and find if the simplified form is the same.
[tex]2/3\cdot9\div3-1[/tex]This can also be writen as:
[tex]=\frac{2}{3}\cdot9\div3-1[/tex]Multiply 2/3 by 9:
[tex]=6\div3-1[/tex]divide 6 by 3:
[tex]=2-1[/tex]Substract 1 from 2:
[tex]=1[/tex]Now, check each option:
6 ÷ 2
Divide both numbers:
[tex]\frac{6}{2}=3[/tex]This is NOT equivalent to the given expression.
- 1 + 2
Add the numbers:
[tex]-1+2=1[/tex]This IS equivalent to the given expression.
3 • 2/3 -1
First, multiply 3 times 2/3:
[tex]3\cdot\frac{2}{3}-1=2-1[/tex]Then, add both numbers:
[tex]2-1=1[/tex]This IS equivalent to the given expression.
2/3 • 9 ÷ 1
Perform the operations from left to right:
[tex]\begin{gathered} \frac{2}{3}\cdot9\div1=6\div1 \\ =6 \end{gathered}[/tex]This is NOT equivalent to the given expression.
Therefore, the expressions that are equivalent to the given one, are:
[tex]\begin{gathered} -1+2 \\ 3\cdot2/3-1 \end{gathered}[/tex]what is the equation for the line that passes through the given point and is parallel to the graph of y=3x-2; (3,2)
a hot air balloon decrease its altitude by 3/8 ft each for two seconds what was the total change in altitude
The rate of change is the decrease in altitude per change in two seconds
[tex]\begin{gathered} \frac{3}{8}\text{ divided by 2} \\ \frac{3}{8}\text{ x}\frac{1}{2} \\ \Rightarrow\frac{3}{16}ft\text{ per second} \end{gathered}[/tex]If the initial altitude is y ft
When the transformation T2,-1 is performed on point A, its image is point A (-3, 4). What are the coordinates ofA?
Answer
A (-5, 5)
Explanation
When the transformation Ta, b is performed on a given coordinate B (x, y), it becomes B' [(x + a). (y + b)]
So, for this question, the transformation is T2, -1, on point A (x, y) to give the image point A' (-3, 4)
A' (-3, 4) = A' [(x + 2), (y - 1)]
x + 2 = -3
x = -3 - 2 = -5
y - 1 = 4
y = 4 + 1 = 5
So, the coordinates of point A is (-5, 5)
Hope this Helps!!!
The function f(T) = a (x - h[ + k is shown in the graph below. 2 0 6 N What is the value of a? What is the value of h? 1 What is the value of k?
As we can see from the graph, the function is shifted from one unit to the right, and two units up, and it is in an inverse way.
Then, we can express this as:
[tex]-1\cdot|x-1|+2[/tex]The value for a = -1.
The value for h = 1.
And the value for k = 2.
Sam bought a stereo that listed for $795. He saved 20% of the originalcost by buying it at a sale and paying cash. How much did he pay for thestereo?a. $159b. $636c. $63.60d. $795
Given:
a.) Sam bought a stereo that was listed for $795.
b.) He saved 20% of the original cost by buying it at a sale and paying cash.
We will be using the following formula:
[tex]\text{ Discounted price = Original Price x (}\frac{100\text{\% - \% Discount}}{100})[/tex]We get,
[tex]\text{ Discounted price = Original Price x (}\frac{100\text{\% - \% Discount}}{100})[/tex][tex]\text{= 795 x (}\frac{100\text{\% - 20\%}}{100})[/tex][tex]\text{ = 795 x (}\frac{80}{100})[/tex][tex]\text{ = 795 x 0.80}[/tex][tex]\text{ Discounted Price = \$}636.00[/tex]Therefore, Sam paid $636 for the stereo.
The answer is letter B.
if planet 1 is 32.7 million miles farther from the sun than planet 2, then planet 3 is 26.5 million miles farther from the sun than planet 1. when the toal of distnaces for these three planets from the sun is 190.0 million miles, how far away from thesun is planet 2?
The distance between planet 2 and sun is of 32.7 million miles.
Let the distance between planet 2 and sun = x
Distance between planet 1 and sun = 32.7 + x
Distance between planet 3 and sun = (32.7 + x) + 26.5
= 59.2 + x
According to question,
Distance between planet 1 and sun + distance between planet 2 and sun + Distance between planet 3 and sun = 190
(32.7 + x) + x + (59.2 + x) = 190
3x + 91.9 = 190
3x = 190 - 91.9
3x = 98.1
x = 98.1 / 3
x = 32.7
Hence, Distance between planet 2 and sun is 32.7 million miles.
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Use the six steps in the "Blueprint for Problem Solving" to solve the following word problem. You may recognize the solution by just reading the problem. Use n as the variable for the number and write the equation used to describe the problem.When 8 is subtracted from three times a number, the result is 4. Find the number.Equation: ? The number is ? .
Let n be the number we don't know.
Three times this number can be express as:
[tex]3n[/tex]The sentence "When 8 is subtracted from three times a number" can be express (using the expression we found before) as:
[tex]3n-8[/tex]Finally we know that this is equal to 4, then we have the equation:
[tex]3n-8=4[/tex]Solving for n we have:
[tex]\begin{gathered} 3n-8=4 \\ 3n=8+4 \\ 3n=12 \\ n=\frac{12}{3} \\ n=4 \end{gathered}[/tex]Therefore the number we are looking for is 4.
the function h(x)=x^2+5 maps the domain given by the set {-2,-1,0,1,2} determine the set that represents the range of h (x)
h(x) = x^2 + 5
h(-2) = (-2)^2 + 5 = 4 + 5 = 9
h(-1) = (-1)^2 + 5 = 1 + 5 = 6
h(0) = (0)^2 + 5 = 5
h(1) = (1)^2 + 5 = 1 + 5 = 6
h(2) = (2)^2 + 5 = 4 + 5 = 9
The range is {9, 6, 5, 6, 7]
18. A line has slope = -9 and goes through the point (-4,-2). What is the equation of this line in point-slope forma A. y + 2 = -91X - 4) B. Y-2= -9(x-4) C. y 2 = -91x + 4) D. y - 2= -9(x +4)
The straight line equation is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept. In our case m=-9. Hence, our line
equations has the form
[tex]y=-9x+b[/tex]In order to find b, we must use the given point (-4,-2) and substitute it and the last equation.
It yields,
[tex]-2=-9(-4)+b[/tex]hence, we have
[tex]\begin{gathered} -2=36+b \\ -2-36=b \\ b=-38 \end{gathered}[/tex]Finally, the answer is
[tex]y=-9x-38[/tex]Now, we can rewrite this equation as
[tex]\begin{gathered} y=-9(x+4)-2 \\ \text{which is equal to} \\ y+2=-9(x+4) \end{gathered}[/tex]then, the answer is C.
Choose whether the number given in specific notation is representing a large or small number.
Given:
[tex]\begin{gathered} a)1.2\times10^3 \\ b)7.5\times10^^{-4} \end{gathered}[/tex]To find:
The number given in a specific notation is representing a large or small number.
Explanation:
a) It can be written as,
[tex]\begin{gathered} 1.2\times10^3=1.2\times1000 \\ =1200 \end{gathered}[/tex]So, it is a large number.
b) It can be written as,
[tex]\begin{gathered} 7.5\times10^{-4}=7.5\times\frac{1}{10^4} \\ =\frac{7.5}{10000} \\ =0.00075 \end{gathered}[/tex]So, it is a small number.
Final answer:
a) Large
b) Small
I need help it says identity the equivalent expression for the expression above
Given:
Expression is
[tex]=\frac{m^{\frac{1}{3}}}{m^{\frac{1}{5}}}[/tex]Required:
Equivalent expression for the given expression.
Explanation:
We will use
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]So,
[tex]\begin{gathered} \frac{m^{\frac{1}{3}}}{m^{^{\frac{1}{5}}}}=m^{\frac{1}{3}-\frac{1}{5}} \\ =m^{\frac{2}{15}} \end{gathered}[/tex]Answer:
Hence, 1st option is correct.
For each system of equations below, determine whether it has one solution, no solution, or infinite solutions. 4x+9y=1510x+15y=25
Let's solve the system of linear equations
[tex]\begin{gathered} 4x+9y=15 \\ 10x+15y=25 \end{gathered}[/tex]A day of the week is chosen at random. What is the probability that it is a Wednesday or Saturday?A.2/7B.1/7C.2/14D. 2
ANSWER
[tex]A)\frac{2}{7}[/tex]EXPLANATION
There are 7 days in a week.
The probability that a chosen day of the week is Wednesday or Saturday is the sum of the probability that the day is a Wednesday and the probability that the day is a Saturday.
Since there is only one Wednesday in a week, the probability that the day is a Wednesday is:
[tex]P(W)=\frac{1}{7}[/tex]The same rule applies for Saturday:
[tex]P(S)=\frac{1}{7}[/tex]Therefore, the probability that the day is a Wednesday or a Saturday is:
[tex]\begin{gathered} P(W-or-S)=\frac{1}{7}+\frac{1}{7} \\ P(W-or-S)=\frac{2}{7} \end{gathered}[/tex]Hi I need help with this homework so I can get a good grade on the test
The answers are indeed nx and m.
Hello can you help with the angles for each letter
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
diagram
Step 02:
angles:
we must analyze the diagram to find the solution.
a = (180 - 115)° = 65°
b = 115°
c = 65°
d = (180 - 135)° = 45°
f = 110°
g = (180 - 110)° = 70°
h = 110°
j = (180 - 65)° = 115°
k = (180 - 45 - 70)° = 65°
m = (180 - 42)° = 138°
n = (180 - 42 - 65)° = 73°
p = (180 - 73)° = 107°
q = (180 - 107)° = 73°
r = (180 - 68)° = 112°
s = (540 - 135 - 115 - 107 - 115)° = 68°
t = (360 - 124 - 73 - 112)° = 51°
u = 135°
v = 45°
w = (180 - 45 - 65)° = 70°
x = (180 - 65)° = 115°
That is the full solution.
whats my test mean by Match the two numbers with their least common multiple (LCM). MatchTermDefinition 8 and 4A) 40 8 and 6B) 24 8 and 10C) 8
LCM of 8 and 10 = 40 ((option C)
LCM of 8 and 4 = 8 (option B)
LCM of 8 and 6 = 24 (option A)
Explanation:We find each of the least common multiple (LCM) of the numbers then we match the result.
We pick the common numbers in both. Then multiplied by other numbers not common to both
8 = 2 × 2 × 2
4 = 2 × 2
LCM of 8 and 4 = 2×2×2
LCM of 8 and 4 = 8 (option B)
8 = 2 × 2 × 2
6 = 2 × 3
LCM of 8 and 6 = 2×2×2×3
LCM of 8 and 6 = 24 (option A)
8 = 2 × 2 × 2
10 = 2 × 5
LCM of 8 and 10 = 2 × 2 × 2 × 5
LCM of 8 and 10 = 40 ((option C)
Please show work for this !!
The midpoint of the given endpoints is (0,4).
From the graph:
points are (-4,4) and (4,0)
Midpoint = (x1+x2 / 2 , y1+y2 / 2)
= (-4+4 / 2 , 4 + 4 / 2)
= (0/2 , 8/2)
= (0,4)
Therefore the midpoint of the given endpoints is (0,4).
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