We are given a question about factory plants making TV panels. The following information holds.
Plant A produces twice as many panels as plant B. This can be expressed mathematically as:
[tex]A=2B[/tex]Also, 2% and 3% of the TV panels from Plant A and Plant B are defective, and both plants produced a total of 490 defective panels. This can be expressed mathematically as:
[tex]\frac{2A}{100}+\frac{3B}{100}=490[/tex]We can clearly see that we have derived two equations. We will substitute the first equation in the second equation to get the number of panels Plant B produced.
[tex]\begin{gathered} \frac{2(2B)}{100}+\frac{3B}{100}=490 \\ \frac{4B}{100}+\frac{3B}{100}=490 \\ \frac{7B}{100}=490 \\ \text{Cross multiply} \\ 7b=490\times100 \\ B=\frac{490\times100}{7} \\ B=70\times100 \\ B=7000 \end{gathered}[/tex]Therefore, the number of panels that plant B produced is:
ANSWER: 7000
Micha starts riding his bike at 12:05pm Her rides for 35 minutes What time does he stop riding his bike?
If Micha rides for 35 minutes, she'll stop riding her bike at 12:40pm
twice a number decreased by 4 Is atleast 12
EXPLANATION
The appropiate relationship is:
2x - 4 = 12
Adding +4 to both sides:
2x = 12 + 4
Adding numbers:
2x = 16
Dividing both sides by 2:
x = 16/2
Simplifying:
x = 8
The solution is 8
Solve VABC if a = 34 feet, b = 20 feet, and c = 18 feet. .
Cosine theorem:
[tex]\begin{gathered} a^2=b^2+c^2-2bccosA \\ b^2=a^2+c^2-2ac\cos B \\ c^2=a^2+b^2-2ab\cos C \end{gathered}[/tex]a= 34ft
b = 20ft
c = 18ft
[tex]\begin{gathered} a^2-b^2-c^2=-2bc\cos A \\ \frac{a^2-b^2-c^2}{-2bc}=\cos A \\ \\ A=\cos ^{-1}(\frac{a^2-b^2-c^2}{-2bc}) \end{gathered}[/tex][tex]B=\cos ^{-1}(\frac{b^2-a^2-c^2}{-2ac})[/tex][tex]C=\cos ^{-1}(\frac{c^2-a^2-b^2}{-2ab})[/tex][tex]\begin{gathered} A=\cos ^{-1}(\frac{34^2-20^2-18^2}{-2(20)(18)}) \\ \\ A=\cos ^{-1}(\frac{432}{-720})=126.86 \end{gathered}[/tex][tex]\begin{gathered} B=\cos ^{-1}(\frac{20^2-34^2-18^2}{-2(34)(18)}) \\ \\ B=\cos ^{-1}(\frac{-1080}{-1224})=28.07 \end{gathered}[/tex][tex]\begin{gathered} C=\cos ^{-1}(\frac{18^2-34^2-20^2}{-2(34)(20)}) \\ \\ C=\cos ^{-1}(\frac{-1235}{-1360})=24.75 \end{gathered}[/tex]VABC:
A=126.86º
B=27.07º
C=24.75º
a=34ft
b=20ft
c=18ft
5 points10) Some sixth-, seventh-, and eighth-grade students spend time at theelementary school tutoring students. Of the students who tutor, 12 aresixth-graders, 18 are seventh-graders, and 6 are eighth-graders. Whatpercent of tutors are seventh-graders? *18%36%50%75%
50%
1) Gathering the data
12 are 6th graders
18 7th graders
6 8th graders
2) Let's add them up at first to get the whole number of students who tutor:
12 +18 +6 = 24 +12 = 36
So we can say that
36 -------------- 100%
The 7th graders: 18 students
So we can write a proportion for that
36-------100%
18 ------- x
36x = 1800 Divide both sides by 36
x =50
3) So the answer is 50% of them are 7th graders.
taliyah 1. If Mrs. Wozniak runs 8 miles a day. How many miles will she run in 4 weeks? Your answer 2. Fach fourth trade class at a local elementan answered 1 209 multiplication fact problems last
Use the given rate to find how many miles will Mrs. Wozniak run in 4 weeks. Remember that 1 week is equal to 7 days, then 4 weeks is 28 days.
[tex]28days\cdot\frac{8miles}{1day}=224miles[/tex]She will run 224 miles in 4 weeks.
metro atlanta home prices are rising rapidly, and much of its a soaring demand from deep-pocketed investors,as reported in the AJC March 21st of this year. In March2022, the median sale price of a home in the Metro area was $401,500. Before the the pandemic hit, in january2020, the median sale price was $279,000 Find the rate increase of the average cost of a home in Atlanta from january2020 before the pandemic hit Atlanta to the present
We are asked to determine the rate of increase in the value of a home,
We need to have into account that at the beginning of the considered period the cost was 279000 and after two years the cost is 401500, therefore, we can use the following formula:
[tex]r=\frac{\Delta C}{\Delta t}[/tex]Where:
[tex]\begin{gathered} \Delta C=\text{ difference in cost} \\ \Delta t=\text{ difference in time} \end{gathered}[/tex]Now, we substitute the values:
[tex]r=\frac{401500-279000}{2}[/tex]Solving the operations:
[tex]r=61250[/tex]Therefore, the rate is an increase of $61250 per year.
Samson buys a newcomputer for class. Thecomputer costs $550, aswell as an additional tax of10.2%.How much does he pay forthe computer?
The cost of the computer is: $550
The additional tax is: 10.2%
To find the final cost of the computer, first, we need to find how much is the tax of 10.2%.
Step 1. Calculate how much is 10.2% of $550.
In general, to calculate a percentage we divide the quantity by 100 and then multiply by the percentage we need. In this case:
[tex]\frac{550}{100}\times10.2[/tex]Solving the operations:
[tex]5.5\times10.2[/tex][tex]=56.1[/tex]The tax is $56.1
Step 2. Add the cost of the computer and the tax to find how much he paid for the computer:
[tex]550+56.1=606.1[/tex]Answer: $606.1
May you help me with this
Given the function
[tex]h(x)=2x^2-3x+5[/tex]Set x=-3 and solve for h(-3) as shown below
[tex]\begin{gathered} x=-3 \\ \Rightarrow h(-3)=2(-3)^2-3(-3)+5=18+9+5=32 \\ \Rightarrow h(-3)=32 \end{gathered}[/tex]Therefore, the answer is 32
The number of compounding periods is equal to what: what is the formuls
Answer
When compound interest is discussed, the time rate for the compound interest is usually mentioned. For example, they would say that
- a certain amount of money has its interest compounded at 5% annually,
- a certain amount of money has its interest compounded at 7% every 3 months,
- a certain amount of money has its interest compounded at 2% every 6 months,
In each of the examples given above, the compounding period is 1 year, 3 months and 6 months respectively.
If one is now asked to calculate the compound interst on a particular amount of money after time, T, we usually express this time T in terms of the number of time periods, t, that exist inside the given time T.
Hence, the time T is expressed in terms of time period t, as
T = nt
Such that the number of compounding periods in T is given as
n = (T/t)
[tex]undefined[/tex]If a = 6, which of the following is equal to a 2?1o-36O O-122
Solution:
The question given is a negative exponent.
To solve this, we apply the law of indices for negative exponents.
Negative exponent law is indicated below;
[tex]a^{-x}=\frac{1}{a^x}[/tex]Thus, applying this law to the question;
[tex]a^{-2}=\frac{1}{a^2}[/tex]Given:
a = 6
Substituting a = 6 into the expression, we have;
[tex]\frac{1}{a^2}=\frac{1}{6^2}[/tex]Therefore, the correct answer is;
[tex]\frac{1}{6^2}[/tex]solve the system. given your answer as (x, y, z)-4x -y - 3z = -5-6x + y - 3z = -172x + 2y - z = - 10
Answer:
(1, -5 ,2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} -4x-y-3z=-5\ldots(1) \\ -6x+y-3z=-17\ldots(2) \\ 2x+2y-z=-10\ldots(3) \end{gathered}[/tex]Make z the subject in the third equation:
[tex]z=2x+2y+10[/tex]Substitute z=2x+2y+10 into the first and second equations:
First Equation
[tex]\begin{gathered} -4x-y-3z=-5 \\ -4x-y-3(2x+2y+10)=-5 \\ -4x-y-6x-6y-30=-5 \\ -4x-6x-y-6y=-5+30 \\ -10x-7y=25\ldots(4) \end{gathered}[/tex]Second Equation
[tex]\begin{gathered} -6x+y-3z=-17 \\ -6x+y-3(2x+2y+10)=-17 \\ -6x+y-6x-6y-30=-17 \\ -6x-6x+y-6y=-17+30 \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Next, solve equations 4 and 5 simultaneously:
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Multiply equation (4) by 5 and equation (5) by 7.
[tex]\begin{gathered} -50x-35y=125 \\ -84x-35y=91 \\ \text{Subtract same sign} \\ 34x=34 \\ x=\frac{34}{34} \\ x=1 \end{gathered}[/tex]Substitute x=1 into equation (4):
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -10(1)-7y=25 \\ -7y=25+10 \\ -7y=35 \\ y=\frac{35}{-7} \\ y=-5 \end{gathered}[/tex]Recall: z=2x+2y+10
[tex]\begin{gathered} z=2x+2y+10 \\ =2(1)+2(-5)+10 \\ =2-10+10 \\ z=2 \end{gathered}[/tex]The solution of the system is:
[tex](1,-5,2)[/tex]Determine whether the relation is a function.13) {(-6, -5), (-3, -7), (4, 6), (4,8)}A) Not a functionB) Function
A) Not a function
ExplanationA function is a relation which describes that there should be only one output for each input
Step 1
let's check the given ordered pair
[tex]\begin{gathered} (x,y),\text{ x is the input, y is the output} \\ (-6,5)\text{ , -6}\Rightarrow5 \\ (-3,-7),\text{ -3}\Rightarrow-7 \\ (4,6),\text{ 4}\Rightarrow6 \\ (4,8).\text{ 4}\Rightarrow8 \end{gathered}[/tex]we can see that
the input 4 has 2 outputs 6 and 8, so
this is not a function, hence the answer is
A) Not a function
I hope this helps you
A metal plate has the form of a quarter circle with a radius of R = 106cm . Two 3 cm holes are to be drilled in the plater r = 95cm from the corner at 30 degrees and 60as shown above. To use a computer controlled milling machine you must know the Cartesian coordinates of the holes. Assuming the origin is at the corner what are the coordinates of the holes (x_{1}, y_{1}) and (x_{2}, y_{2}) ? Round your answer to 3 decimal places
1) Considering that this quarter circle is one sector of the unit circle and that
[tex]30^{\circ}=\frac{\pi}{6}[/tex]2) Let's sketch this out to better grasp the idea:
Note that the first coordinate will be given by its cos(theta), and the second one by its sine(theta)
3) Based on that principle, we can tell the following:
[tex]\begin{gathered} (x_1,y_1)--->(cos(30^{\circ}),\sin(30^{\circ}))=(\frac{\sqrt{3}}{2},\frac{1}{2}) \\ \\ (x_{2,}y_2)-->(\cos(60),\sin(60))=(\frac{1}{2},\frac{\sqrt{3}}{2}) \\ \end{gathered}[/tex]As the holes need to be drilled by the machine, so we need to find approximations to those coordinates:
[tex]\begin{gathered} (x_1,\:y_1)-->(0.866,0.500) \\ (x_2,y_2)-->(0.500,0.866) \end{gathered}[/tex]Thus, these are the coordinates to be put into the computer.
Over the weekend, Devon baked 12 muffins. She divided them evenly among 3 plates to giveto neighbors.The letter m stands for the number of muffins on each plate. Which equation can you use tofind m?12 x 3 = m12 : 3 = m
The information given is listed below:
number of muffins (m) = 12, number of plates = 3
number of muffin on each plate = number of muffins /
My teacher gave the answer on the right but I want know how he did it
the given number is 6^4
here is the calculation.
[tex]6^4=6\times6\times6\times6[/tex]multiply the number 6 by the times of 4
now by multiplication, the answer is
[tex]6^4=1296[/tex]so, the answer is 1296.
I have a practice problem that I need explained an answered, thank you
From the question, we are given the matrices
We are to find which operation is defined and whic one is not
For the operation
[tex]M-N[/tex]For subtraction operation to be definded
The order of the matrices must be the same
Since the order of M is 4 x 2
And the order of N is 4 x 2
Therefore, the operation M - N is defined
For the operation
[tex]L-N[/tex]Similarly, for the operation to be definded
The order of the matrices must be the same
The oder of matrix L is 2 x 2 while the order of matrix N is 4 x 2
Since the oder of the matrices are not the same then
The operation L - N is not defined
For the operation
[tex]M+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix M is 4 x 2 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined
For the operation
[tex]Q+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix Q is 2 x 1 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined
Michael earns a weekly salary of $365 plus a 6% commission of sales for the week. Last week, Michael's sales totaled $3200. How much did he make in commission? What was Michael's total pay?
Michael's sales are $3200, then the comission is
[tex]3200\times0.06=192,[/tex]$192 in comission.
Then the total pay is
[tex]365+192=557.[/tex]$567
The table shows x- and y-values for the equation y = 3x -1 Which number is missing in the table? 23 15 20 37
y = 3x-1
When x = 8
y = 3(8) -1
y = 24-1
y = 23
1 11a.) A sign in a bakery gives the following options. Find each unit price to the nearest cent, and show your reasoning. You can get 3 mini-cakes for $32. What is the cost of ONE mini-cake? * O $10.66 O $10.65 O $10.67 O $10.59
Since we can get 3 mini-cakes for $32, we can find the price of each mini-cake by taking the ratio of price to number of mini-cakes, like this:
unit price = 32/3 = 10.67
Then, the cost of ONE mini-cake is $10.67
Let f(x)=3x - 4. Write a function gwhose graph is a reflection of the graphoff.
hello
the function given is
In ABC, A = 68°, a = 14 and c = 17. Which of these statements best describes the triangle?
Given for the triangle ABC:
[tex]\begin{gathered} \angle A=68\degree \\ a=14,c=17 \end{gathered}[/tex]Using the sine rule, we will solve the triangle by finding the missing angles
So,
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]substitute with the given data:
[tex]\begin{gathered} \frac{14}{\sin68}=\frac{17}{\sin C} \\ \\ \sin C=\frac{17}{14}\cdot\sin 68=1.125866 \end{gathered}[/tex]The value of (sin C) must be 1 or less than 1
So, the triangle ABC cannot be constructed
The answer will be the last option
How do I find the sum of this equation and express it in simplest form [tex]( {n}^{3} - 5n - 2) + (4 {n}^{3} + n - 4)[/tex]
use the function f(x)=-3(x+1)2+18what is the y intercept ?does it have a max or min
hello,
First of all, we must remember that a first degree function must be in the formula f (x) = ax + b, so, lets use this form:
[tex]undefined[/tex]the base of the pyramid is a square. the volume is ___ cubic cm. measurements:l = 6 cmw = 10 h = 15(unable to send pictures of question without app crashing. my apologies.)
Answer:
300 cubic meters.
Explanation:
The volume of any pyramid is obtained using the formula below:
[tex]V=\frac{1}{3}\times\text{Base Area}\times Height[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times(6\times10)\times15 \\ =\frac{1}{3}\times60\times15 \\ =300\operatorname{cm}^3 \end{gathered}[/tex]The volume of the pyramid is 300 cubic meters.
an office administrator has an office supply budget $150. The office administrator will purchase folders, which are $2.15 each and notebooks, which are $4.60 each. which inequality represent the constrain on the number of folders f and notebook n the office administrator can purchase
If the price of each folder is $2.15, and the amount of folders is f, the total price paid for folders is the product of the unitary price by the amount bought.
[tex]\text{price}1=2.15f[/tex]Similarly, the price paid for notebooks is the unitary price of one notebook ($4.60) multiplied by the amount of notebooks (n).
[tex]\text{price}2=4.6n[/tex]Finally, the total cost of both products together is the sum of these products.
[tex]\text{cost}=\text{price}1+\text{price}2=2.15f+4.6n[/tex]The supply budget is $150, so the total cost needs to be lesser than or equal this value.
Therefore, we have that:
[tex]\begin{gathered} \text{cost}\le150 \\ 2.15f+4.6n\le150 \end{gathered}[/tex]So the correct option is B.
Arthur has 20/8 cups of dishwashing detergent. He uses 1/4 cup of detergent for each load of dishes. what is the greatest number of loads of dishes Arthur was with this amount of detergent
Total = 20/8 cups of dishwashing detergent.
he has 20/8 = 5/2 = 2 1/2 cups of dishwashing detergent, per load he uses 1/4
per load
2 1/2 - 1/4
_____________________
The general formula
x= number of loads
20/8 - x* 1/4= 0
20/ 8 = x 1/4
x 1/4 = 20/ 8
x= 4* (20/8 )
x= 10
The greatest number of loads of dishes Arthur was with this amount of detergent is 10
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Keisha has four favorite shirts one blue, one green, one red, one yellow and two favorite pairs of pants one black and one brown she decides to randomly choose a pair of pants and a shirt to wear for the day. What is the probability that Keisha chooses and outfit that is yellow and black or red and brown round your answer to the nearest whole percent?
Answer:
25%
Explanation:
First, let's calculated the total number of outfits that Keisha can choose. So, we will use the rule of multiplication as:
4 * 2 = 8
Shirts Pants
Because she has 4 options for shirts and 2 options for pants. So, there 8 possible outfits.
Then, from those outfits, there is 1 that is yellow and black, and 1 that is red and brown. So, the probability that Keisha chooses an outfit that is yellow and black or red and brown is:
[tex]P=\frac{1+1}{8}=\frac{2}{8}=0.25=25\text{ \%}[/tex]Therefore, the answer is 25%
Hello. I need help with this practice problem. I will include a picture. Thank you soo much
Firstly, we need to compare the information ew have from both sides of the equation, the denominators.
The different between the denominator is that the right side has the factor (w + 6), while the lest side does not.
So, sstarting from the expression on the left side, we can introduce the factor (w + 6) into the denominator by multiplying both the numerator and the denominator by this factor:
[tex]\frac{2}{w+7}=\frac{2}{w+7}\cdot\frac{w+6}{w+6}=\frac{2(w+6)}{(w+7)(w+6)}[/tex]The order of the factor dont change the result, so we can switch the factors on the denominator to get:
[tex]\frac{2}{w+7}=\frac{2(w+6)}{(w+6)(w+7)}[/tex]Now, by comparison, we can see that the blank part is the following:
[tex]2(w+6)[/tex]question is in image
The function f(x) is given by,
[tex]f(x)=x^2[/tex]The function g(x) is given by,
[tex]g(x)=\frac{-2}{3}x^2[/tex]If f(x) becomes -kf(x), where 0Comparing the above functions, we get
[tex]g(x)=-\frac{2}{3}f(x)[/tex]So, k=2/3. Hence, 0 < 2/3 < 1.
Therefore, the graph of g(x) is the graph of f(x) compressed vertically and reflected across the x axis.
Hence, option D is correct.
Make the following conversion in the metric system by multiplying by the appropriate conversion factor. Write your answer as a whole number or decimal.20 m to millimeters ?mm
Each meter has 100 centimeters, each centimeters has 10 milimeters, so 20 meters has 20.000 milimeters.