Answer:
[tex]\frac{h-12-2}{4} = x[/tex] & a² = c² - b²
Step-by-step explanation:
h = 4 (x + 3y) + 2
Expand brackets
h = 4x + 12y + 2
Subtract 12y & 2 from both sides
h - 12y - 2 = 4x
Divide both sides by 4
[tex]\frac{h-12-2}{4} = x[/tex]
a² = c² - b²
Then √ both sides to lose the ²
Fred can mow a lawn in 60 minutes. rocky can mow the same lawn in 40 minutes. how long does it take for both fred and rocky to mow the lawn if they are working together? express your answer as a reduced fraction.
Answer:
24 minutes
Step-by-step explanation:
Fred can mow a lawn in 60 minutes.
Fred's Rate [tex]=\frac{1}{60}[/tex]
Rocky can mow the same lawn in 40 minutes.
Rocky's rate [tex]=\frac{1}{40}[/tex]
Let the time it will take both of them = x minutes
Therefore:
[tex]\frac{1}{60}+\frac{1}{40}=\frac{1}{x}\\$Multiply all through by 1200$\\1200\times \frac{1}{60}+1200\times\frac{1}{40}=1200\times\frac{1}{x}\\20+30=\frac{1200}{x}\\50=\frac{1200}{x}\\$Cross multiply\\50x=1200\\Divide both sides by 50\\x=24\\[/tex]
It would take the two of them 24 minutes to mow the lawn.
Anyone please help me
Answer:
(a) 6
(b) 14
Step-by-step explanation:
Answer: (a) 6
(b) 14
Step-by-step explanation:
Let a represent the unknown digit for Chinese --> 70 + a
Let b represent the unknown digit for Mathematics --> 80 + b
Total scores ÷ Total number of tests = Average
[tex]\dfrac{78 + (70 + a) + (80 + b) + 62}{4}=76\\\\\\\dfrac{290 + a + b}{4}=76\\\\\\290 + a + b=304\\\\\\a+b=14[/tex]
The two digits must add up to 14.
The only options are: (9,5), (8,6), (7,7), (6,8), and (5,9),
Mathematics - Chinese
(9, 5) 89 - 75 = 14 LARGEST Difference
(8, 6) 88 - 76 = 12
(7, 7) 87 - 77 = 10
(6, 8) 86 - 78 = 8
(5, 9) 85 - 79 = 6 SMALLEST Difference
HELP PLEASEEE ASAAAAPPPPPPPPPPPP I WILL GIVE BRAINLY TO THE FIRST ONE!!!!!!!!
Answer:
the total amount is £ 756.
hope it helps..
Help me asap i really need this
Answer:
3
Step-by-step explanation:
6/2
I hope this is right :)
The mean per capita income is 19,292 dollars per annum with a variance of 540,225. What is the probability that the sample mean would be less than 19269 dollars if a sample of 499 persons is randomly selected? Round your answer to four decimal places.
Answer:
The probability is 0.2423.
Step-by-step explanation:
Given mean per capita = 19292 dollars
Given the variance = 540225
Now find the probability that the sample mean will be less than 19269 dollar when the sample is 499.
Below is the calculation:
[tex]\bar{X} \sim N(\mu =19292, \ \sigma = \frac{\sqrt{540225}}{\sqrt{499}}) \\\bar{X} \sim N(\mu =19292, \ \sigma = 32.90) \\\text{therefore the probability is:} \\P (\bar{X}< 19269) \\\text{Convert it to standard normal variable.} \\P(Z< \frac{19269-19292}{32.90}) \\P(Z< - 0.6990) \\\text{Now getting the probability from standard normal table}\\P(Z< -0.6990) = 0.2423[/tex]
Complete the table for different values of X in the polynomial expression -7x^2+32x+240. Then, determine the optimal price that the taco truck should sell it’s tacos for. Assume whole dollar amounts for the tacos.
Answer:
$6
Step-by-step explanation:
Tico’s taco truck is trying to determine the best price at which to sell tacos, the only item on the menu, to maximize profits. The taco trucks owner decided to adjust the price per taco and record data on the number of tacos sold each day with each new price. When the taco truck charges $4 for a taco, it sells an average of 60 tacos in one day. With every $1 increase in the price of a taco, the number of tacos sold per day decreases by 7.
The owner can calculate the daily revenue using the polynomial expression (-7x²+32x+240),
where x is the number of $1 increases in the taco price. In this activity, you’ll interpret and manipulate this expression and the scenario it represents.
x is number of $1 increments above the initial price of $4. (x=0 means a price of $4, x=1 means a price of $5, etc.)
The revenue is -7x²+32x+240. The average number of tacos sold is the revenue divided by the price.
For example, if x = 0, then the taco price is $4, the revenue is $240, and the number of tacos sold is 60.
If x = 1, then the taco price is $5, the revenue is $265, and the number of tacos sold is 53.
Each time x increases by 1, the number of tacos sold decreases by 7.
Continuing:
[tex]\left[\begin{array}{cccc}Value\ of\ x&Taco\ Price\ (\$)&Average\ Number\ of\ Tacos\ Sold&Daily\ Revenue\ (\$)\\0&4&60&240\\1&5&53&265\\2&6&46&276\\3&7&39&273\\4&8&32&256\\5&9&25&225\\6&10&18&180\end{array}\right][/tex]
The optimal price is $6. At this price, the revenue is a maximum at $276.
Which of these systems of linear equations has no solution?
2 x + 8 y = 15. 4 x + 16 y = 30.
2 x minus y = 18. 4 x + 2 y = 38.
4 x + 7 y = 17. 8 x minus 14 y = 36.
4 x minus 3 y = 16. 8 x minus 6 y = 34.
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution
Step-by-step explanation:
Examine the system
2 x + 8 y = 15
4 x + 16 y = 30
We see that these equations are identical except for a factor of 2, and thus recognize that this system has infinitely many solutions.
Next, look at the system
2 x minus y = 18
4 x + 2 y = 38
If we divide the second equation by 2, we get the system
2x - y = 18
2x + y = 19
Combining these two equations, we get 4x = 37, which has a solution.
Third, analyze the system
4 x + 7 y = 17 => 8x + 14y = 34
8 x minus 14 y = 36 => 8x - 14y = 36, or 16x = 70, which has a solution
Finally, analyze the system
4 x minus 3 y = 16 => -8x + 6y = -32
8 x minus 6 y = 34 => 8x - 6y = 34
If we combine these two equations, we get 0 + 0 = 2, which is, of course, impossible. This system has no solution.
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution. the 4th option.
Step-by-step explanation:
What is the equation for a straight line that would allow you to predict the value of Y from a given value of X. That is, calculate the value of "a" and the value of "b" and then substitute the 2 values into the generic equation (Y = a + bX) for a straight line. (Hint: calculate "b" first)
Answer:
[tex]m=-\frac{13}{20.8}=-0.625[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]
So the line would be given by:
[tex]y=-0.625 x +9[/tex]
Step-by-step explanation:
We have the following data:
X: 3,3,2,1,7
Y:6,7,8,9,5
We want to find an equationinf the following form:
[tex] y= bX +a[/tex]
[tex]a=m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i = 3+3+2+1+7=16[/tex]
[tex]\sum_{i=1}^n y_i =6+7+8+9+5=35[/tex]
[tex]\sum_{i=1}^n x^2_i =72[/tex]
[tex]\sum_{i=1}^n y^2_i =255[/tex]
[tex]\sum_{i=1}^n x_i y_i =99[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=72-\frac{16^2}{5}=20.8[/tex]
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=99-\frac{16*35}{5}=-13[/tex]
And the slope would be:
[tex]m=-\frac{13}{20.8}=-0.625[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]
So the line would be given by:
[tex]y=-0.625 x +9[/tex]
Written Response! Please help!
Evelyn believes that if she flips a coin 480 times, it will land tails up exactly 240 times. What would you tell Evelyn about her prediction?
Based on Evelyn's response, it can be said that she predicts that there is a 50% chance of the coin landing on tails and a 50% chance of the coin landing on heads.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the coin lands on tails is half of the number of times the coin is tossed. This means she belives that there is an equal chance that the coin would land on either heads or tails.
To learn more about probability, please check: https://brainly.com/question/13234031
Translate into an algebraic expression:40 increased by x%
Answer:
2/5x
Step-by-step explanation:
x% of 40= x/100×40
= 40/100x = 2/5x
A school contains 357 boys and 323 girls.
If a student is chosen at random, what is the probability that is a girl?
Correct your answer to 2 decimal places.
Answer:
19/40
Step-by-step explanation:
just divide the number of girls by the total number of students.
323/680 = 19/40 or 0.48
Find the distance between a point (–7, –19) and a horizontal line at y = 3. Choices are in the attachment...
Explanation:
The distance we're after is the vertical distance from the point to the line. So we only care about the difference in y values from y = -19 to y = 3
You can count out the spaces or use subtraction along with absolute value
distance from P to Q = |P-Q|
distance from -19 to 3 = |-19-3|
distance from -19 to 3 = |-22|
distance from -19 to 3 = 22
The absolute value is to ensure the result is never negative.
can I get help with this question. I need to find the value of x
Step-by-step explanation:
sides of 2 triangles are proportional
x/12=28/21
x=16
=======================================================
Explanation:
The diagonal pieces are 28 and 21. They pair up to get the fraction 28/21
The horizontal pieces are x and 12, in the same order from left to right. The order is important (so things pair up properly). We get the fraction x/12
-------
Set the two fractions equal to each other and solve for x
28/21 = x/12
28*12 = 21*x .... cross multiply
336 = 21x
21x = 336
x = 336/21 .... divide both sides by 21
x = 16
52:PLEASE HELP Find the slope of the line that passes through the points (8,2) and (9,7)
Answer:
5/1
Step-by-step explanation:it goes up 5 and over 1
Answer:
5Solution,
Let the points be A and B
A ( 8 , 2 ) -----> (X1 , y1 )
B ( 9 , 7 ) -------> (x2 , y2)
Now,
Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{7 - 2}{9 - 8} [/tex]
[tex] = \frac{ 5}{1} [/tex]
[tex] = 5[/tex]
Hope this helps..
Good luck on your assignment...
Jerry wants to buy his grandpa’s old car for $500.00. He works 10 hours a week at $7.50 an hour. How many weeks will he need to work before he earns enough money to buy the car?
Answer:
she needs to save up for 3 months
Step-by-step explanation:
By first calculating the angle of LMN, calculate the area of triangle MNL. You must show all your working.
Answer:
16.66cm²
Step-by-step Explanation:
Given:
∆LMN with m<N = 38°
Length of side NL = 7.2cm
Length of side ML = 4.8cm
Required:
Area of ∆MNL
Solution:
Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b
Where sin(A) = Sin(M) = ?
a = NL = 7.2cm
sin(B) = sin(N) = 38°
b = ML = 4.8cm
Thus,
Sin(M)/7.2 = sin(38)/4.8
Cross multiply
4.8*sin(M) = 7.2*sin(38)
4.8*sin(M) = 7.2*0.6157
4.8*sin(M) = 4.43304
Divide both sides by 4.8
sin(M) = 4.43304/4.8
sin(M) = 0.92355
M = sin-¹(0.92355) ≈ 67.45°
Step 2: Find m<L
angle M + angle N + angle L = 180 (sum of angles in a triangle)
67.45 + 38 + angle L = 180
105.45 + angle L = 180
Subtract 105.45 from both sides
Angle L = 180 - 105.45
Angle L = 74.55°
Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)
Where,
a = NL = 7.2 cm
b = ML = 4.8 cm
sin(C) = sin(L) = sin(74.55)
Thus,
Area of ∆MNL = ½*7.2*4.8*0.9639
= ½*33.31
= 16.655
Area of ∆MNL ≈ 16.66cm²
What is the line of best fit? Why do we want the sum of the residuals to be as close to zero as possible?
Answer:
Step-by-step explanation:
What sis line of best fit?
The line of best fit may be explained as a straight line which is drawn to pass through a set of plotted data point which gives the best and most approximate relationship between the data points. A line of best fit is required to give the best approximate value between the set of plotted data points such that it allows making inference on new data points while also ensuring the least possible deviation from the original data points.
Why do we want the sum of the residuals to be as close to zero as possible?
The line of best fit will be the line which gives the least value of residual error. The residual error is reffered to as the difference between the line drawn and the individual data point plotted. These errors are squared and summed together, the line which produces the least residual error is Considered as the leading ne of best fit for the data.
We want the sum of our residual error to be as close to zero as possible, this is to reduce the deviation between our original or plotted data and the modeled data produced by our line of best fit.
Answer:
Step-by-step explanation:
We wan the residuals to be closest to zero because they will help use later in the equation.
solve this...question
Answer: 5. P = (-4, 6) R = (-4, -4)
6. (a) a = 4, b = 3 (b) BC = 8 (c) B = (3, 4)
7. (a) m = 4, n = 6 (b) PQ = (-2, 6) (c) SR = (2, -6)
Step-by-step explanation:
5. The distance from Q (4, 0) to A (0, 3) is 4 left and up 3.
So the distance from A to P is 4 left (0 - 4) and up 3 (3 + 3)
--> P = (-4, 6)
Similarly, the distance from Q (4, 0) to B (0, -2) is 4 left and down 2.
So the distance from A to P is 4 left (0 - 4) and down 2 (-2 - 2)
--> P = (-4, -4)
6. Follow the same steps as #5 (above) to get the following coordinates:
A = (-3, 4) B = (3, 4)
D = (-3,-4) C = (3, -4)
a) a = 4, b = 3
b) BC = 2(4) = 8
c) B = (3,4)
7. Follow the same steps as #5 (above) to get the following coordinates:
P = (-4, 6) Q = (0, 6)
S = (0, -6) R = (4, -6)
a) m = 4, n = 6
b) midpoint PQ = (-2, 6)
c) midpoint SR = (2, -6)
y = 5x + 2 3x = –y + 10 What is the solution to the system of equations
Answer:
x = 1 , y = 7
Step-by-step explanation:
Solve the following system:
{y = 5 x + 2 | (equation 1)
3 x = 10 - y | (equation 2)
Express the system in standard form:
{-(5 x) + y = 2 | (equation 1)
3 x + y = 10 | (equation 2)
Add 3/5 × (equation 1) to equation 2:
{-(5 x) + y = 2 | (equation 1)
0 x+(8 y)/5 = 56/5 | (equation 2)
Multiply equation 2 by 5/8:
{-(5 x) + y = 2 | (equation 1)
0 x+y = 7 | (equation 2)
Subtract equation 2 from equation 1:
{-(5 x)+0 y = -5 | (equation 1)
0 x+y = 7 | (equation 2)
Divide equation 1 by -5:
{x+0 y = 1 | (equation 1)
0 x+y = 7 | (equation 2)
Collect results:
Answer: {x = 1 , y = 7
Answer:
D) (1,7)
Step-by-step explanation:
just took the test
What single transformation maps ∆ABC onto ∆A'B'C'? A. rotation 90° clockwise about the origin B. rotation 90° counterclockwise about the origin C. reflection across the x-axis D. reflection across the line y = x
Answer:
B. rotation 90° counterclockwise about the origin.
Step-by-step explanation:
Transformation is the process by which the size or orientation of a given figure is altered without any effect on its shape. Examples are; rotation, reflection, translation and dilation.
Rotation is the process of turning a figure about a reference point called the origin. While reflection is turning a figure about a line to produce its image.
In the given question, ∆ABC is mapped onto ∆A'B'C' by rotating it at 90° counterclockwise about the origin.
The correct option is (B). rotation 90°counterclockwise about the origin.
Given, ∆ABC and ∆A'B'C' are shown in attached figure.
We have to map ∆ABC onto ∆A'B'C',.
A transformation is a general term for four specific ways to manipulate the shape and or position of a point, a line, or geometric figure.
Transformation is also the process by which the size or orientation of a given figure is altered without any effect on its shape.
A rotation is a transformation in which the object is rotated about a fixed point.The direction of rotation can be clockwise or anticlockwise.
It is clear from the fig that the ∆ABC can be mapped over ∆A'B'C' by the rotation of 90°counterclockwise about the origin.
Hence the correct option is (B). rotation 90°counterclockwise about the origin.
For more details follow the link:
https://brainly.com/question/1571997
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Penelope has $1,459.75 in her bank account. To pay her bills, she writes 4 checks in the amounts of $200.25, $359.45, $125, and $299.35. Then she deposits $375 into her account. Penelope’s account balance after she pays her bills and makes the deposit is $ .
Answer:
$850.7
Step-by-step explanation:
Penelope has $1459.75 in her account.
She pays different amount that are given above.
i.e.
=1459.75-200.25-359.45-125-299.35
=475.7
Then she deposit $375
Now,
=475.7+375
=850.7
So, She has $850.7 in her account after she pays her bills and makes deposits.
Answer:
$805.7 OwO
Step-by-step explanation:
a right square pyramid has a slant height of 20 feet, and the length of a side of the base is 32 feet. what is the height, h, of the pyramid?
Answer:
The pyramid's height h = 12 ft
Step-by-step explanation:
Notice that the slant height of the pyramid forms a right angle triangle with the segment that joins the bottom end of the slant height with the center of the pyramid's base, and with the pyramid height (h).
The segment joining the slant height with the center of the pyramid's base is one half of the side of the base in length, so that it; 16 feet.
then we have a right angle triangle with hypotenuse given by the pyramid's slant height (20 ft), a leg given by 16 ft, and we need to find the length of the second leg (pyramid's height (h).so we use the Pythagorean theorem:
[tex]hyp^2=leg_1^2+leg_2^2\\(20\,ft)^2= (16\,ft)^2+h^2\\h^2=400\,ft^2-256\,ft^2\\h^2=144\,ft^2\\h=12 \,ft[/tex]
Answer:
C.12ft
Step-by-step explanation:
for people on edmentum
Bacteria in a petri dish doubles every 10 minutes.
a) If there are 10 bacteria initially, how many are there after 120 minutes?
b) If there are 10 bacteria initially, when would there be a million bacteria?
(Show step by step)
Answer:
Step-by-step explanation:
Givens
Petri Dish A sees a double ever 10 minutes
Petri Dish B sees a double ever 6 minutes
Consequences
A doubles 60 / 10 = 6 times.
B doubles 60 / 6 = 10 times.SolutionIf you work best with numbers then suppose there are 100 bacteria in both dishes at the beginningA = 100 * 2^6B = 100 * 2^10A will have 100 * 64 = 6400 bacteria growing inside AB will have 100 * 1024 = 102400 bacteria growing inside BB/A = 102400 / 6400 = 16There are 16 times as many in B than in A
show that the straight line x+y does not intersect the curve x^2-8x+y^2-12y+6=0 if k^2-20k+8>0
Create a birthday Polynomial with 07.01.2006
Answer:
Step-by-step explanation:
the birthday date is : 07/01/2006 so the numbers are : 07012006 let's switch them : 60021070 we have 8 numbers so our highest degree is 7 6*(x∧7)+0*(x∧6)+0*(x∧5)+2*(x∧4)+1*(x³)+0*(x²)+7*x+0*(x∧0) 6*(x∧7)+2*(x∧4)+x³+7xHere is another example :
The perimeter of a rectangular field that measures 2 feet by 18 inches is _________ ft. A. 40 B. 7 C. 84 D. 6
Answer:
B. 7
Step-by-step explanation:
The solution for the following system of linear equation 3m-2n=13 is (2,-1) true or false
Answer:
Not True
Step-by-step explanation:
>_<
[tex]\text{To find your answer, plug in the values to the equation and solve:}\\\\3(2)-2(-1)=13\\\\\text{Solve:}\\\\3(2)-2(-1)=13\\\\6+2=13\\\\8=13\\\\\text{8 does not equal 13, therefore making the equation FALSE}\\\\\boxed{\text{False}}[/tex]
in the function y+3=(1/3x)^2, what effect does the number 1/3 have on the graph, as compared to the graph of y=x^2
Answer:
I think the answer is it stretches the graph horizontally by a factor of 3.
Step-by-step explanation:
Answer: it stretches the graph horizontally by a factor of 3
Step-by-step explanation: I got it correct on a-pex
The width of a rectangle is 38 centimeters. The perimeter is at least 692 centimeters. Write an inequality that represents all possible values for the length of the rectangle. Then solve the inequality.
Answer:
See bolded / underlined / italicized below -
Step-by-step explanation:
This is a great question!
If x were the length of this rectangle, then we could conclude the following,
2( 38 ) + 2( x ) > 692,
As you can see there is a greater than sign present, as the perimeter is at least 692 centimeters. In this case the perimeter is given to be at least 692 centimeters, but can also be calculated through double the width and double the length together. And of course we are given the width to be 38 cm -
2( 38 ) + 2x > 692,
76 + 2x > 692,
2x > 616,
x > 308
Solution = Length should be at least 308 cm
( The attachment below is not drawn to scale )
A package of 8-count AA batteries cost $6.16. A package of 20-count AA batteries cost $15.60. Which statement about the unit prices is true?
Answer:
The unit prices will be within the range of $0.77 ≤x≤$0.78
Step-by-step explanation:
If a package 8-count AA batteries cost $6.16 and a package of same 20-count AA batteries cost $15.60, to calculate the unit price, the following steps must be carried out:
8 counts AA batteries = $6.16
A unit price (i.e 1 count) = x
Cross multiplying
8 × x = 6.16 × 1
x = 6.16/8
x = $0.77 for a unit price
Similarly, if 20-count AA batteries cost $15.60, then:
20 counta = $15.60
1 count = x
Cross multiplying
20 × x = $15.60 × 1
x = $15.60/20
x = $0.78 for a unit price
From above calculation, of can be seen that the unit price is almost similar but with a difference of $0.01 ($0.78-$0.77) which is insignificant. Based on this, we can conclude that a unit price of the battery is between the range
$0.77 ≤x≤$0.78
Answer:
The 8-count pack of AA batteries has a lower unit price of 0.77
per battery.
Step-by-step explanation: