Answer:
205 cars were rejected
Step-by-step explanation:
x 75
____ ____
820 100
cross multiply
100x=61500
simplify
x=615
820-615
anwer:205
hope it helps!
Find the volume of the cube or rectangular prism in cubic centimeters
Answer:
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Cube is the same
Answer:V=h×b×w
Step-by-step explanation:
You have to mulitiply height,width, and the base together to get the volume.
A piece of cardboard measures 10 in. by 15 in. Two equal squares are removed from the corners of a 10-in. side as shown in the figure. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.
(a) Write a formula V(x) for the volume of the box.
(b) Find the domain of V for the problem situation.
(c) Use ANALYTICAL method (my teacher said don't graph) to find the maximum volume and the value of x that gives it.
SEE IMAGE!!!
Answer:
[tex]V(x) = 66.02\ \text{in}^3 \ \vert \ _x_=_1_._9_6[/tex]
Step-by-step explanation:
Part (a)The volume of a rectangular prism is found using the formula: V = lwh.
In order to write a formula in terms of the variable x, we need to write expressions for the length, width, and height of the rectangle.
We can say the length is the bottom of the base of the prism. To find this value, we can subtract x and x from 15 and divide this by 2, since there are two equal rectangles (base and lid).
Length: [tex]\frac{15-2x}{2} =7.5-x[/tex]We can say the width is the side of the base of the prism. To find this value, we can subtract 2x from 10.
Width: [tex]10-2x[/tex]The height of the prism can be x, which is the labeled length of the rectangle next to the base and lid.
Height: [tex]x[/tex]Now we are able to write a formula for volume in terms of x.
[tex]V(x)=(7.5-x)(10-2x)(x)[/tex] [tex]V(x)=x(75-25x+2x^2)[/tex] [tex]V(x)=75x-25x^2+2x^3[/tex] Part (b)The domain of the volume is where x > 0, 2x < 10, and 2x < 15.
This is because our expressions for length ([tex]\frac{15-2x}{2}[/tex]), width (10-2x), and height (x) cannot go below 0, because you cannot have a negative value for measurement - realistically.
Therefore, if we take into account all of these restrictions on x, the domain is where 0 < x < 5.
x cannot be > 5 since that would not satisfy 2x < 10.
The domain of V for this problem situation is D: (0, 5).
Part (c)In order to find the maximum volume of the rectangular prism using our formula we derived, we can use the idea of optimization in calculus.
Start by taking the derivative of V(x).
[tex]V'(x)=75-50x+6x^2[/tex]Set the derivative equal to 0. This gives us the critical point(s) in order to determine the extreme values of the function, aka where the max and min occur.
[tex]0=75-50x+6x^2[/tex] [tex]0=6x^2-50x+75[/tex]Solve for x by using the quadratic formula.
[tex]x=\frac{-(-50)\pm\sqrt{(-50)^2-4(6)(75)} }{2(6)}[/tex] [tex]x=\frac{50\pm\sqrt{2500-1800}}{12}[/tex] [tex]x=\frac{50\pm\sqrt{700} }{12}[/tex]Input this into your calculator and you should get:
[tex]x=6.37, \ 1.96[/tex]We are going to use x = 1.96 since 6.37 is NOT in the domain of V(x).
[tex]\boxed{x=1.96}[/tex]Now, since this value of x is going to give the maximum volume of this rectangular prism, or cardboard box, we can plug it back into the V(x) equation for volume to determine the maximum volume of the box.
[tex]V(1.96)=75(1.96)-25(1.96)^2+2(1.96)^3[/tex] [tex]V(1.96) = 66.02\ \text{in}^3 \ \vert \ _x_=_1_._9_6[/tex]The maximum volume of the cardboard box is 66.02 in³ and the value of x that gives this is 1.96.
Use the quadratic formula to solve x^2 -3x - 5 = 0. Round to two decimal places.
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=\frac{3+\sqrt{29}}{2},\:x=\frac{3-\sqrt{29}}{2}[/tex]
Step-by-step explanation:
Given the equation
[tex]x^2\:-3x\:-\:5\:=\:0[/tex]
solving with the quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-3,\:c=-5[/tex]
[tex]x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{29}}{2\cdot \:1}[/tex]
separating the solutions
[tex]x_1=\frac{-\left(-3\right)+\sqrt{29}}{2\cdot \:1},\:x_2=\frac{-\left(-3\right)-\sqrt{29}}{2\cdot \:1}[/tex]
solving
[tex]x=\frac{-\left(-3\right)+\sqrt{29}}{2\cdot \:\:1}[/tex]
[tex]=\frac{3+\sqrt{29}}{2\cdot \:1}[/tex]
[tex]=\frac{3+\sqrt{29}}{2}[/tex]
also solving
[tex]\:x=\frac{-\left(-3\right)-\sqrt{29}}{2\cdot \:\:1}[/tex]
[tex]=\frac{3-\sqrt{29}}{2\cdot \:1}[/tex]
[tex]=\frac{3-\sqrt{29}}{2}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=\frac{3+\sqrt{29}}{2},\:x=\frac{3-\sqrt{29}}{2}[/tex]
The time taken to build a house is inversely proportional to the number of builders.
If there are 6 builders, it takes 80 days to complete the house.
How many builders must be employed to build the house in just 16 days?
Answer:
30 builders
Step-by-step explanation:
80÷5=16
6x5=30
How much will you spend on an investment if you want to receive $7,000 at an annual rate of 6% compounded weekly in 4 years?
Answer:
The investment required is: $5687
Step-by-step explanation:
Future Amount A= $7000
Rate r = 6% =0.06
Time t = 4
Compounded Weekly = n= 52
We need to find Principal Amount P
The formula used is: [tex]A=P(1+\frac{r}{n})^{n*t}[/tex]
Putting values and finding P
[tex]A=P(1+\frac{r}{n})^{n*t}\\7000=P(1+\frac{0.06}{52})^{4*52}\\7000=P(1.001)^{208}\\7000=P(1.231)\\P=\frac{7000}{1.231} \\P=5687[/tex]
So, The investment required is: $5687
Pls help me I’m really dumb
(x^2-6) (x+6) + 25
plz someone answer correctly
Answer:
x^3+6x^2-6x-11
Step-by-step explanation:
PLEASE GIVE BRAINLIEST
(x² - 6) (x + 6) + 25
x²(x + 6) + -6(x + 6) + 25
x³ + 6x² - 6x - 36 + 25
x³ + 6x² - 6x - 11
34.48 17.065 to the nearest tenth sorry just trying to get work done but yea if u help thx!!
Answer:
34.5
17.1
Step-by-step explanation:
the bill at a restaurant is 58.50, and john wants to leave a 15% tip.approximately how much money should she leave?
a. about $15.00
b. about $9.00
c. about $6.00
d. about $11.00
Help!!! Please help me out
Answer:man I’m sry
Step-by-step explanation:
The price of two dozen candy bars is $4.80. Bridget wants to buy 5 candy bars. what will she have to pay?
Answer:
24
Step-by-step explanation:
4.8×5 you have 5 candy bars that are $4.80 each so you multiply that by 5.
If salmon cost $6.5 per pound, what is the total cost of 1.3 pounds of salmon)
Explanation:
Write out an equation for the total cost. The price per pound multiplied by the number of pounds will give you the total cost.
Total cost
=
Price per pound
⋅
Number of pounds
Rearrange this algebraically to solve for
Price per pound
. To do this, divide both sides of the equation by
Number of pounds
to get
Price per pound
by itself.
Total cost
Number of pounds
=
Price per pound
⋅
Number of pounds
Number of pounds
This leaves us with a new form of the equation.
Price per pound
=
Total cost
Number of pounds
All we need to do now is substitute in the given information and solve.
Price per pound
=
Total cost
Number of pounds
=
38.87
2.6
=
$
14.9
Answer:
Step-by-step explanation:
1.3 * $6.5 = 8.45
The perimeter of a triangle is 37 cm. The lengths of its sides are x cm, x + 3 cm, and x + 7 cm. What is the length, in cm, of the longest
side of the triangle?
Answer:
x + (x +3) + (x +7) = 37
3x = 27
x = 9
Longest side = x + 7 = 16 cm
Step-by-step explanation:
Answer:
16cm
Step-by-step explanation:
x + x + 3 + x + 7 = 37 (make all sides equal 37)
3x + 10 = 37 (Add x's and coefficiants together)
-10 -10 (subtract 10 from each side)
3x = 27 (divide 27 by 3)
x = 9 (answer)
x, x + 3, x + 7 (finding longest length)
9, 9 + 3, 9 + 7 (Substitute 9 for x)
9cm, 12cm, 16cm (add each together)
16cm (answer)
Please hurry please
Answer:
a = -10
Step-by-step explanation:
solving inequation : a [tex]\leq[/tex] -6.5 so a = -10 complies
Answer:
a=-10
Step-by-step explanation:
[tex]2a-7\leq -20\\2a\leq -13\\a\leq -6.5\\[/tex]
The only solution that fits this is a=-10
Which graph represents the function f(x) = |x + 3|?
Answer:
Answer is B
Step-by-step explanation:
If you are unsure about where to start, you could always plot some numbers down until you see a general pattern.
But a more intuitive way is to determine what happens during each transformation.
A regular y = |x| will have its vertex at the origin, because nothing is changed for a y = |x| graph. We have a ray that is reflected at the origin about the y-axis.
Now, let's explore the different transformations for an absolute value graph by taking a y = |x + h| graph.
What happens to the graph?
Well, we have shifted the graph -h units, just like a normal trigonometric, linear, or even parabolic graph. That is, we have shifted the graph h units to its negative side (to the left).
What about the y = |x| + h graph?
Well, like a parabola, we shift it h units upwards, and if h is negative, we shift it h units downwards.
So, if you understand what each transformation does, then you would be able to identify the changes in the shape's location.
Answer:
answer is b
Step-by-step explanation:
because i got it right on E D G E
- A picture frame is 12 inches long and 9 inches wide. In inches, what is the diagonal length of
the picture frame?
O 21 inches
O 15 inches
8 inches
06 inches
how do you identify rational expression?
Answer:
Step-by-step explanation:
Determine the domain. The excluded values are those values for the variable that result in the expression having a denominator of 0.
Factor the numerator and denominator.
Find common factors for the numerator and denominator and simplify.
If four out of ten people vote, then in a town with two hundred thousand people, how many will not vote?
Answer:50000
Step-by-step explanation:
Help meee I don’t understand
can someone please help try the best that you can
-5(−x−1)+4x−1=49 What is X?
Answer:
The solutions are x=4,x=−10. Explanation: The square root property involves taking the square root of both the terms on either side of the ...
1 answer
Step-by-step explanation:
SOMEONE PLEASE HELP QUICK ITS TIMED
Answer:
true
Step-by-step explanation:
Answer:
true is the answer yyyt
anyone smart enough to do this?
Answer:
8 tan 50 deg
Step-by-step explanation:
m<A = 50 deg
tan A = x/8
x = 8 tan 50 deg
Answer: C 8 tan 50 deg
Toni cleans the circular dining room table whose diameter is 6 feet. The label on the can of cleanser claims coverage for 80 square feet, but she noticed that the can is only half full. Will she have enough cleaner to clean the table? Use 3.14 for π. Remember, it takes two applications.
Answer yes or no.
Answer:
'no'
Step-by-step explanation:
The lowest temperature ever recorded on Earth was
-89.2°C in Antarctica. The highest temperature ever
recorded was 56.7°C in California. What is the
difference between the highest and lowest recorded
temperatures?
PLEASE ANSWERRRRR
Answer:
Highest temperature=56.7°C
Lowest temperature= -89.2°C
Difference between the temperatures = 89.2+56.7=145.9
Ill give 15 points Just answer it pleaseeeeeee
Answer:
Miling saves more because he saves 15 dollars a week while Daniel saves 10 dollars a week 10 dollars is less than 15 dollars
are greater than 0 and located to the right of 0 on a number
line.
Integers
O Positive numbers
Negative Numbers
Opposites
Question 2
10 pts
Every whole number, fraction, and decimal has an opposite.
True
False
Answer:
1o
2true I helped it help
What is the range of the function y=e4x?
Oy < 0
Oy>
O y<4
Oy>4
9514 1404 393
Answer:
y > 0
Step-by-step explanation:
The range of the function ...
y = e^(4x)
is the same as the range of any exponential function:
y > 0
The function can take on any positive value, but will never be 0 or negative. It has a horizontal asymptote of y=0.
The range of the given function is y > 0.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given function is,
y = e⁴ˣ
This is an exponential function.
The range of any exponential function is all the real numbers which are greater than 0.
So here also, the range is all the real numbers which are greater than 0.
So range is y > 0.
Hence the correct option is B.
Learn more about Exponential Functions here :
https://brainly.com/question/28596571
#SPJ7
The temperature right now is -3°F, and the forecasted high temperature is 2 °F. How many degrees will it have to warm to reach 2°F? 6.NS.5
Answer:
5
Step-by-step explanation:
Subtract the high temp from the low temp2 - ( -3) = 2 + 3 = 5Help???
Anyone?
Thank you
25% of $35 is 8.75, so the price would be $26.25. plus tax, the final price would be $27.825 or $27.83. if that doesn't work, try $27.82
(i was wrong before, this should be right now)
hope this helps!! :)