Answer:
2/3
Step-by-step explanation:
A = rolling a six
B = rolling a number less than 4
Probability of A or B
P(A) or P(B) = P(A) + P(B) - P(AnB)
Probability = (number of required outcome / Total possible outcomes)
P(A) = 1 / 6
P(B) :
Required outcomes = (3, 2, 1) = 3
P(B) = 3/6 = 1/2
P(AnB) = A={6} ; B = {1,2,3} ; AnB = {}
P(AnB) = 0
Hence,
P(A) or P(B) = 1/6 + 1/2 - 0
= (1 + 3) / 6
= 4/ 6
= 2/3
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.
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
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)
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:
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
I need help pls i don't know the answer to these words
Answer:
a parallel line: is coplanar lines that never interact
a skew: is lines that are not on the same plane and never intersect
an interior angle: is interior lines that lie on the same side of transversal
an exterior angle: is a line that lies between parallel lines that are cut by transversal
a consecutive interior angle: is a line that lies on the same side both parallel lines and the transversal
a corresponding angle: lies in the region not between parallel lines that are cut by transversal
a tranversal: is a line that interacts 2 or more coplanar lines at 2 different points
Have a great day love!
Step-by-step explanation:
Mayzie's Masks has a monthly demand of 250 masks. It costs $100 to place an order
and the holding cost is 20% of the cost of a mask, which is $30. What is the total
cost?
Answer:
$951
Step-by-step explanation:
EOQ = Sqroot{(2*Annual Demand*Ordering cost)/Holding cost}
= Sqroot{(2*250*12*100)/(0.2*30)}
= 317 Units Approximately
Total Holding cost = Average Inventory * Holding cost per unit
= (EOQ/2)*Holding cost per unit
= (317/2)*(0.2*30)
= $951
So by knowing the holding cost and the percentage that it represents, we want to find the total cost of the masks. We will find that the cost is $150.
We know that the holding cost is 20% of the cost of a single mask, so if the cost of a mask is C, the holding cost is:
(20%/100%)*C = 0.2*C
And we know that this is equal to $30, so we get:
0.2*C = $30
Now we can solve this for C, the total cost of a mask:
C = $30/0.2 = $150.
If you want to learn more, you can read:
https://brainly.com/question/14094934
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
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 = 5The 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 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.
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
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
SOMEONE PLEASE HELP QUICK ITS TIMED
Answer:
true
Step-by-step explanation:
Answer:
true is the answer yyyt
Help meee I don’t understand
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 of the shows the correct sums that would be found when clustering is used to find the answer to the problem 41 x 22?
820 + 82 = 912
800 + 2 = 802
820 + 82 = 902
820 + 80 = 900
can someone please help try the best that you can
f(x) = |3x+5| + 6
g(x) =7
find (f+g) (x)
Answer:
(f + g)(x) = |3x + 5| + 13
Step-by-step explanation:
Given
f(x) = |3x + 5| + 6
g(x) = 7
Required
Find (f + g)(x)
In functions
(f + g)(x) = f(x) + g(x)
Meaning that, we simply add the given functions together
So, we have that:
(f + g)(x) = |3x + 5| + 6 + 7
(f + g)(x) = |3x + 5| + 13
Hence, (f + g)(x) when calculated equals |3x + 5| + 13
Per 100 grams, an apple has 5 mg of magnesium whereas a banana has 27 mg, an apple has 6 mg of calcium where a banana has 5 mg, and an apple has 11 mg of phosphorus where a banana has 22 mg. Now, consider the vectors v1 = 2 4 5 6 11 3 5 and v2 = 2 4 27 5 22 3 5. (a) Give a physical interpretation of these two vectors, i.e. write a sentence explaining what these vectors represent in the real-world context described. (b) Give a physical interpretation of the linear combination 4v1 + 2v2. (c) Give a physical interpretation of the span of these two vectors. (What has to be true about the weights of the vectors in this situation.)
Answer:
hello your question lacks some vital information attached below is the complete question
answer :
a) consuming some amount of apple ( x ) and (y) amount of banana will determine the amount of magnesium, calcium and phosphorous you will be getting
b) 74mg of magnesium is consumed
34 mg of calcium consumed
88 mg of phosphorous consumed
c) The span of the two vectors will intercept for any value of X and Y ( whole number values ) and this indicates
The amount of magnesium, calcium and phosphorous consumed is finite and a whole number
Step-by-step explanation:
Given :
per 100 grams, apple has 5 mg of magnesium
per 100 grams , a banana has 27 mg
also an apple has 6 mg of calcium while a banana has 5 mg
An apple has 11 mg of phosphorous while a banana has 22 mg
attached below is the detailed solution
A) Give a physical interpretation of the vectors is that
consuming some amount of apple ( x ) and (y) amount of banana will determine the amount of magnesium, calcium and phosphorous you will be getting
B) Physical interpretation of linear combination : 4v1 + 2v2
Detailed solution attached below
= 74mg of magnesium is consumed
34 mg of calcium consumed
88 mg of phosphorous consumed
C) The span of the two vectors will intercept for any value of X and Y ( whole number values ) and this indicates
The amount of magnesium, calcium and phosphorous consumed is finite and a whole number
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:
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
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:
Pls help me I’m really dumb
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]
there are two equivalent fractions that have a least common denominator of 14. the sum of both of the denominators is 56. the sum of both of the numerators is 12. the smaller numerator is over the smaller denominator. what are these two equivalent fractions brainly
Answer:
11+2=
Step-by-step explanation:
-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:
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.
(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
Help!!! Please help me out
Answer:man I’m sry
Step-by-step explanation: