Please help answer these math riddles
Answer:
Challenge B is 1.827
Step-by-step explanation:
I need more letters to submit this.
A rectangular metal tank with an open top is to hold cubic feet of liquid. What are the dimensions of the tank that require the least material to%E2%80%8B build?
Answer:
[tex]h = 3.5[/tex]
[tex]w = 7[/tex]
[tex]l = 7[/tex]
Step-by-step explanation:
Given
[tex]Volume = 171.5ft^3[/tex]
Required
The dimension that requires least material
The volume is:
[tex]Volume = lwh[/tex]
Where:
[tex]l \to length[/tex]
[tex]w \to width[/tex]
[tex]h \to height[/tex]
So, we have:
[tex]171.5 = lwh[/tex]
Make l the subject
[tex]l = \frac{171.5}{wh}[/tex]
The surface area (A) of an open-top rectangular tank is:
[tex]A = lw + 2lh + 2wh[/tex]
Substitute: [tex]l = \frac{171.5}{wh}[/tex]
[tex]A = \frac{171.5}{wh} * w + 2*\frac{171.5}{wh}*h + 2wh[/tex]
[tex]A = \frac{171.5}{h} + 2*\frac{171.5}{w} + 2wh[/tex]
[tex]A = \frac{171.5}{h} + \frac{343}{w} + 2wh[/tex]
Rewrite as:
[tex]A = 171.5h^{-1} + 343w^{-1} + 2wh[/tex]
Differentiate with respect to h and w
[tex]A_h = -171.5h^{-2} +2w[/tex]
[tex]A_w = -343w^{-2} +2h[/tex]
Equate both to 0
[tex]-171.5h^{-2} +2w=0[/tex]
Make w the subject
[tex]2w = 171.5h^{-2}[/tex]
Divide by 2
[tex]w = 85.75h^{-2}[/tex]
[tex]-343w^{-2} +2h = 0[/tex]
Make h the subject
[tex]2h = 343w^{-2}[/tex]
Divide by 2
[tex]h = 171.5w^{-2}[/tex]
[tex]h = \frac{171.5}{w^2}[/tex]
Substitute [tex]w = 85.75h^{-2}[/tex] in [tex]h = \frac{171.5}{w^2}[/tex]
[tex]h = \frac{171.5}{(85.75h^{-2})^2}[/tex]
[tex]h = \frac{171.5}{85.75^2*h^{-4}}[/tex]
[tex]h = \frac{2}{85.75*h^{-4}}[/tex]
Multiply both sides by [tex]h^{-4}[/tex]
[tex]h^{-4} * h = \frac{1}{85.75*h^{-4}} * h^{-4}[/tex]
[tex]h^{-3} = \frac{2}{85.75}[/tex]
Rewrite as:
[tex]\frac{1}{h^3} = \frac{2}{85.75}[/tex]
Inverse both sides
[tex]h^3 = 85.75/2[/tex]
[tex]h^3 = 42.875[/tex]
Take cube roots
[tex]h = 3.5[/tex] ---- height
Recall that: [tex]w = 85.75h^{-2}[/tex]
[tex]w = 85.75 * 3.5^{-2}[/tex]
[tex]w = 7[/tex] --- width
Recall that: [tex]l = \frac{171.5}{wh}[/tex]
[tex]l = \frac{171.5}{3.5 * 7}[/tex]
[tex]l = 7[/tex] --- length
From the sample space S=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) a single number is to be selected at random. Given event A, that the selected number is even, and event B, that the selected number is a multiple of 4, find P(AIB)
Answer:
[tex]P(A|B) = 1[/tex]
Step-by-step explanation:
Given
[tex]S = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}[/tex]
[tex]A = \{2,4,6,8,10,12,14\}[/tex]
[tex]P(A) = 7/15[/tex]
[tex]B = \{4,8,12\}[/tex]
[tex]P(B) = 3/15[/tex]
Required
[tex]P(A|B)[/tex]
This is calculated as:
[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]
Where
[tex]A\ n\ B = \{4,8,12\}[/tex]
[tex]P(A\ n\ B) = 3/15[/tex]
So, we have:
[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]
[tex]P(A|B) = \frac{3/15}{3/15}[/tex]
[tex]P(A|B) = 1[/tex]
pls help for both 12 and 13!!
Answer:
The answer to 12 is 40 cubic units
Step-by-step explanation:
work out 5 3/5 divided by 2 2/3 in the simplest form
Answer:
2.1
Step-by-step explanation:
Please use the following image for the next 7 questions. Keep in mind
that because XY is tangent to circle M, XY and XM form a right angle. XY is tangent to circle M at point X.
XM = 12 and YM = 43.
Questions:
1. What is the area of circle M?
2. What is the circumference of circle M?
3. Find the length of XY.
4. Find the measure of angle M.
5. Find the area of triangle XYM.
6. Find the area of the minor sector that has been created as a part of triangle XYM.
7. Find the arc length of the minor arc from point C to the point where YM intersects with the circle.
Answer:
Step-by-step explanation:
1). Since, XM is the radius of the circle,
Therefore, area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi (XM)^2[/tex]
= [tex]\pi (12)^2[/tex]
= 452.39 units²
2). Circumference of a circle = 2πr
= 2π(XM)
= 2π(12)
= 24π
= 75.40 units
3). By applying Pythagoras theorem in ΔYXM,
YM² = XY² + XM²
(43)²= (XY)² + (12)²
1849 - 144 = (XY)²
XY = 41.29 units
4). tan(∠M) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{XY}{XM}[/tex]
m∠M = [tex]tan^{-1}(\frac{41.29}{12} )[/tex]
= 73.79°
5). Area of ΔXYM = [tex]\frac{1}{2}(\text{Base)}(\text{Height})[/tex]
= [tex]\frac{1}{2}(41.29)(12)[/tex]
= 247.74 square units
6). Area of the minor sector created by ΔXYM = [tex]\frac{\theta}{360}(\pi r^2)[/tex]
= [tex]\frac{73.79}{360}(452.39)[/tex]
= 92.73 units²
Instructions: Find the value of x
Please help I’ll mark brainilest.
all the lenses inside the circle ar equal and the two chords are also equal distance from the center point so arc x would equal arc CD
X = 50 degrees
cuadrado de binomio
(x-2)(-2+x)
Answer:
x^2-4x+4
Step-by-step explanation:
See image below:)
Pythagorean theorem.
I hope this is help full to you
Answer:
3
Step-by-step explanation:
because this is the formula of Pythagorean theorem a^2 + b^2 = c^2 so all I did was 5^2 = 25 - 4^2 = 25-16 = 9 and square root of 9 = 3 i hope this helps. :D please give brainliest
A spinner has three unequal sections: red, yellow, and blue. The table shows the results of Nolan's spins.
Find the experimental probability of landing on each color. Enter your answers as simplified fractions.
Color
Red 11
Yellow18
Blue4
Frequency
The probability of landing on red is
The probability of landing on yellow is
The probability of landing on blue is
Answer:
Yellow will have the best chance because it’s more red will have the second best chance because it is the second biggest and blue you probably will never get it
Step-by-step explanation:
Can someone’s please help
Answer:
4.87 ft
Step-by-step explanation:
The height of the skylight =
The height of the blue △ - the height of the red △
Let b ft be the height of the blue △.
sin 60° = [tex]\frac{b}{25} [/tex]
b = 25 sin 60°
Let r ft be the height of the red △.
tan 40° = [tex] \frac{r}{20} [/tex]
r = 20 tan 40°
The height of the skylight
= 25 sin 60° - 20 tan 40°
= 4.87 ft (rounded to the nearest hundredth)
Bilal's fishing line was on a spool with a radius of 4 cm. Suddenly, a fish pulled on the line, and the spool spun
16 times before Bilal began to reel in the fish.
What is the distance the fish pulled the fishing line?
Round your answer to the nearest cm.
Answer:
402 cm
Step-by-step explanation:
Given :
Radius = 4 cm
The Circumference of a circle :
C = 2πr
C = 2 * π * 4 = 8π
Spool is spun 16 times :
Circumference * 16
8π * 16
8 * 3.14 * 16
= 401.92
= 402 cm
Answer:
402 cm
Step-by-step explanation:
I NEED HELP QUICK #33 #34 #35
Answer:
34.) 93 + 72 = 165
x = 165
35.) w + z + 9(w - z)
w + z + 9w - 9z
w + 9w + z - 9z
10 w - 8z
13) The graph
represents the
function g(x).
a) Based on the graph
what is g(0)?
-4
-3
b) What is the
domain and range
of the function?
Hi there! g(0) means the value of g(x) at x = 0. Look at x = 0 and see which y-point makes x = 0.
See that y = 4 makes x = 0 for the graph. Thus, g(0) = 4.
Next is to find the domain and range. Domain is the set of all x-values while Range is the set of all y-values.
For domain, look at the horizontal x-axis plane and the graph. Notice how the graph infinitely goes up for both negative and positive. Since the graph is in negative and positive as well. That means the domain is all real numbers
For range, look at the vertical y-axis and the graph. Notice how when y < -2, there are no points that are part of the graph. The graph goes infinitely for range as well but there're no y-values less than -2 for the graph.
Therefore, range is y >= -2.
Answer
g(0) = 4domain is set of all real numbers.range is y >= -2Mike is saving up for a computer. He has $200 saved already. To earn more,
he works part-time at a job that pays $15 per hour. Let y represent the price of
the computer he chooses, and let x represent the number of hours he works.
To purchase the computer, he will need to save at least y dollars.
A. ys 200 + 15x
B. y 2 200 - 15x
C. ys 15x - 200
D. y 2 200x + 15
- PREVIOUS
Answer:
200+15x
Step-by-step explanation:
he will need to save at least 200+15x
y= amount to purchase the computer
x=hours worked for $15 per hour
$200 -money already saved
y ≤ 200+15x
A local school newspaper's editor wants to survey students to determine the approval rating of the current student council president. How would the newspaper apply the cluster sampling method to find this information?
A. The newspaper staff surveys only the female students in the entire school.
B. The newspaper staff surveys random students from every grade in the school.
C. The newspaper staff surveys every student in a randomly selected grade.
D. The newspaper staff surveys 30 students from each grade in the school.
Answer:
B
Step-by-step explanation:
The correct option is B.
The newspaper staff surveys random students from every grade in the school.
Cluster samplingIn cluster sampling, researchers divide a population into smaller groups known as clusters. They then randomly select among these clusters to form a sample. Cluster sampling is a method of probability sampling that is often used to study large populations, particularly those that are widely geographically dispersed.
What is an example of cluster sampling?An example of single-stage cluster sampling – An NGO wants to create a sample of girls across five neighboring towns to provide education. Using single-stage sampling, the NGO randomly selects towns (clusters) to form a sample and extend help to the girls deprived of education in those towns.
Learn more about cluster sampling here https://brainly.com/question/9910540
#SPJ2
The volume of a particular die is 12100 mm3. Use the fact that 10 mm equals 1 cm to convert this volume to cm3.
anyone mind helping me with this problem?
Answer:
x= √65, so B is the answer
Which expressions are equivalent to p+p+p+p+p+p+p? Choose ALL that apply.
7р
6p+2p
4p + 3p
Sp
3p + 5p
5p + 2p
Answer:
It would be 7p, 4p + 3p, and 5p + 2p
Step-by-step explanation:
Overall there is 7 p's
4 + 3 = 7 and 5 + 2 = 7
Unless there is more information, those are the answers.
please help (math) brainliest
Answer:
the answer is the first one
I stores having a sale on jellybeans in trail mix. For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. Find the cost for each pound of jellybeans and each pound of trail mix
Answer: The cost of each pound of jellybean is $2.5
The cost for each pound of trail mix is $1.5
Step-by-step explanation:
Let the cost for each pound of jellybeans be x.
Let the cost of each pound of trail mix be y.
Based on the information given, we can form an equation which will be:
For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. This will be:
2x + 12y = 23 ...... i
For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. This will be:
5x + 3y = 17...... ii
2x + 12y = 23 ...... i
5x + 3y = 17...... ii
Multiply equation i by 5
Multiply equation ii by 2
10x + 60y = 115 ...... iii
10x + 6y = 34 ..... iv
Subtract iv from iii
54y = 81
y = 81/54
y = 1.5
The cost for each pound of trail mix is $1.5
From equation i
2x + 12y = 23
2x + 12(1.5) = 23
2x + 18 = 23
2x = 23 - 18
2x = 5
x = 5/2 = 2.5
The cost of each pound of jellybean is $2.5
Which of these fractions are equivalent to -3/2
Which graph shows the point (-4, 0)?
Answer:
Graph C is the correct answer
Step-by-step explanation:
Hope this helps and,
let me know if it was correct.
If anyone can please help
Answer:
Pretty sure it's H
Step-by-step explanation:
The two parabolas intersect at (-1,0) and (0,-1)
Is the relation exponential or linear or neither (15,10)(16,20)(17,40)(18,70)
9514 1404 393
Answer:
neither
Step-by-step explanation:
The x-values have a common difference of 1. The y-values have first differences of 10, 20, 30. The second differences are constant at 10, indicating a quadratic relation.
The relation is neither exponential nor linear.
_____
y = 5x^2 -145x +1060
Create an example of a situation where there is a negative cash flow.?
Please help me with this problem
Question: 5d - 6 + 8 -3d = 12
5d - 6 + 8 - 3d = 12
Combine like terms:
2d + 2 = 12
Subtract 2 from both sides
2d = 10
Divide both sides by 2
D = 5
Answer:
d = 5
Step-by-step explanation:
5d - 6 + 8 -3d = 12
Regroup
5d - 3d - 6 + 8 = 12
Combine like terms
2d + 2= 12
Subtract 2 from both sides
2d = 10
Divide both sides by 2
d = 5
What is the solution to
3x*2-2x+4=0
Answer:
Step-by-step explanation:
[tex]3x^2 - 2x + 4 = 0[/tex]
a = 3, b = -2, c = 4
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\\\x = \frac{2 \pm \sqrt{2^2 - (4 \times3 \times 4} )}{2 \times 3}\\\\x = \frac{2 \pm \sqrt{4 - 48} }{6}\\\\x = \frac{2 \pm \sqrt{-44} }{6}\\\\x =\frac{2 \pm 2i \sqrt{11} }{6}\\\\x =\frac{1 + i \sqrt{11} }{3}\ , x =\frac{1 - i \sqrt{11} }{3}\\\\\\\\[/tex]
What are the coordinates for b?
Answer:
Step-by-step explanation:
(0,-3.5)
Answer:
(0, -3.5)
Step-by-step explanation:
The x coordinate is first
We stay on the y axis so the x coordinate is 0
The y coordinate is second
We go down 3 1/2 units so the y coordinate is -3 1/2
(0, -3.5)
________ analysis is the statistical process of estimating the relationship between dependent and _______ variables. A. Regression, independent B. Time series, outcome C. Time series, latent D. Regression, outcome
Answer:
A. Regression, independent
Step-by-step explanation:
Regression analysis can be regarded as a statistical methods which is been utilized in estimating the relationships that exist between a dependent variable as well as one or more independent variables. It is tools used in assessment of strength of the relationship that between variables, it could be used to model future relationship between variables.
Regression analysis posses different
variations, These are;
✓ linear
✓ nonlinear
✓multiple linear,
For linear model, this equation can be used.
Y = (a + bX + ϵ)
Where
Y =Dependent variable
a =Intercept
X= Independent variable
ϵ = Residual error
b =Slope
It should be noted that Regression
analysis is the statistical process of estimating the relationship between dependent and independent
variables.