Answer:
A and D
Step-by-step explanation:
Find a formula for the described function. An open rectangular box with volume 3 m3 has a square base. Express the surface area SA of the box as a function of the length of a side of the base, x.
Answer:
[tex]SA(x) = x^2 + \frac{12}{x}[/tex]
Step-by-step explanation:
Given
[tex]V = 3m^3[/tex] --- volume
[tex]x \to base\ length[/tex]
[tex]y \to height[/tex]
Required
The surface area as a function of base length
The volume (V) is calculated as:
[tex]V = Base\ Area * Height[/tex]
[tex]V = x*x*y[/tex]
[tex]V = x^2*y[/tex]
Make y the subject
[tex]y = \frac{V}{x^2}[/tex]
Substitute 3 for V
[tex]y = \frac{3}{x^2}[/tex]
The surface area of the open box is:
[tex]SA = x^2 + 2xy+2xy[/tex]
[tex]SA = x^2 + 4xy[/tex]
Substitute: [tex]y = \frac{3}{x^2}[/tex]
[tex]SA = x^2 + 4x*\frac{3}{x^2}[/tex]
[tex]SA = x^2 + 4*\frac{3}{x}[/tex]
[tex]SA = x^2 + \frac{12}{x}[/tex]
Hence, the function is:
[tex]SA(x) = x^2 + \frac{12}{x}[/tex]
A company that makes hair-care products had 4,000 people try a new shampoo. Of the people, 32 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer: 0.8
Step-by-step explanation:
A pair of dice was rolled many times and the results appear below. Based upon these results, what is the experimental probability of rolling a multiple of 3?
Outcome
2 3 4 5 6 7 8 9 10 11 12
Frequency
3 6 8 11 14 16 15 12 9 5 1 The percent probability is = [ ? ]%
Round to the nearest percent.
Answer:
The exponential probability should be 33%.
Step-by-step explanation:
[tex]4 \div 12 = .33 \\ [/tex]
[tex].33 \times 100 = 33\%[/tex]
The experimental probability of rolling a multiple of 3 will be 33%.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A pair of dice was rolled many times and the results appear below. Based upon these results.
Outcome 2 3 4 5 6 7 8 9 10 11 12
Frequency 3 6 8 11 14 16 15 12 9 5 1
Then the experimental probability of rolling a multiple of 3 will be
Favorable events = 6 + 14 + 12 + 1 = 33
Total events = 100
Then the probability will be
P = (33 / 100) x 100
P = 0.33 x 100
P = 33%
More about the probability link is given below.
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Is this the correct answer?
Answer:
Correct.
Step-by-step explanation:
It looks good to me.
Good job!
Find the value of x.
Answer:
B I think because i did my math
Step-by-step explanation:
Write the equation of the line that passes through the points
Y=2x+5
Answer:
Parallel means that the lines never intersect. If the equation of the new line is y=ax+b , then the system
y=ax+b
y=2x+5
needs to have no solutions. Subtracting the equations gives us
(a−2)x+(b−5)=0
In order for this to ever be 0 we need either a≠2 or b=5 , so to stop this from happening, we will require both a=2 and b≠5 .
Since our line now has the form y=2x+b , and (4,5) is on the line, then the equation
5=2⋅4+b
should be true. Since this implies that b=−3 , we have that the parallel line going through (4,5) has equation
y=2x−3
What is an equation of a line that goes through point (4,-5) and is parallel to y=2x+8?
Which line is parallel to the line y = 2x -4?
What is an equation for a line parallel to y = 5 x -5 and passing through the point (4,19)?
What is an equation for the line that is parallel to y= -4x
use the substitution method to solve the system of equations. enter your answer as an ordered pair.AP3X
4(x+4)=8(y+2)
18y-22=3x+2
a.(12,6)
b.(4,2)
c.(8,10)
d.(4,8)
e.(6,1/2)
Answer:
b. x=4 and y= 2
...........
About 7% of the population has a particular genetic mutation. 800 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 800.
Answer:
The standard deviation is of 7.22 people.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have the mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
About 7% of the population has a particular genetic mutation.
This means that [tex]p = 0.07[/tex]
800 people are randomly selected.
This means that [tex]n = 800[/tex]
Find the standard deviation for the number of people with the genetic mutation in such groups of 800.
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.07*0.93} = 7.22[/tex]
The standard deviation is of 7.22 people.
What is the slope of the line in the graph? Enter answer without spaces
Answer:
-3/4
Step-by-step explanation:
From point (0,3), to get to point (4,0) you would need to go down 3 units, and right 4 units.
Hope this helps
Solve 3|x - 61 = 12.
How to solve this problem
Step-by-step explanation:
x = 180-106 = 74°
y = x/2 = 74/2 = 37°
4z+6 =106
4z = 100
z = 25°
50% of the trees are fruit trees .this means that?
Answer:
Half of the trees are not fruit trees
Answer:
It means that half of the trees are fruits while the other half sprouts vegetables.
Step-by-step explanation:
100% (trees) / 2 (types of trees, in this case, fruits and vegetables) = 50% (fruit trees) : 50% (vegetable trees)
If bc= 12 and cd is 5 then bd =
Answer:
bd would also equal 5 i love math
Step-by-step explanation:
Answer:
There's no diagram.
I guess You forgot to send.
I'll guess its a quadrilateral.
Draw out a little quadrilateral...eg a rectangle
Label your points.
From the labelling ... Distance BD is now the diagonal of the rectangle.
Using Pythagorean theorem to get it...
BD = √12²+5²
BD=13.
which of the following is not an appropriate method of proving triangles congruent. A] .asa B].sas C]ssa. D] sss.
A rectangular bin, completely filled, holds 1,200 cubic feet of grain. If the bin is 6 feet wide and 10 feet long, how deep is it ?
Answer:
20 feet
Step-by-step explanation:
Volume = length x width x height
1200 = 10 x 6 x h
1200 = 60h
h = 1200/60
height = 20
The rectangular bin is 20 feet deep.
What is a cuboid?A cuboid is a three-dimensional shape in which all sides are rectangles. A cuboid has 6 faces, 8 vertices, and 12 edges. All the angles formed at the vertices of a cuboid are right angles. The opposite edges are parallel to each other.
For the given situation,
A rectangular bin is in the shape of a cuboid.
Volume of the rectangular bin,V = 1200 cubic feet
Length of the rectangular bin,l = 10 feet
Width of the rectangular bin,w = 6 feet
Let the height of the rectangular bin be h.
The formula of volume of cuboid is
[tex]V=lwh[/tex]
Now substitute the above values,
⇒ [tex]1200=(10)(6)h[/tex]
⇒ [tex]h=\frac{1200}{60}[/tex]
⇒ [tex]h=20[/tex]
Hence we can conclude that the rectangular bin is 20 feet deep.
Learn more about cuboid here
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Please help!!!! Anyone!!
9514 1404 393
Answer:
g(x) = |x -7|
Step-by-step explanation:
The form given for your answer has parameters 'a', 'h', and 'k'. The parameter 'a' is the vertical scale factor. Since g(x) is a translation only, that factor is 1. The parameters (h, k) identify the translation (right, up). The translation is 7 units right and 0 units up, so (h, k) = (7, 0).
Filling in these values of the parameters, your g(x) is ...
g(x) = |x -7|
If RT is 10 centimeters long, what is ST?
Answer:
Answer: a
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
First, find x
RT = 2x + 3x
10 = 2x+3x
10 = 5x
10/5 = 2
Now place 2 in place of x in the line ST
ST = 3x
ST = 3 * 2
ST = 6
which expression represents these words?
8 more than the quotient of 32 and 4
A. (32-4)+8
B. 32÷4-8
C. (32-4)-8
D. 32÷4+8
Answer:
(32 ÷4) +8
Step-by-step explanation:
More than means it comes after
quotient of 32 and 4
32÷ 4
8 more than
(32 ÷4) +8
Help please asp. !!!
Answer:
16.8 [tex]m^{3}[/tex]
Step-by-step explanation:
Find your answer by using the formula of a cone (v= [tex]\frac{1}{3}[/tex]π[tex]r^{2}[/tex]h)
r= 2 (half of your diameter, which is 4)
h= 4
By inserting your radius and height, you get v= [tex]\frac{1}{3}[/tex]π([tex]2^{2}[/tex])4.
Put that into a calculator and you get 16.75516, which rounds to 16.8.
each exterior of a regular polygon is 30 degree find the sum of interior angles of the polygon
Step 1: 360÷30(exterior angle)= 12 sides
Step 2: (12-2)×180= 1800 (sum of the interior angles of the polygon)
Test: 1800÷ 12 sides= 150 ( 1 interior angle)
Solve for x. Round to the nearest tenth of
a degree, if necessary.
Answer:
x = 60.6
Step-by-step explanation:
tan x = opp/adj
tan x = 3.9/2.2
x = tan^-1 3.9/2.2
x = 60.6
How to find the angle ? Help pls
Answer:
I got :
Angle theta = 7.1° (approximately)Step-by-step explanation:
see attached photo
Step-by-step explanation:
The angle of an equilateral triangle is 180°, and its three internal angles are equal, all being 60°.
is y=2x an inverse variation
Answer:
ha ha ha... yesno
Step-by-step wrong explanation:
becoause it is the dilemma of the miniyamma
A. John wants to find the average time it takes students to run a lap around the track. He will consider 24 students to find the average time. Which unit(s) could be used for the unit of measurement?
1. Pounds
2. Seconds
3. Ounces
4. Minutes
5. Grams
B. Which of the procedures below would be the best way to find the average time?
1. Ask for 24 volunteers to run a lap around the track and have them state their own times.
2. Measure the times of 24 volunteers who run a lap around the track.
3. Randomly pick 24 students to run a lap around the track and measure their times.
4. Randomly pick 24 students to run a lap around the track and have them state their own times.
Answer:
A) 2. Seconds
4. Minutes
B) 2. Measure the times of 24 volunteers who run a lap around the track.
3. Randomly pick 24 students to run a lap around the track and measure their times.
Step-by-step explanation:
A. The unit(s) that could be used for the unit of measurement are the units used to measure time and the correct answer according to the options given above is seconds and minutes.
B. Which of the procedures below would be the best way to find the average time?
2. Measure the times of 24 volunteers who run a lap around the track.
3. Randomly pick 24 students to run a lap around the track and measure their times.
A box with a square base and open top must have a volume of 97556 c m 3 cm3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x x .] Simplify your formula as much as possible.
Answer:
S(x) = x² + 390224/x
Step-by-step explanation:
Volume of the open box = V = 97556 cm³
Material needed:
Let´s call x the side of the square base then the area of the base is
A(b) = x²
For the sides of the box, we have 4 sides each one with area of x*h
where h is the height of the box
The volume of the box V(b) = 97556 = x²*h then h = 97556/x²
S(x,h) = x² + 4*x*h*
The surface area of the box as function of x is:
S(x) = x² + 4*x*97556/x²
S(x) = x² + 390224/x
Find the value of x . PLEASE ANSWER QUICK ILL MARK BRAINLIEST
Answer:
x= 55
Step-by-step explanation:
Answer:
x is 55 degrees
Step-by-step explanation:
since it is a right angle set up the equation
20+x+15=90
then solve to get 55
answer the following questions
1. 2 2/3 divided by 1 1/6.
2. 6 2/3 divided by 2 6/7.
3. 4 1/6 divided by 10.
4. 6 1/2 divided by 3/4.
5. 3 3/4 divided by 5 5/8
Answer:
1. [tex]2 \frac{2}{7} [/tex]
2. [tex]2 \frac{1}{3} [/tex]
3. [tex] \frac{5}{12} [/tex]
4. [tex]8 \frac{2}{3} [/tex]
5. [tex] \frac{2}{3} [/tex]
Step-by-step explanation:
[tex]1. \: \: 2 \frac{2}{3} \div 1 \frac{1}{6} [/tex][tex] \frac{8}{3} \div \frac{7}{6} [/tex]
[tex] \frac{8}{3} \times \frac{6}{7} [/tex]
[tex]8( \frac{2}{7} )[/tex]
[tex] \frac{8 \times 2}{7} [/tex]
[tex] \frac{16}{7} [/tex]
[tex]2 \frac{2}{7} [/tex]
[tex]2. \: \: 6 \frac{2}{3} \div 2 \frac{6}{7} [/tex][tex] \frac{20}{3} \div \frac{20}{7} [/tex]
[tex] \frac{20}{3} \times \frac{7}{20} [/tex]
[tex] \frac{1}{3} \times 7[/tex]
[tex] \frac{7}{3} [/tex]
[tex]2 \frac{1}{3} [/tex]
[tex]3. \: \: 4 \frac{1}{6} \div 10[/tex][tex] \frac{25}{6} \div \frac{10}{1} [/tex]
[tex] \frac{25}{6} \times \frac{1}{10} [/tex]
[tex] \frac{5}{6} \times \frac{1}{2} [/tex]
[tex] \frac{5}{6 \times 2} [/tex]
[tex] \frac{5}{12} [/tex]
[tex]4. \: \: 6 \frac{1}{2} \div \frac{3}{4} [/tex][tex] \frac{13}{2} \div \frac{3}{4} [/tex]
[tex] \frac{13}{2} \times \frac{4}{3} [/tex]
[tex]13( \frac{2}{3} )[/tex]
[tex] \frac{13 \times 2}{3} [/tex]
[tex] \frac{26}{3} [/tex]
[tex]8 \frac{2}{3} [/tex]
[tex]5. \: \: 3 \frac{3}{4} \div 5 \frac{5}{8} [/tex][tex] \frac{15}{4} \div \frac{45}{8} [/tex]
[tex] \frac{15}{4} \times \frac{8}{45} [/tex]
[tex] \frac{1}{4} \times \frac{8}{3} [/tex]
[tex] \frac{2}{3} [/tex]
Hope it is helpful...Witch number line and expression show how to find the distance from 4 to - 1?
Answer:
I would tell you but you do not have a picture
Emelyn is comparing the rates of two different gardening companies for her camp site. The table below shows the rates for Log Edge Landscaping. Log Edge Landscaping Hours Worked 1.5 3 3.5 4.5 Total Cost $26 $44 $50 $62 The equation below represents the rates for Gatewood Gardening Services, where x represents the hours worked and y represents the total cost, in dollars. Compare the rates of both companies, and graph the relationship that represents the cost for the company with a greater rate of change.
Answer:
See Explanation
Step-by-step explanation:
Given
Edge Landscaping:
[tex]\begin{array}{cc}{Hours} & {Total} & {1.5} & {\$26} & {3} & {\$44} & {3.5} & {\$50} & {4.5} & {\$62} \ \end{array}[/tex]
The rates (m) of the above table is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
From the table, we have the following points
[tex](x_1,y_1) = (1.5,26)[/tex]
[tex](x_1,y_1) = (4.5,62)[/tex]
So, the rate is:
[tex]m = \frac{62 - 26}{4.5 - 1.5}[/tex]
[tex]m = \frac{36}{3.0}[/tex]
[tex]m = 12.0[/tex]
This means that the rate of edge landscaping is $12.0 per hour
The equation for Gatewood is not given. Hence, the rate cannot be calculated. However, the general procedure of calculating rates from a linear equation is as follows;
A linear equation is of the form:
[tex]y = mx + b[/tex]
Where:
[tex]m \to slope\ or\ rates[/tex]
In other words, if the equation is:
[tex]y = 20x + 5[/tex]
Then the rate is: 20 ($20/hour)
If the equation is: [tex]y = 10x + 5[/tex]
Then the rate is 10 ($10/hr)
Next, is to compare the rates;
For Edge landscaping, we have:
[tex]m = 12.0[/tex]
For Gatewood, we have:
[tex]m = 10[/tex] ------------ assume the equation is: [tex]y = 10x + 5[/tex]
Compare the rates:
[tex]12 > 10[/tex]
Hence, Edge landscaping has a greater hourly rate
dennis and christine scored 32 and 23, respectively, in the national career assessment examination
Answer:
[tex]\begin{array}{cccc}{Scores} & {f} & {LB} &{CF} & {39-41} & {6} & {39} &{6} & {36-38} & {7} & {36} &{13}& {33-35} & {9} &{33}&{22}& {30-32} & {13}&{30} &{35} & {27-29} & {22} &{27}&{57} & {24-26} & {10} &{24}&{67} & {21-23} & {9} &{21} &{76}& {18-20} & {7} &{18}&{83}& {15-17} & {8} &{15}&{91}& {12-14} & {4} &{12}&{95}& {9-11} & {2} &{9}&{97}& {6-8} & {1} &{6}& {98}&{3-5} & {1} &{3}&{99} \ \end{array}[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
Fill in the blanks
First, we fill in the lower boundary (LB).
This is done by writing out the lower boundary of each class
So, we have:
[tex]\begin{array}{ccc}{Scores} & {f} & {LB} & {39-41} & {6} & {39} & {36-38} & {7} & {36} & {33-35} & {9} &{33}& {30-32} & {13} &{30}& {27-29} & {22} &{27}& {24-26} & {10} &{24}& {21-23} & {9} &{21}& {18-20} & {7} &{18}& {15-17} & {8} &{15}& {12-14} & {4} &{12}& {9-11} & {2} &{9}& {6-8} & {1} &{6}& {3-5} & {1} &{3} \ \end{array}[/tex]
Next, is to fill the CF column
This is done by adding the current with the previous cumulative frequency.
So, we have:
[tex]\begin{array}{cccc}{Scores} & {f} & {LB} &{CF} & {39-41} & {6} & {39} &{6} & {36-38} & {7} & {36} &{6 + 7 = 13}& {33-35} & {9} &{33}&{13+9 = 22}& {30-32} & {13}&{30} &{22+13=35} & {27-29} & {22} &{27}&{35+22=57} & {24-26} & {10} &{24}&{57+10=67} & {21-23} & {9} &{21} &{67+9=76}& {18-20} & {7} &{18}&{76+7=83}& {15-17} & {8} &{15}&{83+8=91}& {12-14} & {4} &{12}&{91+4=95}& {9-11} & {2} &{9}&{95+2=97}& {6-8} & {1} &{6}& {97+1=98}&{3-5} & {1} &{3}&{98+1=99} \ \end{array}[/tex]
Thia is the complete table of filling the values of LB(lower boundaries) and <cf (less than commulative frequency).