The breadth of the cuboid is 9 cm with the volume as 972 cm³.
Given:
length of the cuboid is twice the breadth and thrice of the height.
If the volume of the cuboid is 972 cm³ then find the breadth of the cuboid= ?
Let breadth of cuboid =x cm
(since length=2*breadth)
hence length=2x
(since given length=3*height
hence height=length/3)
hence height=(2x)/3
volume of cuboid
=length*breadth*height
=972 cm³ (given)
or x*2x*2x/3=972
or 4x³=972*3
or x³=243*3
hence x=(729)⅓
x=(9³)⅓ cm.
(breadth) x=9 cm
Hence the breadth of the cuboid is 9 cm.
Learn more about Cuboid here:
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Convert the following complex number into its polar representation:2-2√3i
Given:
[tex]=2-2\sqrt{3}i[/tex]Find-:
Convert complex numbers to a polar representation
Explanation-:
Polar from of the complex number
[tex]z=a+ib=r(\cos\theta+i\sin\theta)[/tex]Where,
[tex]\begin{gathered} r=\sqrt{a^2+b^2} \\ \\ \theta=\tan^{-1}(\frac{b}{a}) \end{gathered}[/tex]Given complex form is:
[tex]\begin{gathered} z=a+ib \\ \\ z=2-i2\sqrt{3} \\ \\ a=2 \\ \\ b=-2\sqrt{3} \end{gathered}[/tex][tex]\begin{gathered} r=|z|=\sqrt{a^2+b^2} \\ \\ r=|z|=\sqrt{2^2+(2\sqrt{3})^2} \\ \\ =\sqrt{4+12} \\ \\ =\sqrt{16} \\ \\ =4 \end{gathered}[/tex]For the angle value is:
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{b}{a}) \\ \\ \theta=\tan^{-1}(\frac{-2\sqrt{3}}{2}) \\ \\ =\tan^{-1}(-\sqrt{3}) \\ \\ =-60 \\ \\ =-\frac{\pi}{3} \end{gathered}[/tex]So, the polar form is:
[tex]\begin{gathered} z=r(\cos\theta+i\sin\theta) \\ \\ z=4(\cos(-\frac{\pi}{3})+i\sin(-\frac{\pi}{3})) \end{gathered}[/tex]Use the formula:
[tex]\begin{gathered} \sin(-\theta)=-\sin\theta \\ \\ \cos(-\theta)=+\cos\theta \end{gathered}[/tex]Then value is:
[tex]\begin{gathered} z=4(\cos(-\frac{\pi}{3})+i\sin(-\frac{\pi}{3})) \\ \\ z=4(\cos\frac{\pi}{3}-i\sin\frac{\pi}{3}) \end{gathered}[/tex]What is the dot product? U=-5,5,-5 v=6,5,-7
The dot product is given by:
[tex]u\cdot v=u_1v_1+u_2v_2+\cdots+u_nv_n_{}[/tex]therefore:
[tex]\begin{gathered} u\cdot v=(-5\cdot6)+(5\cdot5)+(-5\cdot-7) \\ u\cdot v=-30+25+35 \\ u\cdot v=30 \end{gathered}[/tex]What is the probability it lands between birds B and C?
B. 1/9
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes.
[tex]P(A)=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]Step 1
Let A represents the event that the birds lands between b and c
a)so, in this case the favorable outcome is that the birds lands between b and c, the length bewtween b and c is
[tex]BC=2\text{ in}[/tex]and , the total outcome is the total lengt, so total outcome = AD
[tex]\begin{gathered} AD=10\text{ in+ 2 in +6 in} \\ AD=18\text{ in} \end{gathered}[/tex]b) now,replace in the formula
[tex]\begin{gathered} P(A)=\frac{favorable\text{ outcomes}}{\text{total outcomes}} \\ P(A)=\frac{2i\text{n }}{18\text{ in}}=\frac{1}{9} \\ P(A)=\frac{1}{9} \end{gathered}[/tex]therefore, the answer is
B. 1/9
I hope this helps you
Please helpIf the 100th term of an arithmetic sequence is 595, and its common difference is 6, thenits first term a1= ,its second term a2= ,its third term a3=
Given
100th term of an arithmetic sequence is 595 and common difference , d = 6
Find
First three terms of arithmetic sequences.
Explanation
As we know the general nth term of an arithmetic sequence is given by
[tex]a_n=a+(n-1)d[/tex]we have given 100th term = 595 , so
[tex]\begin{gathered} a_{100}=a+(100-1)6 \\ 595=a+99\times6 \\ 595-594=a \\ a=1 \end{gathered}[/tex]so , first term = 1
second term = a + 6 = 7
third term = a + 2d = 1 +2*6 = 13
Final Answer
Therefore , the first terms of an arithmetic sequences are
[tex]a_1=1,a_2=7,a_3=13[/tex]Jim invested $4,000 in a bond at a yearly rate of 4.5%. He earned $540 in interest. Howlong was the money invested? (just type the number don't write years)
Answer:
3 years
Explanation:
The interest simple interest rate formula is
[tex]undefined[/tex]Solve equations: 1. 3x-4=232. 9-4x=173.6(x-7)=364. 2(x-5)-8= 34
1.
3x-4=23
First, add 4 to both sides of the equation:
3x-4+4 =23+4
3x =27
Divide both sides of the equation by 3.
3x/3 = 27/3
x= 9
if triangle ABC has sides of length 9, 15, and 3x, between which two numbers must the value of x lie?
Let's employ the triangle inequality here.
If the sides were to form a triangle.
Then if 3x was the longest side, it must be less than the sum of 15 and 9, being the other 2 sides.
So;
[tex]\begin{gathered} 3x<15+9 \\ 3x<24 \\ x<8 \end{gathered}[/tex]If 3x was the shortest side, then 15 would be the longest side, and thus
3x plus 9 must be greater than 15,
So;
[tex]\begin{gathered} 3x+9>15 \\ 3x>15-9 \\ 3x>6 \\ x>2 \end{gathered}[/tex]So, the range of values for which x must lie is;
[tex]2i.e any values greater than 2 but less than 8.The table below gives the grams of fat and calories in certain food items. Use this data to complete the following 3 question parts.Fat (x)31391934432529Calories580680410590660520570b. Describe the correlation seen in the scatter plot.is it positve or negative or no correlation?
b. We can see throught the scatter plot that as the grams of fat increaseas, so does the calories in certain food, therefore there is a directly proportion relationship between them.
It is a positive relationship because while one increases, the other one too.
Imagine you are working for Hasbro making Gummy Bear containers. On a day to day basis you fill up two different size containers with gummy bears. One of the containers is4.4x5.7 x 6.0 in dimensions and contains 385 gummy bears. The other is 8.1 x 8.1 x 8.3 in dimensions. About how many gummy bears would fit in the box? Round to the nearestwhole number
It is given that,
One of the containers is 4.4 x 5.7 x 6.0 in dimensions and contains 385 gummy bears.
So, 1 gummy bear occupies,
[tex]\frac{4.4\times5.7\times6.0}{385}=0.39086[/tex]The other is 8.1 x 8.1 x 8.3 in dimensions.
So, the number of gummy bears would fit in the box is,
[tex]\frac{8.1\times8.1\times8.3}{0.39086}=1393.24[/tex]Hence, the number of gummy bears is 1,393 (Rounded to the nearest whole number).
LEVEL B 1.b) Solve for x angle relationship X+34" 2x-120
Answer
x = 46 degrees
Step-by-step explanation:
Alternate interior angles are equal
x + 34 = 2x - 12
Collect the like terms
x - 2x = -12 - 34
-x = -46
Divide both sides by -1
-x/-1 = -46/-1
x = 46 degrees
Hence, the value of x is 46 degrees
State if the give binomial is a factor of the given polynomial [tex](9x ^{3} + 57x^{2} + 21x + 24) \div (x + 6)[/tex]
We want to find out if (x+6) is a factor of the polynomial
[tex]9x^3+57x^2+21x+24[/tex]In order to find this, we can use the factor theorem.
If we have a polynomial f(x) and want to find if (x-a) is a factor of this polynomial, we plug in x = a into the function and if we get 0, (x-a) is a factor(!)
Now, let's plug in:
x = -6 into the polynomial and see if we get a 0 or not.
Steps shown below:
[tex]\begin{gathered} 9x^3+57x^2+21x+24 \\ 9(-6)^3+57(-6)^2+21(-6)+24 \\ =-1944+2052-126+24 \\ =6 \end{gathered}[/tex]AnswerSince it doesn't produce a 0, (x + 6 ) is not a factor of the polynomial given.
I am very confused can you help me please thanks!
Solution
For this case we know that :
1/8 of teaspoon for every 3 cups of frosting
Now the amount of cups increase to 4 cups then we can find the number teaspoon
We can use a proportional rule and we got:
[tex]\frac{\frac{1}{8}}{3}=\frac{x}{4}[/tex]The answer is:
C
Solve for x. Enter the solutions from least to greatest.6x^2 – 18x – 240 = 0lesser x =greater x =
Answer:
x = -5
x = 8
Explanation:
If we have an equation with the form:
ax² + bx + c = 0
The solutions of the equation can be calculated using the following equation:
[tex]\begin{gathered} x=\frac{-b+\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-b-\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]So, if we replace a by 6, b by -18, and c by -240, we get that the solutions of the equation 6x² - 18x - 240 = 0 are:
[tex]\begin{gathered} x=\frac{-(-18)+\sqrt[]{(-18)^2-4(6)(-240)}}{2(6)}=\frac{18+\sqrt[]{6084}}{12}=8 \\ x=\frac{-(-18)-\sqrt[]{(-18)^2-4(6)(-240)}}{2(6)}=\frac{18-\sqrt[]{6084}}{12}=-5 \end{gathered}[/tex]Therefore, the solutions from least to greatest are:
x = -5
x = 8
A circle has a radius of 5.5A. A sector of the circle has a central angle of 1.7 radians. Find the area of the sector. Do not round any intermediate computations. Round your answer to the nearest tenth
Answer:
The circle has the following parameters:
[tex]\begin{gathered} \text{Radius = }5.5ft \\ \text{Angle = 1.7 Radians} \end{gathered}[/tex]We have to figure out the area of the sector of this circle that has the given angle and radius.!
[tex]\begin{gathered} A(\text{sector) = }\frac{1.7r}{2\pi r}\times2\pi(5.5)^2ft^2 \\ =(1.7\times5.5)ft^2 \\ =9.35ft^2 \end{gathered}[/tex]This is the area of the sector that we were interested in.!
Use your compass to help with the direction. Also, the question is in the question box
1. Extending the dashed lines
2. Translating the triangle ABC in the direction EF
copy the vector in each vertice
then with the final points draw the new triangle a distance of EF
The blue triangle is the translated triangle (in your case you can your compass to help with the direction and protractor to verify the distance).
v+8 over v = 1 over 2
The given expression is
[tex]\frac{v+8}{v}=\frac{1}{2}[/tex]First, we multiply 2v on each side.
[tex]\begin{gathered} 2v\cdot\frac{v+8}{v}=2v\cdot\frac{1}{2} \\ 2v+16=v \end{gathered}[/tex]Then, we subtract v on each side.
[tex]\begin{gathered} 2v-v+16=v-v \\ v+16=0 \end{gathered}[/tex]At last, we subtract 16 on each side.
[tex]\begin{gathered} v+16-16=-16 \\ v=-16 \end{gathered}[/tex]Therefore, the solution is -16.Question 4 5 points)Part 1: Find the median of the Science Midterm Exam Scores (2 points)Part 2: Explain how you found the median of the Science Midterm Exam Scores. Be sure to explain the process you used to identity at themedian is. (3 points)
median = 75
See explanation below
Explanation:Part 1:
To find the emadian, we can state the data on the dot plot of the science midterm scores:
60, 65, 65, 70, 70, 75, 75, 75, 80, 80, 85, 85, 90, 95, 100
Total number of data set = 15
median = (N+1)/2
N = 15
Median = (15+1)/2 =16/2 = 8
Median = 8th position in the data
The 8th number = 75
Hence, the median of the science midterm scores = 75
Part 2:
The process is to write out all the data on the plot.
Count the number of data.
Then apply the median formula
Or because it is an odd number, the middle number after listing it out is the median.
The middle number here is 75
given two sides of a triangle, find a range of possible lengths for the third side.9yd, 32yd
We have to use the Triangle Inequality Theorem, which states that any of the 2 sides of a triangle must be a greater sum than the third side.
So, to find the correct range of lengths, we have to use the difference of the two sides and their addition to calculate the interval.
[tex]\begin{gathered} 32-9Therefore, the range of possible lengths is 23Express: 12x-9x-4x+3 in factored form
SOLUTION:
Step 1:
In this question, we are given the following:
Expressing:
[tex]12\text{ x - 9x - 4x + 3}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 12\text{ x -9x - 4 x + 3} \\ \text{= -x + 3} \\ =\text{ -\lparen x -3\rparen } \end{gathered}[/tex]CONCLUSION:
The final answer in factored form =
[tex]-(x-3)[/tex]-20k - 5) + 2k = 5k + 5A k = 0B) k = 4k = 1D) k = 2
The equation is:
[tex]\begin{gathered} -2(k-5)+2k=5k+5 \\ \end{gathered}[/tex]We can distribute the -2 into the parenthesis
[tex]\begin{gathered} -2k+10+2k=5k+5 \\ 10=5k+5 \\ \end{gathered}[/tex]now we solve for k
[tex]\begin{gathered} 10-5=5k \\ 5=5k \\ \frac{5}{5}=k \\ 1=k \end{gathered}[/tex]Solve the following equation3(x+1)=5-2(3x+4)
The given equation is expressed as
3(x+1)=5-2(3x+4)
The first step is to open the brackets on each side of the equation by multiplying the terms inside the bracket by the terms outside the bracket. It becomes
3 * x + 3 * 1 = 5 - 2 * 3x + - 2 * 4
3x + 3 = 5 - 6x - 8
3x + 6x = 5 - 8 - 3
9x = - 6
x = - 6/9
x = - 2/3
Calvin is building a staircase pattern as shown in the figure. Each block is one foot high. How many blocks would it take to build steps that would be 10 feet high?
This is an example of an arithmetice series.
Step 1: Write out the formula for finding the nth term of an arithmetric series
[tex]undefined[/tex]Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 6 tiles the firstday. She started to go faster and by the end of day 4, she had placed 36 tiles. She worked at a steady rateafter the first day. Use an equation in point-slope form to determine how many days Lizzy took to placeall of the 100 tiles needed to finish the floor. Solve the problem using an equation in point-slope form.
We know that
• She placed 6 tiles on the first day.
,• By the end of day 4, she had placed 36 tiles.
Based on the given information, we can express the following equation.
[tex]y=3x+6[/tex]If she had placed 36 tiles in 3 days, it means she had placed 12 tiles per day, that's why the coefficient of x is 3. And the number 6 is the initial condition of the problem, that is, on day 0 she placed 6 tiles.
Now, for 100 tiles, we have to solve the equation when y = 100.
[tex]\begin{gathered} 100=3x+6 \\ 100-6=3x \\ 3x=94 \\ x=\frac{94}{3} \\ x=31.33333\ldots \end{gathered}[/tex]Therefore, she needs 32 days to place all the tiles.Notice that we cannot say 31 days, because it would be incomplete.
which values of a and b make the following equation true
Solution
Given that
[tex](5x^7y^2)(-4x^4y^5)=-20x^{7+4}y^{2+5}=-20x^{11}y^7[/tex]Comparing the indiced,
a = 11, b = 7
Option A
raw the hyperbola for each equation in problem l. the partial
B. given the equation of the hyperbola :
[tex]\begin{gathered} 9x^2-y^2=9 \\ \\ \frac{x^2}{1}-\frac{y^2}{9}=1 \end{gathered}[/tex]The graph of the hyperbola will be as following :
As shown in the figure :
vertices are : (-1,0) and (1,0)
Foci are ( -3.2 , 0) and (3.2 , 0)
End points are (0,-3) and (0,3)
Asymptotes are : y = 3x and y = -3x
A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 852 contains 170 green, one-headed Jolos; 284 purple, two-headed Jolos; and 430 one-headed JolosHow many green Jolos are there in Balans colony?A.260B.422C.308D. 138
A. 260
Explanation
Step 1
Let
[tex]\begin{gathered} green\text{ jolos,one-headed jolo=170} \\ \text{Purple ,two-headed jolos=284} \\ one\text{ headed jolos=430} \end{gathered}[/tex]as we can see
the total of green-one headed jolo is 170
and the total for one headed jolo is =430
so, the one-headed in counted twice
[tex]\begin{gathered} total\text{ of gr}en\text{ jolos= }430-170 \\ total\text{ of gr}en\text{ jolos= }260 \end{gathered}[/tex]so, the answer is
A.260
I hope this helps you
The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.2. The initial population is 10.
Answer
Explanation
Using the formula for the population growth:
[tex]P(t)=P_0\cdot(1+r)^t[/tex]where P₀ is the initial population, r is the rate of growth, and t is the time.
From the given information, we know that:
• P₀ = 10
,• r = 0.2
1.
And we are asked to find P(50) (when t = 50), thus, by replacing the values we get:
[tex]P(50)=10\cdot(1+0.20)^{50}[/tex][tex]P(50)\approx91004.3815[/tex]2.
For the population to double, this would mean that P(t) = 2P₀. By replacing this we get:
[tex]2P_0=10e^{0.20t}[/tex][tex]2(10)=10e^{0.20t}[/tex][tex]20=10e^{0.20t}[/tex][tex]\frac{20}{10}=e^{0.20t}[/tex][tex]\ln\frac{2}{1}=\ln e^{0.20t}[/tex][tex]\ln2=0.20t[/tex][tex]t=\frac{\ln2}{0.20}\approx3.5days[/tex]Solve each inequality 15 > 2x-7 > 9
Given the inequality expression
15 > 2x-7 > 9
Splitting the inequality expression into 2:
15 > 2x-7 and 2x - 7 > 9
For the inequality 15 > 2x-7
15 > 2x-7
Add 7 to both sides
15 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in signg
2x/2 < 22/2
x < 11
For the inequality 2x - 7 > 9
Add 7 to both sides
2x-7+7 > 9 + 7
2x > 16
Divide both sides by 2
2x/2 > 16/2
x > 8
Combine the solution to both inequalities
x>8 and x < 11
8 < x < 11
Hence the solution to the inequality expression is n)8 < x < 11
2x/2 < 22/2
x < 11
For the inequality 2x - 7 > 9
Add 7 to both sides
5 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in si)5 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in si)1
Solve the following inequality. Write the solution set in interval notation
Given:
Inequality is
[tex]5(x-3)<2(3x-1)[/tex]To find:
The solution set of the given inequality:
Explanation:
[tex]\begin{gathered} 5(x-3)<2(3x-1) \\ 5x-15<6x-2 \\ 5x-6x<15-2 \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore the solution set is
[tex](-13,\hat{\infty)}[/tex]Final answer:
The solution set is
[tex](-13,\infty)[/tex]whats the simplest form of— 3х + 7 – 2x +11 — x
The given expression is
[tex]-3x+7-2x+11-x[/tex]We have to reduce like terms. -3x, -2x, and -x are like terms. 7 and 11 are like terms.
[tex]-3x-2x-x+7+11=-6x+18[/tex]Then, we factor out the greatest common factor, observe that 6 is the greatest common factor
[tex]6(-x+3)[/tex]Hence, the simplest form is 6(-x + 3).