Step-by-step explanation:
in its basic structure such a prism is like a cube (just rectangular and not squared) : 6 sides (rectangles).
2 rectangles top and bottom 6×8 = 48 m²
48 × 2 = 96 m²
2 rectangles front and back 6×4 = 24 m²
24 × 2 = 48 m²
2 rectangles left and right 8×4 = 32 m²
32 × 2 = 64 m²
the total surface area is
96 + 48 + 64 = 208 m²
it is hard to find other integer dimensions for the same surface area.
but as long as we are not restricted to integer numbers :
let's cut e.g. the height in half.
and we get
2 rectangles left and right 8×2 = 16 m²
16 × 2 = 32 m²
that "nails" already 2 dimensions (width and height).
we need to set now the third dimension (length) to create the same surface area :
length×8×2 + length×2×2 = 208 - 32 = 176
20×length = 176
length = 8.8 m
so, with
length = 8.8 m
width = 8 m
height = 2 m
we still get
2 rectangles top and bottom 8.8×8 = 70.4 m²
70.4 × 2 = 140.8 m²
2 rectangles front and back 8.8×2 = 17.6 m²
17.6 × 2 = 35.2 m²
2 rectangles left and right 8×2 = 16 m²
16 × 2 = 32 m²
as total surface area
140.8 + 35.2 + 32 = 208 m²
My first question is: The LCM of 6 and 9 is_____
The second question is: The GCF of 21 and 35 is______
Answer:
3 and 7
Step-by-step explanation:
The LCM of 6 and 9 is 3
The GCF of 21 and 35 is 7
The sum of an arithmetic series where t1 = -2, t3 = 7, and n = 15 is
The sum of the arithmetic series with the parameters t1 = -2, t3 = 7, and n = 15 is 442.5
How to determine the sum of the series?The given parameters are:
t1 = -2
t3 = 7
n = 15
Start by calculating the common difference using:
Tn = t1 + (n- 1)d
So, we have:
7 = -2 + (3 - 1) * d
Evaluate
7 = -2 + 2d
Add 2 to both sides
2d = 9
Divide by 2
d = 4.5
The sum is then calculated using:
[tex]S_n = \frac n2 * (2a + (n - 1) * d)[/tex]
So, we have:
[tex]S_{15} = \frac {15}2 * (2*-2 + (15 - 1) * 4.5)[/tex]
Evaluate
[tex]S_{15} = 442.5[/tex]
Hence, the sum of the arithmetic series is 442.5
Read more about arithmetic series at:
https://brainly.com/question/6561461
#SPJ1
The fourth term of an arithmetic sequence is 20, and the 13th term is 65. Find the sum of the first 13 terms
Answer:
S₁₃ = 455
Step-by-step explanation:
the sum to n terms of an arithmetic is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
We require to find both a₁ and d
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₄ = 20 and a₁₃ = 65 , then
a₁ + 3d = 20 → (1)
a₁ + 12d = 65 → (2)
subtract (1) from (2) term by term to eliminate a₁
9d = 45 ( divide both sides by 9 )
d = 5
substitute d = 5 into (1) and solve for a₁
a₁ + 3(5) = 20
a₁ + 15 = 20 ( subtract 15 from both sides )
a₁ = 5
Then
S₁₃ = [tex]\frac{13}{2}[/tex] [ (2 × 5 ) + (12 × 5 ) }
= 6.5 (10 + 60)
= 6.5 × 70
= 455
NO LINKS!! What Is Your Answer? Please help me
There are several ways you can prove triangles congruent
Just you have to look at these parts of triangles
Same anglesSame sidesCommon sideThe ways are
Side-Angle-sideAngle-Angle-AngleSide-angle-angleside-side-side#2
Yes we can form
The rule is that sum of two sides must be greater than third side
check
3+4>54+5>33+5>4It cost $91 to rent a car for two days. What is the cost for one day?
Answer:
$45.5
Step-by-step explanation:
Assuming that there is no tax or change in rate its simply $91 divided by two. We know that 45 is half of 91, 45.5 x 2 = 91
a =14.6 rounded to 1 DP
b= 3.25 rounded to 2 DP
Find the maximum of a - b
Answer:
11.405
Step-by-step explanation:
When rounding numbers, check the digit to the right of the one you're rounding to:
If it is 0, 1, 2, 3 or 4 round downIf it is 5, 6, 7, 8 or 9 round upIf a = 14.6 is rounded to 1 decimal place then:
minimum value of a = 14.55 (rounds up to 14.6)maximum value of a = 14.649999... (rounds down to 14.6)If b = 3.25 is rounded to 2 decimal places then:
minimum value of b = 3.245 (rounds up to 3.25)maximum value of b = 3.2549999... (rounds down to 3.25)Therefore, to find the maximum value of a - b, subtract the smallest value of b from the largest value of a:
[tex]\implies \sf a_{max}-b_{min}=14.649999...-3.245=11.405[/tex]
(Brainliest will be given as soon as possible!) Pierre wants to know how many people he can count on to vote for him as the school newspaper editor. He takes a poll of 34 random students and finds that 5 said they would vote for him.
If there are 272 students who will vote at the school, what would be Pierre’s best prediction for how many votes he can expect to receive?
The best prediction for the number votes Pierre should expect to receive is 40 votes
Calculating the number of vote
From the question, we are determine the best prediction for the number of votes Pierre should expect to receive
From the given information,
He takes a poll of 34 random students and finds that 5 said they would vote for him
Then, we can assume that,
Out of every 34 random students, 5 would vote for him
The total number of students that will vote = 272
There are eight 34s in 272
NOTE: 272 ÷ 34 = 8
Then, he should expect 8 × 5 votes
8 × 5 votes = 40 votes
Hence, the best prediction for the number votes Pierre should expect to receive is 40 votes
Lear more on Calculating the number of vote here: https://brainly.com/question/8926818
#SPJ1
Work out the sheet below
Answer:
188 meters cubed
Step-by-step explanation:
radius = 1/2d d=6 radius =3 height 20formula for thia equation is 1/3 (3.14)(3^2)(20)(3.14)(9)(20)3.14 x 9 = 28.2628.26 x 20 = 565.2565.2/3 = 188.40188.4 round to 3sf is 188help me pleaseeeeeeeeeeeeeeeeee
Since the figure is a trapezoid, we must use the trapezoid area formula, [tex]A = (b_1 + b_2) / 2 * h[/tex]. By doing so, we can plug in the shown numbers on the image. After that, we multiply.
[tex]A = (8 + 14) / 2 * 5[/tex]
[tex]A = 22/2 * 5[/tex]
[tex]A = 11 *5[/tex]
[tex]A = 55^2[/tex]
The area of the trapezoid is 55 squared yards.
what id the diameter lenght of
(x-7)^2+(y-2)^2=225
The diameter length is 30.
What is equation of circle?We know that the general equation for a circle is(x−h)²+(y−k)²=r²,
where ( h, k ) is the center and r is the radius.
As we know form of a circle.
We will use this form to determine the diameter of the circle.
(x−h)²+(y−k)²=r²
Given equation is :
(x-7)²+(y-2)²=225
(x-7)²+(y-2)²=(15)²
On comparing the above equation with the with equation of circle, we have
r²=(15)²
r=15
So, the diameter will be the twice the radius.
diameter= 2r
diameter= 2*15
diameter= 30
Learn more about equation of circle here:
https://brainly.com/question/10618691
#SPJ1
The probability of event A is x, and the probability of event B is y.
If the two events are independent, which condition must be true?
A.
P(AlB)=x
B.
P(BlA)=xy
C.
P(BlA)=x
D.
P(AlB)=y
Personal comment- Just to note, I saw two different answers for this one which were P(BlA)=xy and P(BlA)=y. I’m not sure who was correct. I saw an expert verified answer with only bout 40-ish “Thanks” but the other one was not an expert verified and it have bout 230 “Thanks”. I’m hesitant on which to go with. PLEASE HELP. I will send 50 extra brainliest if you give answer, and explain, AND if I get it right on the test. The last part is the only way to get extra. If you put in a random answer just to get easy brainliest, I will report to brainly moderators and have your question taken down, you will get your first and final warning (unless you have already gotten one which in this case your account will be banned) and you will lose brainliest points. I, and the Brainly community guidlines states that there is a ZERO TOLERANCE POLICY for any incorrect, unexplained, disrespectful answers.
Answer:
A. P(A l B) = x
Step-by-step explanation:
For independent events A and B,
P(B | A) = P(B)
P(A | B) = P(A)
P(A ∩ B) = P(A)P(B)
If P(A) = x and P(B) = y then:
⇒ P(B | A) = y
⇒ P(A | B) = x
⇒ P(A ∩ B) = xy
Therefore, the correct solution from the options given is:
A. P(A l B) = x
Are the ratios 1:4 and 3:10 equivalent?
[tex]\pmb{AnSwEr\::}[/tex]
these ratios are not equivalent . Please consult "Explanation" for more details
[tex]\bold{ExPlAnAtIoN}\downarrow[/tex]
We can write the ratios 1 : 4 and 3 : 10 as fractions :
[tex]\text{$\displaystyle\frac{1}{4} $}[/tex]
and
[tex]\text{$\displaystyle\frac{3}{10} $}[/tex]
Put the fractions together :
[tex]\text{$\displaystyle\frac{1}{4} \:and\:\frac{3}{10}$}[/tex]
Both fractions are in their simplest form ; the numerator and denominator do not have any common factors , except 1 , and there's no point in dividing by 1.
[tex]\small\text{hope helpful ( : }[/tex]
40 POINTS!!!!!!!!!!!!!!!!!!!!
Answer:
Shaded square 1: 4
Shaded square 2: 6
Shades square 3: 2
*Sorry all I can get at the moment is the shaded squares I'm still a little new to this
Step-by-step explanation:
100 POINTS if you can get it right! Please answer I'm so tired and want this to be over :(
Answer:
224 cm²
Step-by-step explanation:
Look at the figure below.
All sides are in cm. All areas are in cm².
Triangle A:
A = bh/2 = 8 × 21 / 2 = 84
Rectangle B:
A = LW = 9 × 8 = 72
Rectangle C:
A = LW = 4 × 5 = 20
Triangle D:
A = bh/2 = 6 × 16 / 2 = 48
Total area = 84 + 72 + 20 + 48 = 224
Answer: 224 cm²
Aswer the following using matrices suppose that there are two internet service providers in Kabwe, Eyeconnect and Topconnect. Currently, Eyeconnect has 180 000 customers and Topconnect has 120 000 customers. Assume that, every year, 10% of the customer base of Eyeconnect switches to Topconnect and 5% of the customer base of Topconnect switches to Eyeconnect. For the purposes of this question, suppose no customer leaves a company without switching to the other one and no company attracts customers that are not leaving the other (that is, the only changes in customer base come from switching between the two companies). a) Find the number of customers of Eyeconnect and Topconnect after one year. b) Find the number of customers of Eyeconnect after many years.
Answer:
Sorry
Step-by-step explanation:
Rewrite the function by completing the square.
f(x)=x^2-4x-26
Answer:
[tex](x-2)^2-30[/tex]
Step-by-step explanation:
use the form [tex]ax^2+bx+c[/tex] to find the values of a, b, and c.
[tex]a=1, b= -4, c = -26[/tex]
consider the vertex form of a parabola
[tex]a(x+d)^2+e[/tex]
substitute the values of a and b into the formula [tex]d=\frac{b}{2a}[/tex]
[tex]d=\frac{4}{2(1)}[/tex]
simplify the right side.
find the value of e using the formula [tex]e=c-\frac{b^2}{4a}[/tex]
[tex]e=30[/tex]
A user manual with 500 pages has 4 pages without diagrams.
What percent of the pages do not have diagrams?
0.25%
0.49%
0.8%
1.25%
The percentage of the pages in the user manual that do not have diagrams is 0.8%.
What is the percentage?Percentage is a measure of frequency that is is used to determine the fraction of an amount that is usually expressed as a number out of hundred.
Percentage without diagram = (4/500) x 100 = 0.8%
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
An irrigation system waters in circular patterns.
Each irrigated section is a circle with a diameter
of 40 feet. It terms of n, what is the area of an
irrigated section?
Guys please help me with question 1 , 2 and 3 pleaseeee
Answer: 10 points, please!
Step-by-step explanation:
1. for the medium you want to find the number thats in the middle. so you have to write out all the numbers in order. then you step by step go to the middle and theres your medium.
0, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6, 7, 11
2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6, 7
2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6,
2, 3, 3, 3, 3, 3, 3, 5, 5, 6,
3, 3, 3, 3, 3, 3, 5, 5,
3, 3, 3, 3, 3, 5,
3, 3, 3, 3,
3, 3,
The medium is 3.
2. for the mean you add all the numbers up and then divide based on how many numbers there are.
0 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 5 + 5 + 6 + 6 + 7 + 11 / 16
64/16
4
the average or mean is 4 which tells us that the average number of kids per houshold is 4. and none of the housholds have 4 children. we know this because of the data in the line plot.
the typical houshold size is either 3 or 4. the medium is 3 and the average or mean is 4.
10 points please
10,169 ÷ 342
Estimate:
Quotient:
Remainder:
Answer:
29.7339181287
The short answer:29.73
Cathleen was looking at 13 different colors to paint her bedroom. She liked about 1/4 of the colors.About how many colors did she like
Answer:
3.25 rounded to 3
Step-by-step explanation:
If she liked 1/4 of the colors, then we would divided by 13 by 4 to get 3.25.
She can't like 1/4 of a color though, so we would round to 3.
Factor the expression
7x^2 + 50x + 7
(Type your answer in factored form.)
Answer: (7x + 1)(x + 7)
Step-by-step explanation:
[tex]$$Factor the following:$$7 x^{2}+50 x+7$$Factor the quadratic $7 x^{2}+50 x+7$. The coefficient of $x^{2}$ is 7 and the constant term is 7. The product of 7 and 7 is 49 . The factors of 49 which sum to 50 are 1 and 49. So:\\\\ $7 x^{2}+50 x+7\\=7 x^{2}+49 x+x+7\\=7(7 x+1)+x(7 x+1)$ \\\\Factor $7 x+1$ from $7(7 x+1)+x(7 x+1)$ :$$\\\\Answer:(7 x+1)(x+7)$$[/tex]
Calculate an estimate for the mean of the distribution.
Correct answers will be mark as BRAINLIEST and get 50 points
Wrong answers will be reported
Answer:
The mean is 26Step-by-step explanation:
The frequency table according to the graph looks like
Range | 0-10 10-20 20-30 30-40 40-50Frequency | 6 8 12 4 10Total number of frequencies is
6 + 8 + 12 + 4 + 10 = 40Sum of data, using the midpoint of frequency ranges
6*5 + 8*15 + 12*25 + 35*4 + 45*10 = 1040The mean is the average of data
1040/40 = 26Midpoints of frequency ranges
0+10/210/25They are
5,15,25,35,45Now
sum of frequencies
6+8+12+4+1040Mean:-
6(5)+8(15)+12(25)+4(35)+10(45)/4030+120+300+140+450/401040/4026what is the total annual dividend received from owning 50 shares of stock A, If Company A Issues a $0.10 quarterly dividend to its shareholders
The total annual dividend which is received from owning 50 shares of stock A, when Company A Issues a $0.10 quarterly dividend to its shareholders, is $20.
What is market value?Market value is the current price of a product, company, or something consorting to the stock of the market.
The total annual dividend received from owning 50 shares of stock A has to be found out when Company A Issues a $0.10 quarterly dividend to its shareholders.
Quarterly dividend is paid in each three month of the year.The dividend is paid 4 times in a year.For each quarter, the payment of dividend is,
[tex]0.10\times50\\5[/tex]
In a year,
[tex]5\times4\\20[/tex]
Thus, the total annual dividend which is received from owning 50 shares of stock A, when Company A Issues a $0.10 quarterly dividend to its shareholders is $20.
Learn more about the market value here;
https://brainly.com/question/8084221
#SPJ1
exponential equation
27x+4=9x
Answer:
answer is 45 trust me im passing this concept
Step-by-step explanation:
Answer:
x= -2/9
Step-by-step explanation:
step 1: isolate the variable
27x+4 = 9x
-9x. -9x
18x+4 = 0
-4. -4
18x = -4
step 2: isolate the variable by dividing both sides by the coefficient
18x = -4
÷18. ÷18
=
x = -2/9
(x is equal to negative 2 ninths)
Solve ln (3x + 7) = 1. Round to the nearest thousandth.
Answer:
x = -2
Step-by-step explanation:
Step 1: Subtract 7 from both sides.
3x+7−7=1−7
3x=−6
Step 2: Divide both sides by 3.
3x/3 = −6/3
x = −2
I’m confused. Please help!!!
The values of r and w will be 50 and 140 degrees.
What is the Exterior Angle of a Triangle Property?An exterior angle of a triangle is equal to the sum of the opposite interior angles.
From the Exterior Angle of a Triangle Property;
38° + 103° = w
w = 140°
Let x be the exterior angle so that
x = r + 90°
Similarly,
By vertically opposite angle;
w = x
So, x = r + 90°
140 = r + 90°
r = 140 - 90
r = 50
Hence, the values of r and w will be 50 and 140 degrees.
Learn more about exterior angles;
https://brainly.com/question/14164971
#SPJ1
which expressions are equivalent to the one below? Check all that apply log_7 1* log_5 25
What is 1637,984 rounded to the nearest ten
The number rounded to the nearest ten will be 1640. The number is grater than the 5 on the scale.
What are rule for finding a number rounded to the nearest ten?If the digit in the units place is between 0 and 10 i.e., 5, then the unit digit is substituted by 0.
If the digit in the units place is between 5 and 9, that is, > or 5 but less than 10, the units place is replaced by '0,' and the tens place is incremented by 1.
The given number is;
x=1637.984
The number is 7.9 grater than 5. So that the number is rounded to the nearest whole number,i.e.1640
Hence,the number rounded to the nearest ten will be 1640.
To learn more about the rounding number to the nearest ten refer:
https://brainly.com/question/6685026
#SPJ1
A child pulls a wagon with a force of 22 pounds. The handle of the wagon makes an angle of 45° with the ground. Express the force vector F in terms of i and j. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
The force vector F in terms of i and j, considering it's magnitude and angle, is represented by:
[tex]V = 11\sqrt{2}i + 11\sqrt{2}j[/tex]
How can a vector be represented in i and j notation?Given a magnitude M and angle [tex]\theta[/tex], the a vector V can be represented as follows:
[tex]V = M\sin{\theta}i + M\cos{\theta}j[/tex]
In this problem, we have that the parameters are as follows:
[tex]M = 22, \theta = 45^\circ[/tex]
Hence:
[tex]V = 22\sin{45^\circ}i + 22\cos{45^\circ}j[/tex]
[tex]V = 22\frac{\sqrt{2}}{2}i + 22\frac{\sqrt{2}}{2}j[/tex]
[tex]V = 11\sqrt{2}i + 11\sqrt{2}j[/tex]
More can be learned about vectors at https://brainly.com/question/24606590
#SPJ1