Answers
The surface area (S) of a rectangular prism is given in terms of its length (L), width (W), and height (H) as
... S = 2(LW +WH + LH)
Substitute your numbers and do the arithmetic.
... S = 2(7.2·10 + 10·6.3 + 7.2·6.3)
... = 2(72 + 63 + 45.36)
... = 2·180.36
... = 360.72 . . . . square inches
Related Questions
Log5 wu^6/v^6
Expand each logarithm
Answers
1. You have the following logarithm:
log5(wu^6/v^6)
2. By the logarithms properties, you can rewrite it as below:
log5(wu^6)-log5(v^6)
[log5(w)+log5(u^6)]-log5(v^6)
log5(w)+6log5(u)-6log5(v)
3. Therefore, the answer is:log5(w)+6log5(u)-6log5(v)
find the circumference of a circle with an area of 254.47 square inches
Answers
A circle with an area of 254.47 square inches is given.
We have to determine the circumference of the circle.
Since, Area of circle = [tex] \Pi r^{2} [/tex] where r is the radius of the circle.
[tex] \Pi r^{2}=254.47 [/tex]
[tex] \frac{22}{7} \times r^{2}=254.47 [/tex]
[tex] r^{2}=\frac{254.47 \times 7}{22} [/tex]
[tex] r^{2}=80.97 [/tex]
[tex] r=\sqrt{80.97} [/tex]
r = 8.99
Therefore, r = 9 inches (approximately)
Circumference of a circle = [tex] 2\Pi r [/tex]
= [tex] 2 \times \frac{22}{7} \times 9 [/tex]
= 56.57 inches
= 56.6 inches (approximately).
Therefore, the circumference of the circle is 56.6 inches.
How many pounds of hamburger worth $1.05 per pound must be mixed with 60 pounds of hamburger worth $0.90 per pound to produce hamburger worth $1.00 per pound? Which of the following systems represents the word problem if x = pounds of hamburger worth $1.05 per pound? x + y = 60 and 1.05x + 0.90(60) = 1.00y x + 60 = y and 1.05x + 1.00y = 0.90(60) x + 60 = y and 1.05x + 0.90(60) = 1.00y
Answers
The appropriate choice is the last one:
x + 60 = y and 1.05x + 0.90(60) = 1.00y
Answer:
[tex](x+60)=y[/tex] and [tex]1.05x+0.90(60)=1.00y[/tex]
Step-by-step explanation:
Let
x-----> pounds of hamburger worth [tex]\$1.05[/tex] per pound
we know that
The equation that represent the situation is
[tex]1.05x+0.90(60)=1.00(x+60)[/tex] ------> equation A
Let
[tex]y=(x+60)[/tex] -----> equation B
substitute equation B in equation A
[tex]1.05x+0.90(60)=1.00y[/tex]
Solve x2 − 7x + 12 = 0.
a. x = −3, x = −4
b .x = 3, x = 4
c. x = 2, x = 6
d. x = −2, x = −6
Answers
So,
x^2 - 7x + 12 = 0
(x-4)(x-3) = 0
x-4 = 0 or x-3 = 0
x = 4 or x = 3
Answer is choice B
Select three ratios that are equivalent to 11:1
Answers
B. 22 : 2. 22 : 2 is equivalent to 11 : 1.
C. 55 : 5. 55 : 5 is equivalent to 11 : 1.
E. 110 : 10. 110 : 10 is equivalent to 11 : 1.
In order to determine the ratios that are equivalent to the given ratio, we would evaluate by dividing each of them by their respective common multiple (numerator or denominator):
For 22 : 2, we would divide all through by 11;
22 : 2 = 11 : 1
For 55 : 5, we would divide all through by 5;
55 : 5 = 11 : 1
For 110 : 10, we would divide all through by 10;
110 : 10 = 11 : 1
Complete Question:
Select three ratios that are equivalent to 11 : 1.
Choose 3 answers:
1 :11
22 : 2
55 : 5
9 : 99
110 : 10
A right rectangular prism is shown. What shape best describes the cross section cut perpendicular to the base of a right rectangular prism? Parallelogram Trapezoid Rectangle Square
Answers
Rectangle
_____
That rectangle may be a square, but is not required to be.
The shape that best describes the cross-section cut perpendicular to the base of a right rectangular prism is a rectangle.
A cross-section cut perpendicular to the base of a right rectangular prism will always result in a rectangular shape.
This is because a rectangular prism has six faces, and the base of the prism is one of those faces.
When you make a cross-section cut perpendicular to the base, you are essentially slicing through the prism parallel to one of its other faces.
Since the base is a rectangle, the cross-section will also be a rectangle.
In summary, the cross-section cut of a right rectangular prism perpendicular to its base will consistently yield a rectangular shape due to the inherent geometry of the prism.
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Find the length of each hypotenuse such that KMN = LMN
Answers
1) KM must be congruent with LM→KM=LM→
x+2y=3x-y→x+2y-x-2y=3x-y-x-2y→0=2x-3y→2x-3y=0 (1)
2) KN must be congruent with LN→KN=LN→
5x+3y=8x-7→5x+3y-5x-3y+7=8x-7-5x-3y+7→7=3x-3y→3x-3y=7 (1)
We have a system of two equations and two unkowns:
(1) 2x-3y=0
(2) 3x-3y=7
Subtracting equation (1) from equation (2)
(3x-3y)-(2x-3y)=7-0
3x-3y-2x+3y=7
x=7
Replacing x=7 in equation (1)
(1) 2x-3y=0→2(7)-3y=0→14-3y=0→
14-3y+3y=0+3y→14=3y→14/3=3y/3→14/3=y→y=14/3
The length of the hypotenuse is:
KN=5x+3y=5(7)+3(14/3)=35+14→KN=49
or
LN=8x-7=8(7)-7=56-7→LN=49
Answer: Option C. 49
A school conference room can seat a maximum of 83 people. The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements. If each student must bring a parent with them, what is the maximum number of students that can attend each meeting?
Answers
After subtracting the principal and two counselors from the 83-person room capacity, dividing the remaining space by two shows that a maximum of 40 student-athletes can attend the meeting with their parents.
The maximum number of student-athletes that can attend a meeting in a conference room that has a capacity of 83 people while also accounting for their accompanying parents. Given that the principal and two counselors will also be in attendance, we need to subtract three from the total capacity to accommodate them, leaving us with 80 seats available. Since each student will bring a parent, we divide the remaining seats by two. Therefore, the maximum number of student-athletes that can attend each meeting is 40 students, with each accompanied by a parent.
Please Help: 25 Points!
Jeremy constructed this solid by combining two rectangular prisms and a square pyramid. What is the surface area of this figure?
Answers
A1 = (1/2) * (6) * (7)
A1 = 21
Rectangle area of the base:
A2 = (14) * (6)
A2 = 84
Area of the posterior rectangle:
A3 = (5) * (6)
A3 = 30
Area of the frontal rectangle:
A4 = (6) * (2)
A4 = 12
Area of the rectangle parallel to the base:
A5 = (8) * (6)
A5 = 48
Rectangle area located between posterior and front rectangles:
A6 = (3) * (6)
A6 = 18
Area of the side walls of the figure:
A7 = (14) * (2) + (3) * (6)
A7 = 28 + 18
A7 = 46
Superficial area:
A = 4 * A1 + A2 + A3 + A4 + A5 + A6 + 2 * A7
A = 4 * 21 + 84 + 30 + 12 + 48 + 18 + 2 * 46
A = 368
Answer:
A = 368 m ^ 2
Answer:
368
Step-by-step explanation:
If y varies inversely as the square of x, and y=7/4/ when x=1, find y when x=3
Answers
[tex]y= \frac{k}{ x^{2} } [/tex]
where k is a constant of proportionality. It is given that y = 7/4 when x = 1.
Using these values, we can write:
[tex] \frac{7}{4}= \frac{k}{1} \\ \\ k= \frac{7}{4}[/tex]
So, now the equation in terms of x and y can be written as:
[tex]y= \frac{7}{4 x^{2} } [/tex]
We are to find y when x = 3. So we can write:
[tex]y= \frac{7}{4(9)}=\frac{7}{36} [/tex]
Thus, for x= 3 value of y will be 7/36
stella received a package in the shape of rectangular prism. the box has a length of 21/2 feet, a width of 11/2 feet, and a height of 4 feet. stella wants to cover the box with wrapping paper. how much paper will sge need?
Answers
The dimensions of the box are as follows:
length=21/2 ft
width=11/2 ft
height=4 ft
Area of the box is given by the formula:
SA=2lw+2lh+2hw
SA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)
SA=2(231/4)+2(42)+2(11/2×4)
SA=115.5+84+44
SA=243.5 ft²
Stella will need 243.5 ft²
Answer:
Step-by-step explanation:
To get the amount of paper required to cover the box, we find the area of the box. The dimensions of the box are as follows:length=21/2 ftwidth=11/2 ftheight=4 ftArea of the box is given by the formula:SA=2lw+2lh+2hwSA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)SA=2(231/4)+2(42)+2(11/2×4)SA=115.5+84+44SA=243.5 ft²Stella will need 243.5 ft²
If sinø= 4/7, what is cosø?
Answers
arc sine (4/7) = theta
theta = 34.85 Degrees
cosine (34.85) = 0.82065
triangle abc and triangle bcd have vertices A(-6, -7), B(-6, 4), C(2, -7), D(8, 4) what is the area in square units of trapezoid ABCD which is formed by the two triangles?
Answers
According to the attached graph AC||BD, AB⊥BD and AB⊥AC.
|BD|=14; |AB|=11; |AC|=8.
All the details are in the attachment.
answer: 121 (sq.units).
Two positive numbers have a difference of four and a product of 96 what are the numbers
Answers
Answer:
The two positive numbers are 12 and 8.
Explanation:
The first phrase in the sentence tells us the difference between numbers equals 4, which can be represented a - b = 4
The second phrase tells us when multiplied together, it equals 96, which can be represented by the ab = 96, or a(b) = 96
So, first step is to list the factors of 96. I prefer to list them as pairs:
1, 96; 2, 48; 3, 32; 4, 24; 6, 16; and 8, 12
Now we plug each these pairs into the first equation to see if they satisfy the equation.
96 - 1 = 95 24 - 4 = 20
95 > 4 20 > 4
48 - 2 = 46 16 - 6 = 10
46 > 4 10 > 4
32 - 3 = 29 12 - 8 = 4
29 > 4 4 = 4
Because a = 12 and b = 8 satisfies both equations that represent the given sentence, the two positive numbers are 12 and 8.
What is the equation of the line that passes through the points (-1,2) and (6,3) in slope intercept form
Answers
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -1 &,& 2~) &&(~ 6 &,& 3~) \end{array} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-2}{6-(-1)}\implies \cfrac{3-2}{6+1}\implies \cfrac{1}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=\cfrac{1}{7}[x-(-1)]\implies y-2=\cfrac{1}{7}(x+1) \\\\\\ y-2=\cfrac{1}{7}x+\cfrac{1}{7}\implies y=\cfrac{1}{7}x+\cfrac{1}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{15}{7}[/tex]
Answer:
Step 1: Choose (x1, y1). (6,3)
Step 2: x2= -1 y2=2
Step 3: 1/7
Step 4: b= 15/7
What is the equation of the line in slope-intercept form?
B) y=1/7x+15/7
Step-by-step explanation:
The bold numbers are the answers.
( I need mo pts)
Jenya has 12 bills in her wallet. She has a total of $82. If she has twice as many $5 bill as $1 bills, and two more $10 bills than $5 bills, how many of each does she have?
Answers
if you said you had 7 instead there would be not enough bills to add up to 82
so that means 4 $5 and 6 $10
check you have 12 bills and it adds up to $82
2 $1
4 $5
6 $10
Final answer:
Jenya has 2 $1 bills, 4 $5 bills, and 6 $10 bills, which all adds up to her total of $82.
Explanation:
Jenya has a combination of $1, $5, and $10 bills in her wallet adding up to $82. To find out how many of each she has, we need to set up a system of equations based on the information provided:
Let x represent the number of $1 bills.2x will then represent the number of $5 bills, as she has twice as many $5 bills as $1 bills.2x + 2 represents the number of $10 bills because she has two more $10 bills than $5 bills.We also know that the total number of bills is 12.The total amount of money is $82.Now we can form two equations:
x + 2x + (2x + 2) = 12 (Total number of bills)1x + 2x*5 + (2x + 2)*10 = 82 (Total amount of money)Simplifying the equations gives us:
5x + 2 = 12x + 10x + 20x + 20 = 82Further simplification and solving for x yields:
5x = 10x = 2This means Jenya has 2 $1 bills, 2*2 = 4 $5 bills, and 2*2 + 2 = 6 $10 bills.
Lance lived in Portugal and Brazil for a total of 14 months to learn Portuguese. He learned an average of 130 words per month when he lived in Portugal, and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words write a system of equations to represent this situation. Use x to represent Portugal, and y to represent Brazil.
Answers
Number of months that Lance lived in Brazil: y
Lance lived in Portugal and Brazil for a total of 14 months to learn Portuguese:
(1) x+y=14
He learned an average of 130 words per month when he lived in Portugal:
Number of words that Lance learned in Portugal: 130x
and an average of 150 new words per month when he lived in Brazil:
Number of words that Lance learned in Brazil: 150y
In total, he learned 1920 new words:
(2) 130x+150y=1920
Write a system of equations to represent this situation:
(1) x+y=14
(2) 130x+150y=1920
The expression 5(F-32) divided by 9 yes the Celsius temperature for a Fahrenheit temperature of F degrees C noon Fahrenheit temperature in Centerville was 86° what was the temperature in degrees Celsius
Answers
5(86 -32)/9 = 5(54/9) = 5(6) = 30
The temperature was 30 °C.
Answer:
30°C
Step-by-step explanation:
The following expression can be used to convert Farenheit degrees (°F) to Celsius degrees (°C).
°C = 5 . (°F - 32) / 9
If the temperature in Centerville is 86°F, we can replace this value in the previous expression to find its value in the Celsius scale.
°C = 5 . (°F - 32) / 9
°C = 5 . (86 - 32) / 9
°C = 5 . (54) / 9
°C = 270 / 9
°C = 30°C
write parametric equations of the line 2x+3y=11
Answers
1. You have the following equation of the line given in the problem above: 2x+3y=11.
2. Therefore, you have:
x=t
3. When you substitute x=t into 2x+3y=11, you obtain:
2t+3y=11
4. Now, solve for y, as below:
3y=11-2t
y=(11/3)-(2t/3)
Therefore, the answer is:
x=t
y=(11/3)-(2t/3)
Answer:
C
Step-by-step explanation:
If youre doing the test ;)
A bag of marbles contains 12 red marbles 8 blue marbles and 5 green marbles. If three marbles are pulled out find each of the probabilities. Find the probability of pulling three green marbles out with replacement
Answers
[tex] |\Omega|=25\cdot24\cdot23=13800\\
|A|=5\cdot4\cdot3=60\\\\
P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\% [/tex]
The probability of an event is calculated as = [tex] \frac{Favorable outcomes}{Total number of outcomes} [/tex]
Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles
So, total marbles = 25 marbles
Number of favorable or green marbles = 5 marbles
Probability of three green marbles if drawn with replacement = [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] ×[tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] × [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex]
Probability of three green marbles if drawn with replacement = [tex] \frac{1}{125} [/tex]
what is the factored form of a fourth degree polynomial function with coefficients that has -3,1and 1+5i
Answers
(x +3)(x -1)(x -1 -5i)(x -1 +5i)
If you want the complex factors combined to a real factor, the factorization is
(x +3)(x -1)(x² -2x +26)
3x < 12 what is this in the interval notation
Answers
x < 4
Interval notation uses parentheses around the lower and upper limit of the interval. Here, the lower limit is -∞ and the upper limit is 4. The parentheses are round ( ) if the limits are NOT included as part of the interval. They are square brackets [ ] if the limits are included in the interval.
Here, since -∞ is not an actual number, we use the round bracket on that end of the interval. Since the solution space does not include 4, we use the round bracket on that end of the interval as well.
The solution to your inequality is ...
(-∞, 4)
Q # 15 find the volume of the sphere
Answers
[tex]4 \times 5 \times 5 \times 5 \times \pi \times \frac{1}{3} = \frac{500\pi}{3} \\ = \frac{1570}{ 3} = 523.33[/tex]
good luck
Area = (4/3)πr³
Where r ⇒ radius of the sphere
π=3.14
Area = (4/3)× 3.14 ×5³
=523.33333 in³
To the nearest cubic, the answer is 523 in³
Suppose a1=2,an+1=12(an+2an). assuming an has a limit, find limn→∞an= . hint: let a=limn→∞. then, since an+1=12(an+2an), we have a=12(a+2a). now solve for
a.
Answers
[tex]a_{n+1}=\dfrac{a_n+\frac2{a_n}}2[/tex]
Assume that [tex]\displaystyle\lim_{n\to\infty}a_n=L[/tex]. Then taking the limit of both sides, we have
[tex]L=\dfrac{L+\frac2L}2\implies L=\pm\sqrt2[/tex]
But in order for the sequence to converge, only one of these values must be true. Since [tex]a(1)=2>0[/tex], each successive number will also be positive, so the limit must be [tex]L=\sqrt2[/tex].
The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).
Explanation:This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).
To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).
By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.
Therefore, the limit of the sequence as n tends to infinity is 0.
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limit approaches infinity of 3^n / 3n+1
Answers
SOMEONE PLEASE HELP ME ASAP
Answers
For this case we can use the following trigonometric relationship:
sine (45) = (5 * root (2)) / h
From here, we clear the value of h:
h = (5 * root (2)) / sine (45)
Rewriting we have:
h = (5 * root (2)) / (root (2) / 2)
h = (2 * 5) * (root (2) / root (2))
h = 2 * 5
h = 10
Answer:
h = 10
Option F
Choose the ratio that you would use to convert 5.5 pounds to ounces. Remember that there are 16 ounces in 1 pound. A.
Answers
The correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.
To convert 5.5 pounds to ounces, we need to use the conversion factor that relates pounds to ounces. We know that there are 16 ounces in 1 pound. Therefore, to convert pounds to ounces, we need to multiply the number of pounds by 16.
The appropriate ratio to use for this conversion would be option A : 16 ounces per 1 pound, or [tex]\( \frac{16 \text{ ounces}}{1 \text{ pound}} \).[/tex]
This ratio tells us that for every 1 pound, there are 16 ounces. Using this ratio, we can convert pounds to ounces by multiplying the number of pounds by 16.
Therefore, to convert 5.5 pounds to ounces, we would use the following calculation:
[tex]\[ 5.5 \text{ pounds} \times \frac{16 \text{ ounces}}{1 \text{ pound}} = 88 \text{ ounces} \][/tex]
So, the correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.
The complete question is:
Choose the ratio that vou would use to convert 5.5 pounds to ounces Remember that there are 16 ounces in 1 pound.
A. 88 ounces/1 pound
B. 16 ounces/1 pound
C. 1 pound/16 ounces
D. 1 ounce/88 pounds
The formula for finding the horsepower of a vehicle is: Horsepower = weight × ( velocity 234 ) 3 Weight is the total weight of the vehicle, driver and any passengers. Velocity is determined by the speed at the end of a quarter mile run. The newest hybrid auto weighs 2200 pounds and the driver is 180 pounds. At the end of the quarter mile run, the speed is 98 miles per hour.
What is the horsepower of the car rounded to the nearest whole number?
161 hp
175 hp
209 hp
417 hp
Answers
Power = 175 hp
The correct formula to calculate the power is:
Power = weight * (speed / 234) ³
Where the weight is that of the vehicle plus the driver's
Therefore the calculation is as follows:
Power = (2200 + 180) * (98/234) ³
Power = 174.8266 hp
Rounding ...
Power = 175 hp
Pete has the option of borrowing $380 for one week at an APR of 600% or borrowing the $380 for one week with a fee of $45. Which is the "better" deal?
Answers
Since Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.
There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.
[tex] \frac{600}{365} = 1.643[/tex]
The daily interest rate of the loan will be 1.643%.
The following equation is used to find the total interest payment:
[tex]A = P(1+ \frac{r}{365})^{t} - P[/tex]
A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.
Plug in your values into the equation.
[tex]P = 380, r = 1.643, t = 7[/tex]
[tex]380(1+ \frac{1.643}{365})^{7} - 380 = 12.136[/tex]
Rounded to the nearest hundredths value, the total interest paid will be $12.14.
Compare the total amounts paid for both loans.
$12.14 < $45
The better deal is the loan with the 600% APR.
The better deal is the loan with the 600% APR.
What is interest rate?An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum).
Given that, Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.
There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.
600/365 = 1.643
The daily interest rate of the loan will be 1.643%.
The following equation is used to find the total interest payment:
[tex]A = P(1+\frac{r}{365} )^{t} -P[/tex]
A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.
Plug in your values into the equation.
P = 380 r = 1.643 and t = 7
380(1+1.643/365)^7 - 380 = 12.136
Rounded to the nearest hundredths value, the total interest paid will be $12.14.
Compare the total amounts paid for both loans.
$12.14 < $45
Hence, The better deal is the loan with the 600% APR.
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if a plane leave the ski resort every hour. the first plane leaves at 10 and the second plane leaves at 4 how man planes leave each day
Answers
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