What is the surface area of a rectangular prism that has a length of 9 feet, a width of 5 feet, and a height of 7.5 feet?
Answers
A = 2(LW +H*(L +W))
Filling in the given information, we have
A = 2((9 ft)*(5 ft) +(7.5 ft)*(9 ft +5 ft))
A = 2(45 ft² +(7.5 ft)*(14 ft)) = 2(150 ft²)
The surface area of the rectangular prism is 300 ft².
Answer: 300 ft²
Step-by-step explanation:
Related Questions
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).
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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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
perimeter and circumference 9-1
Answers
How can I derive the first equation to get the second equation?
Answers
[tex]\bf s^2=R^2+r^2-2Rrcos(\theta )\implies 2s^1=0+0-2Rr\left[ \stackrel{chain~rule}{-sin(\theta )\cfrac{d\theta }{ds}} \right] \\\\\\ 2s=2Rrsin(\theta )\cfrac{d\theta }{ds}\implies 2s=\cfrac{2Rrsin(\theta )d\theta }{ds}\implies \cfrac{2s\cdot ds}{2Rr}=sin(\theta )d\theta \\\\\\ \cfrac{s\cdot ds}{Rr}=sin(\theta )d\theta[/tex]
To derive the second equation from the first equation, you can substitute the expression for the unknown in terms of the other known variables. This reduces the equation to one unknown.
Explanation:To derive the second equation from the first equation, you need to substitute the expression for T₂ in terms of T₁. This will reduce the unknowns in the equation to one. Here are the steps:
Start with the equilibrium equation for the problem.Substitute the expression for T₂ in terms of T₁ into the equation.This will eliminate one unknown and result in a new equation with only one unknown left.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
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.
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:
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.
how much interest is earned on 2,700 in one year if it is invested at 3%?
a. $8.10
b.$81.00
c.$810.00
Answers
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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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
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)
Suppose the entering freshmen at a certain college have a mean combined application test score of 1225, with a standard deviation of 120. in the first semester, these students attained a mean gpa of 2.64, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a first-semester gpa of 2.9?suppose the entering freshmen at a certain college have a mean combined application test score of 1225, with a standard deviation of 120. in the first semester, these students attained a mean gpa of 2.64, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a first-semester gpa of 2.9?
Answers
Using the correlation coefficient, mean test scores, and mean GPA, we can predict that a freshman with a GPA of 2.9 would have an approximate combined test score of 1260.71.
Since we know the mean combined application test score is 1225, the standard deviation is 120, the mean GPA is 2.64, and the standard deviation for GPA is 0.58, we can use this information to predict scores.
First, we will use the correlation coefficient (r), which in this case is 0.44, to calculate the slope (b) of the best-fit line. The slope (b) is calculated by dividing the product of the standard deviations by the mean test score, and then multiplying by the correlation coefficient.
b = r * (Sy / Sx)
b = 0.44 * (0.58 / 120)
b = 0.44 * 0.0048333
b ≈ 0.0021
Next, we need to find the intercept (a) of the best-fit line, which can be calculated using the means of the two variables (mean test score and mean GPA).
a = mean of GPA - b * mean of test scores
a = 2.64 - 0.0021 * 1225
a ≈ 0.10
With the slope (b) and the intercept (a), we can now predict the combined test score for a student with a GPA of 2.9.
Predicted Test Score = a + b * GPA
Predicted Test Score = 0.10 + 0.0021 * 2.9
Predicted Test Score ≈ 1260.71
Thus, for a freshman with a first-semester GPA of 2.9, the predicted combined test score would be approximately 1260.71.
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
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
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
Suppose that a test is standardized (normally distributed) with a mean of 75 and a standard deviation of 11. what is the probability that an individual will have a test score greater than 80
Answers
A suitable calculator can help you figure this.
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
https://brainly.com/question/9934382
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
Sally bought a car for 35000 in 2017. If the car loses 5.5% semiannually, what will the value of the value of the car be at the end of 2025
Answers
A=P(1+r/100)^n
where:
A=future value
P=principle
r=rate
n=number of terms
hence for the data given;
p=35000
R=5.5
n=(2025-2017)*2=16
Thus
A=35000(1+5.5/100)^16
A=$82, 434. 20
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)
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]
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 ;)
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
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.
I need yo help B, on dis question
Answers
We have then:
[tex]5 / sine (68) = 5 / sine (x) [/tex]
From here, we clear the value of x.
We have then:
[tex]sine (x) = (5/5) * (sine (68)) [/tex]
Rewriting we have:
[tex]sine (x) = (1) * (sine (68)) sine (x) = sine (68) x = arcsine (sine (68)) x = 68[/tex]
Answer:
The angle R is given by:
x = 68 degrees
option B
Answer:
b
Step-by-step explanation:
Hey can you please help me posted picture of question
Answers
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)
In the equation 6x − 2 = −4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain
Answers
Spencer: 6x - 2 = -4x + 2 /+4x6x - 2 + 4x = -4x + 2 + 4x10x - 2 = 2
Jeremiah:6x - 2 = -4x + 2 /-6x6x - 2 - 6x = -4x + 2 - 6x-2 = -10x + 2
They both are correct. But in Jeremiah's version of solving the equation, we would have to multiply equation by -1, which we don't have to do in the Spencer's version.
Source: Brainly.com
Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.