The surface area of a cuboid is the area of all the six faces of a cuboid. The Paint that is required to paint 3 boxes is 13 pints.
What is the surface area of a cuboid?The surface area of a cuboid is the area of all the six faces of a cuboid. It is given by the formula,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
As it is given the dimensions of the storage box are a length of 8 feet, a width of 5 1/2 feet(5.5 feet), and a height of 4 1/2 feet(4.5 feet). Therefore, the surface area of the box can be written as,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
[tex]\rm \text{Surface area of the box}= 2[(8\times 5.5)+(5.5\times 4.5)+(8 \times 4.5)] = 209.5\ ft^2[/tex]
As it is given that the surface area that can be covered with a pint of paint is 50 square feet, therefore, the paint that will be required to paint 209 square feet is,
[tex]\text{Paint Required} = \dfrac{\text{Total area that is needed to be paint}}{\text{Area covered in a pint of paint}}[/tex]
[tex]\rm \text{Paint Required} = \dfrac{209.5}{50} = 4.19\ pints[/tex]
Now, we know that the surface area of the box is 209 square feet, while the paint required to paint a complete box is 4.19, therefore, the paint that will be required to paint 3 boxes will be,
[tex]\text{Paint required to paint 3 boxes} = 3 \times 4.19 = 12.57 \approx 13[/tex]
Hence, the Paint that is required to paint 3 boxes is 13 pints.
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please helpppp pleaseee
а. 5
b. 180(5-3)=540
,..,,..,.,.,
Let f(x)=4x^2-3 and g(x)=-x^2+2.Find f+g and state the domain. Then evaluate the sum when x=2
Answer:
f+g = 3x^2-1. domain = all real numbers. then plug in two wherever there is an x.
f(x)=4*2^2-3, which equals 13
g(x)= -2^2+2, which equals -2
add
f+g when x=2 is 11
Step-by-step explanation:
Jake is saving for a new tablet. It costs $250, and he has $100. He earns $5 per week for doing chores. Jake wants to figure out how many weeks it will take for him to have at least enough money to buy a new tablet. Write an inequality and solve it to determine the number of weeks it will take.
Answer: 250 ≤ 100+5x
150≤5x divide by 5
30≤x
It will take 30 weeks to earn enough.
Step-by-step explanation:
hurry please im running out of time
ill give brainliest
Answer:
Step-by-step explanation:
16 ticks, the pointer is on 12. there fore it is the second answer.
2 3/4 lb
WILL GIVE BRAINLIEST, THANKS AND 5 STARS! PLEASE HELP! LOTS OF POINTS
Sam kicks a ball off of a rooftop. After t seconds, its height, h (in feet), is given by the formula
h (t) = -16t2 + 64t + 80.
*NOTE: Complete this without using graphing features on your calculator, and show all work for credit. You may type out your work or upload it in the next question.
a. What is the maximum height reached by the ball?
b. When did the ball reach its maximum height?
c. When will the ball hit the ground? (Do algebraically)
d. What is the height of the ball after 1 second?
(THIS IS A 4 PART QUESTION, PLEASE DO ALL PARTS!!!) PLEASE GIVE INDEPTH EXPLANATION FOR ALL PARTS!
Answer:
(a) 144 ft
(b) 2 s
(c) 5 s
(d) 128 ft
Step-by-step explanation:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
Part (a)
To find the turning point of the parabola:
1. differentiate the function:
[tex]\implies h'(t) = -32t + 64[/tex]
2. Set it to zero and solve for t:
[tex]\implies h'(t) =0[/tex]
[tex]\implies -32t + 64=0[/tex]
[tex]\implies 32t = 64[/tex]
[tex]\implies t=2[/tex]
3. Input found value of t back into the function and solve for h:
[tex]\implies h(2) = -16(2)^2 + 64(2) + 80=144[/tex]
Therefore, the maximum height reached by the ball is 144 ft
Part (b)
As found in part (a), the maximum height is reached when t = 2, so the ball reached its maximum height at 2 seconds.
Part (c)
The ball will hit the ground when h(t) = 0
1. Set the function to zero
[tex]\implies h(t)=0[/tex]
[tex]\implies -16t^2 + 64t + 80=0[/tex]
2. Solve for t:
Divide both sides by 16
[tex]\implies -t^2 + 4t + 5=0[/tex]
[tex]\implies t^2 - 4t - 5=0[/tex]
Factor:
[tex]\implies t^2 +t-5t - 5=0[/tex]
[tex]\implies t(t+1)-5(t+1)=0[/tex]
[tex]\implies (t+1)(t-5)=0[/tex]
Therefore:
[tex](t+1)=0 \implies t=-1[/tex]
[tex](t-5)=0 \implies t=5[/tex]
As time is positive, t = 5
So the ball will hit the ground at 5 seconds.
Part (d)
To find the height of the ball after 1 second, input t = 1 into the function and solve for h:
[tex]\implies h(1) = -16(1)^2 + 64(1) + 80=128[/tex]
Therefore, the height of the ball after 1 second is 128 ft
--------------------------------------------------------------------------------------
Parts (a) & (b) - alternative method
Rewrite the function in vertex form by completing the square.
Set the function to zero:
[tex]\implies-16t^2 + 64t + 80=0[/tex]
Subtract 144 from both sides:
[tex]\implies -16t^2+64t-64=-144[/tex]
Factor out -16:
[tex]\implies -16(t^2 - 4t +4)=-144[/tex]
Factor expression in brackets:
[tex]\implies -16(t-2)^2=-144[/tex]
Add 144 to both sides:
[tex]\implies -16(t-2)^2+144=0[/tex]
Therefore:
[tex]\implies h(t)=-16(t-2)^2+144[/tex]
The maximum height is the y-value of the vertex.
The vertex is (2, 144) so the maximum height is 144 ft.
The time the ball reached the max height is the x-value of vertex.
So the time then the ball reached the maximum height is 2 s
Help me someone please
Answer:
150
Step-by-step explanation:
since a circle is 360 degrees, add up all of the other degrees and then subtract from 360
i really need
help on this work it is really difficult help plsss
Answer: 105 square feet
Step-by-step explanation: The answer is 105 square feet because find the area of the pool by multiplying 12 and 20 to get 240. You then want to find the area of the total space. Add 3 to 12 and add 3 to 20. Then multiply 23 by 15 to get 345. You then want to subtract 345 - 240 to get rid of the extra space to get your answer of 105.
Pls help i will give 5 starts and brainliest question is down below 9:22
Answer:
C) 390
Step-by-step explanation:
Area of Blue:
18 × 25 = 450 in
Area of White:
6 × 10 = 60 in
450 - 60 = 390
Therefore, 390 sq in is the correct answer.
50 points, PLEASE HELP
i have a test in 2 hours i really need to know how to do this problem
25g^2 - 15gh - 28h^2
Answer:
the answer is (5g+4h)(5g-7h)
Step-by-step explanation:
25g^2-15gh-28h^2
=(25g^2+20gh)+(-35gh-28h^2)
=5g(5g+4h)-7h(5g+4h)
=(5g+4h)(5g-7h)
The numbers in this sequence increase by 40 each time 30, 70, 110, 150. The sequence is continued with the same rule. Which number in the sequence will be closest to 300?
The value in the sequence closest to 300 is 310
Arithmetic SequenceArithmetic sequence is a sequence where each term increases or decreases by addition or subtraction of a constant term
the first term a = 30
common difference, d = 40
which term is closest to 300 we solve like this
300 / 40 = 7.5 say 7
the 7th term, T7 is solved by
T7 = a + ( n - 1 ) d
T7 = 30 + ( 7 - 1 ) 40
T7 = 30 + 240
T7 = 270
checking for the 8th term to confirm the nearest
T8 = T7 + d = T7 + 40
T8 = 270 + 40
T8 = 310
therefore the 8th term is closest and the value is 310
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solve pls brainliest
Answer:
No, No, Yes, Yes, Yes.
Step-by-step explanation:
A integer is a whole number. 1, 2, 3, etc.
Answer:
Only -46 is an integer number and others are not.
Step-by-step explanation:
An integer is a whole number but not a fractional number that can be positive, negative, or zero.
In this chart -46 is an integer cause it is a whole number and -1/2, 57.68, 24/6, 9/3 are not integers cause they are a fraction.
Melissa owns a catering company . For lunch and dinner parties , she serves appetizers before each meal. The number of appetizers Melissa serves is directly proportional to the number of guests at the party. For lunch parties, she serves 3 appetizers per guest. For dinner parties, she serves 5 appetizers per guest. When serving 22 guests, what is the difference of the number of appetizers she serves for dinner and the number of appetizers she serves for lunch?
Answer:
44
Step-by-step explanation:
Lunch = 3 appetizers per guest
If there are 22 guests: 22 × 3 = 66 appetizers served
Dinner = 5 appetizers per guest
If there are 22 guests: 22 × 5 = 110 appetizers served
Difference = total dinner appetizers - total lunch appetizers
= 110 - 66
= 44
their sum is -11 and difference is 41
Answer:
15 and -26.
Step-by-step explanation:
Answer:
15 and -26
Step-by-step explanation:
just bc
Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the
equation Vh= 500(1.025), where Vh is the value of the account after t years. Andres begins a savings account three
years later with the same initial amount of money at the same interest rate. Which equations represent the value of
Andres's account after t years?
A.
B.
C.
D.
Andre's account after t years is [tex]V_h=538.45(1.025)^t[/tex] since is option C.
Amount at the year endThe Amount accumulated at the end of a interest year is the sum of the principla amount and the interest gained on the principal amount.
How to find amount at the end of interest year?As Andres start the savings account after 3 years so, the equation representing the value of Andre's account after t years is-[tex]v_h=500(1.025)^{t-3}[/tex].
Also, the amount accumulated in the mean 3 years will be-
[tex]A=500(1.025)^3[/tex]
=$538.45
Hence, another way of writing the equation representing the value of Andre's account after t years is-[tex]V_h=538.45(1.025)^t[/tex]
As a result, option C is the correct answer.
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please help i am confused.
Answer:
87.5 percent
Step-by-step explanation:
80 passed the first, 70 passed the second. 7/8 passed both. 7/8 as a percentage is 87.5.
Answer:
C. 87.5%
Step-by-step explanation:
[tex]P(A|B)[/tex]
this is what you are trying to find.
P(A | B) can be found by dividing the percentage who passed both, by the percentage who passed the first.
70/80 = 0.875
multiply by 100 to get percentage instead of decimal
87.5
PLEASE HELP AS I SAID I HAVE A F IN MATH AND I HAVE LIKE 6 OTHER SI TO DO PLEASE ANSWER ALL OF THEM
The prism below is made of cubes which measure of a foot on one side. What is the volume?
Note: Figure is not drawn to scale.
A.
B.
C.
D.
Answer: 32
Step-by-step explanation: count one row and then multiply that by 4 And then it equals 32
A cylindrical-shaped container is 8 in. tall with a diameter of 6 in. How much water could this container hold?
A 24pie cubic inches
B 72pie cubic inches
C 216pie cubic inches
D 288pie cubic inches
Answer:
72pi cubic inches.
Step-by-step explanation:
area = pi r²
r = d / 2
r = 3
3² = 9
9pi x 8 = 72pi.
The prime factorization of 100 is 4x25. Show a factor tree!
Answer:
See details below:
Step-by-step explanation:
We can start with the biggest factors and work our way down to see how arrive at 4 * 25.
In this case, the first part of the tree would be 50 * 2.
2 is prime, but 50 is not and thus must be factored.
Two possible factors of 50 are 2 and 25.
The 25 is not a prime number and must be factored further.
Two possible factors of 25 are 5 and 5.
Thus, the prime factorization of 100 is 2*2*5*5.
Then to simplify, we can combine the similar factors: (2*2) * (5*5) = 4*25
I hope this makes sense
find the value of x in the triangle shown below
Answer:
D
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of thesquares on the other two sides, that is
x² + 8² = 9²
x² + 64 = 81 ( subtract 64 from both sides )
x² = 17 ( take square root of both sides )
x = [tex]\sqrt{17}[/tex]
Answer:
√17 (Option D)⠀
Step-by-step explanation:
This is Right Angled Triangle.⠀
We'll solve this using the Pythagorean Theorem.
⠀
Let,
x be BC, where BC is the Perpendicular.8 be AB, where AB is the Base.9 be AC, where AC is the Hypotenuse.⠀
We know that,
[tex]{ \longrightarrow \pmb{\qquad \: (AB) {}^{2} +( BC) {}^{2} = (AC) {}^{2} }}[/tex]
[tex]{ \longrightarrow \sf \qquad \: (8) {}^{2} +( x) {}^{2} = (9) {}^{2} } [/tex]
[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = (9) {}^{2} - (8) {}^{2}} [/tex]
[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = 81 - 64} [/tex]
[tex]{ \longrightarrow \sf \qquad \: ( x) {}^{2} = 17} [/tex]
[tex]{ \longrightarrow \it \qquad \pmb {x = \sqrt{17 \: \: } } }[/tex]
⠀
Therefore,
The value of x is √17 .Two students in Ms. Romean's class are working on
finding the mean for the following set of numbers: 2,
12, 16, 4, 18, 24, 32. Susan states that the answer is
15.4 when rounded to the nearest tenth. She added all
of the numbers and divided by 7. Sam disagrees and
thinks the answer is 54. She added all of the numbers
and divided by 2. Which student is correct? How do
you know? Explain your thinking!
Answer:
susan is correct
Step-by-step explanation:
2+12+4+18+24+32=108
108 divided by 7=54
my reasoning is that the formula is add all and divide by how many numbers you added
Gabby is working on reducing traffic in her town. Last week, she tracked how many cars
drove down Main Street each hour. This box plot shows the results.
Cars per hour
20
60
100
140
180
120
1) What percent of the time did Main Street have 100 or more cars per hour?
The box plot represents the rate of cars in the Main Street per hour
25 percent of the time, the Main Street have 100 or more cars per hour
How to determine the proportion of the boxplot?From the box plot, we have the following parameter:
The upper quartile of the boxplot is 100
This means that:
Q3 = 100
The upper quartile is the 75% dataset
The actual percentage is then calculated as:
Actual = 100% - 75%
This gives
Actual = 25%
Hence, 25 percent of the time, the Main Street have 100 or more cars per hour
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Can someone help me out with this?
What is the value of x?
Enter your answer in the box.
Answer:
x = 4Step-by-step explanation:
x has the same value as RT since they are equal sides of the isosceles triangle.
RT is also the hypotenuse of ΔRST - 30°×60°×90° right triangle.
Acoording to the property of such triangles, the ratio of sides is:
a : b : c = 1 : √3 : 2We have:
b = 2√3 and c = RTUse the ratio to find the lenght of RT
2√3 : RT = √3 : 2RT = 2*2√3/√3RT = 4So the value of x is 4 units
Find RT
sin60=2√3/RT√3/2=2√3/RTRT=4√3/√3RT=4Now
tan45=x/4x=4Cyrus' tennis match lasted two and a half hours. Everett's tennis match lasted four and a half hours. How much longer did Everett’s match last?
Answer:
2 hours
Step-by-step explanation:
4.5 - 2.5 = 2
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A 70kg person jumps off a staircase. They are going 5 m/s just before they hit the ground. How high up where they.
Answer:
0.02 seconds
Step-by-step explanation: A 70kg man jumps 1.00 meters down onto a concrete walkway. His downward motion stops in 0.02 seconds.
Answer:
1.25m
Step-by-step explanation:
v=u+gt
5=0+10t
5=10t
t=0.5s
s=ut+1/2gt^2
=0+(0.5×10×(0.5)^2)
=1.25m
-
Find the equation of the line that
is perpendicular to y = -2x - 9 and
contains the point (8, -4).
Answer:
[tex]y=\frac{1}{2} x-8[/tex]
Step-by-step explanation:
The final answer is in the slope-intercept form, which is y=mx +c, where m is the slope and c is the y-intercept.
The slope of a perpendicular line is the negative reciprocal of the slope of the given line (the line it is perpendicular to). Thus, let's find the slope of the given line first.
Given line: y= -2x -9
The above equation is already in the slope-intercept from and thus, the slope is the coefficient of x.
Slope of given line= -2
The coefficient is the number that comes before a variable and it includes the positive or negative sign, which explains why the slope of the given line is -2 instead of 2.
Slope of perpendicular line= [tex]\frac{1}{2}[/tex]
Substitute the value of the slope into the equation:
[tex]y=\frac{1}{2} x+c[/tex]
To find the value of c, substitute a pair of coordiantes the line passes through.
When x= 8, y= -4,
[tex]-4=\frac{1}{2}(8)+c[/tex]
-4= 4 +c
c= -4 -4
c= -8
Thus, the equation of the perpendicular line is [tex]\bf{y=\frac{1}{2} x-8}[/tex].
What is reciprocal?
The reciprocal of a number is 1 divided by that numberFor example, the reciprocal of 2 is [tex]\frac{1}{2}[/tex]In this question, we are interested in negative reciprocal. This means that if the slope of the given line is m, the slope of the perpendicular line is [tex]-\frac{1}{m}[/tex].Given five vertices, how many different graphs can be made? will give BRAINLIEST
Answer:
Where is the question?
Step-by-step explanation:
I don't see the graphs.
Solve the following equation for x 13x2 - 5 =0
Step-by-step explanation:
if its x13^2-5=0 then 5/169
but if its x13*2-5=0 then 1.07
∠C and ∠D are complementary.
Let m∠C=(5x)° and m∠D=(7x−6)°.
What is the value of x?
Enter your answer in the box. 10 points!!
Answer:
x = 8
Step-by-step explanation:
The sum of the measures of two complementary angles is 90°.
m<C + m<D = 90°
5x + 7x - 6 = 90
12x = 96
x = 8
can some one answer this question please show work
When you reflect across the Y axis, the Y value remains the same and the x value becomes opposite.
Answer: (5,-3)
3x + y = 4 6x + 4y = 6 equivalent equation and solution
Answer:
x = 5/3 , y = -1
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}3x+y=4\\ 6x+4y=6\end{bmatrix}[/tex]
Solve:
[tex]\mathrm{Substitute\:}x=\frac{4-y}{3}[/tex]
[tex]\begin{bmatrix}6\cdot \frac{4-y}{3}+4y=6\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}2y+8=6\end{bmatrix}[/tex]
[tex]\mathrm{For\:}x=\frac{4-y}{3}[/tex]
[tex]\mathrm{Substitute\:}y=-1[/tex]
[tex]x=\frac{4-\left(-1\right)}{3}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=\frac{5}{3}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=\frac{5}{3},\:y=-1[/tex]
3(5/3) + -1
5-1 = 4
True
6(5/3) + 4(-1)
10 -4 = 6
True
~lenvy~