The length of the floor of the box with an area of [tex]0.43m^2[/tex] is 0.66m
Let the area of the enlarged portion be a square and the formula is expressed as:
[tex]A = L^2[/tex]
L is the side length or the floor of the box.
Given the following parameters:
[tex]A = 0.43m^2[/tex]
Substitute the given parameters into the formula as shown:
[tex]0.43 = L^2\\L =\sqrt{0.43}\\L= 0.6557[/tex]
Hence the length of the floor of the box with an area of [tex]0.43m^2[/tex] is 0.66m
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Question 2. In 2015, a Pew Research poll determined that 56% of teenagers go online several times a day.
You question a sample of 150 area high school students about their online habits. Describe the sampling distribution for the sample proportion, for samples of size 150, of high school students who go online several times a day. You should include a picture that approximates the sampling distribution, and label at least five tick marks in that drawing. Round to the nearest tenth of a percent.
b. You find that, in your sample, 94 of the high school students go online several times a day. Assuming the percentage obtain from Pew, is your result unusual, as defined in class? Justify your answer with a z-score.
Answer:
84 students go online several times a day
Step-by-step explanation:
Use polar coordinates to find the volume of the given solid.
Below the plane
2x + y + z = 4
and above the disk
x2 + y2 ≤ 1
Using polar/cylindrical coordinates, we take
x = r cos(t )
y = r sin(t )
z = z
so that
dV = dx dy dz = r dr dt dz
The solid is given by the set
D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}
or in cylindrical coordinates,
D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}
Then the volume of the solid is
[tex]\displaystyle \iiint_D \mathrm dV = \iiint_Dr\,\mathrm dr\,\mathrm dt\,\mathrm dz \\\\ = \int_0^{2\pi} \int_0^1 \int_0^{4-2r\cos(t)-r\sin(t)} r\,\mathrm dz\,\mathrm dr\,\mathrm d t \\\\ = \int_0^{2\pi}\int_0^1 (4r-2r^2\cos(t)-r^2\sin(t))\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \left(2 - \frac23 \cos(t) - \frac13 \sin(t)\right) \,\mathrm dt \\\\ = \boxed{4\pi}[/tex]
The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.
What is the volume of the solid in polar coordinates?The volume of the solid in polar coordinates can be calculated by the double integral in polar coordinates.
[tex]V = \iint_R f(x,y) \,dA.\\[/tex]
Similarly, by polar coordinates,
x = r cost
y = r sint
z = z
we get, dV = dx dy dz = r dr dt dz
The solid is given
D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}
or in polar coordinates,
D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}
The volume of the solid is
[tex]\rm \int \int\int\ dV = \int \int\int\ rdr dt dz\\ \rm = \int\limits^{2\pi}_0\int\limits^1_0 \int\limits^{4-2rcost-rsint}_0 rdr dt dz\\\rm =\int\limits^{2\pi}_0\int\limits^1_0 {4r-2r^{2} cost-r^{2} sint} dr dt\\\rm =\int\limits^{2\pi}_0( 2-2/3cost-1/3sint) dt\\\rm =4\pi[/tex]
Hence, The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.
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Person 2 worked for 200 minutes and checked 1,325 comments every 5 minutes
Answer: 33.125
Step-by-step explanation:
So you would do 200 divdied by 5 which is 40 then you would do 1,325 divided by 40 which is the anwser 33.125. If you did it another way let me know.
Mikes grandma opened a savings account in mikes name. And deposited. Some money into the account the account pays on annual simple interest rate of 5% after 8 years the interest earned on the account was 3,200 how much money did mikes grandma deposit in the account
Answer: 2285.71
Step-by-step explanation:
Rearranging the simple interest formula, we have P = A / (1 + rt), where P is the Principal, r is the annaul rate and t is the time period.
r = R/100 = 5%/100 = 0.05 per year.
Solving the equation:
P = 3200 / ( 1 + (0.05 × 8)) = 2285.7142857143
Answer:
Grandma deposited 8,000
Step-by-step explanation:
I = 3200
r = 5 %
t = 8 years
[tex]P =\dfrac{I*100}{r*t}\\\\P = \dfrac{3200*100}{8*5}\\\\P= 8000[/tex]
The arithmetic mean of ten numbers is -10. If the sum of six of the numbers is 100, what is the arithmetic mean of the other 4?
Answer:
56
Step-by-step explanation:
Arithmetic mean is simply the sum of the all the number present divide by the total number.
From the question, we obtained the following information:
The arithmetic mean = 5.6
Total number present = 10
Sum of the numbers =?
Arithmetic mean = sum of the numbers / total number
Sum of the numbers = arithmetic mean x total number
Sum of the numbers = 5.6 x 10 = 56
The sum of the other four numbers is equivalent to -200.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the arithmetic mean of ten numbers is -10. The sum of six of the numbers is 100.
We can write -
{a + b + c + d + e + f + g + h + i + j}/10= - 10
{a + b + c + d + e + f + g + h + i + j} = - 10 x 10
{a + b + c + d + e + f + g + h + i + j} = - 100 .... Eq{1}
and
{a + b + c + d + e + f} = 100 .... Eq{2}
We can write Eq{1} as -
{a + b + c + d + e + f} + {g + h + i + j} = - 100
100 + {g + h + i + j} = - 100
{g + h + i + j} = - 100 - 100
{g + h + i + j} = - 200
Therefore, the sum of the other four numbers is equivalent to -200.
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Write an
equivalent fraction for 2/5 with 45 as the denominator.
Answer:
18/45
Step-by-step explanation:
First you set 2/5 equal to x/45.
Then you see what number you need to multiply 5 by to get 45
Multiply 2 by the number you got and you get x.
The equivalent fraction for 2/5 with a denominator of 45 is 18/45.
We need to figure out what number we can multiply the numerator and denominator by to get the necessary denominator in order to discover an equivalent fraction for 2/5 with a denominator of 45.
The denominator must be multiplied by 9 in order to be converted from 5 to 45 (45 ÷ 5 = 9). To keep the ratio and get the equal fraction, we will also multiply the numerator by 9.
2/5 x 9/9 = (2 x 9) / (5 x 9) = 18/45
As a result, 18/45 is the corresponding fraction for 2/5 with a denominator of 45.
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HELP LAST ATTEMPT !?!!
Answer:
x=21
Step-by-step explanation:
10+2x+128=180 [Angles in a straight line]
2x=180-138
x=42/2
x=21
27 equals 2 less than a number
Answer:
23
Step-by-step explanation:
Solve for y: 42/10 = 21/y
Answer:
Y = 5
Step-by-step explanation:
Correct answer: y = 5
By cross multiplication, you multiply 21 × 10, which is 210. Then, you divide 210 by 42, which is 5.
f(x)= x^2. what is g(x)?
A. g(x) = 1/4x^2
B. g(x) =1/4x^2
C. g(x) =4x^2
D. g(x) = 1/2x^2
Answer: g(x)=x/3^2
Step-by-step explanation:
We are given that:
f(x)=x²
We have to find g(x)
Since, we are given that g(3)=1
Hence, we will proceed by the options.
1. g(x)=
at x=3 g(x)=1/9
Hence, this option is incorrect.
2. g(x)=3x²
at x=3, g(x)=27
Hence, this option is incorrect.
3. g(x)= x²/3
at x=3, g(x)=3
Hence, this option is incorrect.
4. g(x)=
at x=3, g(x)=1
Hence, this option is correct
During hockey practice, Jason skates 180 yards in 20 seconds.
Based on his average speed, approximately how many yards will he skate in the next 15 seconds?whoever answers first will be marked the brainliest
The approximate yards Jason will skate in the next 15 seconds is 135 yards
Given that :
Number of yards skate in 20 seconds = 180 yards
The rate per second cannbe calculated thus :
Rate = distance / time Rate = 180 / 20 = 9 yards per secondThe distance skate in 15 seconds will be:
Distance = time × rate Distance = 15 × 9 = 135 yardsTherefore, Jason will skate 135 yards in the next 15 seconds.
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What is a general rule for simplifying expressions like x^a .x^b? where does this rule
comes from
you and your freind are going on a camping trip.you each buy a backpackthat cost $90 and a sleeping bag that costs $60.what is the total cost of the camping eqiptment?
Answer:
$300
Step-by-step explanation:
90 x 2 = 180
60 x 2 = 120
120 + 180 = 300
Does this equation have a solution?
How does the test variable of an object affect the amount of mechanical energy it contains?
Answer:
rg53º
Step-by-step explanation:
grnrgnrn
HELP ASAP! Will award brainliest and crown
A new movie theater holds 350 people with 14 seats in every row. Use division to find how many rows are there in the theater.
Answer:25
Step-by-step explanation:
350 / 14 =25
1) Convert 0.469 dam to cm.
Round 6,823 to the nearest thousand
Answer:
7,000
Step-by-step explanation:
multiplicative inverse of 3/7 x 2/7
Sorry if I didn't understand the question right-
Answer:
[tex]\frac{49}{6}[/tex]
Step-by-step explanation:
The inverse of [tex]\frac{3}{7}[/tex] is [tex]\frac{7}{3}[/tex].
The inverse of [tex]\frac{2}{7}[/tex] is [tex]\frac{7}{2}[/tex].
Now we multiply:
[tex]\frac{7}{3}[/tex] × [tex]\frac{7}{2}[/tex] = [tex]\frac{49}{6}[/tex]
Hope this helped :)
Simple Linear Regression Unit Test Plz help 1 hr 20 mins left.
Answer:
123456
Step-by-step explanation:
it is pie 3.14 because it is
Write an absolute value equation of the form |ax+b|=cx+d that has no solution. Assume that a, b, c and d ≠0
9514 1404 393
Answer:
|3x +5| = 3x +1|3x +5| = x -1Step-by-step explanation:
The left-side expression will not intersect the right side expression if the slopes are the same and the y-intercepts are chosen appropriately. An example is ...
|3x +5| = 3x +1
The right-side line stays below the left-side V, so doesn't intersect.
__
You can choose the slopes to be different, also, if you make the intercepts such that the right-side line does not intersect the left-side V. An example of that is ...
|3x +5| = x -1
__
Graphs of the left- and right-side expressions are shown in the attachment.
2/3 divide 1/8 using kcf
Answer:
2/3 divdied by 1/8 is 5 1/3
Step-by-step explanation:
You first keep the 2/3, change the operation to multiplication, then flip the 1/8 to 8/1, then multiply across to get 16/3. After that, simplify to get 5 1/3
A moderately active man weighing 175 pounds should consume no more than 687 calories per day from fat sources. If fat contains 9 calories per gram, what is the maximum number of grams of fat he should consume? Give me a whole number or decimal rounded to one decimal place. Thanks! Expert only please.
According to the question, therefore, the maximum number of grams of fat he should consume will be 76.3 grams.
Step-by-step explanation:-Directly divide 687 by 9 as both are fat content. Therefore, by dividing them, we get to know about how grams of fat can be consumed.
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What is the fourth term of an arithmetic sequence whose first term is 23 and whose seventh term is 5?
A) 78
B) 32
C) 14
(Explain your work)
We have that the fourth term of an arithmetic sequence is
a_4=14
Option C
From the question we are told
What is the fourth term of an arithmetic sequence whose first term is 23 and whose seventh term is 5?
A) 78
B) 32
C) 14
(Explain your work)
Generally the equation for the arithmetic sequence is mathematically given as
[tex]a_4=a_1+(n-1)d[/tex]
Therefore
For seventh term
[tex]5=23+(6)d\\\\d=5-23/(6)\\\\d=-3[/tex]
Therefore
For Fourth term
[tex]a_4=23+(3*(-3))[/tex]
a_4=14
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1 A boat travels at an average speed of 15 km/h for 1 hour.
a Calculate the distance it travels in one hour.
b At what average speed will the boat have to travel to cover the
same distance in 2 hours?
Answer: 15km, 7.5kmh
Step-by-step explanation:
a. Distance travelled = speed * time = 15* 1 =15km
b. Distance = 15
time = 2hrs
Speed = distance/time = 15/2 = 7.5kmh
vivien needs to proofread a 500 page novel she plans to do 30 page on the first day and increase the number by 5 each dag how many days will it take her to complete the proof reading?
Answer:
Step-by-step explanation:
in the problem it says she plans to do thirty pages so lets let 30 be our y value so ?x +30 and she plans to increase by 5 each day key word is each which means multiply so let 5 be our x value which will give you the equation 500=5x+30 so step by step here we go
500=5x+30
1. 500=5x+30
500 −30= 5
Answer:
I think about 9 days
Step-by-step explanation:
first day is 30 next is 35, 40,45,50,55,60,65,70,75
i dont is this what u wanted but its done and it is
by the 9ths day you would have 525
i dont know what i did
need explanation with these problems! help me please!
Answer: 4
Step-by-step explanation:
Find multiples of 12 and 16
4 is a common multiple
if you start from 1/4 and add 4 to the denominator and 1 to the numerator you get the following sequence:
1/4, 2/8, 3/12 and 4/16
Therefore the answer to the problem is 4
If you have any more simple algebra question pls message me :)
ANSWER QUICK PLEASE!!
combine like terms. 8x + 3 - 5x + 9
A. -13x - 12
B. 13x + 12
C. 3x - 6
D. 3x + 12
NO LINKS OR WEBSITES!!
Answer:
D
Step-by-step explanation:
8x-5x+3+9=3x+12
combine like terms
Which of the following is an equation of the line In the graph? A.3x-y=4 B.3x+y=4 C.-3x-y=4 D.-3x+y=4m
9514 1404 393
Answer:
B. 3x+y=4
Step-by-step explanation:
The constant on the right is positive, so the signs of the coefficients match the signs of the respective intercepts. The graph shows both x- and y-intercepts are positive, so the equation will have positive coefficients everywhere. The appropriate choice is ...
3x +y = 4