Let's use an equation to solve this problem.
Since they are consecutive integers, if we say that the first number is [tex]x[/tex], then the next two numbers (three dimensions in a rectangular prism) are [tex]x+1[/tex] and [tex]x+2[/tex] respectively.
[tex]x*(x+1)*(x+2)=4896[/tex]
[tex]x*(x+1)=x^2+x[/tex]
[tex](x^2+x)*(x+2)=x^3+2x^2+2x[/tex]
[tex]x^3+3x^2+2x=4896[/tex]
[tex]x^3+3x^2+2x-4896=0[/tex]
[tex]x=16[/tex]
B is the correct answer.
What is the quotient of the rational expression below?
Answer:
first answer
Step-by-step explanation:
Hello, you know that
[tex]\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\cdot \dfrac{d}{c}[/tex]
So, the quotient we need to estimate is
[tex]\begin{aligned}\dfrac{x^2-36}{x+8}\cdot\dfrac{4x+32}{x^2+12x+36}&=\dfrac{x^2-6^2}{x+8}\cdot \dfrac{4(x+8)}{(x+6)^2}\\\\&=\dfrac{4(x-6)(x+6)}{(x+6)^2}\\\\&=\dfrac{4(x-6)}{x+6}\end{aligned}[/tex]
Thank you
This is the last one, i truly appreciate all the help u guys have given me.
Answer:
it's rational ..........
2(-2a-4d)-(9a+17d) combining like terms
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 13.6 reproductions and the population standard deviation is known to be 1.9. If a sample of 189 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.
Answer:
The confidence interval is [tex]13.4< \mu < 13.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 13.6[/tex]
The standard deviation is [tex]\sigma = 1.9[/tex]
The sample size is [tex]n = 189[/tex]
given that the confidence level is 85% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 85 )\%[/tex]
[tex]\alpha = 0.15[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{\alpha }{2} } = 1.44[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 1.44* \frac{1.9}{\sqrt{189} }[/tex]
=> [tex]E = 0.1990[/tex]
The 85% confidence interval is mathematically represented as
[tex]\= x - E < \mu <\= x + E[/tex]
=> [tex]13.6- 0.1990 < \mu < 13.6+ 0.1990[/tex]
=> [tex]13.4< \mu < 13.8[/tex]
[128 ÷ (6 + 4 – 2)] X 8
Do parentheses first:
6 +4-2 = 8
Now do brackets:
128/8 = 16
Now multiply:
16 x 8 = 128
The answer is 128
What is the slope of the equation y=5/4x-7/4?
Answer:
[tex]\Large \boxed{\frac{5}{4} }[/tex]
Step-by-step explanation:
The slope - intercept form of a line is written in the form :
[tex]\sf y = mx+b \\ \\ \\ m=slope \\ \\ b=y-intercept[/tex]
The slope of the line is 5/4.
A tortoise is walking in the desert. It walks 43.75 meters in 7 minutes. What is it’s speed?
Answer:
v=0.104167m/s
Step-by-step explanation:
Given:
s=43.75
t=7min
Required:
v=?
Formula:
v=s/t
t in second
Solution:
1min=60s
7min=7*60s=420s
v=s/t
v=43.75m/420s
v=0.104167m/s
Hope this helps ;) ❤❤❤
Given: f(x) = X^2 - 3 and g(x) = X + 1 The composite function g°f is:_______.
Answer:
x² - 2
Step-by-step explanation:
To obtain (g ￮ f)(x), substitute x = f(x) into g(x), that is
g(x² - 3)
= x² - 3 + 1
= x² - 2
Answer:
✔ x² - 2
Step-by-step explanation:
EDG 2020
A work shift for an employee at a restaurant consist of 8 hours.What fraction of the employee’s work shift is represented by 6 hours ?
Answer:
Fraction of work shift represented by 6 hours = 0.6
Step-by-step explanation:
Total work shift of employee = 10 hours
Time considered to find fraction = 6 hours
Fraction of work shift represented by 6 hours 6/10=3/5=0.6=60%
Fraction of work shift represented by 6 hours = 0.6
Answer:
0.75
Step-by-step explanation:
Total work shift of an employee is 8 hours
Time consist to find fraction is 6 hours
The fraction of work shift by 6 hours :
[tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75 = 75%
The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec. How long does it take to reach the ground
This question is incomplete, the complete question is;
A rocket is launched straight into the air with initial velocity 200 ft/s. Assume the launch is instantaneous. How high will it go, and how long will that take (use time increments of 0.01 seconds)? G= - 32.2 ft/s² , H₀=0 (the ground)
V(t)=V₀ + g t
H(t)= H₀ + V₀ t + ½ g t²
The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec. How long does it take to reach the ground
Answer:
a) maximum height S is 621.12 ft and time taken to reach it is 6.21 sec.
b) The rocket deploys a parachute after 9 seconds and descends at a constant rate of 20 ft/sec,
Time taken to travel t = 24.79 sec
NOW total time taken = 27.55 sec
Step-by-step explanation:
Given that,
initial velocity u = 200 ft/s
acceleration a = 32.2 ft/s²
vertical displacement ( maximum height) S = ?
final velocity at highest point Ц = 0
NOW from the equation of motion
v² - u² = 2as
we substitute
0² - (200)² = 2 (-32.2) × s
s = 621.12 ft
time taken t = (v -u)/a = (0-200)/-32.2
t = (-200) / (-32.2)
t = 6.21 sec
distance traveled by rocket from t=6.21sec to t=9sec
Δt = (9-6.21) = 2.79sec
s = ut + 1/2at²
s = 0 + 1/2(32.2)(2.79)² = 125.32 ft
Remaining distance = 621.12 ft - 125.32 ft = 495.8 ft
Time taken to travel = t = s/v = (495.5ft) / (20 ft/sec)
t = 24.79 sec
NOW total time taken = 2.79sec + 24.79sec = 27.55 sec
(23.0lb/gal)(2ft) report in correct number of significant figures and units
Answer:
344.1 Ib/ft²
Step-by-step explanation:
This has to do with conversion
23.0Ib/gal × 2ft
Step 1
First we convert 23.0lb/gal to Ib/ft³
1 Ib/gal = 7.48051948 Ib/ft³
23.0lb/gal = X Ib/ft³
Cross Multiply
1 Ib/gal × X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³
X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³/1 Ib/gal
X Ib/ft³ = 172.05194804 Ib/ft³ =
Step 2
Since 23.0lb/gal = 172.05194804 Ib/ft³
172.05194804 Ib/ft³ × 2 ft
= 344.10389608Ib/ft²
Approximately to 1 significant figure
= 344.1 Ib/ft²
A bicycle tire is 28 inches in diameter. Approximately how far does the bicycle move forward each time the wheels go around (use22/7 as an approximation for pie
Answer: About 88 inches
=============================================
Explanation:
Find the circumference
C = pi*diameter
C = (22/7)*28
C = 88
The tire's circumference is approximately 88 inches. This is the perimeter or distance around the circle. As the bike moves forward one full rotation of the wheel, all of the wheel will touch the ground at some point. The bike will move about 88 inches forward when the wheel does one full rotation.
A good way to visualize this is to imagine cutting the tire so that you can unroll it to lay it out completely flat forming a straight line. This line will be roughly 88 inches long.
Negative of (-5) does not exist is true or false
Answer:
Negative of 5 exists
It continues in the left part of a number line...
Hence the answer is false it does exist
2) 200
3) 20
4) 10
5) 170
6) 55plz help i will mark the brainliest
Answer:
natural numbers - positive integers (whole numbers)
• 1
• 2
• 3
• 4
• 5
whole numbers - a number without fractions
• 10
• 11
• 12
• 13
• 14
rational numbers - a number that can be expressed as the ratio of two integers
• 1/3 or 0.3333...
• 17
• -34
• 25
• -10
integers - a whole number; a value that is not a fraction
• -5
• 49
• 68
• 439
• 35
An object has a potential energy of 14 J and a mass of 17 kg , how far above the ground is the object? An object moving with a speed of 35 m/s and has a kinetic energy of 1500 J, what is the mass of the object. What is the Potential Energy of a 1200 kg object that is 24 m above the ground? What is the Potential Energy of a 478 kg object that is150 m above the ground? What is the Potential Energy of a 100 kg object that is 12.5 m above the ground? An object has a potential energy of 14 J and a mass of 17 kg , how far above the ground is the object? An object is 35 m above the ground and has a potential energy of 1500 J, what is the mass of the object?
1. Potential Energy = mgh
h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.
2. Kinetic Energy = 1/2 mv^2
m = 2K_e / (v^2) = 2.45 kg
3. U_g = mgh = (1200)(9.81)(24) = 282528 J
4. U_g = mgh = (478)(9.81)(150) = 703377 J
5. U_g = mgh = (100)(9.81)(12.5) = 12262.5 J
6. h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.
7. m = U_g / (gh) = 1500 / (9.81 * 35) = 4.37 kg
Subtract 5 - 4i from 19 - 3i.
Answer:
Step-by-step explanation:
19 - 3i - 5 + 4i
14 + i
Simplify: -8 +2 +3 (-7)
Answer:
-8/4-21x
Step-by-step explanation:
Distribute inside the parantheses
Divide -8 and 4
Add the two terms
Simplify
Make the number 18 using six "1"s.
Answer:
(11-1-1)(1+1)
Step-by-step explanation:
revised
A steel pipe which was 16.84 feet long, weighed 20.88 pounds what is the weight of one foot of the steel pipe?
Designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 30 feet which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guest to stand to experience his whisper chamber will be 4 feet from the center of the warehouse space, which will act as the foci. How far out from the center along the minor axis should he built his whisper chamber.
Answer:
14.48 ft
Step-by-step explanation:
The relation between the location of the focus (c), the vertex on the major axis (a) and the vertex on the minor axis (b) with respect the center is:
b² = a² - c²
From the question:
c = 4 ft
a= 30/2 = 15 ft
Replacing into the equation:
b² = 15² - 4²
b = √209
b = 14.48 ft
So, he should build the whisper chamber at 14.48 ft out from the center along the minor axis
Answer: The answer to this questiojn is 14.48 feet, but if rounded to the nearest tenth, then it should be 14.5 (As it was on my question)
Need the answer ASAP
Answer:
Approximately 201 squared inches.
Step-by-step explanation:
So, the composite figure is made up of a square and a semi-circle. The square has side lengths of 12 and the semi-circle has a radius of 6.
The total area of the figure would be the area of the square plus the area of the semi-circle. Thus, find the area of each individual figure.
Square:
The area of a square is given by:
[tex]A=l^2[/tex]
Where l is the side length.
Substitute 12 for l:
[tex]A=(12)^2\\A=144\text{ in}^2[/tex]
So the square is 144 square inches.
Semi-circle:
The area of a semi-circle is given by:
[tex]A=\frac{1}{2}\pi r^2[/tex]
Substitute 6 for r and 3.14 for π:
[tex]A=\frac{1}{2}(3.14)(6)^2\\ A=56.52[/tex]
Therefore, the total area is:
[tex]TA=144+56.52\\TA=200.52\text{ in}^2\approx201\text{ in}^2[/tex]
i need help i will give the brainliest
Answer:
the answers are
13) -6
14) 6
15) -5
16) 3
17) 14
18) -4
19) -15
20) 4
21) 5
22) -12
It is estimated that 65.5% of the students at Foster Middle School will attend the benchmark reward party. Which number is NOT equivalent to 65.5%
Answer:
I am not totally sure but the answer might be 0.0655.
There is 26 letters in the alphabet A=1 B=2 C=3 and so on Z+Z=?+D-A then take the number you get then turn it into a letter ?+F-K+L=? This is One of the hardest questions i made!!!!
Answer:
I got (G^B) +F-K+L= (G^B)
Step-by-step explanation:
From the given figure 7 ,find the value of x if AB is parallel CF and AE = DE, angle BAE = 38°.
*see the given given in the attachment below
Answer:
x = 109°
Step-by-step Explanation:
Since AB is parallel to CF, m<BAE = m<AED = 38° (alternate interior angles are congruent)
Since AE = DE, ∆AED is an isosceles ∆.
The two base angles of any given isosceles ∆ are said to be congruent.
This means, m<EAD = m<EDA = ½(180 - m<AED)
m<EDA = [tex] \frac{1}{2}*(180 - 38) [/tex]
m<EDA = [tex] \frac{1}{2}*(142) = 71 [/tex]
x + m<EDA = 180° (angle on a straight line)
[tex] x + 71 = 180 [/tex]
[tex] x + 71 - 71 = 180 - 71 [/tex]
[tex] x = 109 [/tex]
Value of x = 109°
One is the additive identity. True or False
Answer: false
Additive identity - the number 0; when added to any number, the value of the number does not change
( one is multiplicative identity )
Binomial (-2x - 8) and trinomial (-3x2 + 4x + 5) are the factors of which of the following polynomials?
Answer:
5
Step-by-step explanation:
Write a proper fraction to represent the shaded part. If an improper fraction is appropriate, write the shaded part of the diagram as (a) an improper fraction and (b) a mixed number.
9/7 (a)
(b) 1 whole 2/7 is the answer of ur question
Linda had 72 fliers to post around town. Last week, she posted 1/3
of them. This week, she posted 1/4 of the remaining fliers. How many fliers has she still not
posted?
Answer:
36 fliers
Step-by-step explanation:
1/3*72 = 24 fliers posted last week (.333*72)
72-24 = 48 fliers left
1/4*48 = 12 fliers posted this week (.25*48)
48-12= 36 fliers not posted
Linda has 36 fliers left to post.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given: Linda had 72 fliers to post around town. Last week, she posted 1/3
of them. This week, she posted 1/4 of the remaining fliers.
1st-week Linda posted 72/3=24 and remaining fliers72-24=48
2nd the week Linda posted 48/4=12 and remaining fliers 48-12=36
∴The remaining fliers left to be posted are 36
Hence, Linda has 36 fliers left to post.
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ2
simplify the expression 3+2^2 / 2+3
Ans
8 option b.
Step-by-step explanation:
3+4/2+3
=3+2+3
=5+3
=8