Answer:
Volume = 24 ft³
Step-by-step explanation:
Given a rectangular aquarium whose dimensions are
2ft x 4 ft x 3 ft
Total volume = 3 x 4 x 3 = 24 ft³
Select the expression that is equivalent to (x - 1)2.
O A. x2 - 2x + 2
O B. x2 - x + 2
O C. x2 - x + 1
O D. x2 – 2x + 1
Answer:
x^2 -2x+1
Step-by-step explanation:
(x - 1)^2
(x-1) * (x-1)
FOIL
first: x^2
outer: -1x
inner: -1x
last: 1
Add together
x^2 -1x-1x+1
Combine like terms
x^2 -2x+1
Answer:
[tex] \boxed{\sf D. \ {x}^{2} - 2x + 1} [/tex]
Step-by-step explanation:
[tex] \sf Expand \: the \: following: \\ \sf \implies {(x - 1)}^{2} \\ \\ \sf \implies (x - 1)(x - 1) \\ \\ \sf \implies x(x - 1) - 1(x - 1) \\ \\ \sf \implies (x)(x) - (1)(x) - (1)(x) - (1)( - 1) \\ \\ \sf \implies {x}^{2} - x - x - ( - 1) \\ \\ \sf \implies {x}^{2} - 2x - ( - 1) \\ \\ \sf \implies {x}^{2} - 2x + 1[/tex]
Please answer this correctly
Answer:
Question 2 is the right answer.
Step-by-step explanation:
Answer:
Question 2
Step-by-step explanation:
Temperature in the morning = 2°F above normal temperature = + 2
Temperature at dinner time = 2° F lower than the morning = -2
+2 - 2 = 0° F
h(1)=-17 h(n)=h(n-1)*0.2 find an explicit formula for h(n).
Answer:
h(n) = -17·0.2^(n-1)
Step-by-step explanation:
The explicit formula for a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
Your sequence h has first term a1 = -17 and common ratio r = 0.2. Then the explicit formula is ...
h(n) = -17·0.2^(n-1)
2 + 4x - 4 = 0 which gives x =
Answer:
[tex]x = \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]2 + 4x - 4 = 0 \\ 2 + 4x = 0 + 4 \\ 2 + 4x = 4 \\ 4x = 4 - 2 \\ 4x = 2 \\ \frac{4x}{4} = \frac{2}{4} \\ x = \frac{1}{2} [/tex]
Answer:
x = 1/2
Step-by-step explanation:
2 + 4x - 4 = 0
4x = 0 + 4 - 2
4x = 2
x = 2⁽²/4
x = 1/2
What is the circumference of the circle below? (Round your answer to the nearest tenth.)
Answer:
Its 69.1 cm
Step-by-step explanation:
To find circumstance of any circle main formula is 2*pie*r .
Here pie is equal to 3.14 approx and r =11 cm
so
2*3.14*11 = 69.08 cm
This little difference is just because of pie's approximately value used
Jacob and Dustin collected 245 cast for the school can job they give 55 cast to Dustin's little sister to take to her class how many cans does this leave for the boys class
Answer:
190 cans
Step-by-step explanation:
Total cans collected by Jacob and Dustin for the school can job = 245
Amount of cans they both gave to Dustin's little sister = 55
Now because they gave out cast out of the total they initially had, there would be a deduction in the amount both boys would now have.
To determine the amount the boys are left with, we would deduct 55 casts from the amount they had which 245.
Amount of cans left = 245-55 = 190
Amount of cans left for the boys class = 190 cans
What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)? y = x + 3 y = x + 7 y = 3x – 13 y = 3x + 5
Answer:
y = x-1
Step-by-step explanation:
y = x + 4
This is in slope intercept form ( y = mx+b where m is the slope and b is the y intercept). The slope is 1
Parallel lines have the same slope
y = 1x+b
Using the given point
5 = 6*1+b
5-6 = 6+b-6
-1 =b
The equation becomes
y =1x-1
y = x-1
Answer:
its b ). y = -1/3 x + 7
Step-by-step example
Use the function below to find f(4).
f(x)=1/3x4^x
A. 8/3
B.256/3
C.64/3
D.16/3
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
Simply replace X with 4
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
Pls help see the picture posted
Use a proportion to solve the problem. Round to the nearest tenth as needed.
Triangle in a triangle Find the height of the building. Assume that the height of the person is 5 ft.
104 ft
building
13 ft
5 ft
Answer:
Height of the building is 40 feet
Step-by-step explanation:
From the figure attached,
Height of the person DE = 5 feet
Let height of the building BC = h feet
Since, ΔABC ~ ΔADE,
Their corresponding sides will be proportional,
[tex]\frac{DE}{BC}=\frac{AD}{AB}[/tex]
[tex]\frac{5}{h}=\frac{13}{104}[/tex]
h = [tex]\frac{104\times 5}{13}[/tex]
h = 40 feet
Therefore, height of the building is 40 feet.
The monthly starting salaries of students who receive an MBA degree have a standard deviation of $110. What size sample should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less
Answer:
116.21Step-by-step explanation:
Using the formula for calculating margin error to tackle the question.
Margin error = [tex]\frac{Z \sigma}{\sqrt{n} }[/tex]
Z is the value at 95% confidence
[tex]\sigma[/tex] is the standard deviation
n is the sample size to be estimated
Since the mean monthly income is within $20 or less, our margin error will be $20
Given [tex]\sigma[/tex] = $110, Z value at 95% confidence = 1.96 we can calculate the sample side n.
Making n the subject of the formula from the equation above;
[tex]M.E = \frac{Z \sigma}{\sqrt{n} }\\\\\sqrt{n} = \frac{Z \sigma}{M.E } \\\\[/tex]
[tex]n = (\frac{Z \sigma}{M.E })^{2}[/tex]
Substituting the give value into the resulting expression;
[tex]n = (\frac{1.96 * 110}{20})^{2}\\\\n = (\frac{215.6}{20}) ^2\\\\n = 10.78^2\\\\n = 116.21[/tex]
This shows that the sample size that should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less is approximately 116.21
which expression defies the arithmetic series 10 + 7 + 4 ... for six terms?
Answer:
[tex]a_n = 10-3(n - 1)[/tex]
10 + 7 + 4 + 1 + -2 + -5
Step-by-step explanation:
Explicit Arithmetic Formula: [tex]a_n = a_1 + d(n-1)[/tex]
To find d, take the common difference between 2 numbers.
To find the other terms of the sequence, plug them into the explicit formula or subtract 3 from the given numbers.
As an example, 15,000 Men 18-34 watched program X at 7-8 pm on Monday night. 32,000 Men 18-34 had their TV on during the same time period. There are 200,000 Men 18-34 in the television households in the market. What would be the rating for Men 18-34 for program X? Group of answer choices 47 rating points 7.5 rating points 16 rating points 23.5 rating points
Answer:
7.5 rating points
Step-by-step explanation:
The computation of the rating for Men 18-34 for program X is shown below:
Given that
Number of men 18 -34 watched a program X = 15,000 = X
Number of men 18 - 34 watched in a same time = 32,000
And, the total households in the market = 200,000 = Y
So, the rating for men 18-34 for program x is
[tex]= \frac{X}{Y}[/tex]
[tex]= \frac{15,000}{200,000}[/tex]
= 7.5 rating points
We simply applied the above formula
6.7 grams of aluminum sulfate to moles
Answer:
0.01958mol
Step-by-step explanation:
you want to go from grams to mols so when set up it looks like this
6.7 x [tex]\frac{1mol}{the mass of aluminum sulfate}[/tex]
(you want what your multiplying to cancel out with the denominator(g cancel out g so your left with mols))
to get the mass of aluminum sulfate you must first find the chemical formula which is
Al2(SO4)3
get the amount of every element
so there is:
2 Al
3 S
12 O
(multiply the three to everything inside the parenthesis)
next find the total mass of everything
Al=26.982g x 2
S=32.06g x 3
O=16g x 12
add everything together and you get 342.144g so you plug that number into the first equation
6.7 x[tex]\frac{1mol}{342.144g}[/tex] → [tex]\frac{6.7}{342.144}[/tex]→0.01958mol
The manufacturer of a certain brand of hot dogs claims that the mean fat content per hot dog is 20 grams. Suppose the standard deviation of the population of these hot dogs is 1.9 grams. A sample of these hot dogs is tested, and the mean fat content per hot dog of this sample is found to be 20.5 grams. Find the probability that the sample mean is at least 20.5 when the sample size is 35.
Answer:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]
Step-by-step explanation:
For this case we define our random variable X as "fat content per hot dog" and we know the following parameters:
[tex]\mu = 20, \sigma =1.9[/tex]
We select a sample of n=35 and we want to find the following probability:
[tex] P(\bar X>20.5)[/tex]
For this case since the sample size is >30 we can use the central limit theorem and we use the z score formula given by:
[tex]z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Replacing we got:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]
Alonzo and Cheryl are both members of a population, and a simple random sample is being conducted. If the chance of Alonzo being selected is 1/2900, what is the chance of Cheryl being selected?
Answer:
¿Consideras que la gente que discrimina por aspectos como el color de la piel, clase social, por el género, etc., no saben lo que las personas valen y por eso no las valoran?
¿Consideras que la gente que discrimina por aspectos como el color de la piel, clase social, por el género, etc., no saben lo que las personas valen y por eso no las valoran?
Answer: 1/2900
Step-by-step explanation: if they are both in the same population and they are both being randomly selected then they both have the same possibility of being picked
Plz help me plzzzzzz!!!!
Answer: D, 6
Step-by-step explanation:
Match each side from XYZ to ABC (you are trying to find the scale factor of triangle 1 to triangle 2) into a fraction then simplify
Ex 30/5= 6 or 24/6= 6 or 18/3
Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere
x^2+y^2+z^2=125
The parametrization shown below,
[tex]x(t),y(t),z(t)=10cost,5,10sint[/tex]
Given equation of sphere,
[tex]x^{2} +y^{2} +z^{2} =125[/tex]
Substitute y = 5 in above relation.
[tex]x^{2} +z^{2}=125-25=100\\ \\x^{2} +z^{2}=10^{2}[/tex]
For parametrization,
Substitute [tex]x=rcos(t),z=rsin(t)[/tex] and [tex]r=10[/tex]
So that, [tex]x(t),y(t),z(t)=10cost,5,10sint[/tex]
Learn more:
https://brainly.com/question/23070611
In an aquarium, there are 7 large fish and 6 small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.
Answer:
3/13
Step-by-step explanation:
There are a total of 13 fish (6+ 7 = 13). There are 3 small, red fish. (1/2 · 6 = 3). Put the number of small, red fish over the total number of fish because the small, red fish is being selected from the entire tank of fish. 3/13 cannot be simplified any further.
rationalize root six divided by root three minus root two.
Answer:
0
Step-by-step explanation:
Let's first divide the two roots of [tex]\sqrt{6}[/tex] and [tex]\sqrt{3}[/tex].
[tex]\sqrt{\frac{6}{3} }[/tex]
[tex]\sqrt{2}[/tex]
Now, [tex]\sqrt{2}[/tex] - [tex]\sqrt{2}[/tex] = 0.
So, this equation comes out to be 0.
Hope this helped!
On average, a furniture store sells four card tables in a week. Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is most nearly Select one: a. 0.11 b. 0.075 c. 0.15 d. 0.060
Answer:
Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060
Step-by-step explanation:
In order to calculate the probability that the store will sell exactly seven card tables in a given week we would have to calculate the following formula:
probability that the store will sell exactly seven card tables in a given week= e∧-λ*λ∧x/x!
According to the given data furniture store sells four card tables in a week, hence λ=4
Therefore, probability that the store will sell exactly seven card tables in a given week=e∧-4*4∧7/7!
probability that the store will sell exactly seven card tables in a given week=0.060
Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060
Which function is the result of translating ƒ(x) = x2 + 5 upward by 5 units and to the right by 1 unit? Question options: A) y = (x – 1)2 + 5 B) y = (x – 1)2 + 10 C) y = (x + 1)2 + 5 D) y = (x + 1)2 + 10
Answer:
B. y = (x – 1)^2 + 10
Step-by-step explanation:
Answer: B
Step-by-step explanation:
B y= (x-1)^2 + 10
PLEASE HELP ME!!!!! A quadrilateral with vertices (0,0), (4,0), (3,2), (1,1) is mapped to a quadrilateral with vertices (6,3).(-2,3),(0,-1),(4,1). What is the center of the dilation and what is the scale factor.
Answer:
( 2,1) is the center of dilation and -2 is the scale factor
Step-by-step explanation:
We can use the formula
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
(0,0) becomes (6,3)
( 6,3) = k( 0-a) +a, k( 0-b)+b
6 = -ka+a
3 = -kb+b
We also have
(4,0) becomes (-2,3)
( -2,3) = k( 4-a) +a, k( 0-b)+b
-2 =4k -ka+a
3 = -kb+b
Using these two equations
6 = -ka+a
-2 =4k -ka+a
Subtracting the top from the bottom
-2 =4k -ka+a
-6 = ka -a
-------------------
-8 = 4k
Divide by 4
-8/4 = 4k/4
-2 = k
Now solving for a
6 = -ka +a
6 = - (-2)a +a
6 = 2a+a
6 = 3a
Divide by 3
6/3 =3a/3
2=a
Now finding b
3 = -kb+b
3 = -(-2)b+b
3 = 2b+b
3 = 3b
b=1
Answer:
hope this helps uh.....
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1 to catch rainwater off his roof.he has a full 2 liters tin of paint in his store and decides to paint the tank (not the base) If he uses 25ml to cover 1m^2 will he have enough paint to cover the tank with one layer of paint
Answer:
yes
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = πdh
Putting in the given numbers, we find the area to be ...
LA = π(1.1 m)(1.4 m) ≈ 4.838 m²
At 25 mL per m², the amount of paint Tublu needs is ...
(4.838 m²)(25 mL/m²) = 120.95 mL
2 liters is 2000 mL, so Tublu easily has enough paint for one layer.
___
The amount he has is enough for more than 16 coats of paint, so he could paint inside and out with the paint he has.
Answer:
he should.
Step-by-step explanation:
QUESTION 8
Find Future Value Using Compound Interest Formula:
You deposit $6,000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years?
A $9,677.95
B. $6,100.67
C. $7,325.98
D. $7,200
QUESTION 9
Find Future Value Using Compound Interest Formula:
You deposit $5,000 in an account earning 5% interest compounded quarterly. How much will you have in the account in 10 years?
A $5,661.35
B. $7,500
C. $8,235.05
D. $8,218.10
Answer:
8.) $7325.98
9.) $8218.10
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Simply plug in our known variables into the formula:
A = 6000(1 + 0.04/12)^60 = 7325.98
A = 5000(1 + 0.05/4)^40 = 8218.10
Round 113.04 to the nearest foot
Answer:
113 nearest tenth
Step-by-step explanation:
what do you mean by foot?
Answer:
are u sure it’s not nearest tenth?
Step-by-step explanation:
if so it’s 113
Suppose the following regression equation was generated from the sample data of 50 cities relating number of cigarette packs sold per 1000 residents in one week to tax in dollars on one pack of cigarettes and if smoking is allowed in bars:
PACKS i= 57221.431732 − 1423.696906TAXi + 155.441784BARSi + ei.
BARS i= 1 if city i allows smoking in bars and BARSi = 0 if city i does not allow smoking in bars. This equation has an R2 value of 0.351292, and the coefficient of BARSi has a P-value of 0.086529. Which of the following conclusions is valid?
A. According to the regression equation, regardless of whether or not smoking is allowed in bars, the number of cigarette packs sold per 1000 people decreases by approximately 1424 for each additional dollar of cigarette tax.
B. There is evidence at the 0.05 level of significance to support the claim that cities with a smoking ban have lower cigarette sales than those without a smoking ban.
C. According to the regression equation, cities that allow smoking in bars have lower cigarette sales than cities that do not allow smoking in bars.
D. According to the regression equation, cities that allow smoking in bars sell approximately 155 fewer packs of cigarettes per 1000 people than cities that do not allow smoking in bars.
Answer:
A) According to the regression equation, regardless of whether or not smoking is allowed in bars, the number of cigarette packs sold per 1000 people decreases by approximately 1424 for each additional dollar of cigarette tax.
Step-by-step explanation:
Given the regression equation:
PACKS i= 57221.431732 − 1423.696906TAXi + 155.441784BARSi + eᵢ.
BARS i= 1 if city i allows smoking in bars
BARSi = 0 if city i does not allow smoking in bars
R2 = 0.351292
P-value = 0.086529
Conlusion:
Simnce p value, 0.0865 is greater than level of significance, 0.05, BARS is not significant. Thus, allowing smoking in bars increase cigarette sales, since the coefficient of BARS is positive.
Correct answer is option A.
According to the regression equation, regardless of whether or not smoking is allowed in bars, the number of cigarette packs sold per 1000 people decreases by approximately 1424 for each additional dollar of cigarette tax.
A piece of wire 27 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.(a) How much wire should be used for the square in order to maximize the total area?(b) How much wire should be used for the square in order to minimize the total area?
Answer:
a).length of wire for square = 15.25 m
b). length of wire for triangle = 11.75 m
Step-by-step explanation:
Length of a piece of wire = 27 m
This wire was cut into 2 pieces of length 'x' m and (27 - x) m
One was bent into an equilateral triangle and other into a square.
Area of the square shape = Side²
A = [tex](\frac{27-x}{4})^2[/tex]
Similarly, Area of the equilateral triangle = [tex]\frac{\sqrt{3}}{4}(\text{Side})^2[/tex]
A' =[tex]\frac{\sqrt{3}}{4}(\frac{x}{3})^{2}[/tex]
Total area of both the figures = A + A'
F = [tex]\frac{(27-x)^2}{16}+\frac{\sqrt{3}}{4}(\frac{x}{3} )^2[/tex]
Now we find the derivative of 'F' with respect to x and equate it to zero.
F' = [tex]\frac{1}{16}(-1)[2(27-x)]+\frac{\sqrt{3}}{36}(2x)[/tex] = 0
[tex]\frac{\sqrt{3}}{18}(x)=\frac{1}{8}(27-x)[/tex]
x = 15.25 m
a). Length of wire required for a square = 15.25 m
b). Length of wire required for an equilateral triangle = 11.75 m
A) The amount of wire that should be used for the square in order to maximize the area is; 0 m
B) The amount of wire that should be used for the square in order to minimize the area is; 11.74 m
A) We are told that length of wire is 27 m.
Now, let the length cut for the square be x. Thus, length cut for the triangle will be; (27 - x) m.
Since the length for the square is x, then a side of the square is;
Length of side of square = x/4
Length of side of equilateral triangle = (27 - x)/3
Thus;
Area of square; A_s = (x/4)²
Area of equilateral triangle; A_t = ((27 - x)/3)²(¹/₄√3)
Thus, total area is;
A(x) = (x/4)² + ((27 - x)/3)²(¹/₄)√3)
⇒ A(x) = ¹/₁₆x² + ¹/₃₆((27 - x)²√3)
B) Total area is; A(x) = ¹/₁₆x + ¹/₃₆((27 - x)²√3)
To minimize the total area, we will differentiate and equate to zero.
A'(x) = ¹/₈x - ¹/₁₈((27 - x)√3)
At A'(x) = 0, we have;
¹/₈x - ¹/₁₈((27 - x)√3) = 0
¹/₈x = ¹/₁₈((27 - x)√3)
¹/₈x = ³/₂√3 - ˣ/₁₈√3
¹/₈x + ˣ/₁₈√3 = ³/₂√3
x(¹/₈ + ¹/₁₈√3) = ³/₂√3
x = (³/₂√3)/(¹/₈ + ¹/₁₈√3)
x = 11.74 m
Now, A''(x) = ¹/₈ + ¹/₁₈√3
This is greater than zero and so x = 11.74 m is a minimum
Thus, length cut for triangle = 27 - 11.74
length cut for triangle = 15.26 m
Read more at; https://brainly.com/question/16965977
4 years ago, the population of a city was of "x" inhabitant, 2 years later, that is to say two years ago, the population of this same city was 81,000 inhabitants and today it is 65,610. Using this data, find the population of four years ago.
Answer:
The population of four years ago was 100,783 inhabitants
Step-by-step explanation:
The population of the city after t years is given by the following equation:
[tex]P(t) = P(0)(1-r)^{t}[/tex]
In which P(0) is the initial population and r is the decrease rate, as a decimal.
2 years later, that is to say two years ago, the population of this same city was 81,000 inhabitants and today it is 65,610.
This means that:
[tex]P(2) = 81000, P(4) = 65610[/tex]
We are going to use this to build a system, and find P(0), which is the initial population(four years ago).
P(2) = 81000
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]81000 = P(0)(1-r)^{2}[/tex]
[tex](1-r)^{2} = \frac{81000}{P(0)}[/tex]
P(4) = 65610
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]65100 = P(0)(1-r)^{4}[/tex]
[tex]65100 = P(0)((1-r)^{2})^{2}[/tex]
Since [tex](1-r)^{2} = \frac{81000}{P(0)}[/tex]
[tex]65100 = P(0)(\frac{81000}{P(0)})^{2}[/tex]
Using P(0) = x
[tex]65100 = x(\frac{81000}{x})^{2}[/tex]
[tex]65100 = \frac{6561000000x}{x^{2}}[/tex]
[tex]65100x^{2} = 6561000000x[/tex]
[tex]65100x^{2} - 6561000000x[/tex]
[tex]x(65100x - 6561000000) = 0[/tex]
x = 0, which does not interest us, or:
[tex]65100x - 6561000000 = 0[/tex]
[tex]65100x = 6561000000[/tex]
[tex]x = \frac{6561000000}{65100}[/tex]
[tex]x = 100,783[/tex]
The population of four years ago was 100,783 inhabitants
Binomial factor of 25x2 + 40xy + 16y2 ?
Answer:
(5x +4y)^2
Step-by-step explanation:
The first and last terms are both perfect squares, and the middle term is twice the product of their roots. That means the trinomial is the perfect square trinomial ...
25x^2 +40xy +16y^2 = (5x +4y)^2
_____
It matches the pattern ...
a^2 +2ab +b^2 = (a +b)^2
Answer:
(5x +4y)^2
Step-by-step explanation: