Answer:
[tex]\frac{dy}{dx}[/tex] = - 21[tex]x^{6}[/tex] + 6x² + 1
Step-by-step explanation:
Differentiate each term using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
Given
y = - 3[tex]x^{7}[/tex] + 2x³ + x , then
[tex]\frac{dy}{dx}[/tex] = (7 × - 3 )[tex]x^{6}[/tex] + (3 × 2)x² + (1 × 1 )[tex]x^{0}[/tex]
= - 21[tex]x^{6}[/tex] + 6x² + 1
In a survery of 154 households, a Food Marketing Institute found that 106 households spend more than $125 a week on groceries. Please find the 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries.
Answer:
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 154, \pi = \frac{106}{154} = 0.6883[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 - 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.6151[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 + 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.7615[/tex]
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
i need this asap guys im giving brainliest
An aquarium is in the shape of a rectangular prism. How much water will it take to fill the aquarium if the dimensions are 2ft by 4ft by 3ft? 12 cubic feet 24 cubic feet 36 cubic feet 8 cubic feet
Answer:
24 cubic feet.
Step-by-step explanation:
What we need to do here, is to find the volume of the aquarium.
The Aquarium is a rectangular prism.
The volume of a rectangular prism is length*width*height (we just multiply the dimensions together)
2*4*3=8*3=24
The volume of the aquarium is 24 cubic feet, and therefore 24 cubic feet of water is required to fill the tank.
Answer:
Hello! :) The answer will be under “Explanation”
Step-by-step explanation:
The answer will be 24 cubic feet.
Work:
LxWxH
(Length,Width,Hight)
So you the question is asking about volume, we need to do the formula (length,width, and hight)
Now we have to multiply
2x4=8
8x3=24
So the answer will be 24 cubic feet.
Hope this helps! :)
www.g A survey of athletes at a high school is conducted, and the following facts are discovered: 19% of the athletes are football players, 79% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player
Answer:
84%
Step-by-step explanation:
The probability that the selected player is a football player, P(F)=19%
The probability that the selected player is a basketball player, P(B)=79%
The probability that the selected player play both football and basketball,
[tex]P(B \cap F)=14\%[/tex]
We want to determine the probability that a randomly chosen athlete is either a football player or a basketball player, [tex]P(B \cup F)[/tex]
In probability theory
[tex]P(B \cup F)=P(B)+P(F)-P(B \cap F)\\=79\%+19\%-14\%\\=84\%[/tex]
The probability that a randomly chosen athlete is either a football player or a basketball player is 84%.
Using Volume Formulas: Tutorial
14 of 23 Save & Exit
Question 2
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single
rectangular pyramid. What values of land h for the four square pyramids and what values of I, w, and h for the rectangular pyramid will produce
identical volumes? There is more than one correct answer.
B
TUX
X
Font Sizes
A. A
E JE
Square Pyramids
Rectangular Pyramid
Volume
Base Length Height
Volume
Volume x4 Base Length Base Width Height
(2x)
3
(lxwh
3
I
Characters used: 110 / 15000
Submit
Answer:
For the Square
Base length is 6 units
Height is 4 units
Volume is 48 cubic units
Volume of 4 square pyramids is 192 cubic units
(Rectangular)
Base length is 12 units
Base width is 8 units
Height is 6 units
Volume is 192 cubic units
Step-by-step explanation:
Square pyramids is a geometric shape having square base. The appex is perpendicularly at the center of the square. If all the edges are equal it is equilateral square pyramid.
Rectangular pyramids have four sided base and four triangle sides that are coming together to the appex. Each base and appex form a triange called lateral face. The triangular faces are non rectangular base. Pyramid with n side have n + 1 vertices and 2n edges.
Find the value of x geometry
Answer:
x = 22
Step-by-step explanation:
Since the the 2 bisectors are equal, that means the chords are also equal. Since bisector splits into 2 equal parts, 11 + 11 equals 22
What is the next item in the sequence −10,−3,4,11
Answer:
18
Step-by-step explanation:
The pattern in this sequence is that you add 7 from the previous number to get the next number (-10 + 7 = -3, -3 + 7 = 4, etc). The next item will be 11 + 7 + 18. Hope this helps!
The next item in the sequence is 18.
What is sequence and series ? A series is the total of all elements, but a sequence is an ordered group of elements in which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.A number sequence is a collection of numbers that move from term to term according to a specific pattern or rule.You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.
The sequence is -10 ,-3, 4, 11,........
this sequence is following pattern ,you add 7 from the previous number to get the next number
First term = -10 + 7 = -3,
Second term =-3 + 7 = 4, .
The next item will be 11 + 7 = 18.
Therefore, The next item in the sequence is 18.
Learn more about sequence brainly.com/question/12474324 here
#SPJ2
When would you need to arrange polynomials
What is the area of this composite shape? Enter your answer in the box. in²
Answer:
53 in.
Step-by-step explanation:
to find the area u do 8 times 6 and 1/2 2(5)
triangle = 1/2bh
rectangle = bh
hope this helps
What is y - 8 = 4(x - 4) in slope intercept form?
Answer:
y=4x-8
Step-by-step explanation:
First you must use the distributive property and get y-8=4x-16.
Then you have to add 8 on both sides so just y is left on the left side.
This will get you y=4x-8 in slope-intercept form.
I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!
Answer: (a) [tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]
(b) A = $1680.67
(c) t = 9.99 years
(d) A = $1689.85
Step-by-step explanation:
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex] where
A is the amount accrued (balance)P is the principal (original/initial amount)r is the interest rate (convert to a decimal)n is the number of times compounded per yeart is the number of yearsa) Given: P = 900, r = 7% = 0.07, n = quarterly = 4
[tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]
b) Given: P = 900, r = 7% = 0.07, n = quarterly = 4, t = 9
[tex]A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4(9)}\\\\\\A = 900\bigg(1+\dfrac{0.07}{4}\bigg)^{36}[/tex]
A = 1680.67
c) Given: A = 1800, P = 900, r = 7% = 0.07, n = quarterly = 4
[tex]1800=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\2=\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2=ln\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2 = 4t\ ln\bigg(1+\dfrac{0.07}{4}\bigg)\\\\\\\dfrac{ln\ 2}{4\ ln\bigg(1+\dfrac{0.07}{4}\bigg)}=t\\\\\\\bold{t=9.99}[/tex]
d) [tex]A=Pe^{rt}[/tex]
Given: P = 900, r = 7% = 0.07, t = 9
[tex]A=900e^{0.07(9)}\\\\\\A=900e^{.63}\\\\\\\bold{A=1689.85}[/tex]
A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl
Answer: 7/8
Step-by-step explanation:
Let the boy is letter B and the girl is letter G.
So the possible outcomes are as follows below
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
SO the number of possible outcomes is 8
The number of outcomes where is at least 1 girl ( triples where is 1 girl, 2 girls or all 3 children are the girls) is 7
So the probability, that family with 3 kids has at least 1 girl is
P(number of girls >=1)= 7/8
PLEASE HELP ME!! A hexagon has vertices (3,1) and (4,1). The hexagon is dilated. The new hexagon has vertices (6,1) and (10,1). {In the same spots as the old hexagon}. What is the center of dilation? What is the dilation factor? I can try to add information.
Answer:
( 2,1) is the center of dilation and 4 is the scale factor
Step-by-step explanation:
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
3,1 becomes 6,1
6,1 = k( 3-a) +a, k( 1-b)+b
6 = 3k -ka+a
1 = k -kb +b
4,1 becomes 10,1
10,1 = k( 4-a) +a, k( 1-b)+b
10 = 4k -ka+a
1 = k -kb +b
Using these two equations
6 = 3k -ka+a
10 = 4k -ka+a
Subtracting the top from the bottom
10 = 4k -ka+a
-6 = -3k +ka-a
------------------------
4 = k
Now solving for a
6 = 3k -ka+a
6 = 3(4) -4a+a
6 =12 -3a
Subtract 12
6-12 = -3a
-6 = -3a
Divide by -3
-6/-3 = -3a/-3
2 =a
Now finding b
1 = k -kb +b
1 = 4 - 4b+b
1 =4 -3b
Subtract 4
-3 = -3b
Divide by -3
1 = b
Answer:
Dilation factor: 4.
Center of dilation: (2, 1).
Step-by-step explanation:
The distance between the old vertices was 4 - 3 = 1. The distance between the new vertices is 10 - 6 = 4. 4 / 1 = 4. That means that the dilation factor is 4.
Now that we have a dilation factor, we can use the formulas x1 = d(x-a) +a and y1 = d( y-b)+b to solve for the center of dilation.
In this case, d = 4, x1 = 10, x = 4, y1 = 1, and y = 1.
10 = 4(4 – a) + a
10 = 16 – 4a + a
10 = 16 – 3a
-3a + 16 = 10
-3a = -6
a = 2
1 = 4(1 – b) + b
1 = 4 – 4b + b
1 = 4 – 3b
-3b + 4 = 1
-3b = -3
b = 1
And so, your center of dilation will be (2, 1).
Hope this helps!
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane. y > 2x + 4 x + y ≤ 6
Answer:
Graph is attached.
Step-by-step explanation:
We are to graph the following inequalities:
y > 2x + 4 ... (i)
x + y ≤ 6 ... (ii)
We can graph these inequalities on an online graphing calculator but its recommended that you graph them on your physical graph book.
Your graph is attached below. The shaded region is the required part.
The graph of a system of inequalities represents the solution of the inequalities
The solution to the system of inequalities is [tex]\mathbf{y > \frac 23}[/tex] and [tex]\mathbf{x \le \frac{16}3}[/tex]
The system of inequalities is given as:
[tex]\mathbf{y > 2x + 4}[/tex]
[tex]\mathbf{x + y \le 6 }[/tex]
See attachment for the graphs of [tex]\mathbf{y > 2x + 4}[/tex] and [tex]\mathbf{x + y \le 6 }[/tex]
From the graph, we have:
[tex]\mathbf{y > \frac 23}[/tex]
[tex]\mathbf{x \le \frac{16}3}[/tex]
Read more about system of inequalities at:
https://brainly.com/question/19526736
Which of the following statements about trapezoids is true?
O A. Opposite angles are equal
B. One pair of opposite sides is paralel.
C. Opposite sides are equal
O D. Both pairs of opposite sides are parallel
Answer:
B
Step-by-step explanation:
Trapezoids have only one pair of parallel lines.
A company buys a machine for $575,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n)
Answer:
[tex]V(n) = 575000(0.7)^{n}[/tex]
Step-by-step explanation:
The value of the machine after n years is given by an exponential function in the following format:
[tex]V(n) = V(0)(1-r)^{n}[/tex]
In which V(0) is the initial value and r is the yearly rate of depreciation, as a decimal.
A company buys a machine for $575,000 that depreciates at a rate of 30% per year.
This means, respectively, that: [tex]V(0) = 575000, r = 0.3[/tex]. So
[tex]V(n) = V(0)(1-r)^{n}[/tex]
[tex]V(n) = 575000(1-0.3)^{n}[/tex]
[tex]V(n) = 575000(0.7)^{n}[/tex]
Which is a possible paycheck deduction? Select all that apply.
commission
federal income tax
health insurance premium
overtime hours
state income tax
Answer:
Federal income taxes, health insurance premium, state income tax
Step-by-step explanation:
Commission may be a bonus from a sale you made and overtime hours are extra hours over 40.00 that you worked during the week
2 things are certain in life death and taxes
Select the correct answer from each drop-down menu. The given equation has been solved in the table.
Answer:
1). SUBTRACTION property of equality
2). MULTIPLICATION property of equality
Step-by-step explanation:
Step 2:
When we subtract the same number from both the sides of an equation it represents the subtraction property of equality.
[tex]\frac{x}{4}+5-(5)=23-(5)[/tex]
Here 5 has been subtracted from both the sides.
Therefore, SUBTRACTION property of equality was applied.
Step 4:
If the same number is multiplied to both the sides of an equation, multiplication property of equality is applied.
[tex]4\times \frac{x}{4}=4\times (18)[/tex]
Here 4 has been multiplied to both the sides.
Therefore, MULTIPLICATION property of equality was applied.
Please help ASAP thanks in advance
Answer:
Make a point at (3pm, 45), (4.5 pm, 45), (5.5pm, 30), (6.5pm, 15), and (7.5pm, 0). Then connect the dots starting at (0,0) Then you have your graph :)
Step-by-step explanation:
A simple random sample of size nequals17 is drawn from a population that is normally distributed. The sample mean is found to be x overbar equals 56 and the sample standard deviation is found to be sequals10. Construct a 95% confidence interval about the population mean. The lower bound is nothing. The upper bound is nothing. (Round to two decimal places as needed.)
Answer:
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
Step-by-step explanation:
Step(i):-
Given random sample of size 'n' =17
Given mean of the sample 'x⁻' = 56
Given standard deviation of sample 's' = 10
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 17-1 =16
t₀.₀₅ = 1.7459 (from t-table)
Step(ii):-
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]
( 56 - 4.2344 , 56 + 4.2344)
(51.7656 , 60.2344)
Conclusion:-
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
The price of a vase was increased by 10% to £22.What was the price before the increase
Answer: £20.
Step-by-step explanation:
Let the old price = £x
Percent increase. = 10%
Increment. = 10% of £x
= 10x/100
Now new price = £22
To determine the old price we have
x + 10x/100. = 22
We now multiply everything by 100 to make it a linear expression
100x + 10x = 2200
110x = 2200, therefore
x. = 2200/110
= £20
Therefore, the price before the increase. = £20.
To get from North to East, you walk 12 meters south and 16 meters east, as shown
in the diagram below. If you wanted to walk straight from North to East, what would
the distance be? Solve for x
Answer:
ur pito is to small
Step-by-step explanation:
it to little
g A catering service offers 7 %E2%80%8b Appetizers, 9 main%E2%80%8B courses, and 5 desserts. A banquet committee is to select 2 %E2%80%8b Appetizers, 8 main%E2%80%8B courses, and 4 desserts. How many ways can this be%E2%80%8B done
Answer:
945 ways
Step-by-step explanation:
Total
Number of Appetizers = 7Number of main courses = 9Number of desserts =5Required Selection
Number of Appetizers = 2Number of main courses = 8Number of desserts =42 Appetizers out of 7 can be selected in [tex]^7C_2[/tex] ways
8 main courses out of 9 can be selected in [tex]^9C_8[/tex] ways
4 desserts out of 5 can be selected in [tex]^5C_4[/tex] ways
Therefore, the number of ways this can be done
[tex]=^7C_2 \times ^9C_8 \times ^5C_4[/tex]
=945 ways
3. Find the measure of x.
a 18°
b. 54°
C 126
d. 45
Answer:
18 degrees
Step-by-step explanation:
The triangle is an iscoceles right triangle.
The angles in a triangle add up to 180.
90+2y (iscoceles) =180
2y=90
y=45
So the angles of the right triangle are 45. However, you have to take away 27 because you are solving for only a part of 45. 45-27=18
Now that we have our linear regression model, let’s try to make a prediction for the sales given a new set of advertising budgets as follows: new.dat <- data.frame(TV=200, Radio=10, Newspaper=20) You are required to report the predicted sales as well as the lower and upper bound for the 95% prediction interval. What will you report?
Answer:
The predicted sales for the new set of advertising budgets is 14.
Step-by-step explanation:
The linear regression model is:
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
Compute the value of sales for:
TV = 200,
Radio = 10,
Newspaper = 20
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
[tex]=2.9389+0.0458\cdot(200)+0.1885\cdot(10)-0.0010\cdot(20)\\=2.9389+9.16+1.885-0.0002\\=13.9837\\\approx 14[/tex]
Thus, the predicted sales for the new set of advertising budgets is 14.
A rookie quarterback is negotiating his first NFL contract.His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:________.
1 2 3 4
Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000
Contract 2 $2,000,000 $3,000,000 $4,000,000 $5,000,000
Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000
As his advisor, which contract would you recommend that he accept?
Answer:
He should accept contract 2 because it has a higher present value.
Step-by-step explanation:
we need to find the present value of each contract:
Contract 1 = $3,000,000/1.1 + $3,000,000/1.1² + $3,000,000/1.1³ + $3,000,000/1.1⁴ = $2,727,273 + $2,479,339 + $2,253,944 + $2,049,040 = $9,509,596
Contract 2 $2,000,000/1.1 + $3,000,000/1.1² $4,000,000/1.1³ + $5,000,000 /1.1⁴ = $1,818,182 + $2,479,339 + $3,005,259 + $3,415,067 = $10,717,847
Contract 3 $7,000,000/1.1 + $1,000,000/1.1² + $1,000,000/1.1³ + $1,000,000/1.1⁴ = $6,363,636 + $826,446 + $751,315 + $683,013 = $8,624,410
Phil Nelson deposited $35,000 at Wachovia Bank at 3.5% interest
compounded quarterly. How much money will be in this account at
the end of the year?
Answer:
$36,241.20
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Since we are given P, r, n, and t, simply plug it into the formula:
A = 35000(1 + 0.035/4)⁴⁽¹⁾
A = 35000(1 + 0.00875)⁴
A = 35000(1.00875)⁴
A = 35000(1.03546)
A = 36241.2
A cylinder fits inside a square prism as shown. For every
cross section the ratio of the area of the circle to the
area of the square is on
since the area of the circle is the area of the square,
the volume of the cylinder equals
Cross section
o
o
o
o
the volume of the prism or (20(h) or turh.
the volume of the prism or (47)(h) or 2nuh.
the volume of the prism or (20)(h) or Ph.
the volume of the prism or (47)(h) or iPh.
kl *
Answer:
Volume of cylinder = π/4 (the volume of the prism) or π/4 (4r²)(h) or πr²h (D)
The complete question related to this found on brainly (ID: 4049983 and 4265826) is stated below:
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or πr^2 or π/4. Since the area of the circle is π/4 the area of the square, the volume of the cylinder equals
A) π/2(the volume of the prism) or π/2 (2r)(h) or πrh.
B) π/2 (the volume of the prism) or π/2 (4r2)(h) or 2πrh.
C) π/4(the volume of the prism) or π/4 (2r)(h) or π/4(r2h).
D) π/4(the volume of the prism) or π/4 (4r2)(h) or πr2h.
See attachment for diagram
Step-by-step explanation:
Area of the cross section in the cylinder
Area of circle = πr²
Area of the cross section in the square prism
Area of square = (side length)²
Here the side length = diameter
Diameter = 2×radius = 2r
Area of square = (2r)² = 4r²
Ratio of area of circle to area of square = πr²/4r² = π/4
Area of circle/area of square = π/4
Area of circle = π/4 × area of square
Area of circle = π/4 × 4r²
Volume of cylinder = area of circle × height
Volume = πr² ×h = πr²h
Volume of square prism = area of square × height = (2r)²h = 4r²h
Ratio of volume of cylinder to volume of square prism = πr²h/4r²h = π/4
Volume of cylinder/volume of square prism = π/4
Volume of cylinder = π/4 × volume of square prism = π/4 × 4r²h
= πr²h
Therefore Volume of cylinder = π/4 (the volume of the prism) or π/4 (4r²)(h) or πr²h (D)
plz answer question in screen shot
Answer: 342.32
Step-by-step explanation: sin(25) = h/a
Sin(25)= h/27
27*sin(25) = h
b*h = area
what is the answer to this ??
Answer:
[tex] A.\angle 1\: \\\\D. \angle 3[/tex]
Step-by-step explanation:
[tex] \angle 1\: \&\: \angle 3[/tex] are remote interior angles of [tex] \angle 6[/tex]
please help! the number of candies consumed varies inversely with the number of children present
Answer:
The answer is
210 candiesStep-by-step explanation:
Let n represent the number of children
Let c represent the number of candies
The above variation is written as
[tex]c = \frac{k}{n} [/tex]
when n = 12 c = 140
So we have
[tex]140 = \frac{k}{12} [/tex]
Cross multiply
That's
k = 1680
So the formula for the variation is
[tex]c = \frac{1680}{n} [/tex]
when n = 8
[tex]c = \frac{1680}{8} [/tex]
c = 210
Therefore there are 210 candies consumed when there are 8 children
Hope this helps you