The option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution [tex]\rm \hat{p}[/tex] is not approximate normal because p=0.87 is closer to 1 than zero.
Sampling distribution [tex]\rm \hat{p}[/tex] is skewed to the left.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.
This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.
Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution [tex]\rm \hat{p}[/tex] is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution [tex]\rm \hat{p}[/tex] is skewed to the left.
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Suppose a cylinder that holds 3 L of liquid must be created. Determine the radius and height of the cylinder that will minimize the amount of material used in its construction.(Note: 1 L=1,000 cm^3)
The radius and the height of the dimension that will minimize the amount of material used in the construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.
How to find the dimension that minimizes a cylinder?The dimension that minimizes the surface area of a cylinder can be determined by:
Drawing the picture of the problem, Write down & identify optimization as well as the constraint equations;Use the derivative of the optimization equation to find the dimensions.Given that:
1 L = 1000 cm³3 L = 3000 cm³The area of the cylinder = (2 πr)h + 2(πr²)
A = 2πrh + 2πr²The volume of the cylinder
V = πr²hLet's identify the constraint equation and Optimization equation:
To minimize the surface area of the can, we have:
Area equation = Optimization equationThe constraint equation is the equation that limits us:
Volume equation = constraint equationSo, Let's solve for h in our volume equation, we have:
3000 = πr² h
h = 3000/πr²
Now, from the Area equation
[tex]\mathbf{A = 2 \pi r(\dfrac{3000}{\pi r^2}) + 2\pi r^2}[/tex]
Taking the derivate and setting it to zero, we have;
Derivative:
[tex]\mathbf{A = \dfrac{6000}{ r}+ 2\pi r^2}[/tex]
[tex]\mathbf{A = 6000 r^{-1} + 2\pi r^2}[/tex]
[tex]\mathbf{A' = -6000 r^{-2} + 4\pi r}[/tex]
[tex]\mathbf{A' = 4\pi r-\dfrac{6000}{ r^{2} }}[/tex]
Setting it to zero, we have:
[tex]\mathbf{0=\dfrac{ 4 \pi r^3 - 6000}{r^2}}[/tex]
Factor out 4
0 = 4(πr³ - 1500)
1500 = πr³
r³ = 1500/π
[tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex]
The above is the radius that minimizes the surface area of the cylinder;
From [tex]\mathbf{h = \dfrac{3000}{\pi r^2}}[/tex]
[tex]\mathbf{h = \dfrac{3000}{\pi ( \sqrt[3]{\dfrac{1500}{\pi}} )^2}}[/tex]
[tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex]
Thus, the radius and height that minimize the amount of material to be used in its construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.
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Drag each expression to its equivalent.
Answer:
x-3+2x+3+2x = 5x
x+8+4x-3x-4 = 2x+4
4x+x-11-5X+25+4x = 4x+14
3x+5-2x-5x+9+8x = 4x+14
5+9x-7-4X-3x+6 = 2x+4
6x-9-5x+4-x+5x+5 = 5x
Step-by-step explanation:
Simplified by adding like terms
Full explanation please
Interior and Exterior Triangle Angles (1/5)
Will mark brainlist to you ever answers first
Answer:
∠N = 21
Step-by-step explanation:
Angle sum propertySum of all angles of triangle = 180°
4x - 13 + 2x - 13 + 5x + 19 = 180
4x + 2x + 5x -13 - 13 + 19 = 180
Combine like terms
11x - 7 = 180
11x = 180 + 7
11x = 187
x = 187/11
x = 17
m∠N = 2x - 13
= 2*17 - 13
= 34 - 13
= 21
Hello, please choose the correct answer.
A.) 5
B.) square root of 5
C.) 25
D.) 7
Answer:
A) 5
Explanation:
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 - (y_2 - y_1)^2}[/tex]
Here given points:
(6, 8), (3, 4)Distance:
[tex]\rightarrow \sf \sqrt{(6 - 3)^2 - (8 - 4)^2}[/tex]
[tex]\rightarrow \sf \sqrt{9 +16}[/tex]
[tex]\rightarrow \sf \sqrt{25}[/tex]
[tex]\rightarrow \sf 5[/tex]
Type the correct answer in the box. use numerals instead of words. for this question, any non-integer answers should be entered as decimals, rounded to the hundredths place. consider this data set. 25.5 26 18.2 15.3 28.5 27 20.7 20.2 26.1 18.2 21.4 17.9 24.3 22.6 19.6 the mean of the data set is , and the sample proportion of numbers less than the mean is %.
The mean of the data set is 22.1
The sample proportion of numbers less than the mean is %53
Calculations and Parameters:To find the mean,
We would sum the numbers and then divide them by the number of data.
25.5 + 26 + 18.2 + 15.3 + 28.5 + 27 + 20.7 + 20.2 + 26.1 + 18.2 + 21.4 + 17.9 + 24.3 + 22.6 + 19.6
= 331.5
331.5/15= 22.10.
To find the proportion of numbers, we would order them:
15.3
17.9
18.2
18.2
19.6
20.2
20.7
21.4
---------
22.6
24.3
25.5
26
26.1
27
28.5
The discontinuous line shows the split of the data that are less than the mean.
Those data are 8 in number and their proportion is:
8 / 15
= 0.53
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Iggy is practicing for a marathon by running laps on the
track at school. Each lap covers 0.7 kilometers, and he
has already run 19.6 kilometers. How many laps does he
need to run if he wants to complete 91 kilometers?
Find a function y of x such that 2yy′=x and y(2)=6
Answer:
[tex]y=\sqrt{\frac{x^{2}}{2} +34}[/tex]
Step-by-step explanation:
[tex]2y\left( x\right) y^{\prime }\left( x\right) =x[/tex]
[tex]\Longrightarrow \int 2y\left( x\right) y^{\prime }\left( x\right) dx=\int x\ dx[/tex]
[tex]\Longrightarrow y^{2}\left( x\right) =\frac{x^{2}}{2} +c\ \text{(c is a constant)}[/tex]
[tex]y\left( 2\right) =6\Longleftrightarrow y^{2}\left( 2\right) =36[/tex]
[tex]y^{2}\left( 2\right) =36\Longleftrightarrow \frac{\left( 2\right)^{2} }{2} +c=36\ \Longleftrightarrow c=34[/tex]
[tex]\Longrightarrow y\left( x\right) =\pm\sqrt{\frac{x^{2}}{2} +34}[/tex]
pleae awnser :))) hhoh
Answer:
the answer will be
K' = -9, 5
L' = 0,5
M' = -8,3
Step-by-step explanation:
the x axis is written first and the y axis is written after that.
hope it helps!!
PLEASE MARK BRAINLIEST !!..
Answer:
K': (9,5)
L': (0,5)
M': (8,3)
Step-by-step explanation:
Tell me if im wrong!
Equation of a line that goes through the following points: (4,1) and (7,10)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{9}{3}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y-1=3x-12\implies y=3x-11[/tex]
#53. will give the best answer brainliest
Answer:
8x4-2x2+7
Step-by-step explanation:
it's 100 percent right trust me
I need help with this assignment!
The area of the reflective material is: 284 square yards.
What is a rectangle?A rectangle is a quadrilateral with four sides and four right-angles.
it has two lines of symmetry.
Analysis:
To find the area of the reflecting material we find the area of the following shapes: trapezium + rectangle + triangle
bigger base of trapezium = 2 + 6 + 2 = 10 yard
smaller base of trapezium = 6
length of rectangle = 18 yard
width of rectangle : 2+6+2 = 10 yard
base of triangle is = 10 yard
Area of reflective material = 1/2(6+10) + 18x10 + 1/2(10)(8) = 284 square yards
In conclusion, the area of reflective material is : 284 square yards.
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What is the remainder of (x3+5x2−32x−7)÷(x−4) ? Enter your answer in the box.
Answer:
x^2+5x-36-7/x
Step-by-step explanation:
assuming x^3 and 5x^2
Write the phrase as an expression.
a number t cubed
Answer:
[tex]t^{3}[/tex]
Step-by-step explanation:
cubed means to the power of 3
A sequence is defined recursively by the formula f(n 1) = –2f(n). the first term of the sequence is –1.5. what is the next term in the sequence? –3.5 –3 0.5 3
Given that the first term of the sequence is –1.5, the next term of the sequence would be 3
How to determine the next term?The recursive function is given as:
f(n + 1) = -2f(n)
Substitute 1 for n
f(1 + 1) = -2f(1)
Evaluate
f(2) = -2f(1)
Given that the first term is -1.5, the equation becomes
f(2) = -2 * -1.5
Evaluate
f(2) = 3
Hence, the next term of the sequence is 3
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Answer:
(D) 3
Step-by-step explanation:
Which of the following are roots of the polynomial function? Check all that apply. F(x) = x3 - 5x2 - 13x - 7
Answer:
Write properties of function:
x intercept/zero: [tex]x_{1} =-1;x_{2} =7[/tex]
Step-by-step explanation:
x² - 6x - 7 = x² - 7x + x - 7
⇒ x(x - 7) + 1(x - 7)
⇒ (x + 1) (x - 7)
Thus, x³ - 5x² - 13x - 7 = (x + 1)(x + 1)(x - 7)
[tex]~~~~~~~~x^3 -5x^2 -13x -7=0\\\\\implies x^3 +x^2 -6x^2 -6x-7x-7=0\\\\\implies x^2(x+1) -6x(x+1) -7(x+1)=0\\\\\implies (x+1)(x^2 -6x -7) = 0\\\\\implies (x+1)(x^2 +x -7x-7)=0\\\\\implies (x+1) [x(x+1) -7(x+1)]=0\\\\\implies (x+1)(x+1)(x-7) = 0\\\\\implies (x+1)^2 (x-7) = 0\\\\\implies x = -1,~ x = 7\\\\\text{Hence, the roots are}~ -1~ \text{and}~ 7[/tex]
Please Help Giving Brainlist!!!!! Given that the area of rectangle IJKL is 490 units^2, what are its length and width?
Answer:
Option 4
Step-by-step explanation:
Equating given length and width to the area :
8x(5x) = 49040x² = 490x² = 490/40x² = 12.25x = 3.5Finding the dimensions :
length = 8x = 8(3.5) = 28 unitswidth = 5x = 5(3.5) = 17.5 unitsFind the volume of the solid (pls help me :// )
=====================================================
Explanation:
The triangular face has area of base*height/2 = 4*10/2 = 40/2 = 20 square cm.
Multiply this prism base area by the depth of the prism to get 20*2 = 40 cubic cm.
It might help to place the triangular prism so the triangular face is along the ground, so you can think of that face as the floor of this triangular room. The volume of this room is equal to the floor area times the height of the room.
volume of the room = (floor area)*(height of the room)
volume of the prism = (base area)*(height of the prism)
For any prism, the base faces are always parallel and congruent to each other.
Type the correct answer in the box. use numerals instead of words. a population of beetles increases by 5% every year. if at the start of the year the population is at 10,000 beetles, what will its population be after three years? at the end of the third year the population of beetles will be .
At the end of the third year the population of beetles will be 11,576beetles
Exponential equationsThe standard form of an exponential function is given as:
y = ab^t
Given the following parameters
initial population 'a" = 10,000 beetles
Time = 3 years
rate b = 1.05
Substitute into the formula
y = 10,000(1.05)^3
y = 10,000(1.1576)
y = 11,576 beetles
Hence at the end of the third year the population of beetles will be 11,576beetles
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In the rectangular prism shown above, the distance between any two neighboring points on a line segment is the same. For example, the distance between points 1 and 2 is the same as the distance between points 13 and 20, which is the same as the distance between points 15 and 16. Place the cross sections indicated by the tiles in order from least area to greatest area.
A rectangular prism is a shape that has six faces which are rectangular.
What is a rectangular prism?Your information is incomplete as the diagram of the rectangular prism isn't given. Therefore, an overview will be given.
It should be noted that a rectangular prism simply means a three dimensional sold shape that has six faces that are rectangles.
The formula that's used to calculate the volume of a rectangular prism will be:
= Length × Width × Height
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−5 2/3 − 1/6 = i need more letters
Answer:
-5 5/6
Step-by-step explanation:
convert 2/3 into 4/6 and when u subtract a positive from a negative u add it instead
Part D What is the y-intercept of the correct graph? What is the y-intercept of the incorrect graph? Are the y-intercepts the same?
Part F about what is the average change in distance for each increase of 1 iron number? what does this mean in terms of the situation
The y-intercept of the correct graph is 185 and y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.
What is y-intercept?The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the y-axis.
In the graph it can be seen that the correct graph is intersect y-axis at the value 185. Thus, the y-intercept of the correct graph is 185.
c=185
For the incorrect graph this value is 195. Thus, the y-intercept of the incorrect graph is 195.
b=195
Here, the values of y-intercepts are not the same-
c≠b
185≠195
The average change in distance for each increase of 1 iron number is,
[tex]r=\dfrac{155-145}{3-4}\\r=-10[/tex]
Thus, the y-intercept of the correct graph is 185 and y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.
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PLEASE HELP ILL MARK BRAINEST!! WHAT IS THE RISE, RUN, AND F(X).
Answer:
First question (on left) f(x) = 5x-3. second question (on right) f)x) = 1/2*x
Step-by-step explanation:
rise(left) 4. run (left) 20.
rise(right) 8. run(right) 4.
f(x)
=
2x + 7 - x2
4
f(2)
=
Be sure to simplify your answer.
Enter
Answer:
[tex]f(2)=\frac{7}{4}[/tex]
Step-by-step explanation:
Step 1: Input 2 for x and solve
[tex]f(x) = \frac{2x + 7 - x^2}{4}[/tex]
[tex]f(2) = \frac{2(2) + 7 - (2)^2}{4}[/tex]
[tex]f(2)=\frac{4+7-4}{4}[/tex]
[tex]f(2)=\frac{7}{4}[/tex]
Answer: [tex]f(2)=\frac{7}{4}[/tex]
PLEASE HELP ME!!
find the Trinomial!
Answer:
[tex]a^{4}-2a^{2} -24[/tex]
Step-by-step explanation:
We do FOIL to solve this
Which of the follow box-and-whisker plots correctly displays this data set?
24, 32, 25, 27, 37, 29, 30, 30, 28, 31, 27, 23
Answer:
Since there isn't any of the following attached, I made my wn attached below
Step-by-step explanation:
Population size: 12
Median: 28.5
Minimum: 23
Maximum: 37
First quartile: 25.5
Third quartile: 30.75
Interquartile Range: 5.25
Outliers: none
Hope this helps you a little more for your last day of finishing hmw :)
Let me know if you need anymore help !
OR have questions
(100 points + brainliest)
A box of chocolates contains five milk chocolates, three dark chocolates, and 8 white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate.
What is the probability that this event happens? Show all of your steps used to solve this problem.
Answer:
3.6%
Step-by-step explanation:
This is an example of dependent events. When events are dependent, you have to multiply the probability of each event that happens after each other. Probability is desired outcome over all possible outcomes. For the milk chocolate, there are 5 pieces we can pick out of 16, so it's 5/16. Next, the probability of dark chocolate is 3/15 (There is one less piece of chocolate overall now). For the white chocolate, the possibility is 8/14. So now we have to multiply:
5*3*8 120 1
______ = _____ = ___ = (about) 0.036
16*15*14 3360 28
So, that's 3.6%
Hope this helps!
a roll of netting measures r metres.ryan bought 1/4 of a roll and trimmed 2 metres of the netting.he had 5 meters of netting left.how long was the original role of the netting before Ryan bought it
Answer:
28 m
Step-by-step explanation:
full roll length: r
Ryan bought: r/4
He trimmed 2 m: r/4 - 2
Length left: 5
r/4 - 2 = 5
r/4 = 7
r = 28
Answer: 28 m
1. As shown in the diagram below, the radius of a cone is 2.5 cm and its
slant height is 6.5 cm. How many cubic centimeters are in the volume of
the cone?
6.5
The number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
Calculating the volume of a coneFrom the question, we are to determine the volume of the cone
The volume of a cone can be calculated by using the formula,
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
Where V is the volume
r is the radius
and h is the height
From the given information,
radius, r = 2.5 cm
slant height, l = 6.5 cm
First, we will determine the height of the cone
By Pythagoras' theorem
[tex]l^{2} = r^{2} + h^{2}[/tex]
Where [tex]l[/tex] is the slant height
r is the radius
and h is the height of the cone
Then, we can write that
[tex]6.5^{2} = 2.5^{2} + h^{2}[/tex]
[tex]42.25 = 6.25 + h^{2}[/tex]
[tex]h^{2}=42.25 - 6.25[/tex]
[tex]h^{2} =36[/tex]
[tex]h = \sqrt{36}[/tex]
∴ h = 6 cm
Now, putting the parameters into the equation for the determining the volume of a cone, we get
[tex]V = \frac{1}{3}\times \pi \times 2.5^{2} \times 6[/tex]
[tex]V = \pi \times 6.25\times 2[/tex]
[tex]V = 12.5 \pi[/tex] cm³ OR 39.27 cm³
Hence, the number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
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You plan on making a $235.15 monthly deposit into an account that pays 3.2% interest, compounded monthly, for 20 years. at the end of this period, you plan on withdrawing regular monthly payments. determine the amount that you can withdraw each month for 10 years, if you plan on not having anything in the account at the end of the 10 year period and no future deposits are made to the account. a. $769.27 b. $767.23 c. $78,910.41 d. $79,120.84
Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.
Calculation of monthly withdrawFirst, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = A * (((1 + r)^n – 1) / r) ................................. (1)
Where,
FV = Future value of the amount after 20 years =?
A = Monthly deposit = $235.15
r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667
n = number of months = 20 * 12 = 240
Substituting the values into equation (1), we have:
FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41
The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:
P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)
Where;
P = Monthly withdrawal or payment = ?
PV = Present value = FV calculated above = $78,910.41
r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667
n = number of months = 10 * 12 = 120
Substitute the values into equation (2), we have:
P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27
Therefore, the amount that can be withdrawn each month for 10 years is $769.27.
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The answer is A: $769.27
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integral from 0 to 5 of x^2 + 3 dx
Answer:
=170/3 or (decimal 56.67)
Step-by-step explanation:
Steps
∫⁵ x²+3dx
⁰
Apply the Sum Rule: ∫fx) + gx) dx = ∫f(x)dx +-∫ g(x)
dx
∫⁵ x² dx +∫⁵ 3dx
⁰ ⁰
∫⁵ x² dx=125/3
⁰
∫⁵ 3dx=15
⁰
125/3+15
=170/3