[tex]\ln(n+3)-\ln n=\ln\dfrac{n+3}n=\ln\left(1+\dfrac3n\right)[/tex]
We can show the sequence is bounded and monotonic.
Boundedness: [tex]1+\dfrac3n>1[/tex] for all [tex]n>0[/tex], so [tex]\ln\left(1+\dfrac3n\right)>\ln1=0[/tex] for all [tex]n>0[/tex].
Monotonicity: Consider the function
[tex]f(x)=\ln\left(1+\dfrac3x\right)[/tex]
which has derivative
[tex]f'(x)=\dfrac{1+\frac3x}{-\frac3{x^2}}=-\dfrac3{x^2+3x}[/tex]
which has negative sign for all [tex]x>0[/tex], and so [tex]f(x)[/tex] is strictly decreasing.
[tex]\ln(n+3)-\ln n[/tex] is bounded and monotonic, so the sequence converges.
As [tex]n\to\infty[/tex] we have [tex]\dfrac3n\to0[/tex], leaving us with the limit
[tex]\displaystyle\lim_{n\to\infty}(\ln(n+3)-\ln n)=\lim_{n\to\infty}\ln\left(1+\frac3n\right)=\ln\left(1+\lim_{n\to\infty}\frac3n\right)=\ln1=0[/tex]
The sequence an = ln(n + 3) - ln(n) converges with a limit of 0. This is determined by simplifying the expression and observing its behavior as n approaches infinity.
Explanation:Firstly, the question pertains to the study of the convergence or divergence of a sequence. In this case, we're looking at the sequence an = ln(n + 3) - ln(n). Using logarithmic properties, this can be rewritten as ln((n+3)/n). As n approaches infinity, the sequence converges to the limit ln(1), which equals 0. Therefore, the sequence converges and its limit is 0.
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Find the surface area for the composite solid, round your answer to the nearest tenth. Explain your answer.
Answer:
200.3 in²
Step-by-step explanation:
The area of the top of the cylinder is precisely the area of the cube that the cylinder covers. In other words, the total of that area and the visible area of the cube is precisely equal to the area of the cube with no added parts.
So, the added cylinder only increases the total area by the area of its curved surface. That area is the product of its circumference and height.
cylinder lateral area: π·d·h = π·(4 in)(4 in) = 16π in² ≈ 50.3 in²
cube surface area: 6·(5 in)² = 150 in²
__
total surface area = cube surface area + cylinder lateral area
total surface area = (150 +50.3) in²
total surface area =200.3 in²
In a study conducted at Virginia Tech on the development of ectomycorrhizal, a symbiotic relationship between the roots of trees and a fungus, in whichminerals are transferred from the fungus to the trees and sugars from the trees to the fungus, 20 northern red oak seedlings exposed to the fungus Pisolithus tinctoruswere grown in a greenhouse. All seedlings were planted in the same type of soil and received the same amount of sunshine and water. Half received no nitrogen atplanting time, to serve as a control, and the other half received 368 ppm of nitrogen in the form NaNO3. The stem weights, in grams, at the end of 140days were recorded as follows:No Nitrogen Nitrogen0.32 0.260.53 0.430.28 0.470.37 0.490.47 0.520.43 0.750.36 0.790.42 0.860.38 0.620.43 0.46Construct a 95% confidence interval for the difference in the mean stem weight between seedlings that receive no nitrogen and thosethat receive 368 ppm of nitrogen. Assume the populations to be normally distributed with equal variances.
To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, calculate the mean stem weight for each group, the sample standard deviation, the standard error, and the margin of error. Then, calculate the lower and upper bounds of the confidence interval.
Explanation:To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, we will use a t-distribution and the formula for calculating a confidence interval for the difference in means. First, we find the mean stem weight for each group and calculate the sample standard deviation. Then, we calculate the standard error and the margin of error. Finally, we calculate the lower and upper bounds of the confidence interval.
Calculate the mean stem weight for each group:Therefore, the 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen is approximately (-0.292, -0.052). This means we can be confident that the mean stem weight of seedlings that received no nitrogen is lower than the mean stem weight of seedlings that received 368 ppm of nitrogen.
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A right rectangular pyramid is sliced parallel to the base, as shown What is the area of the resulting two-dimensional cross section? 15cm 18cm 25cm 50cm
Answer:
15 cm^2
Step-by-step explanation:
Simply multiply the base times the height of the cross section. So 3 x 5 is 15
Graph the equations to find the solution(s) to the system.
y = x - 1
y = 1/3(x + 2)(x - 4)
To solve the system of equations, graph the linear equation y = x - 1 and the quadratic equation y = 1/3(x + 2)(x - 4) on the same axes. Look for intersection points between the line and the parabola, which represent the solution(s) to the system. The number of intersections can vary, indicating how many solutions exist.
Explanation:The question involves solving a system of equations:
y = x - 1y = 1/3(x + 2)(x - 4)To find the solution(s), we plot both equations on the same graph and look for intersection points. The first equation, y = x - 1, represents a straight line with a slope of 1 and a y-intercept of -1. For the second equation, y = 1/3(x + 2)(x - 4), it represents a parabola that opens upwards because the coefficient of the x^2 term (which is derived from expanding the equation) is positive. The roots (zeroes) are at x = -2 and x = 4, giving us points where the parabola crosses the x-axis.
To graph these, start with the linear equation by plotting the y-intercept (0, -1) and then using the slope to find another point (for example, (1, 0)). Plot these points and draw a straight line through them. For the quadratic equation, plot the roots (-2, 0) and (4, 0) and find the vertex by computing the axis of symmetry and the maximum or minimum value of y by substituting back into the equation. Sketch the parabola based on these points.
The solution(s) to the system are where the line and the parabola intersect. Depending on the exact shape of the parabola, there might be two, one or no intersection points, representing the solution(s).
Answer:
The solutions to the system of equations are (-0.85, -1.85) and (5.85, 4.85).
Step-by-step explanation:
The system of equations is a set of multiple equations. The solution to a system of equations is the set of all points which make all equations in the system true. The greatest amount of solutions possible in a system is equal to the highest degree present in it.
To find the solutions of a system of equations through graphing, graph all equations in the system and note the locations where they intersect. These are the points where all equations are true, aka the solutions. In this system, there are two points of intersection at (-0.85, -1.85) and (5.85, 4.85).
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Given: m∠EYL=72°
Find: mEHL , mLVE
Answer:
Part 1) The measure of arc EHL is [tex]108\°[/tex]
Part 2) The measure of angle LVE is [tex]54\°[/tex]
Step-by-step explanation:
step 1
Let
x-----> the measure of arc EHL
y----> the measure of arc EVL
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
[tex]m<EYL=\frac{1}{2}(y-x)[/tex]
we have
[tex]m<EYL=72\°[/tex]
substitute
[tex]72\°=\frac{1}{2}(y-x)[/tex]
[tex]144\°=(y-x)[/tex]
[tex]y=144\°+x[/tex] ------> equation A
Remember that
[tex]x+y=360\°[/tex] -----> equation B ( complete circle)
substitute equation A in equation B and solve for x
[tex]x+(144\°+x)=360\°[/tex]
[tex]2x=360\°-144\°[/tex]
[tex]x=216\°/2=108\°[/tex]
Find the value of y
[tex]y=144\°+x[/tex]
[tex]y=144\°+108\°=252\°[/tex]
therefore
The measure of arc EHL is [tex]108\°[/tex]
The measure of arc EVL is [tex]252\°[/tex]
step 2
Find the measure of angle LVE
we know that
The inscribed angle measures half that of the arc comprising
Let
x-----> the measure of arc EHL
[tex]m<LVE=\frac{1}{2}(x)[/tex]
we have
[tex]x=108\°[/tex]
substitute
[tex]m<LVE=\frac{1}{2}(108\°)=54\°[/tex]
The expression _______ is not equivalent to (1 − sin2(x)) tan(-x).
a. (1 - cos^2(x)) cot(-x)
b. (cos^2(x) - 1) cot(x)
c. (sin^(x) - 1) tan(x)
d. (cos^2(x) - 1) cot(-x)
Answer:
D
Step-by-step explanation:
First simplify given expression:
[tex](1-\sin ^2x)\cdot \tan (-x)=\cos^2x\cdot (-\tan x)=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]
Now consider all options:
A. True
[tex](1-\cos^2 x)\cdot \cot (-x)=\sin^2 x\cdot (-\cot x)=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]
B. True
[tex](\cos^2 x-1)\cdot \cot x=-\sin^2 x\cdot \cot x=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]
C. True
[tex](\sin ^2x-1)\cdot \tan x=-\cos^2x\cdot \tan x=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]
D. False
[tex](\cos^2 x-1)\cdot \cot (-x)=(-\sin^2 x)\cdot (-\cot x)=\sin^2 x\cdot \dfrac{\cos x}{\sin x}=\sin x\cos x=\cos x\sin x.[/tex]
Answer:
d. (cos^2(x) - 1) cot(-x)
Step-by-step explanation:
Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1? Part A Part B Part C Part D
Answer:
Part B shaded below first line and above second line.
Step-by-step explanation:
The first inequality corresponds to the second line (-3 = -4+1, for example) The ≥ symbol in that inequality tells you it will be satisfied by y values above those on the line.
The second inequality corresponds to the first line (-4+3 = -1, for example) The ≤ symbol in that inequality tells you it will be satisfied by y values below those on the line.
Hence the solution set is those values shaded below the first line and above the second line — matching Part B.
Please help me this is my last question
X = 1/2(76 + 78)
x = 1/2(154)
x = 77
Multiply
21 lb 13 oz x 5 =
12 gal 3 qt 1 pt × 9 =
15 yd 2 ft 8 in x 7 =
Answer:
• 109 lb 1 oz
• 115 gal 3 qt 1 pt
• 111 yd 8 in
Step-by-step explanation:
The relevant unit relationships are ...
1 lb = 16 oz
1 gal = 4 qt
1 qt = 2 pt
1 yd = 3 ft = 36 in
To convert from one unit to another, multiply by a fraction that has ...
(to unit)/(from unit)
For example, to convert (13 oz)×5 = 65 oz to pounds, multiply by (1 lb)/(16 oz). This will give you ...
(65 oz)·(1 lb)/(16 oz) = 65/16 lb = 4 1/16 lb
Now, if you don't already recognize that 1/16 lb = 1 oz, you can multiply the fraction by the unit conversion from lb to oz: (16 oz)/(1 lb). Doing that gives ...
(1/16 lb)·(16 oz)/(1 lb) = 16/16 oz = 1 oz
When the same units are in the numerator and denominator, they cancel, as do any factors that appear in both numerator and denominator.
___
1. (21 13/16 lb)×5 = 105 65/16 lb = 109 1/16 lb = 109 lb 1 oz
__
2. (12 7/8 gal)×9 = 108 63/8 gal = 115 7/8 gal = 115 gal 3 qt 1 pt
__
3. ((15 2/3 +8/36) yd)×7 = (105 14/3 + 56/36) yd = 109 yd 2 ft + 1 yd 20 in
= 111 yd 8 in
_____
Additional explanation
7/8 gal = 7 pt = 1 pt + 3·2 pt = 1 pt + 3 qt
__
14/3 yd = 4 2/3 yd = 4 yd 2 ft
56/36 yd = 1 20/36 yd = 1 yd + (12 +8)/36 yd = 1 yd + 1 ft + 8 in
Then 14/3 yd + 56/36 yd = (4 yd + 2 ft) + (1 yd + 1 ft + 8 in) = 6 yd + 8 in
How many hours will it take to complete a 76km bike ride if you go bike ride if you go 14km per hour the whole time?
To find the number of hours, divide the total distance by the speed.
Hours = 76 km / 14 km per hour
Hours = 4.529
Round the answer as needed.
. What is the discount on $640 if the discount rates are 25%, 10%, and 5%?
Answer:
Step-by-step explanation:
25%: 640 X .25 =160
640-160= $480
10%: 640 X .10= 64
640- 64= $576
5%: 640 X .05 =32
640- 32= $608
Answer:
the discount with rate 25%=$160,the discount with rate 10%=$64,the discount with rate 5%=$32
Step-by-step explanation:
Hello, I think I can help you with this
the discount is a percentage, a proportion of the real value, we can find that proportion using a simple rule of three
let
100% =$640
Step 1
If
$640= 100%
x? % = 25%
($640/100%)=(x/25%)
isolating x
x=($640*25%)/(100%)
x=$160
the discount with rate 25%=$160
Step2
If
$640= 100%
x? % = 10%
($640/100%)=(x/10%)
isolating x
x=($640*10%)/(100%)
x=$64
the discount with rate 10%=$64
Step 3
If
$640= 100%
x? % = 5%
($640/100%)=(x/5%)
isolating x
x=($640*5%)/(100%)
x=$32
the discount with rate 5%=$32
Have a nice day
If $75 is invested at an interest rate of 8% per year and is compounded monthly, how much money is in the account in 15 years?
Answer:
$248.03
Step-by-step explanation:
The formula you use for this is as follows:
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]
where A(t) is the amount after the compounding is done, P is the initial amount invested, r is the interest rate in decimal form, n is the number of times the compounding is done per year, and t is the time in years. Using that information and filling in our equation gives us this:
[tex]A(t)=75(1+\frac{.08}{12})^{(12)(15)}[/tex]
which simplifies down to
[tex]A(t)=75(1+.0066667)^{180}[/tex]
which simplifies further to
[tex]A(t)=75(3.307118585)[/tex]
which multiplies to $248.0338938. Round to the nearest cent to get your answer.
The amount of money is $248.02.
Principal amount = P=75
Interest rate = r = 8% = 0.08
Number of years = t = 15
Number of times compounded in a year = n = 12
A = Amount after t years.
After 15 years there will be:
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}\\ A=75\left(1+\frac{0.08}{12}\right)^{\left(12\cdot15\right)}\\ A=248.019110806\\ A \approx 248.02[/tex]
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Do you know what this means? And how do I solve it?
a and b are matrices
Garry is studying a square pyramid and wants to draw a net of the figure to help determine its surface area. Which net represents a square pyramid?please hurry than you
The net represents a square pyramid is a net with a square base and 4 triangular sides.
What is a square pyramid?A square pyramid is a pyramid with a square base in geometry. A right square pyramid is one with the tip perpendicular to the square's centre.
There will be five surfaces in the pyramid the base is square and the remaining four will be triangular.
Hence net represents a square pyramid is a net with a square base and 4 triangular sides.
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Please help me on this
Answer:
cos∠FHE = 4/5
Step-by-step explanation:
* Lets revise the trigonometry functions
- In ΔABC
# m∠B = 90°
# Length of AB = a , length of BC = b and length of AC = c
# The trigonometry functions of angle C are
- sin(C) = a/c ⇒ opposite side to ∠C ÷ the hypotenuse
- cos(C) = b/c ⇒ adjacent side to ∠C ÷ the hypotenuse
- tan(c) = a/b ⇒ opposite side to ∠C ÷ adjacent side to ∠C
* Now lets solve the problem
- To find cos∠FHE , we must find the length of the adjacent
side HF and the length of the hypotenuse HE
- We can find the length of HF from ΔFGH
- In ΔFGH
∵ m∠G = 90°
∵ GF = √8
∵ m∠GHF = 45°
∵ sin∠GHF = GF/HF
∴ sin45° = √8/HF ⇒ by using cross-multiplication
∴ HF × sin45° = √8
∵ sin45° = 1/√2
∴ HF × 1/√2 = √8 ⇒ multiply each side by √2
∴ HF = √2 × √8 = √16 = 4
* Lets find the length of HE from ΔHFE
- In ΔHFE
∵ m∠HFE = 90°
∵ EF = 3 ⇒ given
∵ HF = 4
- By using Pythagoras theorem
∵ HE = √(FH² + FE²)
∴ HE = √(4² + 3²) = √(16 + 9) = √25 = 5
* Now we can find cos∠FHE
∵ cos∠FHE = HF/HE
∵ HF = 4 and HE = 5
∴ cos∠FHE = 4/5
20 Points PLEASE Hep .Factorize this
h(t) = -16x^+72x
( negative 16 squared plus 72x )
Answer:
-8x(2x - 9)
Step-by-step explanation:
-16x² + 72x
GCF = 8x
8x(16x² / 8x, -7x/8x)
-8x(2x - 9)
hope this helps!!
The answer would be -8x(2x-9)
Which expression is equivalent to -1/3 (6X +15) -3
[tex] \frac{ - 1}{3} (6x + 15) - 3 \\ \\ 1. \: \frac{ - 6x + 15}{3} - 3 \\ 2. \: \frac{ - 3(2x + 5)}{3} - 3 \\ 3. \: - (2x + 5) - 3 \\ 4. \: - 2x - 5 - 3 \\ 5. \: - 2x + ( - 5 - 3) \\ 6. \: - 2x - 8[/tex]
Final answer:
To simplify -1/3 (6X +15) -3, distribute the -1/3 across the parentheses to get -2X - 5, and then subtract 3 to get the equivalent expression: -2X - 8.
Explanation:
The student's question is asking for the equivalent expression of -1/3 (6X +15) -3. To find the equivalent expression, we start by distributing the -1/3 across the parentheses:
-1/3 × 6X = -2X
-1/3 × 15 = -5
Next, we combine this result with the -3 that is outside of the parentheses:
-2X - 5 - 3 = -2X - 8
Therefore, the equivalent expression is -2X - 8.
i need help 1-9 *dont mind answers*
the answer is -8, the 9 is negative and -9+1= -8
By the substitution property of equality, substitute all x's with ¹/₂ and all y's with -5.
1. -2xy = -2(¹/₂)(-5) = 5
2. 4x² - 3y = 4(¹/₂)² - 3(-5) = 1 + 15 = 16
3. 10y/(12x + 4) = 10(5)/(12(¹/₂) + 4) = -50/10 = -5
4. 11x - 8(x - y) = 11(¹/₂) - 8(¹/₂ - -5) = ¹¹/₂ - 8(¹¹/₂) = -7(¹¹/₂) = -⁷⁷/₂ = -38.5
Substitute a's with -9 and b's with -4
5. 3ab = 3(-9)(-4) = 108
6. a² - 2(b + 12) = (-9)² - 2(-4 + 12) = 81 + 8 - 24 = 65
7. 4b²/(3b - 7) = 4(-4)²/(3(-4) - 7) = 64/-19
8. 7b² + 5(ab - 6) = 7(-4)² + 5((-9)(-4) - 6) = 112 + 150 = 262
9. x = 7.25, y = 3.25 --> 4x: people w/o popcorn, 2(x + y): people w/ popcorn; 4x + 2(x + y) = 4(7.25) + 2(7.25 + 3.25) = 29 + 21 = $50
The ratio of dogs to cats in the neighborhood was 3 to 7. If a total of 210 dogs and cats were in the neighborhood, how many cats were there? Use a proportion.
Final answer:
The number of cats in the neighborhood can be found by using the given ratio of dogs to cats, 3 to 7, and the total number of animals, 210. The calculations lead to a result of 147 cats.
Explanation:
To find the number of cats in the neighborhood, we can set up a proportion using the given ratio of dogs to cats, which is 3 to 7. We know that the total number of dogs and cats is 210. Let's assume the number of cats is 7x and the number of dogs is 3x.
So, 3x + 7x = 210. Combining like terms, we get 10x = 210. Dividing both sides by 10, we find that x = 21. Now, to find the number of cats, we multiply 7x by 21, which gives us 147 cats.
Therefore, there are 147 cats in the neighborhood.
PLEASE HELP ASAP WILL MARK BRAINLIEST FOR THESE ANSWERS!!! PLEASE I NEED TO PASS
Answer:
First one is 64
Step-by-step explanation:
Expand (x+3)^3 and simplify how to do this
Answer:
x^3 +9x^2 +27x +27
Step-by-step explanation:
The expansion of a power of a binomial looks like ...
(a +b)^n = nC0·a^n·b^0 + nC1·a^(n-1)·b^1 + nC2·a^(n-2)·b^2 + ... + nC(n-1)·a^1·b^(n-1) + nCn·a^0·b^n
Of course, nCk = n!/(k!·(n-k)!) and a^0 = b^0 = 1. The list of coefficients nCk corresponds to a row of Pascal's triangle (see attached).
For n=3, this is ...
(a +b)^3 = a^3 +3a^2b +3ab^2 +b^3
You have a=x and b=3, so the expansion is ...
(x +3)^3 = x^3 +3·x^2·3 +3·x·3^2 +3^3
= x^3 +9x^2 +27x +27
Find the radius of the circle circumscribed around an equilateral triangle, if the radius of the circle inscribed into this triangle is 10 cm.
Answer:
20 cm
Step-by-step explanation:
Let a cm be the length of the side of equilateral triangle.
Use formula for the radius of inscribed circle into the equailteral triangle:
[tex]r_{inscribed}=\dfrac{a\sqrt{3}}{6}[/tex]
Hence,
[tex]\dfrac{a\sqrt{3}}{6}=10\Rightarrow a=\dfrac{60}{\sqrt{3}}[/tex]
Now, use formula for the circumscribed circle's radius:
[tex]R_{circumscribed}=\dfrac{a\sqrt{3}}{3}[/tex]
Therefore,
[tex]R_{circumscribed}=\dfrac{\frac{60}{\sqrt{3}}\cdot \sqrt{3}}{3}=20\ cm[/tex]
Answer:
20 cmStep-by-step explanation:
Look at the picture.
The formula of a radius of a circle circumscribed around an equaliteral triangle:
[tex]R=\dfrac{2}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]
The formula od a radius of a circle inscribed into an equaliteral triangle:
[tex]r=\dfrac{1}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]
As you can see in the formulas above, the radius of the circumscribed circle is twice the radius of the inscribed circle.
Therefore
[tex]R=2r[/tex]
Given:
[tex]r=10\ cm[/tex]
therefore
[tex]R=2(10\ cm)=20\ cm[/tex]
Please help and find what the value of x is
Answer:
x=30
Step-by-step explanation:
53+97+x=180
150+x=180
x=30
The sum of all the angles of a triangle is 180 degrees.
Add all the angles together and set it equal to 180, then solve for x
53 + 97 + x = 180
(150-150) + x = 180 -150
x = 30
Hope this helped!
Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1, -1).
Answer:
y = 2x +1
Step-by-step explanation:
The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:
y = 2x + b
-1 = 2(-1) +b . . . substitute for x and y
2 -1 = b . . . . . . add 2
1 = b
So the equation for the parallel line is ...
y = 2x + 1
Please help!!!!!!!!!
Answer:
None of the above
Explanation:
To find the type of lines they create, first find the slope of the equations.(Change form to y intercept)
4x-2y=-5
-2y=-4x-5
y=2x+(5/2)
Slope=2
-2x+3y=-3
3y=2x-3
y=(2/3)x-1
Slope=2/3
So, one has slope=2 and the other has slope=2/3. They’re not parallel because slopes are not the same. They’re not perpendicular because the slopes are not opposites. They’re not equal because their equations are not the same. So, none of the above.
The dot plot shows the number of attempts each basketball player took to make a three-point shot.
Select from the drop-down menus to correctly complete the statement.
The distribution of data is (approximately normal-skewed left-skewed right) , with a mode of (#) , and a range of (#) .
Answer:
The distribution of data is (approximately normal-skewed left-skewed right) , with a mode of (7 ) , and a range of (8 )
Step-by-step explanation:
The data distribution is a normal skewed right with a range of (8) and a mode of (7).
What is the mode?Mode is the most frequently used number.
From the dot plot, it is observed that on the data 7th player took 6 attempts. Which is the greatest. The mode of the data distribution is 7.
The range of the data is the difference between the maximum and the minimum value.
Range = 9-1
Range=8
From the dot plot, it is observed that the maximum value is toward the right. So that it is right-skewed.
Hence, the data distribution is a normal skewed right) with a range of (8) and a mode of (7).
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102.1029 rounded to the nearest tenth
Answer:
102.1
102.10 <--- 0 can be rounded down, so it is 102.1.
On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. What is the probability that Erin will have a heart attack and the test predicts it?
Answer: There is probability of 46.9% that Erin will have a heart attack and the test predicts it.
Step-by-step explanation:
Since we have given that
Probability that her family had a risk of heart attack P(A)= 70%
Probability that the reliability of the stress test P(B)= 67%
Since events A and B are independent events.
so, we can apply the rule of independent events :
We need to find the probability that Erin will have a heart attack and the test predicts it .
[tex]P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.70\times 0.67\\\\P(A\cap B)=0.469\\\\P(A\cap B)=0.469\times 100\%\\\\P(A\cap B)=46.9\%[/tex]
Hence, there is probability of 46.9% that Erin will have a heart attack and the test predicts it.
The probability that Erin will have a heart attack and the test predicts it is 46.9%.
Explanation:To find the probability that Erin will have a heart attack and the test predicts it, we need to multiply the probability of Erin having a heart attack (the family risk of 70%) with the reliability of the stress test (67%).
Probability of having a heart attack = 70% = 0.70
Reliability of the stress test = 67% = 0.67
Probability of Erin having a heart attack and the test predicting it = 0.70 * 0.67 = 0.469 (or 46.9%)
A series of tile patters is shown below. Consider the function that represents the number of white tiles in each figure.
Select all the statements that are true
-W(n)=4n+4 represents the function.
-W(n)=4n+8 represents the function.
-Input values for the function are natural numbers.
-Input values for the function are the number of white tiles in each figure.
-The function is continuous.
-Figure 6 will have 10 white tiles.
-Figure 8 will have 36 white tiles.
Answer:
• W(n)=4n+4 represents the function.
• Input values for the function are natural numbers.
• Figure 8 will have 36 white tiles
Step-by-step explanation:
–W(n)=4n+4 represents the function.
TRUE - For figure 1, this function gives W(1) = 4·1+4 = 8, the number of white tiles. It also gives correct values for the other figures shown.
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–W(n)=4n+8 represents the function.
FALSE - See the other W(n) function above. This function does not give correct values for the figures shown.
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–Input values for the function are natural numbers.
TRUE - the figures are numbered using natural numbers, so natural numbers are the input to the function
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–Input values for the function are the number of white tiles in each figure.
FALSE - The description of the function is that the number of white tiles is its output, not its input.
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–The function is continuous.
FALSE - the domain of the function is natural numbers. It is undefined for numbers other than that, so is not continuous.
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–Figure 6 will have 10 white tiles.
FALSE - using the definition of W(n) above, we find W(6) = 28, not 10.
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–Figure 8 will have 36 white tiles.
TRUE - W(8) = 36
Calculate the Perimeter of a Square Whose area is795.24 Square inches
[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=side's~length\\ \cline{1-1} A=795.24 \end{cases}\implies 795.24=s^2 \\\\\\ \sqrt{795.24}=s\implies 28.2=s \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of a square}}{P=4s\implies P=4(28.2)}\implies P=112.8[/tex]