NO LINKS!! URGENT HELP PLEASE!!
1. Find the area of a regular octagon. Each side is 12 m.
2. The perimeter of a regular polygon is 72 feet. An exterior angle of the polygon measures 40°. Find the length of each side.
3. If the perimeter of a regular pentagon is 50 in. Find the area. Show a drawing and work please.
Answers
Answer:
1) 695.3 m²
2) 8 ft
3) 172.0 in²
Step-by-step explanation:
Question 1To find the area of a regular polygon, we can use the following formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
Given the polygon is an octagon, n = 8.
Given each side measures 12 m, s = 12.
Substitute the values of n and s into the formula for area and solve for A:
[tex]\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}[/tex]
[tex]\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}[/tex]
[tex]\implies A=695.29350...[/tex]
Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.
[tex]\hrulefill[/tex]
Question 2The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.
If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.
To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:
[tex]\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}[/tex]
Therefore:
[tex]\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}[/tex]
[tex]\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}[/tex]
[tex]\implies 40^{\circ}n=360^{\circ}[/tex]
[tex]\implies n=\dfrac{360^{\circ}}{40^{\circ}}[/tex]
[tex]\implies n=9[/tex]
Therefore, the regular polygon has 9 sides.
To determine the length of each side, divide the given perimeter by the number of sides:
[tex]\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}[/tex]
[tex]\implies \sf Side \;length=\dfrac{72}{9}[/tex]
[tex]\implies \sf Side \;length=8\;ft[/tex]
Therefore, the length of each side of the regular polygon is 8 ft.
[tex]\hrulefill[/tex]
Question 3The area of a regular polygon can be calculated using the following formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
A regular pentagon has 5 sides, so n = 5.
If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.
Substitute the values of s and n into the formula and solve for A:
[tex]\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}[/tex]
[tex]\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}[/tex]
[tex]\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}[/tex]
[tex]\implies A=172.047740...[/tex]
Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.
Answer:
1.695.29 m^2
2.8 feet
3. 172.0477 in^2
Step-by-step explanation:
1. The area of a regular octagon can be found using the formula:
[tex]\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}[/tex]
where a is the length of one side of the octagon.
In this case, a = 12 m, so the area is:
[tex]\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}[/tex]
Therefore, the Area of a regular octagon is 695.29 m^2
2.
The formula for the exterior angle of a regular polygon is:
[tex]\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}[/tex]
where n is the number of sides in the polygon.
In this case, the exterior angle is 40°, so we can set up the following equation:
[tex]\bold{40^o=\frac{ 360^0 }{n}}[/tex]
[tex]n=\frac{360}{40}=9[/tex]
Therefore, the polygon has n=9 sides.
Perimeter=72ft.
We have
[tex]\boxed{\bold{Perimeter = n*s}}[/tex]
where n is the number of sides in the polygon and s is the length of one side.
Substituting Value.
72 feet = 9*s
[tex]\bold{s =\frac{ 72 \:feet }{ 9}}[/tex]
s = 8 feet
Therefore, the length of each side of the polygon is 8 feet.
3.
Solution:
A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = [tex]\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}[/tex]
The area of a regular pentagon can be found using the following formula:
[tex]\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}[/tex]
where s is the length of one side of the Pentagon.
In this case, s = 10 in, so the area is:
[tex]\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}[/tex]
Drawing: Attachment
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|x – 4| > –3 will have what type of solution set
Answers
Answer:
The inequality |x – 4| > –3 represents an absolute value inequality.
The absolute value of any real number is always non-negative, meaning it is greater than or equal to zero. Therefore, the left side of the inequality, |x – 4|, will always be greater than or equal to zero.
Since the right side of the inequality, -3, is also greater than or equal to zero, this means that the inequality |x – 4| > –3 holds true for all real numbers x. In other words, there are no restrictions on the value of x.
The solution set for this inequality is the set of all real numbers, often represented as (-∞, +∞).
Answer:
(−∞,∞)
Step-by-step explanation:
|x – 4| > – 3
Since |x – 4| is always positive and - 3 is negative, |x – 4| is always greater than - 3, so the inequality is always true for any value of x.
All real numbers
The result can be shown in multiple forms.
All real numbers
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Answers
Answer:
[tex]A =[/tex] 95.45
Step-by-step explanation:
[tex]A=s(s﹣a)(s﹣b)(s﹣c)[/tex]
[tex]s=a+b+c[/tex]
Solving for A
A=1
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The volume of the cylinder with a height of 12 cm and a diameter of 8 cm is approximately 602.19 cm³.
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Volume = π * (radius²) * height
Given that the diameter of the cylinder is 8 cm, the radius (r) can be calculated by dividing the diameter by 2:
radius (r) = 8 cm / 2 = 4 cm
The height (h) of the cylinder is 12 cm.
substitute these values into the formula:
Volume = π * (4 cm)² * 12 cm
Volume = π * 16 cm² * 12 cm
Volume ≈ 602.19 cm³ (rounded to two decimal places)
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Answers
A relation R on a set X means , R is a subset of the Cartesian product Xⁿ, where n is the number of components of the relation.
Now, A relation R on a set X, where n is the arity or number of components of the relation, is a mathematical phrase that denotes that R is a subset of the Cartesian product Xⁿ
For example,
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We can see that R is a subset of X in this instance, which is composed of the elements (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), and (3,1), (3,2), (3,3).
Since each member of R is an ordered n-tuple consisting of n items that belong to X, it follows that if R is belong in Xⁿ, it is a relation on the set X.
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its ixl please help
Answers
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the center of the circle and r represents the radius.
In this case, the center of the circle is given as (0, 9), and it passes through the point (15/2, 5).
First, we need to find the radius of the circle. The radius can be calculated using the distance formula between the center and any point on the circle.
Using the distance formula:
r = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's substitute the values into the formula:
r = √[(15/2 - 0)^2 + (5 - 9)^2]
r = √[(15/2)^2 + (-4)^2]
r = √[225/4 + 16]
r = √[225/4 + 64/4]
r = √[289/4]
r = 17/2
Now that we have the radius, we can write the equation of the circle in standard form:
(x - 0)^2 + (y - 9)^2 = (17/2)^2
Simplifying:
x^2 + (y - 9)^2 = 289/4
Multiplying through by 4 to eliminate the fraction:
4x^2 + 4(y - 9)^2 = 289
Therefore, the equation of the circle in standard form is 4x^2 + 4(y - 9)^2 = 289.
I hope this helps! :)
A small liberal arts college in the Northeast has 200 freshmen. Sixty of the freshmen are education majors. Suppose thirty freshmen are randomly selected (without replacement).
Find the standard deviation of the number of education majors in the sample. Round your answer to two decimal places, if necessary.
Answers
The standard deviation of the number of education majors in the sample is 0.3.
What is the standard deviation of education majors?The standard deviation of the number of education majors in the sample is calculated as follows;
σ = √ [(N - n) x n(N - k) / ((N - 1) x N²)]
Where
N is the total population size = 200 freshmenn is the sample size = 30 freshmenk is the number of successes in the population = 60 education majorsThe standard deviation of the number of education majors in the sample is calculated as;
σ = √[(200 - 30) x 30(200 - 60) / ((200 - 1) x 200²)]
= √[(170 x 30 x 140 / (199 x 40000)]
= √(714000 / 7960000)
= 0.3
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PLEASE HELP QUICKLY 100 POINTS AND I WILL MARK BRAINLIEST!!
The length of the longest item that will fit in the shipping box is 26.3 inches. Now Use complete sentences to explain the process you would use to find the volume of the shipping box.
Answers
Length = √ (24^2 - 16^2) ≈ 17.9 inches
We have the width and height so
Volume = 17.9 x 16 x 12 ≈ 3434.6 in^3
Answer:
The volume of the shipping box is 3434.6 in³ (to the nearest tenth).
The length of the longest item that will fit inside the shipping box is 26.8 inches (to the nearest tenth).
Step-by-step explanation:
The shipping box can be modelled as a cuboid.
A cuboid is a three-dimensional geometric shape with six rectangular faces and right angles between adjacent faces.
The volume of a cuboid can be calculated by multiplying its length (L), width (W), and height (H) together.
From the given diagram, the width of the cuboid is 16 inches and its height is 12 inches. Therefore, we need to find the measure of its length in order to calculate its volume.
As all sides of a cuboid have interior angles of 90°, and we have been given the face diagonal of the base (24 inches), we can use Pythagoras Theorem to calculate the length (L).
[tex]\begin{aligned}L^2+16^2&=24^2\\L^2+256&=576\\L^2&=320\\L&=\sqrt{320}\\L&=8\sqrt{5}\; \sf in\end{aligned}[/tex]
Substitute L = 8√5, W = 16 and H = 12 into the formula for the volume of a cuboid to calculate the volume of the shipping box:
[tex]\begin{aligned}\sf Volume&=\sf L \cdot W \cdot H\\&=8\sqrt{5} \cdot 16 \cdot 12\\&=128\sqrt{5} \cdot 12\\&=1526\sqrt{5}\\&=3434.60041...\\&=3434.6\; \sf in^3\end{aligned}[/tex]
Therefore, the volume of the shipping box is 3434.6 in³ to the nearest tenth.
[tex]\hrulefill[/tex]
In a cuboid, there are two types of diagonals: face diagonals and body diagonals.
Face Diagonals: These diagonals connect opposite corners of a face of the cuboid and lie entirely within that face.Body Diagonals: These diagonals connect opposite corners of the cuboid, passing through the interior of the cuboid and extending across multiple faces. Body diagonals are longer than face diagonals.The body diagonal of a cuboid is the longest line that can be drawn inside the cuboid. Therefore, to find the length of the longest item that will fit inside the shipping box, we need to calculate the body diagonal of the cuboid.
The formula for the body diagonal of a cuboid is:
[tex]\sf Body \;diagonal=\sqrt{L^2+W^2+H^2}[/tex]
Substitute L = 8√5, W = 16 and H = 12 into the formula to find the body diagonal of the cuboid (marked as a red dashed line on the given diagram):
[tex]\begin{aligned}\sf Body \;diagonal&=\sf \sqrt{L^2+W^2+H^2}\\&=\sqrt{(8\sqrt{5})^2+16^2+12^2\\&=\sqrt{320+256+144}\\&=\sqrt{720}\\&=26.8328157...\\&=26.8\; \sf in\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the length of the longest item that will fit inside the shipping box is 26.8 inches, to the nearest tenth.
The number of hours that you play video games each day for five days are shown in the table. The mean amount of time that
you play video games each day of the week is 1.5 hours. How many total hours do you play video games on Friday and
Saturday
Answers
We play total of 4.5 hours of video games on Friday and Saturday.
How many hours is spent on video games on Friday and Saturday?An expression in math is a statement having minimum of two numbers or variables or both and an operator connecting them.
To get total hours played on Friday and Saturday, we will subtract the sum of hours played from the mean of 1.5 hours per day for the five days given.
The total hours played on Friday and Saturday will be:
= (Mean hours per day * 7) - (Sum of hours played on Sunday to Thursday)
= (1.5 * 7) - (1.75 + 1 + 0.5 + 1.5 + 1.25)
= 10.5 - 6
= 4.5 hours.
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Use Juliana's text message data to answer the questions.
What was the mean number of text messages that Julianna sent per day
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The mean number of text messages that Julianna sent per day is 7.
To calculate the mean number of text messages that Julianna sent per day, we need to sum up the number of text messages she sent each day and divide it by the total number of days.
Total number of text messages sent:
13 + 0 + 4 + 4 + 5 + 6 + 17 = 49
Total number of days: 7
Mean = Sum of all observations/number of observations
Mean =Total number of text messages sent/Total number of days
Mean number of text messages per day: 49 / 7
= 7
Therefore, 7 is the mean number of text messages that Julianna sent per day.
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Use julianna’s text message data to answer the questions.
Text messages sent:
Sun: 13 Mon: 0 tues: 4 wed: 4 thurs: 5 fri: 6 sat: 17
1. What was the mean number of text messages that julianna sent per day ?
A. 4
B.6
C.8
D.7
What are the vertex and range of y = |3x + 6| − 4?
A (−2, −4); −∞ < y < ∞
B (−2, −4); −4 ≤ y < ∞
C (0, −4); −∞ < y < ∞
D (0, −4); −4 ≤ y < ∞
Answers
For the given function:
Vertex is at (-2, -4) and range is −4 ≤ y < ∞
Hence, Option b is correct.
The given function is
y = |3x + 6| − 4
We can see that it is consist of absolute value function or mod function.
Since we know that,
An absolute value function is an algebraic function in which the variable is contained inside the absolute value bars.
The absolute value function is also known as the modulus function, and its most frequent form is f(x) = |x|,
where x is a real integer. In general, the absolute value function may be represented as f(x) = a |x - h| + k,
where a denotes how far the graph extends vertically, h represents the horizontal shift, and k represents the vertical displacement from the graph of f(x) = |x|.
If the value of 'a' is negative, the graph opens downwards; otherwise, it opens upwards.
The appropriate method of finding range and vertex both is to plot its graph:
Therefore after plotting graph we get,
Vertex is at (-2, -4)
And range is (-4 , ∞) ⇒ −4 ≤ y < ∞
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Non Shaded Shaded
Area
Area
8
Find the radius
of the small circle
Answers
Answer:
The answer is 16pi or 50.3cm² to 1 d.p
Step-by-step explanation:
The non shaded=area of shaded
d=8
r=d/2=4
A=pir³
A=p1×4²
A=pi×16
A=16picm² or 50.3cm² to 1d.p
Answer:
3.45 cm (3 s.f.)
Step-by-step explanation:
We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.
To find the radius of a regular polygon given its side length, we can use this formula:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):
[tex]\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}[/tex]
The formulas for the area of a regular polygon and the area of a circle given their radii are:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Therefore, the area of the regular pentagon is:
[tex]\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}[/tex]
The area of the circumcircle is:
[tex]\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}[/tex]
The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.
The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.
Given the shaded area is equal to the unshaded area:
[tex]\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}[/tex]
[tex]\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}[/tex]
Therefore, the radius of the small circle is 3.45 cm (3 s.f.).
Question One:
If a raw score corresponds to a z-score of 1.75, what does that tell you about that score in relation to the mean of the distribution?
Question Two:
What if the raw score corresponds to a z-score of -0.85?
Answers
Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two: , the raw score is relatively lower than the mean.
If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.
A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two:
If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.
To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.
In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.
By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.
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From the observation deck of a skyscraper, Brandon measures a 45
angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Answers
The horizontal distance from the base of the skyscraper out to the ship is 1140 m
What is the angle of depression?
Under the horizontal line, the angle of depression is measured, typically in degrees. It aids in figuring out how steep or incline the line of sight is in relation to the horizontal plane. The line of sight is steeply directed downward and increases with the angle of depression.
In many different disciplines, such as surveying, navigation, engineering, and physics, the angle of depression is frequently utilized.
We know that;
Tan 45 = x/1140
x = 1140 Tan 45
= 1140 m
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The following is a parallelogram. What does A=, B=, X=, QR= and Angle QRS=
Answers
Answer:
a = 4
b=2
x=18
QR =16+1=17
Angle QRS =59
Step-by-step explanation:
4a+1 = 2a + 9
2a = 8
a = 4
6b = 11b-10
-5b=-10
-b= -2
b=2
6x+13 = 7x - 5 (opposite angles are equal)
-x=-18
x=18
QR =16+1=17
Angle QRS = 180 - 18•6+13 =59 (PQR + QRS = 180)
Pure acid is to be added to a 10% acid solution to obtain 90L of 84% solution. How many liter of 10% solution should be in the mixture?
Answers
Answer:
16 liters of the 10% acid solution should be in the mixture.
Step-by-step explanation:
Let x represent the volume of the 10% acid solution to be added.
The volume of pure acid added would be (90 - x).
The equation to solve is: 0.1x + (90 - x) = 0.84(90)
Simplifying, we get: 0.1x + 90 - x = 75.6
Combining like terms, we have: -0.9x + 90 = 75.6
Subtracting 90 from both sides: -0.9x = -14.4
Dividing by -0.9: x = 16
Therefore, 16 liters of the 10% acid solution should be in the mixture.
In a sample of 560 adults, 336 had children. Construct a 95% confidence interval for the true population proportion of adults with children.
Give your answers as decimals, to three places
< p
Answers
Answer:
[tex]\{0.559,0.641\}[/tex]
Step-by-step explanation:
[tex]\displaystyle CI_{95\%}=\frac{336}{560}\pm1.96\sqrt{\frac{\frac{336}{560}(1-\frac{336}{560})}{560}}\approx\{0.559,0.641\}[/tex]
In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1
through 43) and matching the number on the gold ball (1 through 34). If one ticket is purchased, what is the probability
of winning the jackpot?
Answers
The probability of winning the jackpot with one ticket is P ( A ) = 1/34
Given data ,
To calculate the probability of winning the jackpot in the lottery, we need to determine the total number of possible outcomes (the sample space) and the number of favorable outcomes (winning outcomes).
Total number of possible outcomes:
For the white balls, there are 43 numbers to choose from, and we need to select 5 distinct numbers in any order. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of options and r is the number of selections. In this case, we have 43 white balls and need to choose 5, so the number of possible outcomes for the white balls is:
C(43, 5) = 43! / (5! * (43 - 5)!) = 43! / (5! * 38!) = 43 * 42 * 41 * 40 * 39
For the gold ball, there are 34 numbers to choose from, and we need to select 1 number. So the number of possible outcomes for the gold ball is simply 34.
Therefore, the total number of possible outcomes is:
Total outcomes = (43 * 42 * 41 * 40 * 39) * 34
Number of favorable outcomes (winning outcomes):
To win the jackpot, we need to match all 5 distinct numbers from the white balls and the number on the gold ball. Since order doesn't matter for the white balls, we can use the combination formula again:
C(n, r) = n! / (r! * (n - r)!)
In this case, we have 43 white balls and need to choose 5, so the number of favorable outcomes for the white balls is:
C(43, 5) = 43! / (5! * (43 - 5)!) = 43 * 42 * 41 * 40 * 39
For the gold ball, there is only 1 winning number.
Therefore, the number of favorable outcomes is:
Favorable outcomes = (43 * 42 * 41 * 40 * 39) * 1
Probability of winning the jackpot:
The probability of winning the jackpot is the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Plugging in the values, we get:
Probability = [(43 * 42 * 41 * 40 * 39) * 1] / [(43 * 42 * 41 * 40 * 39) * 34]
Simplifying, we find:
Probability = 1 / 34
Hence , the probability of winning the jackpot with one ticket in this lottery is 1 in 34.
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can you find the surface area of the prism of 3.5ft,4.5ft,2ft
Answers
Answer:
Surface Area = 63.5 ft².
Step-by-step explanation:
Length: 3.5 ft
Width: 4.5 ft
Height: 2 ft.
Surface Area = 2(Area of Base) + (Perimeter of Base) × Height
Area of The Base:Area of Base = Length × Width
Area of Base = 3.5 ft × 4.5 ft = 15.75 ft²
Perimeter of The Base:Perimeter of Base = 2(Length) + 2(Width)
Perimeter of Base = 2(3.5 ft) + 2(4.5 ft) = 7 ft + 9 ft = 16 ft
Substitute these values into the surface area formula:
Surface Area = 2(Area of Base) + (Perimeter of Base) × Height
Surface Area = 2(15.75 ft²) + (16 ft) × (2 ft)
Surface Area = 31.5 ft² + 32 ft²
Surface Area = 63.5 ft²
Therefore, the surface area of the given prism with dimensions 3.5 ft, 4.5 ft, and 2 ft is 63.5 ft².
Quadrilateral A'B'C'D'is a translation of quadrilateral ABCD. What is the length
of B'C'?
A
60
A. 7 units
B. 6 units
OC. 4 units
D. 3 units
A'
D'
Answers
The length of B'C' from the given quadrilateral A'B'C'D' is 3 units. Therefore, option D is the correct answer.
A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Here, AB = A'B' = 7 units
AD = A'D'= 6 units
DC = D'C'= 4 units
BC = B'C' = 3 units
Therefore, option D is the correct answer.
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I need to know the percentage of drivers who are at least 45. Using the table in the picture.
Answers
The percentage of drivers who are at least 45 is 62%
How to determine the percentage of drivers who are at least 45.From the question, we have the following parameters that can be used in our computation:
The table of values
From the table, we have
Age 45 = 62 percentile
When represented properly
So, we have
Age 45 = 62%
This means that the percentage of drivers who are at least 45 is 62%
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HELP PLEASE 30 POINTS
Four transformations of the function f(x)=4x
are given below.
For each transformation, drag the expression that shows the result of that transformation into the box under it.
Answers
The expression that shows the result of that transformation are:
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
The given function is f(x) =4ˣ.
We have to find the transformations applied to the function f(x).
Graph transformation involves modifying an existing graph or graphed equation to create a different version of the original graph.
f(x) =4ˣ
We have to find 3f(x), f(3x), f(x+3) and f(x)+3.
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
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Determine the length of the missing side of the triangle. Round your answer to the
hundredths place.
Answers
Answer:
670
We can use the pythagorus theorum which says
The square of hypotenuse is equal to the square of perpendicular added to sq of base
Step-by-step explanation:
Use h2=p2+b2
H=6.708
Rounding to the hundredth place the answer is 670.8
Using Pythagoras Theorem (since the triangle is a right angled triangle)
[tex]( {hyp}^{2}) = ( {base}^{2} ) + ( {per}^{2} )[/tex]
[tex]( {hyp}^{2} ) = ( {3}^{2} ) + ( {6}^{2}) [/tex]
[tex]( {hyp}^{2} ) = 9 + 36[/tex]
[tex] {hyp}^{2} = 45[/tex]
Taking under root on both sides
[tex]hyp = 6.7[/tex]
Hence the missing side is 671
The figure above shows a store's supply-demand graph for coffee makers. If the store sells $600 worth of coffee makers, which of the following is a valid possible price for them?
A. $15
B. $30
C. $40
D. $55
Answers
The possible price for the items if the store sells $600 is (c) $40
How to determine the possible price for the items?From the question, we have the following parameters that can be used in our computation:
The supply-demand graph
If the store sells $600, then there is a supply worth of $600
The equation of the supply line is calculated as
y = mx + c
Where
c = y = 0
i.e. c = 100
So, we have
y = mx + 100
Using another point on the graph, we have
30m + 10 = 400
So, we have
m = 13
This means that
y = 13x + 100
For a supply of 600, we have
13x + 100 = 600
So, we have
13x = 500
Divide by 13
x = 38.4
Approximate
x = 40
Hence, the possible price for the items is (c) $40
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11. The height of a plant over 4 weeks is shown in the graph below.
Height of Plant (cm)
16
23
Week
What is the rate of growth of the plant, in centimeters per week?
A 2
B. 3
C. 8
D. 12
Answers
The rate of growth of the plant is 2 centimeters per week.
Calculate the change in height divided by the change in time (weeks) to find the plant's growth rate.
To calculate the rate of growth of the plant, we need to determine the change in height per week.
Given:
Initial height = 4 cm
Final height = 12 cm
Weeks = 4
To find the rate of growth, we can use the formula:
Rate of growth = (Final height - Initial height) / Weeks
Substituting the given values into the formula:
Rate of growth = (12 cm - 4 cm) / 4 weeks
Rate of growth = 8 cm / 4 weeks
Rate of growth = 2 cm/week
Therefore, the rate of growth of the plant is 2 centimeters per week.
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Mean and Mean Absolute Deviation-Quiz-Level F
The dot plot shows the number of students who attended the first five meetings of a school's
Math Club.
Find the mean of the data,
Mean: 9 students
At the next meeting of the club, there are
15 students, How does including this value
with the data affect the mean?
The mean
increases
from 9 to ?
students.
5 6 7 8 9 10 11 12 13
Number of Students
Answers
The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.
How to calculate the meanThe mean of the data is 9 students because there are 45 students total and 5 meetings.
When 15 students attend the next meeting, the mean increases to 10.5 students because there are now 60 students total and 6 meetings.
Mean of the first 5 meetings:
There are 45 students total.
There are 5 meetings.
Therefore, the mean is:
= 45 / 5
= 9 students.
There are 60 students total.
There are 6 meetings.
Therefore, the mean is:
= 60/6
= 10 students.
The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.
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What is the mode of this data set?
{4, 15, 6, 11, 7, 4, 3, 14}
Answers
Answer:
4
Step-by-step explanation:
A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)