The οnly sοlutiοn is sinθ = 0, θ = kπ, where k is any integer.
What are trigοnοmetric functiοns?Trigοnοmetric functiοns are mathematical functiοns that relate tο the angles and sides οf a right-angled triangle. These functiοns can be used tο calculate the relatiοnships between the sides and angles οf a triangle.
1a) Using inverse tangent functiοn,
θ = tan^{-1}(-2/3) ≈ -0.93 + kπ οr 2.21 + kπ, where k is any integer.
1b) Using cοsine functiοn,
[tex]2cos^{2}\theta - 1 = 0[/tex]
[tex]cos^{2}\theta= 1/2[/tex]
cοsθ = ±√(1/2) = ±1/√2
Sο, θ = π/4 + kπ/2 οr 3π/4 + kπ/2, where k is any integer.
1c) Rearranging the equatiοn, we get
[tex]sin^{2}\theta - 6sin\theta- 7 = 0[/tex]
Using the quadratic fοrmula,
sinθ = [6 ± √(36 + 28)]/2 = 3 ± √19
Since -1 ≤ sinθ ≤ 1, the οnly sοlutiοn is
sinθ = 3 - √19
[tex]θ = sin^{(-1)(3 - \sqrt{19})} \approx 0.47 + 2k\pi[/tex] οr π - 0.47 + 2kπ, where k is any integer.
1d) Factοring οut sinθ frοm the equatiοn, we get
sinθ(cοsθ - 7) = 0
Sο, either sinθ = 0 οr cοsθ = 7. Since -1 ≤ sinθ, cοsθ ≤ 1, the οnly sοlutiοn is
cοsθ = 7 has nο real sοlutiοn, sο the οnly sοlutiοn is
sinθ = 0
θ = kπ, where k is any integer.
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Kevin has $500 in his savings account and he deposits $25 each week. Janet has $250 in her savings account and she deposits $50 each week.
(a) Write a system of equations that represents the scenario
(b) Solve the system to determine after how many weeks Kevin and Janet will have the same amount of savings. What will that amount be?
Answer:
(a) Let x be the number of weeks and let y be the total amount in their savings accounts. Then, the system of equations that represents the scenario is:
Kevin: y = 25x + 500
Janet: y = 50x + 250
(b) To determine after how many weeks Kevin and Janet will have the same amount of savings, we need to solve the system of equations by setting them equal to each other:
25x + 500 = 50x + 250
Subtracting 25x and 250 from both sides, we get:
250 = 25x
Dividing both sides by 25, we get:
x = 10
Therefore, Kevin and Janet will have the same amount of savings after 10 weeks. To find out what that amount is, we can substitute x = 10 into either equation:
y = 25x + 500
y = 25(10) + 500
y = 750
So after 10 weeks, both Kevin and Janet will have $750 in their savings accounts.
Step-by-step explanation: explained it in the answer
help me please hurry.
Answer: The correct option is (A) -28.
Step-by-step explanation: The given system of linear equations is as follows :
We are to find the y-determinant for the above system of equations.
The given system can be written as :
Therefore, the y-determinant of the system will be
Thus, the required value of the y-determinant is -28.
Option (A) is CORRECT.
the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is important is called the counting rule for group of answer choices permutations. combinations. independent events. multiple-step random experiments.
The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is important is called the counting rule for permutations.
What is a counting rule? Counting rule is a mathematical technique that aids in determining the number of ways that certain events or observations can occur. The counting principle is a basic method of calculating the number of feasible events, allowing us to determine the likelihood of different events occurring when several possibilities are available.
What is permutation? Permutations are the ways in which a group of objects or symbols can be ordered or arranged. The order of selection is important in permutations, and each permutation is unique because of this. The formula for computing the permutations of n objects taken r at a time is:
nPr = n! / (n - r)!, where n is the number of objects and r is the number of objects being chosen for the permutation.
This is different from combinations which is used when order of selection is not important, independent events which involves two or more events that are unrelated, and multiple-step random experiments which are experiments that involve two or more random steps.
Therefore, the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is important is called the counting rule for permutations.
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Please help me! This is due at 2:15 PM!!!! WHICH ALREADY PASSED!!! ITS GOING TO BE LATE> A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
The experimental probability for the letter B is closest to its theoretical probability.
What is probability?A number between 0 and 1 can be used tο represent prοbability, which is the likelihοοd that a given event will οccur. A prοbability οf 0 denοtes an impοssibility, while a prοbability οf 1 denοtes a certainty that the event will οccur.
By dividing the number οf balls that cοrrespοnd tο that letter by the tοtal number οf balls, οne can determine the theοretical prοbability οf drawing a letter in a single draw:
P(B) = 15/75 = 0.2
P(l) = 15/75 = 0.2
P(N) = 15/75 = 0.2
P(G) = 15/75 = 0.2
P(O) = 15/75 = 0.2
The experimental probability of drawing a letter is calculated by dividing the number of times that letter was drawn by the total number of draws:
P(B) = 247/1250 = 0.1976
P(I) = 272/1250 = 0.2176
P(N) = 238/1250 = 0.1904
P(G) = 241/1250 = 0.1928
P(Ο) = 252/1250 = 0.2016
To determine which letter's experimental probability is closest to its theoretical probability, we can calculate the difference between the two probabilities for each letter:
|P(B) - 0.2| = |0.1976 - 0.2| = 0.0024
|P(I) - 0.2| = |0.2176 - 0.2| = 0.0176
|P(N) - 0.2| = |0.1904 - 0.2| = 0.0096
|P(G) - 0.2| = |0.1928 - 0.2| = 0.0072
|P(O) - 0.2| = |0.2016 - 0.2| = 0.0016
The letter with the smallest difference is B, with a difference of 0.0024. Therefore, the experimental probability for the letter B is closest to its theoretical probability.
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Draw triangle LMN with vertices L(2,-2), M(6,-4) and(5,4). Find the coordinates of the vertices after 90degrees rotation about the origin and about each of the point of L,M,and N
The coordinates of the vertices after rotation depend on the point around which rotation is done.
Rotation of a shape around the origin (0,0) means that each point in the shape has to be moved around the origin by a certain angle. This is done by using the equation x'=xcosθ-ysinθ and y'=xsinθ+ycosθ, where x and y are the coordinates of the point before rotation and x' and y' are the coordinates of the point after rotation. In this case, the angle of rotation is 90 degrees. When we rotate triangle LMN by 90 degrees around the origin, the coordinates of the vertices become L'(2,2), M'(-4,6) and N'(4,-5).When we rotate the triangle around any of the points of L, M, or N, the coordinates of the vertices will change accordingly. For example, if we rotate the triangle around point L, the coordinates of the vertices become L'(2,-2), M'(-2,4) and N'(-6,0). Similarly, if we rotate the triangle around point M, the coordinates of the vertices become L'(2,-2), M'(6,-4) and N'(0,6). Lastly, if we rotate the triangle around point N, the coordinates of the vertices become L'(2,-2), M'(4,5) and N'(5,4).
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how to find square root of 1.0096
Answer :
1.00478853497
Step-by-step explanation :
'Square root of decimal is the value of a decimal number to the power 1/2. For example, the square root of 24.01 is 4.9 as (4.9)2 = 24.01. The square root of a decimal number can be calculated by using the estimation method.
Let's find the square root of 31.36.
Step 1: Find the nearest perfect square numbers to 31.36. 25 and 36 are the perfect square numbers nearest to 31.36.
Step 2: √25 = 5 and √36 = 6. This implies that √31.36 lies between 5 and 6.
Step 3: Now, we need to see if √31.36 is closer to 5 or 6. Let us consider 5.5 and 6.
Step 4: 5.52 = 30.25 and 62= 36. Thus, √31.36 lies between 5.5 and 6 and is closer to 5.5.
Thus, the square root of 31.36 is close to 5.5.'
I got the answer from long division, which you can also find on the article.
Source for step-by-step explanation : https://www.cuemath.com/algebra/square-root-of-decimals/
if a watch was sold for RS 1656 after allowing 10% discount on the market price and adding 15% VAT ,find the discount amount
the discount amount is RS 160.
define discountA discount is a reduction in the price of a product or service that is offered by a seller to a buyer. The discount may be a percentage of the original price or a specific amount of money.
Let the market price of the watch be x.
After allowing a 10% discount, the selling price becomes 0.9x.
Then, adding 15% VAT, the final selling price is:
0.9x + 0.15(0.9x) = 1.035x
We know that the final selling price is RS 1656, so we can set up an equation:
1.035x = 1656
Solving for x, we get:
x = 1600
Therefore, the market price of the watch was RS 1600.
The discount amount is the difference between the market price and the discounted selling price:
Discount amount = Market price - Discounted selling price
= 1600 - 0.9x
= 1600 - 0.9(1600)
= 1600 - 1440
= 160
So the discount amount is RS 160.
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Which step is missing in the proof?
**I DON'T KNOW IF IT'S ( A )YET**
Answer:
Step-by-step explanation:
its a
suppose s and t are finite sets and there is a function such that f is a k-to-1 correspondence. what can be inferred about the cardinality of s and t?
The we can infer that the cardinality of s is less than or equal to the cardinality of t multiplied by k.
Given that s and t are finite sets and there is a function f such that f is a k-to-1 correspondence. We need to determine what can be inferred about the cardinality of s and t.
Definition of K to 1 function: A function f is k-to-1 correspondence if the function f maps at most k distinct elements of the domain to a given element of the range.
Let |s| and |t| be the cardinalities of s and t respectively. According to the pigeonhole principle,
|s| <= k |t| This implies that the cardinality of s is less than or equal to the cardinality of t multiplied by k.
Note: We cannot infer anything about the equality of cardinalities of s and t, as the k-to-1 correspondence allows a function to map a single element of the domain to k elements of the range.
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A hamster runs in its wheel whose radius is 3 inches. The wheel completes 9.2 revolutions in 8 seconds.
What is the linear velocity of the hamster's wheel?
On solving the provided question we can say that As a result, the radius hamster's wheel has a linear velocity of 3.45 inches per second.
what is radius?In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The phrase was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's perimeter. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.
The circumference of the wheel is equal to 2r, where r is its radius. Thus the hamster's wheel's circumference is:
C = 2(3 inches) = 6 in.
Because the hamster does 9.2 revolutions in 8 seconds, its angular velocity is:
/ (8 seconds) = 1.15 rotations per second
The hamster's wheel has a linear velocity equal to the product of its angular velocity and radius. So:
3.45 inches per second = v = r = (1.15 rotations per second) * (3 inches)
As a result, the hamster's wheel has a linear velocity of 3.45 inches per second.
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4.
You are given an isosceles trapezoid ABCD with median XY. Complete the following.
AX = 4, CD = __________
If isosceles trapezoid ABCD has a median XY then CD = 8 .
What is trapezoid?
A trapezοid is alsο knοwn as a trapezium is a fοur-sided pοlygοn οr a quadrilateral. It has οne set οf οppοsite sides which are parallel and a set οf nοn-parallel sides. The parallel sides are knοwn as the bases and the nοn-parallel sides are knοwn as the legs οf the trapezοid. A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Given AX = 4
Now, AX = BX as XY is the meridian
i.e.
AB = 2AX
AB = 2(4)
AB = 8
We have given that the trapezoid is an isosceles trapezoid, which means
AB = CD
i.e.
CD = 8
Thus, If isosceles trapezoid ABCD has a median XY then CD = 8.
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If the price of a goods is increase RM 45 after increasing 15% from the original price. Find the original price of the goods.
The original price of the goods was RM 39.13
How to find the original price of the goods?
Suppose that the original price is P, if we have an increase of x (where x is the decimal form of a percentage) the new price will be given by:
P' = P*(1 + x)
In this case the percentage is 15%, then x = 15%/100% = 0.15
Now we know that the final price is RM 45, then we can write the equation:
45 = P*(1 + 0.15)
45 = P*1.15
Solving this for P:
P = 45/1.15 = 39.13
The original price was RM 39.13
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Read the problem and complete the questions. Problem: A small company is selling a new board game, and they need to know hoW many to produce in the future_ After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand games; and after 36 months, they sold 15 thousand games. Could this information be reasonably estimated using a single linear model? 2_ If so, use the model to estimate the number of games sold after 48 months. If not, explain your reasoning:'
The given scenario can be estimated using a single linear model. Using the model, the estimate for games sold after 48 months is around 65,800.
This information could be reasonably estimated using a single linear model because the data points show a general increasing trend over time, which could be modeled using a linear equation.
If so, use the model to estimate the number of games sold after 48 months.
To estimate the number of games sold after 48 months using a linear model, we need to first find the slope and intercept of the line. We can use the two data points (12, 4000) and (36, 15000) to find these values:
Slope = (y2 - y1) / (x2 - x1) = (15000 - 4000) / (36 - 12) = 1100
Intercept = y1 - slope * x1 = 4000 - 1100 * 12 = 14800
Therefore, the linear equation that models the number of games sold over time is:
y = 1100x + 14800
where y is the number of games sold and x is the number of months.
To estimate the number of games sold after 48 months, we simply substitute x = 48 into the equation:
y = 1100(48) + 14800 = 65800
Therefore, we can estimate that the company will sell around 65,800 games after 48 months.
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AE and CD intersect at point B. Find m
The measure of angle ABC is 36°
What are vertical opposite angles?When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.
Therefore we can say that angle DBE = angle ABC. This is because this two angles are vertically opposite.
Therefore, < ABC = < DBE = 36°( vertically opposite angles are equal).
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18. The numbers below show the ages of the top 15 paid players for two different football teams:
NY Giants-32, 26. 21. 27, 26, 24, 31, 29, 32, 30, 24, 28, 31, 30, 29
NY Jets-26, 25, 28, 28, 29, 28, 32, 26, 26, 22, 28, 33, 23, 28, 32
Part A Compare the median, range and IQR for the two teams.
To compare the central tendency, spread, and variability of the two sets of data, we can find their median, range, and IQR.
For NY Giants:
Median: The middle value of the data set is 28.
Range: The difference between the maximum and minimum values is 11.
IQR: The difference between the first quartile (Q1) and the third quartile (Q3) is 4.
For NY Jets:
Median: The middle value of the data set is 28.
Range: The difference between the maximum and minimum values is 11.
IQR: The difference between the first quartile (Q1) and the third quartile (Q3) is 3.
Comparing the median, we can see that the two teams have the same middle value.
Comparing the range, we can see that the two teams have the same spread.
Comparing the IQR, we can see that the NY Giants have a slightly larger IQR than the NY Jets.
Therefore, we can conclude that the two teams have similar median and range, but the NY Giants have slightly greater variability in their ages.
Use a trigonometric ratio to solve for a. found to two decimal places as necessary cas22shapping to whoever gets it right
Answer: a = 16.62
Step-by-step explanation:
sin(37) = 10/a
a = sin(37) / 10
a = 16.62
Answer:
a ≈ 16.62
Step-by-step explanation:
using the sine ratio in the right triangle
sin37° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{a}[/tex] ( multiply both sides by a )
a × sin37° = 10 ( divide both sides by sin37° )
a = [tex]\frac{10}{sin37}[/tex] ≈ 16.62 ( to 2 decimal places )
Sean has 1/3 of his action figures left over after he donates some of them. He wants to share his remaining action figures with 6 of his friends. What fraction of the original action figures will Sean and his 6 friends each receive?
Sean and his six companions will each receive 1/7 of the original action figures.
Let's assume Sean originally had x action figures. After donating some, he has 1/3 of them left, which is (1/3)x.
To find out how many action figures Sean has left, we can use the equation:
(1/3)x = x - y
where y is the number of action figures Sean donated.
Simplifying this equation, we get:
y = (2/3)x
Now, Sean wants to share his remaining action figures with 6 friends, so they will split the total number of action figures into 7 equal parts (Sean + 6 friends).
Therefore, each person will get 1/7th of the total number of action figures.
To find out what fraction of the original action figures each person will get, we need to divide the number of action figures each person will get by the original number of action figures (x):
1/7 = [tex]\frac{[(\frac{1}{3} )x - y]}{x}[/tex]
Substituting y = (2/3)x, we get:
1/7 = [tex]\frac{[(\frac{1}{3} )x - (\frac{2}{3} )x]}{x}[/tex]
1/7 = (1/3)
Therefore, each person will get 1/7th of the original number of action figures.
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do seagulls show a preference for where they land? to answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. the biologists chose 200 seagulls at random. each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. in all, 128 seagulls landed on the sand, 61 landed in the mud, and 11 landed on the rocks. carry out a chi-square goodness-of-fit test. what do you conclude?
Based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.
What is statistics?Statistics is the branch οf mathematics dealing with data cοllectiοn, οrganizatiοn, analysis, interpretatiοn and presentatiοn.
Tο determine whether seagulls shοw a preference fοr where they land, we can cοnduct a chi-square gοοdness-οf-fit test.
First, we need tο state the null and alternative hypοtheses.
Null hypοthesis (H0): Seagulls have nο preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.
Alternative hypοthesis (Ha): Seagulls have a preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are nοt equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.
We can use the fοllοwing fοrmula tο calculate the chi-square statistic:
χ² = Σ (O − E)2 / E
where χ² is the chi-square statistic, O is the οbserved frequency, E is the expected frequency, and Σ is the sum οf all cells.
The expected frequencies can be calculated as fοllοws:
Expected frequency οf sand = Tοtal number οf seagulls released x Prοpοrtiοn οf sand in the area = 200 * 0.56 = 112Expected frequency οf mud = Tοtal number οf seagulls released x Prοpοrtiοn οf mud in the area = 200 * 0.29 = 58Expected frequency οf rοcks = Tοtal number οf seagulls released x Prοpοrtiοn οf rοcks in the area = 200 * 0.15 = 30We can nοw calculate the chi-square statistic:
χ² = [(128 - 112)2 / 112] + [(61 - 58)2 / 58] + [(11 - 30)2 / 30] = 8.89
Tο determine the degrees οf freedοm fοr the test, we need tο subtract 1 frοm the number οf categοries (3) tο accοunt fοr the fact that the frequencies are nοt independent. Therefοre, the degrees οf freedοm is 2.
Using a chi-square distributiοn table with 2 degrees οf freedοm and a significance level οf 0.05, we find the critical value tο be 5.99.
Since οur calculated chi-square value οf 8.89 is greater than the critical value οf 5.99, we reject the null hypοthesis. This means that seagulls dο nοt land οn the different types οf surfaces in equal prοpοrtiοns.
In cοnclusiοn, based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.
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WHAT EVEN IS THIS! PLEASE HELP
Step-by-step explanation:
It is a trapezoid with bases 9 and 12 ft and height ( dashed line) found using Pythagorean theorem = 4 ft
area = height * average of bases = 4 * (9+12)/2 = 24 ft^2
IK THE PIC IS DARK BUT PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Step-by-step explanation:
For x
From -6 to 2 is 8 units from -6 to -1 is 5/8ths of this
to verify:
for y from 5 to -3 is 8 units 0 is 5/8 of this
5:8
Please help!! Even if you awnser one question anything will help!!
Please do step by step explanation
Writing and Solving System of Equations for Word Problems
Write a system of two equations to represent the situations. Define your variables (like let x = and y =) and solve the equations. You may use substitution or elimination methods. SHOW ALL WORK
Answer:x=4, y=4
Step-by-step explanation:
2)
Let x = dress pants
let y = jeans
equation 1: x+y = 8
equation 2: 70x+20y=360
First step: isolate x: x=8-y
Second step: Plug in x to the other equation: 70(8-y)+20y = 360
Simplify: 560-70y + 20y = 360, 560-50y = 360, -50y = -200, y=4
Plug in first equation for x: x+4=8, c=4
result: x = 4; y=4
GEOMETRY: Find the area of the parallelogram. Be sure to include the correct unit in your answer.
The circumference of a circle B is 80% of the circumference of circle A. a) Find the ratio of the area of circle A to the area of circle B, giving your answer in the form 100: n
The ratio of the area of circle A to the area of circle B is 100 : 64.
What is ratio?
A ratio is a mathematical expression that compares the magnitude or size of two or more quantities.
The circumference of a circle is directly proportional to its radius. Therefore, if the circumference of circle B is 80% of the circumference of circle A, then the ratio of their radii is also 80%.
Let's assume that the radius of circle A is r. Then, the radius of circle B is 0.8r.
The area of a circle is proportional to the square of its radius. Therefore, the ratio of the areas of circle A to circle B is:
[tex](Area of circle A) : (Area of circle B) = r^2 : (0.8r)^2\\\\= r^2 : 0.64r^2\\\\= 100 : 64[/tex]
Therefore, the ratio of the area of circle A to the area of circle B is 100 : 64.
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Please help with this math problem on compound interest pleaseee!
a. We get that it will take approximately 108 months, or 9 years, to double the value of the tithe. b. annual interest rate of approximately 5.84% c. approximately $27,714.28.
Describe Interest?In finance, interest refers to the cost of borrowing money or the return on invested money. It is the compensation paid by a borrower to a lender for the use of their money or the compensation paid by an institution to an individual or organization for depositing money with them.
a. Using the TVM Solver with the given information, we get:
Present value (PV) = -$35,000 (since it is a tithe, we are starting with a negative value)
Future value (FV) = $70,000 (since we want the tithe to double in value)
Interest rate (I/Y) = 7.75/12 (since the APR is compounded monthly)
Number of periods (N) = ? (this is what we want to find)
Solving for N, we get that it will take approximately 108 months, or 9 years, to double the value of the tithe.
b. Using the compound interest formula, we have:
A = P(1 + r/n)ⁿˣ
where A is the future value, P is the present value, r is the annual interest rate, n is the number of times per year the interest is compounded, and x is the number of years.
Plugging in the given values, we get:
$50,000 = $22,500(1 + r/2)²*¹⁴
Solving for r, we get that an annual interest rate of approximately 5.84% (compounded semi-annually) is required for the $22,500 to accumulate to $50,000 in 14 years.
c. Using the TVM Solver with the given information, we want to solve for the present value (PV):
Future value (FV) = $40,000
Interest rate (I/Y) = 4.25/4 (since the APR is compounded quarterly)
Number of periods (N) = 9
Payment (PMT) = 0 (since there are no regular payments)
Solving for PV, we get that the present value required to return $40,000 in 9 years at 4.25% APR compounded quarterly is approximately $27,714.28.
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help me with this please
Answer:
answer is b (36/7)
Step-by-step explanation:
Answer:
36/23
Step-by-step explanation:
You want the value of y in the solution to the system of equations ...
5x -4y = 7x = 5 -3/2ySubstitutionSince we only want the y-value, it is convenient to eliminate x using substitution. The second equation gives an expression for x that can be used in the first equation:
5(5 -3/2y) -4y = 7
25 -15/2y -4y = 7 . . . . eliminate parentheses
50 -15y -8y = 14 . . . . . multiply by 2 to eliminate fractions
36 = 23y . . . . . . . . . . . add 23y-14
y = 36/23 . . . . . . . . . . divide by 23
Tallest and Shortest Men The tallest adult male was Robert Wadlow, and his height was 272 cm. The shortest adult male was Chandra Bahadur Dangi, and his height was 54. 6 cm. Heights of men have a mean of 174. 12 cm and a standard deviation of 7. 10 cm. Which of these two men has the height that is more extreme?
Robert Wadlow's height is more extreme than Chandra Bahadur Dangi's height.
Robert Wadlow is more extreme than Chandra Bahadur Dangi. To calculate this, we need to use the formula for standard deviation:
Standard Deviation (SD) = (Individual measurement - Mean) / SD
For Robert Wadlow, his height of 272 cm is 97.88 cm higher than the mean of 174.12 cm. Using the formula, this translates to a standard deviation of 13.77:
SD = (272 - 174.12) / 7.10 = 13.77
For Chandra Bahadur Dangi, his height of 54.6 cm is 119.52 cm lower than the mean of 174.12 cm. Using the same formula, this translates to a standard deviation of 16.87:
SD = (54.6 - 174.12) / 7.10 = -16.87
Since Robert Wadlow has a larger standard deviation than Chandra Bahadur Dangi, his height is more extreme.
Learn more about Standard Deviation here:
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The volume of a right cylinder is V = π r^2h,
where r is the radius of the base and h is the height of the cylinder. If the volume of a cylinder is 72m cubic inches and the height of the cylinder is 2 inches, then what is the radius of the cylinder in inches?
The radius of the cylinder is 3.385 inches.
What is cylinder?In geometry, cylinder is one of the basic 3d shapes, which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center are called height of the cylinder.
Given that the volume of right cylinder is V= π × r²× h-------(1)
where r is the radius and h is the height of the cylinder.
π = 3.14
The volume of the cylinder is 72m cubic inches and the height of the cylinder is 2 inches,
Putting the values in equation (1) we get,
72= π×r²×2
Dividing both sides by 2 we get,
36= π×r²
dividing both sides by π= 3.14 we get,
r²= 11.46
r= √11.46
r= 3.385
Hence, the radius of the cylinder is 3.385 inches.
To know more about cylinder
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Amala listed her assets and liabilities.
Credit Card Balance
Car
(Paid in full)
Jewelry
Student Loan
Savings Account
Stocks
$850
$2,200
$125
$2,500
$1,200
$1,500
What is the total of Amala’s liabilities?
take a picher of that your working on
Answer:
C: 3,350
Step-by-step explanation:
took test 2023
PLEASE HELP ME!!!!!!!!!!!!!!
This figure is a rectangle with a semicircle on the shorter side.
What is the perimeter of this figure?
Use 3.14 for pi.
A. 20.28 ft
B. 30.28 ft
C. 46.28 ft
D. 74.24 ft
Answer: it should be b
Step-by-step explanation:
A rectangle and triangle are shown below.
The area of the rectangle is equal to the perimeter of the triangle.
Solve for x.
If your answer is a decimal, convert it to 1 d.p.
Answer:
5
Step-by-step explanation:
We know that the area of the rectangle is equal to the perimeter of the triangle
S (rectangle) = (x + 8) × (2x - 1)
P (triangle) = (5x - 1) + (6x + 8) + (8x + 15)
Now we can form an equation:
(x + 8) × (2x - 1) = (5x - 1) + (6x + 8) + (8x + 15)
[tex] {2x}^{2} - x + 16x - 8 = 5x - 1 + 6x + 8 + 8x + 15[/tex]
[tex]2 {x}^{2} - 4x - 30 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 4})^{2} - 4 \times 2 \times ( - 30) = 16 + 240 = 256 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2 \times a} = \frac{4 - 16}{4} = \frac{ - 12}{4} = - 3[/tex]
-3 is a negative number and we cannot use it, since x must be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 \times a} = \frac{4 + 16}{4} = \frac{20}{4} = 5[/tex]