The distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The the distance can be observed to be of the side of a right triangle with the hypotenuse as the radius of the circle and the base side half of the chord, if x is used to represent the distance of the chord from the centre of the circle.
so by Pythagoras rule we can write:
12² = x² + 8²
144 = x² + 64
x² = 144 - 64 {collect like terms}
x² = 80
x = √80 {take square root of both sides}
x = 8.9443
Therefore, the distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.
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Holly's height decreased by 21 is 62.
Use the variable h to represent Holly's height.
The algebraic expression is h - 21 = 62
How to represent as an algebraic expressionIf we let "h" be Holly's original height,
The phrase "Holly's height decreased by 21 is 62" can be translated into an algebraic expression as:
h - 21 = 62
This equation represents the relationship between Holly's original height and her current height, after a decrease of 21 units.
We can solve for h by adding 21 to both sides of the equation:
h - 21 + 21 = 62 + 21
h = 83
Hence, Holly's original height was 83 units.
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-12,1 and x,7 when m = 1/8
The x has a value of 36. The line's two points are (-12, 1) and (36, 7).
The purpose of slope calculation?The slope of a line frequently represents the steepness and direction of the line. The slope of a straight line between the two locations, (x1,y1) and (x2,y2), can be easily determined by calculating the difference between their coordinates.
We can apply the slope formula to determine the value of x:
m is the slope and (x1, y1) and (x2, y2) are two points on the line, with m = (y2 - y1) / (x2 - x1).
We are given the point (x1, y1) = (-12, 1) and the slope m = 1/8. We are also given the y-coordinate of the other point as y2 = 7.
Plugging in the known values, we get:
1/8 = (7 - 1) / (x - (-12))
Simplifying and solving for x, we get:
1/8 = 6 / (x + 12)
1 = 48 / (x + 12)
x + 12 = 48
x = 36
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Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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A right triangle has acute angles c and d . If c=15/8 and sin d=8/17, what are cos d and cos c?
The value of the right triangle cos d = 15/17 and cos c = 8/17.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given that, the value of tan c = 15/8 and the value of sin d = 8/17.
From the trigonometric functions we can conclude that:
Opposite side to c = 15
Adjacent side to c = 8
Hypotenuse = 17
Opposite side to d = 8
Adjacent side to d = 15
The values of cos d is:
cos d = Adjacent side to d / Hypotenuse = 15/17
cos c = Adjacent side to c / Hypotenuse = 8/17
Hence the value of the right triangle cos d = 15/17 and cos c = 8/17.
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How many solutions does this system have?
Answers:
None
1
2
3
Infinite
A bag contains 2 red marbles and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? Write your answer as a fraction.
The probability of getting both the marbles to be red will be 4/25.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.
Probability = Number of favorable outcomes / Number of samples
Given that two red and three black marbles are in a bag. If Abby takes a marble out of the bag without looking, puts it back, and then draws another marble.
The probability of getting red in the first draw,
P = 2 / 5
Now the marble is returned and again the probability of getting the red marble is,
P = 2 / 5
The probability of getting both the marbles red will be,
Pb = ( 2/ 5 ) x ( 2 / 5 )
Pb = 4 / 25
Therefore, there is a 4/25 chance that both marbles will be red.
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Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.\dfrac{8x}{x^2-49}+\dfrac{5}{x^2-4x-21}= x 2−498x + x 2−4x−215 =start fraction, 8, x, divided by, x, squared, minus, 49, end fraction, plus, start fraction, 5, divided by, x, squared, minus, 4, x, minus, 21, end fraction, equals
The simplified expression after factoring numerator and denominator is (x + 7) / x.
We can start by factoring the numerator and denominator of the first fraction:
x^2 - 49 = (x + 7)(x - 7)
The denominator can also be factored using the quadratic formula or by factoring as a product of two binomials:
x^2 - 4x - 21 = (x - 7)(x + 3)
So, the first fraction can be simplified as:
(x + 7)(x - 7)/[(x - 7)(x + 3)]
We can cancel out the (x - 7) factor in the numerator and denominator, leaving:
(x + 7)/(x + 3)
Next, we can simplify the second fraction by canceling out the common factor of (x + 3) in both the numerator and denominator:
(x + 3)/x
Putting it all together, we get:
[(x + 7)/(x + 3)] * [(x + 3)/x] = x + 7 / x
Therefore, the simplified expression is (x + 7) / x.
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____The given question is incorrect, the correct question is given below:
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
Simplify (x^2-49)/(x^2-4x-21)*(x+3)/x
A person on a moving sidewalk travels 28 feet in 7 seconds. The moving sidewalk has a length of 200 feet. How long will it take to move from one end to the other?
It will take 50 seconds for the person to travel from one end to the other at the current speed.
How long will it take to move from one end to the other?
We know that the person travels 28 feet in 7 seconds, remember that speed is defined as the quotient between distance and time, then the person's speed is:
s = 28ft/7s = 4ft/s
Now we want to find the time T that it takes for the person to travel the 200 feet of the sidewalk, then we need to solve:
(4ft/s)*T = 200ft
T= 200ft/(4 ft/s) = 50s
It takes 50 seconds.
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(a) without adding new vertices, add a single edge to the graph so that the new graph will have an euler path. which vertices does your new edge connect?
To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.
In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.
To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.
Let's consider a graph:
A
/ \
B---C
/ \ / \
D---E---F
In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.
A
/ \
B---C
/ \ / \
D---E---F
Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.
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if we have four variables, then how many equations will we have in our system of linear equations? 5 2 3
For four variables the required number of system of linear equations are at least option d. 4 equations.
Variable is represented by small alphabets : a , b, x, y , z, m , n ... so on.System of linear equations are set of equation relating variables with degree one. To solve the system of linear equations we need to have number of equations same as the number of variables.If there are two variables then we need to have minimum two system of linear equations .If there are n variables then there should be n system of linear equations.Therefore, if there are four variables in the system of linear equations then we should have option d. 4 equations.
The above question is incomplete , the complete question is:
If we have four variables, then how many equations will we have in our system of linear equations?
a. 5 b. 2 c. 3 d. 4
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There are 28 students in a class.
13 of the students are boys.
Two students from the class are chosen at random.
a) If the first person chosen is a boy, what is the probability that
the second person chosen is also a boy?
Give your answer as a fraction.
b) What is the probability that both students chosen are girls?
Give your answer as a fraction.
a) The probability that the second person chosen is also a boy is; 13/28
b) The probability that both students chosen are girls is; 5/18
How to find the probability of selection?The parameters given in the question are;
Total number of students in the class = 28 students
Number of boys in class = 13 students
Number of girls = 28 - 13 = 15 students
a) Probability of the first student being selected as a boy is;
P(First is boy) = 13/28
b) The probability that both students chosen are girls is;
P(both girls) = (15/28) * (14/27) = 5/18
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do you believe that this conjectures "all numbers coming from the question p=n²-n+41 are prime numbers"?
Answer: No
Step-by-step explanation:
Valid only for numbers less than 40.
P(40) = 412 which is not a prime number
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
Answer:
the iqr is the best measure of variability
The IQR is the best measure of variability, and it equals 4.
Option C is the correct answer.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
The appropriate measure of variability for the data is the interquartile range (IQR), which is the range of the middle 50% of the data.
In other words, it is the difference between the third quartile (Q3) and the first quartile (Q1).
From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.
This means that Q1 is 17 and Q3 is 21.
The IQR is:
IQR = Q3 - Q1 = 21 - 17 = 4
Thus,
The IQR is the best measure of variability, and it equals 4.
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find the value of x y and z
The values of x, y and z are;
x. x = 60° y = 55°
xi. x = 68° y = 56° z = 56°
xiii. x = 40° y = 50°
xiv. x = 40° y = 50°
What is a Triangle?A triangle is a 3-sided polygon that has three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle that always equals 180 degrees. This property is called angle sum property of triangle.
x. x = 60° (corresponding angles are equal)
y + 65° + 60° = 180° (Sum of angles in a triangle equals 180°)
y + 125° = 180°
y = 180° - 125°
y = 55°
xi. y = 56° (corresponding angles are equal)
y = z = 56° (angles in equal sides of a triangle are equal)
x + 56° + 56° = 180° (Sum of angles in a triangle equals 180°)
x + 112° = 180°
x = 180° - 112°
x = 68°
xiii. x + 140° = 180° (sum of angles on a straight line equals 180°)
x = 180° - 140°
x = 40°
y + 90° + 40° = 180° (sum of angles in a triangle equals 180°)
y + 130° = 180°
y = 180° - 130°
y = 50°
xiv. y + 130° = 180° (sum of angles on a straight line equals 180°)
y = 180° - 130°
y = 50°
x + 90° + 50° = 180° (sum of angles in a triangle equals 180°)
x + 140° = 180°
x = 180° - 140°
x = 40°
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Perform the operation and simplify the resulting fraction: 7/3a - 8/5 + 4/15a
After solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
What are fractions?A fraction in mathematics is a number that is stated as a percentage, such as 1/2 or 2/3.
The number on top denotes the component of the unit under consideration, while the number at the bottom indicates the total number of parts that make up one unit.
An element of a whole is a fraction.
The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
So, we have the operations:
7/3a - 8/5 + 4/15a
Now, solve as follows:
7/3a - 8/5 + 4/15a
7/3a + 4/15a - 8/5
7*5 + 4 /15a - 8/5
39/15a - 8/5
Therefore, after solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
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Four children are playing a card game. The chart shows the number of cards each child has in his or her stack.
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Which is equivalent to Mike’s portion of the total number of cards?
A.) 2/25
B.) 16%
C.) 8/25
D.) 80%
(PLEASE EXPLAIN HOW YOU GOT THIS ANSWER)
The requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
From the given data,
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Total cards = 50
Now equivalent to Mike’s portion of the total number of cards is given as ,
= Mike cards/total card
= 8 / 50 × 100%
= 4/25×400%
= 16%
Thus, the requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
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a person rolls a standard six-sided die 10 times. in how many ways can he get 6 fives, 3 ones, and 1 two?
There are 840 ways for the person to get 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die.
To calculate the number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die, we can use the formula for combinations with repetition.
The number of ways to choose 6 rolls to be fives out of 10 is given by the combination formula:
C(10, 6) = 10! / (6! * (10 - 6)!) = 210
Similarly, the number of ways to choose 3 rolls to be ones out of the remaining 4 rolls is:
C(4, 3) = 4! / (3! * (4 - 3)!) = 4
Finally, there is only one way to choose the remaining roll to be a two.
Therefore, the total number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die is:
210 * 4 * 1 = 840.
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FIND THE PERIMETER AND AREA OF THE EQUILATERAL TRIANGLE
The area of an equilateral triangle is 16√3 m² and the perimeter of an equilateral triangle is 24 m.
What is area of an equilateral triangle?In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4 ×a².
From the given figure, side of the equilateral triangle is 8 m.
Now, area of an equilateral triangle is
√3/4 ×8²
= √3/4 ×64
= 16√3 m²
The perimeter of an equilateral triangle is 3a.
Now, the perimeter is 3×8
= 24 m
Therefore, the area of an equilateral triangle is 16√3 m².
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96 Vistors in 6 Hours. How many visitors per hour?
Answer:
16 visitors per hour
Step-by-step explanation:
96/6 = 16
John wants to have 600 copies. His local print shop charges $10 for the First 200 copies and $15 for every additional 100 copies
Part A: How much will the 600 copies cost, including a sale tax of 6%?
Part B: If the number of sets of 100 is represented by x, write an equation to express the cost, y.
Part C: Use the equation to determine the cost of 900 copies. Include the 6% sales tax in the total final cost.
The cost of 600 copies is $90.10
The cost of 900 copies is $137.80.
The equation that expresses cost is y = 1.06 x ($10 + $15x)
What is the equation that expresses cost?The equation that represents the information in the question is:
Total cost = 1 + sales tax x [cost of the first 100 copies + (x x cost of every additional 100 copies)]
y = 1.06 x ($10 + $15x)
Cost of 600 copies:
x = (600 - 100) / 100 = 500 / 100 = 5
y = (1 + 6/100) x [$10 + (5 x $15)]
y = 1.06 x [$10 + $75)
y = 1.06 x $85
y = $90.10
Cost of 900 copies:
x = (900 - 100) / 100 = 800 / 100 = 8
y = (1 + 6/100) x [$10 + (8 x $15)]
y = 1.06 x [$10 + $120)
y = 1.06 x $130
y = $137.80
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Solve the word problem below. Enter your answer in simplest terms, using the
slash (/) to represent the fraction bar.
A recipe for a soup calls for 2/4 cup of chopped onion and 1/6 cup of chopped
celery. What is the total amount of celery and onion needed for the soup
Answer:
2/3 cups
Step-by-step explanation:
The recipe calls for 2/4 cup of onion and 1/6 cup of celery. To find the total, we need to add the two fractions together; the amount of onions(2/4 cup or 1/2 a cup if simplified), and the amount of celery(1/6). To do this, we need to find a common denominator. We can do this buy finding a common multiple between 2 and 6.
Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 6: 6, 12, 18, 24, 30...
A common multiple is 6. 1/2x3/3=3/6 <--- an equivalent fraction of 1/2
Now both fractions have the same denominator:
Onions: 3/6
Celery: 1/6
3/6+1/6 = 4/6
4/6 simplifies to 2/3.
The total amount of celery and onion need for the soup is 2/3 cup
Answer:
2/3 cups
Step-by-step explanation:
read the story. clara snacked on a mix of almonds and pecans. she ate 3 almonds for every 1 pecan. pick the diagram that models the ratio in the story. if clara ate 10 more almonds than pecans, how many nuts did she eat altogether?
In all together, Clara ate 20 nuts.
A system of equations is a set of one or more equations involving a number of variables.
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.
Let the number of pecans be x and the number of almonds is y.
We can write the system of equations as:
y = 3x
y = x + 10
Equating the value of {y}, we get -
3x = x + 10
2x = 10
x = 5 ...(1)
y = x + 10 = 15
y = 15 ...(2)
x + y = 15 + 5 = 20
Therefore, in together, Clara ate 20 nuts.
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Triangle JGR is similar to triangle MST. Which
statement is not always true?
A. LJ LM
C. LR LT
B. LG LT
D. LG LS
The angle corresponding to each other of the different triangles are equal. The correct option is D.
What is a similar triangle?"Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion ".
Here given, ΔJGR is similar to a triangle ΔMST
So, from the definition of a similar triangle,
angle J ≅ angle M
angle G ≅ angle S
angle R ≅ angle T
Hence, option D is correct.
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What type of angle are these?
Answer:
alternate exterior angles
Step-by-step explanation:
congruent alternete exterior angles
Simplify.
Rewrite the expression in the form 8n.
(8−8)(8³) =
The above expression in terms of 8n can be written as 8(0).
What is expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.
We are given a an expression (8-8)(8³)
Now the first bracket after simplifying we get an answer is 0.
Hence the expression can be given in the form of 8(n) as 8(0)
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Can anybody answer the question I attached?
Answer:
36 bottles
Step-by-step explanation:
You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.
ProfitThe profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.
profit = selling price - purchase price
profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle
BottlesTo make a profit of $120, you need n bottles such that ...
(10/3)n = 120
n = 36 . . . . . . . . . multiply by 3/10
The club needs to buy, paint, and sell 36 bottles to raise $120.
Keisha must choose a shirt and a pair of pants for today's outfit. She has 4 shirts and 2 pairs of pants to choose from. How many different outfits can she make?
answer: 12
explanation:
the relationship between the amount of time a basketball player spent practicing the day before a game and the number of points he scored in the game is graphed on the scatter plot shown. scatter plot titled basketball players, with the x axis labeled time practicing in minutes and the y axis labeled points scored with points at 0 comma 10, 10 comma 15, 15 comma 18, 25 comma 25, 30 comma 28, 30 comma 30, 45 comma 35, 70 comma 40, 70 comma 45, 80 comma 45, 90 comma 50, and 120 comma 60 describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
By examining the shape and degree of association on the scatter plot, we can gain insights into the nature of the relationship between the variables and make predictions about their behavior in the future.
A scatter plot is a graphical representation of a set of data that shows the relationship between two variables.
The type of association between the two variables can be identified by the shape of the scatter plot. If the points on the plot form a linear pattern, then the association is said to be linear. If the points on the plot form a curved pattern, then the association is said to be nonlinear.
The degree of association between the two variables can be determined by the strength of the correlation coefficient, which is a measure of how closely the points on the scatter plot follow a linear pattern. The correlation coefficient ranges from -1 to 1, where a correlation coefficient of 1 indicates a perfect positive linear association, a correlation coefficient of -1 indicates a perfect negative linear association, and a correlation coefficient of 0 indicates no association between the two variables.
In this scenario, if the scatter plot shows a linear pattern and the correlation coefficient is positive, it means that there is a positive association between the amount of time the player spent practicing and the number of points he scored in the game.
On the other hand, if the correlation coefficient is negative, it means that there is a negative association between the two variables, which implies that the more time the player spent practicing, the lower the number of points he scored in the game.
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Find the prime factorization of
the number 90.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [ ] × [ ] × [ ]
X
X
Enter the number that belongs in the green box.
Answer:
2
Step-by-step explanation:
the prime factorization of the number 90 is
2, 3, 3, 5
A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is 84 square inches. Write an equation you can use to find the width (in inches).
On solving the provided question we cans ay that The side of the square is w/2, then its area is: A = (w/2)² = w²/4
what is a square?A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.
The side of the square is w/2, then its area is:
A = (w/2)² = w²/4
The darkened region represents the difference between the square's and rectangle's areas:
[tex]14w - w^2/4 = 84\\56w - w^2 = 336\\w^2 - 56w + 336 = 0[/tex]
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