use point-slope to write the equation of a line that passes through the point (1,-5) with slope -1
Point slope form is y - y1 = m ( x - x1 ), where m represents the slope, y1 represents the y value of the point, and x1 represents the x value of the point.
filling in the variables with the given information gives you
y - (-5) = -1 ( x - 1 ) which is also y + 5 = -1 ( x - 1)
if a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
The probability of a student being chosen at random and taking exactly one language class is 65%.
Probability is the likelihood or chance of an event happening. In this case, the event is a student taking exactly one language class.
First, we need to find the total number of students taking at least one language class. We have 28 students in the Spanish class, 26 students in the French class, and 16 in the German class. However, some students are taking multiple classes, so we need to subtract these students from the total. The 12 students taking both Spanish and French, 4 taking both Spanish and German, and 6 taking both French and German should only be counted once. In addition, the 2 students taking all three classes should also only be counted once.
So, the total number of students taking at least one language class is
=> 28 + 26 + 16 - 12 - 4 - 6 + 2 = 40 students.
To find the number of students taking Spanish only, we need to subtract the number of students taking both Spanish and French (12) and the number of students taking both Spanish and German (4) from the number of students taking Spanish (28).
So, the number of students taking Spanish only is
=> 28 - 12 - 4 = 12 students.
Similarly, the number of students taking French only is
=> 26 - 12 - 6 = 8 students
and the number of students taking German only is
=> 16 - 4 - 6 = 6 students.
Finally, to find the probability of a student being chosen at random and taking exactly one language class, we divide the number of students taking exactly one language class by the total number of students taking at least one language class.
So, the probability of a student taking exactly one language class is
=> (12 + 8 + 6) / 40 = 26 / 40 = 0.65 or 65%.
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Complete Question:
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 students in the French class,, and 16 in the German class. There are 12 students that are in both Spanish and French, 4 that are in both Spanish and German, and 6 that are in both French and German. In addition, there are 2 students taking all 3 classes.
If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
What is the slope of a line that passes through the points (0, 5) and (8, -2)
Answer:
-7/8
Step-by-step explanation:
slope = Δy/Δx = (-2 - 5) / (8 - 0) = -7/8
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 8 through the point 3 comma 6
Find and interpret the slope and y-intercept in this real-world situation.
The slope is 8, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 8 inches every hour.
The slope is 8, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 8 inches every hour.
The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases three halves of an inch every hour.
The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour. The solution has been obtained by using the concept of slope.
What is a slope?
In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate.
We are given that the graph of the line passes through (0,8) and (3,6) .
So,
Slope of the line = (6 - 8) ÷ (3 - 0) = -2/3
From this, we get the equation of line as
y - 6 = -2/3 (x - 3)
Now, for y-intercept, we need to put x = 0
So, we get
⇒y - 6 = -2/3 (-3)
⇒y - 6 = 2
⇒y = 8
Hence, the slope is negative two thirds, and the y-intercept is 8.
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please help with this maths question
Answer:
Step-by-step explanation:
Find the exact quadratic function with the given zeros and passing through the given point.
zeros(x-intercepts): x= –3, x= 1 and passes through (–8, 5).
y = a/b (x+c) (x-1)
The precise quadratic equation, according to the provided assertion, is y = (1/9)x² + (2/9)x - 1/3.
How is the quadratic function discovered?Three elements decide a quadratic function of the formula f(x) = ax² + bx + c. A quadratic function can be determined by getting a, b, and c algebraically given three locations on the graph. In order to do this, a system of eqs with three unknowns must be solved.
To find the quadratic function that passes through the point (-8, 5) and has zeros at x = -3 and x = 1, we can start by using the factored form of a quadratic function:
y = a(x - r)(x - s)
where r and s are the zeros of the function. Substituting in the given zeros, we get:
y = a(x + 3)(x - 1)
To find the value of a, we can use the fact that the function passes through the point (-8, 5). Substituting these values into the equation, we get:
5 = a(-8 + 3)(-8 - 1)
Simplifying this expression, we get:
5 = a(-5)(-9)
5 = 45a
a = 1/9
Substituting this value of a into the equation we get:
y = (1/9)(x + 3)(x - 1)
Expanding the equation, we get:
y = (1/9)(x² + 2x - 3)
Multiplying both sides by 9 to eliminate the fraction, we get:
9y = x² + 2x - 3
So the quadratic function that passes through the point (-8, 5) and has zeros at x = -3 and x = 1 is:
9y = x² + 2x - 3
or
y = (1/9)x² + (2/9)x - 1/3.
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a survey asked people if they were aware that maintaining a healthy weight could reduce the risk of stroke. a 95% confidence interval was found using the survey results to be (0.54, 0.62). what is the correct interpretation of this interval?
Keeping a healthy weight will lower your risk of stroke, according to the 95% confidence interval of (0.54, 0.62), which suggests that if the survey were conducted repeatedly, 95% of the intervals produced would represent the real population percentage of individual, who are aware of this.
In other words, there is a 95% confidence interval between 0.54 and 0.62 for the genuine population fraction of those who are aware of this knowledge.
It should not be assumed from this range that 95% of respondents indicated that they were aware of this knowledge.
Instead, it offers a range of numbers that, with a given level of certainty, are likely to include thee genuine population percentage.
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I don’t understand this subject at all
The measurements of the given sides are x = 24, y = 40, and z = 40.
Right angle triangle:The triangle in which at least one right angle exists is known as a Right angle triangle.
By the Pythagorean theorem in a right angle triangle, the sum of the squares of sides will equal the square of the hypotenuse.
The altitude drawn on a hypotenuse will divide the triangle into two similar triangles
Here we have
Two right-angle triangle
As we know in right angle triangle,
=> Hypotenuse² = Side² + Side²
From the smaller right-angle triangle,
=> y² = (32)² + (24)²
=> y² = 1024 + 576
=> y² = 1600
=> y = 40
Here the altitude drawn on the hypotenuse of the triangle divides the triangle into two similar triangles
Hence, the ratio of the corresponding angles in two triangles will be equal
=> 32/x = 32/24
=> 24(32) = 32(x)
=> x = 24
In 2nd largest triangle,
=> z² = (32)² + (24)²
=> z² = 1024 + 576
=> z² = 1600
=> z = 40
Therefore,
The measurements of the given sides are x = 24, y = 40, and z = 40.
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You want to make a scale drawing of your bedroom to help you arrange our furniture. You decide on a scale of 3 in. To 2 ft. Your bedroom is a 12 ft-by- 15 ft rectangle. What should its dimensions be in your scale drawing?
The dimensions of furniture in a rectangular bedroom in my scale drawing is equals to the 18 in. by 21 in.
To draw dimensions on scale drawing :
Determine the scale on the drawing . Using the ruler, measure the distance present on the drawing.Multiply the distance we measure by the scale to particular the distance in real life.I want to a scale drawing of my bedroom which help me to arrange my furniture.
Dimensions of rectangular bedroom= 12 ft by 15 ft
that is length of room, l = 15 ft
width of rectangle room, w = 12 ft
Area of rectangular bedroom = l×w = 12 × 15
= 180 ft²
scale of furniture = 3 in. = 2 ft
=> 2 ft = 3 in
=> 1 ft = 3/2 in
Now 12 ft by 15 ft in inches :
=> 12 × 3/2 in by 15 × 3/2 in
=> 18 in by 22.5 in
Hence, required dimensions are 18 inches by 22.5 inches.
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Find the distance between the two points. (2, 1), (-3, 6)
i have 4 more problems like this but i forgot how to do it so i need help
PLS HELP ME! FIND THE DIFFERENCE BETWEEN WHAT IS PAINTED AND WHAT REMAINS TO BE PAINTED
Answer:
51 3/4 %
Step-by-step explanation:
Iris purchased a video game for $85 and then sold it for $56 after she completed the game. What was the percent decrease? Round your answer to the nearest whole percent
The percent decrease in price of video game was equals to the 34% .
When Iris purchased, the price of video game is $85. That is original price of video game = $85
The selling price of video game = $56
As we see Selling price < Original price
=> loss or decrease
Let the decrease in price be "x".
Decrease in value is equals to original price minus selling price.
=> x = $85 - $56 = $29
Now, percent decrease is obtained by dividing the decrease in price by original price, then multiply the resultant by 100.
Decrease percent = decreased price/original price)100
=> x% = (29/85)100
=> x% = 2900/85
=> x% = 34.117
Hence, the required percent decrease is 34%.
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If 3 yellow, 4 red and 6 blue flowers are to be planted in a line, how many different arrangements are possible?
Using permutations and combinations, we know that a total of 60,060 different arrangements of flowers can be made in a row.
What are permutations and combinations?The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations.
When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.
Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colors.
Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.
So, we have:
3 yellow, 4 red, and 6 blue flowers.
3 + 4 + 6 = 13
Now, the number of arrangements in the row will be:
= 13!/3!4!6!
= 6,22,70,20,800/6*24*720
= 6,22,70,20,800/1,03,680
= 60,060
Therefore, using permutations and combinations, we know that total of 60,060 different arrangements of flowers can be made in the row.
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jim is going to buy donuts for his family. each donut costs $1.45. if the number of donuts jim buys is represented using the letter d, which expression represents the total cost? a 1.45d b 1.45/d c 1.45 d d 1.45 - d
By applying total cost concept, it can be concluded that the expression represents the total cost is 1.45d (option A).
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.
It is usually used to solve a problem in various fields of study, such as chemistry, biology, economics, and so on.
One of the most familiar uses of algebra is how to calculate the total cost:
Total cost = n x p , where:
n = number of products
p = product price per piece
We know that Jim is going to buy donuts for his family:
p = $1.45
n = d
So the total cost can be calculated by multiplying 1.45 by d, which equals 1.45d.
Thus the expression represents the total cost is 1.45d (option A).
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a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations. True/False ?
True, a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
What does a simple random sample mean?
A subset of participants is randomly chosen from a population by the researcher using simple random sampling, a sort of probability sampling.
The probability of being chosen is the same for every person in the population. Then, data are gathered from as much of this randomly selected subgroup as possible.
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write a formula for a linear function f(x) that models the situation, where x is the number of years after 2007. in 2007 the average adult ate 52 pounds of chicken. this amount will increase by 0.8 pounds per year until 2012.
Step-by-step explanation:
x = number of years after 2007.
x = 0 for 2007.
PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).
PC(x) = 0.8x + 52
0 <= x <= 5
in 2007 (x = 0) the average adult ate 52 pounds.
in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.
so, in 2012 (x = 5) the average adult will eat
PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.
in the circles so that the sums across (horizontally) and down (vertically) are equal. which number will you place in the middle?
The number 5 will be placed in the middle.
In order to make the sums across and down equal, we have to arrange the numbers in such a way that they balance each other out. We know that the middle number will be the average of the four numbers surrounding it.
So, if we place 2 and 8 on either side of the middle number, the sum of these two numbers is 10. To make the sum equal, we need two more numbers that add up to 10. The only two numbers that fit the criteria are 4 and 6.
Hence, the middle number will be the average of 4 and 6, which is 5. So, the answer is 5.
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--The given question is incomplete; the complete question is
"Place the numbers 2, 4, 5, 6, and 8 in the circles so that the sums across (horizontally) and down (vertically) are equal. Which number will you place in the middle?"--
Box 1 contains 2 red balls and 1 blue ball. Box 2 contains 3 blue balls and 1 red ball. A coin is tossed. If it falls heads up, box 1 is selected and a ball is drawn. If it falls tails up, box 2 is selected and a ball is drawn. Find the probability of selecting a red ball.
Answer:
90°/• is the probability
To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points � B and � C. He measures � � AD, � � DB, and � � DE as marked. Find the distance across the lake ( � � ) (BC), rounding your answer to the nearest hundredth of a meter.
The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.
We can use similar triangles to find the distance across the lake (DE). Since triangle CGF is similar to triangle CED, we can use ratios of the sides to find DE.
Let's call DE = x. Then, we have:
CE/FG = x/142.1
Solving for x, we have:
x = (CE * 142.1) / FG
CE = CF + FD = 130 + 60 = 190m
x = (190 * 142.1) / 142.1 = 190m
The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.
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The complete question is :
To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter.
Help!! View picture:)
The truth table for the statement is
r s ¬r s ∧ ¬r
---------------------
T T F F
T F F F
F T T T
F F T F
How to construct a truth table for the statementFrom the question, we have the following parameters that can be used in our computation:
s ∧ ¬r
To construct the truth table, we make use of the following notations
s, r and ¬r
The truth table for the statement s ∧ ¬r is then represented as follows:
r s ¬r s ∧ ¬r
---------------------
T T F F
T F F F
F T T T
F F T F
The condition for ∧ is that it is true if both statements are true
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You flip a coin.
What is P(tails or heads)?
Write your answer as a percentage
Answer: 50%
Step-by-step explanation: There is an equal chance of both events occurring so there is a half chance for it to occur or no.
2x - 1/2 = 5 1/2
A. x = 2
B. x = 3
C. x = 4
D. x = 2 1/2
how many ways are there to arrange these seven leaders in a row? also, how many ways are there to arrange these seven leaders in a row, so that the leader of japan and the leader of canada stand next to each other? here and throughout show/explain your work.
There are 5040 ways to arrange these seven leaders in a row. There are 1440 ways to arrange these seven leaders in a row, so that the leader of japan and the leader of canada stand next to each other.
Using the multiplication principle, we multiply all the possible arrangements to determine the total number of configurations if we have seven individuals and want to know how many ways there are to place them in a row of seven seats. For instance, the first seat has seven alternatives, the second has six (as one has been taken), the third has five, the fourth has four, and so on.
So, these seven leaders in a row, so that the leader of japan and the leader of canada stand next to each other.
6! * 2! = 720 * 2 = 1440 .
To arrange these seven leaders in a row we just have to find,
7! = 7x6x5x4x3x2x1
= 5040
These two configurations are both permutations. Therefore, in the case, there are only two potential permutations.
It becomes more difficult if there are seven of us. The multiplication concept must be applied.
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800 people attended a football game. If 20% of the people who attended were teenagers, how many teenagers attended the game? Insert the values given in the problem then scale up or down to find the missing value. attendees percent 100 attempt 3 out of 3 Emilia Salkic Proportional Reasoning, Percents (Level 2) Feb 03, 2:20:32 PM 800 people attended a football game. If 20% of the people who attended were teenagers, how many teenagers attended the game?
Using percentages we can conclude that out of 800 people, 20% of the people who attended the football match were teenagers, 160.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction.
Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
So, we know that:
800 people attended the football game.
20% were teenagers.
Then, the number of teenagers was:
= 800/100*20
= 8*20
= 160
Therefore, using percentages we can conclude that out of 800 people 20% of the people who attended the football, match were teenagers, and 160 were.
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Write an expression for the sequence of operations described below.
raise 4 to the 2nd power, then find the quotient of the result and q
Do not simplify any part of the expression.
Both BODMAS and PEMDAS are valid and in use in various parts of the globe. In the UK, BODMAS is frequently utilized, whereas in the US, PEMDAS is. Brackets, Order, Division, Multiplication, Addition, and Subtraction are all referred to as BODMAS.
Which mathematical procedure comes first?The acronym PEMDAS, which stands for parenthesis, exponents, multiplication and division from left to right, as well as addition and subtraction from left to right, can be used to recall the order of operations. Start by using parenthesis first.
For the list of operations, we wish to create an expression.
9 to the second power raised then, determine the ratio between the outcome and z
First, raise 9 to the second power.
9 divided by two equals
Find the product of the result and z in step two.
Today, quotient refers to "division."
The outcome of step 1 is =[tex]9^2[/tex]
Therefore:
Indicator of and z
As a result, the statement that describes the specified order of operations is [tex]\frac{9^2}{z}[/tex]
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[tex]x^{2} -4x=1 find x^{2} +1/x^{2}[/tex]
The value of the expression x²+1/x² is 18
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: x²-4x=1
simplifying we get
x²-4x=1
Dividing both sides by x we get
x²/x-4x/x=1/x
x-4=1/x
x-1/x=4
Now squaring both sides we get
(x-1/x)²=4²
x²-2×x×1/x+1/x² =16
x²+1/x²=16+2
x²+1/x²=18
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Solve the equation round the result to the nearest hundredth 3x-4=3
Answer:
x = 2.33
Step-by-step explanation:
3x - 4 = 3
3x = 7
x = 7/3
x = 2.33
What is the slope of the line that passes through (0,2) and (6,6)
Answer:
Step-by-step explanation:
The slope of the line passing through the points (0,2) and (6,6) can be found using the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0, 2) and (x2, y2) = (6, 6)
slope = (6 - 2) / (6 - 0)
slope = 4 / 6
slope = 2/3
Therefore, the slope of the line is 2/3.
(A) A small mass of 0.60 kg is rotated at the end of a string in a horizontal circle of radius 1.20 m. The string will break if the tension exceeds 60 N. What is the GREATEST frequency of revolution that is possible? (B) the same mass of 0.60 kg is now rotated at the end of another string at a constant speed, v, in a vertical circle of radius 1.20 m. the minimum tension in the string is 2.1N (I) state and explain where the tension in the string is maximum and minimum (ii) find the speed of the mass
Answer:
450
Step-by-step explanation:
the speed of mass is 450
Find the size of angle x using parallel line facts. Give answer in degrees (°).
Answer:
Hi There! Here's your answer.