The range of the number of letters in the sampled last names is 7.
What is the range of the number of letters in the sampled last names?The range of a set of data is the difference between the largest and smallest values. In this case, the data is a set of numbers representing the number of letters in the sampled last names. To find the range, we need to first find the largest and smallest numbers in the set.
From the data, we can see that:
The largest number is 12
The smallest number is 5
Thus, the range of the number of letters in the sampled last names is:
12 - 5 = 7
Learn more about range of data on:
brainly.com/question/24326172
#SPJ1
A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).
What is the percent by mass of Cs in the sample?
A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%
Answer: C. 25%
Step-by-step explanation: This is a basic probability problem. First, you must find the total which is in question. 400 grams is the total in this case. The Cs make up 100 grams of this. Next, you put the part over the whole, and divide. 100/400= 0.25. When you want to find the probability with the probability sign, you move the decimal place two points to the right and then add the sign. Hence, 25%.
Assume that 13% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below.
a) The first lefty is the fifth person chosen.
b) There are some lefties among the 5 people.
c) The first lefty is the second or third person.
d) There are exactly 3 lefties in the group.
e) There are at least 3 lefties in the group.
f) There are no more than 3 lefties in the group.
The first lefty is the fifth person chosen is7.45%
There are some lefties among the 5 people is, 50.16%
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.The first lefty is the fifth person chosen is
[tex](.87)^4(.13)=.07447=7.45 \%[/tex]
There are some lefties among the 5 people is,
[tex]$$1-(.87)^5=.50157=50.16 \%$$[/tex]
The first lefty is the second or third person.
[tex]$(.87)(.13)+(.87)^2(.13)=.211497=21.15 \%_0$[/tex]
There are exactly 3 lefties in the group.
[tex]$(5, .13,3)=.0166=1.66 \%$[/tex]
There are at least 3 lefties in the group,
[tex]1 \text { - binomadf }(5, .13,2)=.0179=1.79 \%[/tex]
There are no more than 3 lefties in the group
[tex]\text { binomcdf }(5, .13,3)=.9987=99.87 \%[/tex]
To learn more about probability refer to:
https://brainly.com/question/13604758
#SPJ4
Recall the equation for a circle with centre (h,k) and radius r. At what point in the first quadrant does the line with equation y=1.5x+5 intersect the circle with radius 5 and centre (0,5)?
The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.
Substituting y=1.5x+5 into the equation, we get (x-0)^2 + (1.5x+5-5)^2 = 25
Simplifying, we get 1.5x^2 +15x+25=25
Solving, we get x=1.
Therefore, the point of intersection is (1,1.5).
The line y=1.5x+5 intersects the circle with radius 5 and centre (0,5) at the point (1,1.5) in the first quadrant.
The equation for a circle with centre (0,5) and radius 5 is (x-0)^2 + (y-5)^2 = 25. When this equation is combined with the line equation y=1.5x+5, it can be solved to find that the line intersects the circle at the point (1,1.5), which is located in the first quadrant.
The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.
Learn more about circle here
https://brainly.com/question/11878555
#SPJ4
What is 2×21 using the distributive property
Answer:
42 is the answer
Step-by-step explanation:
for distributive property of multiplication you could use...
2 x 3 x 7
as 3 x 7 is 21
(07.04 mc) which of the following is the solution to the differential equation dy over dx equals 2 times x times y all over quantity x squared plus 1 end quantity comma with the initial condition y(3)
The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.
Step 1: The given differential equation is dy/dx = 2xy/(x² + 1). Rearranging the equation, we get dy = 2xy dx/(x² + 1).
Step 2: Integrating both sides, we get ∫dy = ∫2xy dx/(x² + 1). On the left side, we have ∫dy = y + C, where C is the constant of integration. On the right side, we have ∫2xy dx/(x² + 1) = x² y + C.
Step 3: Substituting the initial condition y(3) = 6 in the solution, we get 6 = 3² y + C. Solving for C, we get C = 6 - 9y.
Step 4: Substituting C = 6 - 9y in the solution, we get y(x) = (x² + 1)⁴
The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.
learn more about solution here
https://brainly.com/question/30109489
#SPJ4
a segment is created from points a and b. to copy segment ab, which of the following needs to be identified for the construction? the distance between point a and a point not on the segment the midpoint of points a and b the midpoint between point b and a point not on the segment the distance between points a and b
The correct answer among the following option is , the distance between point a and b of segment ab.
What are Points?
A point is denoted by a dot(.). A point represents position only. It has no size.
Points given in the question are a and b.
What is Line Segment?
A line segment is a part of line with a definite start point and a definite end point.
Their are infinite number of point between the end and start point of the segment.
For the construction,
To copy the segment ab, The distance between the two points a nd b is required.
To calculate the distance, Use the distance formula if the co-ordinates of point a and b are given.
The distance can also be measured using a measuring instrument like
a ruler, A measuring tape if the co-ordinates are not given.
As the distance between both the points a and b is known, A new segment can be drawn of the same distance as ab using two new points and can be named cd or a'b'.
To copy the segment ab, The distance between the point a and b is required.
Lear more about Line Segment here:
https://brainly.com/question/30277001
#SPJ12
Answer:the distance between points a and b
Step-by-step explanation: took the test and got it right
ten points are placed on a circle. what is the greatest number of different lines that can be drawn so that each line passes through two of these points(A) 12 (B) 15 (C) 25 (D) 30(E) 36
The greatest number of different line segment that can be drawn so that each line passes through two of these points is 36. This is because every pair of points can be connected by a line, and with ten points, there are 45 pairs.
The greatest number of different lines that can be drawn so that each line passes through two of these points is 36. This is because every pair of points can be connected by a line, and with ten points, there are 45 pairs. Since each line can only be drawn once, the total number of different lines that can be drawn is 45 divided by two, which is equal to 36. In addition, the number of lines that can be drawn from each point to the rest of the points is 9, and since there are 10 points, the total number of lines that can be drawn is 90. However, this number is redundant since each line can only be drawn once, so the greatest number of lines that can be drawn is 36.
Learn more about line segment here
brainly.com/question/30072605
#SPJ4
75% of the Pottery Club members paid their $5.00 dues. If there are 48 members, how many members paid?
Answer:
36 members paid the total money that would be made would be $180
Step-by-step explanation:
48*75%=36
36*5=180
If f(x) = 5x²-3x + 3, find f'(1).
[tex]f(x)=5x^2-3x+3\implies \left. \cfrac{df}{dx}=10x-3 \right|_{x=1}\implies 10(1)-3\implies 7[/tex]
The lengths of the sides of a triangle are 3 cm, 10 cm, and 11 cm. Find the lengths of the segments into which the bisector of each angle divides the opposite side.
The lengths of the segments into which the bisector of each angle divides the opposite side: 12.7, 20.4 and 9.8 respectively
How to find the lengths?The median of a triangle is defined as the length of a line segment that extends from a vertex of the triangle to the midpoint of the opposing side. A triangle can have three medians, all of which will intersect at the centroid (the arithmetic mean position of all the points in the triangle) of the triangle
The medians of the triangle are represented by the line segments ma, mb, and mc. The length of each median can be calculated as follows:
Ma = √(2b²) + (2c²) - a²
. Mb = √(2a²) + (2c²) - b²
Mc = √(2a²) + (2b²) - c²
Applying the formulas
⇒Ma = √(2*3²) + (2*11²) - 10²
Ma = √(18) + (242) - 100
Ma = √160
Ma = 12.7 units
Mb = √(2a²) + (2c²) - b²
Mb = √(2*10²) + (2*11²) - 3²
Mb = √(200) + (242) - 9
Mb = √415
Mb = 20.4 units
Mc = √(2*10²) + (2*3²) - 11²
Mc = √(200) + (18) - 121
Mc = √97
Mc = 9.8
The bisector of each angle divides the opposite side into: 12.7, 20.4 and 9.8 units respectively
Study more about the median of sides of a triangle on https://brainly.com/question/2272632
#SPJ1
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 20.
According to the standard deviation rule, ____% of people have an IQ between 80 and 120. Do not round.
Using the Empirical Rule, it is discovered that the proportion of people in a population with IQs ranging from 80 to 120 is 0.95 = 95%.
What is Empirical Rule?It specifies the following for a normally distributed random variable:
68% of the measurements are within one standard deviation of the mean.
95% of the measurements are within 2 standard deviations of the mean.
99.7% of the measurements are within 3 standard deviations of the mean.
Given a mean of 100 and a standard deviation of 20, we can calculate:
80 = 100 - 2 x 20.
120 = 100 + 2 x 20.
Because these are both the most extreme values within two standard deviations of the mean, then the proportion of people in a population with IQ scores between 80 and 120 is 0.95 = 95%.
To learn more about empirical rule refer to :
https://brainly.com/question/28873888
#SPJ1
grandma famous punch uses a ratio of 5 cups of cranberry juice and 2 cups of sprite. if she needs a total of 56 cups of famous punch how amy cups of cranberry and how many cups of sprite to make 56 cups of punch
You will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.
What is the ratio definition?
A ratio is a mathematical comparison of two or more values or quantities. It is usually written as a fraction, with the first value or quantity being the numerator and the second value or quantity being the denominator.
To make 56 cups of famous punch using the ratio of 5 cups of cranberry juice to 2 cups of Sprite, you can use the following method:
Write the ratio of cranberry juice to Sprite as a fraction: 5 cups cranberry juice / 2 cups sprite
Multiply the fraction by the desired number of cups of punch: (5 cups cranberry juice / 2 cups sprite) x 56 cups punch
Simplify the equation by cross-multiplying: 5 cups cranberry juice x 56 cups punch = 2 cups sprite x 56 cups punch
Solve for the number of cups of cranberry juice: 5 cups cranberry juice x 56 cups punch = 280 cups of cranberry juice
To find the amount of Sprite use the ratio 5:2, meaning you have to use 2 cups of sprite for every 5 cups of cranberry juice. So use 280/5*2 = 56 cups of sprite
Hence, you will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.
To learn more about the ratio, visit:
https://brainly.com/question/2328454
#SPJ4
We choose a number from the set 10, 11,12,...,99) uniformly at random. (a) Let X be the first digit and Y the second digit of the chosen number. Show that X and Y are independent random variables. (b) Let X be the first digit of the chosen number and Z be the sum of the two digits. Show that X and Z are not independent
X and Z are not independent random variable as P(X = x and Z = z) and P(X = x) * P(Z = z) are not equal for most values of x and z by using their joint probability
To prove that two random variables are independent, to show that their joint probability distribution is equal to the product of their individual probability distributions. Start with part (a) and then move on to part (b).
(a) Let X be the first digit and Y be the second digit of the chosen number from the set {10, 11, 12, ..., 99}.
Step 1: Calculate the probabilities of X and Y individually.
To find the probability of X taking any particular value,
there are 9 numbers (10 to 99) that start with each digit from 1 to 9. Since we choose a number uniformly at random, each first digit has an equal chance of being selected.The probability of X taking any value x (where x is a digit from 1 to 9) is given by:
P(X = x) = (number of numbers starting with digit x) / (total numbers)
= 9 / 90
= 1 / 10
Similarly, for Y, since there are 10 digits (0 to 9) and choose the second digit uniformly at random, the probability of Y taking any value y is:
P(Y = y) = (number of numbers with digit y as the second digit) / (total numbers)
= 10 / 90
= 1 / 9
Step 2: Calculate the joint probability P(X, Y).
The joint probability is the probability that X takes a particular value x and Y takes a particular value y simultaneously.
P(X = x and Y = y) = (number of numbers with digit x as the first digit and digit y as the second digit) / (total numbers)
= 1 / 90
Step 3: Check if X and Y are independent.
Two random variables X and Y are independent if and only if their joint probability equals the product of their individual probabilities.
P(X = x and Y = y) = P(X = x) * P(Y = y)
1 / 90 = (1 / 10) * (1 / 9)
Since the equation holds for all values of x and y, conclude that X and Y are independent random variables.
(b) Let X be the first digit of the chosen number and Z be the sum of the two digits.
Step 1: Calculate the probabilities of X and Z individually.
Calculated the probability distribution for X in part (a), which is P(X = x) = 1 / 10 for x = 1 to 9.
To calculate the probability distribution for Z, the sum of the two digits:
For Z = 0: There is only one number, 10, with a sum of digits equal to 0.
P(Z = 0) = 1 / 90
For Z = 1: There are two numbers, 10 and 01, with a sum of digits equal to 1.
P(Z = 1) = 2 / 90
= 1 / 45
For Z = 2: There are three numbers, 11, 20, and 02, with a sum of digits equal to 2.
P(Z = 2) = 3 / 90
= 1 / 30
For Z = 3: There are four numbers, 12, 21, 03, and 30, with a sum of digits equal to 3.
P(Z = 3) = 4 / 90
= 2 / 45
For Z = 4: There are five numbers, 13, 31, 04, 40, and 22, with a sum of digits equal to 4.
P(Z = 4) = 5 / 90
= 1 / 18
For Z = 5: There are four numbers, 14, 41, 23, and 32, with a sum of digits equal to 5.
P(Z = 5) = 4 / 90
= 2 / 45
For Z = 6: There are three numbers, 15, 51, and 24, with a sum of digits equal to 6.
P(Z = 6) = 3 / 90
= 1 / 30
For Z = 7: There are two numbers, 25 and 52, with a sum of digits equal to 7.
P(Z = 7) = 2 / 90
= 1 / 45
For Z = 8: There are two numbers, 26 and 62, with a sum of digits equal to 8.
P(Z = 8) = 2 / 90
= 1 / 45
For Z = 9: There is only one number, 36, with a sum of digits equal to 9.
P(Z = 9) = 1 / 90
Step 2: Calculate the joint probability P(X, Z).
The joint probability is the probability that X takes a particular value x and Z takes a particular value z simultaneously.
Formula:
P(X = x and Z = z) = (number of numbers with digit x as the first digit and the sum of digits equal to z) / (total numbers)
Check the case where X = 1 and Z = 2 as an example:
Numbers with digit 1 as the first digit and a sum of digits equal to 2: 12 and 21 (two numbers)
P(X = 1 and Z = 2) = 2 / 90
= 1 / 45
Step 3: Check if X and Z are independent.
To determine if X and Z are independent, we need to compare their joint probability to the product of their individual probabilities for all values of x and z.
However, if compare the joint probabilities P(X = x and Z = z) to P(X = x) * P(Z = z), find that they are not equal for most values of x and z.
Therefore, conclude that X and Z are not independent random variables.
as P(X = x and Z = z) and P(X = x) * P(Z = z) are not equal for most values of x and z.
Learn more about probability here:
https://brainly.com/question/23846068
#SPJ4
Simplify the following expression. 7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}
The term, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].
What is simplest form?The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top & bottom to remain whole numbers, you cannot divide them further.
Additionally, lowest terms, or simple form, may be used.
The simplest form of a fraction, for instance, is 4/5. Apart from 1, there isn't a number that divides both 4 and 5. Not in its simplest form is the fraction 3/6. Numerator & denominator can both be divided by 3.
Given to simplify the expression
[tex]7^{-\dfrac{5}{6}} \ \cdot\ 7^{-\dfrac{7}{6}}[/tex]
[tex]7^{(-\dfrac{5}{6}-\dfrac{7}{6})}[/tex]
[tex]7^{(\dfrac{-5-7}{6})}[/tex]
[tex]7^{(\dfrac{-12}{6})}[/tex]
[tex]7^{(-2)}[/tex]
[tex]\dfrac{1}{7} \times \dfrac{1}{7}[/tex]
[tex]\dfrac{1}{49}[/tex]
Thus, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].
Learn more about simplest form
https://brainly.com/question/290068
#SPJ1
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 12 cubic feet. A total of 20 boxes of paper were shipped with a combined volume of 216 cubic feet. Graphically solve a system of equations in order to determine the number of small boxes shipped, x,x, and the number of large boxes shipped, yy.
The number of large box is 12 and small box is 8.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
Given :
The volume of small box is 9 cubic feet
The volume of the large box is 12 cubic feet
The volume of all box is 216 cubic feet
There are 20 boxes of paper shipped.
Total Volume covered by small box will be 9x
Total Volume covered by large box will be 24x
Total volume shipped = 216
9x + 24x = 216
33x = 216
x = 6
So The number of large box is 12 and small box is 8.
Learn more about cube, by the following link
https://brainly.com/question/1972490
#SPJ1
19. Zaire gets a bonus with his club for every frisbee golf hole on which he makes a score of 4.
He played last week and scored a 4 on 7 holes. Zaire will get an extra bonus if he has a
total of 60 points from scores of 4 after he finishes today. On how many holes does he
need to score a 4 today?
Please help!!!
Zaire has a total of 7 holes * 4 points/hole = 28 points from scores of 4 from last week.To reach 60 points, he needs to score 4 on 60 - 28 = 32 more holes today. So, Zaire needs to score a 4 on 32 holes today.
How many holes does Zaire need to score a 4 on today in order to reach a total of 60 points?To calculate the number of holes on which Zaire needs to score a 4 today, we can use the following equation:X = (60 - (4 x 7)) / 4Where X is the number of holes on which Zaire needs to score a 4 today, 60 is the total number of points he needs to reach to get the bonus, 4 is the number of points he gets for each hole on which he scores a 4, and 7 is the number of holes on which he scored a 4 last week.Here's the step-by-step explanation:Subtract the total number of points he earned last week (4 x 7) from the total number of points he needs to reach the bonus (60).Divide the result by the number of points he earns for each hole on which he scores a 4 (4).So X = (60 - (4 x 7)) / 4 = (60 - 28) / 4 = 32 / 4 = 8Therefore, Zaire needs to score a 4 on 8 holes today to get the bonus.To learn more about Frisbee problems refer:
brainly.com/question/13372402
#SPJ1
Queen Laetitia is sorting her gem collection. She starts by placing some of her
diamonds into two boxes. In every box after the first two, the Queen puts as many
diamonds as in the previous two boxes combined. If there are 30 diamonds in the
fourth box, and 128 diamonds in the seventh box, how many diamonds did
Queen Laetitia place in the tenth box?
Answer:
Step-by-step explanation:
Let's represent the missing number with "---" -- so we have so far:
--- --- --- 30 --- --- 128 --- --- ?
Now, let's say 5th position number is x and 6th position number is y
So, we have 30 + x = y and x+ y = 128
Combining these 2 equation, we get: x + 30 + x = 128 or x = 49, so y = 79
thus from 4th position, the series can be written as
30, 49, 79, 128, 207, 335, 542....
Thus, at 10th position we will have 542 !!!
The length of a piece of string is x cm long. Another piece measures x+5cm long. If the second piece is 20% longer than the first,calculate the value of x.
Answer:
x = 25 cm
Step-by-step explanation:
20% =
20/100 = 0.20
20% longer =
20% + 100% =
120% =
120/100 = 1.20
Hence, x+5 is 1.20 times that of x:
x * 1.20 = x + 5
1.2x = x + 5
1.2x - x = 5 ==> subtract x on both sides to move x to one side of the
equation
1.2x - 1x = 5 ==> 1x = x
(1.2 - 1)x = 5 ==> distribution property
0.2x = 5
x = 25 ==> multiply both sides by 5 ( 0.2 * 5 = 1 )
Select the law that shows that the two propositions are logically equivalent. -((w V p) ^(-91q1w)) -(w V p) v-(-91qAw) a. DeMorgan's law b. Distributive lawc. Associative law d. Complement law
The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).
What is meant by DeMorgan's law?By using their opposites, De Morgan's Laws explain how mathematical assertions and concepts are connected. The intersection and union of sets are connected by complements according to De Morgan's Laws in set theory. The De Morgan's Laws are rules of propositional logic that use negation to connect conjunctions and disjunctions of propositions.The complement of the intersection of the complements of two sets A and B is equal to the complement of the union of two sets A and B, according to De Morgan's first law. According to De Morgan's Law, "(P and Q)" and "not (not P or not Q)" are logically equal. If they are logically similar, then it should follow that "(P and Q)" implies "not (not P or not Q)," and "not (not P or not Q)" implies "(P and Q)".To learn more about DeMorgan's law, refer to:
https://brainly.com/question/21353067
#SPJ4
solve for X
will give brainliest
based on your calculated values, what can we say about the percentage of students using ipads in public school districts?
Relative to the mean, there are some school districts where many students are using ipads.
What is called the mean?
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is sometimes referred to as the "average" and is the most widely used central tendency metric.
Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
Mean: The "average" number; found by adding all data points and dividing by the number of data points. Example: The mean of 4, 1, and 7 is ( 4 + 1 + 7 ) / 3 = 12 / 3 = 4 (4+1+7)/3 = 12/3 = 4 (4+1+7)/3=12/3=4left parenthesis, 4, plus, 1, plus, 7, right parenthesis, slash, 3, equals, 12, slash, 3, equals, 4.
Learn more about Mean refer to :
brainly.com/question/20118982
#SPJ4
The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 29 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
The distance of the fire from each tower is:
i. From Pine Knob: 41 kilometers
ii. From Colt Station: 15 kilometers
What is Bearing?Bearing as a topic in mathematics can be used to determine the exact position or location of an object considering its angle of position and distance to a reference point.
Considering the given question; let the distance of the fire (F) from Pine knob (PK) be represented by x, and that from Colt Station (CS) be represented by y.
Angle at PK = 80 - 65
= 15^o
Angle at CS = 65 + 70
= 135^o
Angle at F can be determined as;
15 + 135 + F = 180 (sum of angle in a triangle)
150 + F = 180
F = 30^o
So that applying the Sine rule to determine the distances of the fire from PK and CS, we have;
a/Sin A = b/Sin B = c/Sin C
29/Sin 30 = y/Sin 15 = x/ Sin 135
29/Sin 30 = y/Sin 15
y = (29*Sin 15)/ Sin 30
= 7.5052/ 0.5
= 15.0104
y = 15 kilometers
29/Sin 30 = x/Sin 135
x = (29*Sin 135)/ Sin 30
= 20.5059/ 0.5
= 41.0118
x = 41 kilometers
Therefore, the distance from Pine Knob to the fire is 41 kilometers. While the distance from Colt Station to the fire is 15 kilometers.
Learn more about bearing at https://brainly.com/question/22013596
#SPJ1
regina takes yoga classes 2days a week at the community center
The option that will cost less money from Regina is $8 a class.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
Since the cost for the classes at the community center is $72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The amount will be:
= $72 + $12
= $84
The other cost at $8 a class for 2 weeks will be:
= $8 × 10 days
= $80
The second option is cheaper.
Learn more about word problem on
https://brainly.com/question/21405634
#SPJ1
Yoga classes are offered 2 days a week for 6 weeks
at both the community center and the local gym.
The cost for the classes at the community center is
$72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The cost at the
local gym is $8 a class. Regina wants to know which
class she can take for less money.
I need help on getting an answer for "Y"
Answer: 50
Step-by-step explanation:
You can plug in 4 for any of the equations given.
y = 10 + 10(4)
y = 10 + 40
y = 50
OR
y = 30 + 5(4)
y = 30 + 20
y = 50
Answer:
y = 50
Step-by-step explanation:
Since x = 4, plug the value into either equation.
[tex]y =10+10x\\y = 10 + 10(4)\\y=10+40\\y=50[/tex]
Therefore, y equals 50.
Answer all of these I forgot them
A function built from pieces of different functions over different intervals.
How does one locate the piecewise specified formula?Finding a Piecewise Function’s Equation: Find the equation for both y=mx+b lines. If there is an O, the equation is > or; if there is a •, the equation is or. In the equation, the line represents X.
A piecewise function is one that is constructed from parts of distinct functions at different intervals. For example, we may write a piecewise function f(x) that returns -9 when -9 x -5, 6 when -5 x -1, and -7 when -1.
To learn more about piecewise defined to refer:
https://brainly.com/question/12561612
#SPJ1
A recipe for soup calls for 6 tablespoons of lemon juice and cup of olive oil. The given recipe serves 4 people, but a cook wants to make a larger batch that serves 40
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the chef need for the larger batch?
a) The chef needed
(Type a whole number,
cups of lemon juice for the larger batch.
proper fraction, or a mixed number.)
b) The chef needed
pints of olive oil for the larger batch.
(Type a whole number, proper fraction, or a mixed number.)
The chef needed a) 3¾ cups of lemon juice and b) 20 pints olive oil for the larger batch.
What is mixed fraction?A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like 2 1/3 is one where the remainder is 1 and the quotient is 2. Therefore, a mixed fraction is made up of both a whole number and a correct fraction.
The recipe was for 4 person, but now here are 40
The scale multiple is = 40/4
= 10
a) As 1 cup = 16 tablespoon
The number of tablespoon of lemon required for 40 men = 6 × 10
= 60
Converting to cup = 60/16
= 3¾ cups
b) As 1 cup = 0.5 pints
The number of cups of olive oil required for 40 men = 1 × 10
= 10
Converting to pints = 10/0.5
= 20 pints
Thus, The chef needed 3¾ cups of lemon juice and 20 pints olive oil for the larger batch.
Learn more about mixed fraction
https://brainly.com/question/29264210
#SPJ1
44+ 7/8r when r = -1/2
[tex]44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}[/tex]
A poll is given, showing 80% are in favor of a new building project.If 9 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?
help quick!!!!!!
Answer: 30%
Step-by-step explanation:
because e9 people are chosen and 9 divided by 3 is 3 and 3 x 10 =30
write an equivalent expression for 4(w-5)
Answer:
4w - 20
Step-by-step explanation:
hope this help i guess
1/4(x - 12) use your understanding of writing expressions to translate the expression
The expansion of 1/4(x - 12) is x/4 - 3
What is expansion of expression?In order to expand and simplify an expression, we need to multiply out the parentheses and then simplify the resulting expression by collecting the like terms. Expanding brackets (or multiplying out) is the process by which we remove parentheses. It is the reverse process of factorisation.
For example 4(3-y) can be expanded by multiplying the factor 4 by 3 and y = 12- 4y
Similarly the expression 1/4(x - 12) can be expanded by firstly multiply the factor ¼ by x and 12
therefore 1/4(x - 12) = 1/4×x -12×1/4
= x/4 - 3
Therefore the expansion of 1/4(x - 12) is x/4 -3
learn more about expansion of expression from
https://brainly.com/question/29114
#SPJ1
