Answer:
There were 70 choices for the four locations to apply the new ointment
Step-by-step explanation:
The order in which the locations are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different choices were there for the four locations to apply the new ointment
Four locations from a set of 8. So
[tex]C_{8,4} = \frac{8!}{4!(8-4)!} = 70[/tex]
There were 70 choices for the four locations to apply the new ointment
The number of students, in a class of 35 , who improve their score from the first midterm to the second midterm
Note that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.
What is a discrete variable?A discrete variable is one that can only have particular, unique values and cannot have any other values in between. The number of students who increase their score is a whole number that can only take on specific values (e.g., 0, 1, 2, etc.), indicating that it is a discrete variable.
A quantitative variable in mathematics and statistics can be continuous or discrete depending on whether it is normally obtained by measuring or counting. The variable is continuous in that interval if it can take on two specific real values while simultaneously taking on all real values between them.
Thus, it is correct to state that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.
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Full Question:
Is the following variable best thought of as discrete or continuous?
The number of students, in a class of 35 , who improve their score from the first midterm to the second midterm
Complete a table for the rule y = 3-x
a. Draw a complete graph (4 quadrants) for this rule. Either
use a growth triangle or a table to help you.
b. Is (32,-29) a point on this graph? Explain why or why not
a. Drawn a complete graph in the attachment. (32,-29) is a point on this graph.
What is graph?A graph is a mathematical diagram that shows the correlation between two or more sets of numbers or measurements. It is a diagram that shows the relationship between various sets of numbers or quantities using a series of dots, lines, etc., plotted in reference to a set of axes.
a. Using rule y = 3-x
When x = 3
y = 3-(4)
y = -1
A(4, -1)
Using rule y = 3-x
When x = 2
y = 3-(2)
y = 1
B(2, 1)
Using rule y = 3-x
When x = -2
y = 3-(-2)
y = 5
C(-2, 5)
b. Lets put (32,-29) on the rule
-29 = 3 - 32
-29 = -29
Thus, (32,-29) is a point on this graph
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The midpoint of the segment joining points (a, b) and (j, k) is:
The midpoint of the segment joining points (a,b) and (j,k) is, (a+j)/2, (b+k)/2)
The midpoint of the segment joining two points (x1, y1) and (x2, y2) is given by the point ((x1 + x2)/2, (y1 + y2)/2).
So, to find the midpoint of the segment joining the points (a, b) and (j, k), we need to take the average of the x-coordinates and the average of the y-coordinates:
((a + j)/2, (b + k)/2)
So the midpoint of the segment joining points (a,b) and (j,k) is (a+j)/2, (b+k)/2).
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The registration fee for a used car is 0.8% of the sale price of $5,900. How much is the fee? (Simplify your answer.)
Write the coordinates of the vertices after a reflection over the x-axis.
Answer:
J: -5,10
K: -5,5
L: -2,1
M: -2,6
Hope I helped<3
Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
Answer: we have
--------> inequality A
--------> inequality B
Using a graphing tool
the solution of the inequality A is the shaded area above the dashed line
see the attached figure N
the solution of the inequality B is the shaded area below the dashed line
see the attached figure N
therefore
the solution of the compound system of inequalities is the shaded area between the two dashed lines
see the attached figure N
therefor
the answer in the attached figure N
You are pulling a kite back to the ground at a rate of 2 feet per second.
After 4 seconds, the kite is 16 feet above the ground.
a. Write an equation that represents the height y (in feet) above the
ground after x seconds.
b. At what height was the kite when you started pulling it in?
c. When does the kite touch the ground?
The slope of line exists -2 then the value of x is 12 seconds.
What is meant by point-slope form?The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope. The slope is the ratio of the change in the y values over the change in the x values, or the rise over run, and the point form is written as (x, y).
The relationship between x and y is linear because the rate at which the kite is being drawn in is constant. The height reaches 16 feet after 4 seconds, making the point (4, 16) on the line. After 5 seconds, the height is 14 feet since the kite is being dragged in at a rate of 2 feet per second. Therefore, (5, 14) is another point on the line.
slope of line = (16-14)/(4-5) = -2
Using the point-slope form, an equation of the line exists:
y - 16 = -2(x - 4)
y - 16 = -2x + 8
y = -2x + 24
To estimate the original height,
Let x = 0: y = -2(0) + 24 = 24 feet
The kite hits the ground when y = 0:
0 = -2x + 24
x = 12 seconds
Therefore, the value of x = 12 seconds.
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Anything would be great
A bag contains 3 blue marbles, 10 green marbles,
4 yellow marbles, and 8 red marbles. A marble is chosen at random,
replaced, then another marble is chosen. Find each probability of getting
a green then a yellow.
8/125
24/625
12/625
6/125
On solving the provided question, the equation will be and the factors - This cannot be determined from the information given
what is parabola?When points on a curve are equally spaced from a fixed point and line, the curve is said to have a parabola as its equation. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. Remember that the fixed point is not on the fixed line as well. A parabola is the locus of any point that is equidistant from both a focus and a straight line. A conical curve of interest in coordinate geometry is a parabola.
The equation will be
=> 4x+9 = 20x - 2.3y
x = 989-32y
y = 5.4x - 10
Factors - This cannot be determined from the information given
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Pls help please easy
Answer: 204
Step-by-step explanation:
2 goes into 12 six times. 34x6=204
hence, your answer.
if one bird requires half square foot or six square inches of space during brooding how much space is required in total for 30 Birds
Answer: 6 or 7 square inches
Step-by-step explanation: Chicks need enough space under the brooder so that they can keep warm without crowding, piling up or smothering. Under normal conditions, each replacement chick needs about 6 or 7 square inches of brooder space
6 times a number plus 22 is greater than 7
Answer:X>=5/2;
Step-by-step explanation:
(6*5/2)+22>7
Answer:
True
Step-by-step explanation:
(6*5/2+22) it gives you the correct amount. You also need to pay attention to the greater then and less than signs so that you don’t get confused.
→ < >
Therefore, this is true
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If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000 operating hours, what is the probability of unscheduled maintenance in exactly 5,000 hours?
The probability of unscheduled maintenance in exactly 5,000 hours is 4/5.
What is the probability?
We know that the probability deals with the fact that an event may or many not occur. It deals with a chance event. In this case, we have been told that the hospital's CT scan facility is 4,000 operating hours.
We know that the probability can be obtained from;
P = Number of unscheduled maintenance hours/Total operating hours
This would now give us that;
P = 4000/5000
P = 4/5
Hence, there is a probability of 4/5.
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Two angles are complementary to each other. One angle measures 18°, and the other angle measures (8x − 28)°. Determine the value of x.
Since one angle measures 18°, and the other angle measures (8x − 28)°, the value of x is equal to 12.5.
What is a complementary angle?In Mathematics, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical expression:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
Substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
(8x - 28)° + 18° = 90°
8x - 10 = 90
8x = 90 + 10
8x = 100
x = 100/8
x = 12.5
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The radius of a cylindrical construction pipe is 2 ft, and its length is 19 ft. Answer the parts below. Make sure you're using the correct units in your answer.
a. Find the exact volume of the pipe. Write your answer in terms of pi.
The volume of the cylindrical pipe in terms of π is 76π ft³.
The volume of the cylindrical pipe using ALEKS calculator is 238.76 ft³.
How to find the volume of a cylinder?The radius of a cylindrical construction pipe is 2 ft, and its length is 19 ft. The exact volume of the cylindrical pipe can be found as follows:
The answer is in terms of π.
Therefore,
volume of a cylinder = πr²h
where
r = radiush = heightTherefore,
volume of the cylindrical pipe = πr²h
where
r = 2 fth = 19 ftvolume of the cylindrical pipe = π × 2² × 19
volume of the cylindrical pipe = π × 4 × 19
volume of the cylindrical pipe = 76π ft³
Hence, let's approximate the volume of the cylindrical pipe using π in an ALEKS calculator.
Therefore,
volume of the cylindrical pipe = 76 × π = 238.761041673 = 238.76 ft³
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PLEASE THIS ONE'S EASY BUT I'M JUST stu--It's Due Now!
A. The range of the function y = 3x - 2, considering the domain {-1, 2,4}, is given as follows:
Range: {-5, 4, 10}.
B. The set of ordered pairs that represent the function is given as follows:
{(-1,-5), (2,4), (4,10)}
How to obtain the range of the function?The function for this problem is given as follows:
y = 3x - 2.
The domain of the function is given as follows:
{-1, 2,4}.
The range of the function is composed by the numeric values of the function assumed for these input values.
The numeric values of the function are found replacing the lone instance of x by their input values, as follows:
y = 3(-1) - 2 = -5.y = 3(2) - 2 = 4.y = 3(4) - 2 = 10.Hence the range is the set composed by -5, 4 and 10.
An ordered pair has the following format:
(x,y).
In which y is the numeric value of the input x.
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Toby draws an array that has 8 columns with 3 counters in each row. Bai draws an array that has 3 columns with 8 counters. How many counters are there in all
Answer:48 counters
Step-by-step explanation:8x3=2, 3x8=24, 24+24+48
The cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base are of the cylindrical container is 154 sq cm, what is the base area of the cuboidal container?
Note that where the cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base area of the cylindrical container is 154 sq cm, the base area of the Cuboidal Container is 15.2
What is the justification for the above?Let the height of the cylinder and cuboidal container be h m
We know that the base of the cylinder container is given as: 154 sq cm.
Recall that the volume for a cylinder is = Base x Height
That means in this case:
The volume for the cylinder is = 154 x Height
Thus,
1/2 * 154h = 1/3h³
77h = 1/3h³; divide both side by h to get
77 = 1/3h²
Collecting like terms and make h subject of the formula, we have;
h² = 77 * 3
h² = 231
h = √231
h= 15.1986841536
h = 15.199 or [tex]\approx[/tex] 15.2
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y = 4/5x + 1 A. slope: 4/5; y - intercept: -1 B. slope: 4/5; y - intercept: 1 C. slope: 5/4; y - intercept: 1 D. slope: 5/4; y - intercept: -1
Answer:
B
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{4}{5}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{4}{5}[/tex] and y- intercept c = 1
What is the equivalent of 3(x - 6)
Answer:
3x-18
Step-by-step explanation:
IMPORTANT: Given the triangles below are similar, find the missing side length. Show the work that
Answer:
x=15
Step-by-step explanation:
6(5)=30
3(5)=15
The length of the missing side Triangle is 3
As it is given that the given triangle is similar which shows all three sides of both the triangle will be in the same ratio by CPST (corresponding parts of similar Triangles).
so
15/x=30/6 ................. the ratio of two sides of the triangle
x = 15*6/30
x= 3
here the value of x is 3.
Also, the ratio of the side comes out to be 5:1 as 6 and 30 are the length so the first triangle has a side of 15 and the length of another triangle will be 3 to make the ratio 5:1.
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Deon made 2 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for both necklaces was 13.40. If the beads cost
3.60 for each necklace, how much did each pendant cost?
Answer:
$7.40
Step-by-step explanation:
You randomly select a letter from the letters A, B, C, D, E and flip a coin. The table represents the sample space, where H represents the coin landing heads up and T represents landing tails up. What is the probability of selecting the letter “C” or the coin landing tails up?
The probability of selecting the letter C or the coin landing tails up is given by the following option:
3/5.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
From the table representing the sample space, the number of total outcomes is given as follows:
10.
The desired outcomes are given as follows:
5 outcomes in which the coin lands tails up.A sixth outcome in which the coin lands heads up, however with the letter c.(as the or statement means that at least one of the conditions have to be satisfied, that is, one is enough).
Hence the probability is obtained as follows:
p = 6/10
p = 3/5. (dividing both the numerator and the denominator by 2).
Meaning that the last option is the correct option.
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Which of the following rational functions is graphed below?
The rational function f(x)= x/x+3 is graphed in the figure.
What is rational function?
A rational function is the function which can be expressed in terms of the ratio of p and q.
f(x)= p(x)/q(x)
From the given graph , the vertical asymptote is at x=-3
Now, let's find out the vertical asymptote of each function
In order to find out vertical asymptote, we set the denominator =0
a. f(x)= x/(x+3)
x+3=0
x=-3
b. f(x)= x-3/x
x=0
c. f(x)= x/3
3≠0
d. f(x)= 3/x
x=0
The first function has vertical asymptote at x=-3.
Hence, the first option f(x)= x/x+3 is graphed in the figure.
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Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read of it. Without calculating, who do you predict has read more pages of their book? Explain 1/5 your reasoning.
In linear equation, 53% is predict has read more pages of their book .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Total pages = 400
Remaining pages to be read after Monday = 400 - 200 = 200
40% of 200 = 200 × 40/100 = 80
Remaining pages to be read after Tuesday = 400 - 80 = 320
600 × x/100 = 320
Let the remaining percentage of pages remain to be read be x,
so, 600 × x/100 = 320
x = 320/6 = 53.33333% = 53%
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The perimeter of a triangular park shown on the right is 11x-6.
What is the missing angle ?
The missing length of the right-angle triangle will be 6x - 3.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
The third side of the triangle is given as,
11x - 6 = H + 4x + 2 + x - 5
H = 11x - 6 - 4x - 2 - x + 5
H = 6x - 3
The missing length of the right-angle triangle will be 6x - 3.
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The complete question is given below.
Given that 1 inch = 2.54 cm, how many centimeters are there in 7 feet? Answers may be written using decimal form and should be rounded to the nearest hundredth when necessary. (12 inches = 1 foot)
Answer: 30.48
Step-by-step explanation:
2.54x12=30.48
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
(2x + 3)(x - 1) = 0
x = (-b ± √(b^2 - 4ac))/ 2a, where a = 2, b = 12, and c = -3.
2x^2 + 12x = 3
(6/2)^2 = 9
2x^2 + 12x + 9 - 9 = 3 - 9
factor out the 2x^2 + 12x + 9 = 0
The table shows the points scored by a community football team during two seasons. Use the mean and standard deviation to determine during which season the team scored more consistently.
Last Season: 10, 3, 20, 27, 35, 17, 20, 13, 17
This Season: 23, 17, 28, 16, 23, 16, 16, 10, 13
The season the team scored more consistently will be this season because the Standard deviation is less.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
Last Season: 10, 3, 20, 27, 35, 17, 20, 13, 17
The mean is given as,
Mean = (10 + 3 + ...... + 17) / 9
Mean = 18
Then the standard deviation is given as,
Standard deviation = [(10 - 18)² + (3 - 18)² + ...... + (17 - 18)²] / 9
Standard deviation = 8.78
This Season: 23, 17, 28, 16, 23, 16, 16, 10, 13
The mean is given as,
Mean = (23 + 17 + ... + 13) / 9
Mean = 18
Then the standard deviation is given as,
Standard deviation = (23 - 18)² + (17 - 18)² + ...... + (13 - 18)²
Standard deviation = 5.29
The season the team scored more consistently will be this season because the Standard deviation is less.
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A shopkeeper bought 30 pairs of jeans and 10 T-shirts for $2170. Each of jeans cost twice as much as each T-shirt. If he had sold them more than 20% than the price he paid for them, what would the selling price of a T-shirt be?
Answer: The selling price of a T-shirt would be $107.
Step-by-step explanation: The amount paid by the shopkeeper for the Tshirts would be $2170 ÷ 10 = $217
Since the jeans cost twice as much as the T-shirts, we can multiply the cost of the T-shirts by 2 to find the cost of a pair of jeans: $217 x 2 = $434.
We know that the shopkeeper sold the clothes for more than 20% more than he paid for, i.ee, 100 - 20 = 80.
To find the selling price of a T-shirt, we'll divide the cost of the T-shirts by the markup percentage as a decimal: $217 / (80/100) = $107.