Final answer:
1,200 millimeters (mm) is less than 12 meters (m). To compare, we convert 1,200 mm to 1.2 m and directly compare it with 12 m, clearly seeing that 1.2 m is less than 12 m.
Explanation:
To determine whether 1,200 millimeters (mm) is greater or less than 12 meters (m), we need to convert mm to meters. We know that 1 meter is equal to 1,000 millimeters. Therefore, we can convert 1,200 mm to meters:
1,200 mm ÷ 1,000 = 1.2 m
Now we can compare 1.2 m with 12 m directly. Since 1.2 is less than 12, we can conclude that 1,200 mm is less than 12 m.
To use an example for further clarification, imagine you are measuring the length of a room with a tape measure:
If the room is 1,200 mm (or 1.2 m) long, it is shorter than a room that is 12 m long.
Jacobs & Johnson, an accounting firm, employs 15 accountants, of whom 9 are CPAs. If a delegation of 4 accountants is randomly selected from the firm to attend a conference, what is the probability that 4 CPAs will be selected? (Round your answer to three decimal places.)
Using the hypergeometric distribution, it is found that there is a 0.0923 = 9.23% probability that 4 CPAs will be selected.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, there are 15 accountants, 9 are CPAs and 4 will be selected, hence N = 15, k = 9, n = 4.
The probability that 4 CPAs will be selected is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,15,4,9) = \frac{C_{9,4}C_{6,0}}{C_{15,4}} = 0.0923[/tex]
0.0923 = 9.23% probability that 4 CPAs will be selected.
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x y
0 -3
2 5
3 9
4 13
Which equation matches the table?
A) y = x - 3
B) y = x + 3
C) y = 4x - 3
D) y = 4x + 3
Find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer
We want to find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer.
We will get that there are 38 of these.
First, the squares:
To get the number of square numbers not exceeding 1000, we need to find the largest integer that when squared is equal or smaller than 1000.
This is given by:
√1000 = 31.6
Then the largest square number smaller than 1000 is given by:
31^2 = 961
From this, we can conclude that there are 31 integers not exceeding 100 that are the square of an integer.
For the cubes we do the same thing:
∛1000 = 10
The largest cube number that meets the condition is:
10^3 = 1000
Then there are 10 cube numbers that meet the condition.
Now we need to find the common numbers in bot groups (this is, numbers that are a cube and a square of two integers and that are smaller than 1000).
The numbers that meet this condition are:
1)
1^2 = 1
1^3 = 1
64)
4^3 = 64
8^2 = 64
81)
9^3 = 279
27^2 = 729
These 3 numbers are in both groups, so we are counting them twice, thus we need to subtract 3 to the final result, in order to avoid counting the same number two times.
Then the total number of positive integers not exceeding 1000 that are either the square or the cube of an integer is:
31 + 10 - 3 = 38
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One class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.one class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.
The average of the combined list of 400 students is 71.9 and the standard deviation is 13.1.
Explanation:To find the average and standard deviation of the combined list of 400 students, you can use the following formulas:
Average of combined list = (Average of one class * Number of students in one class + Average of another class * Number of students in another class) / Total number of students
Standard deviation of combined list = sqrt(((SD of one class)^2 * (Number of students in one class - 1) + (SD of another class)^2 * (Number of students in another class - 1) + ((Average of one class - Average of another class)^2 * Number of students in one class * Number of students in another class)) / Total number of students)
Applying the values from the given information:
Average of combined list = (67 * 75 + 72 * 325) / 400 = 71.9
Standard deviation of combined list
= sqrt(((12^2 * 74) + (15^2 * 324) + ((67 - 72)^2 * 75 * 325)) / 400)
= 13.1
Determine the equations of the vertical and horizontal asymptotes, if any, for g(x)=x^3/(x-2)(x+1)
a. x=2,x-1
b. x=-2,y=-1
c. x=-2,x=-1
d. x=2,y=-1
A hiker maintains an average speed of 3 3 /4 km/h. How many kilometers will the hiker walk in 3/5 h
Answer:
2 1/4
Step-by-step explanation:
3 3/4 times 3/5= 15/4 times 3/5=45/20=9/4=2 1/4
I did this because speed times time equals distance and we are finding distance
HOPE THIS HELPS!!!!! :)
The distance walked in 3/5 hours is 2(1/4) km.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Average speed = 3(3/4) km per hour
This can be written as,
3(3/4) km = 1 hour
15/4 km = 1 hour
15/4 km = 1 hour
Multiply 3/5 on both sides.
3/5 x 15/4 km = 3/5 hours
9/4 km = 3/5 hours
2(1/4) km = 3/5 hours
Thus,
2(1/4) km is walk in 3/5 hours.
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Solve the equation
3/4=y−1/5 (8)
y=
Emily measures 3 pieces of string. The first piece measures 642 cm. The second piece measures 124 cm, and the third piece is 134 cm. How many meters of string does she have altogether? (hint: 1 meter equals 100 centimeters)
Sophia and Charlie brought potato salad to the company cookout. Sophia brought 2 quarts and Charlie brought 4 pints. How many TOTAL cups of potato salad did Sophia and Charlie bring together? (1 quart = 4 cups; 1 pint = 2 cups) A) 8 cups B) 10 cups C) 16 cups D) 20 cups
Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).
Let u = <-6, 1>, v = <-5, 2>. Find -4u + 2v.
A) <34, -8>
B) <14, 0>
C) <14, 3>
D) <44, -12>
-4u +2v
= -4<-6, 1> +2<-5, 2>
= <(-4)(-6)+2(-5), (-4)(1) +2(2)>
= <14, 0>
The appropriate choice is ...
... B) <14, 0>
To find the result of -4u + 2v, calculate -4u and 2v separately, then add the results together to get <-34, 0>.
To find -4u + 2v, we first need to calculate -4u and 2v separately and then add them together.
Calculate -4u = -4 * <-6, 1> = <-24, -4>Calculate 2v = 2 * <-5, 2> = <-10, 4>Add -4u and 2v: <-24, -4> + <-10, 4> = <-34, 0>Therefore, the answer is: -34, 0.
Can someone answer B please???
PLEASE HELP IM SO CONFUSED BY THIS
If the measure of angle ACB = 30 and the measure of angle A = 80, find the measure of angle B
A: 60
B: 110
C: 180
D: 70
If the measure of angle ACB = 30 and the measure of angle A = 80, the measure of angle B is 70 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
If the measure of angle ACB = 30 and the measure of angle A = 80, To find the measure of angle B
We know that the angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
∠ACB + ∠A + ∠B = 180
30 + 80 + ∠B = 180
∠B = 180 - 110
∠B = 70
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I can't seem to figure out what numbers to use to solve this equation.
Let x be a random variable that takes integer values and is symmetric, that is, p(x = k) = p(x = âk) for all integers k. what is the expected value of y = cos(xÏ) and y = sin(xÏ)?
The expected value of y = cos(xÏ) is 0 and the expected value of y = sin(xÏ) is also 0, due to the symmetry of the random variable x.
Explanation:The expected value (mean) of y = cos(x Ï) is 0.
The expected value (mean) of y = sin(x Ï) is also 0.
Since the random variable x is symmetric, the probability of both positive and negative values cancel out, resulting in an expected value of 0 for both cosine and sine functions.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of ∠A ?
Enter your answer in the box.
Applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.
What is the Inscribed Quadrilateral Conjecture?The inscribed quadrilateral conjecture states that the opposite angles in any inscribed quadrilateral in a circle measures up to 180 degrees.
Thus:
43° + m∠A = 180°
m∠A = 180 - 43
m∠A = 137°
Thus, applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.
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Austin purchase 2/3 of a pound of yum yum treats. If yum yum treats are $6.00 per pound how much does Austin pay
if possible find the area of the triangle defined by the following: a=32, b=24, y=75°
If one of the 99 test subjects is randomly selected, what is the probability of getting a subject who is pregnant?
To calculate the probability of selecting a pregnant subject from the 99 test subjects, the exact number of pregnant subjects in the group is needed. Without this data, the probability cannot be determined.
Explanation:To ascertain the probability of randomly selecting a pregnant subject from a group of 99 test subjects, additional information is required regarding how many subjects are actually pregnant within the group. Without this information, we cannot compute an exact probability.
However, if we had data—let's say 15 out of the 99 subjects are pregnant—the probability would then be calculated using the formula for probability, which is the number of favorable outcomes divided by the total number of possible outcomes. In this scenario, the probability would then be 15/99.
Final answer:
Without specific information on the number of pregnant subjects among the 99 test subjects, it's impossible to compute the exact probability of randomly selecting a pregnant subject.
Explanation:
To answer the question about the probability of randomly selecting a pregnant subject from the 99 test subjects, we would need to know the number of pregnant subjects within the group. Without that information, we cannot calculate the exact probability. However, if we had that information, the probability (P) of selecting a pregnant subject would be calculated as P = (Number of Pregnant Subjects) / (Total Number of Subjects), which in this case is 99.
This is an example of a probability question that falls under the broader subject of mathematics, specifically within the topic of probability and statistics commonly covered at the high school level.
What do you notice about the frequency of the sine function: y=sin(x) and the frequency of the cosine function: y=cos(x) ?]
a. they have the same value
c. the value is the same as the amplitude
b. they have a zero value
d. there is no frequency value for the cosine function
Answer:
they have always the same
Step-by-step explanation:
Therefore, after plotting the points on the graph
What is the trigonometry?
Trigonometry states that the trigon means 'triangle', and the metry means 'metron' is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given angles are:-
[tex]y=sin(x)[/tex] and [tex]y=cos(x)[/tex]
Draw the graph
Hence, after plotting the points on the graph is:-
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When 1 is added to the difference between seven times a number and 9, the result is greater than 10 added to 6 times the number. Find all such numbers.
Find the difference (7a-6b+7) - (8a-2)
Which system of inequalities is represented by the graph?
y ≤ –x
y > –1
y ≥ –x
y < –1
y < –x
y ≥ –1
y > –x
y ≤ –1
Answer:
[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.
Step-by-step explanation:
We are given four option and need to choose correct inequality for given graph.
In graph, we can see two line
Red line: It is horizontal solid line passing through (0,-1) and shaded region above the line.
Equation of line: y≥-1
Blue line: It is slant dotted line passing through origin and (-2,1)
Equation of line: [tex]y<-\frac{1}{2}x[/tex]
System of inequalities represented by the graph.
[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex]
Thus, [tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.
Rewrite as a simplified fraction
2.267 = ?
The decimal 2.267 is equivalent to the simplified fraction 2267/1000.
To express the decimal 2.267 as a simplified fraction, we can consider the place values of each digit. The decimal portion .267 can be written as the fraction 267/1000 since there are three decimal places. Combining this with the whole number 2, we get:
2.267 = 2 + 267/1000.
To simplify this mixed number, we first find a common denominator, which is 1000. We convert the whole number 2 to an equivalent fraction with this denominator: 2 = 2000/1000. Now, we can add the fractions:
2 + 267/1000 = 2000/1000 + 267/1000 = 2267/1000.
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1, yielding the simplified fraction:
2267/1000.
In summary, 2.267 can be expressed as the simplified fraction 2267/1000.
The question probable may be:
Write the following 2.267 in simplified fraction.
A fraction that is equal to 3/5 that has the denominator 10.
I need help I would really thank wheeler answers this for me
Francisca purchased 425 shares of Kellogg Company stock at $14.15 apiece. She earns $374.00 in dividends every year. What is the yield on Francisca's Kellogg Company stock?
Please help me with question 4
Answer:
A. XV
Step-by-step explanation:
The letters identifying the shortest side of ΔMNP are the last (P) and first (M) of the designator for that triangle. The corresponding side of ΔVWX will be identified by the last (X) and first (V) letters of that triangle's name. Hence the segment of interest is XV.
A carpenter builds a rectangular bookcase that is 37 inches long and 60 inches tall. the carpenter uses two braces along the diagonals to support the bookcase. what is the length of the one of the braces, to the nearest tenth of a inch?
The diagonal of the rectangle can be calculated by using the Pythagorean Theorem , because the diagonal and the two sides , length and width, of the rectangle , makes a right triangle .
Now we have the measure of length and width and we have to find the measure of diagonal
So according to the Pythagorean theorem
[tex] d^2 = a^2 +b^2 [/tex]
where , d is the diagonal , a is the length and b is the width
lets plug the values
[tex] d^2 = 37^2 +60^2 [/tex]
[tex] d^2 = 1369+3600 [/tex]
[tex] d^2 = 4969 [/tex]
Taking square root on both sides
d=70.49 Inches
d=70.5 inches
hence the length of one of the braces is 70.5 inches
what is the factor of x^2-11xy-60y?