Answer: The required percentage is 40%.
Step-by-step explanation: We are given to find the percentage of the first 20 natural numbers that are prime.
We know that
first 20 natural numbers are 1, 2, 3, 4, . . . , 19, 20.
And, the prime numbers among them are 2, 3, 5, 7, 11, 13, 17 and 19.
So, if S be the sample space for the experiment and A be the event of selecting a prime number.
Then, we have
n(S) = 20 and n(A) = 8.
Therefore, the probability of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{8}{20}=\dfrac{2}{5}\times100\%=40\%.[/tex]
Thus, the required percentage is 40%.
Solve the system using the elimination method.
2x + y − z =9
−x + 6y + 2z =−17
5x + 7y + z =4
Whats x, y, and z???
Using the elimination method, the given system of equations leads to a solution of x = -1, y = 1, and z = -2.
Explanation:Solving the SystemThe first step in solving this system of equations using the elimination method is to try and eliminate one of the variables. Let's start with eliminating 'z' by adding the first and the third equation: [tex](2x + y - z) + (5x + 7y + z) = 7x + 8y = 13.[/tex]Now we can eliminate 'z' from the second equation as well by subtracting from it twice the first one:[tex]-(-x + 6y + 2z) - 2(2x + y - z) = -3x + 4y = -5.[/tex]Then we solve the new system of two equations: 7x + 8y = 13 and -3x + 4y = -5. Using substitution or elimination on this will give y = 1Substituting y = 1 into the equation -3x + 4y = -5 gives x = -1.Finally, substituting x = -1 and y = 1 into the first original equation 2x + y - z = 9 gives z = -2. So, the solution is x = -1, y = 1, z = -2.Learn more about Elimination Method here:https://brainly.com/question/13877817
#SPJ3
What is 630 rounded to the nearest ten?
find the Factor of
48m - 80n.
Given line L = ax + by + c = 0, b 0 What is the x-intercept? y-intercept?
Answer:
On Odyssey ware it is -c/a
Step-by-step explanation:
The x-intercept and the y-intercept of a line can be found by setting y and x to zero in the line equation respectively. The x-intercept is -c/a and the y-intercept is -c/b.
Explanation:To find the x and y-intercepts of the given line equation L = ax + by + c = 0, we must set one variable to zero and solve for the other.
To find the x-intercept of a line, we can set y to zero (as this is the case when the line crosses the x-axis), we get:
L = ax + b(0) + c = 0 or x = -c/a
Therefore the getX-intercept of the line is -c/a.
Similarly to find the y-intercept of the line equation, we can set x to zero (as this is the case when the line crosses the y-axis), we get:
L = a(0) + by + c = 0 or y = -c/b
Hence, the y-intercept of the line is -c/b.
Learn more about Line intercepts here:https://brainly.com/question/33234142
#SPJ2
y=1x-4 in standard form
Store A advertises a sale for 3 loaves of bread for $5.94. Explain how to use an equivalent rate to find the unit price of the bread at Store A.
Answer: I wrote the rate, with $5.95 in the numerator and 3 loaves in the denominator. I needed to find an equivalent rate expressed as a fraction with the denominator of 1. I noticed 3 loaves divided by 3 gave a denominator of 1, so I divided $5.94 by 3 to find that each loaf costs $1.98.
Just did it on Edge 2021
Btw Can you mark me brainlest pls
The equivalent rate of the bread is $1.98.
Since the store advertises a sale for 3 loaves of bread for $5.94, in order to find the equivalent rate, the person has to divide $5.94 by 3. This will be:
= $5.94/3
= $1.98
Therefore, the equivalent rate of the loaves of bread will be $1.98
Read related link on:
https://brainly.com/question/10884356
If 4 bushels of rye weigh 76 lb, how much do 8.5 bushels of rye weigh?
Answer: 161.5 lbs
Step-by-step explanation:
Given : The weight of 4 bushes of rye = 76 lb
By applying UNITARY METHOD, the weight of 1 bush will be :-
[tex]\text{ Weight of 1 bush}=\dfrac{76}{4}\\\\\Rightarrow\ \text{ Weight of 1 bush}=19\text{lb}[/tex]
Now, the weight of 8.5 bushes = [tex]8.5\times19[/tex]
The weight of 8.5 bushes = 161.5 lbs
Therefore, the weight of 8.5 bushels of rye= 161.5 lbs
Hence, the required answer is "161.5 lbs".
Which of the following functions has the greatest y-intercept?
f(x) x y
−3 −14
−2 −6
−1 −2
0 3
1 5
2 6
or g(x) = 3 cos(2x) + 1
please include explanation
Answer:
g(x) has greatest y-intercept.
Step-by-step explanation:
We are given a table of values for function f(x) as:
x y=f(x)
−3 −14
−2 −6
−1 −2
0 3
1 5
2 6
We know that the y-intercept of a function is a point where the x-value is zero.
i.e. the input value is zero.
Hence, after looking at the table of values of the function f(x) we have the y-intercept of the function f(x) is:
y=3
Also we are given function g(x) as:
g(x) = 3 cos(2x) + 1
Hence, we calculate the y-intercept of the function g(x) by taking x=0
on taking x=0 we have:
g(0)=3 cos(0)+1
g(0)=3+1=4
Hence, the y-intercept of function g(x) is 4.
Hence, g(x) has the greatest y-intercept.
A boat traveled downstream a distance of 80 mi and then came right back. If the speed of the current was 7 mph and the total trip took 3 hours and 20 minutes, find the average speed of the boat relative to the water.
By converting the total trip time to minutes, using the formula for speed (distance/time), and using a system of equations representing the total trip speed when the boat is moving downstream and upstream, we can find the average speed of the boat relative to the water.
Explanation:To solve this problem, we first need to convert the total trip time to minutes to make calculations easier. Given in the problem, 3 hours 20 minutes equates to 200 minutes. Next, we should use the formula for speed, which is distance divided by time. We know that the total distance traveled by the boat is 80 miles downstream and 80 miles back, totaling 160 miles.
When moving downstream, the speed of the boat and the speed of the current both aid in the boat’s motion. Thus we have speed of the boat = speed of the boat in still water + speed of the current. However, when the boat is moving upstream, the speed of the current works against the boat's motion. Thus we have speed of the boat = speed of the boat in still water - speed of the current.
By using the system of these equations and the fact that total time equals total distance divided by the speed of the boat, we can find the speed of the boat in still water, which represents the average speed of the boat relative to the water.
Learn more about Average Speed Calculation here:https://brainly.com/question/680492
#SPJ2
If 5 sandwhich rolls cost 1.10 how much will 14 rolls cost
In an attempt to reduce the growth of its population, China instituted a policy limiting a family to one child. Rural Chinese suggested revising the policy to limit families to one son. Assuming the suggested policy is adopted and that any birth is as likely to produce a boy as a girl, and the successive births are independent, explain the following:
A) What would be the average family size?
B) What would be the ratio of newborn boys to newborn girls?
A survey asked a group of people the size of their households. The results are shown in the frequency distribution.
What is the mean of the frequency distribution? Round your answer to the nearest tenth.
Household size 1 2 3 4 5
f 2 4 6 5 2
3
3.1
3.8
11.6
Answer: 3.1
Step-by-step explanation:
The mean of the frequency distribution is 3.1. Which is the correct answer would be an option (B)
What is arithmetic mean?
Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
Given the frequency distribution as :
Household size (x) Frequency (f) fx
1 2 1 × 2 = 2
2 4 2 × 4 = 8
3 6 3 × 6 = 18
4 5 4 × 5 = 20
5 2 5 × 2 = 10
Summation of fx = (Σfx) = 2 + 8 + 18 + 20 + 10 = 58
Total frequency = (Σf) = 2 + 4 + 6 + 5 + 2 = 19
⇒ Mean = Σfx/Σf
⇒ 58/ 19
⇒ 3.1
Thus, the mean of the frequency distribution is 3.1.
Learn more about the Arithmetic means here:
brainly.com/question/13000783
#SPJ2
If a coin is tossed 4 times, and then a standard six-sided die is rolled 2 times, and finally a group of four cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
[tex]\(1138368400\)[/tex] different outcomes possible when considering all the events together.
Coin Toss: Since each toss is independent of the others, the total number of outcomes for 4 tosses is:
[tex]\(2 \times 2 \times 2 \times 2 = 2^4 = 16\)[/tex].
Die Roll: A standard six-sided die has 6 faces, each with a different number from 1 to 6. When the die is rolled once, there are 6 possible outcomes. If the die is rolled 2 times, the number of different outcomes is:
[tex]\(6 \times 6 = 6^2 = 36\)[/tex]
Card Draw: When drawing a card from the deck, there are 52 possible outcomes. If a second card is drawn without replacing the first, there are now 51 possible outcomes for the second card (since one card has already been drawn). Continuing this pattern, for the third card, there are 50 possible outcomes, and for the fourth card, there are 49 possible outcomes.
The number of different outcomes for drawing 4 cards without replacement is: [tex]\(52 \times 51 \times 50 \times 49\)[/tex].
[tex]\[ \text{Total Outcomes} = (\text{Coin Toss Outcomes}) \times (\text{Die Roll Outcomes}) \times (\text{Card Draw Outcomes}) \][/tex]
[tex]\[ \text{Total Outcomes} = 16 \times 36 \times (52 \times 51 \times 50 \times 49) \][/tex]
[tex]\[ \text{Total Outcomes} = 6^2 \times 52 \times 51 \times 50 \times 49 \][/tex]
[tex]\[ \text{Total Outcomes} = 36 \times 52 \times 51 \times 50 \times 49 \][/tex]
[tex]\[ \text{Total Outcomes} = 36 \times 31625400 \][/tex]
[tex]\[ \text{Total Outcomes} = 1138368400 \][/tex]
List of fractions and decimals in order from least to greatest 1.45 1 1/2 1 1/3 and 1.2
42in to 9 feet insimplest form
what percent of 18 is 63
Joe has 310 baseball cards. He writes the number of cards in expanded form. How many ones will he write?
Answer:
The expanded form of 310 is:
310 = 300 + 10.
Joe will write two numbers to form 310.
Step-by-step explanation:
The expanded form is used to write numbers and see the math value of individual digits. So, the numbers are separated into individual place values and decimal places and form a mathematical expression.
310 in expanded form is 300 + 10 = 310.
Does this set of ordered pairs represent a function?
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
Answer:
Option C is correct
Yes, the set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents the function.
because every x-value corresponds to exactly one y-value.
Step-by-step explanation:
A function states that it is a relation in which every domain value is paired with exactly one element of range.
Given the set of ordered pair:
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
Domain is all the x-values, and range is all the y-values.
Domain: {-5, -1, 0, 3, 8}
Range: {-5, -2, -2, 7, 9}
By definition:
each input value (i.e x values) is paired with exactly one element of y-value.
therefore,the set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents the function.
What is the midpoint of the x-intercepts of
f(x) = (x – 4)(x + 4)?
Answer:
midpoint is (0,0)
Step-by-step explanation:
the midpoint of the x-intercepts of
[tex]f(x) = (x - 4)(x + 4)[/tex]
To find the midpoint of x intercepts, we need to find the x intercepts first
we find x intercepts by replacing f(x) with 0
[tex]0 = (x - 4)(x + 4)[/tex]
Set each factor =0 and solve for x
[tex]x-4=0 , x=4[/tex]
[tex]x+4=0, x=-4[/tex]
X intercepts are -4 and 4
Midpoint of -4 and 4 is [tex]\frac{-4+4}{2} =0[/tex]
X intercepts lies on x axis . So midpoint is (0,0)
How do I write 19.4 in expanded form
To write 19.4 in expanded form, you can break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. Therefore, 19.4 in expanded form is 10 + 9 + 0.4.
Explanation:To write 19.4 in expanded form, we break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. So, we can write 19.4 in expanded form as 10 + 9 + 0.4.
Learn more about Expanded form here:https://brainly.com/question/25632734
#SPJ11
IF b= -8 and a= 3 what are the steps to solve the following:
b -a - 3 =
Let's say the debt in the United States is now near 1.8 × 10^13 dollars and that there are about 300,000,000 people in the United States. If every person paid their fair share of the debt, approximately how much would that be per person?
If the total debt is near $1.8 × 10¹³, then every person has to pay $60,000.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the mentioned data in the question,
Total debt in the United States = $1.8 × 10¹³
Total number of people in the United States = 3 × 10⁸
If every person paid their share, then each person has to pay,
= ($1.8 × 10¹³)/(3 × 10⁸)
= $6 × 10⁴ or,
It can be written as $60,000.
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ5
Tom ate 1/2 of the 1/2 leftovers. How much pie in all did he eat?
Shawn downloads movies at a base price of $2 per movie. If he downloads 5 movies, he will get a 25% discount. How much will Shawn save on the base price if he downloads 5 movies?
Answer:
$2.50
Step-by-step explanation
On a Venn diagram, a value that represents what two circles have in common is written outside of both circles. True or false
Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot. Find the geometric mean of the pair of numbers. A. 20 ft B. 38.4 ft C. 55 ft D. 25 ft
1. Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C.
Step 2: Open the compass to the length of AB.
Step 3: With the same compass setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D.
a. a perpendicular bisector
b. a congruent segment
c. an angle bisector
d. a congruent angle
2. Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Put the compass point on A and draw a long arc. Be sure the opening is grater than 1/2 AB.
Step 2: With the compass on the same setting, put the compass point on B and draw another long arc. Label the points where the two arcs meet as X and Y.
Step 3: Draw XY. Label the point of intersection of AB and XY as M, the midpoint of AB.
a. a perpendicular bisector
b. a congruent segment
c. an a
1. For that accurate reason, CD and AB will be congruent. the answer here is B) A congruent segment. 2. Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.
How to find the correct steps?1. Form opening the compass to the length of AB you are setting the radius of the circle the compass could create to the same length of AB then by intersecting with the ray C, we have to copied the length of AB to ray C.
For that accurate reason, CD and AB will be congruent.
Therefore, The answer here is B) A congruent segment.
2. Given a segment with endpoints A and B.
By using the construction step we will draw the following figure that represents a perpendicular bisector XY of line segment AB.
Hence, Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.
Learn more about this concept here;
https://brainly.com/question/2485485
#SPJ2
Find the scale factor if an airplane is 87 feet long; 2 inches = 15 feet.
How do write 21,070 in standard form
Final answer:
The number 21,070 is already in standard form. Standard form is a straightforward expression of a number as commonly written, without the need for scientific notation for simple numbers like this one.
Explanation:
The number 21,070 written in standard form is simply 21,070 itself. In mathematics, standard form refers to the way a number is commonly written. This number is already in standard form because it is expressed in a direct and straightforward manner. There is no need for further simplification or conversion. When numbers are very large or very small, they can be cumbersome to write out in full, which is why scientists and mathematicians may use scientific notation to express them.
For instance, if we had a larger number like 77,123,450, we could write it in scientific notation as 7.712345 × 10⁷, emphasizing that it is 7.712345 times ten to the seventh power.
For the provided number 21,070, no such conversion is necessary, and it remains 21,070 in standard notation.
"find the third length of the right triangle. give an exact answer and an approximation" HELP PLS