There are 500 students in Davis MiddleSchool. Out of 10 students in a randomsurvey, 2 have last names that beginwith the letter "A." In another randomsurvey of 10 students in the sameschool, 8 passed their most recent mathquiz.From this data, how many students inthe whole school could reasonably beexpected to have a last name beginningwith "A" and also have passed their mostrecent math quiz?
Answers
The probability that a student have last names that begin with the letter "A" is 2/10 = 1/5
The probability that a student passed their most recent math quiz is 8/10 = 4/5
Then, the probability that a student have a last names that begin with the letter "A" and passed their most recent math quiz is 1/5 x 4/5 = 4/25
Since there are 500 students in the school, approximately 4/25 x 500 = 80 of them have a last names that begin with the letter "A" and passed their most recent math quiz.
Related Questions
A local police chief claims that about 51% of all drug related arrests are ever prosecuted. A sample of 900 arrests shows that 47% of the arrests were prosecuted. Is there sufficient evidence at the 0.01 level to refute the chief's claim? State the null and alternative hypotheses for the above scenario.
Answers
Answer:
The null hypothesis is \(H_0: p = 0.51\).
The alternate hypothesis is \(H_1: p \neq 0.51\).
The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.
Step-by-step explanation:
A local police chief claims that about 51% of all drug related arrests are ever prosecuted
At the null hypothesis, we test if the proportion is of 51%, that is:
\(H_0: p = 0.51\)
At the alternate hypothesis, we test if the proportion is different from 51%, that is:
\(H_1: p \neq 0.51\)
The test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.
0.51 is tested at the null hypothesis:
This means that \(\mu = 0.51, \sigma = \sqrt{0.51*0.49}\)
A sample of 900 arrests shows that 47% of the arrests were prosecuted.
This means that \(n = 900, X = 0.47\)
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z = \frac{0.47 - 0.51}{\frac{\sqrt{0.51*0.49}}{\sqrt{900}}}\)
\(z = -2.4\)
P-value of the test:
Probability that the sample proportion differs from 0.51 by at least 0.04, which is P(|z|>2.4), which is 2 multiplied by the p-value of Z = -2.4.
Looking at the z-table, the Z = -2.4 has a p-value of 0.0082.
2*0.0082 = 0.0164.
The p-value of the test is 0.0164 > 0.01, which means that there is not sufficient evidence at the 0.01 level to refute the chief's claim.
Juanita borrowed $600 to purchase a new computer. She
was charged 7% interest for two years. She used the
simple interest formula to find the interest.
|=600(7)(2)
What error did Juanita make and how will her error affect
the interest she calculates? Explain.
Answers
Answer:
Forgot to turn the 7% into a 0.7... if you dont do that, then it will come out larger then it was supposed to be :)
Answer:
Sample response: Juanita did not change the 7% to the decimal 0.07. When she completes the problem as written, the interest will be greater than the money she borrowed.
Step-by-step explanation:
This is a sample response, be sure to change the wording up a bit.
A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs ` 45 per litre, how much money is due to the vendor per day?
Answers
Answer:
4500
Step-by-step explanation:
URGENT!!!! Find the y-intercept of the line that passes through the points (-3, 7) and (3, −9).
Answers
Answer:
\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)
\(7 = - \frac{8}{3} ( - 3) + b\)
\(7 = 8 + b\)
\(b = - 1\)
\(y = - \frac{8}{3} x - 1\)
The y-intercept is -1.
What is the non-negative zero of the function f, where f(1) = 6x^2 – 9x– 6?
NO LINKS PLEASE :)
Answers
Answer:
2
Step-by-step explanation:
6x² - 9x - 6 = 0
Factor
(6x + 3)(x - 2) = 0
x = {-1/2, 2}
non-negative zero = 2
A diphosphonate kit contian 180 mCi of Tc99m in 30 ml when it is prepared at 8am. Immediately, a 20 mCi dose is withdrawn for a bone scan. if the patient arrives late at 9:30 and half the volume is accidentally discharged, how much volume from the kit must now be added to the syringe to correct the dose to 20 mCi? (no other doses have been withdrawn meanwhile, and the decay factor for 1.5 hrs is 0.841)
Answers
The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = Initial activity * Decay factor
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = Initial activity - 20 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = Remaining activity * Decay factor
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30
Calculate the remaining volume at 9:30:
Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume
Let's perform the calculations step by step:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = 180 mCi * 0.841 = 151.38 mCi
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = 180 mCi - 20 mCi = 160 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30
Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml
Calculate the remaining volume at 9:30:
Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml
Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
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Work out the mean mark
Answers
Answer:
8.5
Step-by-step explanation:
To find the mean, you have to add the terms, and divide the sum by the number of terms.
7+8+9+10=34
34/4=8.5
-hope it helps
Find the value of f (3)
y =f(x)
Please help
Answers
Answer:
f=7/3
Step-by-step explanation:
from the figure it can be deduced that x=3 and
y=7
so: y=f(x) → 7=f(3)
put f to the first member: 7=3f → 3f=7 → f=7/3
(I hope that's right)
Answer:
f(3) = 7
Step-by-step explanation:
locate x = 3 on the x- axis, then go vertically up to meet the line at (3, 7) , so
f(3) = 7
Is -0.3 irrational number is 3.14144144414444 a rational number explain your reasoning
Answers
Answer: -0.3 and 3.14144144414444 are both rational numbers.
Step-by-step explanation: Rational numbers are numbers that terminate after a certain number of decimal places. Since -0.3 and 3.14144144414444 both satisfy this, they are both rational numbers.
Absolute vale of x+2 if x is less than 2
Answers
Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).
Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).
❗️URGENT❗️
Chase has won 80% of the 30 football video games he has played with his brother, Jacob. If Chase and Jacob continue to play the video game, how many more games in a row goes Chase have to win to achieve an 85% win percentage?
Answers
Answer:
10
Step-by-step explanation:
24/30 = 0.8
24+x/30+x =0.85
10=x
If you want more clarification just ask
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
We can write the total number game won by Chase as -
w = 80% of 30
w = 80/100 x 30
w = 4/5 x 30
w = 24
Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -
(24 + x)/(30 + x) = 85/100
(24 + x)/(30 + x) = 0.85
(24 + x) = 0.85(30 + x)
24 + x = 25.5 + 0.85x
0.15x = 1.5
x = 10
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
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Fourteen percent of the town's population is over the age of 65. If there are 322 residents over the age of 65, approximately what is the town's population?
Answers
If 14 percent of the town's population is over the age of 65 and there are 322 residents over the age of 65, then the population of the town is 2300
The percentage of people over the age of 65 = 14%
Number of residents over the age of 65 = 322
Consider the total population of the town as x
Then the equation will be
x × (14/100) = 322
From this equation we have to find the value of x, that is the population of the town.
x × (14/100) = 322
x × 0.14 = 322
x = 322/0.14
x = 2300
Hence, if 14 percent of the town's population is over the age of 65 and there are 322 residents over the age of 65, then the population of the town is 2300
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Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
Answers
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
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Select the common ratio and the 4th term of the geometric series: 9, -6,4...
Answers
The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.
A geometric sequence is a special series where every term is the product of the previous term and a common ratio.
The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.
In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........
The first term of the sequence, a = 9.
The second term of the sequence, a₂ = -6.
By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:
a₂ = a.r²⁻¹.
Substituting the values, we get:
-6 = 9(r²⁻¹),
or, r²⁻¹ = -6/9,
or, r = -2/3.
Thus, the common ratio of the given geometric sequence is -2/3.
The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:
a₄ = a.r⁴⁻¹ = a.r³.
Substituting the values, we get:
a₄ = 9(-2/3)³,
or, a₄ = 9.(-8/27),
or, a₄ = -8/3.
Thus, the 4th term of the given geometric sequence is -8/3.
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To estimate 179% of 41 by rounding, use the expression
.
Using the distributive property, the expression is equivalent to
.
179% of 41 is about
Answers
The estimate of 179% of 41 by rounding is about 73.19.
To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.
Since we are rounding, we round this value to the nearest whole number, which is 73. Therefore, the direct answer is 179% of 41 is about 73.When estimating by rounding, we look at the decimal places. In this case, the hundredth place is 3. Since 3 is less than 5, we round down. Hence, the estimate is 73.19. It is important to note that rounding introduces some degree of error, as the actual value is 73.39. However, for most practical purposes, an estimate provides a close approximation that is quick and easy to calculate.For more similar questions on whole number
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.
Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.
From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.
Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.
So,
length of arc LNM=Circumference of circle-length of arc LKM.
We know that length of an arc =Θr
in which Θ is the angle in radian.
length of arc=70*π\(/180*5\)
=70π\(/36\)
Circumference of circle=2π*5
=10π
Length of arc LNM=10π-70π\(/36\)
=(360π-70π)\(/36\)
=290π\(/36\)
Put π=3.14
=290*3.14\(/36\)
=910.6\(/36\)
=25.29m
Hence the length of arc LNM is 25.29 m.
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1. The height of a right triangular prism is 1 5/6 inches. Each side of the triangular base measures 10 inches, and the height of the base is 8 2/3 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.
What is the surface area of the solid formed?
100 POINTS!!! IF YOU DRAW AN ACCURATE DIAGRAM TOO, YOU WILL BE AUTOMTIC BRAINLIEST!!!!!!
Answers
If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
First step:-
Right triangular prism=1⁵/₆ inches= 11/6 inches
Height of the base=8²/₃ inches = 26/3 inches
Second step:-
Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)
Surface area = 5(100) +43.33+ 3(18.33)
Surface area = 500) +43.33 + 55
Surface area = 598.33 in²
Therefore the surface area of the solid formed is about 598.33 in²
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Find the value of y.
Answers
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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Question 3 (Percentage)
3.1.
(2)
A student answered 45 problems on a test correctly and received a
grade 90%. How many problems were on the test, if all the problems were worth the same number
were worth the same number of marks? (Round to the nearest whole
number)
Explain what is the difference between fractions and percentages
and also state the relationship they have with each other
3.2.
(3)
3.3
(5)
40% of the 7920 visitors to an amusement park were children. 25% of
these children and 1/3 of the adults were repeat visitors. How many
percent of the visitors were visiting the amusement park for the first
time?
3.4
(4)
Percentage is not taught in foundation phase level. However, a
primary school has both foundation phase and intermediate phase.
If you were to be asked to teach a grade 4 level to substitute for an
absent teacher who was supposed to introduce the concept of
percentage to the grade 4 class using the topic already taught in
foundation phase. Give a brief description on how you will introduce
the concept of percentage using diagrams,
Te to search
13°C Rain showers
Answers
Answer:
A student answered 45 problems on a test correctly and received a
grade 90%. How many problems were on the test, if all the problems were worth the same number
were worth the same number of marks? (Round to the nearest whole
number)
100/90 * 45 = 50
-------------------------------------------------------------------------------------------------------------
Explain what is the difference between fractions and percentages
and also state the relationship they have with each other
The numbers which are decimals by nature can be represented in the form of fractions. For example, 0.5 can also be written as 5/10. ... Percentages refer to decimal numbers to the base 100. These are represented by a % (percent sign).Since a percent is a ratio a ratio can be written as a fraction. This means any of these forms can be converted to any of the others.
-----------------------------------------------------------------------------------------------------------
40% of the 7920 visitors to an amusement park were children. 25% of these children and 1/3 of the adults were repeat visitors. How many percent of the visitors were visiting the amusement park for the first time?
Total number of visitors = 7920
Find the number of children:
Children = 40% of 7920
Children = 0.4 x 7920
Children = 3168
Find the number of adults:
Adult = 7920 - 3168 = 4752
Find the number of repeated visitors that are children:
Repeated visitors = 25% x 3168
Repeated visitors = 0.25 x 3168
Repeated visitors = 792
Find the number of children that are visiting for the first time:
First time visitors = 3168 - 792 = 2376
Find the number of repeated visitors that are adult:
Repeated visitors = 1/3 x 4752
Repeated visitors = 1584
Find the number of adults that are visiting for the first time:
First time visitors = 4752 - 1584 = 3168
Find the total number of first time visitors:
Total number of first time visitors = 3168 + 2376 = 5544
Answer: There are 5544 visitors that are visiting for the first time
pls help me jajahiaj,vsjava
Answers
Answer:
my name is jajahiaj,vsjava
Please show how you did it so I can learn :)
Answers
Answer:
\( x_{1} = 3 + \sqrt {6} \)
\( x_{2} = 3 - \sqrt {6} \)
Step-by-step explanation:
Given the quadratic equation;
x² - 6x + 3 = 0
To find the roots of the quadratic equation, we would use the quadratic formula;
Note: the standard form of a quadratic equation is ax² + bx + c = 0
a = 1, b = -6 and c = 3
The quadratic equation formula is;
\( x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} \)
Substituting into the formula, we have;
\( x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} \)
\( x = \frac {6 \pm \sqrt {36 - (12)}}{2} \)
\( x = \frac {6 \pm \sqrt {36 - 12}}{2} \)
\( x = \frac {6 \pm \sqrt {24}}{2} \)
\( x = \frac {6 \pm 2 \sqrt {6}}{2} \)
\( x_{1} = \frac {6 + 2 \sqrt {6}}{2} \)
\( x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} \)
\( x_{1} = 3 + \sqrt {6} \)
Or
\( x_{2} = \frac {6 - 2 \sqrt {6}}{2} \)
\( x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} \)
\( x_{2} = 3 - \sqrt {6} \)
Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.
Answers
B. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
D. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
A proportional relationship between y and x When x5, ym
What is the constant of proportionality, K?
Enter your answer as a simplified or improper fraction in the box
k -
Answers
Answer:
-7/5
Step-by-step explanation:
Answer:
-7/5
Step-by-step explanation:
It takes light from the Sun 3.25 minutes to reach Mercury. How far away is the planet from the Sun (in km)? The speed of light, c, is 3 ✕ 105 km/s.
Answers
Answer:
66528 km
Step-by-step explanation:
1 sec = 3*105
60 sec = 1 min = 3*60*105 km
3.25 min-?
3 .25×60×105
The distance of Mercury from sun will be 585,000,000 km.
It is given that it takes 3.25 minutes to light to reach from sun to mercury.
If speed of light is 3 × \(10^{5}\) km/sec , then calculate the distance from sun to mercury.
What will be the value of (2 × \(x^{2}\) ) ÷ 2 ?
The value will be \(x^{2}\) .
Distance travelled by light in 1 seconds = 3 × \(10^{5}\) km
∵ 1 minute = 60 seconds
⇒ Distance travelled by light in 1 minute will be ;
= 60 × 3 × \(10^{5}\) km
⇒ Distance travelled by light in 3.25 minutes will be ;
= 3.25 × 60 × 3 × \(10^{5}\) km
= 585,000,000 km
Thus , distance of Mercury from sun will be 585,000,000 km.
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Type the expression that results from the following series of steps:
Start with G, add X, then divide by A
Answers
Step-by-step explanation:
Start with G => G
Add X => G + X
Divide by A => (G + X)/A
Hebce the expression is (G + X)/A.
Answer:
g
, divide by 7, then add 3.
Step-by-step explanation:
What is slope-intercept form?
O not this one
O a² +6² = = C
O Ax+By = C
O y = mx + b
Answers
Answer:
O y = mx + b
Step-by-step explanation:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
amara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to if she rolls the two number cubes 180 times?
Answers
Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.
To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.
Let's examine the chart and count the number of times each sum occurs:
Sum: 2, Occurrences: 1
Sum: 3, Occurrences: 2
Sum: 4, Occurrences: 3
Sum: 5, Occurrences: 4
Sum: 6, Occurrences: 5
Sum: 7, Occurrences: 6
Sum: 8, Occurrences: 5
Sum: 9, Occurrences: 4
Sum: 10, Occurrences: 3
Sum: 11, Occurrences: 2
Sum: 12, Occurrences: 1
Now, let's calculate the probabilities of each sum occurring.
Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:
Probability of sum 2 = 1/36
Probability of sum 3 = 2/36
Probability of sum 4 = 3/36
Probability of sum 5 = 4/36
Probability of sum 6 = 5/36
Probability of sum 7 = 6/36
Probability of sum 8 = 5/36
Probability of sum 9 = 4/36
Probability of sum 10 = 3/36
Probability of sum 11 = 2/36
Probability of sum 12 = 1/36
To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.
For example, to find the expected number of times the sum is 7:
Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30
Similarly, we can calculate the expected occurrences for all other sums.
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Consider the system of equations.
8x- 6y = 12
| Cx - 3y = 6
What value of C would produce a system
Answers
9514 1404 393
Answer:
C = 4: dependent systemC ≠ 4; independent, consistent system with solution (0, -2)Step-by-step explanation:
If you divide the first equation by 2, you get ...
4x -3y = 6
If C=4, the second equation would be identical to this, giving a dependent system of equations with an infinite number of solutions.
If you want a system of equations with one solution, the value of C must be anything except 4. (That system will have the solution (x, y) = (0, -2).)
Determine the largest power of 10 that is a factor of the following numbers (equivalently, the number of terminal 0's, using ordinary base 10 representation):(a) 50!.
(b) 1000!.
Answers
The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.
(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.
There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.
Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.
(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:
⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249
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A bank customer borrowed $4000 for 1 year at 5% simple interest to buy a computer. How much interest did the customer pay
Answers
$4,200 because 1.05 times 4,000 is 4,200