The first truck in a convoy will carry 12 tons of dirt while each additional truck will carry 8 tons of dirt. Write a rule to model th situation. Then use the rule to find how many tons of dirt can be carried by 7 trucks. Let n represent the number of trucks and t represent the tons of dirt.
Final answer:
To model the situation, use the rule t = 12 + 8(n - 1), where n is the number of trucks. Applying this rule, 7 trucks can carry a total of 60 tons of dirt.
Explanation:
The student should write a rule to model the situation where the first truck carries 12 tons of dirt and each subsequent truck carries 8 tons. The rule can be defined as t = 12 + 8(n - 1), where n represents the number of trucks and t represents the total tons of dirt carried. For 7 trucks, we can plug in the value of n into the equation:
t = 12 + 8(7 - 1)
t = 12 + 8(6)
t = 12 + 48
t = 60 tons
Therefore, 7 trucks can carry a total of 60 tons of dirt.
An American green tree frog tadpole is about 0.00001 kilometer in length when it hatches. Write this decimal as a power of 10
The decimal number 0.00001 can be written as a power of 10 as 1 x 10^-5. This is because the decimal is shifted five places to the right.
Explanation:The student is asked to express the number 0.00001 as a power of 10. This can be achieved by understanding that the power (exponent) of 10 is equal to how many places the decimal is shifted. Here, the decimal is shifted five places to the right so we use the negative exponent -5 to denote this shift. Therefore, 0.00001 written as a power of 10 is 1 x 10^-5.
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A survey asks 1200 workers, "has the economy forced you to reduce the amount of vacation you plan to take this year?" Thirty-five percent of those survey selected. The random variable represents the number of workers who are reducing the amount of vacation. Find the mean, variance and standard deviation of the binomial deviation of the binomial distribution.
The probability of an event is defined as the possibility of an event occurring against sample space.
Let us tackle the problem.
A survey asks 1200 workers → n = 1200
Thirty-five percent of those survey selected → p = 35% = 0.35
To find the mean of a binomial distribution, we can use the following formula:
[tex]Mean = n \times p[/tex]
[tex]Mean = 1200 \times 0.35[/tex]
[tex]\boxed {Mean = 420}[/tex]
To find the variance of a binomial distribution, we can use the following formula:
[tex]Variance = n \times p \times (1 - p)[/tex]
[tex]Variance = 1200 \times 0.35 \times (1 - 0.35)[/tex]
[tex]Variance = 1200 \times 0.35 \times 0.65[/tex]
[tex]\boxed {Variance = 273}[/tex]
To find the standard deviation of a binomial distribution, we can use the following formula:
[tex]Standard ~ Deviation = \sqrt{Variance}[/tex]
[tex]Standard ~ Deviation = \sqrt{273}[/tex]
[tex]\boxed {Standard ~ Deviation \approx 17}[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
what is the interqueartile range for the data set 13,14,17,18,23,27,28,31,34
Three-fourths of the sixth grade students at Ashlee’s school are twelve years old. One-half of the twelve year old students are boys. What fraction of the sixth grade students are twelve year old boys? Use numbers to explain your answer.
An employee's annual salary was increased from $22,464.00 to$24,710.40 last year. If it is increased by the same percent this year, what will the employee's salary?
What is 45 1/2% as a fraction in the simplest form?
Simplify by combining like terms.
12−a+a+12
Thanks!
Melody jackson wishes to enclose a rectangular garden with fencing, using the side of her garage as one side of the rectangle. a neighbor gave her 30 feet of fencing, and melody wants the length of the garden along the garage to be 3 feet more than the width. what is the length of the garden? write your answer without units.
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→8 x2 − 64 x2 − 8x
Take the limit as x approaches 8 to get the answer of 9.
Explanation:To find the limit of (x² - 64) / (x² - 8x) as x approaches 8, we can simplify the expression by factoring and cancelling common factors.
First, we factor in the numerator and denominator:
x² - 64 = (x + 8)(x - 8) and x² - 8x = x(x - 8).
Now we can cancel the common factor of x - 8 to simplify the expression: (x + 8)/(x).
Now, we can take the limit as x approaches 8:
Lim(x→8) (x + 8)/(x) = 8 + 8/8
= 9.
So the limit of the given expression as x approaches 8 is 9.
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Saylor Henshaw earned $120 in simple interest in 9 months at an annual interest rate of 5%. How much money did he invest?
Saylor Henshaw invested $1600.
Explanation:To find out how much money Saylor Henshaw invested, we can use the formula for simple interest:
Interest = Principal × Rate × Time
In this case, Saylor earned $120 in 9 months at an annual interest rate of 5%.
Let's assume the principal amount is P.
Using the formula:
120 = P × 0.05 × (9/12)
Simplifying the equation, we have:
P = 120 ÷ 0.05 × 12/9
P = $1600
So, Saylor Henshaw invested $1600.
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the distance between the points 5,1 and 5,-6 is the square root of length?
Use the distributive property to write the products as sums:7(4n-5m-2)
The distributive property is used to multiply 7 by each term inside the parentheses (4n, -5m, -2) resulting in the expression 28n - 35m - 14.
Explanation:To apply the distributive property to the expression 7(4n-5m-2), you multiply each term inside the parentheses by 7. The distributive property allows us to multiply a single term outside a parenthesis with each term inside the parenthesis, effectively distributing the multiplication.
First term: 7 × 4n = 28nSecond term: 7 × -5m = -35mThird term: 7 × -2 = -14Therefore, the product written as a sum, using the distributive property, is 28n - 35m - 14.
Jimmy has a number cube labeled 1through 6, and a penny. How many different ways can the cube and penny land with one roll of the cube and one flip of the penny . 1. 2. 3. 4. 5. 6
Answer:
12 ways
Step-by-step explanation:
We know that,
When the cube is rolled,
Possible ways = 6 ( i.e. 1, 2, 3, 4, 5 or 6 ),
While, when a penny is flipped,
Possible ways = 2 ( i.e. head or tail ),
Thus, when the cube and penny flipped one time,
Total possible ways = 6 × 2 = 12
( i.e, 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T or 6T )
Which number could replace box the to make this number sentence true?
27 > + 8
In the general linear equation, y = bx + a, what is the value of b called?
The Junior Soccer League takes 12-person vans to the tournament. The league has 146 players and 14 coaches. How many vans are needed and how many people are left over?
Final answer:
The Junior Soccer League will need a total of 14 vans to transport 160 people, with 4 people left over after filling the 13th van.
Explanation:
To calculate the number of 12-person vans needed for the Junior Soccer League event, we first need to determine the total number of people that require transportation. This includes both players and coaches.
We have 146 players and 14 coaches, giving us a total of 160 people. If each van holds 12 people, the next step is to divide the total number of people by the capacity of the van.
Divide the total number of people by the capacity of the van (12).Calculate the number of full vans required.Determine if there are any people left over.160 ÷ 12 = 13 vans with 4 people left over because 12 vans can only carry 144 people (12 × 12), and 16 people are remaining, which requires another van to accommodate them.
So, the league will need a total of 14 vans for transportation, and there will be 4 people left over after filling the 13th van.
The number 72 is between what two perfect squares? Enter a numerical answer only
Find a power series solution to the differential equation at the point x0. (2+x2)y′′-xy′+4y=0
From Monday to Tuesday, the depth of a snowdrift changed by −2 3/8 inches. From Tuesday to Wednesday, the depth changed by half as much. What is the change in the depth of the snowdrift from Tuesday to Wednesday? Please answer I don't have much time, thanks.
divide 2 3/8 inches by 2
2 /2 = 1
3/8 /2 = 3/16
change was - 1 3/16
lily swims a 100-meter race. she swims the first half in 27.8 seconds. she swims the second half in 30.12 seconds. how long does it take lily to swim the whole race?
we know that
1) Lily swims a [tex]100[/tex]-meter race
2) She swims the first half in [tex]27.8[/tex] seconds
3) She swims the second half in [tex]30.12[/tex] seconds
so
To find the total time to swim the whole race sum the time in the first half plus the time in second half
[tex](27.8+30.12)=57.92\ seconds[/tex]
therefore
the answer is
[tex]57.92\ seconds[/tex]
By adding the two given times, we will see that she completes the race in 57.92 seconds.
How to find the time in which she finishes the race?
We know that:
She swims the first half on 27.8 seconds.She swims the second half on 30.12 seconds.Then the time that it took to complete the whole race is just the sum of these two times, we will get:
Total time = 27.8 seconds + 30.12 seconds = 57.92 seconds.
We can conclude that Lily swims the whole race in 57.92 seconds.
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A 30-mi. stretch of highway has markers every 0.2 mi. The first marker is at the 0.2 mi. mark and the last marker is at the end of the highway at the 30 mi. mark. If n is the number of markers, which equation is true?
A. 30 • 0.2 = n
B. 30 • 0.5 = n
C. 30 • n = 0.2
D. 30 ÷ 0.2 = n
Answer would be D
, you need to divide the total distance by the spacing to find total markers
Answer:
Your answer is D. 30 divided by 0.2 = n.
Step-by-step explanation:
Divide 30 by 0.2 and you get your correct answer.
how many tiles in figure 0? Where is the Y intercept?
On Monday, David had $50 in his wallet and withdrew $200 from his bank account. He bought 2 shirts for $12.00 each, and 2 pairs of shoes for $26.00 each. Write the final expression needed to determine how much money David had at the end of the shopping day. 50+200- [2(12) +2(26)] 50+200+[2(12) +2(26)] 50-200[2(12) +2(26)] 50-200/[2(12) +2(26)]
Answer:
50 + 200 - [2(12) + 2(26)] is the correct option
Find the percent of change from $240 to $320
gregorios drive 200 miles per day for 10 days how many miles did he drive in all
what is the correct way to read this number 6.3078
Bill Payne visits his local bank to see how long it will take for $1,000 to amount to $1,900 at a simple interest rate of 12 ½%. Provide Bill with the solution to his problem in years
It will take approximately 0.72 years for $1,000 to accumulate to $1,900 at a simple interest rate of 12 ½%.
Explanation:To find out how long it will take for $1,000 to amount to $1,900 at a simple interest rate of 12 ½%, we can use the simple interest formula:
Interest = Principal × Rate × Time
Where:
Substituting the values into the formula:
Interest = $1,900 - $1,000
$1,900 - $1,000 = $900
$900 = $1,000 × 0.125 × Time
To find Time, we can rearrange the formula:
Time = $900 / ($1,000 × 0.125)
Time = 0.72 years
Therefore, it will take approximately 0.72 years for $1,000 to accumulate to $1,900 at a simple interest rate of 12 ½%.
Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 6
Expressions equivalent to 'log 2 - log 6' are based on the property of logarithms that states 'log a - log b' is equivalent to 'log (a/b)'. Thus, the equivalent expression is 'log (1/3)'.
The expressions equivalent to log 2 - log 6 can be found using the property of logarithms that deals with the difference of logarithms. According to this property, log a - log b is equivalent to log (a/b). Therefore, one equivalent expression for log 2 - log 6 would be log (2/6), which can be simplified to log (1/3).
the following shows a sequence of perfect cube
64,p,216,q
find the value of p+q