Answer:
The answer is C. x÷30 = (x + 300)÷55
Step-by-step explanation:
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph.
The equation will be
Total speed = Total distance / time taken
x ÷ 30 = (x + 300) ÷ 55
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
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Which expression is equal 3(5+6) ?
a. 15+6
b. 5+18
c. 15+18
d. 3+11
please explain
is 8π rational or irrational number?
How many ways can 5 different colored balls be placed into bins labeled 1 through 8 so that no bin contains more than one ball?
The number of ways 5 different colored balls be placed into bins labeled 1 through 8 so that no bin contains more than one ball is 336.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, 5 different colored balls be placed into bins labeled 1 through 8.
We know that, P(n, r) =n!(n-r)!
Here, P(8, 5) = 8!/(8-3)!
= 8×7×6×5!/5!
= 8×7×6
= 336
Therefore, the number of ways 5 different colored balls be placed into bins labeled 1 through 8 so that no bin contains more than one ball is 336.
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A fountain on a lake sprays water in a parabolic arch modeled by the equation
y = −0.4x2 + 3x, where y is the height in feet and x is the horizontal distance. A beam of light is passed through the fountain to create a rainbow effect. If the beam is directed at an angle modeled by the equation -2.2x + 4.9y = 8.18, at what distance from the ground will the beam first touch the water spray?
A. 0.6 feet
B. 2 feet
C. 4.2 feet
D. 5.6 feet
Find an equation for the nth term of the arithmetic sequence.
a16 = 21, a17 = -1
an = 351 + 22(n + 1)
an = 351 - 22(n + 1)
an = 351 + 22(n - 1)
an = 351 - 22(n - 1)
Answer:d
Step-by-step explanation:test
Write an equation of the description
A number x increased by 17 is 118.
how far will a bus travel if it averages a sped of 65 km/h for 7 hours?
The bus will go 455 km far if it averages a speed of 65 km/h for 7 hours the answer is 455 km.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
The speed of the bus = 65 km/h
The time taken = 7 hours
As we know,
The formula for finding the distance is given:
Distance = time×speed
Distance = 7x65
Distance = 455 km
Thus, the bus will go 455 km far if it averages a speed of 65 km/h for 7 hours the answer is 455 km.
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The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?
Which three expressions could be used to represent the numbers?
1st number = x
2nd number = x-4
3rd number = 4x
now you have x + x-4 +4x = 62
combine like terms
6x-4 = 62
add 4 to each side
6x = 66
divide both sides by 6
x = 66/6 = 11
1st number = 11
2nd number = 11-4 = 7
3rd number = 4*11 = 44
11+7+44 = 62
If a data set has 16 data values, the number of values in the upper quartile is ?
Answer:
4
Step-by-step explanation:
Quartiles divide the data into 4 equal parts. So, each quartile will have 16/4= 4 values. Therefore, the number of values in the upper quartile is 4.
Given that x is a number that is not negative, Kelvin conjectured that x^2>x+1 .
Which value is a counterexample to Kelvin's conjecture?
−12
−2
0
5
Answer: x=0 is a counterexample to Kelvin's conjecture.
Explanation:-
Given that x is a number that is not negative, Kelvin conjectured that [tex]x^2>x+1[/tex]
A counter example is an example that contradicts or opposes the conjecture.
Thus -12 and -2 cannot be the value of x for the counter example as they are negative
The positive numbers in options are 0 and 5,such that
[tex]0^2>0+1\\\Rightarrow0>1...\text{which is not true.}[/tex]
[tex]5^2>5+1\\\Rightarrow25>6...\text{which is true.}[/tex]
Thus the value of x=0 contradicts the conjecture made by Kevin.
⇒x=0 is a counterexample to Kelvin's conjecture.
The function c = 2.50(n – 2) + 4.50 represents the cost c in dollars of printing n invitations. Which of the following is not true?
A/Each invitation costs $4.50 to print.
B/The cost depends on the number of invitations printed.
C/For each additional invitation, it costs an extra $2.50 to print.
D/One cannot print just one invitation.
The equation c = 2.50(n - 2) + 4.50 represents the cost of printing n invitations, with $4.50 being a fixed cost and $2.50 as the additional cost per invitation after the first two. Thus, the statement that A. each invitation costs $4.50 to print is not true.
The function in question, c = 2.50(n – 2) + 4.50, represents the total cost c of printing n invitations. To determine which of the provided statements is not true, we can analyze the components of the equation:
4.50 is a fixed cost, indicating a base charge that is applied regardless of the number of invitations printed.The term 2.50(n – 2) shows that each additional invitation, beyond the first two, incurs a variable cost of $2.50.Analyzing the provided options:
Each invitation costs $4.50 to print. This statement is false, as the $4.50 in the equation is a fixed cost and not reflective of the individual cost per invitation.The cost depends on the number of invitations printed. This is true as the cost increases with each additional invitation after the first two.For each additional invitation, it costs an extra $2.50 to print. This is true given the variable cost component of the equation.One cannot print just one invitation. There is nothing in the equation that inherently prevents printing one invitation, so this statement is true.Therefore, the answer to the student's question is option A: Each invitation costs $4.50 to print is not true.
Which of the following numbers is classified as an irrational number?
A.) Square root of 72
B.) 7.444444
C.) -3
D.) -1/20
Devon’s price is a high school teacher and soccer coach his annual salary is 37,440 What is his Biweekly salary
Alex wants to put a fence around his garden. It is square and has an area of 196 square feet. He wants to put a post in each corner, and every 7 feet. How may posts and how may feet of fencing does he need?
N the ideal normal curve, 95% of the population falls within _____ standard deviation(s) of the mean. a. one b. two c. three d. four
Hanks pickup can travel 52 miles on 4 gallons of gas. How many gallons will habh pickup need to travel 26 miles?
To determine how many gallons Hanks' pickup will need to travel 26 miles, a proportional relationship was used based on the known mileage of traveling 52 miles on 4 gallons. The calculation revealed that 2 gallons of gas will be needed for the 26-mile journey.
Explanation:The student's question about fuel consumption can be solved using a simple proportional relationship. Since Hanks' pickup can travel 52 miles on 4 gallons of gas, we can find out how many gallons will be necessary to travel half of that distance, which is 26 miles. By setting up a proportion, we can find the answer.
Steps to solve the problem:
Identify the known relationship between distance and gallons of gas: 52 miles = 4 gallons.Set up a proportion to find out how many gallons are needed for 26 miles, knowing that the relationship should remain constant: (52 miles / 4 gallons) = (26 miles / x gallons).Solve for x by cross multiplying: 52x = 4 * 26.Calculate the value of x: x = (4 * 26) / 52.Simplify to find the number of gallons needed: x = 2 gallons.Therefore, Hanks' pickup will need 2 gallons of gas to travel 26 miles.
The pickup truck will need 2 gallons of gas to travel 26 miles.
Explanation:To find out how many gallons the pickup will need to travel 26 miles, we can set up a proportion using the given information.
Since the pickup can travel 52 miles on 4 gallons of gas, the rate of miles per gallon is 52 miles/4 gallons = 13 miles/gallon.
Using this rate, we can set up the proportion: 13 miles/gallon = 26 miles/x gallons. Solving for x, we can cross multiply and divide: 13x = 26 * 1, x = 26/13 = 2.
Therefore, the truck will need 2 gallons of gas to travel 26 miles.
Find the average weekly earnings. hours worked each week: 20; hourly rate: $3.25; weekly tips: $115.75, $94.80, $73.15, $62.50
Simplify the following expression 5^2-4/5+2
To simplify the expression 5^2-4/5+2, we first simplify the exponent, divide 4 by 5, and add the results together to get 129/5 or 25.8.
Explanation:To simplify the expression 5^2-4/5+2, we need to follow the order of operations which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Using PEMDAS, we first simplify the exponent, so 5^2 = 5 x 5 = 25.
Next, we divide 4 by 5 to get 4/5.
Finally, we add 25 and 4/5 which can be written as 25 + 4/5. To add these two fractions, we need a common denominator which is 5. Converting 25 into a fraction with a denominator of 5 gives us 125/5. Adding 125/5 and 4/5 gives a result of 129/5. Therefore, the simplified expression is 129/5 or 25.8.
Which expression is equal to 2√ -32 ? 8i√2 −8√2 8√2i −8i√2
the first one is the answer
Final answer:
The expression 2√ -32 is equal to 8i√2
Explanation:
To find an expression equal to 2√ -32, we need to recall that the square root of a negative number involves an imaginary unit i. The square root of -1 is defined as i. Thus, we can rewrite the expression as:
2√ -32 = 2√(-1 × 32) = 2√(-1)√(32) = 2i√(16 × 2) = 2i × 4√2 = 8i√2.
which is found by using the property that the square root of -1 is the imaginary unit i.
This demonstrates that the correct expression equivalent to the original one is 8i√2.
three times the square of a non-zero number is equal to fifteen times the number.. what is the number?
Is this increasing decreasing or constant F(x)=3x
The record for the Boston Marathon's wheelchair division is 1 hour, 18 minutes, and 27 secondsThe Boston Marathon is 26.2 miles long. What was the average speed of the record winner of the wheelchair division? Round to the nearest hundredth.
helppppppppppppp maTHHHH
evaluate this piecewise function at x=-4 and x=4
At a baseball game, a vender sold a combined total of 123 sodas and hot dogs. The number of hot dogs sold was 53 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
How to do this exponent and simply and having positive exponents
To multiply exponentials, multiply the base numbers and add exponents. Adjust the format to have one digit before the decimal, if necessary. To divide, divide the base numbers and subtract the exponents.
Explanation:To deal with the multiplication of exponentials, simply multiply the base numbers (digits) as you normally would, and then add the exponents. Remember to keep the result in the acceptable form, meaning that for a number like 2.4×10⁴, there should be only one digit to the left of the decimal point. To handle negative exponents, add them as usual, and adjust the exponent to maintain a positive value. For dividing exponentials, you divide the base numbers and subtract the exponents.
Here's a step-by-step example for multiplication: Suppose you have 5.1×10³ and 4.2×10⁴. You multiply the base numbers to get 21.42, and then add the exponents (3+4) to get 7, which gives you 21.42×10⁷. To adjust the number to proper form, you would change it to 2.142×10⁸. For squaring an exponential like 3×10², you'd square the 3 to get 9 and multiply the exponent by 2 to get 4, leading to 9×10⁴.
When squaring exponential terms, square the digit term and multiply the exponent by 2. For instance, (2×10²)² equals 4×10⁴. And remember, any number to the power of zero equals one, as 0 exponent implies no multiplication of the base number, leaving us with the implicit base of multiplication which is 1.
Anyone wanna help teach me how to do any of this or just give me the answers if you don't wanna teach me
just replace the value in the appropriate equation:
a) says f(-2)
so use the f equation above it and replace x with -2
f(x) = 3x-5 becomes f(-2) = 3x-5 =
3(-2)-5 = -6-5 = -11
for b use the equation for h and replace x with -5
so x^2 - 6 = -5^2 - 6 = -31
for c use the equation for g and replace x with (a+b)
-7x+3 =
-7(a+b)+3 = -7a-7b+3
Find the lowest common denominator of and . A. (p + 2) B. (p + 5)(p + 3) C. (p + 5)(p + 2)(p + 3) D. (p + 2)2
how many thousands go into 90 hundreds
90 hundreds = 90 * 100 = 9000
9000 = 9 thousands
A home file is the place where you should keep financial records that you may need to access regularly? True or False
What is the lcm of 6 ,21 and 28 on?