Write 171 miles in 3 hours as a unit rate
Destiny works on commission as an office supply saleswoman. She sold a computer that cost $700 and received a $126 commission.
What percent of her sale is Destiny's commission?
the total cost of 4 pens and 7 mechanical pencils is $13.25 the cost of each pencil is $0.75 write an equation that could be used to find the cost of a pen
pam read 126 pages of her summer reading book in 3 hours. Zack read 180 pages of his summer reading book in 4 hours. If they continue to read at same speeds, will they both finish the 215 page book after 5 total hours of reading?
While on a one-hour trip, a small boat travels 32 km north and then travels 45 km east. what is the direction of the boat's average velocity for the one-hour trip? 27° north of east 35° north of east due east 54° north of east 45° north of east?
The boat average velocity for the one hour trip is 54° north of east.
What is Average velocity?
Average velocity is defined as the change in position divided by the time interval in which the displacement occurs.
Given that;
A small boat travel 32 km north and then travels 45 km east.
Now,
Average velocity is calculated as;
By figure,
Average velocity = cotθ = 32/45
θ = cot⁻¹ (32/45)
θ = 54°
Thus, The boat average velocity for the one hour trip is 54° north of east.
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The selling price for a classic car is $16000 which is. $1000 more than three times its original price. What was the original price of the car?
The original price of the classic car was $5,000
The student's question seeks to determine the original price of a classic car, given that the selling price is $16,000, which is $1,000 more than three times its original price. To find the original price, we can set up an equation: let the original price be represented by x. The equation based on the information provided would be:
3x + $1000 = $16000
Subtracting $1000 from both sides to isolate the terms with x gives us:
3x = $16000 - $1000
3x = $15000
Finally, dividing both sides by 3 to solve for x, we get:
x = $15000 / 3
x = $5000
Therefore, the original price of the car was $5000.
The original price of the car was $5000
Let the original price of the car be x.
According to the problem, the relationship between the original price and the selling price can be described by the following equation:
[tex]\[ 3x + 1000 = 16000 \][/tex]
To find x :
Isolate x on one side :
Subtract 1000 from both sides to remove the extra cost:
[tex]\[ 3x = 16000 - 1000 = 15000 \][/tex]
Solve for x :
Divide both sides by 3:
[tex]\[ x = \frac{15000}{3} = 5000[/tex]
Thus, the original price of the car was $5000.
Question :
The selling price for a classic car is $16000 which is. $1000 more than three times its original price. What was the original price of the car?
Mike, therese, tristan, and elena want to improve their fico credit score. mike uses 10% of his credit limit, therese uses 30% of her limit, tristan uses 50% of his limit, and elena uses 75% of her limit. who is improving their score the most?
x^2-3=5x simplify this
Enter the solution to the inequality in the box.
−9x−6≥−3(x−4)
Answer:
x ≥ -3
Step-by-step explanation:
i used a calculator, please give brainliest
Question Help A tourist asked a zookeeper how many birds and lions are in the zoo. The zookeeper replied there are 32 heads and 102 feet. Find the number of each.
Final answer:
By setting up and solving a system of equations, we find that there are 13 birds and 19 lions in the zoo.
Explanation:
To solve the problem of determining the number of birds and lions in the zoo given 32 heads and 102 feet, we can set up a system of equations. Birds have 2 feet, and lions have 4 feet. Let B represent the number of birds and L represent the number of lions.
Equations:
B + L = 32 (total heads)
2B + 4L = 102 (total feet)
Solving this system, we'll first multiply the first equation by 2 to facilitate elimination:
2B + 2L = 64
2B + 4L = 102
Subtracting the first modified equation from the second equation gives us 2L = 38, so L=19. Substituting L=19 into the first equation, we find B = 32 - 19 = 13.
Therefore, there are 13 birds and 19 lions in the zoo.
Round 227,985 to the nearest thousand.
:227,000
:228,000
:227,900
:230,000
i already asked this but could you please help me on E F G H four questions on stimultaneous equations. There is also an attachment.
ASAP Thank You So Much
Which number sentence correctly solves this problem?
There are 44,732 people living in Brownville. There are 17,251 living in Crossville. How many more people live in Brownville than in Crossville?
A.
44,732 + 17,251 = 61,983
B.
44,732 – 17,251 = 33,521
C.
44,732 – 17,251 = 27,481
D.
44,732 + 17,251 = 51,983
i got the same question :D
8. Based upon a long period of record keeping the following represents the probability distribution of the number of times the John Jay wifi network is slow during a week. We call the random variable x.
x 0 1 2 3 4 5 6
p(x) .08 .17 .21 k .21 k .13
a. What is the value of k?
b. Calculate the expected value of x.
c. Calculate the expected value of x^2
.
d. Calculate the variance of x.
e. Calculate the standard deviation of x
f. Calculate the variance of 3x.
g. Suppose that network slowness is independent from week to week. What is the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks?
h. Calculate the variance of the random variable x^2
Answer:k=2
Step-by-step explanation:
What is the justification for each step in the solution of the equation?
23x−13=2(x+2)23x−13=2(x+2)
Select from the drop-down menus to correctly justify each step.
The solution involves the application of mathematical properties such as the distributive property, the process of simplifying, the use of additive inverse, and the division property of equality. These steps result in x = 0.81.
Explanation:To solve the given equation, 23x - 13 = 2(x + 2), let's break down the steps:
First, distribute 2 to each term within the parenthesis on the right side of the equation to apply the distributive property. This leads to 23x - 13 = 2x + 4. Second, gather like terms on both sides of the equation in a process known as simplifying the equation. Subtract 2x from both sides to get: 21x - 13 = 4. Next, you should isolate the variable x, by adding 13 to both sides of the equation. This use of additive inverse results in 21x = 17. Finally, divide each side of the equation by 21 to get x by itself—a step justified by the division property of equality. This results in x = 17/21, which simplifies to x = 0.81 (approximately). Learn more about Solving Equations here:
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To solve the equation 23x - 13 = 2(x + 2), distribute the 2, combine like terms, and isolate the variable x.
Explanation:To solve the equation 23x - 13 = 2(x + 2), we need to simplify both sides of the equation step by step.
Therefore, the solution to the equation is x = 17/21.
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If f (x)=2x^2+1 and g (x)=3x-2 what is the value of f (g (-2))?
If EF = 4x − 16, FG = 3x − 6, and EG = 27, find the values of x, EF, and FG.
Carly has 2 more nickels than dimes in her pocket she has 40 cents. How many nickels does she have? How many dimes does she have?
She has 4 nickels and 2 dimes
Let x represent the number of dimes
5+(x+2)+19x=40
5x+10x+10=40
15x=40-10
15x=30
x=30/15
x=2
x+2=4
Inconclusion She has 4 nickels and 2 dimes
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There are four families attending a concert together. each family consists of 1 male and 2 females. in how many ways can they be seated in a row of twelve seats i
The four families consisting of 12 distinct individuals can be seated in 12! (479,001,600) ways. There are no seating restrictions, so each person can occupy any of the twelve seats.
Explanation:The subject of this question is combinatorics, a branch of mathematics. In this problem, you have four families, each consisting of 1 male and 2 females, and you want to know in how many ways they can be seated in a row of twelve seats.
Given there is no restriction about the seating pattern, each member can occupy any seat. So, consider each family member as a distinct person; you then have 12 people to be seated in 12 different ways. This can be done in 12 factorial (12!) ways. Factorial implies the product of all positive integers up to that number. A simple way to calculate 12 factorial is: 12*11*10*9*8*7*6*5*4*3*2*1, which equals 479,001,600.
So, the four families can be seated in a row of twelve seats in 479,001,600 ways. This principle of arrangements is a key part of combinatorics and discrete mathematics.
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Considering each family as a single unit, the total number of ways they can be seated in a row of twelve seats is given by the formula: 12! divided by (2!) to the power of 4.
Explanation:This is actually a problem that is solved using the principles of permutations and combinations in mathematics. Given we have 4 families each with 1 male and 2 females, we have a total of 12 people. Now, if we are to arrange these 12 people in a row of twelve seats, we have 12! (factorial) ways to do it. However, each family group is to be considered as a single unit and within each unit, arrangements don't count, so we must divide by the number of ways to arrange the 2 females within each family of 4, which is 2!. Hence, the total number of ways to seat the group is given by (12! / (2!)^4).
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Select "Rational" or "Irrational" to classify each number. 0.25 Sq. Rt. 0.25 Sq. Rt. 0.33
Becca orders a DVD over the internet. The company’s website says the DVD will be send out the following working day. It will arrive no more that 10 working days later. Working days are Monday to Friday. Becca orders her DVD on Wednesday 4 August. What is the latest data Becca will get her DVD?
We want to create a class that represents a geometric sequence. a geometric sequence is a sequence of numbers that begin at some value and then multiplies each value by some constant to get the next value. for example, the geometric sequence 1, 2, 4, 8, 16 starts at 1 and multiplies each term by 2 to get the next. the geometric sequence 10.8, 5.4, 2.7, 1.35 starts at 10.8 and multiplies each term by 0.5 to get the next. the basic framework of a geometric sequence class is below:
A geometric sequence class in programming can represent a series of numbers where each term is generated by multiplying the previous term by a fixed number. This follows the rules of exponential arithmetic, as seen in examples of exponential increase and decrease.
Explanation:In the context of programming, the basic framework of a geometric sequence class can represent a geometric sequence, following the rules of exponential arithmetic. In mathematics, a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
For instance, a geometric sequence that begins at 1 and multiplies each term by 2 would look as follows: 1, 2, 4, 8, 16. Notice that each subsequent term is twice the value of its previous term i.e., an exponential increase.
Similarly, the geometric sequence 10.8, 5.4, 2.7, 1.35 starts at 10.8 and multiplies each term by 0.5, resulting in an exponential decrease. While not directly related to the question, geometric sequences can also be used to calculate geometric probabilities.
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Please help. A spinner had 7 identical sections. Two sections are blue, 1 us red, and 4 of the sections are green. Suppose the probabilty of an event happening is 2/7 (fraction). What does each number in the ratio represent? What outcome matches this probability?
a tool rental cost $0.65 per minute. if the total bill for the rental was $18.20 then for how many minutes was the tool used?
What does f equal in this equation? 6f-12=-4f+6
round 23.84 to 1 decimal point
convert decimals to fractions do not simplify.
Liam has 9/10 gallon of paint for painting the birdhouse he sells at the craft fair. Each birdhouse requires 1/20 gallon of paint.how many birdhouse can Liam paint? Show your work.
A sphere with a diameter of 16mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. How high is the cylinder?
The height of the cylinder is 8mm.
Explanation:To find the height of the cylinder, we need to first find the surface area of the sphere. The surface area of a sphere is given by the formula: 4πr^2. Since the diameter of the sphere is 16mm, the radius is half of that, which is 8mm. Plugging the value of the radius into the formula, we get: 4π(8^2) = 256π mm^2.
Next, we need to find the surface area of the cylinder. The base diameter of the cylinder is equal to the diameter of the sphere, which is 16mm. Therefore, the radius of the cylinder is also 8mm. The surface area of the cylinder is given by the formula: 2πrh + 2πr^2. Since the height is unknown, we'll use a variable 'h'.
Since the surface area of the sphere is equal to the surface area of the cylinder, we can set up an equation: 256π = 2πrh + 2πr^2. Plugging in the values, we get: 256π = 2π(8)(h) + 2π(8^2).
Cancelling out the common factor of 2π, we have the equation: 128 = 8h + 64. Subtracting 64 from both sides of the equation, we get: 64 = 8h. Dividing both sides by 8, we find that the height of the cylinder is: h = 8mm.
We want to build a box whose base is square, has no top and will enclose 100 m^3. determine the dimensions of the box that will minimize the amount of material needed to construct the box.
The dimensions of the box that minimizes material usage, enclosing 100 m³ with no top, are approximately 5.848 meters for the square base side length and 2.682 meters for the height.
Let's denote the side length of the square base as x meters and the height of the box as h meters. Since the box has no top, the volume (V) of the box is given by the product of the area of the square base and the height:
[tex]\[ V = x^2 \cdot h \][/tex]
Given that [tex]\(V = 100 \, \text{m}^3\)[/tex], we have the equation:
[tex]\[ 100 = x^2 \cdot h \][/tex]
Now, we want to minimize the amount of material needed to construct the box, which is the surface area (A) of the box. The surface area is the sum of the area of the square base and the areas of the four sides:
[tex]\[ A = x^2 + 4xh \][/tex]
To minimize A, we can express h in terms of x from the volume equation and substitute it into the surface area equation:
[tex]\[ h = \frac{100}{x^2} \]\[ A(x) = x^2 + 4x\left(\frac{100}{x^2}\right) \]\[ A(x) = x^2 + \frac{400}{x} \][/tex]
Now, to find the minimum amount of material, we take the derivative of A with respect to x and set it equal to zero:
[tex]\[ \frac{dA}{dx} = 2x - \frac{400}{x^2} = 0 \][/tex]
Multiply through by x^2 to get rid of the fraction:
[tex]\[ 2x^3 - 400 = 0 \][/tex]
Solve for x:
[tex]\[ x^3 = 200 \]\[ x = \sqrt[3]{200} \][/tex]
Now that we have x, we can find h using the volume equation:
[tex]\[ h = \frac{100}{x^2} \]\[ h = \frac{100}{(\sqrt[3]{200})^2} \]\[ h = \frac{100}{\sqrt[3]{400}} \][/tex]
The dimensions of the box that will minimize the amount of material needed are approximately [tex]\(x \approx 5.848\)[/tex] meters and [tex]\(h \approx 2.682\)[/tex] meters.