Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that [tex] \frac{ \sqrt{x^2-36} }{x} [/tex] 0 ≤ θ < π/2.
x=6secФ
Ron Co. sold sweatshirts ($20) and baseball caps ($10). If total sales were $2,860 and people bought 6 times as many sweatshirts as caps, how many of each were sold?
To find the number of baseball caps and sweatshirts sold, we can set up an equation using the given information and solve for the variables. The solution shows that 22 baseball caps and 132 sweatshirts were sold.
Explanation:Let's solve this problem step by step:
Let x represent the number of baseball caps sold.Since people bought 6 times as many sweatshirts as caps, the number of sweatshirts sold would be 6x.The total sales revenue can be calculated by multiplying the price of each item by the number of items sold. So, the equation becomes: 10x + 20(6x) = 2860.Simplifying the equation gives us 10x + 120x = 2860.Combining like terms, we get 130x = 2860.Dividing both sides of the equation by 130, we find that x = 22. So, 22 baseball caps were sold.Since people bought 6 times as many sweatshirts as caps, the number of sweatshirts sold would be 6 * 22 = 132.Therefore, 22 baseball caps and 132 sweatshirts were sold.
The problem is solved by setting up equations based on the given information. Ron Co. sold 132 sweatshirts at $20 each and 22 baseball caps at $10 each to make a total of $2,860 in sales.
Explanation:To solve the problem, let's define the variables representing the number of sweatshirts and caps sold. Let's say 's' equals the number of sweatshirts and 'c' equals the number of baseball caps.
We are given two pieces of information:
The price of a sweatshirt is $20, and the price of a cap is $10. The total sales can be expressed as the sum of the sales from sweatshirts and caps, which gives us the equation 20s + 10c = 2860.
Using the information that s = 6c, we can substitute 6c for s in the total sales equation to get 20(6c) + 10c = 2860. Simplifying this equation, we get 120c + 10c = 2860, which leads to 130c = 2860. Dividing both sides by 130 gives us c = 22.
Now, we can find the number of sweatshirts sold by substituting c into the equation s = 6c. So, s = 6(22) = 132.
Therefore, Ron Co. sold 132 sweatshirts and 22 baseball caps.
A retiree invests $5,000 in savings plan that pays 4% per year. What will the account balance be at the end of the first year ?
if Q(x)=4x^2 -1, find Q (-7)
a car is purchased for 26,000 after each year the resale decrease by 35% what will the resale value be
Pamela's age is two times Jiri's age. The sum of their ages is 63 . What is Jiri's age?
If u bring 10 empty bottles to the bottle shop, the bottle shop will change 10 empty bottles to 1 drink. If u bring 100 bottles to the shop. How many drinks will you get?
By bringing 100 bottles to the shop, you will receive 10 drinks.
The students question relates to a mathematical conversion problem, where empty bottles are exchanged for drinks at a bottle shop. If the conversion rate is 10 empty bottles for 1 drink, then by bringing 100 bottles, we can set up a simple division:
Number of bottles: 100
Conversion rate: 10 bottles per drink
To find out how many drinks you can get for 100 bottles, we divide the total number of bottles by the conversion rate:
Divide 100 (bottles) by 10 (bottles per drink).
100 / 10 = 10
Therefore, by bringing 100 bottles to the shop, you will receive 10 drinks.
In the following distribution of the variable semesters completed, which is the mode: 4, 3, 1, 0, 3, 3, 4, 0, 3, 2?
Area model division 246÷3
Answer:
it is right
Step-by-step explanation:
If net income is $115,000 and interest expense is $30,000 for 2012 what is the rate earned on total assets for 2012 (round percent to one decimal point)?
Solve for B
6=10B+12C
The weight of water is 62 1/2 lb per cubic foot. What is the weight of 1 1/9 cubic feet of water?
Final answer:
To determine the weight of 1 1/9 cubic feet of water, convert the mixed number to an improper fraction and multiply by the weight per cubic foot, resulting in approximately 77.16 pounds.
Explanation:
The student is asking to calculate the weight of 1 1/9 cubic feet of water given that the weight of water is 62 1/2 lb per cubic foot. To find the weight of the water, we multiply the volume by the weight per unit volume:
Convert 1 1/9 to an improper fraction: 1 1/9 = 10/9.
Multiply 10/9 cubic feet by 62.5 lb/ft³ (weight of water per cubic foot).
Calculate: (10/9) × 62.5 = 694.44/9 ≈ 77.16 lb.
Hence, the weight of 1 1/9 cubic feet of water is approximately 77.16 pounds.
A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
How many times do you need to multiply by ten to get from 0.3637 to 363.7
The Martin family's truck gets an average of 25 miles per gallon. Predict how many miles they can drive using 7 gallons of gas.
Tell whether the two ratios form a proportion. Explain. 25/80 and 5/16
what is 694 divided by 41 and what is the remainder please help thank you
We can use long division in finding the remainder.
Place the divisor which is 41, outside the long division sign, and 694 under the long division sign as shown in the diagram.
41 goes into 694 16 times.
Write the 16 on top of the long division sign.
Multiply the 16 by 41, to obtain 656
Write the 656 below the 694 as in the diagram.
Subtract 656 from 694 to obtain 38.
Since 41 is more than 38 , we cannot proceed.
Hence,
[tex]\frac{694}{41}=16\:\:Remainder\:\:38[/tex]
Therefore the remainder is 38
The quotient is 16, and the remainder is 38.
We have,
To find the quotient and remainder when dividing 694 by 41, we can perform the division and observe the results.
Now,
41 x 16 = 656
And,
694 - 656 = 38
This means,
694 divided by 41 is equal to 16 with a remainder of 38.
Therefore,
The quotient is 16, and the remainder is 38.
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4 options but only 3 have sea views what fraction has sea view
explain how you can determine if four points lie on a single parabola
Determine an equation for a function that has a slope of -5 and crosses the x-axis at (3,0)
To find the equation of the line with a slope of -5 that crosses the x-axis at (3,0), use point-slope form to get y = -5x + 15, which is the required equation.
Explanation:To determine an equation for a function that has a slope of -5 and crosses the x-axis at (3,0), you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Here, the slope m is -5 and the point on the line is (3,0). Plugging these values into the point-slope form, we get:
y - 0 = -5(x - 3)
This simplifies to:
y = -5x + 15
This equation represents a line with a slope of -5 that crosses the x-axis at the point (3,0), meeting all the conditions given in the question.
what is the solution to this equation?
ds/dt=cost + sint where s(\pi)=1
a construction company is planning to bid on a building contract. the bid costs the company $1900. the probability that the bid is accepted is 1/10. if the bid is accepted, the company will make $94000 minus the cost of the bid.
a. what is the expected value in this situation?
The expected value for the construction company if they bid on the contract is $7,500, calculated by weighing the potential profit and loss with their respective probabilities.
Explanation:The question is asking us to calculate the expected value of the construction company's bid on a building contract. To find the expected value, we need to multiply each outcome by its probability and sum these amounts.
There are two possible outcomes:
The expected value (EV) is calculated as follows:
EV = (Probability of acceptance × Net profit when accepted) + (Probability of not being accepted × Loss when not accepted)
EV = (1/10 × $92,100) + (9/10 × -$1,900)
EV = $9,210 - $1,710
EV = $7,500
The expected value for the construction company if they bid on the contract is $7,500.
Brandy wants to buy a digital camera that costs $300. Suppose she saves $15 each week. In how many weeks will she have enough money for the camera?
It will take Brandy 20 weeks to save enough money to buy the digital camera.
To find out how many weeks it will take for Brandy to save enough money for the camera, we can set up an equation:
Let x be the number of weeks it will take for Brandy to save enough money.
$15 * x = $300
Solving for x:
x = $300 / $15
x = 20
Therefore, it will take Brandy 20 weeks to save enough money to buy the digital camera.
Terry added 3 and 7 he got the sum of 9 his answer is is not correct described how Terry can find the correct sum
2.8 repeating as a fraction
Two algebraic expressions separated by an equal symbol in between them and with the same value are called equations.
Example = 2 x +4 = 12
here, 4 and 12 are constants and x is variable
A collection of constants, variables connected using one or more arithmetic operator is called an expression
Example = 4 y, 3 x+4.
Consider an equation to prove 2.8 as a repeating fraction.
Let x = 2.8 repeating
Multiply both sides of the equation by 10 to get a whole number.
10 x = 28.8 repeating
Next, we subtract the original equation from the multiplied equation to eliminate the repeating part:
10 x - x = 28.8 repeating - 2.8 repeating
9 x = 26
Now, we can solve for x by dividing both sides of the equation by 9
x = [tex]\dfrac{26}{9}[/tex]
Therefore, the decimal number 2.8 repeating can be expressed as the fraction [tex]\dfrac{26}{9}[/tex].
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For a particular event, 845 tickets were sold for a total of $4162. If students paid $4 per ticket and non students paid $6 per ticket, how many student tickets were sold?
Final answer:
Using a system of equations, we found that 454 student tickets were sold at the event.
Explanation:
To determine how many student tickets were sold for the event, we need to set up a system of equations based on the information given. Let's define x as the number of student tickets sold at $4 each, and y as the number of non-student tickets sold at $6 each.
The total number of tickets sold (student plus non-student) is given as 845 tickets:
x + y = 845
The total amount of money made from selling these tickets is $4162:
4x + 6y = 4162
Now we have a system of two equations:
x + y = 845
4x + 6y = 4162
We can solve this system by multiplying the first equation by 4:
(4)(x + y) = (4)(845)
4x + 4y = 3380
Now, we subtract this new equation from the second equation given by the total amount made to eliminate y:
4x + 6y - (4x + 4y) = 4162 - 3380
2y = 782
Dividing both sides of this equation by 2 gives us:
y = 391
Now, substitute y back into the first equation to find x:
x + 391 = 845
x = 845 - 391
x = 454
So, 454 student tickets were sold.
the sales tax rate for the state of washington was 5.1% . What is the sales tax on a $5900 car in Washington?
what is 84 divide by 4
identify the decimal labeled with the letter A on the scale below
The decimal labeled with the letter A on the scale is 0.75.
What is number line?A number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
Here, the number starts with zero.
There are 8 division between 0 and 1.
So, first one represent 1/8= 0.125
second one =0.25
third one= 0.375
fourth one= 0.50
fifth one= 0.625
sixth one= 0.75
Hence, the decimal labeled with the letter A on the scale is 0.75.
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A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 15 characters long, and that each character is either lowercase, an uppercase letter or a numerical digit. Assume that the hacker makes a random guess.
What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction.
The probability that the hacker guesses the password correctly on the first try is 1 / 62^15.
Explanation:To calculate the probability that the hacker guesses the password correctly on the first try, we need to determine the total number of possible passwords and divide it by the total number of possible guesses.
Since the password is 15 characters long and each character can be a lowercase letter, an uppercase letter, or a numerical digit, there are 26 + 26 + 10 = 62 possible options for each character.
Therefore, the total number of possible passwords is 62^15 (62 raised to the power of 15).
The probability of the hacker guessing the password correctly on the first try is 1 divided by the total number of possible passwords.
So, the probability is 1 / 62^15. This can be left as a fraction or converted to a decimal.