Describe a real-world scenario and which it would be important to apply trigonometric ratios or special right triangles.
Answer:
In forensic science trigonometry can be used to calculate a projectile’s trajectory, to estimate what might have caused a collision in a car accident or how did an object fall down from somewhere, or in which angle was a bullet shot etc.
Electrical engineers also use trigonometry. Modern power companies use alternating current to send electricity over long-distance wires. In an alternating current, the electrical charge regularly reverses direction to deliver power safely and reliably to homes and businesses.
Electrical engineers use trigonometry to model this flow and the change of direction, with the sine function used to model voltage. Every time you flip on a light switch or turn on the television, you’re benefiting from one of trigonometry's many uses.
a physicist working in a large labortory has found out that the light particles traveling in a particle accelerator increase velocity in a manner that can be described by linear function -4x+3y=15, where x is time and y is velocity in kilometers per hour. use this function to determine when a certain particle will reach 30 km/hr
a video store sold 2 vhs tapes for every 4 dvds if 564 dvds were sold how many vhs tapes were sold?
To find the number of VHS tapes sold when 564 DVDs were sold, divide the number of DVDs by 2.
Explanation:To solve this problem, we can set up a ratio comparing the number of VHS tapes sold to the number of DVDs sold. Since the ratio is given as 2 VHS tapes to every 4 DVDs, we can simplify it to 1 VHS tape to every 2 DVDs. If 564 DVDs were sold, we can divide this number by 2 to find the number of VHS tapes sold:
564 DVDs ÷ 2 = 282 VHS tapes
Therefore, 282 VHS tapes were sold.
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PLEASE HELP!!!
Taylor bought 200 shares of stock for $18.12 per share last year. He paid his broker a flat fee of $30. He sold the stock this morning for $21 per share, and paid his broker 0.5% commission.
a. What were Taylor's net proceeds?
b. What was his capital gain?
Taylor's net proceeds from the sale of his stock are $4179, after paying his broker's 0.5% commission. His capital gain on the investment is $525, calculated by subtracting the total purchase cost, including the initial broker's flat fee, from the net proceeds of the sale.
a. What were Taylor's net proceeds?
To calculate Taylor's net proceeds, we need to consider the initial cost of buying the shares, any fees paid to the broker, and the amount earned from selling the shares. Here's the breakdown:
Determine initial cost: 200 shares x $18.12 per share = $3624
Add broker's fee when buying: $3624 + $30 = $3654
Subtract broker's fee when selling: $42 (0.5% of $8400 from selling 200 shares at $21 per share)
Calculate net proceeds: $8400 - $42 = $8358
b. What was his capital gain?
To find Taylor's capital gain, subtract the total cost (initial purchase cost + fees) from the total earnings after selling the shares. The calculation is as follows:
#2
Point C has a _____ abscissa and a _____ ordinate.
positive, negative
negative, positive
negative, negative
positive, positive
Find the side of a square whose diagonal is of the given measure.
Given = 8 miles
To find the side of a square with a given diagonal length, apply the Pythagorean theorem. With a diagonal of 8 miles, the side length is calculated to be 4√2 miles.
Explanation:To find the side of a square whose diagonal is given, we can use the Pythagorean theorem. In a square, the diagonal creates two right-angled triangles, each with the square's sides as the legs.
Let the side of the square be s, and the given diagonal is 8 miles. According to the Pythagorean theorem, the diagonal (d) is calculated as d = √(s² + s²). Simplifying, this becomes d = √(2 * s²) or s = d / √2. Substituting the value of the diagonal, we get s = 8 / √2. To get rid of the radical in the denominator, we can multiply both the numerator and denominator by √2, giving us s = (8√2) / 2, which simplifies to s = 4√2 miles. Therefore, the side of the square is 4√2 miles.
You want to convert a measurement of 800 milliliters to centiliters using back-to-back conversion factors.
The conversion factors you will need are:
1 milliliter = 1/1000 liter
1 centiliters = 1/100 liters
The image shows you the template of the equation.
What is the order of the conversions you must perform?
Peggy needs to pay car insurance 2 times every year. She has divided the payment by 6 and saves that amount each month. Which account below is the best account in which to save this money? a. 401-K retirement fund with matching deposits from Peggy’s employer. b. A checking account, or a savings account for other expenses (predictable), and emergencies. c. A savings account for college tuition. d. Coin jar.
Answer:
b. A checking account, or a savings account for other expenses (predictable), and emergencies.
Step-by-step explanation:
Peggy needs to pay car insurance 2 times every year.
She has divided the payment by 6 and saves that amount each month.
So, the best account in which she can save this money is - A checking account, or a savings account.
Other options are irrelevant as a 401-K retirement fund is some other type of account. It is not used for daily or monthly expenses.
Options C and D are also not correct.
You and 2 friends have a job washing cars. you split the money you make so that you each get the same amount. on the first day, you earn $75. the second day, you earn $84. the third day, you earn $105. how much money will you each get for those 3 days?
Final answer:
Each friend would receive $88 from the total earnings of $264 over three days, after splitting the amount equally.
Explanation:
The question asks how much money each person would get from a total earning of $75 on the first day, $84 on the second day, and $105 on the third day after splitting it equally among three friends. To find this out, first, we need to calculate the total earnings by adding the amounts from all three days, and then we divide the total by three, since there are three friends.
The total earnings over the three days are $75 + $84 + $105 = $264. To find out how much each person gets, we divide this amount by 3:
$264 ÷ 3 = $88
So, each friend would get $88 for their work over those three days.
Jake has $11 left in his pocket. he spent $3 on a bus ticket, $5 on lunch, and $5 on a movie. how much money did he have at the beginning of the day?
Answer:
Jake had twenty-four dollars ($24) at the beginning of the day.
Step-by-step explanation:
Jake has $11 dollars left in his pocket, after spending 3 dollars on a bus ticket, 5 dollars on lunch, and 5 more dollars on a movie. 3+5+5 is equal to 13, therefore if after spending 13 dollars Jake still has 11 dollars, which means that at the beginning of the day Jake had 24 dollars (11+13).
A corporation employs 2000 male and 500 female engineers. a stratified random sample of 200 male and 50 female engineers gives each engineer 1 chance in 10 to be chosen. this sample design gives every individual in the population the same chance to be chosen for the sample. is it an srs? explain your answer.
No, the sample design is not a simple random sample (SRS), but a stratified random sample. In an SRS, every individual in the population has an equal chance of being chosen for the sample.
Explanation:The given sample design is not a simple random sample (SRS). In an SRS, every individual in the population has an equal chance of being chosen for the sample. However, in this case, the sample design is a stratified random sample. It involves dividing the population into groups (in this case, male and female engineers) and then selecting a sample from each group using a different sampling rate.
To determine if a sample design is an SRS, we need to ensure that each individual in the population has an equal chance of being chosen, and this probability is the same for every individual. In the case of the given example, the sample design does not meet these criteria, making it not an SRS.
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I really need help. I just can't quite get it. It involves Triangle Medians and Triangle Centroid
What is the procedure for multiplying a two digit number by a one digit number?
what is the sale tax on item that costs $33.50. if the sale tax is 0.06 on every $1?
(WILL MARK AS BRAINLIEST) Consider the graph of quadrilateral WXYZ.
Which statements about quadrilateral WXYZ are true? Check all that apply.
The slope of ZW is .
The slope of YX is .
The length of ZY is .
The length of WX is 5.
Quadrilateral WXYZ is a square.
Answer:
The slope of ZW is [tex]\frac{2}{5}[/tex]
The lenght of ZY is [tex]\sqrt{29}[/tex]
Quadrilateral WXYZ is a square
Step-by-step explanation:
Statements
case A) The slope of ZW is [tex]\frac{2}{5}[/tex]
The statement is True
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]Z(-3,1),W(2,3)[/tex]
substitute
[tex]m=\frac{3-1}{2+3}[/tex]
[tex]m=\frac{2}{5}[/tex]
case B) The slope of YX is [tex]-\frac{5}{2}[/tex]
The statement is False
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]Y(-1,-4),X(4,-2)[/tex]
substitute
[tex]m=\frac{-2+4}{4+1}[/tex]
[tex]m=\frac{2}{5}[/tex]
case C) The lenght of ZY is [tex]\sqrt{29}[/tex]
The statement is True
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]Z(-3,1),Y(-1,-4)[/tex]
substitute
[tex]d=\sqrt{(-4-1)^{2}+(-1+3)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
case D) The lenght of WX is [tex]5[/tex]
The statement is False
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]W(2,3),X(4,-2)[/tex]
substitute
[tex]d=\sqrt{(-2-3)^{2}+(4-2)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
case E) Quadrilateral WXYZ is a square
The statement is True
Because sides ZW and YX are parallel sides (has the same slope)
Slope ZY
we have
[tex]Z(-3,1),Y(-1,-4)[/tex]
[tex]m=\frac{-4-1}{-1+3}[/tex]
[tex]m=-\frac{5}{2}[/tex]
so
ZW and ZY are perpendicular sides (the product of their slopes is equal to minus one)
[tex]-\frac{5}{2}*\frac{2}{5}=-1[/tex]
Slope WX
we have
[tex]W(2,3),X(4,-2)[/tex]
[tex]m=\frac{-2-3}{4-2}[/tex]
[tex]m=-\frac{5}{2}[/tex]
ZY and WX are parallel sides (has the same slope)
distance ZW
we have
[tex]Z(-3,1),W(2,3)[/tex]
[tex]d=\sqrt{(3-1)^{2}+(2+3)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
distance YX
we have
[tex]Y(-1,-4),X(4,-2)[/tex]
[tex]d=\sqrt{(-2+4)^{2}+(4+1)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]
[tex]d=\sqrt{29}\ units[/tex]
The four sides are congruent
case F) [tex]YZ=\sqrt{(-3-(-1))^{2}+(1-4)^{2}}[/tex]
The statement is False
[tex]YZ=\sqrt{(-2)^{2}+(-3)^{2}}[/tex]
[tex]YZ=\sqrt{13}[/tex] ----> is not correct
the value of YZ is [tex]\sqrt{29}[/tex]
How to solve 2(2d+4)=-3(d+2) ?
This question is based on the following paragraph
Which transformation is not isometric?
The elevation of Niagara Falls which is located between Lake Erie and Lake Ontario, is 326 feet. How far is this above sea level?
How can u tell
Whether 1080 is cube number
The solution is, 1080 = 2*2*2*3*3*3*5, is not a cube number.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
the number is 1080
Split into prime factors
1080 = 2*2*2*3*3*3*5
so, we have,
Its not a cube
because although there are 2 triplicates there is also a 5.
as, we know that,
Note 2*2*2*3*3*3 is a cube.
so, 1080 = 2*2*2*3*3*3*5, is not a cube number.
Hence, The solution is, 1080 = 2*2*2*3*3*3*5, is not a cube number.
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Determine the value of r so that the line through (5, 2) and (7, r) has a slope of m= -1/2
Final answer:
The value of r that makes the line through (5, 2) and (7, r) have a slope of -1/2 is 1.
Explanation:
To determine the value of r so that the line through the points (5, 2) and (7, r) has a slope of m= -1/2, we use the slope formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is (5, 2) and (x2, y2) is (7, r).
Slope calculation:
-1/2 = (r - 2) / (7 - 5)
-1/2 = (r - 2) / 2
Multiplying both sides by 2 to isolate the variable r:
-1 = r - 2
r = 2 - 1
r = 1
Therefore, the value of r that makes the slope -1/2 is 1.
Maddie has a retangular garden in her backyard. The perimeter of the garden is eighty-two feet. The width is five shorter than the length. What are the length and width of the garden?
Terry had $43 in a checking account. If Terry writes a check for $62, what is the new account balance? a. $105 c. -$19 b. $19 d. -$9
Harry has 1/4 of apple pie that he wants to cut into 3 equal slices.what fraction of the whole pie is each slice?
If Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that, Harry has 1/4 of apple pie that he wants to cut into 3 equal slices.
We have to apply the ratio which is the comparison of two quantities to determine how many times one obtains the other.
Suppose the fraction of the whole pie is each slice will be x,
x = 1/4 / 3
x = 1 /12
Thus, if Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.
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Write the equation of the piecewise function ƒ that is represented by its graph.
Piecewise function with 3 pieces: [tex]x^2+1, 4x-8, 2[/tex]
The piecewise function ƒ that is represented by the graph in the image is:
ƒ(x) =
[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]
[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]
[tex]5^2+1 = 26, & \text{if } x = 5[/tex]
This is because the graph of the function consists of three distinct pieces:
For 0≤x<4, the graph is a parabola with vertex at (0,1) and opening upwards. This suggests that the function is of the form [tex]ax^{2} +bx+c.[/tex]
We can find the values of a, b, and c by substituting the points (0,1), (1,1), and (4,16) into the equation.
This gives us the system of equations:
\begin{cases}
[tex]a \cdot 0^2 + b \cdot 0 + c = 1[/tex]
[tex]a \cdot 1^2 + b \cdot 1 + c = 1 \\[/tex]
[tex]a \cdot 4^2 + b \cdot 4 + c = 16[/tex]
\end{cases}
Solving this system gives us a=1, b=0, and c=1, so the equation of the function for this interval is [tex]x^{2} +1[/tex].
For 4≤x<5, the graph is a line with slope 4 and y-intercept −8.
This suggests that the function is of the form mx+b.
We can find the values of m and b by substituting the points (4,2) and (5,25) into the equation.
This gives us the system of equations:
\begin{cases}
[tex]4m+b = 2 \\[/tex]
5m+b = 25
\end{cases}
Solving this system gives us m=4 and b=−8, so the equation of the function for this interval is 4x−8.
For x=5, the graph is a horizontal line at y=26.
This suggests that the function is of the form c.
We can find the value of c by simply looking at the graph.
This gives us c=26, so the equation of the function for this interval is 26.
Therefore, the complete piecewise function is:
ƒ(x) =
\begin{cases}
[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]
[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]
[tex]5^2+1 = 26, & \text{if } x = 5[/tex]
\end{cases}
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A culture started with 4,000 bacteria. After 5 hours, it grew to 4,800 bacteria. Predict how many bacteria will be present after 15 Hours.
Round your answer to the nearest whole number
Answer:
6900 rounded answer -
Step-by-step explanation:
Plato users, correct.
translate the phrase into a variable expression. use the letter b to name the variable. is necessary, use the asterisk ( * ) for multiplication and the slash ( / ) for division
.......the total number of slices of bread used for the sandwiches and the 7 still left in the loaf....
The translation of a phrase into a variable expression is given by:
b+7
Step-by-step explanation:The letter ' b ' is used to name the variable.
The total number of slices of bread used for the sandwiches and the 7 still left in the loaf.
Let b be the total number of slices that were used for the sandwiches.
and also 7 are still left in the loaf
The total number of slices of bread= Number of slices used fro sandwich+Left over
Hence, the expression is:
b+7
(60 POINTS! I NEED HELP NOW PLEASE!)
Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions.
-When f(x) becomes f(x) -3
-When f(x) becomes -2 * f(x)
If a triangle has an angle greater than 90 degrees, then it is not a right triangle true or false?
A bank contains 35 coins, all nickels and quarters. The total value of coins is $8.15. How many of each coin does the bank contain?
n + q = 35
n = 35-q
0.05n + 0.25q = 8.15
0.05(35-q) +0.25q = 8.15
1.75 -0.05q + 0.25q =8.15
1.75 + 0.20q = 8.15
0.20q = 6.40
q = 6.40 / 0.20 = 32
32 quarters and 3 nickels