[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]
15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaurant need to make 40 quarts of a milk mixture that is 5% fat?
a. 24 quarts of the 2% milk and 16 quarts of the 7% milk
b. 16 quarts of the 2% milk and 24 quarts of the 7% milk
c. 16 quarts of the 2% milk and 16 quarts of the 7 milk
d. 24 quarts of the 2% milk and 24 quarts of the 7% milk,
The perimeter of the rectangle is 64 cm. Find the value of x.
A. 7
B. [tex] \frac{64}{33} [/tex]
C. 32
D. 50
The value of x is 7 and the right option is A. 7.
What is perimeter?Perimeter is the total distance around an object.
To find the value of x, we use the formula of the perimeter of a rectangle.
Formula:
P = 2(L+W)............... Equation 1Where:
P = Perimeter of the rectangleL = Length of the rectangleW = Width of the rectangleFrom the question,
Given:
L = 3xW = 11 cmP = 64 cmSubstitute these values into equation 1 and solve for x
64 = 2(11+3x)64 = 22+6x6x = 64-226x = 42x = 42/6x = 7Hence, the value of x is 7 and the right option is A. 7.
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How to find the derivative of a fraction without using the quotient rule?
Final answer:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule.
Explanation:
To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule. Here's an example:
Let's differentiate the function f(x) = (3x + 2) / (2x + 1).
First, identify the numerator and the denominator. In this case, the numerator is 3x + 2 and the denominator is 2x + 1.Apply the product rule by differentiating the numerator and the denominator separately. The derivative of the numerator is 3, and the derivative of the denominator is 2.Next, apply the chain rule by multiplying the derivative of the numerator by the denominator, and subtracting the derivative of the denominator multiplied by the numerator. In this case, the derivative of f(x) is (3 * (2x + 1) - (2 * (3x + 2))) / ((2x + 1)^2).Simplifying further, the derivative of f(x) is (6x + 3 - 6x - 4) / ((2x + 1)^2) = -1 / ((2x + 1)^2).
In which quadrant of the coordinate graph does point F lie?
The sign notations for four Quadrants is as follows:
Quadrant I : both x and y positive.
Quadrant II : x negative and y positive
Quadrant III: x and y both negative.
Quadrant IV: x positive and y negative.
Point F has coordinates (1,-5)
x is positive and y is negative.
So point F is in quadrant IV.
Simplify 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n
Final answer:
The simplified expression of 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n is -2 + 5.5n - 0.5p after combining like terms.
Explanation:
To simplify the algebraic expression 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n, we need to combine like terms. The constants 1 and -3 can be combined, and the terms with 'n' and 'p' can each be combined respectively. Let's do this step by step:
Combine the constants: 1 - 3 = -2.Combine the 'n' terms: 4.25n + 5/4n = (17/4)n + (5/4)n = (22/4)n = 5.5n.Combine the 'p' terms: (3/2)p + (-2p) = (1.5 - 2)p = -0.5p.The simplified expression is -2 + 5.5n - 0.5p.
True of False: If the measure of theta is A radians and B degrees, then A = 180B/pi. Please explain!
What is the inverse of the following statement? If you live in Toronto, then you live in Canada
The inverse of the statement "If you live in Toronto, then you live in Canada" is:
"If you do not live in Toronto, then you do not live in Canada."
What is a conditional statement?A conditional statement is a type of logical statement that consists of two parts: a hypothesis (or antecedent) and a conclusion (or consequent).
The hypothesis is a statement that serves as a condition, while the conclusion is a statement that follows from the condition.
A conditional statement is usually written in the form "If p, then q", where p is the hypothesis and q is the conclusion.
The symbol "→" is often used to represent the phrase "if...then".
We have,
To make the inverse of a conditional statement "if p, then q", you simply negate both the hypothesis and the conclusion, and then switch their positions.
The inverse of "if p, then q" is "if not p, then not q".
This can be symbolically represented as:
Original Statement: If p, then q
Inverse Statement: If not p, then not q
So,
The inverse of a conditional statement:
If p, then q is If not p, then not q".
Therefore,
The inverse of the statement "If you live in Toronto, then you live in Canada" is:
"If you do not live in Toronto, then you do not live in Canada."
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What is the equation of the line?
A) x + 3y = 9
B) 3x - y = 9
C) x - y = 9
D) 3x + y = 9
At the end of a factory assembly line, completed widgets are deposited into a box until it is filled. if after 10 minutes the box contains 25 widgets and it takes 2 hours total to fill up a box, how many widgets must each box hold?
Final answer:
Each box must hold a total of 300 widgets.
Explanation:
To determine how many widgets must each box hold, we need to calculate the rate of production and then use it to find the total number of widgets produced in 2 hours (the total time it takes to fill the box).
First, we'll find out how many widgets are produced per minute. Since 25 widgets are deposited in 10 minutes, we divide the number of widgets by the time (in minutes) to get the rate:
Rate of production = 25 widgets / 10 minutes = 2.5 widgets per minute.
Now, we need to find out how many minutes are in 2 hours:
2 hours = 2 hours * 60 minutes/hour = 120 minutes.
Finally, we multiply the rate of production by the total production time (in minutes) to find out the total number of widgets per box:
Total widgets per box = 2.5 widgets/minute * 120 minutes = 300 widgets.
There were some pencils in a pencil box. Zoe added 7 more pencils to the pencil box. Now there are 24 pencils in the box. How many pencils were in the box to start with?
The number of mosquitoes in anchorage, alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by: m(x)=-x^2+14xm(x)=−x 2 +14xm, left parenthesis, x, right parenthesis, equals, minus, x, start superscript, 2, end superscript, plus, 14, x how many centimeters of rain will produce the maximum number of mosquitoes?
Answer:
Step-by-step explanation:
49 million misquitos
How do you prove cotx/(cscx-sinx)=secx
Which of the following equations can be used to solve for the radius (r)
Answer:
The last option is the correct answer: [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Step-by-step explanation:
The area of a circle is given by :
[tex]A=\pi r^{2}[/tex] ; where r is the radius.
Now, lets find the radius.
[tex]\frac{A}{\pi } =r^{2}[/tex]
[tex]\sqrt{\frac{A}{\pi}} =r[/tex]
or [tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Therefore, the last option is the correct answer.
Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 f(n) = 35n Which one of these formulas show the sequence written rercursively and which shows it written explicity? Justify your explanantions. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations. Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.
The value of f(40) is 1400 .The sequence can be considered a function because each position has a unique value.
Let's analyze the given formulas for Bill's savings:
The recursive formula is: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
The explicit formula is: f(n) = 35n
A recursive formula defines each term based on the previous terms, which we see in f(n) = f(1) + f(n-1). An explicit formula provides a direct calculation, shown in f(n) = 35n.
Recursive Formula Table for 1 ≤ n ≤ 5n = 1: f(1) = 35n = 2: f(2) = 35 + f(1) = 35 + 35 = 70n = 3: f(3) = 35 + f(2) = 35 + 70 = 105n = 4: f(4) = 35 + f(3) = 35 + 105 = 140n = 5: f(5) = 35 + f(4) = 35 + 140 = 175Using the Explicit Formula to Find f(40)The explicit formula f(n) = 35n allows us to directly calculate:
f(40) = 35 * 40 = 1400
This method is chosen because it provides a straightforward calculation without needing to compute all the preceding values.
Analyzing the Sequence 5, 6, 8, 11, 15, 20, 26, 33, 41, ...This sequence can be considered a function because each input (position in the sequence) has a unique output (value in the sequence).
If you take Coleman's test grade and divide by 2 and add 27, you get 67. Write and solve an equation to find Coleman's test grade.
To find Coleman's test grade, set up the equation x/2 + 27 = 67, solve for x by first subtracting 27 and then multiplying by 2 to get x = 80.
Explanation:The student is asking to find Coleman's test grade given that if you take Coleman's test grade, divide by 2, and add 27, the result is 67. To solve for Coleman's test grade, we can set up an equation where Coleman's test grade is represented by x. The equation based on the provided information would be x/2 + 27 = 67. We can solve for x by first subtracting 27 from both sides of the equation to get x/2 = 40, and then multiplying both sides by 2 to find x. Therefore, x = 80, which means Coleman's test grade is 80.
To find Coleman's test grade, we can set up an equation: (x/2) + 27 = 67. By solving this equation, we find that Coleman's test grade is 80.
Explanation:To find Coleman's test grade, we can set up an equation using the information given. Let's represent Coleman's test grade as 'x'. We have the equation: (x/2) + 27 = 67.
To solve this equation, we need to isolate 'x'. We can start by subtracting 27 from both sides of the equation: (x/2) = 40.
Next, we need to get rid of the fraction by multiplying both sides of the equation by 2: x = 80.
So Coleman's test grade is 80.
Read the word problem. George has 2 times the amount of points that is 4 less than his sister’s. His sister has 16 points. How many points does George have? What operations are needed to solve this word problem, and in what order should they be used?
addition and subtraction, in that order
addition and multiplication, in that order
subtraction and division, in that order
subtraction and multiplication, in that order
D- subtraction and multiplication, in that order.
Step-by-step explanation:
EDG 2022
Anybody have any answers?
From an airplane at an altitude of 1200m the angle of depression to a rock on the ground measures 28. Find the distance from the plane to the rock
The distance from the plane to the rock can be calculated using trigonometry. Here, the tangent of the given angle is used, with the formula: Distance = 1200m / tan(28°).
Explanation:The subject matter in the question relates to trigonometry. We can use the tangent of the given angle to find the distance to the rock. We are given an altitude of 1200m (which is equivalent to the opposite side in a right angle triangle) and an angle of depression of 28°. We know from trigonometry that the tangent of an angle is equal to the opposite side divided by the adjacent side (tan(θ) = opposite / adjacent).
Since we want to know the distance from the plane to the rock, we're trying to find the length of the hypotenuse. This forms a right-angled triangle with the height of the plane as the opposite side, and the line of sight to the rock as the hypotenuse.
We can use the following formula which is derived from the principles of trigonometry:
Distance to the rock (hypotenuse) = Opposite side / tan(θ)
Plugging the given values into this formula gives:
Distance to the rock = 1200m / tan(28°) This calculation will give the answer.
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Find all the zeroes of the equation. -3x4+27x2+1200=0 I need to learn how to do it! Just not the answer please
A map of a public park shows a circular pond. there is a bridge along a diameter of the pond that is 0.85 mi long. you walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. how much farther does your friend walk? round your answer to the nearest hundredth. use 3.14 for π.
Answer:
Your friend walks about 0.48 miles farther than you.
Step-by-step explanation:
Find the circumference of the park.
C = πd Use the circumference formula.
C ≈ 3.14(0.85) Substitute for the diameter and π.
C ≈ 2.669 Multiply.
The circumference of the park is about 2.669 centimeters.
Find how far your friend walks when he or she walks halfway around the pond to meet you on the other side of the bridge. Divide the circumference by two.
0.785 ÷ 2 = 1.33
Your friend walks 1.33 miles.
Find how much farther your friend walks. Subtract the miles you walk from the miles your friend walks. Round your answer to the nearest hundredth.
1.33 − 0.85 ≈ 0.48
Each morning papa notes the birds feeding on his bird feeder. so far tis month he has seen 59 blue jays, 68 black crows, 12 red robins and 1 cardinal. if 300 birds list papa's birdfeeder, how many blue jays can we expect to see?
Help plz and explain. ..........
Which of the following is the image of C after a rotation of 180° about the origin?
(-5, 2)
(-5, -2)
(-2, 5)
Answer:
Option A.(-5, 2).
Step-by-step explanation:
Picture attached in the question we know the coordinates of the point C are (5, -2). Now we rotate C with a rotation of 180° about the origin.
As we can see a line connecting C and a new point C'. This line shows the rotation of the poit by 180°.
Therefore the new coordinates of C will be C'(-5, 2).
Option A is the correct option.
Find the product of (x + 7)2. (1 point)
x2 − 14x + 49
x2 + 14x + 49
x2 − 49
x2 + 49
A dress that retails for 160 dollars was on sale 96 dollars by what percent was the dress discounted?
PLEASE HELP ASAAAPPPPP
Julia surveyed her friends to find the number of hours they spend on homework during the week. The data from her survey is displayed in the first table. She then took a random sample of five responses from the population as shown in the second table. Compare the mean of the population with the mean of the given sample.
Population Data
4
5
3
1
3
2
2
3
5
7
3
6
3
0
1
5
0
4
3
6
Sample Data
5
4
6
2
1
What is the difference between the mean of the sample and the mean of the population?
0.2
0.3
0.4
0.5
Solution:
we are given with two kind of data set , one is Population data and the other is sample data.
we have been asked to Compare the mean of the population with the mean of the given sample.
Given Population Data
is
[tex] 4
, 5
, 3
,1
,3
,2,2
,3
,5
,7
,3
,6
,3
,0
,1
,5
,0
,4
,3
,6 [/tex]
Its mean can be calculated as below
[tex] Mean=\frac{4+5+3+1+3+2+2+3+5+7+3+6+3+0+1+5+0+4+3+6}{20} \\\\\Mean=\frac{66}{20}=3.3\\ [/tex]
Now the Sample data is
5,4,6,2,1
[tex] Mean=\frac{5+4+6+2+1}{5}\\\\Mean=\frac{18}{5}= 3.6\\ [/tex]
Hence the value of difference of the Mean is [tex] =3.6-3.3=0.3 [/tex]
Answer:
The answer is B. 0.3
Step-by-step explanation:
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what is the slope? 0 or undefined
If i give my sister 17 dollars, then we will have the same amount of money. if instead she gives me 23 dollars, then i'll have three times as much money as she will have. how much money does she currently have (in dollars)
The total number of dollars my sisters have is $60.
Given that, if I give my sister 17 dollars, then we will have the same amount of money.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of dollars I have be x and number of dollars my sisters have be y.
Now, if I give my sister 17 dollars, then we will have the same amount of money
y-17 = x
x - y = -17 ---------(1)
If she gives me 23 dollars, then I'll have three times as much money as she will have.
3(x-23) = y
3x-69 = y
3x-y = 69 ---------(2)
Subtract equation (1) from (2)
3x-y-(x-y) = 69 - (-17)
⇒ 2x = 86
⇒ x = $43
Put x = 43 in equation (1), we get
43 - y = -17
43+17 = y
y = $60
Therefore, the total number of dollars my sisters have is $60.
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I understand that the remainder is 0, I kinda guessed and it told me.
But we're using long division or synthetic division.
Can you explain to me what the quotient is?
Thanks!