Take into account:
x = speed of the airplane
y = speed of the air
consider that the product in between time and speed is equal to the distance traveled in the time.
Then, if the airplane took 3 hours complete 600 miles, agaist the wind, you have that the distance traveled by the airplane is 3x without wind. The speed of the wind decelerates the airplane. The "distance traveled by the wind is 3y"
Then, when you subtract the previous terms you obtain:
3x - 3y = 600 factorize 3 left side
3(x - y) = 600
The table shows the number of books donated to a library each month. Suppose the growth continues exponentially.How many books were donated to the library in Month 8?Round to the nearest whole number.Enter your answer in the box.
The general exponential function is,
[tex]f(x)=a\cdot(b)^x[/tex]For x = 0, f(x) = 80. So,
[tex]\begin{gathered} 80=a\cdot(b)^0 \\ 80=a\cdot1 \\ a=80 \end{gathered}[/tex]For x = 1, f(x) = 100 and a = 80. So,
[tex]\begin{gathered} 100=80\cdot(b)^1 \\ b=\frac{100}{80} \\ =1.25 \end{gathered}[/tex]So exponential function is,
[tex]f(x)=80\cdot(1.25)^x[/tex]Substitute 8 for x in the function to determine the number of books in 8th month.
[tex]\begin{gathered} f(8)=80\cdot(1.25)^8 \\ =476.83 \\ \approx477 \end{gathered}[/tex]So in 8th month number of book denoted is 477.
Use the graph, which shows the profit,y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980.linear graph with negative slope with points (15,150) and (25,130)Find the linear function y, where y depends on t, the number of years since 1980. Type your function in slope intercept form (y=mx+b) without any commas or spaces and be sure to use a lowercase t for your variable.The linear function is y=Answer
First, locate any two point from the line.
(15, 150) and (25, 130)
x₁ = 15 y₁= 150
x₂ = 25 y₂ = 130
[tex]\text{Slope(m)}=\frac{130-150}{25-15}[/tex][tex]=\frac{-20}{10}[/tex][tex]=-2[/tex]Next, is to find the intercept.
Substitute x=15 y=150 and m=-2 into y=mx + b and solve for b
That is;
150 = 15(-2) + b
150 = -30 + b
Add 30 to both-side of he equation
150 + 30 = b
180 = b
Form the equation by substituting m=-2 and b=180 into y=mx + b
y = -2x + 180
Hence, the line function is y = -2x + 180
Four employees of Papa Tony's
Pizza are cleaning up at the end
of a busy night. There is a list of 43 clean-up tasks that need to be
completed. If each employee does the same number of tasks, how
many tasks should each employee do? Solve. Explain how you
interpreted the remainder.
The required number of tasks should each employee do are 10.
What is Remainder?
The Remainder of the worth left after the division. In the event that a number (profit) isn't totally distinguishable by another number (divisor) we are left with a worth once the division is finished. This worth is known as the rest of. For instance, 10 isn't precisely separated by 3. Since the nearest esteem, we can get 3 x 3 = 9.
According to question:As there are 43 clean-up tasks that need to be completed,
And four employees
Number of task for one employee = 43/4 = 10, and 3 is remainder.
So, each employee does the 10 number of tasks, and 3 is obtain as a remainder.
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Given Rhombus ABCD, Solve for X
The value of x for the rhombus sides will be equal to 7 units.
What is a rhombus?A rhombus is a quadrilateral with four equal-length sides. The term equilateral quadrilateral refers to the fact that all of its sides are the same length. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.
Given that there is a rhombus ABCD, and the sides are AB = 2x - 3, BC = 5y + 1, CD = 11, and AD = 20 - z.
The value of x will be calculated by equating the sides AB and CD
AB = CD
2x - 3 = 11
2x = 11 + 3
2x = 14
x = 7
Therefore, the value of x for the rhombus sides will be equal to 7 units.
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Determine whether a relation is a function.
Write 250 metres as a fraction of a kilometre.
Find the values of each variable.
Step-by-step explanation:
x + y = 180° (linear pair)
Also, x = 3y (corresponding angles are equal)
So, 4y = 180
y = 45°
x = 135°
A line passes through the point (−8, – 7) and has a slope of
-5/4
Write an equation in point-slope form for this line.
The equation in the point-slope form of the line is -7 = -5/4x -8.
What do we mean by point-slope form?One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form.
This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the point-slope form is:
The equation of the point-slope form: y = MX + b
Where y is the y coordinate and b is the x coordinate and m is the slope.
Now, get the point-slope form as follows:
y = MX + b
-7 = -5/4x -8
Therefore, the equation in the point-slope form of the line is -7 = -5/4x -8.
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What is the difference of -3 multiplied by a number and the product of two and another number
Let a number be "a" and the other number be "b".
-3 multiplied by a number "a" is:
[tex]-3\cdot a[/tex]The product of two and another number "b" is:
[tex]2\cdot b[/tex]And the difference between the numbers is:
[tex]-3a-2b[/tex]Answer: - 3a - 2b.
What is the equation of a circle with diameter endpoints of (-14, 1) and (-10, 9)
Given data:
The first end point of the diameter is (-14, 1).
The second end point of the diameter is (-10, 9).
The centre of the circel is,
[tex]\begin{gathered} x=\frac{-14-10}{2} \\ =\frac{-24}{2} \\ =-12 \\ y=\frac{1+9}{2} \\ =5 \end{gathered}[/tex]The diameter of the circle is,
[tex]\begin{gathered} d=\sqrt[]{(-10+14)^2+(9-1)^2} \\ =\sqrt[]{16+6}4 \\ =4\sqrt[]{5} \end{gathered}[/tex]The radius is,
[tex]\begin{gathered} r=\frac{4\sqrt[]{5}}{2} \\ =2\sqrt[]{5} \end{gathered}[/tex]The equation for the circle is,
[tex]\begin{gathered} (x-(-12))^2+(y-5)^2=(2\sqrt[]{5})^2 \\ (x+12)^2+(y-5)^2=20 \end{gathered}[/tex]Thus, the equation for the circle is (x+12)^2 +(y-5)^2 =20.
Translate the sentence into an equation.
Twice the difference of a number and 2 is 6.
Use the variable w for the unknown number.
Answer: 2(x-2)=6
Step-by-step explanation: when they say twice, so you make is times 2, then it said the difference of a number which would be a variable, or x, and 2, is 6, so one part is =6, next is the variable -2, so you can use x-2, then in order to multiply everything, you need to make parenthesis. So, it would be x-2=6, but you forgot the parathesis, so 2(x-2)=6
Craig is making 3 recipes for his party. He has a containerof flour on his kitchen scale. The table shows the totalchange in weight of the flour on the scale after each ofthe 3 recipes. What is the average change in the amountof flour, in ounces, used in the 3 recipes?
Answer:
C
Step-by-step explanation:
The average change in the amount of flour is the sum of the changes after each recipe divided by the number of recipes.
Sum of changes:
[tex]-2-3\frac{1}{2}-4\frac{1}{2}=-2-\frac{3\ast2+1}{2}-\frac{4\ast2+1}{2}=-2-\frac{7}{2}-\frac{9}{2}[/tex][tex]-2-\frac{7}{2}-\frac{9}{2}=-2-\frac{7+9}{2}=-10[/tex]Average:
3 recipes.
Total is -10.
-10/3 = 3 with rest 1. So as a mixed number, the correct answer is option C.
Please help I will crown you
The value of b in the given angle is 25°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.Six Different Angles
Acute Angles.Obtuse Angles.Right Angles.Straight Angles.Reflex Angles.Full Rotation.So, the balance of b is:
We can easily tell that the angle is a 90°.And ∠90° is divided into two portions which are:
b + 7 2b + 8Now, calculate for b as follows:
b + 7 + 2b + 8 = 903b = 15 = 903b = 90 - 153b = 75b = 75/3b = 25°Therefore, the value of b in the given angle is 25°.
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How do I do this my teacher just assigned this and I don’t know what to do ?
We need to subtract both expressions, then simplify it and make only one expression:
First, subtract both expressions:
[tex](-3x+9y)-(8x-6y)[/tex]Then:
[tex]-3x+9y-8x+6y[/tex]Now, simplify like terms:
[tex]-11x+15y[/tex]Therefore, the result expression is -11x+15y.
If both pairs of opposite sides of a quadrilateral are congruent, then thequadrilateral is a parallelogram.A. TrueB. False
Answer:
True
Explanation:
Three more than the square of the sum of five times a number and two. written as a math problem is?
Let the number be x.
The mathematical expression for the statement is,
[tex]3+(5x+2)^2[/tex]A line has an x-intercept of 8 and a y-intercept of 3. What is the equation of the line?
Answer
y = (-3/8)x + 3
Multiply through by 8
8y = -3x + 24
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, we just need to solve for the slope of this line.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question, the x and y intercepts are given. Since these are points where the line crosses the x and y axis, we can write them in coordinates form as
x-intercept = (8, 0)
y-intercept = (0, 3)
(x₁, y₁) and (x₂, y₂) are (8, 0) and (0, 3)
[tex]\text{Slope = }\frac{3-0}{0-8}=\frac{3}{-8}=-\frac{3}{8}[/tex]y = mx + b
m = slope = -(3/8)
b = y-intercept = 3
y = mx + b
y = (-3/8)x + 3
Multiply through by 8
8y = -3x + 24
Hope this Helps!!!
help please!! forr 40 points
Answer:
C.
Step-by-step explanation:
you have to divide the numbers
Answer:
C and about 400 hats
Step-by-step explanation:
So you'd have to round up to 1600 for the first equation and for the second one it's about 400 because 1600/4=400
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Select the correct answer.
What is the height, x, of the equilateral triangle shown?
an equilateral triangle with the angles labeled as 60 degrees and a side length of 10 inches, the height labeled as x
Answer:
x = 5√3
Step-by-step explanation:
We will use the Pythagorean theorem with a and b as the lengths of the legs, and c as the length of the hypotenuse.
a² + b² = c²
We need two of the three lengths of a, b, and c, so we can find the third length.
The height divides the equilateral triangle into two right triangles.
Look at one of the right triangles.
One leg is half the side of the triangle.
a = 10/2 = 5
One leg is the height.
b = x
The hypotenuse is the side of the equilateral triangle.
c = 10
a² + b² = c²
5² + x² = 10²
25 + x² = 100
x² = 75
x = √75
x = 5√3
Answer: b
Step-by-step explanation:
Ricardo started a savings account for his daughter Ruth by depositing
$500 into the account for her
1st birthday. For each successive birthday, Ricardo deposits
$200 more than the amount deposited for the previous birthday. This is the only money deposited into the account. What is the total amount of money Ricardo will have deposited into the account for Ruth up to and including her 6th birthday?
Answer big number
Step-by-step explanation: you start with 500 then 700 for 2nd then 900 for 3rd 1100 for 4th 1300 for 5th 1500 for 6th
Answer: 6,000
Step-by-step explanation:
If it starts with 500 on the first birthday, and each year he deposits the same amount as the previous plus 200 then we get 700 for the 2nd year.
3rd year: deposits 900
4th year: deposits 1100
5th year: deposits 1300
6th year: deposits 1500
500+700+900+1100+1300+1500=6000
Answer: $6000
This morning Justin’s car had 19.17 gallons of fuel.now, 2.6 gallons are left.how much fuel did Justin use?
Answer:
16.57
Step-by-step explanation:
19.17 - 2.6 = 16.57
Use trigonometry to determine the m
Here, we seek the angle adjacent to one of the given sides' length.
When given the hypothenuse and the adjacent lengths, we employ the SOH CAH TOA formulae.
This gives us:
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypothenuse}\text{ | Notice the first letters were used for the acronym} \\ \text{Therefore, }\theta=\cos ^{-1}\frac{adjacent}{hypothenuse} \end{gathered}[/tex]Where
adjacent = 15
Hypothenuse = 34
Employing back into the formulae, we have:
[tex]\begin{gathered} \theta=\cos ^{-1}(\frac{15}{34}) \\ \theta=63.82^o \end{gathered}[/tex]The missing angle is approximately 64 degrees
When comparing two decimal numbers, you should always line up the decimals and then compare the digits from left to right.
TrueFalse
Answer:True
example:
89 and 84, 8 are equal, but next 9 is bigger than 4
The average height of students at uh from an srs of 19 students gave a standard deviation of 3. 2 feet. Construct a 95% confidence interval for the standard deviation of the height of students at uh. Assume normality for the data.
The 95% confidence interval for the standard deviation of the height of students at UH is given by; CI = (1.81, 4.03)
How to find the confidence interval for standard deviation?
The formula for the confidence interval for the standard deviation is given by the formula;
CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]
We are given;
Sample size; n = 19
D F = n - 1 = 19 - 1 = 18
Standard Deviation; s = 3.2
Confidence Level; CL = 95% = 0.95
Significance level; α = 1 - 0.95 = 0.05
Thus, using Chi-square distribution table online we have;
χ²₁₃, ₀.₀₂₅ = 24.736
(χ²₁₃, ₀.₉₇₅) = 5.01
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
CI = √[(18 * 3.2²/(24.736)], √[(18 * 3.2²/(5.01)]
CI = (1.81, 4.03)
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Isabell will rent a car for a day. The rental company offers two pricing options: Option A and option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below. It’s Isabell drive the rental car 200 miles which option cost more?How much more does it cost than the other option?For what number of miles driven do the two options cost the same?If Isabell drives more than this amount, which option cost more?
From the graph of miles driven and pricing, it can be observed that for 200 miles option A price is $100 and option B price is $70.
So option A cost more than option B.
Determine the difference between $100 and $70 to obtain how much option A cost more than option B.
[tex]100-70=30[/tex]So option A cost $30 more than option B.
From the graph, it can be observed that lines of option A and option B intersect each other at (50,40). So option A and option B cost same for 50 miles.
4. Determine the root of the following equation. x-6/4-4= 3x/2+2x+1/5
The root of the given equation is x = -114/33.
We are given an equation. The equation has one variable. It is linear in nature. The equation is given below.
(x-6)/4 - 4 = (3x/2) + (2x+1)/5
We need to find the root of the equation. First of all, we will move all the terms containing the variable "x" to one side of the equation.
(x-6)/4 - (3x)/2 - (2x+1)/5 = 4
Now we will multiply the terms with the LCM of all the denominators.
20*[(x-6)/4 - (3x)/2 - (2x+1)/5] = 20*4
5(x-6) - 10(3x) - 4(2x+1) = 80
5x - 30 - 30x - 8x - 4 = 80
-33x - 34 = 80
-33x = 114
x = -114/33
Hence, the root of the given equation is x = -114/33.
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△ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.
What is CA ?
The value of side CA of the right angle triangle is 8.85.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angles of right-angle triangles. The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths.
Given that △ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.
The value of side CA is calculated, from the right angle triangle applying the angle property,
tan41 = (7.7)/(CA)
CA = (7.7)/(tan41)
CA = 8.85
Therefore, the value of side CA of the right angle triangle is 8.85.
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suppose you get a cash prize of $100 if you win a game. the probability of winning the game is 0.7. what is the probability of winning $600 or less if you play the game 10 times, assuming that each game is independent?
The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.
Define binomial distribution.A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials when each trial has an equal chance of producing a particular result. The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.
Given,
Cash prize = $100
Probability of winning the game = 0.7
Using binomial distribution,
P(4 ≤X≤ 6) = P( X = 4) + P( X = 5) + P( X = 6)
P( 4 ≤ X ≤ 6)
= 1/4(0.6)⁴(0.4)⁴ + 10/5 (0.6)⁵(0.4)⁵ + 10/6 (0.6)⁶(0.4)⁶
= 0.1115 + 0.2007 + 0.2508
= 0.5630
The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.
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Question
If the cost of filing a floor is $1.75 per square foot, how much will it cost to file a rectangular floor that is 9
foot by 12 feet?
(Area Length x Width)
Answer:
[tex]3x - 6 = 9[/tex]
solve forA banner maker was asked to redesign a squarebanner by increasing the width by 4 feet anddecreasing the length by 2 feet. The total area of thenew banner was 91 square feet.What was the length of the side of the original squarebanner?
Let:
x = original sides.
x + 4 = new width
x - 2 = new feet
So:
(x + 4)(x - 2) = 91
x² - 2x + 4x - 8 - 91 = 0
x² + 2x - 99 = 0
Factoring:
(x + 11)(x - 9) = 0
x = -11 (the lenght can't be negative so this answer is not valid)
x = 9 ft