The rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.
What is rate ?
A rate is a ratio of two quantities, typically a change in one quantity over a corresponding change in another quantity, often over a specific time period. For example, the interest rate on a loan is the ratio of the interest paid to the amount of the loan. A speed is a rate at which an object covers distance, velocity is a rate of change of position, etc.
To find the rate of the jet in still air:
Rate = Distance / Time
The distance is 2964 miles, and the time is 4 hours. So the rate of the jet in still air is:
Rate = 2964 / 4 = 741 mph
To find the rate of the wind, you can use the formula:
Wind Rate = (Distance with wind - Distance against wind) / Time
The distance with the wind is 3564 miles, the distance against the wind is 2964 miles, and the time is 4 hours. So the rate of the wind is:
Wind Rate = (3564 - 2964) / 4 = 600 / 4 = 150 mph
So the rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.
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The vertices of YEAR are Y(1,-4) E(3,0), A (-1,2) and R( -3,-2) . prove that YEAR is a Square
To prove that YEAR is a square, we need to show that all four sides have the same length and all four angles are right angles (90 degrees).
Side Lengths: To find the lengths of the sides, we can use the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
For example, to find the length of the side that connects Y and E, we can use the following calculation:
d = √((3 - 1)² + (0 - (-4))²) = √((2)² + (4)²) = √(4 + 16) = √20
We can use the same formula to calculate the lengths of the other sides. By doing so, we will find that the length of all four sides are the same, which is √20. This means that all four sides of YEAR are congruent, and therefore it is a square.
What are the domain and range of f (x) = -5/6 (x + 2)^2 - 8?
Answer:
Option B
Domain: all real numbers
Range [tex]f(x) \le -8[/tex]
Step-by-step explanation:
Given function is:
[tex]f\left(x\right)=-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
The domain is the set of all x values that result in a real and defined value for f(x).
The function has no undefined points and x is free to range from -∞ to +∞
So the domain is -∞ < x <∞ which is
All real numbers
The range is the set of all possible values for f(x) given a specific domain. In order to determine the range without too much hard work, let's first examine the function f(x)
The above function is the equation for a parabola.
Some things to note about a parabola equation:
The vertex form equation of a parabola is:Let us compare the general vertex form equation of the parabola with the specific f(x) equation given
General Equation: [tex]a (x - h)^2 + k[/tex]
This example: [tex]-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
Comparing the similarity between the two equations we easily see that
[tex]\boxed{a = -\dfrac{5}{6}}[/tex]
This means the parabola opens downward and (h, k) represents a max point in the parabola
[tex]x - h = x + 2\\\\-h = 2\\\\h = -2\\[/tex]
[tex]k = -8[/tex]
So the vertex is at (-2, -8)
Since -8 is the maximum value for f(x), and the parabola extends to infinity on both sides, the range is :
[tex]\boxed{f(x) \le -8}[/tex]
The attached graph may help you understand better
6x−10y=-40 in slope intercept form
Which of the following graphs represents the function g(x) = 3∛x – 1?
A graph which represent the function g(x) = 3∛x – 1 is: graph A.
How to graph the given function?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis and y-axis respectively.
Based on the information about this graph, it represents the following function:
Function, g(x) = 3∛x – 1
By rewriting the cube root in the above function, we have the following:
Function, g(x) = 3∛x – 1
Function, g(x) = 3(x^{1/3}) – 1.
Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
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Write and compound inequality-4 is greater than x and less than 2
The compound inequality is x<-4 and x<2.
What is a compound inequality?
A compound inequality in mathematics is a clause that joins two claims with the conjunction "and" or "or." Both of the statements in a compound sentence are true simultaneously if the conjunction "and" is used to connect the statements. If "or" is used to connect the statements, the compound phrase is true if at least one of the statements is true.
We are given that -4 is greater than x
This means that -4>x
Also, it is given that x is less than 2
Therefore, x<2
Hence, the compound inequality is x<-4 and x<2.
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In the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week, 135 more people went to the pool than in the second week. In the fourth week, 137 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
If in the first week of July, a record 1,120 people went to the local swimming pool. the percent decrease in the number of people who went to the pool over these four weeks is 10%.
How to find the percentage decrease?First week:
Number of people went to the local swimming pool =1120
Second week:
Number of people went to the local swimming pool =1120-110
Number of people went to the local swimming pool =1010
Third week:
Number of people went to the local swimming pool =1010+135
Number of people went to the local swimming pool =1145
Fourth week:
Number of people went to the local swimming pool =1145-137
Number of people went to the local swimming pool =1008
Decrease in number of people over four week=1120 -1008
Decrease in number of people over four week = 112
Percentage decrease = 112 /1120 × 100
Percentage decrease = 10%
Therefore the percentage decrease is 10%.
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The triangle below is equilateral. Find the length of side x to the nearest tenth.
x
12
Answer:
Step-by-step explanation:
Please answer!!! The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drink
The equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
The inspector at a bottling plant checks 25 bottles, and two bottles do not pass inspection.
To find the amount of sports drinks in milliliters that pass inspection, we can subtract the amount in the two bottles that do not pass inspection from the total amount in all 25 bottles.
Let x be the amount of sports drinks in milliliters in each bottle.
The expression for the milliliters of sports drink that pass inspection is = 25x - 2x
Now, simplifying the expression, we get,
25x - 2x = (25-2)x = 23x
Hence, the equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
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The complete question is -
The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drinks. Write an expression for the milliliters of sports drink that pass inspection. Then simplify it to create an equivalent expression.
Assume that when adults with smartphones are randomly selected, 37% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 19 of them use their smartphones in meeting or classes the probability is (Round to four decimal places as needed.
The probability of adults using smartphones in meetings or classes as per the randomly selected adults is equal to 0.3375.
Percent of randomly selected adults use smartphones in meetings or classes represents the probability of success 'p' = 37%
= 0.37
1 - p = 1 - 0.37
= 0.63
Number of randomly selected adults use smartphone in meetings or classes represents sample size 'n' = 30
Exactly 19 adults use smartphone represented by x
x = 19
Using binomial distribution :
Required probability is :
P(x) = ⁿCₓ× pˣ × ( 1 - p )ⁿ⁻ˣ
⇒P(x) = [ n! / x! (n - x)! ] × pˣ × ( 1 - p )ⁿ⁻ˣ
Substitute the values
⇒P(19) = [ 30! / 19! (30 - 19)! ] × 0.37¹⁹× ( 0.63 )³⁰⁻¹⁹
⇒P(19) = ( 30!/19! ×11! ) × 0.37¹⁹× ( 0.63 )¹¹
⇒P(19 ) = 0.3375
Therefore, the required probability of selecting exactly 19 adults who use their smartphones in meetings or classes is equal to 0.3375.
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help me out pleaseeeeeeeeeeeeeeeeeee
Answer:
3 and 5
Step-by-step explanation:
Please help will give brainliest
Write a letter to a student who will be taking this math class next year and give them some advice about this class
A letter to a student who will be taking this math class next year to give them some advice about this class has been written below.
(Sender's address)
20/01/2023
Dearest,
I was happy to see your letter, and I hope this letter finds you in the best of health. I have wanted to go on a trip with you for a long time but I guess that would happen later since you have to start attending classes soon.
I have a list of things to keep in mind when you start your classes. I was always too scared of mathematics, and I know you are too, but I have always wanted to tell you how fruitful it is to learn a subject that will help you in every field you want to go in. Let me know what you think about it after you finish reading this letter. I know it is no secret that maths is a difficult subject but you can master it if you keep what I am going to tell you in mind. Practice your concepts daily. Keep brushing up on whatever your teacher teaches you. Remember the formulas and you will know how to answer any question. I know for sure that it is going to be worth it too.
I will make sure that I meet you next weekend so that we can meet before you begin the classes. If you try hard, you can make this work. See you soon.
Love,
(Sender's name)
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Are 3/8 and 3/4 equivalent fractions with a number line
Find the mean, median, mode, and range for each data set given.
a. 7, 12, 1, 7, 6, 5, 11
b. 85, 105, 95, 90, 115
c.15, 11, 11, 16, 16, 9
Answer:
Answers are in bold
Data set A:
Mean: 7
Median: 7
Mode: 7
Range: 11
Data set B:
Mean: 78
Median: 95
Mode: No mode or all the numbers (85, 105, 95, 90, 115)
Range: 30
Data set C:
Mean: 13
Median: 13
Mode: 11 and 16
Range: 7
Step-by-step explanation:
You're welcome.
The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number, the number of bacteria in the culture after 8 hours. The exponential function is b(t)=. After 8 hours, there are about bacteria in the culture
If the growth rate of bacterial culture is 150% each hour , then the correct exponential function is b(t) = 10(2.5)^t instead of b(t) = 10(1.5)^t , and after 8 hours there are about 15259 bacteria in culture .
The percent growth in the bacterial culture is = 150% = 1.5 ;
the initial amount of bacteria present is = 10 ;
the exponential function used to denote this situation is written as :
⇒ b(t) = 10(1 + 1.5)^t
⇒ b(t) = 10(2.5)^t
to find number of bacteria after 8 hours ,
we substitute t = 8 in b(t) ;
we get ;
⇒ b(8) = 10(2.5)⁸ ;
⇒ b(8) = 15258.789 ≈ 15259
Therefore , there will be 15259 bacteria present after 8 hours .
The given question is incomplete , the complete question is
The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in the data below, in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number,
"The number of bacteria in the culture after 8 hours. The exponential function is b(t) = 10(1.5)^t , b(8) = 10(1.5)⁸ . After 8 hours, there are about 256 bacteria in the culture ."
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what is the axis of symmetry of this graph?
Answer:
The axis of symmetry is x = -3.
If you draw a line at x = -3, the graph is reflected over it.
a factory (f) is producing smoke that causes damage of $80 per month to a local residents laundry (l). the damage can be eliminated in one of two ways:
The following two methods can be used for eliminating the damage to the laundry (l).
Factory (f) can install a scrubber at a cost of $500 to reduce the smoke, thereby eliminating the damage to the laundry (l).Local resident (l) can purchase and install a clothesline at a cost of $100, thereby eliminating the damage to their laundry.The factory and the local resident must decide whether to install the scrubber or the clothesline, depending on which option will result in the lowest cost. The best option for each party depends on their own willingness to pay for the damage reduction and their ability to pay for the solution.
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Drag each tile to the correct box. Consider the given circles. Sector B 9 units 820 Sector c Sector A 6 units 1690 4 units Order the sectors from least to greatest according to their areas, in square units. Sector C Sector B Sector A A
The order from least to greatest is: A, B, C
The order of the sectors from least to greatest according to their areas is:
Sector A, Sector B, Sector C
To find the area of each sector, we need to multiply the central angle measure (in degrees) by the radius squared and divide by 360.
Sector A: 4 units * (1690 / 360) = 46 square units
Sector B: 6 units * (820 / 360) = 69 square units
Sector C: 9 units * (820 / 360) = 103.5 square units
Hence, the order from least to greatest is: A, B, C
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One company estimates same-day delivery as more than three less than half the total number of miles which graph represents the overall equation represented by the scenario or points may not apply to the scenario note that the graphs have similar miles for the independent variable on the X axis and the Y axis is a unit of time dependent on the number of miles
A graph that represents the overall equation represented by this scenario is shown in the image attached below.
How to determine the graph?Based on the information provided about this company with respect to its same-day delivery and total number of miles to be covered, we would assign variables to the parameters as follows:
Let the variable x represent be the total number of miles.Let the variable y represent same-day delivery.Next, we would translate the word problem into an algebraic equation by using an inequality:
Half the total number of miles = x/2.
y > x/2 - 3
Furthermore, we would determine the x- and y-intercepts as follows:
When x = 0, we have;
y = 0/2 - 3
y = -3.
Therefore, y-intercept = (0, -3).
For the x-intercept (y = 0), we have:
0 = x/2 - 3
x/2 = 3
x = 6.
Therefore, x-intercept = (6, 0).
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PLEASE HURRY I HAVE LIMITED TIME!
Question- Find the standard form equation of a circle given a center of (7, 14) and a point on the circle of (4, 15).
Answers-
A.(x-7)^2 + ( y-14)^2 = 10
B.(x-7)^2 + (y-14)^2 = 15
C.(x-7)^2 + (y-14)^2 = 25
D.(x+7)^2 + (y+14)^2 = 2
Answer:
A
Step-by-step explanation:
R = sqrt((7-4)^2+(14-15)^2)=sqrt(10)
The answer is A since that's the only answer with the proper radius, using the formula for a circle.
An airplane takes off from the airport. After 2 minutes the plane is at 500 ft. Assume the plane continues at the same rate. The plane’s height and minutes above the ground are related to each other.
A. Write an equation for the situation.
An equation for the situation described above is h = 2m + 500.
How to write an equation to model this situation?In order to write an algebraic equation that model this situation, we would assign a variable to the number of minutes after an airplane takes off from the airport and the plane’s height respectively, and then translate the word problem into algebraic equation as follows:
Let the variable m represent the number of minutes.Let the variable h represent the plane’s height.Next, we would translate the word problem into an algebraic equation based on the fact that after 2 minutes the plane is at 500 feet as follows;
h = 2m + 500.
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Find the length of x. Please help I will mark brainlist
Answer:
its 4, but give the other guy brainliest he answered first :D
Step-by-step explanation:
Need Help ASAP!!!! 15 POINTS
Using Quadratic formula, the roots of the equation are -11 + √217/6, -11 - √217/6 .
Equations involving quadratics The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0.
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).
Using Quadratic formula,
3x² + 11x - 8
(-b±√(b²-4ac))/(2a)
⇒ (-11 ± √11² - 4(3)(-8)/2(3))
⇒ -11 ± √217 / 6
⇒ -11 + √217/6, -11 - √217/6
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The function f(x) is shown on the graph.
f(x)
O Logarithmic
B 7
O Polynomial
654
-10-9-8-7-6-5-4-3-2-10
3
2
-1
-2
-3
47999
-7
-10
Which type of function describes f(x)?
O Exponential
X
2 3 4 5 6 7 8 9 10
An exponential function is represented by taking into account the fact that the graph has an asymptote and does not cross it.
What is exponential function?A function with the formula f(x)=ax is an exponential function. Here, x is the input and an is a positive, real integer (referred to as the base) (independent variable). The independent variable is always in the exponent for exponential functions, which is important to keep in mind.
It is based on:
where a represents the y-intercept.
The rate of change is b.
The asymptote, which the function does not cross, is y = c.
Consequently, the graph in this issue models an exponential function with an asymptote at y = 0.
An exponential function is represented by taking into account the fact that the graph has an asymptote and does not cross it.
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Solve pleaaase i really need help
The equation of the model is (b) 2x = 5
How to determine the equation of the model?From the question, we have the following parameters that can be used in our computation:
Left = x x
Right hand side = 1 1 1 1 1
The above parameters mean that
Left = 2x
Right = 5
When represented as an equation, we have
2x = 5
Hence, the equation is (b)
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The supermarket has 20 aisles. 10 of the aisles are empty. What percentage of the aisles are empty?
The percentage of the aisles that are empty, given the number of aisles in total in the supermarket, is 50 %
How to find the percentage of aisles ?To find the percentage of the aisles that are empty, you can use the formula :
= Number of aisles that are empty / Number of total aisles in the supermarket x 100 %
Number of aisles that are empty = 10 aisles
Number of total aisles in the supermarket = 20 aisles
The percentage of aisles empty is:
= 10 / 20 x 100 %
= 0. 5 x 100 %
= 50 %
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if 12% of a number is 75, find 4% of that number
Answer:
25.60
Step-by-step explanation:
first divide 12%of a number with 75 Ans will be 6.25 then multiply with 4 Ans will be 25.60
Answer: 25
Step-by-step explanation:
12 divided by 4 = 3
75 divided by 3 = 25
25 = 4%
What is the solution to StartFraction 5 over 6 EndFraction x minus one-third greater-than 1 and one-third?
x > StartFraction 25 over 18 EndFraction
x < StartFraction 25 over 18 EndFraction
x > 2
x < 2
The value of x is x > 2.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Any number can be expressed as fractions.
The given expression is [tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]
We have to rewrite the expression with x on one side.
[tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > 1 [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > [tex]\frac{4}{3}[/tex] + [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > [tex]\frac{5}{3}[/tex]
x > [tex]\frac{5}{3}[/tex] × [tex]\frac{6}{5}[/tex]
x > 2
So the value of x is greater than 2.
Hence the correct option is x > 2.
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I NEED HELP ON THIS ASAP!!!!
The volume of an ice cream cone is the measure of how much ice
cream fits inside the cone. An ice cream cone company wants to
make an ice cream cone with a greater height that still holds the
same amount of ice cream.
Write an equation to calculate the volume of a cone.
Then rewrite the equation to solve for the height.
Explain how your equation determines a linear measurement when the original equation determined a cubic measurement
The volume of a cone is V = πr²h/3
The equation rewritten to solve for the height is V = πr²h/3
How to determine the equationIt is important to note that the formula for volume of a cone is expressed as;
V = πr²h/3
The parameters are;
V is the volume of the coneπ takes the constant value, 22/7 or 3. 142h is the height of the coneSince the ice cream fits inside the cone and the height still holds the ice cream, let's make the height subject of formula.
Let's take the following steps;
V = πr²h/3
cross multiply the equation, we get;
V × 3 = πr²h × 1
Multiply the values
3V = πr²h
To make the variable 'h' stand alone, let's divide both sides of the equation by its coefficient
3V/πr² = πr²h/πr²
Divide the values
c
Hence, the equation determines a linear measurement since the value 3 multiply the volume and not divides it.
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Jacob has 6. 15 meters of rope. He is going to use 1. 2 meters of rope to tie up his boat. How many centimeters of rope does he have left?
The remaining rope he left is 495cm
Now, According to the question:
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Jacob has 6. 15 meters of rope.
He is going to use 1. 2 meters of rope to tie up his boat.
When you do the subtraction, whatever is left (the decimal part) is the length in cm when multiplied by 100.
Remaining rope = starting length - what was used.
Remaining rope = 6.15 - 1.2
Remaining rope = 4.95 meters
Hence, The remaining rope he left = 4.95 × 100 = 495 cm
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Tamisha works as an intern in an architect’s office. A designer drew a scale drawing of a kitchen without using grid paper. In the drawing, 1 inch represents 2 1/2 feet. Tamisha’s supervisor wants her to determine the skill factors for the length and the skill factors for the areas of.
a. Find the scales factor for the lengths
b. Find the scales factors for the areas
Answer:
length: 1:30, area: 1:900
Step-by-step explanation:
1ft = 12 inches, so 2.5' = 30". scale for length is 1:30, for area it's square - 1:900