The speed of the car is 48 miles per hour, based on the given information that the car travels 2/5 miles in 1/2 minute.
Explanation:To solve this problem, we first need to recognize that the car has traveled 2/5 miles in 1/2 minute. To calculate the speed in miles per hour (mph), we need to find how far the car would go in 1 hour. In other words, how many 1/2 minutes are there in an hour? An hour has 60 minutes, so there are 2*60=120 half-minutes in an hour. If the car travels 2/5 mile in each half minute, then in one hour (or 120 half-minutes), the car would travel 2/5*120=48 miles. Consequently, the car's speed is 48 miles per hour.
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What is the constant of variation for the quadratic variation?
A. 5
B. 10
C. 15
D. 25
A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
The length of the shadow of a flagpole was found to be 72 feet. the shadow of a 3 foot picket fence in line with the flagpole was 4 feet. what is the height of the flagpole?
We can solve this problem by simply using ratio and proportion. Let us call the height of the flagpole to be X. Therefore the ratio and proportion would be:
3 ft is to 4 ft and X ft is to 72 ft
3 / 4 = X / 72
X = (3 / 4) * 72
X = 54 ft
The height of the flagpole is 54 ft.
What type of transformation can be defined as turning a figure about a fixed point with no change to the size or shape of the figure?
Stanfing in your tree house 50ft off the ground you look down at a 60 degree angle how many feet from the base of the tree is the frisbee
multiply 50 x tan(60) = 86.6 feet.
round your answer as needed
the volume of a gas varies inversely as the pressure upon it. if the volume of the gas is 160 cubic centimeters at a pressure of 108 centimeters find the volume when the pressure is 87 centimeters
PLEASE HELP!! Use the following image↓
Answer? Multiple choice?
Which of the following is true when probability answer is written in the form of a fraction
In probability, a fraction does not need to be simplified but converting to a percentage or decimal can aid in interpretation, with percentages being fractions with a denominator of 100. (First option)
When a probability answer is written in the form of a fraction, it is important to know how to handle the result. Simplifying the fraction is not generally required, especially in Probability Topics, where the focus is on understanding the probability itself rather than the arithmetic of fractions.
However, converting the probability to a percentage is a common practice that can help with interpretation. This is done by writing the value of the percent as a fraction with a denominator of 100 and then simplifying it if possible.
Converting a fraction to a decimal is another common step, which involves dividing the numerator by the denominator. It's also important to note that for rounding answers to probability problems, the convention is to round to four decimal places.
What are the exact solutions of x2 − 3x − 1 = 0?
Select one:
a. x = the quantity of 3 plus or minus the square root of 5 all over 2 Incorrect
b. x = the quantity of negative 3 plus or minus the square root of 5 all over 2
c. x = the quantity of 3 plus or minus the square root of 13 all over 2
d. x = the quantity of negative 3 plus or minus the square root of 13 all over 2
helpppppppppppppppppppppppppppp
a plane intersects a prism parallel to the base of the prism. the cross section is a polygon with eight sides. The base of the prism had how many sides
Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, –5).
The equation of the circle with a diameter between (7, 3) and (7, -5) is (x - 7)² + (y + 1)² = 2².
Explanation:To find the equation of the circle, we first need to find its center. The center of a circle is the midpoint of its diameter. To find the midpoint of (7, 3) and (7, -5), we can add the x-coordinates and divide by 2 to get 7. For the y-coordinates, we add -5 and 3 and divide by 2 to get -1. So, the center of the circle is (7, -1).
The radius of the circle is half the length of the diameter. The distance between the center of the circle and one of the endpoints of the diameter (7, 3) is the radius. Using the distance formula, the radius is √((7-7)² + (3+1)²) = 2.
Now, we can use the center and radius to write the equation of the circle, which is (x - 7)² + (y + 1)² = 2².
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(04.01 LC)
Which of the sets of ordered pairs represents a function?
A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Only A
Step-by-step explanation:
Let's remember the definition of a function:
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
In A, each input has exactly one output so it's a function.
But in B, the inputs 4 and 9 have two different outputs, it can't represent a function.
The answer is only A.
1,226 days late to answer this question but that will not stop me!
The answer is... drumroll please ... Only A :]
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A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°23'. When the boat stops, the angle of depression is 49°29' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]
Further explanation:
The Pythagorean formula can be expressed as,
[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]
Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.
The formula for tan of angle a can be expressed as
[tex]\boxed{\tan a = \frac{P}{B}}[/tex]
Explanation:
The perpendicular AB. The length of AB is [tex]200{\text{ feet}}.[/tex]
The angle of depression is [tex]\angle ACB = {14^ \circ }52'.[/tex]
One degree has 60 minutes.
[tex]{1^ \circ } = 60'[/tex]
[tex]\begin{aligned}\angle ACB &= 49 + \frac{{29}}{{60}}\\&= 49 + 0.48\\&= 49.48\\\end{aligned}[/tex]
The angle ADB is [tex]\angle ADB = {16^ \circ }23'.[/tex]
[tex]\begin{aligned}\angle ADB&= {16^ \circ }23' \\&= 16 + \frac{{23}}{{60}}\\&= {16.38^ \circ }\\\end{aligned}[/tex]
In triangle ABC.
[tex]\begin{aligned}\tan\left( {{{49.48}^\circ }} \right)&=\frac{{200}}{{BC}}\\1.13&= \frac{{200}}{{BC}}\\BC &= \frac{{200}}{{1.13}}\\BC &= 177{\text{ feet}}\\\end{aligned}[/tex]
In triangle ABD.
[tex]\begin{aligned}\tan \left( {{{16.38}^ \circ }} \right)&= \frac{{200}}{{BD}}\\0.30&= \frac{{200}}{{BD}}\\BD&= \frac{{200}}{{0.30}}\\BD &= 666.67{\text{ feet}}\\\end{aligned}[/tex]
The distance boat can travel can be obtained as follows,
[tex]\begin{aligned}DC& = BD - BC\\&= 666.67 - 177\\&= 489.67{\text{ feet}}\\\end{aligned}[/tex]
The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]
Kindly refer to the image attached.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Trigonometry
Keywords: perpendicular, person watching boat, top, lighthouse, angle of depression, angle of elevation, 200 feet tall, travel, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.
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Compare the following functions:
(see attachment)
Which function has the smallest minimum?
A. All three functions have the same minimum
B. f(x)
C. g(x)
D. h(x)
Answer:
Step-by-step explanation:
We are given three functions and we have to find which one has the smallest minimum.
I function is
[tex]f(x) = -5sin(2x-\pi) +2[/tex]
Since sine varies from -1 to 1, we get this function has a minimum when sine takes value 1.
Minimum of f(x) =1(-5)+2 =-3
II function is
a graph of parabola with minimum at x=3 and y =-2
III function is shown in tabular form.
From the table we find that minimum is x=1 y=3
Tabulating we have
f(x) (3pi/4, -3)
g(x) (3,-2)
h(x) (1,3)
Smallest is for f(x) with least value of -3
in the system shown below, what are the coordinates of the solution that lies in quadrant I? x^2-y^2=25, x+y=25
The table shows the ages and weights of babies at a hospital.
What is the correlation between age and weight as shown in the table?
A.) none
B.) positive
C.) negative
D.) constant
Answer:
Option (b) is correct.
The correlation between age and weight shown in the table is positive.
Step-by-step explanation:
Given: The table shows the ages and weights of babies at a hospital.
We have to determine the correlation between age and weight as shown in the table.
We first Plot these points to obtain the graph as show in attachment below.
Since, Using correlation calculator , we find the correlation as 0.83113
Which is positive
Thus, The correlation between age and weight shown in the table is positive.
As age increases the weight increase.Hence, positive.
The correlation between age and weight as shown in the table is positive, This is further explained below, Option B is correct
What is correlation?Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.
In conclusion, Therefore we look at the table to decipher the correlation between age and weight.
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A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.15 for each minute of calls. Plan B costs $16 plus an additional $0.20 for each minute of calls.
For what amount of calling do the two plans cost the same?
What is the cost when the two plans cost the same?
Plan A = 30 +0.15x
Plan B = 16 +0.20x
30+0.15x = 16+0.20x
subtract 16 from each side
14 +0.15x = 0.20x
subtract 0.15x from each side
14=0.05x
x = 14/0.05 = 280 minutes
280*0.15 = 42 +30 = $72
280 * 0.20 = 56 +16 = 72
280 minutes and cost $72 each
Find the number of permutations of the first 10 letters of the alphabet taking 2 letters at a time.
Choose the graph below that correctly represents the equation 15x − 5y = 30.
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Final answer:
To choose the correct graph that represents the equation 15x - 5y = 30, isolate y, find the slope and y-intercept, and compare to the given graphs.
Explanation:
In order to choose the correct graph that represents the equation 15x - 5y = 30, we need to solve the equation for y.
First, let's isolate y by subtracting 15x from both sides of the equation:
15x - 5y - 15x = 30 - 15x
-5y = -15x + 30
Next, divide both sides of the equation by -5 to find the value of y:
-5y/-5 = (-15x + 30)/-5
y = 3x - 6
Now that we have the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can determine the graph that represents the equation. The slope of the equation is 3, which means that for every 1 unit increase in x, y increases by 3 units. The y-intercept is -6, which means that the graph intersects the y-axis at the point (0, -6).
Based on this information, we can determine that the graph that correctly represents the equation 15x - 5y = 30 is the one where the slope is 3 and it intersects the y-axis at (0, -6).
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What is the length of CF? look at image attached
Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
2 Questions~
Evaluate the expression.
38+16⋅12÷2−(30⋅2)
Simplify this expression.
5 + 10 ÷ 5
3
7
10
15
Your answer would be a.
Answer: 3
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~Izzie
8% of x is equal to 48
divide 48 by 8%
48/0.08 = 600
check
600*0.08 = 48
x=600
monique deposited 1800 at the beginning of each quarter for 6 years into an ira. given an interest rate of 6% compounded quarterly find the value
Find the measure of each interior angle and each exterior angle of the following regular polygons. Show your work
Answer:
Step-by-step explanation:
As we know for a regular polygon sum of all interior angles is represented by n A = 180 (n-2)
and sum of all exterior angles is represented by n A' = 360°
Here n represents number of sides of the polygon.
Now we will go for each options given.
(A) Decagon : (Having 10 sides)
(1) 8A = 180 ( 8-2 )
8A = 180 × 6
A = [tex]\frac{1080}{8}[/tex] = 160° ( interior angle )
(2) n A' = 360°
8 A' = 360°
A = 45° ( exterior angle )
(B) Pentagon ( having 5 sides )
(1) 5A = 180 ( 5-2 )
5A = 180 × 3 = 540
A = 108° ( interior angle )
(2) 5A' = 360
A' = 72° (exterior angle )
(C) Dodecagon : ( having 12 sides )
(1) 12A = 180 (12-2)
12 A = 180 × 10 = 1800
A = 150° ( interior angle )
(2) 12 A' = 360
A' = 30° ( exterior angle )
(D) 16-gon ( having 16 sides )
(1) 16 A = 180 ( 16 - 2 )
16A = 180 × 14
16 A = 1520
A = 157.5° ( interior angle )
(2) 16 A' = 360
A' = 22.5°
(E) 25-gon ( having 25 sides )
(1) 25 A = 180 ( 25-2)
25A = 180 (23)
A = 165.6° ( interior angle )
(2) 25A' = 360
A = 14.4° ( exterior angle)
12.38 in expanded form
The course for the frog hopping race is 59 inches long. Max's frog has jumped 2 feet and 3 inches. How much further does Max's frog need to jump in order to reach the finish line?
To find the remaining distance Max's frog needs to jump in the race, convert the initial jump to inches, and subtract it from the total race length.
The frog hopping race's course is 59 inches long. Max's frog has jumped 2 feet and 3 inches. To find out how much further Max's frog needs to jump to reach the finish line, convert 2 feet and 3 inches to inches and subtract it from 59 inches.
The conversion is: 2 feet x 12 inches = 24 inches. Adding 24 + 3 inches gives 27 inches. Subtract 27 inches from 59 inches to find the remaining distance Max's frog needs to jump.
The distance Max's frog still needs to jump is 32 inches.