the speed of the car
=========================================================
Reason:
The term "gradient" is the same as "slope".
Recall that slope = rise/run = (change in y)/(change in x).
The change in y represents how far you travel, as the distance is along the vertical axis. The change in x is the time duration.
Then,
speed = distance/time
which helps show the slope of this distance-time graph is the speed of the car. The steeper the slope, the faster the car.
-------------
An example:
The equation y = 50x has slope 50. The x is the time and y is the distance traveled.
At time x = 0 hours, you have traveled y = 0 miles.
At time x = 1 hour, you have traveled y = 50 miles.
The two points (0,0) and (1,50) are on this line. Use the slope formula to get a slope of 50, which represents the speed of the car in miles per hour (mph). Or note that y = 50x is in the form y = mx+b
m = slope = 50
b = y intercept = 0
As a 11 1/3 inch candle burns down, its height decreases 1/6 inch each hour. How many hours does it take for the candle to burn completely?
SHOW YOUR WORK
The number of hours after which the candle is burned completely is
68 hours.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Candle height = 11(1/3) inches
Each hour the height decreases by 1/6 inch.
Now,
The equation to find the number of hours x after which the candle is burnout is 11(1/3) - (1/6)x = 0
Solve for x.
11(1/3) - (1/6)x = 0
11(1/3) = (1/6)x
34/3 = (1/6)x
x = (34 x 6) / 3
x = 34 x 2
x = 68
Thus,
After 68 hours the candle is completely burnt.
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What is the name of the point where the two axes cross?
As per the concept of graph, the name of the point where the two axes cross is origin.
Graph in math is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Here we have to identify the name of the point where the two axes cross.
As we all know that the horizontal axis in the coordinate plane is called the x-axis and the vertical axis is called the y-axis.
Here we have also know that the point at which the two axes intersect is called the origin.
Where the origin is at 0 on the x-axis and 0 on the y-axis.
And these intersecting x- and y-axes divide the coordinate plane into four sections
Finally all these four sections are called quadrants.
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Can 30 60 and 90 be the angles of a triangle?
No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.
The sum of the angles of a triangle must always add up to 180 degrees. To determine if a set of angles can form a triangle, add the angles together. If the sum is 180, the angles can form a triangle. In this case, 30 + 60 + 90 = 180, which does not equal 180. Therefore, these angles cannot form a triangle.
No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.
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A certain movie is 105 minutes long. It started at 6:15 pm. During the movie, there were two commercial breaks, one lasting 9
minutes and one lasting 6 minutes. At what time did the movie finish?
Answer: 8:15pm
Step-by-step explanation:
9+6=15 +105 = 120, 120/60=2 hours (total duration), 6:15 + 1 hour = 7:15 + 1 hour = 8:15pm
A survey of 6000 adults found that 58% say that they would take a ride in a fully
self-driving car. A normal distribution may be used to model the sample proportion.
At 95% confidence, the margin of error for this estimate was 2. 4%. Find the 95%
confidence interval of the true proportion who said that they would take a ride in a
self-driving car.
Source: World Economic Forum and Boston Consulting Group
As per the conditions given by the question, the 95% confidence interval of the true proportion who said that they would take a ride in a self-driving car is (53.3856%, 62.6144%).
Now, According to the question:
What is confidence interval?
A confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
To find the 95% confidence interval of the true proportion, we need to use the following formula:
point estimate +/- (margin of error * z-score)
The point estimate in this case is the sample proportion, which is 58%. The margin of error is 2.4%, and the z-score for a 95% confidence interval is 1.96.
Plugging these values into the formula, we get:
58% +/- (2.4% * 1.96)
This simplifies to:
58% +/- 4.6144%
So the 95% confidence interval is:
(53.3856%, 62.6144%)
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Which mixed number is equal to 35
Answer:
35 [tex]\frac{0}{1}[/tex]
Step-by-step explanation:
given that y=15-2x,copy and complete the table below giving the values of y for x=-4,0,4,8,12
Match the partition type to its description.
1 . Logical partition A partition with an extended partition 2 . System partition The partition where you place the boot loader 3 . Primary partition The section of the hard drive that will become the bootable drive
Logical partition - A partition within an extended partition
System partition - The partition where you place the boot loader
Primary partition - The section of the hard drive that will become the bootable drive
IBM and Microsoft initially kept internal lists of designated partition types to be used in the MBR partition table. As the market for PC operating systems and disc tools expanded and became more open, other suppliers also needed to give their products specialised partition kinds. Third parties began to merely allocate partition types on their own behalf in a largely uncoordinated trial-and-error fashion because Microsoft neither documented all of the partition types already given by them nor wished to retain foreign assignments. This resulted in several conflicting assignments, which occasionally caused serious compatibility issues between certain products. [1]
In the 1990s, a number of industry professionals including Hale Landis, Ralf D. Brown, Matthias R. Paul, and Andries E. Brouwer began investigating partition kinds.
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Which of the following lists of ordered pairs is a function?
Answer:
C is a function
Step-by-step explanation:
for a relation to be a function each value of x must map to exactly one unique value of y
A
2 → 5 and 2 → 2 ← not a function
B
- 1 → 6 and - 1 → 7 ← not a function
C
all values of x map to exactly one unique y ← function
D
3 → 1 and 3 → 2 ← not a function
How do you check if an inverse is a function?
If a value of y relates only to one value of x, then the function does have an inverse function.
Define the term function and its inverse?A relation between such a collection of inputs and outputs is known as a function.
A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is just the input.If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f does have an inverse (passing from the vertical line test).Thus, if a value of y relates only to one value of x, then the function does have an inverse function.
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Which angles are alternate exterior angles?
1. EFH and BCF
2. EFH and DCA
3. EFH and EFC
4. EFH and BCA
∠EFH and ∠ACD are angles of alternate exterior angles in the figure as alternate external angles are those that are generated on the outer side of the parallel lines .
what are angles ?When two straight lines connect at a 90° angle or are perpendicular to one another, an angle is formed. The symbol denotes a right angle. In the picture up above, many right angle formations are visible. Shapes include the correct angles. Triangles classified as right triangles have one of their internal angles at a 90 degree right angle. The three interior angles of a triangle add up to 180 degrees, so the three interior angles of a right triangle must always add up to 90 degrees because one of them is always 90 degrees.
given
The pair of angles known as alternate external angles are those that are generated on the outer side of the parallel lines but on the transverse side.
sum up to 180 degrees, you can calculate the size of the inner angle adjacent to it if you know the size of the outer angle (since together they are the angle on a straight line). The internal angles at the other two vertices are added to create the outer angle of a triangle.
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The moon orbits earth at 384400km. The distance from earth to the sun is 149600000km. The diamiter of the sun is 1391000km. What would the diamiter of earth have to be to appear the same size as the sun from the moon if the celestial objects are in the order shown here : Sun, earth, moon.
Answer:
The diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers
Step-by-step explanation:
To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to know the distance from the Moon to the Sun and the distance from the Moon to Earth.
Since the distance from the Moon to the Sun is much greater than the distance from the Moon to Earth, the angle subtended by the Sun at the Moon will be much smaller than the angle subtended by Earth at the Moon.
Therefore, the size of Earth as seen from the Moon will be much larger than the size of the Sun as seen from the Moon.
To find the ratio of the size of Earth to the size of the Sun as seen from the Moon, we can use the formula:
size ratio = (distance to Earth / distance to Sun) x (Sun's diameter / Earth's diameter)
Substituting in the given values, we get:
size ratio = (384400km / 149600000km) x (1391000km / Earth's diameter)
Simplifying, we get:
size ratio = 0.00257 x (1391000km / Earth's diameter)
To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to solve for Earth's diameter. Dividing both sides of the equation by 0.00257, we get:
Earth's diameter = (1391000km / 0.00257) = 54304839.858km
Therefore, the diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers.
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What is 62% of $10.50?
Answer:
$6.51
Step-by-step explanation:
To make a percent a decimal, divide by 100
62% = .62
.62 x 10.50 = 6.51
We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.
On a coordinate plane, a line is drawn from point C to point D. Point C is at (negative 1, 4) and point D is at (2, 0).
Point C has the coordinates (–1, 4) and point D has the coordinates (2, 0). What is the distance between points C and D?
d = StartRoot (x 2 minus x 1) squared + (v 2 minus v 1) squared EndRoot
units
The length of the line is 5 units.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Given that, endpoints are (-1,4) and (2,0) of the line segment.
The length= √(2+1)²+(0-4)²
=5units
Hence, The length of the line is 5 units.
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Question 17
Galle bought a purse for $22.50. Gale's thend Brenda saw the purse and said she would give Gale $35 if Gale would sell her the new purse right then.
mely how much profit as a percent did Gale make from selling the purse to Brenda?
A.35.7%
B.55.6%
C.64.3%
D.155.6%
So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%
What is profit and loss?Profit and Loss is a financial statement that shows a company's revenue, costs, and expenses over a certain period of time, such as a month or a year. The purpose of a P&L statement is to show the company's financial performance and to determine whether the company is making a profit or incurring a loss.
What is Profit Percentage?The proportion that the retailer makes after selling a good at a price greater than its cost is the product's profit margin. P% indicates it.
Profit Percentage P% = {(selling price – cost price) / cost price} x 100.
The selling price of the purse is $35 and the original cost of the purse is $22.50. So the profit is $35 - $22.50 = $12.50
Profit as a percent = (Profit / Original cost) * 100
Profit as a percent = ($12.50 / $22.50) * 100 = 55.6%
So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%
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Can you help me with this
The square on the right is a scaled copy of the square on the left. Identify the scale
factor. Express your answer as a whole number or fraction in simplest form.
8
8
4
Writing the whole number in the numerator and 1 in the denominator. Fraction in simplest form is 8
In the simplest form, how do you write an answer as a fraction?How to Find the Most Basic Form
Determine the GCF of the fraction’s numerator and denominator.
Divide the created GCF by the numerator and denominator.
Fill in the blanks with the simplified fraction of the supplied fraction.
The most basic form, If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase “lowest terms” when referring to the simplest form.
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Solve the equation 2^x=1/32•x=
Answer:
2^x=1
x=0
32•x=0
32.0=0
maybe
This box plot represents the marks gained by students in an exam. Nobody gained exactly 30, 48 or 70 marks. 120 students gained less than 70 marks. How many students gained more than 48 marks?
Therefore , the solution of the given problem of scatter plot comes out
to be 2 regions contain 2 x 40 (or 80) students.
Definition of a scatter plotSeveral dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).
Here,
A box plot separates a data set into four areas, each identified by five lines. The lowest line displays the result, while the highest line displays the result. 25% of the data points are distributed across each region, and the median score is indicated by the middle line.
In this box plot, for instance, there are lines at 10, 30, 48, 70, and 100. The fact that no student received a score exactly equal to 30, 48, or 70 allows us to deduce the following:
Because the middle two sections represent the interquartile range (IQR), which comprises the middle 50% of the data, they are frequently "boxed" together.
We are informed that 120 students received test scores below 70. Additionally, since there are three regions with scores below 70 and each region has a 25% weighting, 3 x 25% (or 75% of the students) had scores below 70.
In other words, 75% of 120 students.
If there are 120 students total throughout the three regions, then each
region has 40 pupils, or one-third of the total.
The box plot indicates that there are two areas, and since each region has 40 students, there are 80 students total in the two regions.
As a result, two zones with two sets of 40 students each make up the solution to the scatter plot problem.
Therefore , the solution of the given problem of scatter plot comes out
to be 2 regions contain 2 x 40 (or 80) students.
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On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C is dilated to create triangle A prime A C prime. The points of A B C are (negative 3, 3), (negative 1, 1), and (negative 3, 1). The points of A prime A C prime are (negative 9, 9), (negative 3, 3), and (negative 9, 3).
The dilation DO,3 (x, y) → (3x, 3y) is performed on the pre-image △ABC to make a similar triangle. Which statements are true? Check all that apply.
∠A corresponds to ∠A'.
∠A'AC' corresponds to ∠B.
CB corresponds to C'A.
Segment A'A is parallel to segment C'C.
△ABC ~ △A'AC'.
The true statements after a dilation of scale factor 3 are,
∠A corresponds to ∠A' and Triangle ABC is similar to triangle A'B'C'.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, The points of ABC are (negative 3, 3), (- 1, 1), and (- 3, 1).
The points of A'BC' are (- 9, 9), (- 3, 3), and (- 9, 3) after a dilation of 3, (x, y) ⇒ (3x, 3y).
We know dilation maintains the similarity of the dilated figures.
Therefore, The statements that are true,
∠A corresponds to ∠A' as dilation maintains similarity.
Triangle ABC is similar to triangle A'B'C'.
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Answer:
Options A,B,C,E
Step-by-step explanation:
(i) Six horses are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
Answer:22 days
Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,
Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)
so, 2000/90 = we will get number of days
therefore 22.22 days
Which emplies 22 days.
if a flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches what is the height of the screen?
Draw a picture the in solve for the missing side.
The height of the screen will be;
⇒ h = 28 inches
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
A flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches.
Here,
The diagonal of the screen television = 53 inches
And, The width of the screen television = 45 inches
Let the height of the television = h
So, By the Pythagoras theorem, we get;
⇒ AC² = AD² + DC²
Where, AC = Diagonal of television.
AD = Height of the television
DC = Width of the television.
Substitute all the values, we get;
⇒ 53² = h² + 45²
⇒ 2809 = h² + 2025
⇒ 2809 -2025 = h²
⇒ h² = 784
⇒ h = √784
⇒ h = 28 inches
Thus, The height of the screen = 28 inches
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Convert one three fifths to a percent find that percent of 30 Divide your answer by 25% of 16
Answer:
40%
Step-by-step explanation:
1 and 3/5 as a fraction is 8/5 which as a percent is 160%.
25% of 16 is 4
160%/4 = 40%
please help!!!!
Solving Systems of Linear Equations by Elimination
C.
0.6x = 1.2 +0.3y
2.2x-1.8y-1.6=0
By using systems of linear equations by elimination, it can be determined that x = 0.5 y +2 and 2.2x-1.8y-1.6=0 are equivalent to x=0.818182 and y+0.727273.
What do you meant by Systems of Linear Equations by Elimination ?Using elimination, let's fix your system. 0.6 x=1.2+0.3 y, 2.2 x-1.8 y-1.6=0 in the graph, and y=2 x-4, y=1.222222 x-0.88888
Step 1: Divide both sides by 0.6 to find the solution for x = 0.6 x=1.2 + 0.3 y.
[tex]$$\begin{aligned}& \frac{0.6 x}{0.6}=\frac{0.3 y+1.2}{0.6} \\& x=0.5 y+2\end{aligned}$$[/tex]
Let's figure out what x is, 2.2 x-1.8 y-1.6=0.
First, multiply both sides by 1.8 y.
[tex]$$\begin{aligned}& 2.2 x-1.8 y-1.6+1.8 y=0+1.8 y \\& 2.2 x-1.6=1.8 y\end{aligned}$$[/tex]
Add 1.6 to both sides in step two.
[tex]$$\begin{aligned}& 2.2 x-1.6+1.6=1.8 y+1.6 \\& 2.2 x=1.8 y+1.6\end{aligned}$$[/tex]
3. Multiply both sides by 2.2.
[tex]$\frac{2.2 x}{2.2}=\frac{1.8 y+1.6}{2.2}$[/tex]
x=0.818182 y+0.727273
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8.5x + 0.5 + 3.5x - 2x
Answer:
-0.05
Step-by-step explanation:
10x+0.5
10x=-0.5
x=-0.5/10
x=-0.05
Question 1
Solve for x.
x(x + 6) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
X =
|
X =
Answer:
[tex]x=-6, 0[/tex]
Step-by-step explanation:
Using the zero-product property, we know that [tex]x=0[/tex] or [tex]x+6=0[/tex].
This means [tex]x=-6, 0[/tex].
Select the correct answer.A wooden board that is 108 inches long is cut into two equal parts. What is the length of each part in feet
4.5 is the length of each part in feet. This can be solved by using the concept of feet.
What is feet?foot, plural feet, any of a wide range of ancient, medieval, and modern linear measurements (often 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.
The foot measured [tex]11^{\frac{1}{42}[/tex] inches in antiquity. The typical man's foot measures 12 inches in length nowadays.
Given that:
The length of the wooden board is given as = 108 inches.
As it is cut in 2 equal parts, it becomes: 108/2 = 54 inches in each
We have to calculate the length of each part in feet, so divide 54 by 12.
As we know,
12 inches = 1 feet
Thus, 54 inches = 54/12 feet = 4.5 feet
So, the length of each part is 4.5 feet.
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Mrs. Hanover borrows $1,413 at a
rate of 5% per year. How much
Simple Interest will she owe if it
takes her 9 months to repay the
loan? Round your answer to the
nearest cent
well, let's recall that a year has 12 months, so 9 months is really 9/12 of a year
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1413\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1413)(0.05)(\frac{3}{4}) \implies I = 1413(\frac{3}{80})\implies I\approx 52.99[/tex]
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A measurement which could be the side lengths of a right triangle include the following: C. √24 in, √6 in, √30 in.
How to determine the side lengths?In order to determine which measurements could be the side lengths of a right triangle, we would have to apply Pythagorean's theorem.
Mathematically, Pythagorean's theorem is given by this formula:
x² + y² = z²
From the side lengths of the first triangle, we have the following:
(√6)² + (√30)² = (√33)²
6 + 30 = 33
36 = 33 (False).
From the side lengths of the first triangle, we have the following:
(√27)² + (√18)² = (√48)²
27 + 18 = 48
45 = 48 (False).
From the side lengths of the first triangle, we have the following:
(√6)² + (√24)² = (√30)²
6 + 24 = 30
30 = 30 (True).
From the side lengths of the first triangle, we have the following:
(√18)² + (√21)² = (√48)²
18 + 21 = 48
39 = 48 (False).
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The double number line shows that a traffic signal allows traffic through the intersection for 363636 seconds. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. Complete the table to show different percentages of the time the signal allows. Time (\text{s}sstart text, s, end text) Percentage 100\%100%100, percent of 36\,\text{s}36s36, start text, s, end text 25\%25%25, percent of 36\,\text{s}36s36, start text, s, end text 125\%125%125, percent of 36\,\text{s}36s36, start text, s, end text Report a problem
The percentages for this problem are calculated as follows:
100% of 36 seconds: 36 seconds.25% of 36 seconds: 9 seconds.125% of 36 seconds: 45 seconds.How to obtain the percentages?The percentages in this problem are obtained applying proportions, multiplying the total amount by the decimal equivalent of the percentage.
Hence the amount that represents 100% of 36 seconds is obtained as follows:
1 x 36 = 36 seconds.
(as a percentage of 100% has a decimal equivalent of 1).
The amount that represents 25% of 36 seconds is obtained as follows:
0.25 x 36 = 9 seconds.
(as a percentage of 25% has a decimal equivalent of 1).
The percentage of 125% of 36 students can be obtained combining the two previous expressions as follows:
1.25 x 36 = 1 x 36 + 0.25 x 36 = 36 + 9 = 45 seconds.
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