The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.
What is a Speedometer?
The instrument on a car that measures and shows speed is called a speedometer, and it is crucial for safety on roads and highways all over the world.By instantly sensing the speed on the ground, the speedometer on a car, truck, or motorbike can instantly notify the driver how fast the vehicle is travelling at any given moment.The instrument currently appears in many forms as a motorcycle speedometer or a bike speedometer and is digital in many modern automobiles.What is Distance?
The measurement of the distance between two objects or locations can be quantitative or occasionally qualitative.Distance in physics or common language can refer to a physical length or an assumption based on other factors. The term is also frequently used metaphorically to denote a measurement of the degree of separation or difference between two related objects.A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.How is Distance Calculated?
The distance between two locations can be calculated using the formula,
d = s x t,------ (1)
where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.
In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.
So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].
The total travelling time for the round trip, T = 15h ------(2)
Let the distance from Ottawa to Toronto be x.
From (1), we get that, the formula for the time taken is,
[tex]t=\frac{d}{s}[/tex]
So, the time taken to travel from Ottawa to Toronto,
[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex] ------- (3)
And, the time taken for the return trip (back from Toronto to Ottawa),
[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex] --------(4)
Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.
T = t_1 + t_2------(5)
Substituting the values of (2), (3), and (4) in (5), we get
15 = x/40 + x/35
--> 15 = 0.0535x
Simplifying,
x = 15/0.0535
--> x = 280.37 miles
Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.
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In this triangle, angle W equals (3x-24) degrees, and angle C equals (4x-11) degrees, and angle T equals 2x degrees, what does angle W equal?
Traingle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The sum of the three angles is equal to 180 degrees.
The value of angle W is 47.67
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In this triangle:
angle W = (3x-24) degrees.
angle C = (4x-11) degrees.
angle T = 2x degrees.
Now,
The sum of the three angles is equal to 180 degrees.
3x - 24 + 4x - 11 + 2x = 180
9x - 35 = 180
9x = 180 + 359x = 215
x = 215/9
Now,
The angle W.
= 3x - 24
= (3 x 215/9) - 24
= 215/3 - 24
= 71.67 - 24
= 47.67
Thus,
The value of angle W is 47.67
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Johnny has some nickels and dimes in his pocket, and the change is worth $0.75. He has twice as many dimes as nickels. How many of each type of coin does Johnny have?
| BTW this is a system of equations question
The number of dimes and nickels that Johnny has are 6 and 3 respectively.
How to calculate the value?The following should be noted:
Nickel = 5 cent = 0.05
Dime = 10 cents = 0.10
Let the number of nickels = n
Let the number of dimes = 2n
Total worth = $0.75
This will be illustrated as:
0.05(n) + 0.10(2n) = 0.75
0.05n + 0.20n = 0.75
0.25n = 0.75
Divide
n = 0.75/0.25
n = 3
Number of nickels = 3
Number of dimes = 2n
= 2 × 3
= 6
Number of dimes = 6
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A statistician proposed a new method for constructing a 90 percent confidence interval to estimate the median of assessed home values for homes in a large community. To test the method, the statistician will conduct a simulation by selecting 10,000 random samples of the same size from the population. For each sample, a confidence interval will be constructed using the new method. If the confidence level associated with the new method is actually 90 percent, which of the following will be captured by approximately 9000 of the confidence intervals constructed from the simulation?
(A) The Sample Mean
(B) The Sample Median
(C) The Sample Standard Division
(D) The Population mean
(E) The Population Median
The measure that will be captured by approximately 9000 of the confidence intervals is given as follows:
(E) The Population Median.
What is the interpretation of a x% confidence interval?The interpretation of a x% confidence interval is that it is x% likely that the population parameter(mean/proportion/standard deviation/median) is between a and b, which are the bounds of the confidence interval.
The bounds of the confidence interval are obtained by the estimate plus/minus the margin of error.
The measure for which the confidence intervals are calculated in this problem is given by:
Median.
The sample median for each sample is used for the estimes, and then these estimates are inferred for the population median, which is the population parameter, hence option e is correct.
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✓ Completed
Part 1 of 3
In Progress
Given the following functions, find the indicated values.
f(x)=8-4x
(a) f(-7) (b) f(0) (c) f(4)
(a) f(-7)=
Answer:
(a) 36, (b) 8, (c) - 8======================
Given functionf(x) = 8 - 4xFind the indicated values(a) f(-7)
f(-7) = 8 - 4(-7) = 8 + 28 = 36(b) f(0)
f(0) = 8 - 4(0) = 8 - 0 = 8(c) f(4)
f(4) = 8 - 4(4) = 8 - 16 = - 8Answer:
a) f(-7) = 36 b) f(0) = 8 c) f(4) = -8Step-by-step explanation:
a) f(-7) = ?
→ f(x) = 8 - 4x
→ f(-7) = 8 - 4(-7)
→ f(-7) = 8 + 28
→ f(-7) = 36
Hence, f(-7) = 36.
b) f(0) = ?
→ f(x) = 8 - 4x
→ f(0) = 8 - 4(0)
→ f(0) = 8 - 0
→ f(0) = 8
Hence, f(0) = 8.
c) f(4) = ?
→ f(x) = 8 - 4x
→ f(4) = 8 - 4(4)
→ f(4) = 8 - 16
→ f(4) = -8
Hence, f(4) = -8.
Can anybody help me with this?
The slope of the line -1 and the y-intercept is 3.
From the question, we have
x+y = 3
y = -x+3
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
m = -1
c = 3
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope. The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
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485.2635 Find the digits in the hundreds place, in the tenths place, and in the ten thousandths place for the following number.
Answer:
Hundreds: 6 Tenths: 2 Ten Thousands: 5
Step-by-step explanation:
Hundreds are 2 decimal places (0.02)
Tenths are 1 decimal place (0.1)
Ten Thousands are 4 decimal places (0.0004)
Hope this helped!
tossing a fair coin 20 times and counting the number of heads (x). what is the chance that the number of heads is 13 or more?
By using Binomial Distribution of probability, it is obtained that
Probability that the number of heads is 13 or more = [tex]137980(\frac{1}{2})^{20}[/tex]
What is Binomial Distribution?
Binomial distribution is a discrete type probability distribution whose probability mass function is
P(X = k) = [tex]{n \choose k} p^k(1 - p)^{n-k}[/tex]
p is the probability of success.
Here Binomial distribution of probability is used
P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + ........ + P(X = 20)
P(X = 13) = [tex]{20 \choose 13} (\frac{1}{2})^{13}( 1 - \frac{1}{2}})^{20-13}[/tex]
= [tex]{20 \choose 13} (\frac{1}{2})^{13}( \frac{1}{2}})^{7}[/tex]
=[tex]{20 \choose1 3} (\frac{1}{2})^{20}[/tex]
P(X = 14) = [tex]{20 \choose14} (\frac{1}{2})^{20}[/tex]
P(X = 20) = [tex]{20 \choose20} (\frac{1}{2})^{20}[/tex]
Total Probability = [tex]({20 \choose 13} + {20 \choose 14} + .... {20 \choose 20})(\frac{1}{2})^{20}[/tex]
= (77520 + 38760 + 15504 + 4845 + 1140 + 190 + 20 + 1)[tex](\frac{1}{2})^{20}[/tex]
= [tex]137980(\frac{1}{2})^{20}[/tex]
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express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of the standard unit vectors.
a. 3i + 3j
b. 5i + j
c. 3i - 3j
d. -3i + 3j
e. 3i + 4j
f. none of these
The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .
In the question ,
it is given that ,
the initial point of the vector = (1 , -1)
the terminal point of the vector = (4,2)
we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula
V = (x₂ - x₁)i + (y₂ - y₁)j
Substituting the values from the point ,
we get the vector as
V = (4 - 1)i + (2 -(-1))j
V = 3i + (2 + 1)j
V = 3i + 3j
Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .
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Explain how you can use a part:part ratio to determine the part:whole ratio.
Let's say we have blue and red balls
Blue : Red
3 : 5
Now we can add another ratio for the whole.
Blue : Red : Total
Total is Blue + Red = 3 + 5 = 8
So
Blue : Red : Total
3 : 5 : 8
Then the part : whole ratio for Blue is...
Blue : Total
3 : 8
A cereal company packs cereal boxes into large cardboard boxes. The large boxes are 12 inches long and 8 inches wide. How tall are the large boxes if the volume is 3,456 cubic. In.?
The height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.
According to the question,
We have the following information:
A cereal company packs cereal boxes into large cardboard boxes. The large boxes are 12 inches long and 8 inches wide.
Volume of box = 3456 cubic inches
We know that the box is in the shape of cuboid.
Following formula is used to find the volume of cuboid:
Volume = length*width*height
12*8*height = 3456
96*height = 3456
Dividing both sides by 96:
Height = 3456/96
Height of the box = 36 inches
Hence, the height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.
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Rio went to Wal-mart and bought 1 pounds of Turkey for $5.50
What is the cost per pound of Turkey?
Round your answer to the nearest CENT, if necessary.
$4.75
$4.40
$5.00
$0.23
Answer:
It says right there that he bought a pound of turkey for $5.50.
One pound of turkey is $5.50?
Step-by-step explanation:
This is extremely confusing
Is the following statement a good definition?
An equilateral triangle is a triangle with all sides congruent.
yes
or
no
Answer: Yes
Step-by-step explanation:
An equilateral triangle has three equal sides and angles, therefore all of the sides are congruent.
Write an equation of the line passing through point
P(-8, 0) that is perpendicular to the line y=-3
The equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0 which can be found out from slope intercept formula.
It is given to us that -
The point is P(-8,0)
The line is represented as y=-3
The point P is perpendicular to the given line.
We have to find out the equation of the line passing through P which is perpendicular to the given line.
We know that the equation of a line is given by -
y = mx + c
where, (x, y) = coordinates of the point
m = slope of the line
c = a constant
Comparing this with the equation of the given line, we have
m=0 and c =-3
This implies that the slope of the perpendicular is also equal to 0.
The slope intercept formula for the perpendicular line can be represented as -
y = mx + c
Using the coordinates of P(-8,0), we have
0 = 0*(-8) +c
=> c = 0.
Thus, the equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0.
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Which inequality is represented by the graph
Inequality represented by the given graph is equal to 5x -3y > 9.
As given in the question,
For the given graph,
Consider two points on the line represented on the graph ,
( x₁ , y₁) = (0,-3)
(x₂ , y₂) = ( 3,2)
Equation of the line given by two points on the graph,
( y - y₁)/ (x -x₁) = ( y₂ - y₁)/ (x₂ -x₁)
⇒(y +3)/(x-0) = ( 2 + 3)/(3 -0)
⇒(y + 3) / x = 5/3
⇒3(y+ 3) = 5x
⇒3y + 9 = 5x
⇒5x -3y = 9
As per shaded region inequality of the graph is given by,
5x -3y > 9
Therefore, inequality represented by the given graph is equal to 5x -3y> 9.
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Chris earned $17,000 last year. If the first $25,000 is taxed at 8% and income above that is taxed at 16%, how much does Chris owe in tax?
well, we know the first $25,000 is taxed at 8%, wait a second!!!!! Chris didn't make 25,000 bucks, he only made $17,000, so he'd be in the range of $0 - $25,000 because $17,000 is in that range, that means he owes 8% of 17,000
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 17000}}{\left( \cfrac{8}{100} \right)17000}\implies 1360[/tex]
The amount Chris owes in tax is $1360.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The first $25,000 is taxed at 8%.
This means,
Amount from 0 to $25000 is taxed at 8%.
Now,
Chris earned = $17,000
Tax amount.
= 8% of 17,000
= 8/100 x 17,000
= 8 x 170
= $1360
Thus,
The tax amount is $1360.
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X i a poitive integer 33 divided by x i a poitive interger write 4 poible value of x
27x + 35y = -105
what is x and what is y
Answer:
x-intercept: -([tex]\frac{35}{9}[/tex],0)
y-intercept: (0,-3)
Step-by-step explanation:
So if I get paid every 12 days and I put 80$ back every 12 days how long would it take to get to 2000 dollars
It will take 300 days to get to 2000 dollars.
According to the question,
We have the following information:
One gets paid every 12 days and one puts back $80 every 12 days.
Now, the total amount of dollars is $2000.
Now, we have the following progression:
80, 160, 240, ...
This is an arithmetic progression.
an = a+(n-1)d where a is the first term and d is the common difference
2000 = 80+(n-1)80
2000 = 80+80n-80
2000 = 80n
n = 2000/80
n = 25
Now, the number of days one is paid is after 12 days.
So, the number of days to get 2000 dollars:
25*12
300 days
Hence, it will take 300 days to get to 2000 dollars.
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531/4
Please give step by step explanation, must be long division.
Answer: 132.5
Step-by-step explanation:
Answer:
132.75
Step-by-step explanation:
*in picture below*
a rectangle is drawn so the width is 49 inches longer than the height. if the rectangle's diagonal measurement is 61 inches, find the height.
Refer to the attachment for figure:
The height of the rectangle = 11 inches
What is rectangle?
A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Let x= height
Width becomes x+49
Diagonal BD=61 inches
By pythagoras theorem,
BD²=BC²+CD²
61²= (x+49)²+x²
3721=x²+98x+2401+x²
On simplification,
x²+49x-660=0
Find the factors
(x+60)(x-11)=0
x=-60, x=11
Consider positive value for height
height = 11 inches
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50 POINTS TO WHOEVER SOLVES THIS QUESTION!!!! PLEASE HELP
The total segment AE is 46.
What is SAS(Side -Angle-Side) triangle?
"SAS" is when we know two sides and the angle between them.
To solve an SAS triangle we use "The Law of Cosines" to calculate the unknown side.
The Law of Cosines = a² = b² + c² − 2bc cosA
where
'b' and 'c' are two given sides
'A' is the angle between side 'b' and 'c' and
a' is the unknown side which we have to find.
In ΔABC , b=21, c=20, a= AC
By the Cosine law
a² = 21²+20² - 2*21*20 cos90°
a² =441 + 400 - 0 (∵cos 90° =0)
a² = 841
a=√841
a=29= AC.
Now, in ΔCDE, b=8, c=15 and a = CE
By the Cosine law
a² = 8² + 15²- 2*8*15cos90°
a² = 64 + 225 - 0 (∵cos 90° =0)
a²= 289
a = 17 = CE.
AE = AC + CE
AE = 29+17= 46.
Therefore, the total segment AE is 46.
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Can you write an equation to show how much the total cost, y, to travel in x miles?
Don’t forget: in slope-intercept form, y=mx+b, m is the slope and b is the y-intercept.
Answer:
y = 3x + 2
Step-by-step explanation:
The slope is the rate of change. The y intercept is the y value when x is 0.
what is the equation in standard form of the line that passes through the point (1,24) and has a slope of (-3/5)
y = -3/5x - 123/5 is slope-intercept form .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately visible. This form is frequently known as the y = mx + b form.Point = ( 1,24 )
slope = -3/5
the equation in standard form of the line that passes through the point
y - y₁ = m ( x - x₁)
y - 24 = -3/5 ( x - 1)
5 (y - 24) = -3( x - 1 )
5y - 120 = -3x + 3
5y = -3x + 3 + 120
5y = -3x + 123
y = -3/5x - 123/5
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2 3/5 x 1 3/7 i need help
Answer:
26x/7
Step-by-step explanation:
A scientist measures the mass of a metal to be 682 grams. There are 1000 grams in a kilogram and a kilogram is equal to about 2.2 pounds.
What is the mass of the metal in pounds?
Answer: The answer to this question is: the mass of the metal in pounds is 1.5 grams.
Step-by-step explanation: Search a free gram to pounds calculator and input your given input or output into there for further help if needed.
Hope this helps
The mass of the metal in pounds is 1.5 pounds.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
Given that, a scientist measures the mass of a metal to be 682 grams
682 grams = 0.682 kg
0.682 kg = 0.682*2.2 = 1.5 pounds.
Hence, The mass of the metal in pounds is 1.5 pounds.
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What effect do you think the sample size have on the mean of the sampling distribution of the mean?.
The effect of the sample size on the mean of the sampling distribution is that it effects the variations .
In the question ,
If the sample size is increased ,
that is if the number of sample is increased then the errors in the sampling distribution becomes less .
and if the sample size is decreased then it will lead to the increase in the errors of the distribution .
The formula for relationship between variation and sample size is given as ,
σx = σ / sqrt (n)
we can see that variation and sample size are inversely proportional .
that means increase in the sample size results in reduction of variation.
Therefore , The effect of the sample size on the mean of the sampling distribution is that it effects the variations .
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refer to exercise 9. what proportion of 9-ounce bags of this brand of potato chips weigh more than 9.2 ounces?
Percentage of bags that weigh more than 9.25 ounces is 19.3%.
Given:
Mean μ = 9.12
standard deviation σ = 0.15
z = x - μ / σ
= 9.25 - 9.12 / 0.15
= 0.13/0.15
= 0.867
P(x>Z) = 0.193
= 0.193/100
= 19.3%
Therefore Percentage of bags that weigh more than 9.25 ounces is 19.3%.
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Maxine and her daughter are going grocery showing after she gets off work. Maxine sees that apples are $0.25, while bananas are $0.79. She has $2.50 to spend on apples, x, and bananas. y. Write the equation, in standard form that represents her situation.
HELP ME PLEASE
Her situation can be modeled by the linear equation (in standard form):
x*$0.25 + y*$0.79 = $2.50
How to write the equation that represents her situation?The variables that we will use here are:
x = number of apples that she can buy.
y = number of bananas that she can buy.
We know that she has $2.50 to spend, that each apple costs $0.25 and each banana costs $0.79, then the cost of the x apples and y bananas is:
x*$0.25 + y*$0.79
and that must be equal to the amount she has to spend, then we can write the linear equation:
x*$0.25 + y*$0.79 = $2.50
That is the linear equation in standard form that represents her situation.
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The ratio of the number of red cubes to the total number of small plastic cubes in a classroom is 3:14. How many red cubes are there if there are 560 cubes altogether?
Answer:
red cubes = 99, plastic cubes = 462
Step-by-step explanation:
total number of cubes/total ratio
= 560/17
= 33 (approximately)
red cubes
= 33 × 3
= 99
plastic cubes
= 33 × 14
= 462
Though 462 + 99 equals 561 rather than 560, I had to approximate the values because if not, the result will be 461 which is a prime number.
A survey was given to people who owend a certain type of car. What percent of the people surveyed were completely sastified with the car?