(*6./Sean drives from Manchester to Gretna Green.
He drives at an average speed of 50 mph for the first 3 hours of his journey.
He then has 150 miles to drive to get to Gretna Green.
Sean drives these 150 miles at an average speed of 30 mph.
Sean says,
"My average speed from Manchester to Gretna Green was 40 mph."
Is Sean right?
You must show how you get your answer.
Sean's real average speed was less than his predicted 40 mph.
What is average speed?Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time.
Student must calculate average speed, compare it to Sean's response, and determine total distance traveled and time expended. First, the formula must be stated: Average speed = Total distance traveled / Time required.We can rearrange this to determine the distance traveled.Total mileage equals time divided by average speed.We only need to compute the first leg of his travel as we already know the total distance was 150 miles. As a result, we can calculate 150 miles at 50 mph for 3 hours.We now know that the overall distance from Manchester to Greta Green was 300 miles after including the second half of the voyage.Now we have to think about how long it took overall. Rearranging the equation yields the necessary result: Time taken=distance/speed. This brings us back to the comparatively easy formula of 150 miles at 30 miles per hour equals 5 hours. This indicates that the total travel time from Manchester to Gretna Green was 8 hours, not including the initial 3 hours. We now possess all the knowledge required to calculate his average speed over the entire journey. The original equation is still used: Average speed = Total distance traveled / Time taken. After entering all the data, we get the result 300 miles in 8 hours = 37.5 miles per hour.Hence, Sean's real average speed was less than his predicted 40 mph.
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please help me with this math problem
Answer:
a - April
b - may
c - they neither made nor lost money that month
hope that helps :)
Step-by-step explanation:
Answer: a) - March
b) - May
c)- it neither made nor lost money that month
Step-by-step explanation:
a) - because -386 is the least out of all of them
b) - because 271 was the most out of all of them
c) - it didn't lose or make it just stayed the same as it was
Write the equation of the line that is perpendicular to the line (y= 2/3x + 4) in the graph and gird through the point (-1,5)
Answer:y= -2/3+3 is the answer since you are just flipping the same line and move down by 1
Step-by-step explanation:
(2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)
Hello,
I hope you and your family are doing well!
To simplify the expression, you can combine like terms and simplify:
[tex](2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)[/tex]
[tex]= 2x^2+x+1 - x^2+x-7 - 4x^2-2x-8[/tex]
[tex]= (2x^2 - x^2 - 4x^2) + (x - x - 2x) + (1 - 7 - 8)[/tex]
[tex]= -3x^2 - 3x - 14[/tex]
Therefore, the simplified expression is [tex]-3x^2 - 3x - 14[/tex]
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Happy Holidays!
Please answer both parts
the area will be fall in between 100≤ 20x ≤1000.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,A quadrilateral should be closed shape with 4 sides
All the internal angles of a quadrilateral sum up to 360°.
The area of a rectangle is A = a*b
Here in the figure the length is given 4x and the breadth is 5.
The area is given in between 100≤A≤1000
So this area will be A = 5x*4 = 20x
Now the area will be lie in between 100≤ 20x ≤1000
hence, the area will be fall in between 100≤ 20x ≤1000.
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please anyone help I need help right or wrong I need to pass my classes
Answer:
B second one
Step-by-step explanation:
2000-750/5=250
can somebody please help
Step-by-step explanation:
The diagram is very helpful, so really go off of that. Coordinates are written in the form (x,y). If you look at the signs (either there's a negative sign, - , or no sign at all, meaning it's +) for each number in a coordinate pair, you can see where each coordinate should go.
If you look at the last example (3, -3), the first digit is positive + and the second digit is negative - . When you look at the diagram, coordinates in the form of (+, -) are put in quadrant 4.
Find h(−5) when h(x) = −3|x − 1| + 4. Show every step.
The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.
How to solve function?
Algebraically evaluate and resolve functions.Analyze functions using data from a table or a graph.The supplied value should be used as the input variable in the formula.Determine the outcome.h(x) = −3|x − 1| + 4
Substitute x = -5
h(-5) = −3|(-5) − 1| + 4
= -3|-6| + 4
= -18 + 4
= -14
h(-5) = -14
Hence, The value of h(-5) for the given function h(x) = −3|x − 1| + 4 is h(-5) = -14.
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An investor invested a total of $1,800 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $76, how much was
invested in each mutual fund?
The amount invested in the mutual fund that earned 6% was $
a) Using a system of equations, the amount invested in the mutual fund that earned 6% was $1,600.
b) The amount invested in the mutual fund that earned 4% was $200.
What is a system of equations?A system of equations is two or more equations solved concurrently.
A system of equations is also called simultaneous equations.
Total investment = $1,800
Profit from investment A = 6%
Profit from investment B = 4%
The total investment profit = $76
Let A = Investment A and B = Investment B
A + B = 1,800
A = 1,800 - B
0.06A + 0.04B = 76
0.06(1,800 - B) + 0.04B = 76
108 - 0.06B + 0.04B = 76
108 - 0.02B = 76
-0.02B = -32
B = 1,600
A = 200 (1,800 - 1,600)
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The original scale factor for a scale drawing of a house plan is 180, and the length of the original scale drawing is 12 inches. What is the length of a new scale drawing if the scale factor of the new scale drawing to actual length of the house is 1180?.
Answer:mutplion
Step-by-step explanation:
Boy : girl
11 : 9
there are 124 more boy than girl
how many pupil are in the chool?
There are 1240 students in the school.
What is Proportionalities (Ratios)?
It is possible to represent absolute connections using ratios or proportions, independent of the variables' actual raw values. For instance, if your business always produces widgets packaged in bundles of 20 widgets each, you will always have a 20 widgets to 1 bundle ratio regardless of how many bundles you produce. Accordingly, if you produce 100 bundles per day, you will have produced 2000 widgets in a single day. The proportion of widgets to bundles is constant and does not change. As long as the other ratio factor quantity is known or can be known, the ratio or proportion can then be used as a conversion factor to calculate the number of an unknown quantity of one ratio factor.
In our problem, we know that there are 11 boys : 9 girls in the school. We also know that there are 124 more boys than girls.
If we let x equal the number of girls in the school, the number of boys will then be x+124. We know the ratio of boys to girls and produce a conversion factor to determine the number of girls present in the school:
( number of boys)[tex]$\left(\frac{\text { girls }}{\text { boys }}\right)=$[/tex] number of girls
[tex](x+124)\left(\frac{9}{11}\right)=x[/tex]
Note that since we are looking to find the number of girls, it appears in the numerator of the conversion factor and boys in the denominator. If we were looking for the number of boys, we would flip the conversion factor to have the number of boys in the numerator and girls in the denominator.
Now let's simplify the equation and solve for x :
[tex]\begin{aligned}(x+124)\left(\frac{9}{11}\right) & =x \\\frac{9 x+1116}{11} & =x \\9 x+1116 & =11 x \\1116 & =11 x-9 x \\1116 & =2 x \\\frac{1116}{2} & =x=558\end{aligned}[/tex]
If we have 558 girls, the number of boys is then:
x+124=558+124=682boys
Adding the number of boys and girls together, we will have the total number of students in the school: 558+682=1240 students
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You are standing on a ledge and throw a ball from 10 feet above the ground. The speed the ball leaves your hand is 16 feet per second and the acceleration of gravity is -16 feet per second squared.
1. How many seconds does it take to reach the highest point (vertex)?
The ball reached its maximum height at a time of 1 second.
How many time is needed for the ball to reach its maximum height?
In this problem we have the case of a ball that experiments a free fall, that is, a case of an uniform accelerated motion due to gravity. The position of the ball as a function of time is represented by a quadratic equation:
y' = y + v · t + 0.5 · g · t²
Where:
y - Initial position, in feet.v - Initial velocity, in feet per second.t - Time, in seconds.g - Gravitational acceleration, in feet per square second.And to determine the time related to the highest point, we need to rearrange the expression into its standard form:
y' - k = C · (t - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantFirst, write the quadratic equation:
y' = y + v · t + 0.5 · g · t²
y' = 10 + 16 · t - 8 · t²
Second, complete the square until the standard form is found:
y' - 10 = 16 · t - 8 · t²
y' - 10 = - 8 · (t² - 2 · t)
y' - 18 = - 8 · (t² - 2 · t + 1)
y' - 18 = - 8 · (t - 1)²
The ball takes a time of 1 second to reach its maximum height.
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Russel wants to buy 3 identical gift cards. He wants to make sure the total cost is no more than $2 above or below $60. Which of the following inequalities represents the situation?
Let the cost of each gift card be x.
Three of them will cost 3x.
We need the total cost be no more than $2 above or below $60.
This can be represented as:
3x ≤ 60 + 2 ⇒ 3x ≤ 62,and
3x ≥ 60 - 2⇒ 3x ≥ 58,or as combined inequality:
58 ≤ 3x ≤ 62how do i solve (4x-5)/(3x+5)>=3?
Answer:
x = -4
Step-by-step explanation:
(4x-5)/(3x+5) = 3
1. Multiply both sides by 3x+5
4x-5 = 3(3x+5)
2. Expand
4x-5 = 9x+15
3. -4x from both sides
-5 = 5x+15
4. -15 from both sides
-20 = 5x
x = -4
It is greater than 3
x = 4
We can solve the equation as
(4x-5) = (3x+5)*3
4x-5=9x+15
x = 4
There are 300 teenagers in a park. 32% of them are boys, how
many more girls than boys are there in the park?
Answer: 108
Step-by-step explanation:
We find the number of boys by taking 300 timed 0.32 = 96 boys
Then we subtract 300 from 96 = 204 girls
Then we removed 204 by 96 = 108
So there are 106 girls more than boys
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Answer: 108
Step-by-step explanation: There are 300 teenagers in all. To find how many boys they are, multiply 32/100 times 300/1. You get 96, so there are 96 boys. This means that there are 204 girls. There are 108 more girls than boys. Hope this helps!
question 3 in the analyze stage of the data life cycle, what might a data analyst do? select all that apply.
In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle
The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems
The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system
Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations
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If f(x) = 3x² - x, find f{-3, 0, 3}
Step-by-step explanation:
so pretty much replace -3, 0 and 3 into the equation
-3 to the power of 2 is 9 and 9(3) is 27. 27-(-3) is 27+3, 30
0 squared is 0 so the 2nd one would be 0
3 squared times 3 is 27 and subtracted by 3 is 24.
classify the series -1+2+(-4)+8+...as arithmetic or geometric. Then, determine whether the series is convergent or divergent.
Answer:
The series -1+2+(-4)+8+... is an arithmetic series because it has a common difference between consecutive terms. Specifically, the common difference is -4 - 2 = -6.
To determine whether the series is convergent or divergent, we need to find its sum. The sum of an arithmetic series is given by the formula:
sum = (n/2)(a1 + an)
where n is the number of terms in the series, a1 is the first term, and an is the nth term.
Since the series is infinite, we cannot determine its sum using this formula. However, we can determine its sum by taking the limit as n approaches infinity. Using the formula above, we find that the sum is equal to:
sum = (infinity/2)(-1 + infinity)
Since the series contains an infinite number of negative terms, it is divergent.
a square has two diagonals, and a convex pentagon has five diagonals. how many diagonals does a convex decagon have?
35 is diagonals does a convex decagon have .
What does a pentagon basic definition entail?
A geometric figure with five sides and five angles is called a pentagon. Here, "Penta" stands for five, while "gon" is an angle.
One of the different kinds of polygons is the pentagon. For a standard pentagon, the total internal angles come to 540 degrees.
There are a total of ¹⁰C₂ ways to connect two different vertices. But connecting neighbouring vertices doesn't count, so we have to exclude the sides from our consideration. There are 10 sides, so we need to take away 10 ways from the 45 ways possible to get the number of diagonals.
Number of diagonals in a decagon = 35
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please help begging on knees rn.
10. if mB is two more than three times the measure of ZC, and ZB and Care
complementary angles, find each angle measure.
Step-by-step explanation:
First, you should translate everything into math. So,
"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)
"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)
Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:
(3C + 2) + C = 90
4C + 2 = 90
4C = 88
C = 22
Plugging C = 22 back into either equation (1) or (2) gives us
B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)
Thus, ∠B = 68º; ∠C = 22º
hope this helps
mrs jones gave 1/5 of a cake to her neighbour. she then sliced the remainder into 3 pieces for her 3 children, ken, ron and david, in the ratio 1 : 3 : 4. what is the fraction of the cake was ron's pieces
The fraction of the cake that was ron's pieces is 1/5.
What is the fraction of the cake was ron's pieces?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:
= 1 - 1/5
= 4/5
The fraction of the cake that was ron's pieces will be:
= 2/(1+3+4) × 4/5
= 2/8 × 4/5
= 8/40
= 1/5
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Chad is decorating a rectangular ballroom ceiling with decorative lights. Beginning in a corner, Chad strings the lights along the length of the ceiling, a distance of 55 feet. Next, Chad strings the lights along the width of the ceiling, a distance of 48 feet. Then Chad strings the lights straight back to the original corner. At this point, how many feet of lights has Chad used? If necessary, round your answer to the nearest tenth. feet
The number of feet of light used by Chad is 176 feet
How to determine the number of feet of light?From the question, we have the following parameters that can be used in our computation:
Length = 55 feet
Width = 48 feet
We start by calculating the distance from the end of the width till the beginning of the length
This is represented by the following Pythagoras theorem
Distance = √(Length² + Width²)
So, we have
Distance = √(55² + 48²)
Evaluate
Distance = 73
The number of feet is then calculated as
Feet = Length + width + distance
So, we have
Feet = 55 + 48 + 73
Evaluate
Feet = 176
Hence, the total distance is 176 feet
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What is the axis symmetry
The axis of symmetry of equation y = 3x² - 18x + 5 is x = 3.
What is axis symmetry?The object's shape becomes symmetrical when a straight line acts as the axis of symmetry. Each side of the axis of symmetry produces a perfect reflection of the other. It can be lateral, vertical, or any combination of the three.
Given equation:
y = 3x² - 18x + 5
The line symmetry of y = [tex]ax^2+bx+c = 0[/tex] is x = -b / 2a,
Hence, x = -(-18) / 2 × 3
Therefore, x = 3 is the axis of symmetry of equation y = 3x² - 18x + 5.
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in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks? if necessary, round your answer to the nearest tenth.
The weight of all of the rocks to the nearest tenth is 6.085 pounds .
Given :
in a science lab, a number of rock samples are weighed. if the scientist finds one of the rocks to weigh 3 pounds and this is 49.3% of the total weight of all of the rocks, what is the weight of all of the rocks if necessary, round your answer to the nearest tenth.
Let x be the total weight or all the weight of rocks .
3 = 49.3 % * x
3 = 49.3 * 1 / 100 * x
3 * 100 = 49.3 * x
300 = 49.3 * x
divide with 49.3 on both sides
300 / 49.3 = 1 * x
x = 300 / 49.3
= 6.085 pounds
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Solve for X, the figure is a trapezoid. I will give brainiest!!
Answer:
6
Step-by-step explanation:
RS and QT are parallel because it is a trapezoid. This means that the transversal applies. Look at the picture attached to understand what I mean.
So, we know that 18x - 13 = 180(degree of a line)-85. Then, solve the equation.
18x-13=95
18x=108
x=6
Let f(x) be a continuous function such that f(1) = 3 and f '(x) = [tex]\sqrt{x^3+4}[/tex]. What is the value of f(5)?
The price of a video game console was
marked down $25, but then marked up by
12. If the original price was $225, what
is the new price?
Answer:
$227
Step-by-step explanation: if the console gets marked downed $25 it will be $200 then the 12% increase which it $27 so that will be $227
CEDAR
1
SOULANICTA
ARANTEN
In the figure below, mZ1 = (x-6)° and m/2=5x°.
Find the angle measures.
2
Answer:
∠ 1 = 25° , ∠ 2 = 155°
Step-by-step explanation:
∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is
x - 6 + 5x = 180
6x - 6 = 180 ( add 6 to both sides )
6x = 186 ( divide both sides by 6 )
x = 31
Then
∠ 1 = x - 6 = 31 - 6 = 25°
∠ 2 = 5x = 5 × 31 = 155°
Solve for n
8n+7=-4n+19
Answer: n= 1
Step-by-step explanation:
8n+7=-4n+19
First, subtract 7 from both sides
8n = 4n +12
Then add 4n from both sides
12n = 12
Then divide by 12 from both sides
n= 1
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Answer: n = 1
Step-by-step explanation:
First, you could start off by bringing the -4n to the left side:
8n + 7 = -4n+19 → 12n + 7 = 19
Next, you take the 7 on the left side of the equals sign and subtract it from the 19:
12n + 7 = 19 → 12n = 12
Finally, you divide the 12 on the right by the 12 on the left:
12n = 12 → n = 12/12
A number over itself will always be 1, so n = 1.
For males in a certain town, the systolic blood pressure is normally distributed with a
mean of 110 and a standard deviation of 5. Using the empirical rule, determine the
interval of systolic blood pressures that represent the middle 99.7% of males.