Mike has under 1/4 of a tank of gas, and he decides to fill up his gas tank. his gas tank holds 16 gallons. the gas cost $3.59 per gallon. It will cost Mike $43.08 to fill up his car.
To help you with your question, we first need to determine the amount of gas Mike needs to fill up his car. Since he has less than 1/4 of a tank, let's assume he has exactly 1/4 of a tank for simplicity.
Mike's car has a 16-gallon gas tank, so:
1/4 * 16 gallons = 4 gallons already in the tank.
To fill up the tank, Mike needs to add:
16 gallons - 4 gallons = 12 gallons.
The gas costs $3.59 per gallon, so to find the total cost:
12 gallons * $3.59 = $43.08.
Approximately, it will cost Mike $43.08 to fill up his car.
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The circular area covered by a lawn sprinkler has a 24.25-foot diameter. What is the area of the space covered by the sprinkler? Use 3.14 for π
. Round to the nearest hundredth if necessary.
The area covered by the lawn sprinkler is approximately 461.63 square feet.
What is the area covered sprinkler?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
Where r is radius and π is constant pi ( π = 3.14 )
Given that; the diameter of the circle is 24.25 feet.
The radius of the circle is half of the diameter, so:
Radius r = diameter/2
Radius r = 24.25 / 2
Radius r = 12.125 feet
Next, plug the values into the above formula and solve for area.
Area = πr²
Area = 3.14 × ( 12.125 ft )²
Area = 3.14 × ( 12.125 ft )²
Area = 461.63 ft²
Therefore, the area is 461.63 ft².
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the most recent earthquake in texas reached a magnitude of 3.3 on the richter scale. determine the seismograph reading of the earthquake. using M(I)=log (I/.001)
The seismograph reading of the earthquake is approximately 1.99526.To determine the seismograph reading of the earthquake with a magnitude of 3.3 on the Richter scale, we can use the formula M(I) = log(I/0.001), where M(I) represents the magnitude and I represents the intensity of the earthquake.
In this case, we are given the magnitude of 3.3. Let's substitute this value into the formula and solve for I:
3.3 = log(I/0.001)
To isolate I, we need to convert the equation into exponential form:
10^(3.3) = I/0.001
Simplifying the equation, we have:
I = 10^(3.3) * 0.001
Using a calculator, we find that 10^(3.3) is approximately 1995.26.
So, the seismograph reading of the earthquake is:
I = 1995.26 * 0.001
≈ 1.99526.
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complete the point-slope equation of the line through (-5 4) and (1 6)
Answer:
y - 4 = 1/3(x + 5)
Step-by-step explanation:
The general equation for the point-slope form of a line is given by:
y - y1 = m(x - x1), where
(x1, y1) is a point on the line, and m is the slope of the line.Step 1: To find the equation of the line through (-5, 4) and (1, 6), we first need to find the slope of the line using the slope formula, which is:
m = (y2 - y1) / (x2 - x1), where
(x1, y1) are one point on the line,and (x2, y2) are another point on the lineWe can allow (-5, 4) to be our (x1, y1) point and (1, 6) to be our (x2, y2) point:
m = (6 - 4) / (1 - (-5))
m = 2 / (1 + 5)
m = 2/6
m = 1/3
Now we can use the point-slope form of the equation with either of the two points.
Since we already used (-5, 4) as our (x1, y1) point, let's use it for the point-slope form:y - 4 = 1/3(x - (-5))
y - 4 = 1/3(x + 5)
Thus, the point-slope equation of the line through (-5, 4) and (1, 6) is:
y - 4 = 1/3(x + 5)
A container has 56 gallons of water and is being filled at a rate of gallon per second. Another container has 64 gallons of water is
draining at a rate of gallon per second. After how many seconds will the two containers will have the same amount of water?
Round your answer to the nearest tenth.
After 4 seconds, both containers will have the same amount of water.
Let's assume that after "t" seconds, both containers will have the same amount of water.
In "t" seconds, the first container will have 56 + t gallons of water.
In "t" seconds, the second container will have 64 - t gallons of water.
To find out when both containers will have the same amount of water, we need to solve the equation:
56 + t = 64 - t
By solving for "t", we get:
2t = 8
t = 4
Therefore, after 4 seconds, both containers will have the same amount of water.
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I'm having a really hard time on this question and it's really late I just want to get this done
Answer:
48cm³
Step-by-step explanation:
volume = (7 X 6 X 1) + (3 X 2 X 1)
= (42 + 6)
= 48cm³
The quantity 1.0 mg/cm2 is the same as 1.0 x ________ kg/m2.
A. 10-4
B. 102
C. 106
D. 10-2
E. 104
The quantity 1.0 mg/cm2 is the same as 1.0 x 10-4 kg/m2.
To convert from milligrams per square centimeter (mg/cm2) to kilograms per square meter (kg/m2), we need to use conversion factors to adjust the units. The given options represent different powers of 10 that can be used as conversion factors.
We know that 1 kilogram (kg) is equal to 1,000,000 milligrams (mg), and 1 meter (m) is equal to 100 centimeters (cm). Therefore, we can express the conversion factors as follows:
1 kg = 1,000,000 mg (1)
1 m2 = 10,000 cm2 (2)
To convert from mg/cm2 to kg/m2, we can combine these conversion factors:
1 mg/cm2 = (1 mg / 1 cm2) x (1 kg / 1,000,000 mg) x (10,000 cm2 / 1 m2)
Simplifying the expression, we have:
1 mg/cm2 = (1 / 1,000,000) kg/m2 = 1 x 10-6 kg/m2
Therefore, the quantity 1.0 mg/cm2 is the same as 1.0 x 10-6 kg/m2.
Among the given options, the value that matches the conversion is option A: 10-4
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How do you calculate the rate of change of a periodic function
The rate of change of a periodic function is itself a periodic function. In the case of a sinusoidal wave, the derivative is also a sinusoidal wave with the same period, but shifted by a phase angle of [tex]π/2.[/tex]
The rate of change of a periodic function at a specific point is equal to the instantaneous slope of the tangent line to the graph of the function at that point.
To calculate the rate of change of a periodic function, you need to take the derivative of the function with respect to the independent variable (usually time). If the function is a sinusoidal wave, you can use trigonometric identities to find the derivative.
For example, let's say we have a function f(t) = sin(t), which represents a sinusoidal wave. To find the rate of change of the function at a particular point t = a, we need to take the derivative of the function with respect to t:
f'(t) = cos(t)
Then we can evaluate this derivative at t = a to find the rate of change at that point:
f'(a) = cos(a)
This tells us the instantaneous rate of change of the function at the point t = a.
Note that the rate of change of a periodic function is itself a periodic function. In the case of a sinusoidal wave, the derivative is also a sinusoidal wave with the same period, but shifted by a phase angle of [tex]π/2.[/tex]
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Find the sector area for the following where 2pi/3 r=6 m
The sector area is 6π square meters.
We can use the formula for the area of a sector of a circle, which is:
A = (θ/2π) × πr²
where θ is the representation of the central angle in radians, and r is the representation of the radius of the circle.
In this case, we are given that 2π/3 is the central angle and r = 6 m. We can simplify 2π/3 as 120 degrees or π/3 radians.
When we enter these values into the formula, we get:
A = (π/3 × 1/2π) × (36)
= (1/6) × 36π
= 6π
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Pls help due today xx
Answer:
21x+6
Here is the answer
Its a pleasire
Answer:
21x+6
Step-by-step explanation:
first distrbute the 3 on the brackets
and note that in mathematics when there is no sign just like after the 3 it means it's multiplication
3(2x+5)+3(5x-3)
=6x+15+15x-9
now add or subtract
=21x+6
that is the simplest we can get and we can't find the value of x cuz this is not an equation
(there is no equal sign and numbers on both sides )
a company orders 29 boxed lunches from a deli for $339.30. assume each boxed lunch is the same price. if c represents the total cost in dollars and cents of the lunch order for any number, b, of boxed lunches ordered, write a proportional equation for c in terms of b that matches the context.
Answer:
11.7b
Step-by-step explanation:
If you do 339.30 divided by 29 it equals 11.7 but the full equation would be c=11.7b
The proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:
c = (339.30 / 29) * b
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.
Let's assume that each boxed lunch costs the same amount, denoted by the variable 'x'.
We are given that the company ordered 29 boxed lunches for a total cost of $339.30. Therefore, we can write the equation:
29x = 339.30
To find the cost 'c' for any number 'b' of boxed lunches, we can set up a proportion:
29x / 29 = 339.30 / b
Simplifying this equation, we get:
x = 339.30 / 29
Now, we can substitute this value of 'x' back into the equation:
c = bx = b * (339.30 / 29)
Therefore, the proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:
c = (339.30 / 29) * b
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Write a quadratic function in standard form that passes through (-7,0) , (-1,0) and (-6,-20)
Answer:
y = 4x^2 + 32x + 28
Step-by-step explanation:
Before we can find the standard form of the quadratic function with the given coordinates, we must first start with the intercept form, whose general equation is
y = a(x - p)(x - q), where
a is a constant determining concavity (essentially, whether the parabola opens upward or downward)(x, y) are any point on the parabola,and p and q are the x-intercepts/rootsStep 1: We can plug in (-6, -20) for x and y, -7 for p and -1 for q into the intercept form. This will allows us to solve for a:
-20 = a(-6 - (-7))(-6 - (-1))
-20 = a(-6 + 7)(-6 + 1)
-20 = a(1)(-5)
-20 = -5a
4 = a
Thus, the full equation in vertex form is
y = 4(x + 7)(x + 1).
Step 1: The general equation for standard form is
y = ax^2 + bx + c.
We can convert from vertex to standard form by simply expanding the expression. Let's ignore the 4 for a moment simply focus on (x + 7)(x + 1).
We can expand using the FOIL method, where you multiply
the first terms, the outer terms,the inner terms, and the last terms,then simplify by combining like termsWe see that the first terms are x and x, the outer terms are x and 1, the inner terms are 7 and x and the last terms are 7 * 1. Now, we multiply and simplify:
(x * x) + (x * 1) + (7 * x) + (7 * 1)
x^2 + x + 7x + 7
x^2 + 8x + 7
Step 3: Now, we can distribute the four to each term with multiplication:
4(x^2 + 8x + 7)
4x^2 + 32x + 28
Optional Step 4: We can check that our quadratic function in standard form, by plugging in -7, -1, and -6 for x and seeing that we get 0 as the y value for both x = -7 and x = -1 and -20 as the y value for x = -6:
Checking that (-7, 0) lies on the parabola of 4x^2 + 32x + 28:
0 = 4(-7)^2 + 32(-7) + 28
0 = 4(49) - 224 + 28
0 = 196 - 196
0 = 0
Checking that (-1, 0) lies on the parabola of 4x^2 + 32x + 28:
0 = 4(-1)^2 + 32(-1) + 28
0 = 4(1) - 32 + 28
0 = 4 - 4
0 = 0
Checking that (-6, -20) lies on the parabola of 4x^2 + 32x + 28:
-20 = 4(-6)^2 + 32(-6) + 28
-20 = 4(36) -192 + 28
-20 = 144 -164
-20 = -20
I attached a graph from Desmos to show how the function y = 4x^2 + 32x + 28 contains the points (-7, 0), (-1, 0), (-6, 20), further proving that we've correctly found the quadratic function in standard form passing through these three points
how are the pairs of figures alike? how are they different?
Answer: illustrates similarity of figures
Step-by-step explanation: more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
A nervous kicker usually makes 71% of his first field goal attempts. If he makes his first attempt, his success rate rises to 89%. What is the probability that he makes his first two kicks?
Answer: 0.632
The probability that the kicker makes his first two kicks is 63.21%. This means that out of 100 attempts, the kicker is likely to make both kicks 63 times.
To solve this problem, we need to use conditional probability. We know that the kicker usually makes 71% of his first field goal attempts. So, the probability that he makes his first kick is 0.71. If he makes his first attempt, his success rate rises to 89%. So, the probability that he makes his second kick given that he made his first kick is 0.89.
Now, to find the probability that he makes his first two kicks, we need to multiply the probability of him making his first kick by the probability of him making his second kick given that he made his first kick. This can be represented as:
P(2 successful kicks) = P(1st kick is successful) x P(2nd kick is successful | 1st kick is successful)
P(2 successful kicks) = 0.71 x 0.89
P(2 successful kicks) = 0.6321 or 63.21%
Therefore, the probability that the kicker makes his first two kicks is 63.21%. This means that out of 100 attempts, the kicker is likely to make both kicks 63 times.
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Trapezoid ABCD is congruent to trapezoid A′′B′′C′′D′′ . Which sequence of transformations could have been used to transform trapezoid ABCD to produce trapezoid A′′B′′C′′D′′ ? Responses Trapezoid ABCD was reflected across the y-axis and then across the x-axis. , , trapezoid A B C D, , , , was reflected across the y -axis and then across the x -axis. Trapezoid ABCD was reflected across the y-axis and then translated 7 units up. , , trapezoid A B C D, , , , was reflected across the y -axis and then translated 7 units up. Trapezoid ABCD was translated 7 units up and then 12 units left. , , trapezoid A B C D, , , , was translated 7 units up and then 12 units left. Trapezoid ABCD was reflected across the x-axis and then across the y-axis. , , trapezoid A B C D, , , , was reflected across the x -axis and then across the y -axis.
The correct sequence of transformations that could have been used to transform Trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.
To transform trapezoid ABCD into trapezoid A''B''C''D'', we need to apply a sequence of transformations that will result in the same size and shape of the two trapezoids, which means that they are congruent.
One possible sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is:
Trapezoid ABCD was reflected across the y-axis and then across the x-axis.
This sequence of transformations would result in the same size and shape of the two trapezoids, which means that they are congruent. Let's see why this is true.
When we reflect trapezoid ABCD across the y-axis, each point on the trapezoid is reflected across the y-axis, which means that its x-coordinate is multiplied by -1 while its y-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the y-axis.
Next, when we reflect the trapezoid across the x-axis, each point is reflected across the x-axis, which means that its y-coordinate is multiplied by -1 while its x-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the x-axis.
The resulting trapezoid is now in the same position and orientation as trapezoid A''B''C''D'', but it may not be in the same location. However, since the trapezoid is congruent, we can translate it to match the position of trapezoid A''B''C''D''.
Therefore, the correct sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.
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Shadrach rents out 30 offices for $1,600 per month for each office and 10 offices for $2,000 per month for
each office. What is the total rent per month that Shadrach collects for these 40 offices?
Answer:
$68000
Step-by-step explanation:
Answer:
$6800
Step-by-step explanation:
30x1600+10x2000
=48000+2000
=68000
A flower bed has the shape of a rectangle 21 feet long and 12 feet wide. What is its area in square yards?
The area of the flower bed in square yards is 28 Square yards.
The area of the rectangular flower bed in square yards, we need to convert the measurements from feet to yards. There are 3 feet in 1 yard, so:
Length in yards = 21 feet / 3 = 7 yards
Width in yards = 12 feet / 3 = 4 yards
Now we can calculate the area in square yards:
Area = Length × Width
Area = 7 yards × 4 yards
Area = 28 square yards
Therefore, the area of the flower bed in square yards is 28 square yards.
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the mean of a sampling distribution of mean is: a. equal to the population mean b. less than the population mean c. less than the population standard deviation d. none of the above
The mean of a sampling distribution of mean is equal to the population mean.
The mean of a sampling distribution of the mean is equal to the population mean. This is a fundamental property of sampling distributions. When repeatedly taking random samples from a population and calculating the mean of each sample, the distribution of those sample means will have a mean that is equal to the population mean. This is known as the central limit theorem, which states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution centered around the population mean. Therefore, the mean of the sampling distribution of the mean will be the same as the population mean.
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The theoretical probability that you will try out for the school play is 1/10. There at e22 students in your grade that try out for the school play. How many students are in your grade?
Use Theoretical probability there are 220 students in the grade.
We can use the formula for theoretical probability to find the number of students in the grade:
P(event) = number of favorable outcomes / number of total outcomes
In this case, the probability of a student trying out for the school play is 1/10, so we have:
1/10 = number of students who try out / total number of students in the grade
We can simplify this equation by multiplying both sides by the total number of students in the grade:
total number of students in the grade * 1/10 = number of students who try out
Multiplying both sides by 10, we get:
total number of students in the grade = 10 * number of students who try out
Substituting the given value of 22 for the number of students who try out, we get:
total number of students in the grade = 10 * 22
total number of students in the grade = 220
Therefore, there are 220 students in the grade.
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Which statement is not true?
An event can have a probability of 0.
An event can have a probability of .
A game is fair if the probability of winning is .
An event can have a probability of 1.
Whoever answers correctly, I will mark brainliest!
Need the solution right now in a hurry
Answer:
”an event can have a probability of 0”
Step-by-step explanation:
A probability can not be 0 it has to be more then 0
In △RST, what is the length of segment RT? Right triangle RST with RS measuring 36 and angles R and T measure 45 degrees. 18 72 36radical 3 36radical 2
The length of segment RT is given as follows:
[tex]RT = 36\sqrt{2}[/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The right angle in this problem is given as follows:
S, as R = T = 45º.
As the other two angles have the same measure, we have that the two sides are RS = ST = 36, hence the hypotenuse RT is given as follows:
h² = 36² + 26²
[tex]h = \sqrt{2 \times 36^2}[/tex]
[tex]RT = 36\sqrt{2}[/tex]
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Each small meat loaf uses three quarters pound of meat. How much meat do you need to make 8 small meat loaves
To make 8 small meat loaves, you will need a total of 6 pounds of meat.
This is because each small meat loaf requires three quarters (0.75) of a pound of meat, and 8 loaves multiplied by 0.75 pounds per loaf equals 6 pounds of meat.
When preparing the meat, it's important to measure out each loaf accurately to ensure they are all the same size and cook evenly. You can use a kitchen scale to measure out the appropriate amount of meat for each loaf.
Once the meat is prepared, you can add your desired seasonings and mix-ins to create a flavorful dish. Some popular additions to meatloaf include onions, garlic, Worcestershire sauce, breadcrumbs, and eggs.
When shaping the loaves, you can use a muffin tin or form them by hand. Bake them in the oven at 350°F for 25-30 minutes or until they reach an internal temperature of 160°F.
Overall, making small meat loaves is a delicious and easy way to enjoy a classic comfort food.
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1=10km
. A photocopier makes 8 copies in 20 seconds. At that same rate, how many whole
copies can the photocopier make in 48 seconds?
Answer:
Step-by-step explanation:
20 seconds = 8 copies
so every 2.5 seconds, 1 page is made( 20sec/8 page = 2.5 page per second)
2.5 sec = 1 page
48 sec = x page
now you cross multiply, and that goes to: 2.5x = 48
isolate for x
x= 48/2.5
x= 19.2 but it says whole pages so you round down
x = 19 pages in 49 seconds
If xy + 4ey = 4e, find the value of y'' at the point where x = 0. y'' = Need Help? Read It Chat About It Submit Answer Save Progress Practice Another Version
We cannot find the value of y'' at the point where x = 0 using this method.
To find y'' at the point where x = 0, we need to differentiate the given equation twice with respect to x.
First, we take the derivative of both sides with respect to x:
y + xy' + 4ey' = 0
Next, we take the derivative of this equation with respect to x:
y' + xy'' + y' + 4ey'' = 0
Simplifying this expression, we get:
2y' + xy'' + 4ey'' = 0
We are given that xy + 4ey = 4e. Differentiating this equation with respect to x, we get:
y + xy' + 4ey' = 0
Substituting y' = -(y + 4ey')/x from this equation into the previous equation, we get:
2y' - (y + 4ey') + 4ey'' = 0
Simplifying this expression, we get:
y'' = (y + 4ey' - 2y')/(4e)
When x = 0, we have y = 4e/4e = 1 and y' = -(1 + 4e*y')/0, which is undefined.
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three fifth of work is done on the first day. On the second day three quarters of the remainder is completed,if on the third day seven eighth of what remained is done,what fraction of work still remains to be done?
Let's say the total work to be done is represented by 1.
On the first day, three-fifths of the work is completed. Therefore, the remaining work to be done is 1 - 3/5 = 2/5.
On the second day, three-quarters of the remainder is completed. The remainder after the first day's work is 2/5. So, the work completed on the second day is 3/4 x 2/5 = 3/10. The remaining work to be done is 2/5 - 3/10 = 1/5.
On the third day, seven-eighths of what remained is done. The remaining work to be done after the second day's work is 1/5. So, the work completed on the third day is 7/8 x 1/5 = 7/40.
Therefore, the fraction of work still remaining to be done is 1/5 - 7/40 = 8/40 - 7/40 = 1/40.
Could someone explain this to me???
For vector arithmetic, vector addition (adding two vectors) and scalar multiplication (multiplying a vector by a scalar) is "component-wise". So when adding two vectors you add each component in the first vector to the corresponding one in the second to get the resulting vector. In scalar multiplication you multiply each vector component by the scalar and that gives the resulting vector.
So if u = <3,-2> and v = <-1,4>,
3u = <3*3,-2*3> = <9,-6>
2v = <-1*2,4*2> = <-2,8>
3u + 2v = <9,-6> + <-2,8> = <9+(-2),-6+8> = <7,2>
During a snowstorm, Nathan tracked the amount of snow on the ground. When the
storm began, there were 5 inches of snow on the ground. For the first 3 hours of the
storm, snow fell at a constant rate of 1 inch per hour. The storm then stopped for 5
hours and then started again at a constant rate of 3 inches per hour for the next 3
hours. Make a graph showing the inches of snow on the ground over time using the
data that Nathan collected.
Leanne is 5 years older than Jose
Write an equation to represent the situation:
Answer:
L = J + 5
Step-by-step explanation:
Let's use "L" to represent Leanne's age and "J" to represent Jose's age.
From the given information, we know that Leanne is 5 years older than Jose, so we can write:
L = J + 5
This equation states that Leanne's age "L" is equal to Jose's age "J" plus 5 years.
Un joven sale de la posición xo = 200Km a las 8 h y llega a la posición xf = 500Km a las 11 h. (fue en línea recta y con v = constante). Se pide:
a) Calcular con qué velocidad se movió.
b) Calcular la ecuación que determinar la posición del joven en función del tiempo.
c) Calcular la posición a las 9 h
Para calcular la velocidad del joven, Podemos utilizar la fórmula de la velocidad promedio Por lo tanto, la posición del joven a las 9 h es 1100 km.
a) Para calcular la velocidad del joven, podemos utilizar la fórmula de la velocidad promedio:
velocidad = distancia / tiempo
La distancia recorrida por el joven es xf - xo = 500 km - 200 km = 300 km, y el tiempo transcurrido es 11 h - 8 h = 3 h. Entonces, la velocidad del joven es:
velocidad = 300 km / 3 h = 100 km/h
Por lo tanto, el joven se movió a una velocidad constante de 100 km/h.
b) La ecuación que determina la posición del joven en función del tiempo puede ser expresada como:
x = xo + velocidad × tiempo
donde x es la posición del joven en un momento dado, xo es la posición inicial (xo = 200 km), velocidad es la velocidad constante a la que se mueve el joven, y tiempo es el tiempo transcurrido desde la posición inicial.
Sustituyendo los valores conocidos, obtenemos:
x = 200 km + 100 km/h × t
donde t es el tiempo en horas.
c) Para calcular la posición del joven a las 9 h, podemos utilizar la ecuación que determina la posición del joven en función del tiempo:
x = 200 km + 100 km/h × t
Sustituyendo t = 9 h, obtenemos:
x = 200 km + 100 km/h × 9 h = 1100 km
Por lo tanto, la posición del joven a las 9 h es 1100 km.
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A right triangle has an opposite side of 8th and an adjacent side of 6ft. What is the length of the missing side?
The length of the missing side (the hypotenuse) is 10 ft.
We have,
We can use the Pythagorean theorem to find the length of the missing side of the right triangle.
So,
a² + b² = c²
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
In this case,
The opposite side (which is the leg) has a length of 8 ft, and the adjacent side (which is the other leg) has a length of 6 ft.
Let x be the length of the missing side. Then we have:
a = 8 ft
b = 6 ft
c = x
Plugging these values into the Pythagorean theorem, we get:
8² + 6² = x²
64 + 36 = x²
100 = x²
Taking the square root of both sides, we get:
x = √100 = 10 ft
Therefore,
The length of the missing side (the hypotenuse) is 10 ft.
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Haley is shipping these cubes in a wooden box. The inside measurements of the box are shown. Haley will put as many cubes in the box as possible. She wants to be able to close the box using a lid. What is the greatest number of cubes that Haley can fit in the box and still be able to close the lid? Show or explain how you got your answer.
The greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.
First, we need to determine the dimensions of the box in terms of the length of a side of a cube. We can do this by finding the smallest dimension of the box and dividing it by the length of the side of a cube.
The smallest dimension of the box is the height, which is 6 cm. Therefore, the length of the side of a cube must be a factor of 6.
The length and width of the box are both 8 cm, so the length of the side of a cube must be less than or equal to 8 cm.
We can check the factors of 6 to find the largest possible size of the cube that can fit in the box:
A cube with side length 6 cm would fit in the box, but the lid would not be able to close.
A cube with side length 4 cm would fit in the box, and the lid would be able to close, so this is the largest size cube that can fit in the box.
To determine how many 4 cm cubes can fit in the box, we need to find the volume of the box and divide by the volume of a single cube. The volume of the box is:
V_box = length x width x height
V_box = 8 cm x 8 cm x 6 cm
V_box = 384 cm³
The volume of a single 4 cm cube is:
V_cube = side length³
V_cube = 4 cm x 4 cm x 4 cm
V_cube = 64 cm³
Dividing the volume of the box by the volume of a single cube gives us the maximum number of cubes that can fit in the box:
384 / 64 = 6
Therefore, the greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.
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