Answer:
1.486m/s
Step-by-step explanation:
The rate of change is defined as the change in distance divided by the change in time
Rate = ∆distance/∆time
Distance = 16.5 and 5.5
Time = 10.9 and 3.5
When we put this into the formula above, we have:
Rate of change = 16.5 - 5.5 / 10.9 - 3.5
= 11/7.4
= 1.486m/s
The constant rate of change has been calculated to be equal to 1.486m/s
You can use the fact that the rate of the change of a value when some other independent value changes is the ratio of change in the dependent variable to the change in the independent variable.
The constant rate of the current is given by 1.4865 meters per second.
How to measure the rate of change of something as some other value changes?Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where we have
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)
How to measure the constant rate of the current for the given situation?The distance traveled by the tracker depends on the time passed.
Let the variable "t" tracks the amount of time passed and let the variable "d" tracks the distance traveled by the tracker, then we have:
[tex]\rm At \: t = t_1 = 3.5, d=d_1 = 5.5 \: m\\At \: t = t_2 = 10.9, d = d_2 = 16.5 \: m[/tex]
Thus, the constant rate of current is obtained by
[tex]Rate = \dfrac{d_2 - d_1}{t_2 - t_1} = \dfrac{16.5 - 5.5}{10.9 - 3.5} = \dfrac{11}{7.4} \\\\Rate \approx 1.4865 \: \text{meters per second}[/tex]
Thus,
The constant rate of the current is given by 1.4865 meters per second.
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Write in standard form.
Please help with this. Two different tutors gave me two different answers!
Answer:
16x+4y=2
Step by step explanation
Can I have help solving this, or at least setting up the equation. Please and thank you, Due in 3 minutes (picture below)
The length of the midsegment of the trapezoid with bases 18 and 28 is gvien as follows:
23.
What is the trapezoid midsegment theorem?The trapezoid midsegment theorem, states that the length of the midsegment of the trapezoid is equals to the mean of the length of the bases of the trapezoid.
The bases of the trapezoid are given as follows:
18 and 28.
Hence the length of the midsegment of the trapezoid is given as follows:
(18 + 28)/2 = 23.
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100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
The required exact value of cos(-10π/3) or cos(2π/3) is -1/2.
To find the exact value of the expression cos(-10π/3), we can use the periodicity and symmetry properties of the cosine function.
In this case, we have cos(-10π/3). Since -10π/3 is equivalent to 2π/3 radians (because it completes a full revolution plus an additional 2π), we can rewrite the expression as cos(2π/3).
Now, let's find the exact value of cos(2π/3).
In the unit circle, an angle of 2π/3 (or 120 degrees) is located in the second quadrant. In the second quadrant, the x-coordinate is negative.
Since the cosine function gives the x-coordinate of a point on the unit circle, we can conclude that cos(2π/3) is negative.
Therefore, the exact value of cos(-10π/3) or cos(2π/3) is -1/2.
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The area of the triangle below is 17.8cm^2.
work out the size of angle ∅, given that it is acute.
give your answer in degrees (°) to s.f.
Answer:
Set your calculator to Degree mode.
(1/2)(11.3)(5.2)(sin A) = 17.8
29.38sinA = 17.8
sin A = 890/1,469
A = sin^-1 (890/1,469) = 37.3°
Solve. Prisms. Surface area.
The surface areas of the solids are listed below:
Case I: A = 216 ft²
Case O: A = 204 mm²
Case H: A = 216 ft²
Case L: A = 284.6 cm²
Case E: A = 25.657 yd
Case N: A = 356 yd²
Case S: A = 361.88 ft²
Case T: A = 150 cm²
How to determine the surface area of a solidIn this problem we find eight solids, whose surface areas, that is, the sum of the areas of all faces of the solid, must be found. Each face can be represented by the following area formula:
Rectangle
A = w · h
Triangle
A = 0.5 · w · h
Where:
w - Widthh - HeightNow we proceed to determine the surface areas:
Case I:
A = 6 · (6 ft)²
A = 216 ft²
Case O:
A = 4 · 0.5 · (6 mm) · (14 mm) + (6 mm)²
A = 204 mm²
Case H:
A = 2 · (8 ft) · (6 ft) + (8 ft) · (5 ft) + (6 ft) · (5 ft) + (10 ft) · (5 ft)
A = 216 ft²
Case L:
A = 2 · 0.5 · (7 cm) · (5 cm) + 2 · (6.1 cm) · (13 cm) + (7 cm) · (13 cm)
A = 284.6 cm²
Case E:
A = 2 · 0.5 · (2 yd)² + 2 · (2 yd) · (4 yd) + (√2 yd) · (4 yd)
A = 25.657 yd
Case N:
A = 2 · (3 yd) · (8 yd) + 2 · (8 yd) · (14 yd) + 2 · (14 yd) · (3 yd)
A = 356 yd²
Case S:
A = 2 · 0.5 · (8 ft) · (6 ft) + 2 · (14 ft) · (7.21 ft) + (14 ft) · (8 ft)
A = 361.88 ft²
Case T:
A = 6 · (5 cm)²
A = 150 cm²
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
The correct answer:
(B) SAS Similarity
MISTERBRAINLYY!!
The paint in a certain container is sufficient to paint an area equal to 9.375m2. How many bricks of dimensions 22.5cm×10cm×7.5cm can be painted out of this container?
There are three area options for the number of bricks:
4165551250How many bricks can be painted out of a container?
The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:
n = A / A'
A' = w · h
Where:
w - Width of the brick, in centimeters.h - Height of the brick, in centimeters.There are three possible answers:
Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm
A' = 22.5 · 10
A' = 225
n = 93750 / 225
n = 416.667
n = 416
Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm
A' = 22.5 · 7.5
A' = 168.75
n = 93750 / 168.75
n = 555.556
n = 555
Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm
A' = 10 · 7.5
A = 75
n = 93750 / 75
n = 1250
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A balloon rises 2,0000ft every 2 min which equation models the relationship between the time x and the distance from the ground y
Answer:
The equation that models the relationship between the time x (in minutes) and the distance y (in feet) from the ground is:
y = 2000x
This is because for every 2 minutes that go by (i.e. for every increase of x by 1), the balloon rises by 2000ft (i.e. a constant rate of change). So, the equation y = 2000x represents a straight line with a slope (rate of change) of 2000, passing through the origin.
Hi. Could someone please help me with this !!
Answer:
The slope is 5.
Hope this helps!
Step-by-step explanation:
( x, y )
( 6, 50 ) and ( 12, 80 )
[tex]\frac{80-50}{12 - 6} < = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
[tex]\frac{30}{6} = \frac{5}{1} = 5[/tex]
The slope is 5.
What is 35 degree angle in standard position?
After using ruler and following the steps described below
We get the standard position of 35 degree.
The given angle is = 35 degree
To draw standard position of angle:
We proceed it to draw by ruler
So, in order to get position,
Follow the following steps:
1: Draw a straight line with your ruler.
2: Place your protractor on the line and align the base of the protractor with the line.
3: Find the 35 degree mark on the protractor and make a small mark on the line at that point.
4: Move your protractor to the mark you just made.
5: Align the base of the protractor with the line and make another small mark on the line at the 35 degree mark.
6: Draw a straight line connecting the two points you just marked.
And there you have it! A 35 degree angle drawn on paper.
And after following these steps we get the standard potion angle 35 degree.
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CAN SOMEONE TELL ME IS HE CORRECT OR WRONG HOW TO DO IT
Answer:
The answer is 33°
Yes you are correct
Step-by-step explanation:
angles on a straight line equal 180°
57+90+x=180
x+147=180
x=180-147
x=33°
Hi, I can't tell if there's a little square drawn in red to indicate that there's a right angle in the middle. There's some squiggly lines and so it's kind of hard to tell.
I am going to assume that there is. Let me know if there isn't.
The sum of these 3 angles would be 180 degrees.
As an equation, 57 + 90 + x = 180
Solve for x.
147 + x = 180
x = 33 degrees.
So this would be correct ASSUMING that there's a little red square drawn indicating that there's a right angle.
What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
The probability that either event will occur is 0.62
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
Event A = 6 + 6 = 12
Event B = 20 + 6 = 26
Both A and B = 6
Other Events = 20
Using the above as a guide, we have the following:
Total = A + B + C + Others - Both
So, we have
Total = 12 + 26 - 6 + 20
Evaluate
Total = 52
So, we have
P(A) = 12/52
P(B) = 26/52
Both A and B = 6/52
For either events, we have
P(A or B) = (12 + 26 - 6)/52
Evaluate
P(A or B) = 0.62
Hence, the probability that either event will occur is 0.62
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Measure of angle 1 is,
Angler ACB = 36 degree
We have to given that;
In a parallelogram we get;
Angler CAD = 36 degree
Now, We know that;
Opposite sides are parallel to each other in a parallelogram.
Hence, We get;
Angler CAD = Angle ACB
Since, Angler CAD = 36 degree
Hence, We get;
Measure of angle 1 is,
Angler ACB = 36 degree
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PLEASE HELPP!!!!!
If the sample follows a normal distribution, does this make sense? Why?
It is possible for a sample to follow a normal distribution, depending on the nature of the data being accumulated.
The regular distribution is a bell-shaped curve that is symmetric across the mean, and it's far typically used to model various natural phenomena and measurements in fields such as information, engineering, and social sciences.
If the data being gathered is continuous and the sample length is large sufficient, it is regularly assumed that the pattern follows a normal distribution.
This assumption is based at the critical limit Theorem, which states that the sampling distribution of the suggest of any independent, random variable will tend toward a ordinary distribution because the sample size increases.
But, it's far critical to notice that not all samples will observe a ordinary distribution, and in a few cases, different distributions may be greater suitable for the records being amassed.
It's far consequently essential to analyze the information and evaluate the assumptions being made before using the regular distribution as a model.
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A university professor and his students did a study to determine the mean length of bass in a lake. Each time a bass was caught, its length was measured in inches, and then it was released. The distribution of the lengths is shown in the graph below.
image
Based on this graph, which measurement represents the BEST estimate for the mean length of bass in the lake?
Based on this graph, a measurement which represent the best estimate for the mean length of bass in the lake include the following: 17 inches.
What is a mean?In Mathematics and Statistics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
Mathematically, the mean of a data set can be calculated by using the following formula:
Mean = [F(x)]/n
By critically observing the graph (histogram) shown in the image attached below, we can logically deduce that the distribution is symmetrical. This ultimately implies that, the mean length of bass in the lake would be in the middle, with an estimated value of 17 inches.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Complete Question:
A university professor and his students did a study to determine the mean length of bass in a lake. Each time a bass was caught, its length was measured in inches, and then it was released. The distribution of the lengths is shown in the graph below. Based on this graph, which measurement represents the best estimate for the mean length of bass in the lake?
12 inches
17 inches
20 inches
23 inches
A 9-foot roll of plastic wrap costs $1.08. What is the price per inch?
The price per inch of the wrap is $0.01 or 100cent
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
For example, If the age of Roy is x what will be his age in five years time.
His age five years time will be x+5
9 foot roll cost $1.08
1 foot = 12 inches
9 feet = 9 × 12
= 108 inches
Therefore 108 inches = 1.08
1 inch = 1.08/108
= $0.01
= 100cents
therefore the price of the wrap per inch is $0.01 or 100 cent.
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Multiply: (Hint - use one of the formulas)
(s - 3)³
The multiplication of the expression (s - 3)³ is determined as s³ - 9s³ + 27s - 27.
What is the product of the expression?The product of the expression given as (s - 3)³ is calculated as follows;
The given expression;
(s - 3)³, this can also be written as;
(s - 3)³ = (s - 3) (s - 3) x (s - 3)
We will simplify the expression as follows;
(s - 3)(s - 3) x (s - 3)
= (s - 3)(s - 3) x (s - 3)
= (s² - 3s -3s + 9 )(s - 3)
= ( s² - 6s + 9 ) (s - 3)
= s³ - 3s² - 6s² + 18s + 9s - 27
= s³ - 9s³ + 27s - 27
Thus, the given expression can be simplified using binomial theorem or using simple multiplication method as shown above.
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Assuming the formula of a cylinder, with a height of 2r, if the square area of a can of beans is x square inches, and the volume is x cubic inches, what's the value of x?
Remove the parentheses from the following expression, and combine like terms: 4(ab²+1/₂c + x) - 2(c+x) A. 4ab² + 2x B. 4ab2 + 2x + C C. 4+abc2 + 2x D. 2ab²+2c + X
Answer:
A. 4ab² + 2x
Step-by-step explanation:
If you want to get rid of those pesky parentheses, you have to use the superpower of distributive property. It lets you multiply everything inside the parentheses by the number outside. For example:
4(ab²+1/₂c + x) = 4ab² + 2c + 4x
Boom! No more parentheses!
To combine like terms, you have to add or subtract the numbers in front of the terms that have the same variable and exponent. For example:
2x - 4x = -2x
Bam! Only one x left!
Here are the steps to simplify the expression:
4(ab²+1/₂c + x) - 2(c+x)
= 4ab² + 2c + 4x - 2c - 2x (use superpower)
= 4ab² + 4x - 2x (combine like terms)
= 4ab² + 2x (simplify)
So, the answer is A. 4ab² + 2x.
Find the value of X.
150 degrees is the measure of the angle x from the figure
Measuring the measure of angle in a circleThe given diagram is a circle and the angle x and 30 degrees can be seen to be on a straight line.
The sum of the measure of angle on a straight line is 180 degrees, hence:
x + 130 = 180
Subtract 130 degrees from both sides to have:
x + 30 - 30 = 180 - 30
x = 180 - 30
x = 150 degrees
Hence the measure of the angle x from the given equation is 150 degrees
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SOMEONE HELP 45 POINTS!!!!!! WILL GIVE BRAINLIEST!!!!!! PLEASE
RIGHT ANSWER ONLY
If f(x) = 2x + 1 and g(x) = x − 2, find the quantity f divided by g of 7.
3
10
15
75
Answer:
3
Step-by-step explanation:
Step 1: First, we must plug in 7 for x in f(x) and g(x):
f(7) = 2(7) + 1
f(7) = 14 + 1
f(7) = 15
g(7) = 7-2
g(7) = 5
Now, we can divide f(7) by g(7)
f(7) / g(7) = 15 / 5
f(7) / g(7) = 3
Thus, the quantity of f divided by g of 7 is 3
Find (if possible) a. AB and b. BA.
A=
-
2
-
8
B=
||||
6
S
3
2
The products of the matrices A and B are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]
Finding the products of the matrices A and BFrom the question, we have the following parameters that can be used in our computation:
Matrix A = [tex]\left[\begin{array}{cc}-3&-8\\2&8\end{array}\right][/tex]
Matrix B = [tex]\left[\begin{array}{cc}6&3\\4&-2\end{array}\right][/tex]
Using the above as a guide, we have the following:
[tex]AB = \left[\begin{array}{cc}-3 * 6 + -8 * 4 &-3 * 3 -8 * -2\\2 * 6 + 8 * 4 &2 * 3 + 8 * -2\end{array}\right][/tex]
Evaluate
[tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex]
Next, we have
[tex]BA = \left[\begin{array}{cc}6 * -3 + 3 * 2&6 * -8 + 3 * 8 \\4 * -3 + -2 * 2&4 * -8 + -2 * 8\end{array}\right][/tex]
Evaluate
[tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]
Hence, the values are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]
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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, the period, phase shift, and vertical shift of the function. Then graph the function. Thank you!
For the function y = 3sin[2(θ-90°)] + 2, the amplitude is 3, the period is π, the phase shift is -45° and the vertical shift is 2 units up.
The amplitude of a sine function represents the maximum displacement from the midline.
The coefficient in front of the sine function is 3, so the amplitude is 3.
The period of a sine function is the length of one complete cycle. It can be calculated using the formula T = 2π/b, where b is the coefficient of θ inside the sine function brackets.
Here, b = 2, so the period is T = 2π/2 = π.
The phase shift of a sine function indicates a horizontal shift to the left or right.
In this case, c = 90°, so the phase shift is θ = 0° - 90°/2 = -45°.
The vertical shift indicates a shift up or down on the y-axis.
The constant term outside the sine function is 2, so the vertical shift is 2 units up.
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What is the solution to the following system of equations? (1 point) x − 3y = 6 2x + 2y = 4
Answer:
x = 3
y = -1
Step-by-step explanation:
Solving system of equations:Method: substitution
x - 3y = 6 --------------(I)
x = 6 + 3y -------------(II)
2x + 2y = 4 ----------(III)
Substitute x = 6 +3y in equation (II),
2*(6+3y) + 2y = 4
Use distributive property to open the parenthesis,
2*6 + 2*3y + 2y = 4
12 + 6y + 2y = 4
Combine like terms.
12 + 8y = 4
Subtract 12 from both sides,
8y = 4 - 12
8y = -8
Divide both sides by 8,
y = -8÷ 8
[tex]\boxed{\bf y = (-1)}\\[/tex]
Substitute y = -1 in equation (II) and find the value of x.
x = 6 + 3*(-1)
= 6 - 3
[tex]\sf \boxed{\bf x = 3}[/tex]
Answer:
(3, - 1 )
Step-by-step explanation:
x - 3y = 6 ( add 3y to both sides )
x = 3y + 6 → (1)
2x + 2y = 4 → (2)
substitute x = 3y + 6 into (2)
2(3y + 6) + 2y = 4
6y + 12 + 2y = 4
8y + 12 = 4 ( subtract 12 from both sides )
8y = - 8 ( divide both sides by 8 )
y = - 1
substitute y = - 1 into (1)
x = 3(- 1) + 6 = - 3 + 6 = 3
solution is (3, - 1 )
Kamila wants a puppy. She and her family want to estimate the mean lifespan, in years, of all dog breeds registered with the American Kennel Association. Kamila selects a random sample of 8 registered dog breeds and looks up their estimated lifespan on the internet. The results are shown. 13 11 12 14 12 10 11 12 Part A What is the mean for Kamila’s sample? Round your answer to the nearest tenth. The mean lifespan for dogs from Kamila’s sample is years.
Rounding to the nearest tenth, the mean lifespan for Kamila's sample is 11.9 years.
To find the mean (average) for Kamila's sample, you need to sum up all the lifespans and then divide by the total number of breeds in the sample.
Sum of lifespans = 13 + 11 + 12 + 14 + 12 + 10 + 11 + 12 = 95
Total number of breeds = 8
Mean = Sum of lifespans / Total number of breeds
= 95 / 8 = 11.875
Rounding to the nearest tenth, the mean lifespan for Kamila's sample is 11.9 years.
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a square pyramid sitting on its base. The sides are 8cm, 14cm, and 14cm. whats the surface area of the pyramid in square centimeters?
The surface area of the square pyramid is 224 square centimeters.
Since the base of the square pyramid is a square, all sides are equal in length.
Let's call the length of one side of the square base "s".
Then the surface area of the pyramid can be found using the formula:
Surface area = Area of base + Area of four triangles
The area of the base is just s², and the height of each triangle can be found using the Pythagorean theorem.
Let's call the height "h". Then:
h² = 14² - (s/2)² (using the longer side of the triangle as the hypotenuse)
h² = 196 - (s²/4)
Now, we need to find the surface area in terms of "s" and simplify:
Surface area = s² + 4(1/2)(s)(h)
Surface area = s² + 2sh
Surface area = s² + 2s√196 - s²/4))
Surface area = s²+ 2s√(784 - s²))/2
Surface area = s² + s√(784 - s²))
We are given that one side of the square base is 8cm, so:
Surface area = 8² + 8√784 - 8²
Surface area = 64 + 8√400
Surface area = 64 + 8(20)
Surface area = 224
Therefore, the surface area of the square pyramid is 224 square centimeters.
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What trinomial can be added to x^2+5x-8 to give me a sum of 2x-5
Help Quickly! Find the slope of the line.
A. -1/3
B. -3
C. 3
D. 1/3
Graph by completing the square x2-4x+y2-2y-4=0
The graph will look like a circle centered at (2, 1) with radius 3.
To graph the equation [tex]x^2 - 4x + y^2 - 2y - 4 = 0[/tex] by completing the square, we need to rearrange the terms as follows:
[tex](x^2 - 4x + 4) + (y^2 - 2y + 1) = 9[/tex]
This can be simplified to:
[tex](x - 2)^2 + (y - 1)^2 = 3^2[/tex]
So the equation represents a circle with a center at (2, 1) and a radius 3. To graph the circle, we can plot the center point (2, 1) and then draw a circle with radius 3 around that point.
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Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.
If y varies inversely as the square of x, and y
a.
b.
5
-—; y(5) -
y-
125
7x²y(5) = 4
175
48
63
when x-3, find y when x = 5.
C.
d.
y=
7
4x²
(5) - 7
100
y = - 52+ (5)
5x²
125
a. The constant of variation is k = 45.
b. The equation for the relation is y = 45/x².
c. x = 5, y is approximately equal to 1.8.
d. The equation provided, y = -52 + (5)/(5x²), seems to be incorrect or incomplete as there are misplaced parentheses and missing values.
The constant of variation for the relation "y varies inversely as the square of x," we can use the general form of an inverse variation equation:
y = k/x², where k represents the constant of variation.
The given information, we have y = 5 when x = -3.
Substituting these values into the equation, we get:
5 = k/(-3)²
5 = k/9
k = 45
The constant of variation is k = 45.
The equation for the relation is y = 45/x².
To find y when x = 5, we can substitute the value of x into the equation:
y = 45/(5)²
y = 45/25
y = 1.8
x = 5, y is approximately equal to 1.8.
The equation provided, y = -52 + (5)/(5x²), seems to be incorrect or incomplete as there are misplaced parentheses and missing values. Please clarify the equation and I'll be happy to assist you further.
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