It will take 2.2 hours for the two trains to meet.
We can find the time taken by the two trains to meet by using the formula,
large Time=Distance/Speed
Let's consider the time taken by the two trains to meet be "t".The distance between two trains = 418 miles.
Now, the first train is traveling at a speed of 85 mph and the second train is traveling at a speed of 105 mph.
Let's calculate the distance covered by both the trains in time "t".The distance covered by the first train in time "t"=85t.
The distance covered by the second train in time "t"=105t.
So, the total distance covered by both the trains in time "t" is,
Distance covered = 85t+105t=190t.
But we know the distance between the two trains is 418 miles.
Therefore,190t = 418
Now, solve for "t"t = 418/190t = 2.2 hours
Therefore, the two trains will meet in 2.2 hours.
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Question 4(Multiple Choice Worth 2 points)
(Comparing Data MC)
The data given represents the height of basketball players, in inches, on two different girls' teams.
Allstars
73 62 60
63 72 65
69 68 71
66 70 67
60 70 71
Super Stars
66 68 62
63 47 64
65 50 60
64 65 65
58 60 55
Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.
The Allstars, with a mean of about 67.1 inches
The Super Stars, with a mean of about 60.8 inches
The Allstars, with a median of 68 inches
The Super Stars, with a median of 63 inches
Answer:
The answer to your problem is, A. The Allstars, with a mean of about 67.1 inches
Step-by-step explanation:
Allstars mean height:
= (73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15
= 1007 / 15
= 67.6 inches
Super Stars mean height:
= (66 + 68 + 62 + 63 + 47 + 64 + 65 + 50 + 60 + 64 + 65 + 65 + 58 + 60 + 55) / 15
= 912 / 15
= 60.2 inches
We can see that the Allstars team has a higher mean height than the Super Stars team, with an average of 67.6 inches compared to 60.2 inches. Therefore, the Allstars team typically has the tallest players
Thus the answer to your problem is, A. The Allstars, with a mean of about 67.1 inches
Which expressions are equivalent to
−
7
+
3
(
−
4
�
−
3
)
−7+3(−4e−3)minus, 7, plus, 3, left parenthesis, minus, 4, e, minus, 3, right parenthesis ?
Choose all answers that apply:
The expressions -4(3e+4) is equivalent to -7+3(-4e-3)
How to find the equivalent expressions?Given expression:
[tex]-7+3(-4e-3)[/tex]
Expand expression:
[tex]-7-12e-9[/tex]
Regroup like terms:
[tex]-12e-9-7[/tex]
= [tex]-12e-16[/tex]
Factor -4 to get:
[tex]-4(3e+4)[/tex]
What is mathematical expression?A mathematical expression is a combination of numbers, symbols, and/or variables that represent a mathematical statement. It can be a simple expression like "2 + 3," or a more complex one like "sin(x) + 3y^2 - 7."
Expressions can be used to perform calculations, represent relationships between different quantities, or describe geometric shapes and structures. They are an essential tool in mathematics and are used in a wide range of fields, including science, engineering, finance, and economics.
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Complete question:
Which expressions are equivalent to -7+3(-4e-3)?
Choose all answers that apply:
(Choice A)
-4(3e+4)
(Choice B)
12e
(Choice C)
None of the above
a local university reports that 3% of their students take their general education courses on a pass/fail basis. assume that fifty students are registered for a general education course what is the probability that less than four are registered on a pass/fail basis? (4 decimal format
The probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601 (rounded to four decimal places).
The probability of an event is defined as the number of ways the event can occur divided by the total number of possible outcomes. To solve the given problem, we will use the binomial distribution formula.
The formula for the probability of less than 4 successes in n trials, given the probability of success p, is:P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)Where X is a binomial random variable with n = 50 trials and p = 0.03 probability of success, i.e., taking general education courses on a pass/fail basis.
Now, let's calculate each term:
P(X = 0) = C(50, 0) (0.03)⁰ (0.97)⁵⁰P(X = 0) = 1 × 1 × 0.97⁵⁰ ≈ 0.3669P(X = 1) = C(50, 1) (0.03)¹ (0.97)⁴⁹P(X = 1) = 50 × 0.03 × 0.97⁴⁹ ≈ 0.3937P(X = 2) = C(50, 2) (0.03)² (0.97)⁴⁸P(X = 2) = 1225 × 0.0009 × 0.97⁴⁸ ≈ 0.1872P(X = 3) = C(50, 3) (0.03)³ (0.97)⁴⁷P(X = 3) = 19600 × 0.000027 × 0.97⁴⁷ ≈ 0.0123P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)P(X < 4) = 0.3669 + 0.3937 + 0.1872 + 0.0123P(X < 4) ≈ 0.9601
Hence, the probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601.
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Jeff has a life insurance policy,
and his insurance company
expects that it would have to put
$2,225,000 into a bank account
if it ever had to make payments
on the policy. The insurance
company also expects interest
rates to be at 1.4% at that time.
How much will the life insurance
policy pay to Jeff's beneficiaries
per year?
The life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year. The solution has been obtained by using the simple interest.
What is simple interest?
A way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time is by using simple interest. The principal amount in a basic interest calculation is constant.
We are given that Jeff has to put $2,225,000 into a bank account if it ever had to make payments on the policy and the company also expects interest rates to be at 1.4% at that time.
So, from this we get,
⇒ Total Interest = $2225000 × 1.4% × 1
⇒ Total Interest = $31,150
Amount payable by company = $2225000 + $31,150
Amount payable by company = $2,256,150
Hence, the life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year.
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Which equation would demonstrate the inverse property?
A. B. C. D
Option D : The equation that demonstrates the inverse property is D. 3/4 x 4/3= 1, which shows that the multiplication of the reciprocal of a number equals 1.
According to the multiplicative property known as the inverse property, the result of multiplying any non-zero number by its inverse or reciprocal will equal the multiplicative identity, which is 1.
The inverse property of multiplication states that for any non-zero number a, its inverse or reciprocal, when multiplied by a, will result in 1. The reciprocal of a number is the number that when multiplied by the original number results in 1.
For example, the reciprocal of 3 is 1/3 because 3 x 1/3 = 1.
Similarly, the reciprocal of 4/3 is 3/4 because (4/3) x (3/4) = 1.
So, if we multiply 3/4 by its reciprocal 4/3, we get:
(3/4) x (4/3) = (3 x 4) / (4 x 3) = 12 / 12 = 1
This shows that the product of 3/4 and 4/3 is 1, which is the multiplicative identity. Hence, this equation demonstrates the inverse property of multiplication.
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Which equation would demonstrate the inverse property?
A. (3x4) + (3x5) = 3(4+5)
B. 3x5 = 5x3
C. 3x4x5= (3x4)x5
D. 3/4 x 4/3= 1
Brody and his children
Went into a movie theater and he bought 44. T0 worth of drinks and pretzels. Each drink costs $6 abd each pretzel costs $3. 25 he bought a total of 12 drinks and pretzels all together
Brody bought 2 drinks and 10 pretzels. Let's use algebra to solve this problem. Let d be the number of drinks that Brody bought, and let p be the number of pretzels that he bought. We know that he bought a total of 12 drinks and pretzels, so:
d + p = 12
We also know that each drink costs $6 and each pretzel costs $3.25, and he spent a total of $44.10 on drinks and pretzels. So:
6d + 3.25p = 44.10
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:
p = 12 - d
Substituting this into the second equation, we get:
6d + 3.25(12 - d) = 44.10
Simplifying:
6d + 39 - 3.25d = 44.10
2.75d = 5.10
d = 1.85 (rounded to two decimal places)
Since d represents the number of drinks, we can't have a fractional value for it. However, we can round it to the nearest whole number and use that to solve for p:
d ≈ 2
p = 12 - d = 12 - 2 = 10
Therefore, Brody bought 2 drinks and 10 pretzels. We can check that this solution satisfies both equations:
2 + 10 = 12 (first equation)
6(2) + 3.25(10) = 44.10 (second equation)
Therefore, our solution is correct
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Brody and his children went into a movie theater and he bought $44.50 worth
of drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He
bought a total of 12 drinks and pretzels altogether. Determine the number of
drinks and the number of pretzels that Brody bought
In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box. 63 degrees 85 cm
Using the sine's function in the given triangle, the value of x is 75.7 respectively.
What is the triangle?
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.
There are three sides and three angles in every triangle, some of which may be the same.
The angle total of a triangle will always be equal to 180°.
A quadrilateral can be divided in half from corner to corner to form a triangle because the angle total of a quadrilateral is equal to 360°.
A triangle is effectively half of a quadrilateral, therefore it makes sense that its angle measurements are also half. 180° is one-half of 360°.
So, right triangles are used to depict figures like this one, which has a hypotenuse of 85, a base of x, and a top angle of 63°.
The hypotenuse and the side that faces the angle are both present.
The sine function's opposite/hypotenuse ratio is as follows:
sin 63° = x/85
Now, solve as follows:
sin 63° = x/85
85(sin 63°) = x
75.7 = x
Therefore, using the sine's function in the given triangle, the value of x is 75.7 respectively.
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Complete question:
In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box.
A bowl contains pink and red marbles. A scoop of marbles that is a representative sample contains 56 pink marbles and 24 red marbles.
a. Can you predict if there are more pink marbles or more red marbles in the bowl? Explain.
b. There are 750 marbles in a bowl. If you pick one marble from the bowl, are you more likely to pick a pink marble or a red marble?
a. Can you predict if there are more pink marbles or more red marbles in the bowl?
Explain. Choose the correct answer below.
A. No. Because the sample is random, there is no way to predict what the bowl contains.
B. No, because it is unknown whether the bowl contains other colored marbles
C. Yes. Because the representative sample contains more pink marbles than red marbles, you can predict that the bowl contains more pink marbles than red marbles.
D. Yes. Because the representative sample contains more red marbles than pink marbles, you can predict that the bowl contains more red marbles than pink marbles.
Part b. There are 750 marbles in a bowl. If you pick one marble from the bowl, are you more likely to pick a pink marble or a red marble?
red marbles. So, you are
If there are 750 marbles in the bowl, then there are about pink marbles and
(Type whole numbers.)
marble.
a. Correct answer is C as sample contains more pink marbles than red marbles, so it's predicted that the bowl has more pink marbles.
b. With 750 marbles in the bowl and proportion of pink marbles being 0.7, there are approximately 525 pink marbles and 225 red marbles, thus you are more likely to pick a pink marble.
a. The correct answer is C. Yes. Because the representative sample contains more pink marbles than red marbles, you can predict that the bowl contains more pink marbles than red marbles.
b. If there are 56 pink marbles and 24 red marbles in a sample of 80 marbles, then the proportion of pink marbles in the sample is 56/80 = 0.7, and the proportion of red marbles in the sample is 24/80 = 0.3. If there are 750 marbles in the bowl, then there are about 0.7750 = 525 pink marbles and 0.3750 = 225 red marbles. So, you are more likely to pick a pink marble.
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Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 degree angle of elevation from the ground. How high will the ramp rise from the ground at its highest end?
The ramp will rise 16.8 inches from the ground at its highest end, when the angle of elevation is 19 degrees and the length of the fiberboard is 27 inches.
To calculate the height of the ramp at its highest end:
1. First, calculate the length of the hypotenuse of the triangle formed by the ramp, using the Pythagorean Theorem. This can be done by squaring the length of the ramp (27 inches) and the angle of elevation (19 degrees) and adding them together. The result is 750.41 inches.
2. Next, take the square root of the result from step 1. This gives us 27.45 inches, which is the length of the hypotenuse.
3. Then, subtract the length of the ramp from the length of the hypotenuse. This gives us 8.45 inches.
4. Finally, divide the result from step 3 by 2. This gives us the height of the ramp at its highest end, which is 16.8 inches.
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Solving Exponential Equations with Logarithms Solve each equation. Round your answers to the nearest ten-thousandth.
1) 3^b = 17 2) 12^r= = 13
3) 9^n = 49 4) 16^v = 67
5) 3^a = 69
Answer:
1. =2.5759 ; 2. =0.8290 ; 3. =2 ; 4. =1.7959 ; 5. = 3.9138
Step-by-step explanation:
1. Taking logarithm with base 3 on both sides, we get:
b = log₃(17)
b ≈ 2.5759
2. Taking logarithm with base 12 on both sides, we get:
r = log₁₂(13)
r ≈ 0.8290
3. Taking logarithm with base 9 on both sides, we get:
n = log₉(49)
n = 2
4.Taking logarithm with base 16 on both sides, we get:
v = log₁₆(67)
v ≈ 1.7959
5.Taking logarithm with base 3 on both sides, we get:
a = log₃(69)
a ≈ 3.9138
Helep plez.... :S
it gave a hint: convert all into base 3.
i tried it and still couldnt make that much progress
The simplification of the logarithm is determined as [tex]\log_32 - 11[/tex].
What is the simplification of the logarithm?To solve the problem, we can first convert all the logarithms into the same base, which will be base 3. Using the logarithmic identity that
[tex]\log_a b = \frac{\log_c b}{\log_c a}[/tex]
where;
c is any positive basewe get:
[tex]3\log_9(18) + \log_3\left(\sqrt{\frac{8}{27}}\right) - \log_{\frac{1}{27}}(81) - \log_{\sqrt{3}}(2\sqrt{2}) &\\\\= 3\frac{\log_3(18)}{\log_3(9)} + \frac{1}{2}\log_3\left(\frac{8}{27}\right) - \frac{\log_{3}(81)}{\log_{3}(1/27)} - \frac{\log_{3}(2\sqrt{2})}{\log_{3}(\sqrt{3})}[/tex]
[tex]= 6\frac{\log_3(2)+\log_3(3)}{2\log_3(3)} + \frac{1}{2}\left(\log_3(2^3)-\log_3(3^3)\right) - \frac{\log_{3}(3^4)}{\log_{3}(3^{-3})} - \frac{\log_{3}(2\sqrt{2})}{1/2}\\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) + \frac{3\log_3(2)-9\log_3(3)}{6} - \frac{12}{3} - 2\log_{3}(2\sqrt{2})[/tex]
[tex]= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) - \frac{3}{2} + \frac{\log_3(2) }{2} - 4 - \log_3(8) \\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{\log_3(2) }{2} - \log_3(2^3)\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{1}{2} (\log_3(2) )- \log_38\\\\= 6\left (\frac{\log_3(2)}{\log_3(3)}\right) -5+ \log_3(2) - 2\log_3(8)\\\\= 6\log_32 \ - \ 6\log_33 - 5 + \log_32-2\log_38\\\\= \log_3\left (\frac{2^6\times 2 }{3^6\times 8^2}\right) - 5\\\\[/tex]
[tex]= \log_3\left (\frac{2^7 }{3^6\times 2^6}\right) - 5\\\\= \log_3\left (\frac{2 }{3^6}\right) - 5\\\\= \log_32 - \log_33^6 - 5\\\\= \log_32 - 6 - 5\\\\=\log _32 \ - 11[/tex]
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What is the area in square millimeters of the yellow triangle outlined on the origami figure at the right (b = 3cm h= 1.76)
Answer:
2.64
Step-by-step explanation:
b*h=5.28
5.28/2=2.64
The diagram below shows a triangle and some of its dimensions.
20 cm-
tcm
15 cm
What is the value of t?
30 cm
40 cm
35 cm
25 cm
Answer:
25 cm
Step-by-step explanation:
You want to know the length of the hypotenuse in a right triangle with legs 15 cm and 20 cm.
Pythagorean tripleThe given leg lengths have the ratio ...
15 : 20 = 3 : 4 . . . . . . . scale factor of 5
This means they are part of a 3 : 4 : 5 right triangle.
The length "t cm" is 5·5 cm = 25 cm.
The value of t is 25.
__
Additional comment
In case you've never heard of a {3, 4, 5} right triangle, you can figure the missing hypotenuse from the Pythagorean theorem:
c² = a² +b²
t² = 15² +20² = 225 +400 = 625
t = √625 = 25
The {3, 4, 5} Pythagorean triple is used repeatedly in algebra, geometry, and trig problems, along with some others: {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. These can appear as multiples of the basic triple, as here, where the multiple is 5 × {3, 4, 5} = {15, 20, 25}.
is x^2+3x+4 linear or quadratic
Answer:
Quadratic
Step-by-step explanation:
I have no idea how to explain it except that it follows the standard ax² + bx + c format
Quadratic is the answer to your question! :)
The diameter of a circle is___________the length of its radius
Answer:
hey kid the answer is twice
the diameter of a circle is twice the length of its radius
Step-by-step explanation:
Answer: (2 times) the length of the radius
Step-by-step explanation:
r= 2D
see attachment
HELP
What is the correct numerical expression for "9 times 4 added to the difference of 3 and 2?"
9 x 4 + (3 − 2)
9 x (4 + 3) − 2
9 + (4 x 3) ÷ 2
9 − 2 x 4 + 3
The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:
9 x 4 + (3 − 2)
First, we need to calculate the difference of 3 and 2, which is 1. Then, we add it to the product of 9 and 4, which is 36. So the final expression is:
36 + 1 = 37
Therefore, the correct numerical expression is 9 x 4 + (3 − 2) = 37.
Pls someone help me i need this
The formula for the volume of the shaded region is given as follows:
V = π/3[(R² - r²)(H - h)]
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
Hence, for the large cone, the volume is given as follows:
Vl = πR²H/3.
For the smaller cone, the volume is given as follows:
Vs = πr²h/3.
Hence the volume of the shaded region is given as follows:
V = Vl - Vs
V = πR²H/3 - πr²h/3
V = π/3[(R² - r²)(H - h)]
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What is the area of this partial circle?
Step 1: What is the radius?
Step 2: What is the radius squared?
Step 3: What is the area of the circle?
Step 4: What is the area of the quarter circle?
1.8 m
Answer:
1. is the distance from the center of the circle to any point on it's circumference
Let h(x)=,[tex]\sqrt{3x^{2} -5x+2}[/tex] find the domain and range for h(x). Write in set builder notation.
In set-builder nοtatiοn, we can write:
Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }
Range οf h(x): { y ∈ R | y ≥ 0 }
What is Functiοn?In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο a unique element in anοther set, called the range. It is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput.
The dοmain οf h(x) is the set οf all values οf x that make the functiοn well-defined, i.e., there shοuld be nο negative number inside the square rοοt.
Tο find the dοmain οf h(x), we set the expressiοn inside the square rοοt tο be nοn-negative and sοlve fοr x:
3x² - 5x + 2 ≥ 0
Factοrizing the quadratic expressiοn, we get:
(3x - 2)(x - 1) ≥ 0
The sοlutiοn set fοr this inequality is given by the interval:
x ≤ 1/3 οr x ≥ 2/3
Therefοre, the dοmain οf h(x) is:
{ x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }
The range οf h(x) is the set οf all pοssible values that the functiοn can take. Since the square rοοt is always nοn-negative, the range οf h(x) is:
{ y ∈ R | y ≥ 0 }
In set-builder nοtatiοn, we can write:
Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }
Range οf h(x): { y ∈ R | y ≥ 0 }
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What is the missing length?
5.3 cm
12 cm
area = 128.885 cm²
W =
centimeters
The missing length w of the given trapezium with the area of 128.885 cm² is found to be: w = 14.9 cm.
Explain about the trapezium?A closed-form, two-dimensional quadrilateral with two parallel, opposite sides is called a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. Four sides as well as four corners make up the trapezium.
The term "isosceles trapezium" refers to a trapezium with equal-length legs, meaning that the 2 non parallel sides are equal.
Area of Trapezium = ½ (Sum of parallel sides) × (Height between parallel sides)
128.885 = ½(5.3 + 12) × w
128.885 * 2 = 17.3 w
w = 128.885 * 2 / 17.3
w = 14.9
Thus, the missing length w of the given trapezium with the area of 128.885 cm² is found to be: w = 14.9 cm.
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A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 60% magical syrup by volume (and the rest is just water), and blue potion, which is 30% magical syrup by volume.
(a) Find the amount of red potion (in mL) that must be added to 500 mL of blue potion in order to produce potion that is 40% magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 100 mL of a potion that is 54% magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume?
need help
In system equation method,
a) Amount of red portion = 240 ml.
b) There are 300 mL of blue potion used and 100 mL of red potion used.
c) There is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
(a) We can use a system equation here to solve this.
Let x=amount of red potion used
Let y=total amount of potion in solution
Then,
=>200 + x = y
=> 0.15(200) + 0.75x = 0.25y
0.15(200) because 15% of the blue potion=.15 and there is 200mL.
0.75x because 75% of the red potion=.75 and there is x amount of it
0.25y because we want 25% of the total potion=.25 and there is y amount of it.
We can substitute for y in the second equation:
=>0.15(200) + 0.75x = 0.25(200 + x)
=> 30 + 0.75x = 50 + 0.25x
=> -20 = -0.5x
=> x = 40
Knowing that x=40, we know that y=240, meaning our answer is 240.
b.) We can again use a system for this problem
Let x=Amount of red potion
Let y=Amount of blue potion
=> x + y = 400
=> 0.3(400) = 0.15y + 0.75x
0.3(400)=30% of the 400 mL
0.15y=15% of the magic syrup
0.75x=75% of the magic syrup
We can substitute for x in this equation:
=>120 = 0.15y + 0.75(400 - y)
120 = 0.15y + 300 - 0.75y
-180 = -0.6y
y = 300, x = 100
There are 300 mL of blue potion used and 100 mL of red potion used.
c.) Let x=amount of red potion
Let y=amount of blue potion
=> 0.15x + 0.75y = 0.35(x + y)
0.35(x+y) because the total amount of the potion is x+y
=>0.15x + 0.75y = 0.35x + 0.35y
0.4y = 0.2x
2y = x
Whenever there is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.
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The vertices of triangle PQR are P(3,4), Q(5,8) and R(7,4). State the coordinates of the midpoint S of side PR
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad R(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 +3}{2}~~~ ,~~~ \cfrac{ 4 +4}{2} \right) \implies \left(\cfrac{ 10 }{2}~~~ ,~~~ \cfrac{ 8 }{2} \right)\implies \stackrel{ \textit{\LARGE S} }{(5~~,~~4)}[/tex]
(Translations LC)
Use the graph to answer the question.
Answer:
put 5 units up
Enter your answer and show all the steps that you use to solve this problem in the space provided.
The diameter of a tire is 2.5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit.
Find the circumference of the tire.
About how many times will the tire have to rotate to travel 1 mile? (1 mile = 5,280 ft)
this is my answer
part A 7.85 we do 3.14 x 2.5 witch equals 7.85
3.14 x 2.5= 7.85
then we do part B and part B is 5,280 / 7.85 which equals 672 5,280 / 7.85= 672 so to travel 1 mile the tire have to rotate 672 times
i want to know if my answer is correct and if i did good
Answer:
a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:
Circumference = 2π × radius; but diameter = 2 × radius. Hence:
Circumference = π * diameter.
Given that diameter of the tire = 2.5 ft:
Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft
b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.
1 mile = 5280 ft
The number of rotation required to cover 1 mile (5280 ft) is:
number of rotation =
Step-by-step explanation:
Thats the best i can find.
Answer:
Your answer is correct and you showed all the necessary steps to find the circumference and the number of times the tire would have to rotate to travel one mile. Well done!
use the substitution method
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Javier and his brothers are going to ride go-karts. They decide whoever
picks a red king from a standard deck of cards gets to ride first. What is the
probability of drawing a red king?
(B)
(A)
1
13
2
13
1
26
1
52
The probability of getting a red king card from the deck of cards is 1/26.
Define probability?The probability formula can be used to determine the likelihood of an event by only dividing the favourable number of possibilities by the entire number of possible outcomes.
As there can never be more favourable outcomes than there are possible outcomes, the probability of an event happening can range from 0 to 1. As a result, 0 cannot represent the percentage of successful outcomes.
Given,
We have a deck of cards.
So, total no of cards = 52
Now, no of red cards = 26.
Now total no. of kings = 4.
Total no. of red kings = 2
Probability of picking a red king from the deck =
2/52
=1/26
Therefore, the probability of getting a red king card from the deck of cards is 1/26.
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Find the area of the regular hexagon if length of XY= 6cm and BC= 5cm.
PLEASEEEEE HELPP MEE!!
Answer:
[tex]90 { \: cm}^{2} [/tex]
Step-by-step explanation:
First, we can find one triangle's area (they are all the same and isosceles):
h = XY = 6 cm, a = BC = 5 cm
[tex]s(triangle) = \frac{1}{2} \times h \times a = \frac{1}{2} \times 6 \times 5 = 15[/tex]
And now, multiply this number by 6 (since there are 6 of these identical triangles):
S(hexagon) = 15 × 6 = 90 cm^2
the length of a rectangle is three times its width. If the area of the rectangle is 300 m², find its perimeter.
Answer:
Let's assume that the width of the rectangle is 'w' meters.
According to the problem, the length of the rectangle is three times its width, so the length is:
l = 3w
The area of the rectangle is given as 300 m², so we have:
lw = 300
Substituting the value of 'l' in terms of 'w', we get:
(3w)w = 300
Simplifying the above equation, we get:
3w^2 = 300
Dividing both sides by 3, we get:
w^2 = 100
Taking the square root on both sides, we get:
w = 10
So the width of the rectangle is 10 meters.
Using the value of 'w', we can find the length of the rectangle:
l = 3w = 3(10) = 30
So the length of the rectangle is 30 meters.
The perimeter of the rectangle is given by:
P = 2(l + w)
Substituting the values of 'l' and 'w', we get:
P = 2(30 + 10) = 2(40) = 80
Therefore, the perimeter of the rectangle is 80 meters.
Step-by-step explanation:
y = 3x + 19
8x + 2y = -18
Answer: i don't know what type of answer ur looking for but
the answer for substitution is x=-4, y=7
Step-by-step explanation:
y = 3x + 19
8x + 2y = - 18 ====> y = -4x - 9
Equate the two expressions of 'y'
3x + 19 = - 4x- 9
7x = -28
x = -4 then y = 3x + 19 = 3(-4) + 19 = 7
(-4, 7)
For each of the following parabolas, identify the following properties:
Vertex
Max/min
Axis of
Symmetry
Zero(s)
Direction of
Opening
y-intercept
A parabola is a U-shaped curve that can open upwards or downwards. Its equation is typically in the form y = ax^2 + bx + c, where a, b, and c are constants. The properties of a parabola are determined by these constants.
Description about vertex,max/min,axis of
Description about vertex,max/min,axis ofsymmetry,zero(s),direction of opening,y-intercept of parabola:
Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards. The vertex is located at the point (-b/2a, f(-b/2a)), where f(x) is the
function that defines the parabola.
Max/min: The maximum or minimum value of the parabola is the y-coordinate of the vertex. If the parabola opens downwards, the maximum value occurs at the vertex. If the parabola opens upwards, the minimum value occurs at the vertex.
Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two mirror-image halves. The equation of the axis of symmetry is x = -b/2a.
Zero(s): The zero(s) of the parabola are the x-values where the parabola intersects the x-axis. These are also called roots or solutions of the quadratic equation. If the discriminant (b² - 4ac) is positive, the parabola intersects the x-axis at two points. If the discriminant is zero, the parabola intersects the x-axis at one point (which is also the vertex). If the discriminant is negative, the parabola does not intersect the x-axis and has no real roots.
Direction of Opening: The direction of opening of the parabola is determined by the sign of the coefficient a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.
y-intercept: The y-intercept is the point where the parabola intersects the y-axis. It is located at the point (0, c), where c is the constant term in the quadratic equation.
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Correct question is "For each parabolas, describe the following properties:
Vertex
Max/min
Axis of
Symmetry
Zero(s)
Direction of
Opening
y-intercept."