To solve the equation (x - 3)^2 = 49, we can take the square root of both sides to eliminate the exponent of 2. However, when taking the square root, we need to consider both the positive and negative square roots.
(x - 3)^2 = 49
Taking the square root of both sides, we get:
√((x - 3)^2) = ±√49
Simplifying, we get:
x - 3 = ±7
Adding 3 to both sides, we get:
x = 3 ± 7
So the possible values of x are:
x = 3 + 7 = 10
x = 3 - 7 = -4
Therefore, the correct values of x are -4 and 10. The options given are -46, -4, 10, and 52. So the correct values of x from the options are -4 and 10.
Answer:
-4 and 10.
Step-by-step explanation:
a tutor works with a group of students. the tutor charges 40 +30 for each student in the group. Today the tutor has s students and charges a total of $220.
Answer:
6600 is the answer
Step-by-step explanation:
9. It is estimated that a certain model rocket will reach an altitude of 200 ft. A photographer is setting up a camera 50 ft away from the launch pad. At what angle should he set the tripod to get a picture at the maximum altitude?
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
We have,
We can use trigonometry to solve this problem.
C
/ \
/ \
/θ \
/ \
/ \
A-------------B
50 ft
In this diagram, A represents the launch pad, B represents the maximum altitude of the rocket, C represents the position of the photographer, and θ represents the angle at which the tripod should be set.
We want to find θ.
First, we can find the height of the triangle ABC using the Pythagorean theorem:
AB² = AC² + BC²
200² = AC² + 50²
AC² = 200² - 50²
AC = √(200² - 50²)
AC = 190.526 ft
Next, we can use the tangent function to find θ:
tan(θ) = opposite/adjacent = AB/BC = 200/50 = 4
Taking the arctangent of both sides, we get:
θ = [tex]tan^{-1}(4)[/tex]
θ = 75.96 degrees
Therefore,
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
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What is the example of trigonometric function.....????
Find the Surface Area of a cone that has a slant height of 14 in and a diameter of 6 in. Remember to use the symbol when you plug it into your calculator. Round the answers to the nearest tenth.
Surface Area = ___ in2
The surafce area of the cone with a slant height of 14 in and a diameter of 6 in is 160.2 in².
What is the surface area of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The surface area of a cone can be expressed as;
SA = πrl + πr²
Where r is radius of the base, l is the slant height of the cone and π is constant pi.
Given that:
Slant height l = 14 in
Diameter d = 6 in
Radius r = diameter/2 = 6/2 = 3in
S.A = ?
Plug the given values into the above formula and solve for the surface area.
SA = πrl + πr²
SA = ( π × 3in × 14in ) + ( π × (3in)² )
SA = 160.2 in²
Therefore, the surface area is 160.2 in².
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What is the value of a?
The value of z with a p-value of 0.262 is given as follows:
z = -0.64.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.For this problem, we want the z-score with a p-value of 0.262, hence, looking at the z-table, we have that it is:
z = -0.64.
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Factor the polynomial 2x^2+7x+6
Factorization is a mathematical process of breaking down a number or an expression into smaller numbers or simpler expressions that can be multiplied together to get the original number or expression.
Expressions, which are essentially mathematical statements containing numbers and letters, can be factorized in algebra. For illustration, consider the phrase 2x + 4. Finding the expressions or numbers that are common to each term allows us to factorize the expression. Since 2 appears in both terms, we can remove it by factoring to get 2(x + 2).
Given equation = [tex]2x^{2} + 7x + 6[/tex]
⇒ [tex]2x^{2} + 4x + 3x + 6[/tex]
⇒ [tex]2x ( x+2) +3(x+2)[/tex]
⇒[tex](2x + 3) (x+2)[/tex]
Therefore the factors of the expression [tex]2x^{2} + 7x + 6[/tex] are [tex](2x + 3) (x+2)[/tex].
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From the 12 albums released by a musician the recording company wishes to release 10 in a boxed set. How many different boxes sets are possible?
Ask a dif site if this one dont have it
Find the value of x for the following
Applying the right triangle altitude theorem, the value of x in the given right triangle is: x = 4.
How to apply the right triangle altitude theorem?According to the right triangle altitude theorem, we have the following from the theorem as:
h = √(xy), where h is the altitude of the triangle and x and y are the segments divided on the hypotenuse.
Therefore, we have:
2√6 = √(x*3)
(2√6)² = x*3
12 = 3x
x = 12/3
x = 4
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How do I solve this? I'm so confused!
Answer: 46
Step-by-step explanation:
368/8 = 46
36/8 = 4R4
48/8 = 6
46
what is the probability that a random point on AK will be on BE?
The probability of a random point which is located on AK will be present on BE is equal to 0.3.
From the attached figure we have,
On the number line point A is located at -10.
And on the same number line point K is at 10.
Distance between AK = ( 10 ) - ( -10 )
⇒ Distance between AK = 10 + 10
⇒ Distance between AK = 20
Now, on the same number line location of point B is -8.
And location of point E is -2.
Length of BE = ( -2 ) - ( -8 )
⇒ Length of BE = -2 + 8
⇒ Length of BE = 6
Probability of random point on AK will be on BE
= Favorable outcomes / total number of outcomes
= Length of BE / Length of AK
= 6 / 20
= 3 / 10
= 0.3
Therefore, the probability of a random point located on AK will be on BE is equal to 0.3.
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The above question is incomplete , the complete question is:
What is the probability that a random point on AK will be on BE?
Attached figure.
a solid with volume 8 cubic units is dated by a scale factor of k. find the volume of the image for each given value of
k = 1/2
k = 0.6
k = 1
k = 1.5
The volumes of the image for each given value of k are computed below
Find the volume of the imageFrom the question, we have the following parameters that can be used in our computation:
Volume = 8
Scale factor = k
The volume of the image is calculated as
Volume = 8k^3
Using the values of k, we have
Volume = 8(1/2)^3 = 1
Volume = 8(0.6)^3 = 1.728
Volume = 8(1)^3 = 8
Volume = 8(1.5)^3 = 27
Hence, the volumes are calculaed above
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need The sum of the base areas of the regular hexagons is
The prism is a right hexagonal prism.
The lateral area of the right hexagonal prism is 1008 square centimeters.
The sum of the area of a regular hexagon is 187.06 cm².
The surface area of the prism is 1196.06 cm².
We have,
7)
The prism is a right hexagonal prism.
8)
Perimeter = 6 x side length = 6 x 12 cm = 72 cm
Each rectangular face of the prism has a height of 14 cm and a width equal to one of the sides of the hexagon, which is 12 cm.
The area of each face.
= height x width
= 14 cm x 12 cm
= 168 cm²
And,
Lateral Area
= 6 x Area
= 6 x 168 cm²
= 1008 cm^2
9)
The formula for the area of a regular hexagon is given by:
Area = (3 x sqrt(3) / 2) x side length^2
Side length = 12 cm
Area = (3 x √(3) / 2) x 12²
Area = (3 x √(3) / 2) x 144
Area = 54 x √(3)
Area ≈ 93.53 cm² (rounded to two decimal places)
Now,
The sum of the area of a regular hexagon.
= 2 x 93.53
= 187.06 cm²
10)
There are 6 surfaces.
Each surface is in rectangular shape.
So,
Surface area
= 6 x (12 x 14)
= 1008 cm²
And,
The surface area of the prism.
= 1008 + 187.06
= 1196.06 cm²
Therefore,
The prism is a right hexagonal prism.
The lateral area of the right hexagonal prism is 1008 square centimeters.
The sum of the area of a regular hexagon is 187.06 cm².
The surface area of the prism is 1196.06 cm².
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Which equation is used to calculate an object's speed? speed= distance time speed=time distance speed= distance x time speed=time x distance
The equation to calculate an object's speed is Speed = Distance ÷ Time.
Option A is the correct answer.
We have,
Speed is the ratio of distance and time.
Mathematically,
It can be written as,
Speed = Distance / Time
Speed = Distance ÷ Time
Thus,
The equation to calculate an object's speed is Speed = Distance ÷ Time.
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Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. sin(11°) cos(49°) + cos(11°) sin(49°) and Find its exact value.
The exact value for the trigonometric function of numbers is derived to be √3/2.
What are trigonometric identitiesTrigonometric identities are equations that involve the trigonometric functions (such as sine, cosine, tangent, cosecant, secant and cotangent) and are true for all possible values of the variables involved. These identities can be used to simplify trigonometric expressions, solve equations, and prove other mathematical statements.
Then sum and difference identities states that:
sin(A ± B) = sinAcosB ± cosAsinB
cos(A ± B) = cosAcosB ∓ sinAsinB
so;
sin(11°) cos(49°) + cos(11°) sin(49°) = sin(11 + 49)
sin(11°) cos(49°) + cos(11°) sin(49°) = sin(60°)
sin(11°) cos(49°) + cos(11°) sin(49°) = √3/2.
Therefore, the exact value for the trigonometric function of numbers is derived to be √3/2.
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PLEASE HELP ME!!!!!! I WILL APPRECIATE IT SO MUCH
giselle has 40 prizes for raffle ticket winners. She gives away 2 prizes each day until she runs out of prizes
Answer:20
Step-by-step explanation:
40/2=20
20 days of giving away 2 tickets
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
The correct options are:
[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
What Is Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Now, We have the quadratic equation is:
[tex]8x^2 + 16x + 3 = 0[/tex]
We separate variables from constants
[tex]8x^2+16x = -3[/tex]
Taking the common factor 8
[tex]8(x^2+2x)=-3[/tex]
Completing squares in the brackets and balancing the equation in the right side
[tex]8(x^2+2x+1)=-3+8[/tex]
Factoring the perfect square
[tex]8(x+1)^2=5[/tex]
[tex](x+1)^2=\frac{5}{8}[/tex]
[tex](x+1)=[/tex] ± [tex]\sqrt{\frac{5}{8} }[/tex]
x = -1 ± [tex]\sqrt{\frac{5}{8} }[/tex]
The correct options are:
[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
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The given question is incomplete, complete question is:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot
8(x2 + 2x + 1) = 3 + 1
8(x2 + 2x) = –3
¿Cuál es el resultado de la multiplicación de los números complejos z1*z2 expresados en su forma polar, z1= 230° y z2= 540°?
The result of the multiplication of the complex numbers z₁ and z₂ expressed in their polar form is -0.866 + 0.5i.
To multiply complex numbers expressed in polar form, we need to multiply their magnitudes and add their angles.
Let z₁ = r₁(cosθ₁ + isinθ₁) and z₂ = r₂(cosθ₂ + isinθ₂) be two complex numbers in polar form. Then their product is given by:
z₁*z₂ = r₁r₂(cosθ₁cosθ₂ - sinθ₁sinθ₂ + i(cosθ₁sinθ₂ + sinθ₁cosθ₂))
In this case, we have z₁ = 230° and z₂ = 540°. So, we need to convert these angles to radians and then find the cosine and sine values:
z₁ = 230° = 230/180 * π radians = 1.27 radians
z₂ = 540° = 540/180 * π radians = 3π radians
Now we can substitute these values in the formula above:
z₁z₂ = r₁r₂(cosθ₁cosθ₂ - sinθ₁sinθ₂ + i(cosθ₁sinθ₂ + sinθ₁cosθ₂))
= 1 * 1(cos1.27cos3π - sin1.27sin3π + i(cos1.27sin3π + sin1.27*cos3π))
= -0.866 + 0.5i
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Of the cartons produced by a company, 8% have a puncture, 10% have a smashed corner, and 0.5% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 17.5%.
Given that, a company has 8% puncture, 10% have a smashed corner, and 0.5% have both a puncture and a smashed corner cartons,
We need to find the probability that a randomly selected carton has a puncture or a smashed corner,
So,
P(A or B) = P(A) + P(B) - P(A and B)
= 0.08 + 0.10 - 0.005
= 0.175
= 17.5%
Hence, the probability that a randomly selected carton has a puncture or a smashed corner is 17.5%.
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What would happen if you put the wrong place value of a specific number
Writing the correct number relies on what our number system calls the place value system. The 9, the 3, and the 1 are all located in different spots in the larger number, and each of them is called a digit.
Putting the digits in the wrong locations could result in disaster when dealing with money and in many other situations.
AASAAAP. NEEDD HELLPPPPP
The coordinates of B'(6, 3) and C'(4, 4).
We have,
The point A (6, 8) is translated to A' (2, 5).
So, here the points are translated as
(x₁ - x₂ , y₁ - y₂)
= (6 -2, 8-5)
= (4, 3)
So, the coordinates of B'
= (8 -2, 8-5)
= (6, 3)
and, the coordinate of C'
= (6-2, 9-5)
= (4, 4)
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The resistance, R, of a wire varies as its length and inversly as the square of its diameter. If the resistance of a wire 700ft long with a diameter of 0.2inches is 15611ohms, what is the resistance of 1800ft of the same type of wire with a diameter of 0.45inches? (Leave k in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredths)
The resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.
How to find the resistance of 1800ft of the same type of wire with a diameter of 0.45inchesLet R be the resistance of the wire,
L be the length of the wire,
d be the diameter of the wire, and
k be a constant of variation.
Then we have the equation:
R = k * L / d^2
Solving for k to find the resistance of a wire of varying length and diameter.
We can create an equation using the information provided:
15611 = k * 700 / 0.2^2
Solving for k, we get:
k = 15611 * 0.2^2 / 700
k ≈ 0.1799
Using k to calculate the resistance of a wire with a length of 1800 feet and a diameter of 0.45 inches:
15037.45 ohms = 0.1799 * 1800 / 0.452 R
As a result, the resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.
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The USDA estimates that 15 million households in the United States were food insecure in 2017. To help people in their community who might be food insecure, a school has a fundraiser to fill a truck with canned goods for the local food bank. If the cube-shaped boxes used to store the canned goods have a surface area of 24 square feet and the truck will hold 128 boxes, what is the maximum volume of canned goods the students can transport?
Question 1
Part A
What is edge length of 1 box?
The edge length of one cube-shaped box used to store canned goods is 2 feet.
The surface area of a cube-shaped box is given as 24 square feet. Let's assume that the length of each edge of the cube is 'a'.
The surface area of the cube is given as 6a² since a cube has 6 faces, each with an area of 'a²'.
We are given that the surface area of one box is 24 square feet. Therefore,
6a² = 24
Dividing both sides by 6, we get
a² = 4
Taking the square root of both sides, we get:
a = 2
Therefore, the edge length of one box is 2 feet.
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school administrators asked a group of students and teachers which of two school logo ideas logo A or logo B they prefer. Are beining a student and prefering logo A independent events? why or why not?
Being a student and preferring logo A are dependent events.
We have,
Being a student and preferring logo A are not independent events because they are related to each other.
If a student prefers logo A, then they belong to the group of students who prefer logo A.
On the other hand, if a student belongs to a different group, such as the group of students who prefer logo B or are undecided, then they cannot be said to prefer logo A.
In general, two events are considered independent if the occurrence of one event does not affect the probability of the other event occurring.
However,
In this case, knowing whether someone is a student does affect the probability of them preferring logo A.
Thus,
Being a student and preferring logo A are dependent events.
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Solve the following systems of inequalities and select the correct graph: 2x − y < 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.
The solution to the system of inequalities 2x − y < 4 and x + y < −1 is the intersection of the shaded regions below the lines 2x - y = 4 and x + y = -1, labeled AB on the graph. Regions A and B represent the solutions to each individual inequality.
To solve the system of inequalities 2x − y < 4 and x + y < −1, we can use the following steps
Solve each inequality for y in terms of x
2x - 4 < y
-x - 1 < y
Plot the boundary lines for each inequality as dotted lines. To do this, we can use the equality signs instead of the inequality signs.
2x - 4 = y
-x - 1 = y
Shade the region that satisfies each inequality. To do this, we can test a point that is not on the boundary line in each inequality. For example, we can test (0,0) in the first inequality
2(0) - 0 < 4
0 < 4
Since (0,0) satisfies the first inequality, we shade the region below the line 2x - y = 4. Similarly, we can test (0,-2) in the second inequality
(0) + (-2) < -1
-2 < -1
Since (0,-2) satisfies the second inequality, we shade the region below the line x + y = -1.
The solution to the system of inequalities is the intersection of the shaded regions, which is labeled AB in the graph. The shaded region labeled AB is the region that satisfies both inequalities, which is the region below both lines.
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pls help me with this questions quick! right answer lol pls
The function given in the table is an exponential function.
The function given in the table is clearly not linear, since the y value is changing rapidly.
Here we can see that the function value is changing as the multiplication of 7.
y = 7⁰ = 1, when x = 1
y = 7¹ = 7, when x = 2
y = 7² = 49, when x = 3
y = 7³ = 343, when x = 4
y = 7⁴ = 2401, when x = 5
So here the equation of the function can be written as,
y = 7ˣ⁻¹
Here the variable x is in the exponent.
So it is an exponential function.
Hence the given function is an exponential function.
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please help! maths functions (find the equation of the line…)
Answer:
a) y = -2x + 3
b) y = -3x + 7
c) y = -1/2x + 4
d) y = 2
Step-by-step explanation:
Gradient is also known as slope
a) y = mx + b
3 = (-2)0 + b
b = 3
y = -2x + 3
b) y = mx + b
1 = (-3)(2) + b
1 = -6 + b
b = 7
y = -3x + 7
c) Slope m = (y2 - y1)/(x2 - x1)
m = (2 - 3)/(4 - 2) = -1/2
y = mx + b
3 = -1/2(2) + b
3 = -1 + b
b = 4
y = -1/2x + 4
d) The x‐axis or any line parallel to the x‐axis has a slope of 0.
y = mx + b
2 = -3(0) + b
b = 2
y = 2
Answer:
a) The equation of this line is y = -2x + 3
b) The equation of this line is y = -3x + 7
c) The equation of this line is y = -1/2x + 4 or y = -0.5x + 4
d) The equation of this line is y = 2
Step-by-step explanation:
The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.
a) The equation of the line with a gradient of -2 and cutting the y-axis at 3 can be found using the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Substituting m = -2 and (x1, y1) = (0, 3), we get:
y - 3 = -2(x - 0)
Simplifying the right-hand side gives:
y - 3 = -2x
Adding 3 to both sides gives the final equation:
y = -2x + 3
b) The equation of the line with a gradient of -3 and passing through the point (2, 1) can be found using the point-slope form again. Substituting m = -3 and (x1, y1) = (2, 1), we get:
y - 1 = -3(x - 2)
Simplifying the right-hand side gives:
y - 1 = -3x + 6
Adding 1 to both sides gives the final equation:
y = -3x + 7
c) To find the equation of the line passing through the points (2, 3) and (4, 2), we first need to find its gradient. The gradient is given by:
m = (y2 - y1)/(x2 - x1)
Substituting the coordinates of the two points, we get:
m = (2 - 3)/(4 - 2) = -1/2 or -0.5
Now, we can use the point-slope form again, this time with (x1, y1) = (2, 3) and m = -1/2:
y - 3 = (-1/2)(x - 2)
Simplifying the right-hand side gives:
y - 3 = (-1/2)x + 1
Adding 3 to both sides gives the final equation:
y = (-1/2)x + 4 or y = -0.5x + 4
d)The line is parallel to the x-axis and passes through the point (-3 ; 2). A line parallel to the x-axis has a gradient of 0. The general equation of a line is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = c. Since the line passes through the point (-3 ; 2), we can substitute y = 2 into the equation to find that c = 2. Therefore, the equation of this line is y = 2.
A bag contains 100 marbles that are all the same size. Each marble is either red, white, or blue. A student randomly selects 10 marbles. Four of the marbles are white and 6 are blue. Which conclusion about the bag of marbles is MOST likely true?
Select one:
a. There were 40 white marbles in the bag.
b. There was only one red marble in the bag.
c. The number of red marbles in the bag was the fewest of the three colors.
d. The number of white marbles in the bag was equal to the number of blue marbles.
Answer:
C is most likely
Step-by-step explanation:
Answer:
d. The number of white marbles in the bag was equal to the number of blue marbles.
Ryan is a runner. He can run 100 meters in 13 seconds. He
frequently races against Juan, who can run at a speed of 15
miles per hour. Which runner is faster? (1 mile = 1609.34
meters)
Answer:
Ryan: (100/13)(1/1,609.34)(3,600) =
17.21 miles per hour
Ryan is faster than Juan, by about 2.21 miles per hour
I noticed that people were giving the wrong answers for this question before so here is the correct answer.
In 34 pound of a spice mix, there is 56 cup of cinnamon.
How much cinnamon does the spice mix contain per pound?
ANSWER: 1 1/9
One pound of spice mix will have 1 1/9 cups of cinnamon.
Given that in 3/4 pound of a spice mix there are 5/6 cups of cinnamon,
we need to find the amount of cinnamon in a pound,
Since, 3/4 pound = 5/6 cinnamon
So,
1 pound = 5/6 x 4/3
= 20/18 = 10/9
= 1 1/9 cups
Hence, one pound of spice mix will have 1 1/9 cups of cinnamon.
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