Based on the data displayed in the two box plots, the group of athletes that ran the least miles is Group A, with a median value of 2.
the product of a number and -6 amounts to five times the sum of that number and 33. Find the number.
By setting up the equation and solving for the unknown variable, we find that the number in question is -15. The answer provides a step-by-step method for solving an equation that represents a word problem.
Let's start by translating the given problem into an equation.
"The product of a number and -6" can be written as "-6x", where "x" is the unknown number. "Five times the sum of that number and 33" can be written as "5(x+33)".
Putting these together, we get:
-6x = 5(x+33)
Now we can solve for "x":
-6x = 5x + 165
-11x = 165
x = -15
Therefore, the number we're looking for is -15.
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Select the statement that is not true.
A. The reflection of a line is a pair of parallel lines.
B. The translation of a line is a line.
C. The rotation of a line is a line.
D. The rotation of a pair of parallel lines is a pair of parallel lines.
The claim that a line's reflection is actually two parallel lines is false. correct answer is option (A).
Why is the statement a false statement?A line is reflected by another line, which is the original line's mirror image. Each point on the original line is reflected across a line of reflection, which is often perpendicular to the original line, to create the mirror image. The resulting line is consistent with the original line while being oriented in the other direction.
The statement that a line can be translated into another line with the same length and that it is parallel to the original line is true.
The statement that a line rotates into another line that is the same length and shape as the original line but is orientated at a different angle is also correct.
The rotation of a pair of parallel lines is also valid for a second pair of parallel lines that have the same distance between them but are orientated at a different angle from the initial pair.
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Mary visits the local coffee shop to use the WiFi for school projects. Mary has an English book review to write, a social studies paper, and a science presentation to complete. They first arrive and order a coffee at $2.15 and tip 5% at the counter. Two hours later, they finish their English review and the waitress stops by. Mary decides to order a latte at $4.50but doesn't tip. Over the next hour, the waitress returns and Mary orders another coffee and leaves a 15% tip for both the latte and coffee. An hour later, Mary completes all of their projects and leaves.
What is the total tip Mary left at the coffee shop? Round the price to the nearest hundredth. Do not include $ in your answer. For example, if the price is $19.546, enter 19.55.
the total tip left by Mary at the coffee shop is $0.11 + $0.99 = $1.10 (rounded to the nearest hundredth).
Why is it?
Let's break down the transactions and calculate the total tip left by Mary.
Mary orders a coffee at $2.15 and tips 5% at the counter:
Cost of coffee = $2.15
Tip = 0.05 x $2.15 = $0.11
Mary orders a latte at $4.50 and doesn't tip:
Cost of latte = $4.50
Mary orders another coffee at $2.15 and leaves a 15% tip for both the latte and coffee:
Cost of coffee = $2.15
Total cost of latte and coffee = $4.50 + $2.15 = $6.65
Tip = 0.15 x $6.65 = $0.99
Therefore, the total tip left by Mary at the coffee shop is $0.11 + $0.99 = $1.10 (rounded to the nearest hundredth).
A tip is an extra amount of money given as a gratuity or a gift to someone for their services, such as for a meal in a restaurant, a hairdresser, or a taxi driver. Tips are typically a percentage of the total cost of the service or goods provided.
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in a recent year, 34.8% of all registered doctors were female. if there were 56,500 female registered doctors that year, what was the total number of registered doctors? round answer to whole number.
162,356 doctors were registered that year.
Explanation:
The questions says, "34.8% of all registered doctors are females"
(Consider, total number of registered doctors as [tex]x[/tex])
that's, [tex]34.8\%[/tex] of [tex]x[/tex] are female.
and [tex]34.8\%[/tex] of [tex]x[/tex] is 56,500.
Mathematically,
[tex]\dfrac{34.8}{100} \times x=56500[/tex]
[tex]x=56500\times\dfrac{100}{34.8}[/tex]
[tex]x=162356[/tex] doctors were registered that year.
2. The base of a triangular prism is an equilateral triangle with sides 20 inches long. The height of the prism is 8 inches. Find the volume of the prism.
Answer:
The volume of the prism is 800(sqrt(3)) cubic inches.
Step-by-step explanation:
The volume of a triangular prism can be calculated by multiplying the area of the base (which is an equilateral triangle in this case) by the height of the prism.The area of an equilateral triangle can be calculated using the formula:A = (sqrt(3)/4) x s^2where A is the area and s is the length of one side of the triangle.In this case, the length of one side of the equilateral triangle is 20 inches, so we can substitute that into the formula:A = (sqrt(3)/4) x 20^2
A = (sqrt(3)/4) x 400
A = 100(sqrt(3)) square inchesNow that we have the area of the base, we can calculate the volume of the prism:V = A x h
V = 100(sqrt(3)) x 8
V = 800(sqrt(3)) cubic inches
To find the volume of a triangular prism, one must calculate the area of the base (in this case an equilateral triangle), and then multiply this by the height of the prism. Using the provided dimensions, the volume is calculated to be 800√3 cubic inches.
Explanation:The question is asking us to find the volume of a triangular prism with an equilateral triangle as the base and a given height. The formula for the volume of a prism is Volume = Base Area * Height. Since the base is an equilateral triangle, its area can be calculated using the formula: Area = (sqrt(3) / 4) * side². By substituting the given side length of 20 inches, we find that the area of the base is sqrt(3) * 100 square inches. We then multiply this by the height of the prism, which is 8 inches, to find the total volume. So, the volume of the prism is 800√3 cubic inches.
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Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g. HEEEELP
Answer:
The answer to your problem is, g(3) = 18
Step-by-step explanation:
Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of - 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8
Listed in order 1 - 4
The value(s) of x must be between -1 and 4The values of g(x) must be between 0 and 18.g(-1)=2g(2)=9A. The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.
B. The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.
C. The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.
D. This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.
Thus the answer to your problem is, D. g(3) = 18
Sorry for the blurry picture!
1. Find the critical points for the graph of
y = 2x² +22x + 48
Write your answers as ordered pairs (x, y).
y-intercept(s):
x-intercept(s):
vertex:
Answer:
X-intercept(s): (-3,0), (-8,0)
Y-intercept(s): (0,48)
Vertex: (-11/2,-25/2)
Step-by-step explanation:
X-intercepts: When you are finding the x-intercepts, there are two ways to find your x-intercepts like you can find in the Quadratic Formula or plug the equation into your calculator and see it on the graph/ table. If you like the quadratic formula, you need plug into the a, b, and c and it will look like x= -22±√(22^2)-4(2)(48))/2(2). It will be the same answer. on the another hand, if you like the calculator way, you get your calculator that need be TI-84 plus CE or TI-84 then go on y= then put your equation like 2x^2+22x+48 after that you click on graph. if you cant find the x-intercepts on the graph, you can do 2nd then above the graph buttom you can see it in the table. When you looking at the table, look for the 0s in the y table.
Y-intercept: When you are finding the y-intercepts, there are two ways to find your y-intercepts like you need plug in 0 for x or plug the equation into your calculator and see it on the graph/ table. If you like the quadratic formula, you need plug in 0 for x and it will look like y=2(0)^2 +22(0)+48. it would the get the same answer. if you like the calculator way, you get your calculator that need be TI-84 plus CE or TI-84 then go on y= then put your equation like 2x^2+22x+48 after that you click on graph. if you cant find the x-intercepts on the graph, you can do 2nd then above the graph buttom you can see it in the table. When you looking at the table, look for the 0s in the x table.
Vertex:
1. Get your equation in the form like this y=ax^2+bx+c
2. Calculate -b/2a. This is the x-coordinate of the vertex.
3. To find the y- coordinate of the vertex, simply plug the x to the quadratic equation and solve for y.
Comment if i am right or wrong
5. Use the formula
A = ¹h(b₁ + b₂) to
find the area of the
trapezoid.
The area of the
trapezoid is
9 cm
3 cm
5 cm
-1.5 cm
21
27 square centimeters.
29.3
The area of the trapezoid [tex]36^{2}[/tex] centimeters
To use the formula A = ¹h(b₁ + b₂) to find the area of a trapezoid, you need to know the height (h) and the lengths of the two parallel bases (b₁ and b₂).
For example,
The formula for finding the area of a trapezoid is A = ¹h(b₁ + b₂),
Where A represents the area of the trapezoid, h represents the height, and b₁ and b₂ represent the lengths of the two parallel bases.
By plugging in the given values for the height and bases and performing the necessary arithmetic operations, you can find the area of the trapezoid.
It's important to remember to use the correct units and follow the order of operations to obtain the correct result.
If the height of the trapezoid is 9 cm, the lengths of the two bases are 3 cm and 5 cm, you can plug these values into the formula to find the area :
A = ¹h(b₁ + b₂)
= ¹(9)(3 + 5)
= ¹(9)(8)
= 36 square centimeters
So, the area of this trapezoid is 36 square centimeters.
If you have different values for the height and bases, you can use the same formula to find the area.
Just make sure to use the correct units and follow the order of operations (parentheses first, then multiplication and division, then addition and subtraction).
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Armando realiza un trabajo en 20 segundos y Bernardo realiza el mismo trabajo en dos segundos como le llamarías a la magnitud física que determina la diferencia entre uno y otro
La magnitud física que determina que un trabajador haga el trabajo en un tiempo menor que otro puede ser la RAPIDEZ.
determina la diferencia entre uno y otro?La rapidez o también velocidad (si hablamos de vector) define porque un trabajador realiza un trabajo en 20 segundos y el otro en 12 segundos, significa que el primero es menos rápido que el segundo.
De cierta manera pudieran estar otras magnitudes relacionadas como la potencia.
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a right triangle has sides 8,15, and 17 Use these lengths to find tanL, sinL, and cosL
The cosine of an angle in a right triangle is defined as the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse.
[tex]tanL = 15/8[/tex][tex]sinL = 15/17[/tex][tex]cosL = 8/17[/tex]
What are the properties of a right triangle?In a right triangle, the side opposite the right angle is called the hypotenuse (in this case, it's the side with length 17).
The other two sides are called the legs. We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
hypotenuse^2 [tex]= leg1^2 + leg2^2[/tex]
For this triangle, we have:
[tex]17^2 = 8^2 + 15^2[/tex]
Simplifying this equation, we get:
[tex]289 = 64 + 225[/tex]
Therefore, the equation is true, and we have verified that this is a right triangle.
Now, we can use the trigonometric ratios to find the values of tanL, sinL, and cosL, where L is the angle opposite the leg with length 8.
The tangent of an angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Therefore, we have:
tanL = opposite/adjacent [tex]= 15/8[/tex]
The sine of an angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the hypotenuse. Therefore, we have:
sinL = opposite/hypotenuse [tex]= 15/17[/tex]
The cosine of an angle in a right triangle is defined as the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse. Therefore, we have:
cosL = adjacent/hypotenuse = 8/17
Therefore, , the values we found are:
[tex]tanL = 15/8[/tex]
[tex]sinL = 15/17[/tex]
[tex]cosL = 8/17[/tex]
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a group of private investors purchased a condominium complex for $5 million. they made an initial down payment of 15% and obtained financing for the balance. if the loan is to be amortized over 11 years at an interest rate of 9.1%/year compounded quarterly, find the required quarterly payment. (round your answer to the nearest cent.)
With the given compound interest, the required quarterly payment is $38,745.74.
What is Compound interest?
Compound interest is the interest that is calculated on the initial principal as well as the accumulated interest of previous periods. In other words, it is the interest on interest. The interest is added to the principal at the end of each compounding period, and then the new total amount becomes the principal for the next period's interest calculation.
Now,
The amount financed is equal to the purchase price minus the down payment:
Amount financed = $5,000,000 - 0.15($5,000,000) = $4,250,000
To find the quarterly payment,
PV = Pmt * (1 - (1 + r)⁻ⁿ) / r
where PV is the present value (amount financed), Pmt is the quarterly payment, r is the quarterly interest rate, and n is the total number of quarterly payments (11 years x 4 quarters/year = 44 quarters).
The quarterly interest rate is equal to the annual interest rate divided by 4:
r = 0.091 / 4 = 0.02275
Substituting the values, we get:
$4,250,000 = Pmt * (1 - (1 + 0.02275)⁻⁴⁴) / 0.02275
Solving for Pmt, we get:
Pmt = $38,745.74
Therefore, the required quarterly payment is $38,745.74 (rounded to the nearest cent).
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Given the triangle below, find the angle θ.
Give your answer in radians rounded to four decimal places.
By using the trigonometric identities we get ∅ = 0.5542.
What are the trigonometric identities?The six trigonometric ratios serve as the foundation for all trigonometric equations. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The sides of the right triangle, such as the adjacent side, opposite side, and hypotenuse side, are used to describe each of these trigonometric ratios.
The given figure is a right-angled triangle.
We can use trigonometric identities,
Sin∅ =[tex]\frac{adjacent }{hypotenuse}[/tex]
Here we get the value adjacent = 10 and the hypotenuse = 19
Therefore we get the value,
sin∅ = [tex]\frac{10}{19}[/tex] = 0.5263
∅ = [tex]sin^{-1} (0.5263)[/tex]
∅ = 0.5542
Therefore the angle ∅ = 0.5542
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A science teacher needs up to 15 female and male students for a competition. The science teacher needs at least 6 male volunteers.
Let x represent the number of male volunteers and y represent the number of female volunteers.
Which inequalities model the situation?
The situation can be modeled by the following system of linear inequalities:
x ≥ 6 (The number of male volunteers should be at least 6)
x + y ≤ 15 (The total number of volunteers should be no more than 15)
y ≥ 0 (The number of female volunteers should be non-negative)
What is inequality model?
A formula exists for inequality. Less than, larger than, or not equal are used in place of the equal sign when there are inequalities. Rules for resolving disparities are unique. Here are a few examples of inequalities that are mentioned. When disparities are connected, the centre inequality can be jumped over.
The situation can be modeled by the following system of linear inequalities:
x ≥ 6 (The number of male volunteers should be at least 6)
x + y ≤ 15 (The total number of volunteers should be no more than 15)
y ≥ 0 (The number of female volunteers should be non-negative)
Explanation:
The first inequality states that the number of male volunteers, represented by x, should be greater than or equal to 6. This ensures that the science teacher has at least 6 male volunteers.
The second inequality states that the total number of volunteers, represented by x + y, should be no more than 15. This ensures that the science teacher does not exceed the maximum number of volunteers required for the competition.
The third inequality states that the number of female volunteers, represented by y, should be non-negative. This ensures that there are no negative values for the number of female volunteers.
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Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.
AB = 16, BC = 8, and CD = 9
The value of x cannot be determined and the answer is undefined.
To find the value of x in this scenario, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, triangle ABC is a right triangle with AB as the hypotenuse. So, we can use the Pythagorean theorem to solve for AC, which is equal to the square root of (AB^2 - BC^2).
Using the given values, we have:
AC = sqrt(16^2 - 8^2)
AC = sqrt(256 - 64)
AC = sqrt(192)
AC ≈ 13.86
Now, we can use triangle ACD to solve for x. This triangle is also a right triangle with CD as the hypotenuse. So, we can use the Pythagorean theorem again to solve for AD, which is equal to the square root of (CD^2 - AC^2).
Using the given values, we have:
AD = sqrt(9^2 - 13.86^2)
AD = sqrt(81 - 192.23)
AD = sqrt(-111.23)
We can't take the square root of a negative number, so there is no real solution for x in this scenario.
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Ahmed and Tiana buy a cake for $14 that is half chocolate and half vanilla. They cut the cake into 8 slices. If Ahmed likes chocolate four times as much as vanilla, what is the dollar value that Ahmed places on a chocolate slice?
The dollar value, if Ahmed likes 4 times more the chocolate than the vanilla slice, then he finds C four times more valuable than V. Thus, Ahmed placed a chocolate slice is $1.75.
What is meant by arithmetic?The foundational subject in mathematics, arithmetic covers operations with numbers. They include addition, subtraction, multiplication, and division. One of the major branches of mathematics, arithmetic serves as the cornerstone for students studying the subject of mathematics. Mathematical arithmetic is the study of the characteristics of the conventional operations on numbers.
Using C for the chocolate slice's value and V for the vanilla slice's value
4 slices × C + 4 slices × V = $14
If Ahmed likes 4 times more the chocolate than the vanilla slice, then he finds C four times more valuable than V, thus
C = 4×V
4 slices ×4V + 4 slices ×V = $24
20 slices ×P = $14
P=$0.7/slice
V= 4×P = 4×$0.7/slice = $2.8/slice
Thus for a slice that is half chocolate and half vanilla
value= 1/2 slice× C + 1/2 slice × V
= 1/2 slice ( $0.7 /slice + $2.8/slice)
= $1.75
Hence, Ahmed placed a chocolate slice is $1.75.
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Calculate.
9×10²
2×10²
Write your answer in scientific notation.
0
X
Answer: 4.5×10^0
Step-by-step explanation:
To calculate 9×10²/2×10², you can follow these steps:
Step 1: Simplify the expression by cancelling out the common terms:
9×10²/2×10² = (9/2)×(10²/10²)
Step 2: The 10² terms cancel each other out:
(9/2)×(10²/10²) = (9/2)×1 = 9/2
Step 3: Convert the simplified expression to scientific notation:
9/2 = 4.5, so the expression in scientific notation is 4.5×10^0 (since any number raised to the power of 0 is 1).
The result of the calculation is 4.5×10^0.
Triangle LMN is shown below. What is the length of LM?
Option D is the correct answer, As a result, LM is 16.1 centimeters long.
The mid-segment of a triangle is aligned to the base and is half the length of the triangle.
MQ = therefore 1/2 LN.
LN = 16.1 centimeters because we know MQ = 8 cm.
MQ is parallel to side LM and half of its length because it is also the midpoint of the triangular LMN.
What exactly is midsegment?A line segment linking the midpoints of two of the triangle's sides is known as a mid-segment. It is half the length of the triangle's third edge and parallel to it. In other words, the mid-segment linking the midpoints of sides a and b has length c/2 and is parallel to side c if a triangle has sides of lengths a, b, and c.
Because of this, LM = 2MQ = 16.1 centimeters.
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A chemical injection system tank is 3/4 full and pumps out at a rate of 1/8 of a tank per week. You won't be back for five weeks. How much will be left in the tank when you return? Your answer should be in the form of a fraction reduced to its lowest terms.
find an angle theta that makes the statement true use cofunction identity
cot(5theta - 32 degree)=tan(theta + 26 degrees)
Answer: Using the cofunction identity for tangent and cotangent:
cot(θ) = 1/tan(θ)
We can rewrite the given equation as:
cot(5θ - 32°) = 1/tan(θ + 26°)
Next, using the identity for the tangent of the sum of two angles:
tan(a + b) = (tan(a) + tan(b))/(1 - tan(a)tan(b))
We can rewrite the right side of the equation as:
1/tan(θ + 26°) = tan(90° - (θ + 26°)) = tan(64° - θ)
Substituting this back into the original equation:
cot(5θ - 32°) = tan(64° - θ)
Using the identity for the cotangent and tangent of the difference of two angles:
cot(a - b) = (cot(a)cot(b) - 1)/(cot(b) - cot(a))
tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))
We can rewrite the equation as:
(cot(5θ)cot(32°) - 1)/(cot(32°) - cot(5θ)) = (tan(64°)tan(θ) - tan(θ))/(1 + tan(64°)tan(θ))
Simplifying both sides:
(cot(5θ)cot(32°) - 1)/(cot(32°) - cot(5θ)) = (sin(64°)sin(θ))/(cos(64°)cos(θ) + sin(64°)sin(θ))
Cross-multiplying and simplifying:
cos(64°)cos(θ)cot(5θ) - sin(64°)sin(θ)cot(5θ) = -sin(64°)sin(θ)
cos(64°)cos(θ)cot(5θ) = sin(64°)sin(θ)(cot(5θ) + 1)
cos(64°)cos(θ)cot(5θ) = sin(64°)sin(θ)csc(5θ)
cos(64°)cos(θ) = sin(64°)sin(θ)sin(5θ)/cos(5θ)
cos(64°)cos(θ)cos(5θ) = sin(64°)sin(θ)sin(5θ)
Using the identity for the cosine of the sum of two angles:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
We can rewrite the equation as:
cos(64° + θ - 5θ) = 0
cos(64° - 4θ) = 0
64° - 4θ = 90° + k(180°) or 64° - 4θ = 270° + k(180°) where k is an integer
Solving for θ:
64° - 4θ = 90° + k(180°)
-4θ = 26° + k(180°)
θ = -(26°/4) - (k/4)(180°)
θ = -6.5° - 45°k
or
64° - 4θ = 270° + k(180°)
-4θ = 206° + k(180°)
θ = -(206°/4) - (k/4)(180°)
θ = -51.5° - 45°k
Therefore, there are two sets of solutions for θ, given by:
θ = -6.5
Step-by-step explanation:
Find the sum or difference. Write your answer in standard form.
(m2−m)+(2m+m2)
The standard form of the expression is 2m² + m.
What is standard form formula?The standard form is referred to as the general way of representing any type of notation. The standard form formula represents the standard form of an equation which is the commonly accepted form of an equation. For example - The standard form of a polynomial is to write the terms with a higher degree first (descending order of degree) and its coefficients must be in integral form.
Equation:Combining like terms, we get:
(m² - m) + (2m + m²) = m² + m² - m + 2m
Simplifying further, we get:
2m² + m
Therefore, the sum of the given expressions is 2m² + m.
To write the answer in standard form, we arrange the terms in descending order of degree of the variable:
2m² + m = 2m² + 1m¹ + 0m⁰
So the standard form of the expression is 2m² + m.
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A group of 500 middle school students were randomly selected and asked about their preferred frozen yogurt flavor. A circle graph was created from the data collected.
a circle graph titled preferred frozen yogurt flavor with five sections labeled Dutch chocolate 21.5 percent, country vanilla 28.5 percent, sweet coconut, espresso 10 percent, and cake batter 27 percent
How many middle school students preferred sweet coconut-flavored frozen yogurt?
130
65
31
13
Answer:
13%
Step-by-step explanation:
I have a test on this an i'm missing Cake batter. But I have sweet coconut and it says its 13%.
PLEASE HELP!!! DUE TODAY
in PQR, what is m
Answer:
B.
Step-by-step explanation:
I hope this is what you needed. =)
The table gives the number of cellular telephone subscribers in a country (in thousands) from 2007 through 2012. Find the average annual rate of change during this time period.
The average annual rate of change during the time period 2007-2012 is
I Need help ASAP!!!!!!
The average annual rate of change during the time period 2007-2012 is approximately 10,797 thousand subscribers per year.
What is rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.
Equation:To find the average annual rate of change for this time period, we need to determine the total change in the number of cellular telephone subscribers from 2007 to 2012, and then divide by the number of years in the time period.
The total change in the number of subscribers from 2007 to 2012 is:
335,244 - 270,461 = 64,783
The number of years in the time period is:
2012 - 2007 + 1 = 6
So the average annual rate of change is:
64,783 / 6 = 10,797.17 (rounded to two decimal places)
If we round the average annual rate of change to the nearest unit, it would be 10,797 subscribers per year.
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does religion cause war
Which pair of ratios does NOT form a proportion? (1
03 24
5 40
-30 15
10
S
3
The pair of ratios that does not form a proportion is 103/24 and 5/40.
To check if two ratios form a proportion, we need to simplify them to their simplest form and compare them. If the two ratios are equal after simplification, then they form a proportion.
In this question, we are given five ratios: 103/24, 5/40, -30/15, 10/5, and 3/S.
To simplify the first ratio, we can divide both the numerator and denominator by their greatest common factor, which is 1. Therefore, the simplified form of 103/24 is 4.29 (rounded to two decimal places).
To simplify the second ratio, we can also divide both the numerator and denominator by their greatest common factor, which is 5. Therefore, the simplified form of 5/40 is 0.125.
When we compare these two simplified ratios, we can see that they are not equal. Therefore, the pair of ratios that does not form a proportion is 103/24 and 5/40.
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Which pair of ratios does NOT form a proportion?
103 24
5 40
-30 15
10 5
3 S
Solve the exponential equation for x. 3^3x-2 = 9^4x-1 x=
The solution of the exponential equation 3^(3x-2) = 9^(4x-1) is x = 0.
We can solve this exponential equation for x by using logarithms. We can take the logarithm of both sides of the equation, using any base that we prefer. For instance, we can use the natural logarithm, ln:
ln(3^(3x - 2)) = ln(9^(4x - 1))
Now, we can use the properties of logarithms to simplify both sides of the equation. First, recall that ln(a^b) = b ln(a), for any positive value of a and any real value of b. Therefore, we have:
(3x - 2) ln(3) = (4x - 1) ln(9)
Next, we can use another property of logarithms, namely ln(a^b) = b ln(a) = ln(c) → a^b = c, to eliminate the natural logarithms from both sides of the equation. Specifically, we can rewrite ln(9) as ln(3^2), and then use the power rule for logarithms, ln(a^b) = b ln(a), to get:
(3x - 2) ln(3) = (4x - 1) ln(3^2) = 2 (4x - 1) ln(3)
Now, we can simplify the equation by multiplying out the coefficients of ln(3) on the left-hand side:
3x ln(3) - 2 ln(3) = 8x ln(3) - 2 ln(3)
Then, we can collect like terms:
3x ln(3) - 8x ln(3) = -2 ln(3) + 2 ln(3)
Finally, we can solve for x by factoring out ln(3) and dividing both sides by the resulting factor:
(3 ln(3) - 8 ln(3)) x = 0
-5 ln(3) x = 0
x = 0
Therefore, the solution of the exponential equation 3^(3x-2) = 9^(4x-1) is x = 0.
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2m^2+4m-8=0
1. Up or down ?
2. Maximum or minimum?
3. What is the x- intersect?
4. X= -b/2(a) = ?
5. What is the vertex?
6. What is the y- intersect?
A ship traveled 25° South of West. After 250 miles changed direction to 70° East of South. After it traveled 45 miles further, find the distance and direction of the ship from its starting point.
We can approach this problem by breaking down the two displacements of the ship into their respective x- and y-components and then adding them together to find the net displacement.
For the first displacement, the ship traveled 25° South of West for 250 miles. This can be broken down into an x-component and a y-component as follows:
x = 250 cos(25°) (to the west) y = -250 sin(25°) (to the south)
For the second displacement, the ship changed direction to 70° East of South and traveled 45 miles further. This can also be broken down into an x-component and a y-component:
x = 45 cos(70°) (to the east) y = -45 sin(70°) (to the south)
To find the net displacement, we can add the x-components and y-components separately:
total x = 250 cos(25°) + 45 cos(70°) total y = -250 sin(25°) - 45 sin(70°)
We can use these values to find the distance of the ship from its starting point by using the Pythagorean theorem:
distance = sqrt((total x)^2 + (total y)^2)
Substituting the values from above and evaluating:
distance = sqrt((250 cos(25°) + 45 cos(70°))^2 + (-250 sin(25°) - 45 sin(70°))^2)
distance ≈ 272.8 miles
To find the direction of the ship from its starting point, we can use the inverse tangent function to find the angle:
angle = atan(total y / total x)
Substituting the values from above and evaluating:
angle ≈ -65.1°
Since the angle is negative, we know that the direction is to the west of south. Therefore, the ship is approximately 272.8 miles away from its starting point in a direction that is 65.1° west of south.
Choose all of the expressions that are equal to 61.
a. |−61|
b. the distance from zero to −61
c. the opposite of 61
d. −(−61)
e. the opposite of −61
f. −|−61|
g. −|61|
Answer:
a mode of negative number again gives the positive value
d. -(-61) =61 by multiplication sign rule
e. opposite of -61 =61
Answer: e
Step-by-step explanation:
the opposite is 61
A company had inventory of 5 units at a cost of $20 each on November 1. On November 2, it purchased 10 units at $22 each. On November 6 it purchased 6 units at $25 each. On November 8, it sold 18 units for $54 each. Using the LIFO perpetual inventory method, what was the cost of the 18 units sold?
Using the LIFO perpetual inventory method, the cost of the 18 units sold is $420.
The perpetual inventory strategy known as LIFO (Last In, First Out) is predicated on the idea that the most recent inventory purchases are sold first.
In order to account for the number of units sold, we use this method to count backward from the most recent inventory acquisition.
The business sold 18 units on November 8, which is more than its most recent purchase of 6 units on November 6. Therefore, starting with a total of 18 units, we first use the 10 units from the November 2 purchase and the 8 units from the November 6 buy.
10 units were bought on November 2 for a total of $220, or $22 each unit. The 8 pieces that were bought on November 6 cost $25 apiece, for a total of $200. Hence, $220 plus $200 equals $420 for the 18 units that were sold.
The cost of the 18 sold units, calculated using the LIFO perpetual inventory approach, is $420.
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