Step-by-step explanation:
The coordinates and vertices
which reflected over the y- axis are
r(-2,0) , s(2,-3) , and t(2,3).
13.9 m
21 m
16 m
Find surface area
The Total Surface Area of the given prism is: 1,230.4 m²
How to find the surface area of the prism?The volume of the prism is calculated as:
Volume = Base Area * Height
The total surface area is the sum of the surface area of all individual surfaces and as such we have:
Total Surface Area = (21 * 16) + (21 * 16) + (21 * 16) + 2(0.5 * 16 * 13.9)
Total Surface Area = 336 + 336 + 336 + 222.4
Total Surface Area = 1,230.4 m²
That is the final total surface area of the given rectangular based prism
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Which expression is always equivalent to sin x when 0° < x < 90°?
(1) cos (90°- x)
(3) cos (2x)
(2) cos (45° - x)
(4) cos x
The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1
To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.
Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.
Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.
On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.
Option 1 is correct.
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How should the experimental probability compare to the theoretical probability in a trial 10 versus 500
In a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case).
The experimental probability and theoretical probability can be compared in a trial of 10 versus 500 by understanding the concepts behind each type of probability.
Theoretical probability is based on mathematical calculations and is determined by analyzing the possible outcomes of an event. It relies on the assumption that the event is equally likely to occur, and it can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Theoretical probability is often considered the expected or ideal probability.
On the other hand, experimental probability is determined through actual observations or experiments. It involves conducting the event multiple times and recording the outcomes to determine the relative frequency of a specific outcome. The experimental probability is an estimation based on the observed data.
In the given trial of 10 versus 500, we can expect the experimental probability to be closer to the theoretical probability when the number of trials (or repetitions) is larger. In this case, with 500 trials, the experimental probability is likely to be a more accurate representation of the true probability.
When the number of trials is small, such as only 10, the experimental probability may deviate significantly from the theoretical probability. With a smaller sample size, the observed outcomes may not accurately reflect the expected probabilities calculated theoretically.
In summary, in a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case). As the number of trials increases, the observed frequencies are likely to converge towards the expected probabilities calculated theoretically.
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A rock is thrown upward with a velocity of 11
meters per second from the top of a 43
meter high cliff, and it misses the cliff on the way back down. When will the rock be 10
meters from ground level? Round your answer to two decimal places.
Step-by-step explanation:
We can use the equation h(t) = -4.9t^2 + vt + h0, where h0 is the initial height of the rock, v is the initial velocity and t is time in seconds, to solve the problem.
h0 = 43 meters (the top of the cliff)
v = 11 meters per second (upwards direction)
To find the time when the rock is 10 meters from ground level, we set h(t) = 10 meters and solve for t:
10 = -4.9t^2 + 11t + 43
0 = -4.9t^2 + 11t + 33
Solving this quadratic equation, we get t = 4.04 seconds or t = 1.37 seconds.
Since the rock is thrown upwards, it will be 10 meters from ground level twice - once on the way up and once on the way down. We can discard the negative time answer as that would correspond to when the rock is thrown from the ground.
Therefore, the rock will be 10 meters from ground level after 4.04 seconds (on the way down).
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answer:
(-2, 2)
Step-by-step explanation:
We will start by just plugging in the numbers to see if they work.
(-3, 5)
5<-(-3)+1
5<4
This is not possible, so the answer is not (-3, 5).
(-2, 2)
2<-(-2)+1
2<3
2>-2
The point (-2, 2) works for both equations, so that is the answer.
The perimeter of a basketball court is 96 meters and the length is 6 meters longer than twice the width, what are the length and width?
Answer:
the length of the basketball court is 34 meters and the width is 14 meters.
Step-by-step explanation:
According to the given information, the length is 6 meters longer than twice the width. Therefore, the length can be expressed as 2x + 6.
The perimeter of a rectangle is calculated by adding all four sides. In this case, the perimeter is given as 96 meters.
Perimeter = 2(length + width)
Plugging in the values, we have:
96 = 2((2x + 6) + x)
Simplifying the equation:
96 = 2(3x + 6)
96 = 6x + 12
6x = 96 - 12
6x = 84
x = 84/6
x = 14
So, the width of the basketball court is 14 meters.
To find the length, we can substitute the value of x back into the expression for the length:
Length = 2x + 6
Length = 2(14) + 6
Length = 28 + 6
Length = 34
what is the graph of f(x) = 5(2)^x
The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.
The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.
As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:
When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).
As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.
For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.
The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.
Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.
The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.
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Question 4 a) Show that y₁= 1/t is a known solution of -t²y" + 3ty' + 5y = 0, where t > 0, and find the second solution.
y₁ = 1/t is indeed a known solution of the given differential equation.
The second solution can be found using reduction of order or other methods specific to the equation.
Let's find the first and second derivatives of y₁ with respect to t:
y₁ = 1/t
First derivative:
y'₁ = d/dt (1/t) = -1/t²
Second derivative:
y''₁ = d/dt (-1/t²) = 2/t³
Now, let's substitute y₁, y'₁, and y''₁ into the differential equation:
-t²y'' + 3ty' + 5y = 0
Substituting the values:
-t²(2/t³) + 3t(-1/t²) + 5(1/t) = 0
Simplifying the expression:
-2/t + (-3/t) + 5/t = 0
(-2 - 3 + 5)/t = 0
0/t = 0
We can see that the expression simplifies to 0/t, which is equal to 0.
Therefore, y₁ = 1/t is indeed a known solution of the given differential equation.
To find the second solution, we can use the method of reduction of order. Let's assume the second solution is of the form y₂ = v(t)y₁, where v(t) is a function to be determined.
Substituting this into the differential equation, we have:
-t²(y₂'' + v'y₁' + v''y₁) + 3t(y₂' + vy₁') + 5y₂ = 0
Expanding and rearranging the terms, we get:
-t²(v''y₁ + v'y₁' + v'y₁ + vy₁'') + 3t(vy₁' - v'y₁) + 5vy₁ = 0
Simplifying further:
(-t²v''y₁ - 2t²v'y₁' + 3tvy₁' + 5vy₁) + (-t²v'y₁ + 3tvy₁ - 5v'y₁) = 0
Combining like terms:
-t²v''y₁ - 2t²v'y₁' - t²v'y₁ - t²v'y₁ + 3tvy₁' + 3tvy₁ + 5vy₁ - 5v'y₁ = 0
Simplifying:
-t²v''y₁ - 3t²v'y₁' + 6tvy₁' + (5v - 5v')y₁ = 0
Since y₁ = 1/t, we have:
-t²v''(1/t) - 3t²v'(1/t²) + 6tv(1/t²) + (5v - 5v')(1/t) = 0
Simplifying further:
-v'' - 3v' + 6v(1/t) + (5v - 5v')(1/t) = 0
Reducing the equation:
-v'' - 3v' + 6v/t + (5v/t - 5v'/t) = 0
-v'' - 3v' + (6v + 5v - 5v')/t = 0
-v'' - 3v' + (11v - 5v')/t = 0
To simplify the equation, we can multiply through by t:
-tv'' - 3tv' + 11v - 5v' = 0
Now, we have a differential equation in terms of v(t) only. To solve this equation, we can apply appropriate techniques such as separation of variables, integrating factors, or other methods depending on the specific form of the equation. Solving for v(t) will give us the second solution to the original differential equation -t²y" + 3ty' + 5y = 0.
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what steps are needed to find the equation of a line given the graph?
The equation of the line is y = x.
To find the equation of a line given its graph, you need to follow the steps below.
Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.
Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.
Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.
Example:Let's say you are given the graph of a line below: .
Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.
Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.
Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.
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5 Which of the following is the simplified form of the expression 15x - 12 - 4x + 3x + 13? O 14x+1 O 14x-1 O-14x+1 O-14x-1 4 Skip >> 4/10 complete
The simplified form of the expression 15x - 12 - 4x + 3x + 13 is 14x+1. Option A
To simplify the expression 15x - 12 - 4x + 3x + 13, we can combine like terms. Like terms are those that have the same variable and exponent.
First, let's combine the x terms:
15x - 4x + 3x = (15 - 4 + 3)x = 14x
Next, let's combine the constant terms:
-12 + 13 = 1
Putting it all together, the simplified form of the expression is:
14x + 1
Therefore, the correct answer is "14x + 1."
To simplify the expression, we added the coefficients of the x terms (15, -4, 3) to get 14x. Then, we added the constant terms (-12, 13) to get 1. This final expression, 14x + 1, does not have any like terms that can be combined further, so it is considered simplified.
It's important to note that when simplifying expressions, we group like terms together and perform the indicated operations, such as addition or subtraction. By doing so, we reduce the expression to its simplest form, where no further combining of like terms is possible.
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Which property best describes the conditional statement below If triangle ABC= triangle DEF then triangle DEF=triangleABC
Answer:
would this not be a converse statement?
Step-by-step explanation:
triangle ABC is the hypothesis and it's conclusion is triangle DEF
Alonso brings
$
21
$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost
$
2.50
$2.50dollar sign, 2, point, 50. Then, he notices that the store only sells avocados in bags of
3
33 for
$
5
$5dollar sign, 5. He wants to buy as many avocados as he can with his remaining money.
Let
�
BB represent the number of bags of avocados that Alonso buys.
Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.
Alonso has $21.00 to spend on eggs and avocados. He buys eggs that cost $2.50, which leaves him with $18.50. Since the store only sells avocados in bags of 3, he will need to find the cost per bag in order to calculate how many bags he can buy.
First, divide the cost of 3 avocados by 3 to find the cost per avocado. $5.00 ÷ 3 = $1.67 per avocado.
Next, divide the money Alonso has left by the cost per avocado to find how many avocados he can buy.
$18.50 ÷ $1.67 per avocado = 11.08 avocados.
Since avocados only come in bags of 3, Alonso needs to round down to the nearest whole bag. He can buy 11 avocados, which is 3.67 bags.
Thus, he will buy 3 bags of avocados.Let's test our answer to make sure that Alonso has spent all his money:
$2.50 for eggs3 bags of avocados for $5.00 per bag, which is 9 bags of avocados altogether. 9 bags × $5.00 per bag = $45.00 spent on avocados.
Total spent:
$2.50 + $45.00 = $47.50
Total money had:
$21.00
Remaining money:
$0.00
Since Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.
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What are the dimensions of the rectangle shown on the coordinate plane?
The base is 5 units and the height is 3 units.
The base is 4 units and the height is 7 units.
The base is 7 units and the height is 5 units.
The base is 7 units and the height is 3 units.
Answer:
D The base is 7 units and the height is 3 units.
Step-by-step explanation:
The answer is d I counted the width/base then the height/length and found answer.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: D
Step-by-step explanation:
Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.
D) 4x2=8
12x2=24
15x2=30 All sides were multiplied by 2 so D is similar
Answer:
D)
Step-by-step explanation:
Figure D is similar in all mesurements .
...
calculate the area of the following shapes
The area of the shaded part is 640.56 m²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The figure is a concentric circle, i.e a circle Ina circle. Therefore to calculate the area of the shaded part,
Area of shaded part = area of big circle - area of small circle
area of big circle = 3.14 × 20²
= 1256
area of small circle = 3.14 × 14²
= 615.44
Area of shaded part = 1256 - 615.44
= 640.56m²
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Which complex number is equivalent to this expression? 1/3(6+3¡)-2/3(6-12¡)
So, the complex number equivalent to the given expression is 0 + 9i, which can also be written as 9i.
To simplify the expression 1/3(6 + 3i) - 2/3(6 - 12i), we can perform the necessary calculations.
First, let's simplify each term separately:
1/3(6 + 3i) = 2 + i (divide each term by 3)
2/3(6 - 12i) = 4 - 8i (divide each term by 3)
Now, let's substitute these simplified terms back into the original expression:
2 + i - (4 - 8i)
When subtracting complex numbers, we distribute the negative sign:
2 + i - 4 + 8i
Combine like terms:
(-2 + 2) + (i + 8i) = 0 + 9i
The expression 1/3(6 + 3i) - 2/3(6 - 12i) simplifies to 9i.
We can make the necessary computations to simplify the statement 1/3(6 + 3i) - 2/3(6 - 12i).
Let's first simplify each phrase individually:
Divide each term by 3 to get 1/3(6 + 3i) = 2 + i.
Divide each term by 3 to get 2/3(6 - 12i) = 4 - 8i.
Let's now add these abbreviated terms back into the original phrase:
2 + i - (4 - 8i)
Distributing the negative sign while subtracting complex numbers is as follows:
2 + i - 4 + 8i
combining similar terms
(-2 + 2) + (i + 8i) = 0 + 9i
A simplified version of the phrase 1/3(6 + 3i) - 2/3(6 - 12i) is 9i.
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Determine the equation of the midline of the following graph.
Answer:
y = -3
Step-by-step explanation:
The midline of a sinusoidal function is the horizontal center line about which the function oscillates periodically.
The midline is positioned halfway between the maximum (peaks) and minimum (troughs) values of the graph. It serves as a baseline that helps visualize the oscillations of the function.
To find the equation of the midline, we need to determine the average y-value between the maximum and minimum y-values.
In this case, the maximum y-value is -1, and the minimum y-value is -5. To find the equation of the midline, sum the maximum and minimum y-values, and divide by 2:
[tex]y=\dfrac{-1 + (-5)}{2} = \dfrac{-6}{2}=-3[/tex]
Therefore, the equation of the midline for the graphed sinusoidal function is y = -3.
Complete the item by performing the proper operations of evaluation. (8y)2, (y=5)
Answer:
Step-by-step explanation:
To evaluate the expression (8y)², where y = 5, we substitute the value of y into the expression and perform the operations.
First, substitute y = 5:
(8y)² = (8 * 5)²
Next, perform the operation inside the parentheses:
(8 * 5)² = 40²
Now, calculate the square of 40:
40² = 1600
Therefore, when y = 5, (8y)² is equal to 1600.
In RST, the measure of T=90°, RT=16, SR=65, and TS= 63. What is the value of
the cosine of S to the nearest hundredth?
Work Shown:
cos(angle) = adjacent/hypotenuse
cos(S) = TS/SR
cos(S) = 63/65
cos(S) = 0.969231
cos(S) = 0.97
Each decimal value is approximate. See the diagram below.
Cellular phone usage grew about 22% each year from 1995 (about 34 million) to 2003. Write a function to model cellular phone usage over that time period. What is the cellular usage in 2003?
Answer:
Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:
`y = a * b^(x - h) + k`
where:
- `y` is the quantity you're interested in (cell phone usage),
- `a` is the initial quantity (34 million in 1995),
- `b` is the growth factor (1.22, representing 22% growth per year),
- `x` is the time (the year),
- `h` is the time at which the initial quantity `a` is given (1995), and
- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).
So, our specific model becomes:
`y = 34 * 1.22^(x - 1995)`
To find the cellular usage in 2003, we plug 2003 in for x:
`y = 34 * 1.22^(2003 - 1995)`
Calculating this out will give us the cellular usage in 2003.
Let's calculate this:
`y = 34 * 1.22^(2003 - 1995)`
So,
`y = 34 * 1.22^8`
Calculating the above expression gives us:
`y ≈ 97.97` million.
So, the cellular phone usage in 2003, according to this model, is approximately 98 million.
Let f(x) = 4x² - 7.
Using the definition of derivative
Answer:
56
Step-by-step explanation:
f(x)=4x^2-7
f'(x)=8x
f'(7)=56
In AMNO, the measure of 0=90°, ON = 15, MO = 8, and NM = 17. What is the value of the cosine of M to the nearest hundredth?
To find the value of the cosine of angle M in triangle AMNO, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides [tex]\displaystyle a[/tex], [tex]\displaystyle b[/tex], and [tex]\displaystyle c[/tex], and angle [tex]\displaystyle C[/tex] opposite side [tex]\displaystyle c[/tex], the following equation holds:
[tex]\displaystyle c^{2} =a^{2} +b^{2} -2ab\cos( C)[/tex]
In triangle AMNO, we have the following information:
[tex]\displaystyle AM=17[/tex] (side [tex]\displaystyle a[/tex])
[tex]\displaystyle MN=15[/tex] (side [tex]\displaystyle b[/tex])
[tex]\displaystyle AN=8[/tex] (side [tex]\displaystyle c[/tex])
Angle M = 90 degrees
We can apply the Law of Cosines to find the value of [tex]\displaystyle \cos( M)[/tex]:
[tex]\displaystyle AN^{2} =AM^{2} +MN^{2} -2\cdot AM\cdot MN\cdot \cos( M)[/tex]
Substituting the given values:
[tex]\displaystyle 8^{2} =17^{2} +15^{2} -2\cdot 17\cdot 15\cdot \cos( M)[/tex]
Simplifying:
[tex]\displaystyle 64=289+225-510\cdot \cos( M)[/tex]
[tex]\displaystyle 64=514-510\cdot \cos( M)[/tex]
Rearranging the equation:
[tex]\displaystyle 510\cdot \cos( M) =514-64[/tex]
[tex]\displaystyle 510\cdot \cos( M) =450[/tex]
Dividing both sides by 510:
[tex]\displaystyle \cos( M) =\frac{450}{510}[/tex]
Simplifying:
[tex]\displaystyle \cos( M) =\frac{15}{17}[/tex]
Therefore, the value of the cosine of angle M in triangle AMNO, to the nearest hundredth, is approximately [tex]\displaystyle 0.88[/tex].
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
The slope of the tangent line to the curve y= 3/x
at the point 5, 3/5 is-
The equation of this tangent line can be written in the form y = mx + b
where:
m is:
b is:
The tangent line at that point is:
y = (-3/25)*x + 6/5
so m = -3/25, and b = 6/5
How to find the slope of the tangent line?To find the slope at that point, we need to evaluate the derivative at that point.
y = 3/x
The derivative is:
y' = -3/x²
When x = 5, we have:
y' = -3/5² = -3/25
So that is the slope, m.
Now let's find the line.
The line must pass trhough the point (5, 3/5), then:
3/5 = (-3/25)*5 + b
3/5 = -3/5 + b
3/5 + 3/5 = b
6/5 = b
The equation of the line is:
y = (-3/25)*x + 6/5
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What is the z score for Brazil?
The z-score for Brazil is given as follows:
Z = 0.87.
What is the z-score formula?The z-score formula is defined as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The parameters for this problem are given as follows:
[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]
Hence the z-score for Brazil is given as follows:
Z = (6.24 - 4.8)/1.66
Z = 0.87.
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Sam’s Swimming Pool Cleaning has an annual gross profit of $88,400. Sam charges $25 per week for each of his customers for 52 weeks. His annual operating expenses, including labor and supplies, are $48,000. How many customers does Sam’s Swimming Pool Cleaning have?
a.
17
b.
35
c.
68
d.
105
Answer:
D.
Step-by-step explanation:
To find the number of customers Sam's Swimming Pool Cleaning has, we need to calculate the total revenue generated by the business and divide it by the weekly charge per customer.
Total revenue = 52 x $25 x number of customers
We know that the annual gross profit is $88,400. So, we can set up an equation to find the number of customers:
$88,400 = 52 x $25 x number of customers - $48,000
$88,400 + $48,000 = 52 x $25 x number of customers
$136,400 = $1,300 x number of customers
Number of customers = $136,400/$1,300
Number of customers = 105
Therefore, Sam's Swimming Pool Cleaning has 105 customers. The correct answer is D.
Sam’s Swimming Pool Cleaning have 105 customers.
What is an expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is:
To get how many customers Sam has, write an equation that will relate to the gross profit. Let n be the customers. Since for 52 weeks, Sam charges $25 per week per person, multiply n by the number of weeks and the charge. The equation is written as $88,400 = 52 weeks x $25 per week x n persons. Divide $88,400 by the product of 52 weeks and the $25 charge. The answer will be 105.
Therefore, Sam’s Swimming Pool Cleaning have 105 customers.
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a. The absolute maximum of g is 4.
The absolute minimum of g is -4.
b. The absolute maximum of h is 3.
The absolute minimum of h is -4.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of the polynomial function g shown above, we can logically deduce that its vertical asymptote is at x = 3. Furthermore, the absolute maximum of the polynomial function g is 4 while the absolute minimum of g is -4.
In conclusion, the absolute maximum of the polynomial function h is 3 while the absolute minimum of h is -4.
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if A-B=2, B-C=7 and A+C=17, then (A+B+C) is equal to
Answer:
A+B+C=28
Step-by-step explanation:
let
A-B=2 -----1 EQUATION
B-C=7-------2
A+C=17------3
FROM 1 AND 2
A-C=9---------4
FROM 2 AND 3
A+B=24 -------5
FROM 3 AND 4
2A=26
A=13 SUBSTITUTING A=13 IN 5
WE GET B=11 SUBSTITUTING IT IN 2
WE GET C=4
NOW
A+B+C=13+11+4=28
22. Ms. Hernandez has $150 to spend on parking and admission to the zoo. The parking will cost $3, and
admission tickets will cost $10.40 per person, including tax. Write and solve an equation that can be
used to determine the number of people that she can bring to the zoo, including herself.
SHOW ALL WORK
23.A car travels 50+ miles in of an hour. What is the average speed, in miles per hour, of the car?
SHOW ALL WORK
Answer:
Step-by-step explanation:
Let's represent the number of people that Ms. Hernandez can bring to the zoo as "x". Each person will require an admission ticket, which costs $10.40 per person. Additionally, there is a parking fee of $3.
The total cost of admission tickets and parking is given as $150. We can set up the equation as follows:
10.40x + 3 = 150
To solve for x, we need to isolate the variable:
10.40x = 150 - 3
10.40x = 147
Now, divide both sides of the equation by 10.40 to solve for x:
x = 147 / 10.40
Using a calculator, we find:
x ≈ 14.13
Since we can't have a fractional number of people, we need to round down to the nearest whole number since we can't bring a fraction of a person. Therefore, Ms. Hernandez can bring 14 people to the zoo, including herself.
The average speed of a car is calculated by dividing the total distance traveled by the total time taken. In this case, the car travels 50+ miles in "of an hour".
To calculate the average speed in miles per hour, we need to determine the value of "of an hour". If the value is given as a fraction, we need to convert it to a decimal.
Assuming "of an hour" is 1/2 (0.5), the average speed can be calculated as:
Average speed = Total distance / Total time
Average speed = 50+ miles / (1/2) hour
To divide by a fraction, we can multiply by its reciprocal:
Average speed = 50+ miles * (2/1) hour
Average speed = 100+ miles per hour
Therefore, the average speed of the car is 100+ miles per hour.
GEOMETRY 50POINTS
TY GUYS
Answer:
35.7 ft
Step-by-step explanation:
Given
Hypotenuse (length of the ladder) = 50 ft
Base (distance from the ladder to wall) = 35 ft
Height (of the wall) = [tex]\sqrt{50^{2}-35^{2} }[/tex] = [tex]\sqrt{1275}[/tex] = 35.7 ft
Find the missing side. 27° y= ?] 11
Answer:
21.6
Step-by-step explanation:
Tan 27= 11
y
y×tan27=11
y=21.6
The answer is:
y = 21.6
Work/explanation:
We are asked to use SOH-CAH-TOA. But what does it mean?
SOH CAH TOASOH stands for Sine = Opposite ÷ Hypotenuse
CAH stands for Cosine = Adjacent ÷ Hypotenuse
TOA stands for Tangent = Opposite ÷ Adjacent
Since we do not have the hypotenuse, we will use the TOA ratio:
[tex]\sf{Tangent=\dfrac{Opposite}{Adjacent}}[/tex]
The opposite is 11, and the adjacent is y:
[tex]\sf{\tan27=\dfrac{11}{y}}[/tex]
Take the tangent of 27 & approximate it:
[tex]\sf{0.5095=11\div y}[/tex]
Multiply each side by y
[tex]\sf{0.5095y=11}[/tex]
Divide each side by 0.5095
[tex]\sf{y=21.6}[/tex]
Hence, y = 21.6