one number is seven less than a second number. Six times the first is 10 more than 2 times the second. Find the numbers.

The z-score for Brazil is given as follows:

Z = 0.87.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

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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The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

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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The computed mean of 52.4 and the actual mean of 52.7 suggest a close relationship in terms of central tendency.

A computed mean is a statistical measure calculated by summing up a set of values and dividing by the number of observations. In this case, the computed mean of 52.4 implies that when the values are averaged, the result is 52.4.

The actual mean of 52.7 refers to the true average of the population or data set being analyzed. Since it is higher than the computed mean, it indicates that the sample used for computation might have slightly underestimated the true population mean.

However, the difference between the computed mean and the actual mean is relatively small, with only a 0.3 unit discrepancy.

Given the proximity of these two values, it suggests that the computed mean is a reasonably accurate estimate of the actual mean.

However, it's important to note that without additional information, such as the sample size or the variability of the data, it is difficult to draw definitive conclusions about the relationship between the computed mean and the actual mean.

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The volume of the right prism is equal to 312 cubic units.

In this problem we find the representation of a right prism, whose volume  must be found by means of the following formula:

V = A · h

Where:

And the area of the base can be found by following formula:

Triangle

A = 0.5 · w · l

Rectangle

A = w · l

Where:

The volume of the solid is now computed:

V = (0.5 · 3 · 4 + 5 · 4) · 12

V = (6 + 20) · 12

V = 26 · 12

V = 312

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Answer:

x ≈ 77.79 ft

Step-by-step explanation:

using the sine ratio in the right triangle

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{50}{x}[/tex] ( multiply both sides by x )

x × sin40° = 50 ( divide both sides by sin40° )

x = [tex]\frac{50}{sin40}[/tex] ≈ 77.79 ft ( to the nearest hundredth )

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).

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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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.

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.

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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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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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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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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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.

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

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).

The given functions are f(x) = 3x² and g(x) = -2².

To understand the difference between their graphs, let's examine the characteristics of each function individually:

Function f(x) = 3x²:

The coefficient of x² is positive (3), indicating an upward-opening parabola.

The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.

The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.

Function g(x) = -2²:

The coefficient of x² is negative (-2), indicating a downward-opening parabola.

The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.

The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.

Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.

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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].

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♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

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

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 .

...

The area of the shaded part is 640.56 m²

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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The Total Surface Area of the given prism is: 1,230.4 m²

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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Answer:

Perimeter = 40 inches

Step-by-step explanation:

The formula for the perimeter of a rectangle is given by:

P = 2l + 2w, where,

Thus, we can allow the 11-inch side to represent the length and the 9-inch side to represent the width and plug in 11 for l and 9 for w in the perimeter formula to find P, the perimeter of the rectangle:

P = 2(11) + 2(9)

P = 22 + 18

P = 40

Thus, the perimeter of the rectangle is 40 inches.

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.

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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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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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 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]

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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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.

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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