find the value of each variable provide proofs​

Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.

If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.

Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.

Step-by-step explanation:

Answer:

maybe your friend gets stuck because youre not supposed to divide the denominator, only make a common one by multiplying one or both untill they are the same. Least common multiples

The length of the lake is 100 ft

Form a right-angled triangle according to the given data in the problem. Chose which trigonometric ratio can be used to find the side that is considered as the side of the lake.  

From the trigonometric ratio table,

Here we have

Yoshi swam across a lake but did not know how far he swam.

He found that it was 100√) feet from point A to point C.

Angle C was a right angle and angle A is 30°.

We represent the given scenario in the form of a right angle triangle as shown in the picture.

Let 'B' be the point where Yoshi swam started and  BC be the length of the lake.  

From the triangle,  

Tan A = BC/AC

From the given data,

Tan 30° = BC/100√3

=> BC = Tan 30°(100√3)

=> BC = (1/√3)(100√3)  

=> BC = 100 ft

Therefore,

The length of the lake is 100 ft

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A student would have to score approximately 0.84 standard deviations above the mean to be publicly recognized.

The dispersion of asset prices from their average price, or market volatility, can be calculated with the use of standard deviation. A large standard deviation indicates a dangerous investment when prices move erratically. Low standard deviation indicates stable prices, which lowers the risk associated with investments.

The remaining 79 percent of pupils are not recognised if just the top 21% of students receive public recognition. Since a normal distribution is assumed, the conventional normal distribution and its corresponding z-scores can be used to provide the solution.

The percentage of scores that are higher than a certain z-score is shown by the area under the standard normal distribution to its right. Finding the z-score that represents the top 21% of scores is equivalent to locating the z-score that represents the bottom 79% of scores. By using a calculator or a table of the ordinary normal distribution, we can determine that the z-score for the bottom 79 percent of scores is roughly 0.84.

In order to be officially acknowledged, a student would need to get a score that is roughly 0.84 standard deviations above the mean.

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The quotient is -3x²/2 + 7x/4 + 7/8 and the remainder is 23x/8 - 1. The solution has been obtained by using polynomial long division method.

What is polynomial long division?

A formula for multiplying one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.

We are given dividend as -3x⁴+5x³+0x²+2x-1 and divisor as 2x²-x.

Using Polynomial Long Division,

Dividing : -3x⁴+5x³+0x²+2x-1 ("Dividend")

By : 2x²-x ("Divisor")

Dividend                   -3x⁴ + 5x³ + 0x² + 2x - 1

- divisor * -3x²/2       -3x⁴ + 3x³/2

Remainder                       + 7x³/2 + 0x² + 2x - 1

- divisor * 7x/4                  + 7x³/2 - 7x²/4

Remainder                                      7x²/4 + 2x - 1

- divisor * 7/8                                   7x²/4 - 7x/8

Remainder                                                  23x/8 - 1

Quotient : -3x²/2 + 7x/4 + 7/8

Remainder: 23x/8 - 1

Hence, the solution has been obtained.

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Answer:

x=-13

Step-by-step explanation:

Since the two angles given are equivalent, you set up the equation as 7x+205=114.

7x+205=114

7x=114-205

7x=-91

7x/7=-91/7

x=-13

Hope this helps! Please give brainliest!

Answer:

RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.

For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.

For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.

For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.

For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.

So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340

The equation that shows the length of the table is  length = 11/5 × 22/5

A fraction can be defined as the part of a whole number, variable or element.

The different types of fractions are;

From the information given, we have that;

Length = 2 1/5 × Width

Width = 4 2/5 feet

Turn into improper fractions

Width = 22/5 feet

Then, length = 11/5 × 22/5

Hence, the equation is 11/5 × 22/5

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The amount you made per share is $8.50.

From the question, we have the following parameters that can be used in our computation:

Initial amount = $63.00

Final amount = $71.50

To calculate the profit made, we need to find the difference between the selling price and the buying price per share, and then multiply by the number of shares.

The difference in price per share is:

Difference = $71.50 - $63.00

Evaluate the difference

Difference = $8.50

Hence, the profit per share is $8.50.

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The ratio 10:35 can be simplified to 2:7.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

The ratio 10:35 can be simplified to 2:7.

To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.

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Simply the following ratio 10:35

yearly multiplication growth factor is  (1+0.011) = 1.011.  the year 2017, seven years after 2010, the population will be  [tex]24800*2A1.011^7 = 26,774[/tex]

what is multiply ?

Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.

yearly multiplication growth factor is  (1+0.011) = 1.011.

the year 2017, seven years after 2010, the population will be  [tex]24800*2A1.011^7 = 26,774[/tex]

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For the function f(x) = log4(x - 2) + 2, the domain is (2,∞) and range is (-∞,∞).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The logarithmic function f(x) = log4(x - 2) + 2 is defined only for x-2 > 0, or equivalently, x > 2.

So, the domain of the function is all real numbers greater than 2, or -

Domain: x > 2

Now let's consider the range of the function.

The logarithmic function takes positive values for positive inputs, and it approaches negative infinity as x approaches zero from the right.

Since f(x) = log4(x-2) + 2, the function takes values greater than 2 when x is greater than 4, and it approaches 2 as x approaches 2 from the right.

So, the range of the function is -

Range: -∞ > f(x) > ∞

Therefore, the function has range and domain as (-∞,∞) and (2,∞) respectively.

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The required equation in terms of r is r = (W - FB) / F

An equation is a mathematical statement given by connecting two expressions by equal sign.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example: 3x=9y, 67x = 90+39y

Given that an equation W = F(r + B) we need to solve the equation for r,

Therefore, rearranging for r,

W = F(r + B)

Using the distributive law,

W = Fr+FB

Transposing FB to the LHS

Fr = W - FB

Diving the equation by F

r = (W - FB) / F

Hence, the equation in terms of r is r = (W - FB) / F

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The battery level after two hours of constant use unplugged is found replacing the instance of x on the line of best fit by 2.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The variables for this problem are given as follows:

Hence after a time of two hours the battery level is found as the numeric value at x = 2.

The problem is incomplete, hence the general procedure to solve the problem is presented.

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The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Let 'x' be the amount of investment at a rate of 4.75%. Then the amount of investment at a rate of 2.75% is ($18,000 - x). Then the equation is given as,

(18,000 - x) × 0.0275 + 0.0475x = 579

495 - 0.0275x + 0.0475x = 579

0.02x = 84

x = $4,200

Then the value of ($18,000 - x) is given as,

$18,000 - x = $18,000 - $4,200

$18,000 - x = $13,800

The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.

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Answer:

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.

Step-by-step explanation:

Since h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction, we know that:

The x-coordinates of f(x) and h(x) are the same, so x is unchanged.

The y-coordinates of f(x) and h(x) are reflected across the x axis, so we need to negate the y-coordinate.

The y-coordinate of h(x) is shifted up by 3 units, so we need to add 3 to the y-coordinate.

Given the equation of f(x) = x^2, the equation of h(x) can be written as:

h(x) = -x^2 + 3

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.

Answer:

3 lunch specials are possible.

Answer:

  (4, 0)

Step-by-step explanation:

You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.

When the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.

  (1, 0) ⇒ 4(1, 0) = (4, 0)

The image of the point is (4, 0).

The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:

Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )

Midpoint = ( (-2-6)/2 , (-9+7)/2 )

Midpoint = (-4,-1)

Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (7 - (-9)) / (-6 - (-2))

Slope = 4

The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.

Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:

y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.

Plugging in the values we found, we get:

y - (-1) = (-1/4)(x - (-4))

y + 1 = (-1/4)(x + 4)

y + 1 = (-1/4)x - 1

y = (-1/4)x - 2

Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.

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Answer: The correct system of linear inequalities that represents Leslie's situation is:

4x + 10y ≥ 120 (to represent the requirement to raise at least $120)

x + y ≥ 18 (to represent the requirement to sell at least 18 items in total)

x ≥ 0, y ≥ 0 (to represent that Leslie must sell a non-negative number of keychains and t-shirts)

Where x represents the number of keychains sold and y represents the number of t-shirts sold. The first inequality represents the minimum amount of money Leslie needs to raise, and the second inequality represents the minimum number of items she needs to sell. The last two inequalities represent that Leslie can only sell a non-negative number of items.

Step-by-step explanation:

The equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.

What is the slope-point form of the line?

The point-slope form of the equation of a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the given slope of 3 and the point (2, 5), we can substitute into the point-slope form to get:

y - 5 = 3(x - 2)

Expanding the right-hand side:

y - 5 = 3x - 6

Adding 5 to both sides:

y = 3x - 1

Hence, the equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.

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The value of the final velocity before striking the ground will be 9.899 meters per second.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

If an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s.

We know that if the object is projected horizontally, so initially the object has a vertical speed is zero. Then it increases due to acceleration due to gravity.

The speed of the object before striking the ground is given as,

v² - u²= 2gh

v² - 0² = 2 × (9.8) × (5)

v² = 98

v = 9.899 meters per second

The value of the final velocity before striking the ground will be 9.899 meters per second.

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On solving the provided question, we can say that in the equation,Often, there is only one variable, which also serves as the symbol. An illustration would be , [tex]D = 4(82-D)+2[/tex]

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.The two sentences on either side of a letter are connected by a mathematical formula.

Each equation has a formula. Not every equation has a formula. Equations are created with the intention of being solved for a variable. If an equation meets the requirements for a function, it is a function. But not every equation is a function.

M+D = 82 marbles

[tex]M= 82- D[/tex]

[tex]D= 4M+2[/tex]

[tex]D= 4(82-D) +2[/tex]

[tex]D= 328 - 4D+2[/tex]

[tex]5D = 330[/tex]

[tex]D= 66[/tex]

Therefore, Don has 66 and Mark has 82-66 = 16

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In a linear equation. , $12,215 did he save in tax by using Schedule A .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Given,

      Taxable income with out deductions = $63,110

                     total deductions = $10,312

       the tax is given in the row 63.100 63,150 and in the column 'single' of the tax table is

                          tax = $12,215

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Answer:

Step-by-step explanation:

5=cx-ax=x(c-a)

x(c-a)/5=1

(c-a)/5=1/x

x=5/(c-a)

The system of equations are parallel lines and they do not intersect. Thus, the system has no solution.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

No matter how far we extend a parallel line, it will never meet another parallel line.

Given that,

y=x-2

y=x-1

For x = 1:

y = x - 2 = 1 -2 = -1

y = x - 1 = 1 - 1 = 0

For x = 2:

y = 2- 2 = 0

y = 2 -1 = 1

Plot the graph using the points.

The two lines have the same slope hence they are parallel lines.

Since, the two lines are parallel the system has no solutions.

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The graph of the quadratic function y = -6x² + 1 is given by the image presented at the end of the answer.

The parent quadratic function is given as follows:

y = x².

The transformed quadratic function is given as follows:

y = -6x² + 1.

The transformations are given as follows:

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Answer:

[tex] \sf \: f(2) = - 2[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 4x - 5x

Now we have to,

→ Find the required value of f(2).

Then the value of f(2) will be,

→ f(x) = 4x - 5x

→ f(2) = 4(2) - 5(2)

→ f(2) = 8 - 10

→ [ f(2) = -2 ]

Hence, the value of f(2) is -2.

An example of a continuous random variable is a Normal random variable.

What is a normal random variable?

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).

Here, we have

We have to determine the example of a continuous random variable.

We concluded that the example of a continuous random variable is a normal random variable.

Hence, an example of a continuous random variable is a Normal random variable.

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