Wolfrich lived in Portugal and Brazil for a total period of 141414 months in order to learn Portuguese. He learned an average of 130 new words per month when he lived in Portugal and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words. How long did Wolfrich live in Portugal, and how long did he live in Brazil?

Answer:

Equations that represent the problem:

172 = q + d

28.60 = 0.25q + 0.10d

Solved = 96 dimes and 76 quarters

Answer:

# of quarters: 76

# of dimes: 96

Step-by-step explanation:

Thomas has 172 coins in the bucket. Let 'd' describe the number of dimes and let 'q' decide the number of quarters.

So, we can write: d+q=172

The total in the bucket is $28.60. The total amount of money in dimes is equal to the number of dimes multiplied by the value of one dime ($0.10), and the total amount of money in quarters is equal to the number of quarters multiplied by the value of one quarter ($0.25).

So, we can write: 0.1d+0.25q=28.6

We know d+q=172, which means q=172-.

Let's sub this into our second equation to get our answer:

0.1d+0.25q=28.6

0.1(172-q)+0.25q=28.6

17.2-0.1q+0.25q=28.6

0.15q=11.4

q=76

Now let's sub this value for q into our first equation:

d+q=172

d+76=172

d=96

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:  I am sorry if this doesn't answer you but I don't know this answer

Step-by-step explanation: Please accept.

The density function of X = XY is f(x,z) = x²e^(-x)(Z + X) / (XZ).To find the conditional density of X given Y = y, we use the formula:f(x|y) = f(x,y) / f(y),

where f(x,y) is the joint density function and f(y) is the marginal density function of Y.

1. Conditional Density of X given Y=y:

Given the joint density function f(x,y) = xe^(-x)(y+1), x > 0, y > 0, and the marginal density function of Y is obtained by integrating f(x,y) over all possible x values:

f(y) = ∫(0 to ∞) xe^(-x)(y+1) dx

To find f(y), we integrate f(x,y) with respect to x:

f(y) = ∫(0 to ∞) xe^(-x)(y+1) dx = (y+1) ∫(0 to ∞) xe^(-x) dx

We recognize that the integral is the gamma function, Γ(2), which equals 1! = 1:

f(y) = (y+1) * 1 = y+1

Now, we can find the conditional density of X given Y = y:

f(x|y) = f(x,y) / f(y)

       = (xe^(-x)(y+1)) / (y+1)

       = xe^(-x)

Therefore, the conditional density of X given Y = y is f(x|y) = xe^(-x).

2. Density function of X = XY:

To find the density function of X = XY, we need to transform the joint density function f(x,y) into the joint density function of X and X = XY.

Let's define a new variable Z = XY. To find the joint density function of X and Z, we use the transformation rule:

f(x,z) = f(x,y) / |(∂(x,z) / ∂(x,y))|,

where |(∂(x,z) / ∂(x,y))| is the absolute value of the Jacobian determinant of the transformation.

First, we solve Z = XY for y:

y = Z / X.

Next, we calculate the Jacobian determinant:

|(∂(x,z) / ∂(x,y))| = |(1 * Z / X²)|

                    = |Z / X²|

                    = Z / X² (since Z and X are always positive)

Now, we can find the joint density function of X and Z:

f(x,z) = f(x,y) / |(∂(x,z) / ∂(x,y))|

       = (xe^(-x)(y+1)) / (Z / X²)

       = x²e^(-x)(y+1) / Z

Substituting y = Z / X, we have:

f(x,z) = x²e^(-x)((Z / X) + 1) / Z

      = x²e^(-x)(Z + X) / (XZ)

Therefore, the density function of X = XY is f(x,z) = x²e^(-x)(Z + X) / (XZ).

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Equation of tangent line is x − 6y + 9 = 0

The given equation is f(x) = √x and the given point is (9, 3)

To find the equation of tangent line, we have to differentiate the given equation and find the slope at the given point.

Now, y = √x

⇒ y' = 1/2√x = m

Putting x = 9 and y = 3 in above equation, m= 1/2√x = 1/2√9 = 1/6

Therefore, slope of tangent line, m = 1/6

Now, we use the point-slope form of a linear equation.

y − y1 = m(x − x1) where (x1, y1) is the point of tangency and m is the slope.

We know that the point of tangency is (9, 3) and the slope m is 1/6.

Substituting these values, we get

y − 3 = 1/6(x − 9)

⇒ 6(y − 3) = x − 9

⇒ 6y − 18 = x − 9

⇒ x − 6y + 9 = 0

∴ The required equation of the tangent line is x − 6y + 9 = 0.

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Answer:

time = 70 minutes

The maximum abundance of species 1 if 250 of species 2 coexists with it is B. 500.

Determine the carrying capacity ratio between species 1 and 2.
Carrying capacity of species 1 = 1000
Carrying capacity of species 2 = 500
Ratio = 1000 / 500 = 2

Calculate the abundance of species 1 considering the presence of species 2.
Abundance of species 2 = 250
Abundance of species 1 = 2 * 250 = 500

So, the maximum abundance of species 1 if 250 of species 2 coexists with it is 500 (Option B).

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Volume of a solid whose  base is a circle of radius 5 and cross sections perpendicular to the x-axis are squares is 785.4 cubic units.

Therefore, the answer is 785.4 cubic units.

The base of the solid is a circle, so considering basic solids it can be either a cylinder or a cone. It is given that the cross section perpendicular to the x-axis is square.

Two facts can be inferred from the above statement, one the solid is a cylinder and second the height of the cylinder equal to the diameter of the base circle, that is h = 2r.

Now, volume of a cylinder is given by

V = πr²h

V = πr² × (2r)

V = 2πr³

V = 2 × π × 5³

V = 785.4

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Answer:

C. y=x

Step-by-step explanation:

If you use a graphing calculator and plot the points (-3,5) & (5,-3) and then graph y=x you can see it is the line of reflection.

Also when reflecting over the line y=x, we switch our x and y.

The proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.

What is square of correlation coefficient?

A helpful number in linear regression is the square of the correlation coefficient, or r2.

The percentage of the variance in one variable that can be partially explained by another variable is represented by this value.

The summary table in the Regression output contains the "R" value, which is the coefficient of correlation.

Coefficient of determination is another name for R square. To calculate R squared, multiply R by R.

The square of the correlation coefficient is what is meant by the term "coefficient of determination."

Hence, the proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.

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The new length, width, and the height of the cuboid are (L+2) inches, (W+2) inches, and (H+2) inches respectively

It is defined as the six-faced shape, a type of hexahedron in geometry. As the old length, width, and height are not given so we are assuming the length of the box is L, width is W, and height is H.

Dave wants to add 2 inches to the minimum length, width, and height of the box. Including the additional space. So the new length = (L+2) inches

New width = (W+2) inches

New height = (H+2) inches

Thus, the new length, width, and height are (L+2) inches, (W+2) inches, and (H+2) inches respectively.

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Answer:

Step-by-step explanation:

Assuming the oatmeal raisin and sugar cookies have an equal probability, it is less likely that a chocolate chip cookie will be picked since the other two cookies have a 37.5% chance of being picked. Despite this, it is still both likely and unlikely since it is only a small difference.

To conclude, it depends on what your teacher or textbook think. If they think a 12.5% difference between the other two cookies means that chocolate chip is unlikely, then it's unlikely. In my opinion, it is not equally but near equally likely and unlikely.

The likelihood that the CD rack will be organized alphabetically is 1 in 28.

The first step is to count all conceivable arrangements.

Use combinations if you want to organize 6 of the 8 CDs. Combinations can be calculated using the formula C(n, r) = n! / [r!(n - r)!!], where n denotes the total number of items and r denotes the number of items being selected. Here, n = 8 and r = 6, respectively.

C(8, 6) = 8! / [6!(8 - 6)!] = 8! / [6!2!] = 28

The six CDs can therefore be organized in 28 different ways.

Step 2: Count how many configurations lead to an alphabetical order.

When they are placed precisely in that sequence, there is only one configuration in which the CDs are organized alphabetically.

3. Determine the likelihood.

Probability equals the product of the number of successful outcomes and the total number of conceivable outcomes.

Probability equals 1/28

You want to put 6 of the 8 CDs you have in this issue in a CD rack. We discover that there are 28 different possible arrangements using combinations. Only one of these configurations causes the CDs to be arranged alphabetically. As a result, there is a 1/28 chance that the CD rack will be organized alphabetically.

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The solution for theta in the equation cos2theta = -1 in the range [0, 2π) is Ф = π/2

Given the equation

cos2theta = -1

Express properly

cos(2Ф) = -1

Take the arc cos of both sides

So, we have

2Ф = π

Divide both sides by 2

Ф = π/2

Hence, the value of theta in the range is π/2

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Answer:

  number 4: frequency 8

  number 5; frequency 2

Step-by-step explanation:

The mean of all rolls is their sum divided by their number, which is 30. Let x and y represent the number of rolls of 4 and 5, respectively. Then the mean is  ...

  (1×6 +2×3 +3×5 +4x +5y +6×6)/30 = 3.5

This simplifies to ...

  (6 +6 +15 +4x +5y +36) = 3.5×30 . . . . . multiply by 30

  4x +5y = 42 . . . . . . subtract 63

Of course, the total number of rolls must be 30:

  6 +3 +5 +x +y +6 = 30

  x + y = 10

We can solve this system of equations by substitution, using x=10-y:

  4(10 -y) +5y = 42

  40 +y = 42

  y = 2

  x = 10 -2 = 8

The two missing numbers are 8 and 2. The frequency of 4 is 8; the frequency of 5 is 2.

Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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The zero of the polynomial 3x³ 4x² 7 is -7/3.

In order to find the zeros of a polynomial, one must first factor the equation and then set it equal to zero. The zeros of a polynomial are the values of x that make the equation equal to zero. The zeros of a polynomial can be found by factoring the polynomial and then solving for x, which will produce the x values that make the equation equal to zero.

The zero of the polynomial 3x³ 4x² 7 is -7/3. This can be calculated by setting the polynomial equal to 0 and solving for x.

3x³ 4x² 7 = 0

3x³ 4x² = -7

3x(x² - 4) = -7

x(x² - 4) = -7/3

x² - 4 = -7/3

x² = -7/3 + 4

x² = 1/3

x = ±√(1/3)

x = ±(1/√3)

x = -7/3

Therefore, the zero of the polynomial 3x³ 4x² 7 is -7/3.

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Complete question : What is the value of the zero?

Answer:

AB=2 ft

ED=4.5 ft

BD=9 ft

m∠ABC=105°

m∠BCD=105°

m∠ADC=75°

Step-by-step explanation:

Answer:

l = 40 m and b = 30 m

Step-by-step explanation:

Let the length and breadth of a rectangle be 4x and 3x.

We know that,

The perimeter of a rectangle is given by :

P = 2(l+b)

140 = 2(4x+3x)

70 = 7x

x = 10

Length, l = 4x = 4(10) = 40 m

Breadth, b = 3x= 3(10) = 30 m

So, the length and breadth of a rectangle are 40 m and 30 m respectively.

The expression that represents the sum of a number decreased by three, and eight more than the quotient of triple the number and five is (8x + 25) / 5.

The expression that represents the sum of a number decreased by three, and eight more than the quotient of triple the number and five can be obtained by using the following expression.

Expression as an expression: (x - 3) + (8 + (3x / 5))where 'x' is the given number. Let's simplify the expression using the following steps:

Simplifying the expression:(x - 3) + (8 + (3x / 5))= x - 3 + 8 + (3x / 5)= x + (3x / 5) + 5= (5x + 3x + 25) / 5= (8x + 25) / 5

Therefore, the expression that represents the sum of a number decreased by three, and eight more than the quotient of triple the number and five is (8x + 25) / 5.

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To prove the identity sin(x − ) = −sin(x), we can start by using the subtraction formula for sine, which states that sin(x − ) = sin(x)cos() − cos(x)sin().

Substituting in the given value of , we get:

sin(x − ) = sin(x)cos( ) − cos(x)sin( )
sin(x − ) = sin(x)cos() − cos(x)(−1)   (since sin() = 0 and cos() = −1)
sin(x − ) = sin(x) + cos(x)

Now we can see that this is not equal to −sin(x), but rather sin(x) + cos(x). However, we can use another identity to simplify this expression further.

Recall that sin() = 1 and cos() = 0, since the angle is 90 degrees. Therefore, we have:

sin(x − ) = sin(x) + cos(x)
sin(x − ) = sin(x) + sin(90 − x)
sin(x − ) = sin(x) + sin(90)cos(x) − cos(90)sin(x)   (using the subtraction formula for sine again)
sin(x − ) = sin(x) + 1cos(x) − 0sin(x)
sin(x − ) = sin(x) + cos(x)

And now we can see that this is equal to the expression we derived earlier. Therefore, we have proven the identity sin(x − ) = −sin(x).

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Answer:

y = 3x + 1

Step-by-step explanation:

The slope is 3 (rise over run)

It cross the y axis at 1

Answer:

y=3x+1

Step-by-step explanation:

The chi-square goodness-of-fit test can provide important information about whether the observed data significantly deviates from the expected distribution, which categories or bins contribute to the deviation, and the overall goodness-of-fit of the data to the expected distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if a sample of data comes from a population with a specific distribution. Specifically, the test compares the observed frequencies of data in different categories or bins with the expected frequencies of data in those categories based on a hypothesized distribution.

It can determine whether the observed data significantly deviates from the expected distribution. If the test results in a p-value less than the chosen level of significance, it indicates that the observed data significantly deviates from the expected distribution, and the null hypothesis (that the data follows the expected distribution) can be rejected.

It can identify which categories or bins contribute the most to any significant deviation. The test statistic and associated p-value can help to identify which categories or bins show significant differences between the observed and expected frequencies.

It can provide information on the overall goodness-of-fit of the data to the expected distribution. The test statistic provides a measure of the overall goodness-of-fit, with higher values indicating greater deviation from the expected distribution.

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The final answer is -1.

The definition of Imaginary Numbers is actually i2 = -1. With this definition, we can evaluate i10 by using the rules of exponents and the fact that i2 = -1. Here are the steps to evaluate i10:

1. Rewrite i10 as (i2)5 using the rule of exponents that (ab)c = abc.
2. Substitute -1 for i2 using the definition of Imaginary Numbers.
3. Simplify (-1)5 to get -1.

So, i10 = (i2)5 = (-1)5 = -1. The final answer is -1.

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Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

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Answer:

13 dollars

and slope is 3

Step-by-step explanation:

In doing a quantity takeoff for 100 square feet of single wythe concrete masonry wall, with a thickness of 8", we would need  14.06 8x8x16 block and 10.14 cubic feet mortar.

Number of blocks:

Since each block is 8x8x16 inches, the volume of one block is:

Volume of one block = Length x Width x Height

                                   = 8 inches x 8 inches x 16 inches

                                   = 1024 cubic inches

To calculate the number of blocks needed, we divide the wall area by the area of one block:

Number of blocks = Wall area in square inches / Area of one block

                              = 14,400 square inches / 1024 cubic inches

                              ≈ 14.06

Rounding to the nearest whole number, the correct answer is 14 blocks.

Amount of mortar:

To determine the amount of mortar needed, we multiply the wall area by the joint thickness:

Volume of mortar = Wall area x Joint thickness

                              = 100 square feet x 1 square foot/144 square inches x 8 inches x 3/8 inches

                              ≈ 10.14 cubic feet

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