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The new equation obtained after substituting the expression equivalent to x from the first equation into the second equation is -18 - 13y = -6.

To solve the given system of equations using the substitution method, we need to substitute the expression equivalent to x from the first equation into the second equation.

To find the new equation, we can follow these steps:

Start with the first equation: x + 4y = -9.

Solve the first equation for x: x = -9 - 4y.

Substitute the expression (-9 - 4y) for x in the second equation: 2x - 5y = -6 becomes 2(-9 - 4y) - 5y = -6.

Simplify the equation by performing the multiplication: -18 - 8y - 5y = -6.

Combine like terms: -18 - 13y = -6.

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The direction and magnitude of the vector A + B are approximately 5.22m at an angle of -33.5°.

To find the direction and magnitude of the vector A + B, we need to perform vector addition using the given components. Given: Vector A: [10.22m, 145.1°], Vector B: [10m, 30°]. Step 1: Resolve the vectors into their Cartesian components. Vector A: A_x = 10.22m * cos(145.1°), A_y = 10.22m * sin(145.1°), Vector B: B_x = 10m * cos(30°), B_y = 10m * sin(30°)

Step 2: Add the respective components of vectors A and B. Resultant vector R: R_x = A_x + B_x, R_y = A_y + B_y. Step 3: Calculate the magnitude of the resultant vector. Magnitude of R: |R| = √(R_x^2 + R_y^2). Step 4: Calculate the direction of the resultant vector. Direction of R: θ = atan2(R_y, R_x). Let's calculate these values: Vector A: A_x = 10.22m * cos(145.1°) ≈ -4.329m, A_y = 10.22m * sin(145.1°) ≈ -7.923m

Vector B: B_x = 10m * cos(30°) ≈ 8.66m, B_y = 10m * sin(30°) ≈ 5m. Resultant vector R: R_x = -4.329m + 8.66m ≈ 4.331m, R_y = -7.923m + 5m ≈ -2.923m, Magnitude of R: |R| = √(4.331^2 + (-2.923)^2) ≈ √(18.731 + 8.551) ≈ √27.282 ≈ 5.22m. Direction of R: θ = atan2(-2.923, 4.331) ≈ -33.5°. Therefore, the direction and magnitude of the vector A + B are approximately 5.22m at an angle of -33.5°.

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The expression for the profit function P(x) is P(x) = 2x^4 - 24x^2 - 2x - 1.3.

To find the expression for the profit function P(x) when given the revenue function R(x) and cost function C(x), we can substitute the given functions into the equation P(x) = R(x) - C(x).

Given:

R(x) = 2x^4 - 30% + 2^(2-1)

C(x) = 24x^2 + 2x + 3

We substitute the functions into the expression for P(x):

P(x) = R(x) - C(x)

= (2x^4 - 30% + 2^(2-1)) - (24x^2 + 2x + 3)

Simplifying the expression:

P(x) = 2x^4 - 0.3 + 2 - 24x^2 - 2x - 3

= 2x^4 - 24x^2 - 2x - 0.3 - 3 + 2

= 2x^4 - 24x^2 - 2x - 1.3

Therefore, the expression for the profit function P(x) is P(x) = 2x^4 - 24x^2 - 2x - 1.3.

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We can use the formula to calculate the length of an arc given byθ/360° × 2πr = lwhereθ is the central angle, r is the radius, and l is the length of the arc.

Using the values given in the problem,θ = 45°,l = 1.5 km.Substituting these values in the formula, we get:45/360 × 2πr = 1.5.Therefore, the radius of the circle is 3 km/π or approximately 0.955 km rounded to 3 decimal places.Explanation:Given: A central angle of measure 45° intercepts an arc of length 1.5 km.To find: The radius of the circle.Solution:Let us consider a circle of radius r with central angle θ.

Let l be the length of the arc subtended by the central angle θ.Since the central angle is 45°,θ = 45°l = 1.5 kmSubstituting the values of θ and l in the formula to calculate the length of an arc, we get:θ/360° × 2πr = l45/360 × 2πr = 1.5 km2πr/8 = 1.5 kmMultiplying both sides by 8/2π, we get:r = 1.5 × 8/2πr = 3 km/πTherefore, the radius of the circle is 3 km/π or approximately 0.955 km rounded to 3 decimal places.

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The calculated radius of the circle is 3.82 km

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

Intercepted arc, l = 1.5 km

Central angle = π/8

The radius (r) of the circle can be calculated from

l = rθ

So, we have

r = l/θ

This gives

r = (1.5)/(π/8)

Evaluate

r = 3.82

Hence, the radius of the circle is 3.82 km

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Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares. These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.

To identify the models that represent the sum 1.2 + 0.3, let's analyze the given options:

Number line from 0 to 4 by tenths - This model represents the sum as it includes the values 1.2 and 0.3 on the number line, allowing for visualizing the addition of these numbers.

An arrow shows a jump starting at 0 and ending 2 marks past 1 - This model does not directly represent the sum of 1.2 + 0.3. It only illustrates a jump on the number line, which may not correspond to the sum in question.

Another arrow shows a jump starting at 2 marks past 1 and ending at 5 marks past 1 - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It demonstrates another jump on the number line, unrelated to the given sum.

One column, divided into 10 small squares - This model does not directly represent the sum 1.2 + 0.3 as it only presents a column without any values or operations.

Two small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.

Two 10 by 10 grids of 100 squares - This model does not directly represent the sum of 1.2 + 0.3. It shows two grids of squares but does not include the given numbers or an addition operation.

All 10 columns of the first square and 2 columns of the second square shaded one color - This model does not directly represent the sum 1.2 + 0.3. It describes shading specific columns in squares, which is unrelated to the given sum.

Three columns of the second square shaded a different color - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It focuses on shading specific columns in squares without providing a representation of the sum.

Large square divided into a 10 by 10 grid of 100 small squares - This model does not directly represent the sum 1.2 + 0.3. It describes a large square divided into smaller squares but does not include the given numbers or an addition operation.

Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two columns divided into 10 small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.

Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color - This model does not directly represent the sum 1.2 + 0.3. It focuses on shading specific columns in a grid of squares, which is unrelated to the given sum.

Based on the analysis, the models that represent the sum 1.2 + 0.3 are:

Number line from 0 to 4 by tenths

Two small squares. Plus sign. Three columns, each divided into 10 small squares

Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares

These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.

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The distance of this point from the center of the earth is 5280248.56 m.

Newton's law of gravitation is used to calculate the distance of an object from the center of the earth. The distance of this point from the center of the earth and the masses of the earth and the moon are both determined using Newton's law of gravitation.

The distance of a point from the center of the earth can be calculated using Newton's law of gravitation, which states that

[tex]F = \frac{G(m1\times m2)}{d^2}[/tex],

where F is the force between the two masses, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

Given that the masses of the earth and the moon are 5.98 * 10²⁴ kg each, we can substitute these values into the formula and solve for d. We know that the force of gravity between the earth and the moon is the centripetal force acting on the moon that keeps it in orbit.

Thus, we can equate the gravitational force to the centripetal force. So,

[tex]F_{gravity} = F_{centripetal}[/tex]

[tex]G(m_1m_2)/r^2 = m\omega^2r[/tex]

Here, ω is the angular velocity of the moon.

So, [tex]d = [(Gm)/(\omega^2)]^{1/3}[/tex]

Where G = 6.674×10^-11 Nm²/kg², m is Mass of earth, ω is angular speed of the moon which is 2.7*10-6/s.

From the above formulas, we can calculate the distance of this point from the center of the earth as follows:

[tex]d = [(6.674\times10^{-11} Nm^2/kg^2 \times 5.98 \times 10^{24} kg)/(2.7\times10^{-6}/s^2)]^{1/3}[/tex]

d = 5280248.56 m

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Cathy was driving at a speed of 50 miles per hour when she received a speeding ticket.  Cathy was driving at a speed of 50 miles per hour when she received the $110 speeding ticket.

To determine how fast Cathy was driving, we can calculate the difference between the fine amount and the base fine for exceeding the speed limit. The base fine is obtained by multiplying the number of miles per hour over the speed limit by the fine rate. In this case, the base fine is $11 per mile per hour over the speed limit. Since Cathy was fined $110, we can divide this amount by the base fine to find the number of miles per hour over the limit.

$110 / $11 = 10

Therefore, Cathy was driving 10 miles per hour over the speed limit. Since the speed limit was 40 miles per hour, we add the excess speed to the limit to find Cathy's actual speed:

40 mph + 10 mph = 50 mph

Thus, Cathy was driving at a speed of 50 miles per hour when she received the $110 speeding ticket.

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In order to fill in the blanks to achieve quotients close to 100, close to 1, and greater than 100, we can assign the values 1000, 0.001, and 10, respectively, to the corresponding expressions.

To find a quotient close to 100, we can assign the value 1000 to the expression. By dividing 1000 by 10, we obtain a quotient of 100, which is close to 100.

To achieve a quotient close to 1, we can assign the value 0.001 to the expression. When we divide 0.001 by 0.001, we get a quotient of 1, which is close to 1.

To obtain a quotient greater than 100, we can assign the value 10 to the expression. By dividing 10 by 0.12127, we obtain a quotient of approximately 82.34. This value is greater than 100.

Therefore, by filling in the blanks with 1000, 0.001, and 10, respectively, we can ensure that each quotient falls into the desired range.

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The total cost of Mimi's haircut and perm, including the 15% tip, is $46.10.

The amount of the tip must be calculated and added to the base price.

The $40.09 original cost of the haircut and perm can be multiplied by the tip percentage to determine the amount of the tip:

Tip = 15% * $40.09

= (15/100) * $40.09

= $6.01

Now we can find the total cost by adding the initial cost and the tip amount:

Total cost = Initial cost + Tip

= $40.09 + $6.01

= $46.10

So, the total cost of Mimi's haircut and perm, including the 15% tip, is $46.10.

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The equation that best compares the y-intercepts of f(x) and g(x) is:

f(y-intercept) < g(y-intercept)

To compare the y-intercepts of the functions f(x) and g(x), we need to examine the values of the functions when x is equal to zero.

From the given table, we can see that when x is equal to zero:

f(0) = -2[tex](1.07)^0[/tex] = -2(1) = -2

g(0) = -4

So, the y-intercept of f(x) is -2, and the y-intercept of g(x) is -4.

To compare the y-intercepts, we can write the equation as:

f(y-intercept) < g(y-intercept)

Plugging in the values:

-2 < -4

This inequality is true, indicating that the y-intercept of f(x) is less than the y-intercept of g(x).

Therefore, the equation that best compares the y-intercepts of f(x) and g(x) is:

f(y-intercept) < g(y-intercept)

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The correct answer is:

Becca should have multiplied the dividend and the divisor by 10 and moved the decimal point in the quotient to the right.

In order to divide decimals, both the dividend and the divisor should be adjusted so that there are no decimal places in the divisor. Becca's mistake was not considering this adjustment.

To correctly divide 1.8 by 0.3, Becca should have multiplied both the dividend (1.8) and the divisor (0.3) by 10 to eliminate the decimal places. This would result in the problem becoming 18 ÷ 3.

Performing the division correctly, we find that 18 ÷ 3 equals 6, with no remainder.

Therefore, Becca's mistake was not adjusting the dividend and the divisor by multiplying both by 10.

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We calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).= 0.25%. ( fictional )

To calculate the average change in the inflation rate, we require the inflation rates for each of the five years, including 2021. Let's assume the inflation rates for the five years are: 2.5%, 3.2%, 2.8%, 4.1%, and 3.9%.

To find the change in inflation rate for each consecutive year, we subtract the inflation rate of the previous year from the inflation rate of the current year. For example, the change in inflation rate from 2020 to 2021 would be 3.2% - 2.5% = 0.7%.

Next, we calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).

Finally, we divide the sum by the number of years (five in this case) to find the average change in the inflation rate over the five-year period. After rounding the result to two decimal places, we will have the desired average change in the inflation rate.

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the radius of the spherical balloon is 8.53 cm.

The volume of a sphere of radius r is given by the formula (4/3)πr³ cm³.

Given that the volume of the spherical balloon is 950 cm³, we have:(4/3)πr³ = 950 cm³

Dividing both sides of the equation by (4/3)π, we get:r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5

Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)

Given that the volume of the spherical balloon is 950 cm³, we need to find the radius of the balloon.

To do this, we will use the formula for the volume of a sphere, which is given by (4/3)πr³ cm³, where r is the radius of the sphere. Using this formula, we can write:

4/3)πr³ = 950 cm³

Dividing both sides of the equation by (4/3)π, we get:

r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)

Hence, the radius of the spherical balloon is 8.53 cm.

The radius of a spherical balloon was to be calculated based on the given volume of the balloon. The formula for the volume of a sphere was used which is (4/3)πr³.

On substituting the given volume and simplifying the obtained equation, we get the value of the radius of the spherical balloon. The final answer for the radius of the balloon was calculated to be 8.53 cm.

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A sphere has a radius of 1. 5 inches. What is the volume of the sphere rounded to the nearest tenth, The volume of the sphere with a radius of 1.5 inches is approximately 14.1 cubic inches.

To calculate the volume of a sphere, we use the formula: V = (4/3) * π * r^3

Given that the radius (r) is 1.5 inches and π is 3.14, we substitute these values into the formula:

V = (4/3) * 3.14 * (1.5)^3

V = (4/3) * 3.14 * 3.375

V ≈ 14.1375

Rounding to the nearest tenth, the volume of the sphere is approximately 14.1 cubic inches.

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In a 30-60-90 triangle, the ratio of the side lengths is as follows:

The length of the shorter leg is x.

The length of the longer leg (opposite the 60-degree angle) is x√3.

The length of the hypotenuse is 2x.

Given that the hypotenuse is 16, we can set up the equation:

2x = 16

Dividing both sides of the equation by 2:

x = 8

Therefore, the length of the shorter leg is 8.

To find the length of the longer leg (opposite the 60-degree angle), we can multiply the length of the shorter leg by √3:

Longer leg = x√3 = 8√3

So, the length of the longer leg is 8√3.

In summary, in a 30-60-90 triangle with a hypotenuse of 16, the shorter leg is 8 and the longer leg (opposite the 60-degree angle) is 8√3.

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lemonade accounts for 20% of the recipe.

We have,

To find the percentage of the recipe that is lemonade, we can calculate the ratio of lemonade concentrate to the total recipe and then convert it to a percentage.

The ratio of lemonade concentrate to the total recipe is:

= 6 cups / 30 cups

= 0.2.

To convert this ratio to a percentage, we multiply it by 100.

= 0.2 x 100

= 20%.

Therefore,

lemonade accounts for 20% of the recipe.

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Answer: 4,322.883

Step-by-step explanation:

Assuming that the interest rate is per year:

4,322.883

At 4 : 30 Sami arrive at the library.

We have,

Sami leave his house at 3:45 PM and walks to Karla's house in 15 minutes he stays at Karla's house for five minutes and then walks to the library in 10 minutes.

Since, Sami leave his house at 3:45 PM and walks to Karla's house in 15 minutes.

Hence, Time to reach at Karla's house is,

3:45 + 15 minutes

4 : 15

Since, he stays at Karla's house for five minutes and then walks to the library in 10 minutes.

Hence, Time when Sami arrive at the library is,

4 : 15 + 5 minutes + 10 minutes

4 : 30

Therefore, At 4 : 30 Sami arrive at the library.

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The length of XW in coordinate units is [tex]\sqrt{34}[/tex] units.

Given that X (4,1), Y(7,1) and Z(4,6) are the coordinates of a rectangle XYZW in the standard (x,y) coordinate plane.

We need to find the length, in coordinate units, of XW.

Since XZ is perpendicular to XY and XZ and XY are sides of rectangle XYZW, lets use the Pythagorean Theorem to find the length of XW. The length of XZ can be calculated by finding the distance between the coordinates of X and Z.

Using the distance formula, we have;

[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex] = [tex]\sqrt{(4 - 4)^2 + (6 - 1)^2}[/tex][tex]\sqrt{(0)^2 + (5)^2}[/tex][tex]\sqrt{25}[/tex] = 5 units

The length of XY is calculated by finding the distance between the coordinates of X and Y.

Using the distance formula, we have;

[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex] = [tex]\sqrt{(7 - 4)^2 + (1 - 1)^2}[/tex][tex]\sqrt{(3)^2 + (0)^2}[/tex][tex]\sqrt{9}[/tex] = 3 units

Therefore, the length of XW can be calculated as follows:

XW = [tex]\sqrt{(XZ)^2 + (XY)^2}[/tex]XW = [tex]\sqrt{(5)^2 + (3)^2}[/tex]XW = [tex]\sqrt{34}[/tex] units

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The solution to the inequality 2a + 4 > 12, where a is greater than 2, 4, 8, and 10, is a > 4.

We start with the inequality 2a + 4 > 12 and simplify it by subtracting 4 from both sides: 2a > 8. Next, we divide both sides by 2 to isolate the variable a, giving us a > 4.

Now, let's consider the given conditions: a > 2, a > 4, a > 8, and a > 10. Among these conditions, the strongest restriction is a > 4. When we combine all the conditions, the common range for a that satisfies all the conditions is a > 4.

Therefore, the solution to the inequality 2a + 4 > 12, with the additional conditions a > 2, a > 4, a > 8, and a > 10, is a > 4.

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Degree: 8, Leading coefficient: 1, End behavior: The polynomial increases without bound as x approaches both positive and negative infinity.

To find the degree, leading coefficient, and end behavior of the polynomial (x-5)(x-3)^6(x+5)^8, let's first expand the polynomial:

(x-5)(x-3)^6(x+5)^8 = (x^1-5)(x^6-3^6)(x^8+5^8)

Simplifying further, we have:

= (x-5)(x^6-729)(x^8+390625)

Now, we can determine the degree, leading coefficient, and end behavior:

Degree:

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power occurs in the term (x^8), so the degree of the polynomial is 8.

Leading coefficient:

The leading coefficient is the coefficient of the term with the highest power. In this case, the coefficient of the term (x^8) is 1, so the leading coefficient is 1.

End behavior:

To determine the end behavior of the polynomial, we examine the behavior of the polynomial as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the term (x^8) dominates the polynomial since it has the highest power. Since the coefficient of (x^8) is positive (1), the end behavior of the polynomial as x approaches positive infinity is that the polynomial increases without bound.

As x approaches negative infinity, again the term (x^8) dominates the polynomial. However, since the exponent is even, the value of (x^8) will always be positive, regardless of the sign of x. Thus, the end behavior of the polynomial as x approaches negative infinity is that the polynomial also increases without bound.

In summary:

Degree: 8

Leading coefficient: 1

End behavior: The polynomial increases without bound as x approaches both positive and negative infinity.

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To find the area of the region formed by the given coordinates, we can use the method of Shoelace Formula or Gauss's Area formula. The area of the polygon formed by the given coordinates is 25 square units

1. Plot the given coordinates: (1,2), (1,7), (9,7), (9,3), (6,5). These points represent the vertices of the polygon.

2. Connect the plotted points in order to form the polygon.

3. Use the Shoelace Formula or Gauss's Area formula to calculate the area of the polygon. The Shoelace Formula involves multiplying the differences of the x-coordinates with the corresponding y-coordinates and summing them up.

4. Apply the Shoelace Formula:

  Area = 1/2 * |(1*7 + 1*7 + 9*3 + 9*2 + 6*7) - (2*1 + 7*9 + 7*9 + 3*6 + 5*1)|

       = 1/2 * |(7 + 7 + 27 + 18 + 42) - (2 + 63 + 63 + 18 + 5)|

       = 1/2 * |101 - 151|

       = 1/2 * |-50|

       = 25

Therefore, the area of the polygon formed by the given coordinates is 25 square units.


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Among the given numbers (46, 53, 89, 21, 48, 47, and 32), two numbers differ by 43 units.

To find the two numbers that differ by 43, we can compare each pair of numbers and check if their difference is equal to 43.

Pair-wise differences:

46 - 53 = -7

46 - 89 = -43

46 - 21 = 25

46 - 48 = -2

46 - 47 = -1

46 - 32 = 14

53 - 89 = -36

53 - 21 = 32

53 - 48 = 5

53 - 47 = 6

53 - 32 = 21

89 - 21 = 68

89 - 48 = 41

89 - 47 = 42

89 - 32 = 57

21 - 48 = -27

21 - 47 = -26

21 - 32 = -11

48 - 47 = 1

48 - 32 = 16

47 - 32 = 15

From the calculations, we can see that the numbers 46 and 89 differ by 43 units. Therefore, among the given numbers, 46 and 89 are the two numbers that differ by 43.

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The correct equation to find the number of tea bags Sarah has is D. t + 39 + 22 = 87. The total number of tea bags they have altogether (87).

In the equation D. t + 39 + 22 = 87, t represents the number of tea bags Sarah has. We add the quantities of tea bags her mom and sister have, which are 39 and 22, respectively. The sum of these three quantities should equal the total number of tea bags they have in total, which is given as 87.

To solve the equation, we can simplify it by adding 39 and 22: t + 61 = 87. Next, we can isolate t by subtracting 61 from both sides of the equation: t = 87 - 61. Simplifying further, we find that t = 26. Therefore, Sarah has 26 tea bags.

In conclusion, Sarah has 26 tea bags based on the given information and the equation t + 39 + 22 = 87.

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The sampling distribution of the sample minimum would show the possible values of the minimum age that can be obtained when randomly selecting two family members from a particular family consisting of individuals aged 2, 4, 6, 30, and 32.

To understand the sampling distribution of the sample minimum, we consider all possible combinations of two family members that can be selected from the given family of 5 individuals. These combinations include (2,4), (2,6), (2,30), (2,32), (4,6), (4,30), (4,32), (6,30), (6,32), (30,32).

The minimum age in each of these combinations is calculated, resulting in the following set of possible sample minimum ages: 2, 2, 2, 2, 4, 4, 4, 6, 6, 30.

The sampling distribution of the sample minimum represents the frequencies or probabilities associated with each possible value of the sample minimum age. In this case, the distribution would show that the sample minimum age of 2 has the highest frequency or probability, occurring four times, while the sample minimum ages of 4, 6, and 30 occur three times each.

By examining the sampling distribution, we can gain insights into the range and likelihood of obtaining different sample minimum ages when randomly selecting two family members from the given family.

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Therefore, the required simple interest rate is approximately 3.8%.

To find the required simple interest rate, we can use the formula:

Simple Interest = Principal * Interest Rate * Time

We know the principal (P) is $4790, the final amount (A) is $6500, and the time (T) is 9 years. We need to find the interest rate (R).

First, let's calculate the interest (I):

I = A - P = $6500 - $4790 = $1710

Now we can substitute the values into the formula and solve for the interest rate:

I = P * R * T

$1710 = $4790 * R * 9

Dividing both sides by ($4790 * 9):

R = $1710 / ($4790 * 9) ≈ 0.038 (rounded to three decimal places)

To convert this to a percentage, we multiply by 100:

R ≈ 0.038 * 100 ≈ 3.8

Therefore, the required simple interest rate is approximately 3.8%.

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The scenario in which an athlete cuts the time it takes to complete a 10K race by 5% each week represents an exponential function.

An exponential function is a mathematical function in which the independent variable is an exponent. It is characterized by a constant ratio between successive values.

In the given scenarios, the first two options involve a fixed amount or average (monthly rent payments or number of patrons per hour) and do not demonstrate exponential growth or decay. These scenarios can be represented by linear functions.

The third option, where an athlete cuts the time it takes to complete a 10K race by 5% each week, represents exponential decay. The time reduction each week can be expressed as a percentage of the previous week's time, resulting in a constant ratio between successive time values. This is a characteristic of exponential functions.

The fourth option describes the volume of a cube, which is calculated by raising the length of the side to the third power. This is an example of a polynomial function, specifically a cubic function, rather than an exponential function.

Therefore, the scenario in which an athlete cuts the time it takes to complete a 10K race by 5% each week represents an exponential function.

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The solution is that Kenny ordered 35 premium guitar strings and 45 standard guitar strings, which is a total of 80 guitar strings.

Kenny ordered guitar strings for Glenn’s Guitar Shop. The premium guitar strings are $4.50 apiece. The standard guitar strings are $1.50 apiece. The bill smeared in the rain, but Kenny knows he ordered a total of 80 strings for $225. Kenny wants to solve for the number of each type of string, so he represents variables as shown.Let x represent the number of premium guitar strings and y represent the number of standard guitar strings. Since a total of 80 strings were ordered, then x + y

= 80.

Since the premium guitar strings cost $4.50 apiece, then the cost of x premium guitar strings is 4.5x. Since the standard guitar strings cost $1.50 apiece, then the cost of y standard guitar strings is 1.5y. Since the total cost was $225, then we can set up the equation

4.5x + 1.5y

= 225.

Substituting

x + y

= 80

into the equation

4.5x + 1.5y

= 225

, we have:

4.5x + 1.5(80 - x)

= 225

Simplifying the expression above, we get

:4.5x + 120 - 1.5x

= 2253x + 120

= 2253x = 225 - 1203x

= 105x

= 35

Therefore, the number of premium guitar strings is 35, and the number of standard guitar strings is

80 - 35

= 45

. The solution is that Kenny ordered 35 premium guitar strings and 45 standard guitar strings, which is a total of 80 guitar strings.

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To receive a free T-shirt at the clothing store, Lyndon needs to spend $75 or more. He has already spent $36.95. The statement that best represents all the amounts he can spend to get a free T-shirt is:

Lyndon can spend any amount that, when added to $36.95, results in a total of $75 or more.

This means that Lyndon can spend any amount greater than or equal to $75 - $36.95, which is approximately $38.05. In other words, he needs to spend at least $38.05 to reach the minimum requirement for a free T-shirt. Any amount above this minimum threshold will also qualify him for a free T-shirt.

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The total amount of money in her account at the end of 3 years is, $80.7

We have,

Lesly deposits $65 into a new savings account. The account earns 7. 5% interest per year.

We can use the formula,

For final amount,

A = P (1 + r%)ⁿ

Here, P = 65

r = 7.5% = 0.075

n = 3

Substitute all the values,

A = 65 (1 + 0.075)³

A = 65 (1.075)³

A = 65 × 1.24

A = $80.7

Therefore, The total amount of money in her account at the end of 3 years is, $80.7

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