Estimate 17.154+5.46 by rounding each number to the nearest tenth

We can write 2 equations from the information given.

Let the amount invested in CD be "x" and the amount invested in bond be "y".

The total amount invested is $600,000. Thus, we can write,

The CD pays 2% (0.02) and the bond pays 8.5% (0.085). Total interest needed is $27,000. Thus, we can craft another equation,

Solving the first equation for "x", we can substitute it into the second equation and solve for "y" first. The steps are shown below:

Now, we can find "x",

Rounded to the nearest dollar, we write our answer >>>

x+2x+x=d is solution set of a linear system whose augmented matrix.

What does matrix mean?

First statement

[ 1 2 3 | d][x]

[ 1 2 3]x=d

x+2x+3x=d

Second statement

Ax=d

Given that A = [ 1 2 3]

[ 1 2 3]x=d

x+2x+3x=d

x+2x+x=d

Then, they are going to have the same solution

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Answer:

C. 40%

Step-by-step explanation:

8 - black

12 - red

total: 20

8/20 = 40%

Therefore, The density of air enclosed in a sphere with a radius halved will be 9.6 kg/m3. This is because the volume reduces by a factor of 8, resulting in an increase in density by a factor of 8.

When the radius of the sphere is halved, the volume of the sphere reduces by a factor of 8. Since the mass of the air enclosed remains constant, the density of the air within the sphere will increase by a factor of 8. Therefore, the density of the air within the sphere will be 9.6 kg/m3 after compression.
The density of the air enclosed within a sphere is given as 1.2 kg/m3. When the radius of the sphere is halved, the volume of the sphere reduces by a factor of 8 (since volume is proportional to the cube of radius). However, the mass of the air enclosed remains constant. Therefore, the density of the air within the sphere will increase by a factor of 8, resulting in a new density of 9.6 kg/m3.


Therefore, The density of air enclosed in a sphere with a radius halved will be 9.6 kg/m3. This is because the volume reduces by a factor of 8, resulting in an increase in density by a factor of 8.

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To graph the equation y= −4/5x on the coordinate plane, we can plot two points that satisfy the equation and then draw a straight line through those points. For example, we could choose the points (-1, 4/5) and (2, -8/5), which both satisfy the equation. To plot these points, we first locate the point (-1, 4/5) on the coordinate plane. This point is 1 unit to the left of the y-axis, and 4/5 units above the x-axis. We can then draw a straight line through this point and the point (2, -8/5), which is 2 units to the right of the y-axis and 8/5 units below the x-axis. This line will be the graph of the equation y= −4/5x.

Here is a visual representation of the process:

 (0,0)

  |

  |

  |

  |     (2, -8/5)

  |     *

  |

  |     (1, 4/5)

  |     *

  |

  |

  |

  |

  +-----------------------------------> (x, y)

Answer:

a. 120 degrees

b. 2.0944 radians

Step-by-step explanation:

From 12:00 to 12:15 there forms a 90 degree angle. If we divide this by 3 we get that every 5 minutes the hand moves 30 degrees. Since in this scenario, the minute hand moved from 12:10 to 12:30 it, therefore, moved a total of 20 minutes so we can do the following math

20 / 5min = 4 times

4 * 30 degrees = 120 degrees

We can see that in this time it moved a total of 120 degrees. Now we can use this value to turn it into radians using the degree to radians formula

degrees * \(\pi /180\) = radians

120 * \(\pi / 180\) = radians

2.0944 = radians

Answer:

The statement that best describes how to determine if the plane clears the tower is;

Use the Pythagoras Theorem where the distance to the tower is a leg of the right triangle and the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height

Step-by-step explanation:

The given parameters are;

The length the plane will travel before lifting = 1300 yards

The distance further the plane will travel after lifting off the ground = 705 yards

The horizontal distance from the point of lifting off the ground to control tower = 700 yards

The distance of the path of the plane after lifting off the ground, the horizontal distance from the point of lifting off the ground to control tower and the height of the control tower form a right triangle with sides given as follows;

The distance of the path of the plane after lifting off the ground = The hypotenuse side of the triangle

The horizontal distance from the point of lifting off the ground to control tower and the height of the control tower = The two legs of the right triangle

Let h, represent the height of the control tower, let x represent the horizontal distance from the point of lifting off the ground to control tower and let R represent the distance of the path of the plane after lifting off the ground, we have;

h = √(R² - x²)

We have;

R = 705 yards

x = 700 yards

∴ h = √(R² - x²) = h = √(705² - 700²) = 5·√281

The height of the control tower, h = 5·√281 yards

1 yard = 3 feet

∴ 5·√281 yards = 3 × 5·√281 feet ≈ 251.446 feet

Therefore, given that the height of the control tower = 250 feet, the plane at the height of approximately 251.446 feet clears the tower.

The height of the control tower = 250 feet and the plane  the height of approximately 251.446 feet clears the tower.

The statement that best describes how to determine if the plane clears the tower is;

Use the Pythagoras Theorem where the distance to the tower is a leg of the right triangle and the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height

The given parameters are;

The length the plane will travel before lifting = 1300 yards

The distance further the plane will travel after lifting off the ground = 705 yards.

The horizontal distance from the point of lifting off the ground to control tower = 700 yards

The distance of the path of the plane after lifting off the ground, the horizontal distance from the point of lifting off the ground to control tower and the height of the control tower form a right triangle with sides given as follows.

The distance of the path of the plane after lifting off the ground = The hypotenuse side of the triangle.

The horizontal distance from the point of lifting off the ground to control tower and the height of the control tower = The two legs of the right triangle.

Let h, represent the height of the control tower, let x represent the horizontal distance from the point of lifting off the ground to control tower and let R represent the distance of the path of the plane after lifting off the ground, we have;

\(h = \sqrt{(R^2 - x^2)}\)

We have given that

R = 705 yards

x = 700 yards

\(h = \sqrt{(R^2 - x^2)} \\ h = \sqrt{(705^2 - 700^2)}\\ h= 5\times \sqrt {281}\)

The height of the control tower,\(h = 5 \sqrt {281}\) yards.

1 yard = 3 feet

\(5\sqrt {281} yards= 3 \times 5\times \sqrt{281} feet \approx 251.446 feet\)

Therefore, given that the height of the control tower = 250 feet, the plane at the height of approximately 251.446 feet clears the tower.

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The most general antiderivative of the given function is (8/5)x^5 - (3/2)ln|x^4 - 3| + C.

To find the most general antiderivative of the function f(x) = 8x^4 - 6/(x^4 - 3), we can use the following steps:

Step 1: Rewrite the function f(x) as a sum of simpler functions. Here, we can split the given function into two parts:

f(x) = 8x^4 - 6/(x^4 - 3)

= 8x^4 - 6(x^4 - 3)^(-1)

Step 2: Find the antiderivative of each part separately.

The antiderivative of 8x^4 is (8/5)x^5 + C, where C is a constant of integration.

To find the antiderivative of 6(x^4 - 3)^(-1), we can use the substitution u = x^4 - 3, which gives du/dx = 4x^3 and dx = (1/4x^3)du. Substituting these values, we get:

∫6(x^4 - 3)^(-1)dx = 6 ∫(x^4 - 3)^(-1)dx

= 6 ∫u^(-1) (1/4x^3)du

= (3/2)ln|x^4 - 3| + C

where ln denotes the natural logarithm.

Step 3: Combine the antiderivatives and simplify.

The most general antiderivative of the function f(x) is thus:

∫f(x)dx = ∫[8x^4 - 6/(x^4 - 3)]dx

= (8/5)x^5 - (3/2)ln|x^4 - 3| + C

where C is a constant of integration.

Therefore, the most general antiderivative of the given function is (8/5)x^5 - (3/2)ln|x^4 - 3| + C.

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Answer:

the possible combinations of $5 and $10 gift cards your club can purchase are :

eight $5 gift cards and twelve $10 gift cards

nine $5 gift cards and eleven $10 gift cards

or ten each of $5 gift cards and $10 gift cards

Step-by-step explanation:

From the information given:

You plan to buy a combination of $5 and $10 gift cards

You plan to buy exactly 20 gift cards and want to spend between $150 and $160.

The objective is to determine the possible combinations of $5 and $10 gift cards your club can purchase?

Let assume the g is the number of the $5 gift cards bought;

then (20 - g) will be the number of the $10 gift card bought.

Thus; the compound inequality for the amount spent between $150 and $160 will be:

= 150 ≤ 5g + 10(20 - g) ≤ 160

=  150 ≤ 5g + 200 - 10g ≤ 160

= 150 ≤ 5g -10 g + 200 ≤ 160

= 150 ≤ -5g + 200 ≤ 160

= 150-200 ≤ -5g ≤ 160 -200

= -50  ≤ -5g ≤ -40

Divide through by -5

= 10 ≥ g ≥ 8

= 8 ≤ g ≤ 10

Thus; the possible combinations of $5 and $10 gift cards your club can purchase are :

eight $5 gift cards and twelve $10 gift cards  = i.e 8 ×$5 + 12 ×$10

= $40+$120

=$160

nine $5 gift cards and eleven $10 gift cards

 =  9 ×$5 + 11 ×$10

= $45 + $110

= $155

or ten each of $5 gift cards and $10 gift cards

=  10 ×$5 + 10 ×$10

= $50 + $100

= $150

These combinations falls in between the range of $150 and $160.

Answer:

74

Step-by-step explanation:

The step 3 follow the subtraction property of equality.

Given,

The Equation is : 1/4 (12x + 8) + 4 = 3

There is some steps:

Step                          Solution

   1                          3x + 2 + 4 = 3

   2                           3x + 6 = 3

   3                              3x = -3

   4                                 x = -1

To find the which step shows the result of applying the subtraction property of equality?

Now, According to the given steps:

From the table, we can know

From Step 2: 3x + 6 = 3

 Subtract 6 on both sides

3x + 6 - 6 = 3 - 6

3x = -3

Hence, The step 3 follow the subtraction property of equality.

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The Angle ∠MTU from the figure is 65°

The study of shapes and their measurements falls under the umbrella of geometry, a subfield of mathematics. It also emphasizes how the shapes are arranged in relation to one another and their spatial characteristics. We are aware that geometry is divided into 2D and 3D categories. All geometrical shapes are first created by the intersection of points, lines, rays, and plane surfaces. The distance measured between two lines is referred to as a "Angle" when the rays or lines converge at a single point.

Given,

∠STM=31X-3;

∠MTU=20X+5;

∠STU=155°;

From the figure we can say that

∠STU= ∠STM+∠MTU;

⇒ 155=31x-3+20x+5;

⇒155=51x+2;

⇒x=3;

Now substitute x in ∠MTU;

⇒∠MTU=20(3)+5=65°

The Angle ∠MTU from the figure is 65°

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Answer: green

Step-by-step explanation:

Answer:

yellow and blue what ? and whyyy

Answer: this is

1 3/10= 1.3

Answer:

Step-by-step explanation:

The property of 30°-60°-90° :

The side opposite the 30° angle is the shortest and the length of it is equal to half of the length of the hypotinuse.

Answer:-2

Step-by-step explanation: hope this helps!!

Answer:

-2

Step-by-step explanation:

5x + 2x -8 = 5x + x - 10

2x - x = 8-10

x = -2

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer:

Slope is -2

The Y-intercept is (3,0)

The equation Is y=-2(x-3)

Step-by-step explanation:

Don't use my answer right away but when someone else answers you can compare to figure out which one is right.

Answer: The slope is 1/2.

The y-intercept is point (0,3)

The equation of the line in slope-intercept form is y = 1/2x + 3.

The solution to the initial-value problem x(x + 1) dy/dx + xy = 1, y(e) = 1 is y = ln(x + 1) / x.

To solve the given initial-value problem, we can use the method of integrating factors. Rearranging the equation, we have dy/dx + (xy / (x(x + 1))) = 1 / (x(x + 1)).

The integrating factor is given by μ(x) = exp ∫ (xy / (x(x + 1))) dx. Simplifying the integral, we have μ(x) = exp ∫ (1 / (x + 1)) dx = exp(ln(x + 1)) = x + 1.

Multiplying the entire equation by the integrating factor, we obtain (x + 1)dy/dx + xy = (x + 1) / (x(x + 1)).

The left side of the equation can be written as d((x + 1)y)/dx. Integrating both sides with respect to x, we have ∫ d((x + 1)y)/dx dx = ∫ (x + 1) / (x(x + 1)) dx.

Simplifying the right side of the equation, we get ∫ dx / x = ln|x| + C.

Dividing both sides by (x + 1), we have (x + 1)y = ln|x| + C.

Finally, solving for y, we find y = (ln|x| + C) / (x + 1). Using the initial condition y(e) = 1, we can substitute x = e and solve for C to obtain the specific solution y = ln(x + 1) / x.

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Answer:

The answer is 11.1

Step-by-step explanation:

First you need to figure out what all of the possible combinations of the two dice being thrown then divide it by the number of faces on both dice and you get your probability.

Answer: what is ur questions?

Step-by-step explanation:

Answer:

I think it's just about everyone

Answer:

X=2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

you take 7 - 4x = - 1 and you add -1 to 7 to cancel it out.

so you're left with  8 - 4x.

you take 4x and divide it by itself and 8. 4x divided by 4x cancels out and you are left with 8 divided by 4x.

this equals 2.

Answer:

NM=5, NL=4.3

Step-by-step explanation:

a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

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The score assigned by the logistic regression classifier to the positive class is 8.

In logistic regression, the score assigned to a class is calculated by taking the dot product of the weight vector and the feature vector, and adding the bias term. Here, the weight vector is [2, 5, -10, 0, -1], the feature vector is [0, 1, 1, 3, -5], and the bias term is 0.

To calculate the score for the positive class, we multiply each corresponding element of the weight vector and feature vector, and sum up the results.

(2 * 0) + (5 * 1) + (-10 * 1) + (0 * 3) + (-1 * -5) + 0 = 8

Therefore, the score assigned by the classifier to the positive class is 8.

The cross-entropy loss is a measure of how well the classifier is performing. It quantifies the difference between the predicted class probabilities and the true class labels. In logistic regression, the cross-entropy loss is given by the formula:

-1 * (y_true * log(y_pred) + (1 - y_true) * log(1 - y_pred))

Where y_true is the true label (0 for NEG and 1 for POS) and y_pred is the predicted probability for the positive class.

If the correct label for the example is POS, the cross-entropy loss would be calculated using y_true = 1 and y_pred = sigmoid(score). In this case, the score is 8, and the sigmoid function squashes the score between 0 and 1.

If we assume the correct label is NEG, then the cross-entropy loss would be calculated using y_true = 0 and y_pred = sigmoid(score).

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Answer:

A - True
B - False
C - True

Step-by-step explanation:

A:
Parallel lines never intersect each other because in order for them to be classified as parallel, they must have the same slope, which will never cross over each other at any point; True
B:
A transversal does intersect two or more parallel lines, but crossing two parallel lines at three distinct points is not possible; False
C:
Perpendicular distance between parallel lines is always the same because they have the same slope and therefore are always the same distance away from each other; True

Answer:

--------------------------------

Recall properties of special right triangles.

45° right triangle has side ratios: 1 : 1 : √2.

It gives us:

30°×60° right triangle has side ratios: 1 : √3 : 2.

It gives us: