Jane just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Jane works out that's 62 hats for each hospital. Does that sound about right?

Answer:

Step-by-step explanation:

Of course! I'd be happy to help you.

Let's simplify the expression f(x) + 8x - 8x^3 - x^4 + 6 step by step:

The given expression is: f(x) + 8x - 8x^3 - x^4 + 6

Since we don't have any specific information about f(x), we'll assume that f(x) is a constant or a function that doesn't depend on x. In that case, f(x) can be treated as a constant term.

Combining like terms, we have:

f(x) - x^4 - 8x^3 + 8x + 6

There is no further simplification we can do without additional information about the function f(x) or any specific values of x. Therefore, the simplified expression is:

f(x) - x^4 - 8x^3 + 8x + 6

1. The difference of two supplementary angles is 70° which is the larger angle?

A/ 135°

B/145

C/55

Answer:

B)  There are two solutions, but only one is viable.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}A=w^2+4w\\A=4w+45\end{cases}[/tex]

To solve the system of equations, substitute the first equation into the second equation:

[tex]w^2+4w=4w+45[/tex]

Solve for w using algebraic operations:

[tex]\begin{aligned}w^2+4w&=4w+45\\w^2+4w-4w&=4w+45-4w\\w^2&=45\\\sqrt{w^2}&=\sqrt{45}\\w&=\pm \sqrt{45}\\w &\approx \pm 6.71\; \sf cm\end{aligned}[/tex]

Therefore, there are two solutions to the given system of equations.

However, as length cannot be negative, the only viable solution is w ≈ 6.71 cm.

The cost per trainee for the 5-week training course is $7,000.

To find the cost per trainee, we divide the total cost of the training course by the number of trainees.

Total cost of the training course = $140,000

Number of trainees = 20

Cost per trainee = Total cost of the training course / Number of trainees

Cost per trainee = $140,000 / 20

Cost per trainee = $7,000

Therefore, the cost per trainee for the 5-week training course is $7,000.

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The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

To form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.

The given equation is: y + 4x - 1 = 0

To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.

Let's multiply the given equation by 2:

2(y + 4x - 1) = 2(0)

2y + 8x - 2 = 0

The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.

Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

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Answer:

(fg)(x) = x^4 - x^3 + 15x^2 - 6x + 54

Step-by-step explanation:

We want to multiply and simplify as much as possible:

f(x) * g(x)

(x^2 + 6)(x^2 - x + 9)

(x^2 * x^2) + (x^2 * - x) + (x^2 * 9) + (6 * x^2) + (6 * - x) + (6 * 9)

Note that when you're multiplying exponents, we add them:

x^4 + - x^3 + 9x^2 + 6x^2 - 6x + 54

Now we add 9x^2 and 6x^2 as they are like terms:

x^4 - x^3 + 15x^2 - 6x + 54

Thus, (fg)(x) simplified is x^4 - x^3 + 15x^2 - 6x + 54.

Optional:  Check the validity of the answer:

We can check that our answer is correct by plugging in a number for x in both the unsimplified and simplified expression and seeing if we get the same answer.  Let's try 5:

Plugging in 5 for x in (x^2 + 6)(x^2 - x + 9):

(5^2 + 6)(5^2 - 5 + 9)

(25 + 6)(25 - 5 + 9)

(31)(20 + 9)

(31)(29)

899

Plugging in 5 for x in x^4 - x^3 + 15x^2 - 6x + 54:

5^4 - (5)^3 + 15(5)^2 - 6(5) + 54

625 - 125 + 15(25) - 30 + 54

625 - 125 + 375 - 30 + 54

500 + 375 - 30 + 54

875 - 30 + 54

845 + 54

899

Thus, our answer is correct.

Answer:

Step-by-step explanation:

To solve the equation (2/3)t - (1/5)t = 2 for t, we need to combine like terms and isolate the variable t. Here are the steps:

(2/3)t - (1/5)t = 2

To combine the fractions, we need to find a common denominator for 3 and 5, which is 15.

[(2/3)(5/5)]t - [(1/5)(3/3)]t = 2

(10/15)t - (3/15)t = 2

[(10 - 3)/15]t = 2

(7/15)t = 2

To isolate t, we can multiply both sides of the equation by the reciprocal of (7/15), which is (15/7).

[(7/15)t][(15/7)] = 2[(15/7)]

t = (2 * 15) / 7

t = 30/7

Therefore, the solution for t in the equation (2/3)t - (1/5)t = 2 is t = 30/7 or t ≈ 4.286.

The transformation that moves the shape is (a) translation

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

The figure

Where, we have:

This means that the only transformation is translation

So, the transformation is (a) translation

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Answer:

Step-by-step explanation:

a. sin(0) = 0

The sine of 0 degrees is 0.

b. tan(N) = 6√5

We don't have enough information to determine the value of tan(N) without knowing the specific value of N.

c. cos(0) = 1

The cosine of 0 degrees is 1.

d. cos(N) = 6√5/6

Again, we can't determine the specific value of cos(N) without knowing the value of N.

For accelerated motion, changes in distance compare with equal changes in velocity as follows:

B. Distance increases faster than time.

A reason why a person will not compute a slope for the accelerated motion graph is that it graphed as a straight line.

Accelerated motion is a form of motion in which the motion is not equal and the object moving does not complete the same distances in the same intervals of time.

The graph formed in the case of an accelerated motion is not a straight line. So, a reason why a person would not compute a slope for the accelerated motion is that it graphed as a straight line.

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The perimeter of the rectangle is 140 inches.

Let's denote the width of the rectangle as w. According to the given information, the length of the rectangle is six times its width, so we can express the length as 6w.

The area of a rectangle is given by the formula A = length × width. Substituting the values we have:

A = (6w) × w

600 = 6w^2

To solve for w, we divide both sides of the equation by 6:

w^2 = 100

Taking the square root of both sides:

w = ±10

Since width cannot be negative in this context, we discard the negative value and consider the positive value, w = 10.

Now that we have the width, we can find the length of the rectangle:

Length = 6w = 6 × 10 = 60

The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values:

P = 2(60 + 10)

P = 2(70)

P = 140

Therefore, the perimeter of the rectangle is 140 inches.

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Answer: O (4, -4)

Step-by-step explanation:

To solve the system of equations using elimination, we can multiply the second equation by -3 to eliminate the y term:

Original equations:

5x + 3y = 8 (Equation 1)

4x + y = 12 (Equation 2)

Multiply Equation 2 by -3:

-3(4x + y) = -3(12)

-12x - 3y = -36 (Equation 3)

Now we can add Equation 1 and Equation 3 to eliminate the y term:

(5x + 3y) + (-12x - 3y) = 8 + (-36)

Simplifying:

5x - 12x + 3y - 3y = 8 - 36

-7x = -28

Divide both sides by -7:

x = -28 / -7

x = 4

Now substitute the value of x back into either of the original equations, let's use Equation 2:

4(4) + y = 12

16 + y = 12

y = 12 - 16

y = -4

Therefore, the solution to the system of equations is x = 4 and y = -4.

The vertex and the x-intercepts of the quadratic equation are:

The vertex is (-1, -4)

The x-intercepts are -3 and 1.

To express the quadratic equation [tex]y = x^2 + 2x - 3[/tex]in vertex and intercept form, we need to complete the square to find the vertex and rewrite the equation in terms of the x-intercepts.

First, let's complete the square to find the vertex. We can do this by taking half the coefficient of x, squaring it, and adding/subtracting it to both sides of the equation:

[tex]y = x^2 + 2x - 3\\y = (x^2 + 2x + 1) - 1 - 3\\y = (x + 1)^2 - 4[/tex]

Now we have the equation in the form [tex]y = a(x - h)^2 + k[/tex], where the vertex is at the point (-h, k). The vertex is (-1, -4).

Next, let's find the x-intercepts by setting y = 0:

[tex]0 = x^2 + 2x - 3\\0 = (x + 3)(x - 1)[/tex]

The x-intercepts are -3 and 1.

In vertex and intercept form, the equation is:

[tex]y = (x + 1)^2 - 4[/tex]

The vertex is (-1, -4)

The x-intercepts are -3 and 1.

This form allows us to easily identify the vertex and the x-intercepts of the quadratic equation.

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The exact volume of a cone with the same dimensions is 9428.57 cubic inches

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

The cylinder

The volume of the cone with the same dimensions is calculated as

Volume = 1/3 * Volume of cylinder

So, we have

Volume = 1/3 * 22/7 * (30/2) * (30/2) * 40

Evaluate

Volume = 9428.57

Hence, the exact volume of a cone with the same dimensions is 9428.57 cubic inches

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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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Answer:

Comparing the centers of the data sets:

- The median for Data Set A is greater than the median for Data Set B.

- The mean for Data Set A is greater than the mean for Data Set B.

Comparing the variability of the data sets:

- The range of Data Set A is 22, while the range of Data Set B is 27. Therefore, the range of Data Set B is greater.

- The standard deviation of Data Set A is greater than the standard deviation of Data Set B, indicating higher variability in Data Set A.

The point A divides the line segment AB into the ratio 3:1, while the point B divides it into the ratio 1:3.

1. To find the ratio in which each point divides AB, we need to calculate the distances from each endpoint to the dividing point.

2. Let's calculate the distance from point A to the dividing point. The x-coordinate of point A is -7, and the y-coordinate is -14. Similarly, the x-coordinate of point B is 5, and the y-coordinate is 10.

3. We'll use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

  distance = sqrt((x2 - [tex]x1)^2 + (y2 - y1)^2)[/tex]

4. Applying the distance formula, we find the distance from point A to the dividing point:

[tex]distance_A[/tex] = sqrt((5 -[tex](-7))^2 + (10 - (-14))^2)[/tex]

             = sqrt((5 + [tex]7)^2 + (10 + 14)^2)[/tex]

             = sqrt([tex]12^2[/tex] + [tex]24^2[/tex])

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

5. Similarly, let's calculate the distance from point B to the dividing point:

[tex]distance_B[/tex] = sqrt((-7 - [tex]5)^2 + (-14 - 10)^2)[/tex]

             = sqrt((-[tex]12)^2 + (-24)^2)[/tex]

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

6. The dividing ratio can be determined by comparing the distances from each endpoint to the dividing point. Since distance_A:distance_B = 3:1, we conclude that point A divides the line segment AB into the ratio 3:1, and point B divides it into the ratio 1:3.

Thus, the endpoints A and B divide the line segment AB into the ratios 3:1 and 1:3, respectively.

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Answer:

the ratio for point C is 1 : 2.

the ratio for point D is 3 : 1.

the ratio for point E is 2 : 1.

Step-by-step explanation:

I just got it right on the test

Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )

The measure of the interior angle at vertex F is 72 degrees.

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]

[tex]20\text{x} = 720[/tex]

[tex]\text{x} = 36[/tex]

[tex]\bold{2x = 72^\circ}[/tex]

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

The torque experienced by the rigid body is -17.10375 k N·m.

To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.

Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:

Torque = r x F

The cross product between two vectors is calculated as follows:

Torque = (r_x * F_y - r_y * F_x)k

Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.

Substituting the given values, we have:

Torque = ((1.801 * -3.25) - (2.50 * 4.501))k

Calculating the cross product:

Torque = (-5.85125 - 11.2525)k

Simplifying:

Torque = -17.10375k

Therefore, the torque experienced by the rigid body is -17.10375 k N·m.

The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.

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Answer:

To write the polynomial function m(x) = x + x^2 - 1 in standard form, we rearrange the terms in descending order of degree:

m(x) = x^2 + x - 1

Polynomial name: Quadratic polynomial

Degree: 2 (the highest exponent is 2)

Leading coefficient: 1 (the coefficient of the highest-degree term)

Constant term: -1 (the term without any variable)

Answer: 2 1/2 pounds of more clay

Step-by-step explanation:

To calculate how much more clay Ms. Garcia needs, we need to add up the clay requirements for each grade level and then subtract the amount she already has.

For the sixth graders:

Number of students: 25

Clay required per student: 3/4 pound

Total clay required for sixth graders: 25 * (3/4) = 75/4 = 18 3/4 pounds

For the seventh graders:

Clay required for sculptures: 20 pounds

Total clay required for both grade levels: 18 3/4 + 20 = 38 3/4 pounds

Clay leftover from last year: 5 2/5 pounds

To find out how much more clay Ms. Garcia needs, we subtract the clay she already has from the total required:

38 3/4 - 5 2/5 = 38 3/4 - 27/5 = 38 3/4 - 27/5 = (155 - 108 + 3)/20 = 50/20 = 5/2 = 2 1/2 pounds

Therefore, Ms. Garcia needs an additional 2 1/2 pounds of clay.

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 .

...

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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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer:

C

Step-by-step explanation:

x ≥ 25

Because this inequality has an equal sign, it will be a close circle. x ≥ -25 meaning the x go to the right of -25.

So, the answer is C