David is working two summer jobs, making $13 per hour landscaping and making $8 per hour clearing tables. In a given week, he can work no more than 16 total hours and must earn no less than $160. Also, he must work at most 13 hours landscaping. If
� x represents the number of hours landscaping and �y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

The statement "the equations of motion of a two-degree-of-freedom system can be expressed in terms of the displacement of either of the two masses" is TRUE.

The equations of motion refer to a set of mathematical equations that describe the behavior of a physical system over time. These equations define how the position, velocity, and acceleration of an object are related. The equations of motion are applicable to both single and multi-degree-of-freedom systems.

A two-degree-of-freedom system is a physical system with two independent modes of motion or two degrees of freedom. It is defined by two generalized coordinates that completely define the system's state.

A two-degree-of-freedom system can be either linear or nonlinear, depending on the nature of the force. It is used in the study of structural dynamics, mechanical vibrations, and control engineering.

In a two-degree-of-freedom system, the equations of motion can be expressed in terms of the displacement of either of the two masses. The equations of motion are usually derived using Lagrange's equations, which are a set of equations that describe the dynamics of a mechanical system in terms of its energy. They are given as follows:

Where q₁ and q₂ are the generalized coordinates, m₁ and m₂ are the masses, k₁ and k₂ are the spring constants, and c₁ and c₂ are the damping coefficients.

These equations of motion are nonlinear and can be solved analytically or numerically using various techniques.

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Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem

To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:

Sum of measures of interior angles of triangle = (n-2) × 180 degrees

= (3-2) × 180 degrees [since we are dealing with a triangle]

= 1 × 180 degrees

= 180 degrees

Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.

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The perimeter of the figure is 16p + 10.

The whole length of a two-dimensional or three-dimensional shape's sides or edges is known as its perimeter. It is frequently referred to as the shape's perimeter or circumference. It is possible to determine the perimeter of many geometric forms with accuracy. The perimeter is a key idea in geometry and has several practical uses, such as determining the radius of a circular racetrack or determining the length of fencing required for a certain property.

The perimeter of a figure is the sum of the lengths of all its sides.

Thus,

Perimeter = (p - 9) + (7p + 5) + (p - 9) + (7p + 5)

Perimeter = 2p + 2(7p) + 2(5)

Perimeter = 16p + 10

Hence, the perimeter of the figure is 16p + 10.

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A patient weighing 220 pounds needs 293 milligrams of medicine.

We have given that,

patient weighing 162

pounds requires 216 milligrams of medicine

We have to calculate the amount of medicine required by a patient weighing 220 pounds

Consider the value of amount of medicine is x.

Set up a proportion.

pounds / milligrams of medicine

What is the proportion we get?

[tex]162/216=220/x[/tex]

So,

[tex]162/216=220/x[/tex]

[tex]162x=216\times220[/tex]

[tex]162x=47,520[/tex]

[tex]x=47,520/162[/tex]

[tex]x=293[/tex]

A patient weighing 220 pounds needs 293 milligrams of medicine.

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Answer:

Step-by-step explanation:

a.  ∠ACB

b.  AC

c.  AB

d.  BC

e.  tangent, opposite, adjacent

f.  m∠ACB = tan⁻¹(34/45) = 37°

Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.

In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.

Here,

One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=25\\ y=100 \end{cases} \\\\\\ 100=\cfrac{k}{25}\implies 2500=k\hspace{12em}\boxed{y=\cfrac{2500}{x}} \\\\\\ \textit{when x = 10, what's "y"?}\qquad y=\cfrac{2500}{10}\implies y=250[/tex]

Answer:

See Below.

Step-by-step explanation:

To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.

In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.

Perimeter = 8 cm + 10 cm + 16 cm + 10 cm

Perimeter = 44 cm

Therefore, the perimeter of the trapezoid is 44 cm.

The volume of iron needed to create the rectangular prism is approximately 28650.5 cubic cm.

what is volume?

Volume is the amount of space occupied by a three-dimensional object. It is a measure of how much an object can hold or how much space it takes up. The volume of a solid object is typically measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

The volume of the rectangular prism without the cylinder can be calculated as:

[tex]$$V_1 = A \times h$$[/tex]

where A is the base area and h is the height

[tex]$$V_1 = 2250 \times 100$$[/tex]

[tex]$$V_1 = 225000 \ \text{cubic cm}$$[/tex]

The volume of the cylinder can be calculated as:

[tex]$$V_2 = \pi r^2 h$$[/tex]

where r is the radius and h is the height

[tex]$$V_2 = \pi \times 25^2 \times 100$$[/tex]

[tex]$$V_2 = 196349.54 \ \text{cubic cm}$$[/tex]

The volume of the rectangular prism with the cylinder missing can be calculated as:

[tex]$$V = V_1 - V_2$$[/tex]

[tex]$$V = 225000 - 196349.54$$[/tex]

[tex]$$V = 28650.46 \ \text{cubic cm}$$[/tex]

Therefore, the volume of iron needed to create the rectangular prism with a base area of 2250 square cm, a cylinder missing through the center of the prism with a radius of 25 cm, and the height of the cylinder and the prism being 100 cm, is approximately 28650.5 cubic cm (rounded to the nearest tenth of a cubic cm).

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[tex] \Large{\boxed{\sf C = 31.40 \: inches}} [/tex]

[tex] \\ [/tex]

The circumference of a circle can be calculated using the following formula:

[tex] \Large{\sf C = 2 \pi r } [/tex]

Where:

[tex] \\ [/tex]

Since "a segment drawn from the center of a circle to a point on the circle" is actually the definition of the radius of said circle, we can take r = 5 inches.

[tex] \\ [/tex]

Applying our formula and using 3.14 for π, we get:

[tex] \sf C = 2 \times 3.14 \times 5in \\ \\ \implies \boxed{\boxed{\sf C = 31.4 \: inches = 31.40 \: inches}} [/tex]

Answer:

31.40 inches

Step-by-step explanation:

The circumference of a circle can be calculated using the formula:

Given:

Substitute the given value into the formula:

Simplifying the expression:

[tex]\therefore[/tex] The circumference of the circle is 31.40 inches.

The 95% confidence interval for the population mean is equal to (30.4,39.6).

A confidence interval is a range of values that surrounds the point estimate, such as a sample mean, and provides a sense of the precision of the estimate. The confidence interval (CI) contains the estimated parameter at a given level of confidence, usually 95% or 99%.

The 95% confidence interval for the population mean is given by:

x(bar) ± Zα/2 * σ/√n

Where,

x(bar) = 35σ = 100n = 25Zα/2 = Z0.025 = 1.96

Substituting the values, we get:

CI = 35 ± 1.96 * 100/√25

CI  = (30.4,39.6)

Hence, the 95% confidence interval for the population mean is (30.4,39.6).

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Ryan makes a profit of £240.  the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

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Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.

(a) Slope, b = r*(sy/sx) = 0.5*(8/40) = 0.1

Intercept = y - bx = 75 - 0.1*280 = 47

The regression equation is:

y = 47 + 0.1*x

(b) Put x = 300

y = 47 + 0.1*300

y = 77

(c) r2 = 0.5*0.5 = 0.25

Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

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Answer:

  C, E

Step-by-step explanation:

You want the equations that represent 2 boys for every 5 girls in a class.

The number of boys is represented by x, and the number of girls is represented by y, so you have ...

  x : y = 2 : 5

As fractions, this is ...

  x/y = 2/5

Multiplying by 5y gives ...

  5x = 2y . . . . . . matches equation C

Dividing by 5, we have ...

  x = 2/5y . . . . . . matches equation E

The range of the quadratic function above is (-∞, 7].

In mathematics, a quadratic prοblem is οne that invοlves multiplying a variable by itself, alsο knοwn as squaring. In this language, the area οf a square is equal tο the length οf its side multiplied by itself. The term "quadratic" cοmes frοm the Latin wοrd fοr square, quadratum.

Tο determine the quadratic functiοn's range, we must first determine the functiοn's minimum and maximum pοints. The given functiοn is in vertex fοrm, with the vertex at the pοint (h, k), where h is the vertex's x-cοοrdinate and k is the vertex's y-cοοrdinate.

We can see frοm the given equatiοn that the vertex is at the pοint (1, 7). Because the cοefficient οf the x² term is pοsitive, the parabοla οpens upwards and the vertex is the functiοn's minimum pοint.

Thus, The range of the quadratic function above is (-∞, 7].

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The coordinate matrix LFE of L relative to the ordered bases E and F is given by:

LFE=12,3,0,12,3,0,0

LFE =

[[5, 1, 3, 3],

[0, 0, 3, 0],

[0, 0, 0, 0]]

This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:

LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12

LFE[1,2] = L(e2) =  = 0 + 0 + 3 + 0 = 3

LFE[1,3] = L(e3) =  = 0 + 0 + 0 + 0 = 0

LFE[2,1] = L(f1) =  = 5 + 1 + 3 + 3 = 12

LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3

LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0

LFE[3,1] = L(f4) =  = 0 + 0 + 0 + 0 = 0

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None of the available options match the parabola's equation.

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.

A parabola's vertex form is given by:

[tex]y = a(x-h)^2 + k[/tex]

where (h,k) is the parabola's vertex.

[tex]y = a(x-5)^2 - 3[/tex]

These values are substituted into the equation to produce:

[tex]-15 = a(2-5)^2 - 3[/tex]

[tex]-15 = 9a - 3[/tex]

[tex]-12 = 9a[/tex]

[tex]a = -4/3[/tex]

[tex]y = (-4/3)(x-5)^2 - 3[/tex]

This equation is expanded and simplified to produce:

[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]

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The correct answer is: (4, 3) is a member. Its cardinality is 4.

Matching the sets on the left with a true statement about the Cartesian product of those sets on the right:{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}{1, 2, 3, 4} × {3, 4, 5, 6} = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 3), (4, 4), (4, 5), (4, 6)}{4, 5, 6, 7} × {4, 5, 6, 7} = {(4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), (7, 7)}{a, e, i, o, u} × {b, g, t, d} = {(a, b), (a, g), (a, t), (a, d), (e, b), (e, g), (e, t), (e, d), (i, b), (i, g), (i, t), (i, d), (o, b), (o, g), (o, t), (o, d), (u, b), (u, g), (u, t), (u, d)}{1, 2, 3} × {1, 2, 4} = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (3, 1), (3, 2), (3, 4)}The following are true statements about the Cartesian product of these sets:its cardinality is 4. (4, 3) is a member.

Therefore, the correct answer is: (4, 3) is a member. Its cardinality is 4.

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The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.

To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.

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Using the mean formula we know that the new mean height of 14 people is 159.7 cm.

A mean in math is the average of a data set, calculated by adding all numbers together and then dividing the total of the numbers by the number of numbers.

For illustration, with the dataset containing: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.

The mean height given is 159 cm.

Let, x1, x2, x3 ..... x15 be the height of 15 people.

x1+x2+x3 ..... x15/15 = 159

x1+x2+x3 ..... x15 = 159 * 15 = 2385 cm ...(1)

Let, x1 = 148 cm, who leaves the group.

148+x2+x3 ..... x15 = 2385 cm

x2+x3 ..... x15 = 2237 cm

Now, we have 14 people.

New mean = x2+x3 ..... x15/14

= 2237/14

= 159.7 cm

Therefore, using the mean formula we know that the new mean height of 14 people is 159.7 cm.

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Solving a system of equations we can see that he cost of a corn dog is $1.25 and the cost of the fries is $3.50

We can define two variables here:

x = cost of a corn dog.

y = cost of the fries.

With the information in the question we can write two equations, these two equations form a system of equations that we can solve, the system of equations is the one below:

2x + 3y = 13

4x + y = 8.50

We can isolate y in the second equation to get:

y = 8.50 - 4x

Replace it in the other one:

2x + 3*(8.5 - 4x) = 13

2x + 25.5 - 12x = 13

-10x = 13 - 25.5

x = -12.5/-10 = 1.25

Then:

y = 8.5 - 4*1.25 = 3.5

The cost of a corn dog is 1.25 dollars and the cost of the fries is 3.50 dollars.

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To conclude, the probability of the Acme Drug Company seeing a percent difference of -.13 or less if the true difference is 0 is quite low and is equal to 0.0934.

The probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is quite low. This is because a difference of -.13 is a very small percentage in comparison to a true difference of 0.

Mathematically, the probability of this happening would be equal to the area under the standard normal distribution curve for values between -0.13 and 0. In other words, the probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is equal to the area from the left tail of the standard normal distribution curve up to the mean (0) of the curve.

Using a standard normal distribution calculator, we can see that the probability of the Acme Drug Company seeing a percent difference of -.13 or less is 0.0934. This probability is extremely low and it is not likely that the Acme Drug Company would experience such a small percent difference.

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Answer: 4.5

Step-by-step explanation:

A^2 +B^2 =C^2

A^2 + 6^2 =7.5^2

A^2 + 36= 56.25

A^2= 20.25

A= square root of 20.25

A= 4.5

Answer: $15.25

Step-by-step explanation:

Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:

2.25x + 1.25y ≤ 20 (Jose has $20 to spend)

x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)

x ≥ 3 (Jose must buy at least 3 apples)

y ≤ 9 (Jose can buy at most 9 mangos)

To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.

First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:

When x = 0, we have 1.25y = 20, so y = 16.

When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).

Plotting these intercepts and connecting them with a line, we get:

     |       *

 16  |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    8.89

Next, we graph the line x + y = 9 by finding its intercepts:

When x = 0, we have y = 9.

When y = 0, we have x = 9.

Plotting these intercepts and connecting them with a line, we get:

    |      

 9   |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    9  

Finally, we shade the feasible region by considering the remaining constraints:

x ≥ 3: This means we shade to the right of the line x = 3.

y ≤ 9: This means we shade below the line y = 9.

Shading these regions and finding their intersection, we get:

   |       *

 16  |   *    |

     |       |

     |  /    |

     | /     |

     |/      |

 9   *--------*---

     |       | /

     |       |/

     |       *

 0   *--------*

      3    8.89

The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.

To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.

Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.

How to solve?

To add the fractions 4/7, 1/8, and 1/3, we need to find a common denominator.

The prime factorization of 7 is 7, the prime factorization of 8 is 2²3, and the prime factorization of 3 is 3. The least common multiple (LCM) of these three numbers is 7× 2²3× 3 = 168.

So, we can rewrite the fractions with the common denominator of 168:

4/7 = 96/168

1/8 = 21/168

1/3 = 56/168

Now we can add these fractions:

96/168 + 21/168 + 56/168 = 173/168

To check if this sum is a prime number, we can use trial division by checking all the integers between 2 and the√ of 173/168 (which is approximately 1.053):

2 does not divide 173/168

3 does not divide 173/168

4 does not divide 173/168

5 does not divide 173/168

6 does not divide 173/168

7 divides 173/168 (24 times)

8 does not divide 173/168

9 does not divide 173/168

...

Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.

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Complete question:

What is the result of adding 4/7, 1/8, and 1/3, and is the sum a prime number?

Answer:

the numbers are

[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]

Step-by-step explanation:

then there difference is

square root of 10 + 5 -(- square root of 10 +5)

=

[tex]2 \sqrt{10} [/tex]

and the cube of there sum is 15^3 = 15* 15* 15

= 3375

The number of minutes she must run to reach her goal is 65.1 minutes.

The time she must run for is found by dividing the distance by the speed:

Time = Distance / Speed

We need to convert the distance from kilometers to miles before substituting values into the formula.

11.7 km = 11.7 / 1.609344 = 7.270043 miles

The formula now becomes:

Time = 7.270043 miles / 6.7 mi/h

Time = 1.085081 h

To get the time in minutes, we need to convert the time in hours to minutes. There are 60 minutes in an hour, so there are

Time = 1.085081 h x (60 minutes/1 hour)

Time = 65.104863 minutes = 65.1 minutes

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Answer:

the cross is the blue color