A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation?
Question 1 options:

A)

The number of hours the car has traveled

B)

The age of the car

C)

The distance the car has traveled

D)

The speed at which the car travels

Answer:

Step-by-step explanation:

9x - 7y > -7

-7y > -9x - 7

y < 9/7x + 1

The only items she can add to the box to make it less than 12 pounds are;  either the package of socks or the book

The list of items and their weight that she has already packed are;

Boots = 5.2 pounds

Jeans = 1.25 pounds

Sweater = 2.05 pounds

Running Shoes = 2.25 pounds

We are told that the package must weigh less than 12 pounds. Thus, let the weight of the additional item be x and as such we have the inequality;

5.2 + 1.25 + 2.05 + 2.25 + x < 12

10.75 + x < 12

Subtract 10.75 from both sides to get;

x < 1.25

The only item that is less than 1.25 pounds that she can carry is either the package of socks or the book

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The value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.

The given integral is;

y = ∫18x sin (9x² + 8) dx

Put u = 9x² + 8

Then, on differentiation

18x dx = du

substitute the values:

y = ∫ sin (u) du.

y = -cos u

Put u = 9x² + 8

y = -cos (9x² + 8) + c

c is the constant of integration.

Thus, the value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.

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The solution is Option C.

The measure of TR of triangle STR is TR = 30

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔPQR

Let the second triangle be represented as ΔSTR

The measure of PR = 35

The measure of SR = 25

The measure of QR = 42

The measure of QT = x

The measure of TR = 42 - x

Now , PQ is similar to ST

Now , the triangles PQR and STR are similar triangles

And , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

SR / PR = TR / QR

25 / 35 = ( 42 - x ) / 42

On simplifying the equation , we get

Multiply by 42 on both sides of the equation , we get

( 42 - x ) = ( 25 x 42 ) / 35

On further simplification , we get

42 - x = 30

Adding x on both sides of the equation , we get

x + 30 = 42

Subtracting 30 on both sides of the equation , we get

x = 12

Now , the measure of TR = 42 - x

Substitute the value of x in the equation , we get

The measure of TR = 42 - 12 = 30

Hence , the measure of TR of triangle is 30

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[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=6\\ r=8 \end{cases}\implies SA=2\pi (8)(6+8) \\\\\\ SA=16\pi (14)\implies SA=224\pi \implies SA\approx 703.72~units^2[/tex]

They are congruent by the by the Angle-Side-Angle (ASA) congruence criterion.

Angle-Side-Angle (ASA) congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. In this case, the angles angle E = angle I and EG=FI (a non-included side), so the triangles ADEF and AHIG are congruent by ASA.

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The Gourmet Grill Co. produces propane and electric grills with varying cost and hours required in 4 manufacturing processes. Aim is to maximize profit by determining the production plan using LP model, feasible region and level curves.

a. The LP model for this problem can be formulated as follows:

Maximize: $320P + $260E (profit from selling propane and electric grills)

Subject to:

2P + E <= 2400 (hours of machine press time available)

4P + 5E <= 6000 (hours of fabrication time available)

2P + 3E <= 3300 (hours of assembly time available)

P + E <= 1500 (hours of testing time available)

P, E >= 0 (non-negativity constraints)

Where P is the number of propane grills and E is the number of electric grills produced.

b. The feasible region for this problem is a polygon with vertices (0, 0), (600, 0), (300, 900), (0, 1200). This region represents the combination of P and E that satisfies all the constraints.

c. To determine the optimal solution using level curves, we can start by plotting the feasible region and then finding the level curve that represents the maximum profit. The level curve would be a straight line with slope equal to $320/$260 (the ratio of price per unit for the two types of grills). The intersection of this line with the feasible region would represent the optimal solution, which would be the combination of P and E that maximizes the profit.

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The area of the triangle is  2. 6 square units

The formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Given that the parameters are;

using the trigonometric identity, sine, we have;

sin 60 = h/4

substitute the values

0. 8660 (4) = h

h = 3.5

substitute the value

Area = 1/ 2 × 3. 5 × 1. 5

multiply the values

Area = 2. 6 square units

Hence, the value is 2. 6 square units

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The expression that represents the combined inventory of these two stores is given as follows:

A. 7g²/2 - 4g/5 + 15/4.

The combined inventory is obtained adding the inventories for each store, combining the like terms.

The addition of the like terms for g² is given as follows:

1/2 + 3 = 0.5 + 3 = 3.5 = 7/2g².

The term with g is given as follows:

-4g/5.

The constant like terms are combined as follows:

7/2 + 1/4 = 14/4 + 1/4 = 15/4.

Hence the simplified expression is given as follows:

7g²/2 - 4g/5 + 15/4.

Meaning that the correct option is given by option A.

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Therefore , the solution of the given problem of volume comes out to be density  1.15625 g/ cm³.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.

Here,
Given:

Density = mass /volume

mass = 370 gm

volume = 320  cm³

Density = 370/320

=>Density = 1.15625 g/ cm³

thus , density  1.15625 g/ cm³

Therefore , the solution of the given problem of volume comes out to be density  1.15625 g/ cm³.

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If each value is equally likely and the mean of x is 6, x = 24.

The arithmetic mean (arithmetic average or simply the mean or average) in statistics is the sum of a collection of numbers divided by the count of numbers in the collection, which is is often a set of results from an experiment, a survey, or observational study.

The arithmetic mean A is defined to be the formula: [tex]A = \frac{1}{n} \sum_{i=1}^{n} a_i=\frac{a_1+ ... +a_n}{n}[/tex].

We're given a set of {0, 1, 2, 3, x} where x is unknown and the mean of x is 6. In order to find the value of x, we can plug all the known values in the formula first and then we're going to simplify the equation:

[tex]A = \frac{a_1+...+a_n}{n}\\\\6 = \frac{0+1+2+3+x}{5}\\\\6 = \frac{6+x}{5}\\\\30 = 6 + x\\\\30 - 6 = x\\\\x = 30 - 6\\\\x = 24[/tex]

We've confirmed that x is indeed equal to 24.

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Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔABC is congruent to the triangle ΔXYZ.

In triangles ΔABC and ΔXYZ, then we have

∠B = ∠Y               (Corresponding angles)

∠A = ∠X              (Corresponding angles)

AB = XY               (Common side)

Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.

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Answer: 1, 2, and 4.

Step-by-step explanation: Each must be wider than the angle than a "L" has.

The value of the variable x is 53.

The measures of the angles include the following:

m∠P = 96°.

m∠Q = 95°.

m∠R = 53°.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

m∠P + m∠Q + m∠R = 180

Substituting the given parameters into the mathematical expression, we have the following;

(2x - 10)° + (x + 42)° + x° = 180°

4x - 32° = 180°

4x = 180° + 32°

x = 53.

For the measure of the angles, we have:

m∠P = (2(53) - 10)° = 96°.

m∠Q = (53 + 42)° = 95°.

m∠R = 53°.

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The relation between total salary and saving can be represent by the equation, Y =  X + 292

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Catniss is saving money to take a trip to the Capitol with her sister

Every week,

After taking out the $292, which she needs for her weekly expenses

And that amount she sets aside the same portion of her paycheck

After 10 weeks ,

Catniss has $405

Suppose, she is saving X amount every week,

And her total salary is, Y

Total salary = saving + weekly expenses

    Y            =  X + 292

So, she saved money after 10 week,

⇒ 10X

Given saving after weeks, $405

⇒ 10X = 405

⇒  X = 40.5

Y =  X + 292

   =  40.5 + 405

   =   $445.5

Hence, the equation is Y =  X + 292

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Answer:

= [tex]-\frac{5}{2}[/tex]

= m = -2.5

Step-by-step explanation:

Hope it helps on your assignment/quiz/test/homework

Answer:-5/2

Step-by-step explanation:

(3,-9) and (1,-4)

(x1,y1)       (x2,y2)

[tex]\frac{-4+9}{1-3\\}[/tex] = [tex]\frac{-5}{2}[/tex]

Answer:

Step-by-step explanation:

The value of the given expression will be 4.

The system shown consists of a rotational mass, a pinion, and a linear mass.

The equations of motion for this system can be formulated in terms of x, theta, and theta a in terms of rotational and linear acceleration.

The equation of motion for rotational acceleration is given by:

θ¨ = (1/J) * (T - (b*x¨))

Where J is the moment of inertia of the rotational mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.

The equation of motion for linear acceleration is given by:

x¨ = (1/m) * (T - (b*θ¨))

Where m is the mass of the linear mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.

The equations of motion for the system shown can be formulated in terms of rotational acceleration (θ¨) and linear acceleration (x¨) using the moment of inertia (J) and mass (m) of the rotational and linear masses, respectively, as well as the coefficient of friction (b) between the two.

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The value of the expression given as √2(2+6)​ is 4

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

√2(2+6)​

We start by evaluating the expression in the bracket

So, we have the following

√2(2+6)​ = √2(8)

Evaluate the products

This gives

√2(2+6)​ = √16

Lastly, we have

√2(2+6)​ = 4

Hence, the solution is 4

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The sampling distribution of xM - xB is normally distributed with a mean of 18 mg/dl and a standard deviation of 35.4 mg/dl.

The sampling distribution of xM - xB is a normal distribution. This can be calculated by subtracting the mean of the men (188mg/dl) from the mean of the boys (170mg/dl), which gives a mean of 18 mg/dl. To calculate the standard deviation, we first calculate the standard deviation of the men (41 mg/dl) and the boys (30mg/dl). Then we use the formula: standard deviation of xM - xB = sqrt(standard deviation of men^2 + standard deviation of boys^2). This gives us a standard deviation of 35.4mg/dl. To calculate the probability of getting a difference in sample means xM - xB that's less than 0 mg/dl, we use the z-score formula: z = (x-mean)/standard deviation. Plugging in x = 0, mean = 18 and standard deviation = 35.4 gives us a z-score of -0.5197. Using a z-table, this gives us a probability of 0.3085. It should not be a surprise if the sample mean cholesterol for the 14 - year - olds exceeds the sample mean for the men as the mean cholesterol level for the boys is lower than the men.

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Answer:

B

Step-by-step explanation:

Start with 200    in 5 mins  = 100     then cut in half for another 5 min = 50

   another 5 min cut in half again = 25

The solution to the equations -5m + 6n = 25 and -7m + 8n = 33 is (1, 5)

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

a) Given the equations:

-5m + 6n = 25    (1)

And:

-7m + 8n = 33     (2)

From both equations simultaneously:

m = 1, n = 5

The solution is (1, 5)

b) Given the equations:

8x - 3y = -16    (1)

And:

50 = -9x - 2y     (2)

From both equations simultaneously:

x = -4.23, y = -5.95

The solution is (-4.23, -5.95)

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The sum of residuals (error) for any first order simple linear regression least squares line is zero (0).

To show that the sum of residuals (error) for any first order simple linear regression least squares line is zero (0), we can use the following equation:

Where b0 is the intercept and b1 is the slope of the line, and xi and yi are the x and y values of the ith data point. This equation can be expanded by substituting the least squares solution for b0 and b1 into the equation:

∑i = 1n (yi − (∑i = 1n yi)/n − (∑i = 1n xiyi − (∑i = 1n xi)(∑i = 1n yi))/(∑i = 1n xi2 − (∑i = 1n xi)2/n)) = 0

Simplifying both sides of the equation, we get:

∑i = 1n (yi − (∑i = 1n xiyi)/(∑i = 1n xi2)) = 0

Therefore, the sum of residuals (error) for any first order simple linear regression least squares line is zero (0).

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The average yearly salary of an individual with each of these final degrees is $22333 and $16666.6.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form

Ax + B = 0.

Given;

The average yearly salary of an individual whose final degree is a​ master's is ​$43000 less than twice that of an individual whose final degree is a​ bachelor's.

Combined, two people with each of these educational attainments earn ​$110 thousand.

Now, let the salary of bachelors be x

Then salary of masters= 2x-43000

x+2x-43000=110000

3x=67000

x=22333.33

2x-43000=16666.66

Therefore, by solving equations answer will be $22333 and $16666.6.

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Answer:

Domain

Step-by-step explanation:

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Therefore, for the given values of 3, 4, and 5, these lengths can indeed form a right triangle. Specifically, this triangle is a 3-4-5 triangle, which is a special type of right triangle whose sides have integral lengths and whose angles are all multiples of 30°.

Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse. The theorem is a fundamental result in geometry and has wide-ranging applications in mathematics, physics, engineering, and other fields.

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The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.

The linear system is given as follows:

x1 + x2 - x3 = 6

2x1 + x2 + 2x3 = 8

3x1 + 2x2 + 3x3 = 14

To solve this system, we will use the Gauss-Jordan elimination method. First, we will subtract twice the first equation from the second equation and three times the first equation from the third equation.

2x1 + x2 + 2x3 = 8

- 2(x1 + x2 - x3 = 6)

2x1 + x2 + 2x3 = 8

3x1 + 2x2 + 3x3 = 14

- 3(x1 + x2 - x3 = 6)

0x1 + 3x2 + 5x3 = 6

Next, we will subtract three times the second equation from the third equation.

3x1 + 2x2 + 3x3 = 14

- 3(0x1 + 3x2 + 5x3 = 6)

3x1 + 2x2 - 2x3 = 8

Finally, we will divide the first equation by 1, the second equation by 3, and the third equation by -2.

x1 + x2 - x3 = 6

/ 1

x1 + (1/3)x2 + (5/2)x3 = 3

(-1/2)x1 + x2 + x3 = -4

The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.

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The initial value for Marcos to the grand canyon is 400 miles.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given Marco is driving to the grand canyon. His distance from the Grand Canyon decreases by 150 mi every 3h.

We know that every 3 hours that distance decreases by 150 miles, then the distance decreased by the hour is:

150mi/3h = 50mi/h

since the distance is reducing we can take the rate of change negative,

so rate of change = -50 mi/h

and y = distance from the Grand Canyon

x = the number of hours he drives,

so the equation of slope is y = mx + c

where m = rate of change and c is the initial value at x = 0

m = -50 mi/h

y = -50x + c

And we know that after 4 hours the distance is 200 miles, then we can replace that to get:

200mi = (-50 mi/z)*4h + c

200mi = -200mi + c

200mi + 200mi = c  =400mi

equation is y = -50x + 400

Hence the initial value is 400 miles.

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