in some states, the law requires drivers to turn on their headlights when driving in the rain. a highway patrol officer believes that less than one-quarter of all drivers follow this rule. as a test, he randomly samples 200 cars driving in the rain and counts the number whose headlights are turned on. he finds this number to be 41. does the officer have enough evidence to support his belief? express his research question in terms of two competing hypotheses.

The percentage of the size of Jill is as follows:

Jack's height is 80% of Jill's height (Jack is 80% of the size of Jill). 80% of Jill's height can be calculated as: 80% × 125 cm = 100 cm. Therefore, Jack is 100 cm tall.

The percentage of Heather's height relative to Jack's height is as follows:

Heather is 25% taller than Jack. To calculate the percentage of Heather's height, add 25% to Jack's height: 100 cm + 25% × 100 cm = 125 cm. Thus, Heather is 125 cm tall.

The percentage of the difference between Jack's and Heather's height is as follows:

Heather is 25% taller than Jack, so Jack is 25% smaller than Heather. This can be calculated by dividing Jack's height by the total amount of Heather's height (Jack's height divided by Heather's height). The calculation is as follows: 100 cm ÷ 125 cm = 0.8. 1 - 0.8 = 0.2. Finally, convert the decimal to a percentage by multiplying it by 100: 0.2 × 100 = 20%. As a result, Jack is 20% smaller than Heather.

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To determine whether the series converges or diverges, we use the limit comparison test.

We use the limit comparison test to determine whether the series converges or diverges. Using the limit comparison test, we will compare the given series with a p-series whose sum converges.

We will compare the given series with a p-series whose sum converges. Let p = 3. Since this is a p-series and p > 1, it is guaranteed that the sum converges. We will use the following form of the limit comparison test:

limₖ→∞ aₖ/bₖ = c, where c is a finite constant greater than 0. If c is finite and positive, both series converge or diverge. However, if c = 0, the series are identical, and if c = ∞, the ratio test may be used.

The nth term of the given series is aₙ = n³/15n(n⁴-5n²).

aₙ = n³/15n(n⁴-5n²)

aₙ = 1/15n²(n²-5)

We will compare it to the nth term of the p-series bₙ = 1/n³.

bₙ = 1/n³

limₖ→∞ aₖ/bₖ = limₖ→∞ 1/15(k²-5) = 1/15

We know that the limit exists and is finite, and that it is a nonzero constant. As a result, the given series converges by the limit comparison test. Thus, the series converges.

Therefore, the limit comparison test was used to determine if the series converges.

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The cοrrect answer is 18. Ricardο's answer wοuld be incοrrect because he used curly braces instead οf square brackets and ignοred the missing οpening bracket.

Assuming the cοrrect expressiοn is 3x[(2x8)-6-4], we can simplify it using the οrder οf οperatiοns (PEMDAS) tο get:

3x[(16)-6-4]

3x[6]

= 18

Therefοre, the cοrrect answer is 18. Hοwever, if the missing bracket is nοt added and the expressiοn is evaluated as 3x{2x8-6-4], it wοuld be interpreted as: 3x[2x8-6-4] 3x[8] = 24

Thus, Ricardο's answer wοuld be incοrrect because he used curly braces instead οf square brackets and ignοred the missing οpening bracket. It's essential tο fοllοw the cοrrect syntax and οrder οf οperatiοns when evaluating mathematical expressiοns tο οbtain accurate results.

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Answer: 3 - y/4

Step-by-step explanation:

In system of equations the value of a + b is  (40/(5a-8)) + a ≠ 0, it is indeterminate. The given option are incorrect. The value of c in isosceles XZY triangle  is 69 degree in  the length of segment AB is 30. so the value of cos B is 0.27. the complex number equivalent to 7 + 2i/2 - 3i is 8/13 + 25/13i.  the length of each short advertisement is 15 seconds. In equation  x - n/m = 1/8, the x is 11/4

To have infinitely many solutions, the two equations must be dependent, which means that one of them must be a multiple of the other. Multiplying the first equation by 5 and comparing it to the second equation, we get:

5ax + 25y = 40

5ax + by = 10

For these equations to be dependent, we need:

5ax + by = k(5ax + 25y)

where k is some constant. Expanding both sides and simplifying, we get:

by - 25ky = 0

For this to be true for all values of y, we need b - 25k = 0, which implies k = b/25. Substituting this into the above equation, we get:

by - b/5 x = 0

Solving for y, we get y = (b/5)x

Substituting this into the first equation, we get ax + 5(b/5)x = 8

Simplifying, we get x(a+b) = 8

Since we know that the system has infinitely many solutions, a+b cannot be zero. Therefore, we can divide both sides by a+b to get:

x = 8/(a+b)

We are given that this is a valid solution, so x = 8/(a+b) = (b/5)x

Solving for b in terms of a, we get b = 40/(5a-8)

Substituting this into the expression for x, we get x = 8/[a + 40/(5a-8)]

Multiplying the numerator and denominator by 5a-8 and simplifying, we get x = 40/(9a-32)

Since we know that x is a non-zero real number, we must have 9a-32 ≠ 0, which implies a ≠ 32/9. Therefore, a+b = (40/(5a-8)) + a ≠ 0.

To find a + b, we need to find the value of a. However, we are not given enough information to determine this. Therefore, the answer is indeterminate.

Let the length of the shared side be x. Then, by the interior angles of a triangle, we have:

c + c + a = 180 (1)

b + c + c = 180 (2)

a = 2b - 24 (3)

Since WXY is equilateral, we have:

a = 60

Substituting this into equation (3), we get:

2b - 24 = 60

b = 42

Substituting this into equation (2), we get:

c + 42 + c = 180

c = 69

The value of c is 69 degree.

We are given sin A = 0.27. Using the Pythagorean identity sin^2 A + cos^2 A = 1, we can find cos A:

cos^2 A = 1 - sin^2 A = 1 - 0.27^2 = 0.9249

Taking the square root of both sides, we get:

cos A = ±0.9616

Since B is an acute angle, we have:

cos B = sin(90° - B) = sin A = 0.27

Therefore, the value of cos B is 0.27.

we can simplify the given expression as follows 7 + 2i/2 - 3i

= (7/2) + (2/2)i - (3/2)i - (3/2)i^2

= (7/2) - (1/2)i - (3/2)i^2

= (7/2) - (1/2)i - (3/2)(-1)

= (7/2) - (1/2)i + (9/2)

= 8/13 + 25/13i

Therefore, the complex number is 8/13 + 25/13i.

We can set up the following equation based on the given information:

7x + 3(x + 10) = 180

Simplifying this equation, we get:

10x + 30 = 180

10x = 150

x = 15

Therefore, the length of advertisement is 15 seconds.

We can substitute the given values of m and n into the equation and solve for x:

x - 1/2 = 1/8 * 18

x - 1/2 = 9/4

x = 9/4 + 1/2

x = 11/4

Therefore, the value of x is 11/4.

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____The given question is incomplete, the complete question is given below:

ax + 5y = 8, 5x + by = 10.

In the system of equations above, a and b are constants if the system has infinitely many solutions, what is the value of a + b? 10 41/4 45/4 18 In the figure above, an equilateral triangle WXY and an isosceles triangle XYZ share a side. The measure of angle XWY is a degree and measure of angle ZXY = ZYX= c degree and measue of angle XZY is b. If b = a/2 - 12. what is the value of c ? the figure, the length of segment AB is 30. and the of sin A is 0.27. What is the value of cos B? Which of the following complex numbers is equivalent to 7 + 2i/2 - 3i ? (i = Squareroot-1) 7/2 - 2/3i 7/2 + 2/3i 8/13 - 25/13i 8/13 + 25/13i A television network fills breaks between television programs with short and long advertisements. Each long advertisement is 10 seconds longer than each short advertisement. If 7 short advertisements and 3 long advertisements were used to fill a break 3 minutes long, what is the length, in seconds, of each short advertisement? x - n/m = 1/8 In the equation above, m = 18 and n = 1/2 What is the value of x ?

The average rate of change of f(x) = x^2 - 3x + 7 with respect to x from x = 2 to x = 2 + h is given by

Average Rate of Change = (f(2 + h) - f(2)) / h

Average Rate of Change = (x^2 - 3x + 7) / h

Average Rate of Change = ( (2 + h)^2 - 3(2 + h) + 7 ) / h

Average Rate of Change = ( 4 + 4h + h^2 - 6 - 3h + 7 ) / h

Average Rate of Change = (h^2 + h + 1) / h

When h = 0, Average Rate of Change = (h^2 + h + 1) / h = 1

Therefore, the average rate of change of f(x) = x^2 - 3x + 7 with respect to x from x = 2 to x = 2 + h is 1 when h = 0.

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A function is a mathematical rule that assigns a unique output (or value) for each input (or value) in its domain.

In other words, a function is a relationship between two sets, where each element in the first set (called the domain) corresponds to exactly one element in the second set (called the range).

Functions can be represented in different ways, such as algebraic expressions, graphs, tables, or verbal descriptions. For example, the function f(x) = x^2 + 1 represents a rule that squares the input value x, adds 1 to the result, and assigns it as the output value f(x).

Functions are used extensively in mathematics, science, engineering, economics, and many other fields to model real-world phenomena, analyze data, make predictions, and solve problems.

To find the value of H(2), we need to substitute x=2 in the given function H(x) and simplify:

[tex]H(x) = -10x - 42\\H(2) = -10(2) - 42\\H(2) = -20 - 42\\H(2) = -62\\Therefore, H(2) = -62.[/tex]

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pivot positions are (1, 1)

Answer:For matrix 3[1 2 3 4] [4 5 6 7] [6 7 8 9] [1 3 5 7]Multiplying R1 by -4 and adding to R2, and multiplying R1 by -6 and adding to R3, then multiplying R1 by -1 and adding to R4 gives,[-4 -3 -2 -1] [16 17 18 19] [30 31 32 33] [-6 -5 -4 -3]Multiplying R2 by -17/3 and adding to R3, then multiplying R2 by 1/3 and adding to R4 gives,[-4 -3 -2 -1] [16 17 18 19] [0 0 0 0] [-14/3 -10/3 -2/3 2/3]And finally multiplying R3 by -3/4 and adding to R1, then multiplying R3 by -19/4 and adding to R2 gives, [1 0 1 2] [0 1 2 3] [0 0 0 0] [0 0 0 0]The pivot positions are (1, 1), (2, 2) and the pivot columns are columns 1 and 2.For matrix 4[3 5 7 9] [5 7 9 1] Multiplying R1 by -5/3 and adding to R2 gives, [3 5 7 9] [0 -2 -4 -14]The pivot positions are (1, 1) and the pivot column is column 1.

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To find the surface area that minimizes weight for an open-top storage bin in the shape of a rectangular prism with a square base, we need to use calculus to find the minimum value of the surface area function.

First, let's find the surface area function. The surface area of a rectangular prism with a square base is given by the formula SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

Since the base is a square, we know that l = w, so we can simplify the formula to SA = 2l^2 + 2lh + 2lh = 2l^2 + 4lh.

Next, we need to find the volume function. The volume of a rectangular prism with a square base is given by the formula V = lwh. Since we know that V = 3500 cm^3 and l = w, we can substitute and solve for h:

3500 = l^2h

h = 3500/l^2

Now we can substitute this value of h back into the surface area function:

SA = 2l^2 + 4l(3500/l^2)

SA = 2l^2 + 14000/l

To find the minimum value of the surface area function, we need to take the derivative and set it equal to zero:

dSA/dl = 4l - 14000/l^2 = 0

Multiplying both sides by l^2 gives us:

4l^3 - 14000 = 0

Dividing both sides by 4 gives us:

l^3 = 3500

Taking the cube root of both sides gives us:

l = 15.18 cm

Now we can substitute this value of l back into the volume function to find the value of h:

h = 3500/15.18^2 = 15.18 cm

Finally, we can substitute these values of l and h back into the surface area function to find the minimum surface area:

SA = 2(15.18)^2 + 4(15.18)(15.18)

SA = 460.52 + 920.93

SA = 1381.45 cm^2

So the minimum surface area that minimizes weight is 1381.45 cm^2.

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Step-by-step explanation:

The given equation is:

x^2 + 6x + 5 = 0

To solve this quadratic equation, we can use several methods, including:

Factoring method

Completing the square method

Quadratic formula method

Let's apply each method to solve the given equation:

Factoring method:

To factor the given quadratic equation, we need to find two numbers whose product is 5 and sum is 6. These numbers are 1 and 5. So, we can factor the quadratic equation as:

(x + 1)(x + 5) = 0

Applying the zero product property, we get:

x + 1 = 0 or x + 5 = 0

Solving for x, we get:

x = -1 or x = -5

Therefore, the solutions of the quadratic equation are x = -1 and x = -5.

Completing the square method:

To use the completing the square method, we need to write the given quadratic equation in the standard form:

x^2 + 6x + 5 = 0

(x + 3)^2 - 4 = 0 [Note: (a+b)^2 = a^2 + 2ab + b^2 ]

(x + 3)^2 = 4

Taking the square root on both sides, we get:

x + 3 = ±2

Solving for x, we get:

x = -3 + 2 or x = -3 - 2

x = -1 or x = -5

Therefore, the solutions of the quadratic equation are x = -1 and x = -5.

Quadratic formula method:

To use the quadratic formula, we need to know the values of the coefficients a, b, and c in the quadratic equation:

x^2 + 6x + 5 = 0

Here, a = 1, b = 6, and c = 5. Substituting these values in the quadratic formula, we get:

x = [-b ± √(b^2 - 4ac)] / (2a)

x = [-6 ± √(6^2 - 4(1)(5))] / (2 × 1)

x = [-6 ± √(16)] / 2

x = [-6 ± 4] / 2

x = -3 ± 2

Solving for x, we get:

x = -1 or x = -5

Therefore, the solutions of the quadratic equation are x = -1 and x = -5.

In conclusion, the solutions of the given quadratic equation x^2 + 6x + 5 = 0 are x = -1 and x = -5, which we obtained by using each of the three methods: factoring, completing the square, and quadratic formula.

To prove that |a+b| = |a|+|b| if ab is greater than or equal to 0, we need to use the triangle inequality:

When a and b have the same sign, they are both greater than or equal to 0. Thus, the triangle inequality tells us that |a+b| ≥ |a| + |b|. We can then conclude that if a and b have the same sign, then |a+b| = |a|+|b|.

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When considering all earthquakes around the world per year, earthquakes with a magnitude of 3 occur about as half as earthquakes of a magnitude 6.

Earthquakes (also known as quakes, tremors or tremors) shake the Earth's surface caused by seismic waves generated by a sudden release of energy from the Earth's lithosphere. Earthquakes range in magnitude from weak and imperceptible tremors to those strong enough to knock objects and people through the air, damage critical infrastructure and wreak havoc on entire cities. Seismicity in an area refers to the frequency, type, and magnitude of earthquakes that occur during a specified period of time. Seismicity at a particular location on Earth is the average rate at which seismic energy is released per unit volume. The term tremor is also used for non-seismic earthquakes.

On the surface of the Earth, earthquakes appear as shaking, displacement or disturbance of the ground. When the epicenter of a large earthquake is offshore, the displacement of the seabed is sufficient to generate a tsunami. Earthquakes can also cause landslides.

In its most general sense, the term earthquake is used to describe any seismic event - whether natural or man-made - that produces seismic waves. Earthquakes are mainly caused by the rupture of geological faults, but are also caused by other events such as volcanic activity, landslides, mine explosions and nuclear tests.

The initial breaking point of an earthquake is called epicenter or epicenter. The epicenter is the point on the ground directly above the source of the earthquake.

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Answer:

Let x be the number of $10 CDs and y be the number of $15 CDs. Then, the system of inequalities representing this situation is:

10x + 15y ≥ 30 (the customer wants to spend at least $30)

10x + 15y ≤ 60 (the customer wants to spend at most $60)

x ≥ 0 (the customer can't buy a negative number of CDs)

y ≥ 0 (the customer can't buy a negative number of CDs)

Simplifying the first two inequalities:

2x + 3y ≥ 6

2x + 3y ≤ 12

To graph the solution region, we first graph the boundary lines:

2x + 3y = 6 (or y = (-2/3)x + 2)

2x + 3y = 12 (or y = (-2/3)x + 4)

Then, we shade the region that satisfies both inequalities (the region below the upper line and above the lower line), as well as the regions to the right and above the x and y axes:

Let x be the number of $10 CDs and y be the number of $15 CDs. Then, the system of inequalities representing this situation is:

10x + 15y ≥ 30 (the customer wants to spend at least $30)

10x + 15y ≤ 60 (the customer wants to spend at most $60)

x ≥ 0 (the customer can't buy a negative number of CDs)

y ≥ 0 (the customer can't buy a negative number of CDs)

Simplifying the first two inequalities:

2x + 3y ≥ 6

2x + 3y ≤ 12

To graph the solution region, we first graph the boundary lines:

2x + 3y = 6 (or y = (-2/3)x + 2)

2x + 3y = 12 (or y = (-2/3)x + 4)

Then, we shade the region that satisfies both inequalities (the region below the upper line and above the lower line), as well as the regions to the right and above the x and y axes:

inequality graph

As an example of one possible production situation within these restrictions, let's say the customer buys 2 $10 CDs and 2 $15 CDs. This would cost $50, which falls within the customer's desired spending range of $30 to $60. Plugging in x = 2 and y = 2 into the inequalities:

10x + 15y = 10(2) + 15(2) = 50, which satisfies 10x + 15y ≥ 30 and 10x + 15y ≤ 60

x = 2 ≥ 0

y = 2 ≥ 0

Therefore, (2,2) is a valid solution within the given restrictions.

Step-by-step explanation:

The matrix of the given determinant is singular as the value of both the given determinant is equal to zero.

The determinant of the matrix is equal to,

[tex]\left|\begin{array}{ccc}3&1\\6&2\\\end{array}\right|[/tex]

= (3) × (2) - (1) × (6)

= 6 - 6

= 0

Since the determinant is zero, the matrix is singular.

[tex]\left|\begin{array}{ccc}2&-1&3\\-1&2&-2\\1&4&0\end{array}\right|[/tex]

= 2 ( 2(0) - 4(-2) ) + 1 ( -1(0) - 1 (-2) ) + 3 ( -1(4) - 1(2) )

= 2 ( 0 + 8 ) + 1 ( 0 + 2 ) + 3 ( -4 -2 )

= 16 + 2 - 18

= 18 - 18

= 0

Since the determinant is zero, the matrix is singular.

Therefore, the value of both determinant is equal to zero it implies that matrix is singular.

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The above question is incomplete, the complete question is:

For each of the following, compute the determinant and state whether the matrix is singular or nonsingular:

(a) [tex]\left|\begin{array}{ccc}3&1\\6&2\\\end{array}\right|[/tex]

(b) [tex]\left|\begin{array}{ccc}2&-1&3\\-1&2&-2\\1&4&0\end{array}\right|[/tex]

The final answer of the given question is- (4√6 - 4√2) / (-4) = -√6 + √2 .

A quotient is the result obtained from dividing one quantity by another. It is the answer to a division problem and represents how many times one number is contained in another.

To simplify the expression, we can do rationalize of the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:

(2√8) / (4+√12) × (√12-4) / (√12-4)

Simplifying the numerator:

(2√8) × (√12-4) = 22√22√3 - 2×2√2 = 4√6 - 4√2

Simplifying the denominator:

(4+√12) × (√12-4) = 12 - 16 = -4

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For a line parallel to the given line, the slope will be -5.

For a line perpendicular to the given line, the slope will be 1/5.

What is meant by the slope of a line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The given line is y=-5x+2

The standard slope-intercept form for a line is y=mx+c

where m is the slope and c is the intercept.

For the given line m=-5

That is the slope is equal to -5, so for a line parallel to the given line, the slope will be -5.

For the line perpendicular to the given line slope will be -1*-1/5=1/5

Because the product of the slopes of two perpendicular lines is equal to -1.

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The solution for question a is ln |y| = (1/2) x²- cos x - 1. The solution for question b is y = -8 - (16/√3) sin x. The solution for question c is ln |y/x + x sin x| = ln |x| + ln |y(π)| - ln |π|. We can show the working in the following manner.

To solve a differential equation with initial conditions, we usually follow these steps:

Separate the variables and integrate both sides to get a general solution that contains an arbitrary constant.

Use the initial conditions to find the value of the arbitrary constant and obtain a particular solution.

Check the solution by verifying that it satisfies the differential equation and the initial conditions.

For the given differential equations with initial conditions:

a. yy' = x sin x and y(0) = -1

We can separate the variables:

y' / y = x sin x / y

Integrating both sides:

ln |y| = (1/2) x² - cos x + C

where C is the arbitrary constant.

To find the value of C, we use the initial condition:

ln |-1| = (1/2) (0)² - cos 0 + C

C = -1

Therefore, the particular solution is:

ln |y| = (1/2) x²- cos x - 1

b. y' tan x = y + 8, y(π/3) = 8

We can separate the variables:

y' / (y+8) = cot x

Integrating both sides:

ln |y+8| = ln |sin x| + C

where C is the arbitrary constant.

To find the value of C, we use the initial condition:

ln |8+8| = ln |sin π/3| + C

C = ln 16 - ln √3

Therefore, the particular solution is:

ln |y+8| = ln |sin x| + ln 16 - ln √3

Simplifying:

|y+8| = (16/√3) |sin x|

y+8 = ± (16/√3) sin x

y = -8 ± (16/√3) sin x

We use the initial condition to determine the sign of the constant:

y(π/3) = -8 ± (16/√3) √3/2

y(π/3) = 8/√3

Since y(π/3) = 8, we take the negative sign:

y = -8 - (16/√3) sin x

c. xy' = y + x^2 sin x and y(π) = 0

We can separate the variables:

y' / (y/x + x sin x) = 1/x

Integrating both sides:

ln |y/x + x sin x| = ln |x| + C

where C is the arbitrary constant.

To find the value of C, we use the initial condition:

ln |y(π)/π + π sin π| = ln |π| + C

ln |y(π)| = ln |π| + C

C = ln |y(π)| - ln |π|

Therefore, the particular solution is:

ln |y/x + x sin x| = ln |x| + ln |y(π)| - ln |π|

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Answer: M= 6/2, 2/2, and when they ask you to simplify it, the answer is 3,1

Step-by-step explanation:

Acellus said it was right:D

Answer:

f(x) = 0.5x^3 + 2.5x^2 - 75x

Step-by-step explanation:

To write the equation of a polynomial with given x-intercepts and passing through a point, we can use the factored form of the polynomial:

f(x) = a(x - r1)(x - r2)(x - r3) ...

where r1, r2, r3, ... are the x-intercepts, and a is a constant that scales the polynomial vertically. Since the x-intercepts are 0, 10, and -15, we can write:

f(x) = a(x - 0)(x - 10)(x + 15)

Expanding this expression gives:

f(x) = a(x^3 + 5x^2 - 150x)

To find the value of a, we can use the fact that the polynomial passes through the point (2, -136):

-136 = a(2^3 + 5(2^2) - 150(2))

Simplifying this equation gives:

-136 = -272a

Dividing both sides by -880 gives:

a = 0.5

Therefore, the equation of the polynomial is:

f(x) = 0.5x^3 + 2.5x^2 - 75x

The answers of the expression is ,

1)55

2)21

3)160

4)6(2x+3)

5)13(x+3y)

6)width=3x+4

7)35b+56

8)28m+24f

9)-25

10)27c+36d.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expressions , we need to simplifying them . Then,

1) 30+25

=> 30+25=55

2) 35-14

=> 35-14=21

3)60+100

=> 60+100= 160

4)12x+18

=> 6.2x+6.3

=>6(2x+3)

5)13x+39y

=> 13x+13.3y

=>13(x+3y)

6) Length of rectangle = 6 in

Area of rectangle = 18x+24

=> 18x+24 = 6*width

=> width = 3x+4

7)7(5b+8)

=>7.5b+7.8

=>35b+56

8)4(7m + 6f)

=> 4.7m+4.6f

=> 28m+24f

9). 5(3 – 8)

=> 5(-5) = -25

10)9(3c + 4d)

=> 9.3c+9.4d

=>27c+36d.

Hence the answers of the expression is ,

1)55

2)21

3)160

4)6(2x+3)

5)13(x+3y)

6)width=3x+4

7)35b+56

8)28m+24f

9)-25

10)27c+36d.

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Answer:

Step-by-step explanation:

Use the distributive property:

[tex]2x^3 - 3x^2 - 7x + 2x^2 - 3x -7[/tex]

Combine like terms:[tex]2x^3 -x^2 -10x-7[/tex]

Bre purchased a total of 17 cups of coffee in the month of July by dividing the total amount spent by the cost per cup, which was $1.95.

The problem asks us to find the number of cups of coffee Bre purchased in July given the price of the reusable mug, the discounted price of a coffee with the mug, and the total amount she spent on coffee.

First, we can calculate the cost of each cup of coffee without the mug by subtracting the price of the mug from the total spent: $41.90 - $8.75 = $33.15.

Next, we can divide the cost of coffee without the mug by the discounted price of each cup of coffee to find the number of cups she purchased: $33.15 ÷ $1.95 = 17 cups.

Therefore, Bre purchased 17 cups of coffee in July.

This problem demonstrates how to use unit rates to solve real-world problems involving discounts and total cost. It also highlights the importance of understanding the problem and breaking it down into smaller, manageable parts to arrive at the solution.

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Answer:

m∠DAC = 72°

Step-by-step explanation:

Figure ABCD is a parallelogram.

As the diagonals BD and AC intersect each other, they form two pairs of vertical angles.  Since the vertical angles created by two lines intersecting each other are congruent:

⇒ m∠AFD = m∠BFC = 49°

The interior angles of a triangle sum to 180°. Therefore, for ΔADF:

⇒ m∠DAF + m∠AFD + m∠FDA = 180°

From inspection of the given parallelogram, m∠FDA= 59°.

Therefore, substitute the measures of ∠AFD and ∠FDA into the equation and solve for ∠DAF:

⇒ m∠DAF + 49° + 59° = 180°

⇒ m∠DAF + 108° = 180°

⇒ m∠DAF = 72°

As m∠DAF = m∠ DAC, then m∠DAC = 72°.

The volume of the fiberglass shell is approximately 891.484 cubic inches

Volume is a measure of the amount of space occupied by an object or a substance. It is a three-dimensional quantity that describes the amount of space that an object or substance occupies in the physical world.

The formula for the volume of a cube is given by

where s is the length of a side of the cube.

Here we have

Side of the cube = 11 inches

The cube is covered with fiberglass 0.7 inch

Using the formula V = s³,

The volume of the original cube is:

V₁ = s₃ = 11³ = 1,331 cubic inches

Since the coating is 0.7 inches thick, the new length of each side of the cube is:

s' = s + 2t = 11 + 2(0.7) = 12.4 inches

The volume of the coated cube,  

V₂ = s'³ = (12.4)³ = 1,906.624 cubic inches

The volume of the fiberglass shell is the difference between V₂ and V₂

V_fiber = V₂- V₁ = 575.624 cubic inches

To estimate the volume using differentials, we can use the following formula:  dV = (dV/ds) ds

where dV is the change in volume,

dV/ds is the partial derivative of the volume with respect to s,

ds is the change in length of a side of the cube.

Taking the partial derivative of V = s³, we get:

=> dV/ds = 3s²

=> dV/ds = 3(11)²

=> dV/ds = 363

Now, we can use the formula for differentials to estimate the change in volume:

dV = (∂V/∂s) ds = 363(0.7) = 254.1

Therefore,

The estimated volume of the fiberglass shell is:

V_fiber = 575.624 + 254.1 = 829.724 cubic inches

Therefore,

The volume of the fiberglass shell is approximately 891.484 cubic inches.

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The solution to the proportion 10/3 = 20/x is x = 6.

To solve the proportion 10/3 = 20/x using equivalent ratios, we need to find a ratio that is equal to the left-hand side and then find the equivalent ratio on the right-hand side. We can do this by cross-multiplying.

First, we can multiply both sides of the equation by 3 to eliminate the fraction on the left-hand side

10/3 × 3 = 20/x × 3

This simplifies to

10 = 60/x

Next, we can cross-multiply by multiplying both sides of the equation by x

10x = 60

Finally, we can solve for x by dividing both sides of the equation by 10

x = 6

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The given question is incomplete, the complete question is:

Solve the proportion using equivalent ratios. Explain the steps you used to solve the proportion, and include the answer in your response.

10/3 = 20/x

To multiply matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

The result of the multiplication is a matrix with a number of rows equal to the number of rows in the first matrix, and a number of columns equal to the number of columns in the second matrix.

Matrix is a collection of numbers arranged into rows and columns. It is a mathematical representation of a situation and is used in many aspects of mathematics, such as linear algebra, calculus, and game theory.

Matrix multiplication is the process of taking two matrices and multiplying them together. Matrices are a set of numbers arranged in rows and columns, and are used to represent linear transformations.

To calculate the result of each element in the product matrix, take the elements in each row of the first matrix and multiply them by the elements in each column of the second matrix. Sum the products and place the result in the cell at the intersection of the row and column. Repeat the process for each cell in the product matrix.

For example, if we want to multiply two matrices A and B, where A is a 3x2 matrix and B is a 2x3 matrix, we would take the first row of A and multiply it by the columns of B. The resulting matrix, C, would be a 3x3 matrix. Once we have multiplied the matrices, we can then add and subtract them to calculate their product.

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The measurement  of angle [tex]x[/tex] is = 57°

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin term "angulus," which means "corner," is where the word "angle" originates. The shared endpoint of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane.

The angles [tex]x[/tex] and 36 ° are alternate interior angles in the illustration, which indicates they are equal. Also equivalent are the angles [tex]x[/tex] and 87° because they are corresponding angles.

Using these angle connections, we can construct the following equation:

[tex]x + 36= 180 - 87[/tex]

When we simplify this solution, we obtain:

[tex]x + 36 = 93[/tex]

36 is subtracted from both parts to yield:

[tex]x= 57[/tex]

As a result, angle [tex]x[/tex] has a 57° value.

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The value of x is 102°

A triangle is a closed two-dimensional geometry with three angles that has three sides. It is a fundamental geometric shape that is frequently studied in mathematics. Triangles can be categorized based on the size of their angles and the length of their sides. Triangles typically come in the following forms: A triangle with three equal sides and three equal angles is called an equilateral triangle (60 degrees each). Triangle having two equal sides and two equal angles is called an isosceles triangle.

Big triangle angles are:

36°, 87° and third angle = 180 - (36+87)° = 57°

similarly,  left side small triangle angles are:

45°, 57° and third angle = 180 - (45+57)° = 78°

Two parallel line is there so, corresponding angles are equal,

So, x + 78° = 180°

x = 102°

Therefore, value of x is 102°

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