Solve the following inequality using the algebraic approach:
3x > -6
a.
b.
C.
d.
X > -2
x<-2
x > 2
x < 2

Answer:

Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:

7 + 24 + 14 + 1 + 4 = 50

Therefore, there are 50 individuals included in the summary.

Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.

Given:

The number of pets for each of 14 students is,

1, 4, 4, 2, 3, 4, 3,0,0,0,3,0,0,1.

Mode: It is the number that appears the most.

In the given data,

0 appears the most that is for 5 times.

So, the mode of the given data is 0.

Answer: Mode is 0.

Answer:

Gradient normal x gradient tangent = -1 is a mathematical expression that relates the normal and tangent vectors of a curve in three-dimensional space. The gradient of a scalar function is a vector that points in the direction of the greatest rate of increase of the function. The normal vector is perpendicular to the surface defined by the function, and the tangent vector is a vector that lies on the surface and points in the direction of the curve.

In mathematics, the cross product of two vectors is a vector that is orthogonal to both vectors, and the magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. In this case, the normal and tangent vectors of a curve form an orthogonal basis, meaning that they are perpendicular to each other. The expression gradient normal x gradient tangent = -1 says that the magnitude of the cross product of the normal and tangent vectors is equal to -1. This means that the normal and tangent vectors form a right-handed coordinate system, where the cross product is negative because the normal vector points in the opposite direction to the positive z-axis.

The equation which is in the quadratic form is 6x⁴ + 7x² - 3 = 0. So Option B is correct.

An equation is quadratic in form if it can be written in the form of ax + bx + c = 0, where a, b, and c are constants and x is the variable.

Among the given equations, we can see that the first, third, and fourth equations are not quadratic in form, since they contain x raised to powers other than 2.

The second equation, 6x⁴ + 7x² - 3 = 0, can be written in quadratic form by making a substitution.

If we let y = x², then we can write the equation as 6y² + 7y - 3 = 0,

which is a quadratic equation in y. Substituting back x² for y,

we get:

6x⁴ + 7x² - 3 = 0

So the second equation is quadratic in form.

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Answer:

Step-by-step explanation:

answer b, trust

Answer:

 2,575,384 =

 2,000,000  

+ 500,000  

+ 70,000  

+ 5,000  

+ 300  

+ 80  

+ 4

Step-by-step explanation:

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Given:

Distance travelled with the wind = 260 miles

Distance travelled against the wind = 180 miles

Speed of wind = 20 mph.

Let's find the rate of the plane in still air.

Apply the formula:

Thus, we have the equations:

Now, the rate in still air will be:

Now, let's solve for r in the equation above.

Cross multiply:

Divide both sides of the equation by 20:

Solving further:

Divide both sides by 4:

Therefore, the rate in still air is 110 mph.

ANSWER:

110 mph

Answer:

54,000

Step-by-step explanation:

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

Given :

The statistician reported that the mean serve speed was 100 miles per hour

the standard deviation of the serve speeds was 15 mph

Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric

To find :

What percentage of the player's serves were between 115 mph and 145 mph?

Solution :

μ =100

σ = 15

P ( 115 < x <145)

= P ( \(\frac{115-100}{15}\) <  x-μ /6 <\(\frac{145-100}{15}\) )

= P ( \(\frac{15}{15}\) < z < \(\frac{15}{15}\) )

= p ( 1<z<3)

= p( z<3)-p(z-1)

=0.9987-0.8413

=0.1574

p ( 115<xx<145)= 15.74 %

p( 115<x<145)= approximately 16%

The percentage of players serves were between 115 mph and 145 mph is approximately 16%.

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The expression O cos(k0 + 0) + i sin(k0 + 0) is commonly used in proofs involving complex numbers and trigonometric functions, representing the complex exponential function \(e^(ik0)\).

The expression that will complete the proof depends on the given context and what exactly needs to be proved. However, in general, the expression O cos(k0 + 0) + i sin(k0 + 0) is often used in proofs involving complex numbers and trigonometric functions.

This expression represents the complex exponential function \(e^(ik0)\), where k0 is a constant. The cosine term represents the real part of the complex number, while the sine term represents the imaginary part.

The addition of 0 in the arguments of both cosine and sine indicates that the complex number is in polar form, with a magnitude of 1 (\(since cos^2 +\) \(sin^2 = 1\) for all angles).

Using this expression, we can perform various operations and manipulations to prove different results, such as De Moivre's theorem or Euler's formula.

Ultimately, the choice of expression will depend on the specific problem and what needs to be proved.

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The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².

Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.

The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.

So, 1/2 * ( 9+5) * 3

   = 1/2 * 14 * 3

   =  1/2 * 42

   =  21 cm²

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Answer:

No

Step-by-step explanation:

3(x+2) = y

3(4+2) = 9

3(6) = 9

18 does NOT equal 9

The height of the tower is 2358 feets.

David is standing 500 feet away from the base of a cell phone tower.

The angle of elevation from his eyes to the top of the tower is 78°. David eyes are 6 feet above the ground . The height of the tower can be found as follows:

This situation forms a right angle triangle. Therefore,

using trigonometric ratios,

tan 78° = opposite / adjacent

tan 78° = x / 500

cross multiply

x = 500 tan 78°

x = 500 × 4.70463010948

x = 2352.31505474

Therefore,

height of the tower = 2352 + 6

height of the tower = 2358 ft.

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The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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Answer:

20 books

Step-by-step explanation:

can u help me with my math question please

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:

I think its C

Step-by-step explanation:

Answer:

the answer is 57

Step-by-step explanation:

because you round to the nearest foot which it means that the answer good luck hope this helps

The sum of the first 8 terms in the given geometric series is 65,535.

A geometric series is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed non-zero constant called the common ratio.

In this case, the common ratio is 4, and the first term is 3. So, the first 8 terms of the series are:

3, 12, 48, 192, 768, 3072, 12288, 49152

To find the sum of the first 8 terms, we can use the formula for the sum of a finite geometric series:

S = a(1 - r^n) / (1 - r)

where S is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we get:

S = 3(1 - 4^8) / (1 - 4)

Simplifying the expression, we get:

S = 65,535

Therefore, the sum of the first 8 terms in the given geometric series is 65,535.

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--The question is incomplete, answering to the question below--

"The common ratio in a geometric series is 4 and the first term is 3. Find the sum of the first 8 terms in the series."

The number of buses are 3 they took if each van holds 6 students and each bus holds 20 students.

What are the number of buses?

Let's use V and B to represent the number of vans and buses, respectively.

We know that:

V + B = 5 (since there were 5 vehicles in total)

6V + 20B = 72 (since there were 72 students in total)

We can use the first equation to solve for V in terms of B:

V = 5 - B

Then we can substitute this expression for V into the second equation:

6(5 - B) + 20B = 72

30 - 6B + 20B = 72

14B = 42

B = 3

Therefore, the class took 3 buses.

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Complete question is: A class of 72 students went on a field trip. They took 5 vehicles, some vans and some buses. the number of buses are 3, they took if each van holds 6 students and each bus holds 20 students.

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

the answer is 23

Step-by-step explanation:

2x9+15-10

18+15-10

33-10

23

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

(48, 3), (80, 5), (160, 10)

Answer:

Surface Area = (2 • π • r²) + (2 • π • r • height)

Surface Area = 2 * 3.14 * 3*3 + 2 * 3.14 * 3 * 15

Surface Area = 56.52 +  282.60

Surface Area = 339.12

Formulas: http://www.1728.org/diamform.htm

Step-by-step explanation:

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

he spent 2hours 50minutes snowboarding

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

5hours minus 2hours 10minutes