if x is 6 then 7x=_____.

Answer:

x=7 is the answer

Step-by-step explanation:

Answer:

x = five over two and x = −3

Step-by-step explanation:

Let's solve your equation step-by-step.

2x2+x=15

Step 1: Subtract 15 from both sides.

2x2+x−15=15−15

2x2+x−15=0

Step 2: Factor left side of equation.

(2x−5)(x+3)=0

Step 3: Set factors equal to 0.

2x−5=0 or x+3=0

x=5/2 or x=−3

Answer:

6 .... 1

3 ... 1/100

9.... 1/1000

The most appropriate conclusion is: A) This is convincing evidence of an association between longer hand and longer foot.

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. It is used to compare observed frequencies of data to the expected frequencies to determine if they differ significantly. The test is based on the principle of comparing the difference between the observed frequencies and the expected frequencies, and then determining if this difference is statistically significant.

Here,

At the 0.05 significance level, with a chi-square statistic of 11.942 and 4 degrees of freedom, the P-value is 0.018.

Since the P-value is less than the significance level, we reject the null hypothesis of no association and conclude that there is evidence of an association between longer hand and longer foot.

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Complete question:

Imani was curious if there was a relationship between one hand being longer than the other and one foot being longer than the other for 100 randomly selected students. Here is a summary of the data and the results from a chi-square test:

The equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

To determine the equation of a parabola that opens to the right, has a focus at (-1, -3), and a focal diameter of 8

we can use the standard form of the equation for a parabola with a horizontal axis:

(x - h)² = 4p(y - k)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus.

Since the parabola opens to the right, the vertex will be to the left of the focus.

Therefore, the vertex will be at (-1 - p, -3).

The focal diameter is given as 8, which means the distance between the vertex and the focus is p = 8/2 = 4.

Plugging these values into the equation, we have:

(x - (-1 - 4))² = 4 × 4 × (y - (-3))

Simplifying:

(x + 5)² = 16(y + 3)

x² + 10x + 25 = 16y + 48

Rearranging to isolate y:

16y = x² + 10x + 25 - 48

16y = x² + 10x - 23

Dividing by 16:

y = (1/16)x² + (10/16)x - (23/16)

Therefore, the equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

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The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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Answer:

3

Step-by-step explanation:

There are 8 pints in a gallon. If there are 24 pints needed for this party then you divide 24 by 8.

24/8= 3

3 is the amount of gallons

Answer:

y>18

Step-by-step explanation:

Move all terms not containing y to the right sideof the inequality.

Inequality Form:

y>18

Answer:

5. 12 : 3 is equivalent 4 : 1

A. A table of values and graph of the function is shown below.

B. The object would hit the ground at approximately 8.963 seconds.

Based on the information provided, we can logically deduce that the height (s) in meters, of this object above the​ ground is related to time by the following quadratic function:

s(t) = -4.9t² +39.2t + 42.3

When t = 0, s(t) is given by;

s(0) = -4.9(0)² +39.2(0) + 42.3

s(0) = 42.3

When t = 1, s(t) is given by;

s(1) = -4.9(1)² +39.2(1) + 42.3

s(1) = 76.6

When t = 2, s(t) is given by;

s(2) = -4.9(2)² +39.2(2) + 42.3

s(2) = 101.1

Therefore, the table can be created as follows;

Time (t)     Height s(t)

0                  43.3

1                   76.6

2                  101.1

3                  115.8

4                  120.7

5                  115.8

Part B.

Generally speaking, the height of this object would be equal to zero (0) when it hits the ground. By critically observing the graph (see attachment), we can logically deduce that the object would hit the ground at approximately 8.963 seconds.

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Answer:

option b .....is answer

Answer:

189.25

Step-by-step explanation:

multiply 15 by 10 to find area of rectangle.

The area of rectangle is 150.

To find area of semicircle 1/2(pi r^2)

divide 10 by 2 to find radius, which is 5

area of semicircle would be 39.27

add 150 to 39.27

the answer is 189.27

189.25 is close enough so that is answer

The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5

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

(12 + 3) ÷ 5

The above expression is a quotient expression

However, we can apply some algebraic properties

Take for instance;

12 + 3 can be expressed as 3 + 12

So, we have

(12 + 3) ÷ 5 = (3 + 12) ÷ 5

Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5

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The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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The way the numbers will be placed in the square box will be:

First row = 4 12 14

Second row = 2 10 18

Third row = 6 8 16

It should be noted that the question is simply about adding the numbers and getting 39 in each place.

This will be:

First row = 4 12 14 = 4 + 12 + 14 = 30

Second row = 2 10 18 = 2 + 10 + 18 = 30

Third row = 6 8 16 = 6 + 8 + 16 = 30

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The series for this problem is absolutely convergent, as the limit assumes a value lower than 1.

The infinite series for this problem is defined as follows:

\(\sum_{i = 1}^{\infty} \frac{1}{n!}\)

Hence the general term is given as follows:

\(a_n = \frac{1}{n!}\)

The limit is given as follows:

\(L = \lim_{n \rightarrow \infty} \left|\frac{a_{n + 1}}{a_n}\right|\)

The (n + 1)th term is given as follows:

\(a_{n + 1} = \frac{1}{(n + 1)!}\)

The factorial can be simplified as follows:

(n + 1)! = (n + 1) x n!.

Hence the limit will be calculated of:

1/[(n + 1) x n!] x n! = 1/(n + 1).

The result of the limit is given as follows:

\(L = \lim_{n \rightarrow \infty} \frac{1}{n + 1} = 0\)

As the limit assumes a value of zero, the series is absolutely convergent.

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Answer:

\(f(x) = \frac{1}{ {x}^{14} } \\ f'(x) = - \frac{14}{x {}^{15} } \)

Answer:

Step-by-step explanation:

You want the distances north and east of the origin that a plane ends up after flying 400 km at a bearing of 25°, then 700 km at 80°.

For some distance r and bearing angle θ, the (north, east) coordinates will be ...

  (north, east) = (r·cos(θ), r·sin(θ))

For the trip at hand, the final coordinates of the plane are ...

Distance north = (400 km)cos(25°) +(700 km)cos(80°)

  = 362.52 km +121.55 km = 484.07 km

B is about 484 km north of O.

Distance east = (400 km)sin(25°) +(700 km)sin(80°)

  = 169.05 km +689.37 km = 858.41 km

B is about 858 km east of O.

__

Additional comment

Rectangular coordinates of a point at distance r from the origin and an angle θ measured CCW from the +x axis are given by ...

  (x, y) = (r·cos(θ), r·sin(θ))

You may notice the similarity to the coordinates described above. That is why we can use a calculator the way we have in the attachment. The imaginary part of the complex number represents the distance east.

The number of points gained overall by Julia playing the game is 30 point

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

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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Solution:

Given that;

Collins buy 60 eggs at a cost price of R110.

Where

If 5 dozens cost R110, then a dozen will cost

Hence, the cost price for a dozen of eggs is R22

b) He sold half of the eggs at R65 and the remaining half at R60

To find the profit,

Since half of the eggs is 30,

The total selling price will be

The profit made will be

The average profit per eggs will be

Hence, profit made per eggs is R0.25

Answer:

True

Step-by-step explanation:

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

9514 1404 393

Answer:

Step-by-step explanation:

The dimensions of the rectangle are 3 by 5 units, so the perimeter is ...

  P = 2(W+L) = 2(3+5) = 16 . . . units

__

The area is ...

  A = WL = (3)(5) = 15 . . . square units

The given expression can be expressed in the trinomial in standard form as,

Thus, the above expression is the requried trinomial.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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The midpoint of the line segment with the endpoints is (4, 1)

The endpoints are given as:

E= (-2,8) and F = (10, -6)

The midpoint of the line segment with the endpoints is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (-2 + 10, 8- 6)

Evaluate the sum

So, we have:

Midpoint = 0.5 * (8, 2)

Evaluate the products

So, we have:

Midpoint = (4, 1)

Hence, the midpoint of the line segment with the endpoints is (4, 1)

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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