saeng wants to run the 100-meter-dash in a certain number of seconds.the table shows the change in times from her goal and her actual times for five races. between which two race numbers is saeng's third race.


race change in time from goal (s)

1 -1.2

2 +1 1/10


3 -1 1/4


4 -1.4

5 +1 1/2

If a rock needs to weigh 2,000 lb in order not to be shifted by waves, the volume of this basalt rock is equal to 0.625 in³.

In Science, the density of a chemical substance such as lead can be calculated by using this formula:

Density = M/V

Where:

Making volume the subject of formula, we have the following:

Volume = Mass/Density

Volume = 2,000/3,200

Volume = 0.625 in³.

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On solving the provided question, we can say that The function that can be made are f(x)= INT (x) + 5 and g(x)= INT (x) + 8

Quantities and their variations, equations and related structures, shapes and their placements, and locations where they can be found are all included in the study of mathematics.

The relationship between a group of inputs, each of which has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a codomain, often known as a scope. F is typically used to denote functions (x).

An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

The function that can be made are -

Let x = dollar spent

coffee shop rewards program offered 1 point for every whole dollar spent and an additional 5 points for each purchase

⇒ f(x)= INT (x) + 5

the shop changes the points offered to an additional 8 points for each purchase and 1 point for every whole dollar spent

⇒ g(x)= INT (x) + 8

The graph of g will be a vertical translation and 3 units up from the graph of f.

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Answer:

(i) 38.9%

(ii) 33.3%

(iii) 0%

Step-by-step explanation:

The total number of sweets is 18.  The probability of picking a color can be determined by dividing the number of each color by the total:

Blue:      5/18 or 27.8%

Red:       7/17 or 38.9%

Green:   6/18 or 33.3%

Yellow:  0/18 or 00.0%

Totals    18/18   100%

Note that the question askes for Yellow sweets, but there are none.

Answer:

D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)

The new coordinates of A would be (3, -2)

Answer:

A prime = (3,-2)

x=3

y=-2

The volume of the 14 cylindrical pillars made of concrete is 8.8 m³

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The volume of a cylinder is:

Volume = π * radius² * height

A temple has 14 cylindrical pillars made of concrete. If the radius of base of each pillar is 20 cm and height is 5 m.

Radius = 20 cm = 0.2 m

Volume of each cylindrical pillar = π * 0.2² * 5 = 0.628 m³

Volume of 14 cylindrical pillar = 14 * 0.628 m³ = 8.8 m³

The volume of the pillars is 8.8 m³

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The triangle that's created has angles of 90°, 45° and 45°.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The triangle is attached.

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The period of the function is 1.57 s.

The amplitude of the function is 6.

The equation of the midline, y = 6 sin 4x + 0.

The general form of a sinusoidal function is y = A sin(Bx - C) + D,

where:

For the given function y = 6 sin 4x, we can see that:

A = 6 (the amplitude is the absolute value of the coefficient of the sine function)

B = 4 (the coefficient of x inside the sine function determines the period)

C = 0 (there is no horizontal shift)

D = 0 (there is no vertical shift, so the midline is the x-axis)

Therefore, the period T is given by:

T = 2π/B = 2π/4 = π/2 = 1.57 s

The midline is the x-axis, so its equation is y = 0.

The amplitude is A = 6.

Therefore, we can write the equation of the function in the general form as:

y = 6 sin 4x + 0

or

y = 6 sin(4x)

Note that since the midline is the x-axis and there is no vertical shift, the sine function will oscillate between -6 and 6.

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Gabriel would have $45,985.67 more than Ava in his account. This is because Gabriel's account is compounded daily, meaning that his interest would be compounded 365 times a year, while Ava's account is compounded continuously,

Compounding is the process of combining two or more elements to create a new, more complex product. In finance, compounding refers to the interest earned on an investment that is reinvested and earns additional interest. This cycle continues, allowing the principal to grow exponentially over time. The effective rate of return is greater than the stated interest rate.

The calculation for Gabriel's account is: 23,000 * (1.11^(365*8)) = $69,985.67. The calculation for Ava's account is: 23,000 * e^(0*8) = $24,000. The difference between the two is $45,985.67.

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Answer:997

Step-by-step explanation:

The table shows a proportional relationship is:

Number of Necklaces         2        4       6      8

Number of Beads                20     40     60    80

As per the data given:

The tables show the number of necklaces made and the number of beads used.

Number of Necklaces         2        4       6      8

Number of Beads                20     40     60    80

From the table:

2 : 20 = 1 : 10

4 : 40 = 1 : 10

6 : 60 = 1 : 10

8 : 80 = 1 : 10

As there is a common ratio between each value there will be a proportional relationship

Number of Necklaces         2       4        6       8

Number of Beads                10     15      20     25

From the table:

2 : 10 = 1 : 5

4 : 15

6 : 20 = 3 : 10

8 : 25

As there is no common ratio between each value there will not be any proportional relationship

Number of Necklaces        2       4         6        8

Number of Beads               14      21      28      35

From the table:

2 : 14 = 1 : 7

4 : 21

6 : 28 = 3 : 14

8 : 35

As there is no common ratio between each value there will not be any proportional relationship

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The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.

Let X be the amount of mix A (in pounds), and Y be the amount of mix B.

The constraints are

20X + 10Y >= 400

10X + 30Y >= 960

5X + 10Y >= 210

X >= 0,  Y >= 10.

The objective function to minimize is  F(X, Y) = 20X+40Y.

In the equivalent form, the constraints are

2X + 1Y >= 40

X+ Y >= 33

X+2Y >= 42

The feasibility area is the infinite area in the first quadrant which lies ABOVE each of the following straight lines :

A red   (which represents the constraint (1'));

The green (which represents the constraint (2')),

A blue  (which represents the constraint (3')).

Plot 2X + 1Y = 40 (const. (1'), red);  

X+Y = 33 (const. (2'), green)

X+2Y = 42 (const. (3'), blue)

The four corner points of the area are:

P1 = (0,40), P2 = (7,26), P3 = (24,9), P4 = (42,0)

As per the Linear Programming method, we can calculate and compare the values at these 4 points.

These values of P1, P2, P3,P4 are:

P1: F(0,40) = 0 + 40*40 = 1600

P2: F(7,26) = 20*7+40*26 = 1180

P3: F(24,9) = 20*24+40*9 = 840

P4: F(42,0) = 20*42+0 = 840.

By comparing the numbers, any value of (X, Y) that lies on the segment [P3, P4] satisfies the minimum requirements.

The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.

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The angles m∠w and m∠y are supplementary angles and their measures are 50° and 130° respectively.

If two angles add up to 180°, they are considered supplementary angles, we can observe that the positions of the angles formed by the transversal cutting the parallel lines makes the two angles on a straight line which are supplementary so;

4x + 6 + 12x - 2 = 180

16x + 4 = 180°

16x = 180 - 4 {subtract 4 from both sides}

16x = 176

x = 176/16 {divide through by 16}

x = 11.

m∠w = 4(11) + 6 = 50°

m∠y = 12(11) - 2 = 130°

Therefore, the supplementary angles m∠w and m∠y have their measures as 50° and 130° respectively.

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Answer:

The system of equations are solved by eliminating a variable and solving for the remaining variable. Add the two equations together to eliminate the y, then solve for x.

The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.

Let H be the height and W be the width of the parallelogram. Then the area of the parallelogram will be given as,

Area of the parallelogram = H × W square units

The width of the parallelogram is 32.2 units and the height of the parallelogram is 12.6 units. Then the area of the parallelogram is given as,

A = 32.2 x 12.6

A = 405.72 square units

The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.

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In Step 3, Mike made an error. He incorrectly calculated his value for m by multiplying 2 by 22 instead of 2 by (22 + 4). The correct equation should have been m = 2(22 + 4).

Sally's formula for calculating b is correct:

b = 11

Sally's formula for calculating m is also correct:

m = 2(11) + 4 = 26

Mike's formula for calculating b is correct:

b = 22

However, Mike's formula for calculating m is incorrect. Instead of using the formula m = 2(b + 4), he used the formula m = 2(22 + 4), which gives him a value of 50 instead of the correct value of 50.

Therefore, Mike made a mistake in Step 3. He computed his answer for m erroneously by multiplying 2 by 22 rather than 2 by (22 + 4). The proper formula would have been m = 2(22 + 4).

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Answer:

The leading coefficient is -1. The degree of the polynomial is cubic.

Step-by-step explanation:

The leading coefficient is the number in front of the variable showcasing the biggest exponent. The degree of the polynomial is considered by looking at the biggest exponent, and identifying which one it is. In this case, it's a cubic polynomial.

Difference of (-x² + 9xy) and  (x² + 6xy - 8y²) is - 2x² + 3xy + 8y².

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Given expression,

(-x² + 9xy) - (x² + 6xy - 8y²)

Distributing negative sign

-x² + 9xy - x² - 6xy + 8y²

Adding like terms

- 2x² + 3xy + 8y²

Hence, - 2x² + 3xy + 8y² is the difference of (-x² + 9xy) and (x² + 6xy - 8y²).

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Answer:

f(-4) = -18

Step-by-step explanation:

So we have f(x) and we have f(-4). The X is where the -4 is so that means x = -4.

Since we know that, we plug it into the equation. Everywhere we see an X

So instead of 5(x) + 2, it will be 5(-4)+2.

5 times -4 is -20, which makes it -20 + 2

-20 + 2 = -18. Giving us our answer

Answer:

[tex]-18[/tex]

Step-by-step explanation:

f is a function of x. f depends on x. For every value of x, a certain value of f(x) is obtained.

This question requires us to determine the value of f(x) for x = [tex]-4[/tex]:

Substitute x = [tex]-4[/tex] into the provided function:

[tex]f(-4) = 5(-4) +2[/tex]

         = [tex]-20 + 2[/tex]

         = [tex]-18[/tex]

The dimension of rectangular dining room measures length 24.3 and breadth  1.73 metres.

In mathematics, dimensions refer to the length or width of an area, region, or space in one direction. It is just the measurement of something's length, width, and height. Length, breadth, and height are common ways to describe dimensions.

Our world has three dimensions.

Height, length, and width are the three dimensions that define everything around us, including the homes we live in and the everyday items we use.

Length, breadth, and height are the common three dimensions that can be described in three distinct ways.

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Divergence and curl are two important concepts in vector calculus. They are used to describe the behaviour of vector fields, which are functions that assign a vector to each point in space.

Divergence is a scalar function that describes the extent to which a vector field is spreading or contracting at a given point. If the vector field is spreading, the divergence at that point is positive; if it is contracting, the divergence is negative.

If the vector field is unchanged in size, the divergence is zero. The formula for the divergence of a vector field is given by the dot product of the gradient of the field with the unit normal vector at a point.

Curl, on the other hand, is a vector function that describes the rotational aspect of a vector field. It is defined as the cross-product of the del operator and the field. Curl measures the rate at which the vectors in a field are rotating about a point. If the curl is zero, the field is said to be irrotational. If the curl is non-zero, the field is said to be rotational.

Divergence and curl cannot be defined for a scalar function because a scalar function assigns a single scalar value to each point in space, while divergence and curl describe the behaviour of vector fields.

A scalar function has no direction or rotational component, so there is no way to describe the spreading or contracting behaviour or the rotational behaviour of the function.

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At the end of 24 hours, 48 cupcakes will have grown. Every 8 hours, two cupcakes are grown, so after 24 hours, 24 sets of two cupcakes have been grown. Therefore, 48 cupcakes have grown.

At the end of 24 hours, 48 cupcakes will have grown. This is because every 8 hours, two cupcakes are grown. After 24 hours, 24 sets of two cupcakes have been grown. This means that in the 24 hours, two cupcakes were grown a total of 24 times. When this total is multiplied by two, it results in 48 cupcakes being grown. Therefore, after 24 hours, 48 cupcakes have grown. It is important to note that this is only the number of cupcakes that have grown in the 24 hour period, and not the total number of cupcakes. This number includes any cupcakes that were already present at the beginning of the 24 hour period, so the total number of cupcakes at the end of the 24 hour period could be higher than 48.

1. Calculate the number of sets of cupcakes grown in 24 hours: 24 hours divided by 8 hours = 3 sets

2. Calculate the number of cupcakes grown in 24 hours: 3 sets multiplied by 2 cupcakes = 6 cupcakes

3. Calculate the total number of cupcakes grown in 24 hours: 6 cupcakes multiplied by 4 sets = 24 cupcakes

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Answer:

she can buy 2 outfits

Step-by-step explanation:

Answer:

t = 6

Step-by-step explanation:

-(t+2) = -31 +23

Solve for t.

Combine like terms on the right.

-(t+2) = -8

Divide each side by -1.

t+2 = 8

Subtract 2 from each side.

t+2-2 = 8-2

t = 6

(c) When x is 2.3, the predicted value is 0.02 less than the actual value first from database (d). When x is 3 and the predicted value is compared to the actual figure from the table, the residual is -1.27.

For instance, rounding these values with two decimal places to one nearest tenth (3.4 + 5.5) would result in an approximate reply of 8.9. The estimated result would be 9, but they might potentially be increased to the next full number (3 + 6). The correct response is 8.91.

(c). Nearly 6.2 Minus 6.18 = 0.02 separates the projected result from the actual value. As a result, there is hardly any change. The residual is thus 0.02

(d). Y Equals 4.47 whenever x = 3 because 2.45 × 3 + 11.82. Since the true value is 3.2 and the anticipated value is 4.47, the differences between the two is 1.27. The residual is thus 1.27.

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Answer:

Step-by-step explanation:

There are 6 possible outcomes for each of the two rolls, so there are 6 x 6 = 36 possible outcomes for the sum of two rolls.

Event A: The sum is greater than 8.

There are five possible ways to achieve a sum greater than 8: (3, 6), (4, 5), (4, 6), (5, 4), and (6, 3). Each of these outcomes has a probability of 1/36. Therefore, the probability of event A is:

P(A) = 5/36

Event B: The sum is an even number.

There are three possible ways to achieve an even sum: (1, 1), (2, 2), and (3, 3). Each of these outcomes has a probability of 1/36. There are also three possible ways to achieve a sum of 4: (1, 3), (2, 2), and (3, 1). Each of these outcomes has a probability of 1/36. Similarly, there are three possible ways to achieve a sum of 6, 8, 10, and 12. Therefore, the probability of event B is:

P(B) = (3 + 3 + 3 + 3 + 3 + 3)/36

P(B) = 18/36

P(B) = 1/2

Therefore, the probability of event A is 5/36 and the probability of event B is 1/2.

Answer:

1+(2×m)

Step-by-step explanation:

We can break the problem down and find the keywords.

1 plus the product of 2 and m

plus=+

product=×

1+(2×m)

Answer:

- 3cos²Θ

Step-by-step explanation:

using the identity

sin²Θ + cos²Θ = 1 , then

sin²Θ = 1 - cos²Θ

given

3sin²Θ - 3

= 3(1 - cos²Θ) - 3

= 3 - 3cos²Θ - 3

= - 3cos²Θ