Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the -values in order from least to greatest (read the graph from left to right).

First you must know the standard equation of a line and this is expressed as:

where:

m is the slope of the line

c is the intercept

Given

Slope m = 5/2

Next is to get the intercept c:

To do that, you will substitute m = 5/2 and the coordinate (0, -4) into the equation above as shown:

Next is to get the required equation by substituting m = 5/2 and c = -4 into the equation above as shown:

Hence the required equation is espressed as:

For Fredrico to make an average of at least 7.4 on all four dives, he must get at least 5.6 in his last dive.

The average is the mean of the total scores that Fredrico scored in his dives.

The average can be computed by dividing the total scores by the number of dives.

The average is the quotient of the division operation of the total scores and the number of dives.

The total score based on an average of 7.4 = 29.6

The total scores obtained = 24 (7.2 + 8.4 + 8.4)

The remaining score to obtain to get the average of 7.4 = 5.6 (29.6 - 24)

Thus, Fredrico needs an additional 5.6 score in the last dive to make the average.

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Fredrico needs to score at least 5.6 on his final dive in order to achieve an average of at least 7.4 on all four dives.

Let's assume the required score would be x on his final dive

Mean = ∑x/n

The average represents the mean of all of Fredrico's dive-related scores.

Here, n = 4

Sum of Observations (∑x) = 7.2 + 8.4 + 8.4 + x

∑x  = x + 24

Mean = ∑x/n

Substitute the values in the above formula,

⇒ 7.4 = (x + 24) / 4

Apply the cross-multiplication operation in the above equation,

⇒ 7.4 × 4= (x + 24)

⇒ 29.6 = x + 24

⇒ x = 29.6 - 24

Apply the subtraction operation to get

⇒ x = 5.4

Therefore, Fredrico needs to score at least 5.6 on his final dive

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INFORMATION:

STEP BY STEP EXPLANATION:

ANSWER:

The first step to solving this problem is to put the variable on one side. Thus, you must move 7 to the right side to make   [tex]\frac{f}{25} \leq -3[/tex]

Next, you must multiply the 25 to the right side to isolate the variable

You get [tex]f \leq -75[/tex]

With this explained, the answer would be the second option (f=-75)

Hope this helped :)

1.volume = mass*density

v = 1.2 * 3.6 = 4.32 cm3

The density of a substance quantifies how tightly its molecules are packed, which affects how heavy or light it is.

Density is calculated as follows: density=mass/volume. Most often, mass is measured in grams or kilograms. Most often, volume is measured in cubic centimeters (cm3), cubic meters (m3), or millileters (mL).

How can you find mass from density?

multiply the volume by the density.

Mass per unit volume is the definition of density.

ρ = m V

This can be rearranged to yield the mass expression.

m = ρ × V

Example:

What mass of the liquid is present if 500 mL of it has a density of 1.11 g/mL

m = ρ × V = 500 mL × 1.11 g

1 mL = 555 g

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Remember the definition of the tangent function:

Then, we notice that:

Then, we can conclude that:

Something important to remember is that, in quadrant II, the value of sin(x) is positive, whereas the value of cos(x) is negative

So,

Therefore, the answer to the question is option A

The composition of functions g(x) and f(x) evaluated in x = 5 is:

(g o f)(5) = 6

Here we have two functions f(x) and g(x), and we want to find the composition evaluated in x = 5, this is:

(g o f)(5) = g( f(5) )

So first we need to evaluate f(x) in x = 5, and then g(x) in f(5).

f(5) = 5² - 6*5 + 2 = 25 - 30 + 2 = -3

Then we have:

(g o f)(5) = g( f(5) ) = g(-3)

Evaluating g(x) in x = -3 gives:

g(-3) = -2*(-3) = 6

Then the composition is:

(g o f)(5) = 6

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Given:

To Determine: The numbers of calls for the which the two plans are equal

Solution

Let x be the number of minutes of calls for which the two plans are equal

The cost of plan A is

The cost of plan B

If the cost for the two plans are equal, then

Solve for x

Hence, the number of minutes of calls for which two plans are equal is 625 minutes

All of the base of the slice corresponds to the circumference of the circle, but since half of it just accounts for the base of the parllelogram therefore, the base is approximately equal to only half of the circumference.

Let us start with the following quadratic function:

the X-intercepts are the collection of values to X which makes f(x) = 0, and it can be calculated by the Bhaskara formula:

where the values a, b, and c are given by:

Substituting the values from the proposed equation, we have:

From the above-developed solution, we are able to conclude that the solution for the first box is:

Now, the y-intercept, is just the value of y when x = 0, which can be calculated as follows:

From this, we are able to conclude that the solution for the second box is:

Now, the vertex is the value of minimum, or maximum, in the quadratic equation, and use to be calculated as follows:

substituting the values, we have:

which means that the solution for the thirst box is:

Now, the line of symmetry equation of a quadratic function is a vertical line that passes through the vertex, which was calculated to be in the point: (1/2, -49,4).

Because this is a vertical line, it is represented as follows:

A qualitative variable, also called a categorical variable, is a variable that isn’t numerical. It describes data that fits into categories.

From the given options below, the arrival status of a train ( early, on time, late, canceled) and a person's blood type are the only qualitative variables.

Hence, Option 3 and Option 5 are the correct answers.

We have the following inequality

We must graph this inequality, In order to understand this I will explain term by term

But first, we must remember that in mathematics, the absolute value or modulus of a real number x, denoted by |x|, is the non-negative value of x regardless of the sign, positive or negative. This must be taken into account for the |x+3| term.

That is to say that the value will always be assumed by its magnitude and we will tend to have the same behavior on both the negative and positive x-axis.

Taking this into account and that the slope is -2/3 the graph would look like this:

Now, we must remember two rules of function translation, these are as follows:

y = f(x) original funtion

y = f(x+c) it is moved horizontally "c" units to the left

y = f(x)+c it moves vertically "c" units upwards

So taking into account these rules our graph is shifted 3 units to the left and 4 units upwards.

In conclusion, this graph looks like this:

The empirical formula should be used after calculating the standard deviation and collecting the exact data needed for a forecast.

The empirical rule is a term used in statistics also known as the 68–95–99.7 rule. This rule is majorly used in forecasting the final outcome of events.

The empirical rule can be used to therefore determine a rough estimate of the outcome of the impending data to be collected and analyzed. This is done after calculating the standard deviation and collecting the exact data needed.

68–95–99.7 rule,

Given:

80 feet is the final answer.

The angle subtend an arc length of 7 feet is 44.56°

Given,

Radius of a circle = 9 feet

Arc length of a circle = 7 feet

Arc length :

The distance between two places along a segment of a curve is known as the arc length.

Formula for arc length:

AL = 2πr (C/360)

Where,

r is the radius of the circle

C is the central angle in degrees

Now,

AL = 2πr (C/360)

7 = 2 × π × 9 (C/360)

7 = 18 π (C/360)

7/18π = C/360

C = (7 × 360) / (18 × π)

C = (7 × 20) / π

C = 140 / π

C = 44.56°

That is,

The angle subtend an arc length of 7 feet is 44.56°

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EXPLANATION:

We are given a dot plot as shown which indicates the ages of members of an intermediate swim class.

The dot plot indicates a cluster to the right for the values;

This indicates that a reasonable amount of the members are within that age range.

For this reason, it is not likely that Mira will be able to convince her mother.

This is because Mira's age (13 years old) is within the area where the data are clustered.

Therefore;

ANSWER:

(1) The data are clustered between 11 and 14 years old

(2) It is not likely that she will be able to convince her mother

(3) Mira's age is within the area where the data are clustered.

The expression of the mathematical statement given as the difference of 4R and 108 is |4R - 108|

From the question, the mathematical statement is given as

The difference of 4R and 108

In mathematics, the difference of numbers or expressions implies that we subtract one of the numbers from the other number or expression

This in other words means that difference means subtraction

So, we have the following representation

The difference of 4R and 108 ⇒ 4R - 108

However, we do  not know the bigger number.

So, the expression can be rewritten as

The difference of 4R and 108 ⇒ 108 - 4R

So, we have two options

4R - 108 and 108 - 4R

When both expressions are combined, we introduce the absolute value symbol i.e. |.....|

|4R - 108|

Hence, the expression represented by the statement is |4R - 108|

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The following are the primary factors that the Cvp analysis employs to determine if the sales price per unit and variable costs per unit are impacted

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Answer:

Explanation:

Here, we want to find the value of m and n

If we substituted a supposed root into the parent polynomial, the value after evaluation is the remainder. If the remainder is zero, then the value substituted is a root.

for x+ 3

x + 3 = 0

x = -3

Substitute this into the first equation as follows:

We do this for the second value as follows:

x-2 = 0

x = 2

Substitute this value into the polynomial:

Now, we have two equations so solve simultaneously:

Add both equations:

To get the value of n, we simply susbstitute the value of m into any of the two equations. Let us use the second one:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

area = ?

Step 02:

We are given the following two equations

Let us subtract the second equation from the first equation.

Therefore, the result of subtracting the second equation from the first is

The terminal ray of 145° lies in II Quadrant.

The terminal ray of -83° lies in IV Quadrant.

The terminal ray of -636 lies in I Quadrant.

The terminal ray of 442 lies in I Quadrant.

Reflexive Property

1) For this assertion m∠GHK ≅ m∠GHK we have the Reflexive Property, which states that the same segment or geometric entity has the same measure.

"A quantity is congruent to itself"

m∠GHK ≅ m∠GHK

a =a

For two given simple statements P and Q, if they are connected with the logical connectivity 'if and only if', then the compund statement is called biconditional statement.

Now,

P: x+4=13

q: x=9

Then, their biconditional statement is x+4=13 if an donly if x=9

Hence the correct answer is (c)

Let's begin by listing out the information given to us:

We proceed to use the quadratic formula, we have:

Given data:

Principal Amount=$2000.

Final Amount=$2400

Time period(t)=12 years

Let the rate of return be r.

As per formula of continous compunding:

Thus, the rate of interest required is 1.519%.

Answer:

Explanation:

Given the irrational numbers:

In order to arrange the numbers from the least to the greatest, we convert each number into its decimal equivalent.

Finally, sort these numbers in ascending order..

The given numbers in ascending order is:

Note: In your solution, you can make the conversion of each irrational begin on a new line.

Rotation 90° about the origin.

First, choose a point from triangle A.

For example: (-2,2)

For any point (x,y) rotated 90° =(-y,x)

So:

(-2,2) becames = (-2,-2)

Triangle D

Answer: 8i

Total money $392

half of $392 is 196

one half would be paid through fundraising

The debt would be the other half

THE FINAL ANSWER

x=-196 dollars