In the formula for average rate of change, what does the triangle in front of the x and y stand for? a. interval between x and y c. delta notation-change in y over change in x b. initial value of x and y d. the percent rate of change of y and x

Answer:

27.6•\• is the answer from me

The graph of y = k/x has k = 4.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = k/x

The coordinates from the graph:

(1, 4) and (2, 2).

This can be considered as,

(1, 4) = (x, y) = (2, 2)

Now,

y = k/x

4 = k/1

k = 4

y = k/x

2 = k/2

k = 4

Thus,

The value of k is 4.

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Answer:

The x-intercept is x = 0.

The local maximum is (-0.38, -0.46).

The local minimum is (0.38, -0.46).

The function is increasing when x < -0.38 and x > 0.38.

The function is increasing when -0.38 < x < 0.38.

Step-by-step explanation:

To find the x-intercepts, we can set the function equal to 0 and solve for x. This gives us the equations:

0.5x^3 - 2x + 2.5 = 0

To find the points where the function has local maximums and minimums, we can take the derivative of the function and set it equal to 0. This gives us the equation:

1.5x^2 - 2 = 0

To find the intervals where the function is increasing or decreasing, we can take the derivative of the function and determine the sign of the derivative. A positive derivative indicates that the function is increasing, while a negative derivative indicates that the function is decreasing.

Based on the information above, we can fill in the blank answers as follows:

The x-intercept is x = 0.

The local maximum is (-0.38, -0.46).

The local minimum is (0.38, -0.46).

The function is increasing when x < -0.38 and x > 0.38.

The function is increasing when -0.38 < x < 0.38.

The relative frequencies for the following number set is 10 30 40 50 60 70 10 30 40 60 60 80 20 30 50 60 70 90 20 30 50 60 70 90

How do you find the relative frequency in a frequency distribution?

Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency. Divide the total number of occurrences of the result you're interested in by the total number of occurrences if your data are observational. This may be expressed mathematically as relative frequency = frequency of the desired result / all occurrences.

There are 24 items.

Relative Frequency:

10 - (2) - 8.33%

20 - (1) - 4.17%

30 - (4) - 16.67%

40 - (2) - 8.33%

50 - (3) - 12.5%

60 - (5) - 20.83%

70 - (3) - 12.5%

80 - (1) - 4.17%

90 - (2) - 8.33%

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Answer:

9

Step-by-step explanation:

a.) cube root of 729

³√729

= 9

b.) look for a number that you will multiply thrice to get 729

which is 9 or u will use your calculator

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The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

42 48 52 54 59 61 61 64 65 67 68 70 72 75 80

The given set of numbers is in ascending order.

There are 15 numbers.

The middle number will be the 8th number.

8th number = 64

Thus,

The median is 64.

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(17) The value of x would be 20 degrees.

(18) The value of x would be 21.25 degrees.

(20) The value of x would be 6 degrees.

What is the sum of the angles of a triangle?

The sum of the angles of a triangle is 180 degrees. This is a fundamental property of triangles and is known as the triangle sum theorem.

(17)

By using the property of the sum of angles of a triangle, we get

(x+6) + (3x+9) + (4x+5) = 180

Simplifying the left side of the equation gives:

8x + 20 = 180

Subtracting 20 from both sides of the equation gives:

8x = 160

Dividing both sides of the equation by 8 gives:

x = 20°

(18) In a right triangle, one angle is a right angle, which measures 90 degrees. If we know the measures of the other two angles in the triangle, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees to find the value of x.

(2x-4) + (6x+14) + 90 = 180

Simplifying the left side of the equation gives:

8x + 10 = 180

Subtracting 10 from both sides of the equation gives:

8x = 170

Dividing both sides of the equation by 8 gives:

x = 21.25

(20) To find the value of x, we can use the fact that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. We can write an equation using this fact and the measures of the three angles given in the problem:

(2x+13) + (15x+19) = (7x+92)

Simplifying the left side of the equation gives:

17x + 32 = 7x + 92

Subtracting 7x from both sides of the equation gives:

10x + 32 = 92

Subtracting 32 from both sides of the equation gives:

10x = 60

Dividing both sides of the equation by 10 gives:

x = 6

Hence,

(17) The value of x would be 20 degrees.

(18) The value of x would be 21.25 degrees.

(20) The value of x would be 6 degrees.

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The x−intercept is 6 and the y-intercept is 5.

What is an equation of a line?

In high school algebra, "the equation of a line" is a crucial concept. This refers to an equation in the (x,y) plane with a line as its solution set. The "slope-intercept" form is the most widely used form in algebra. y = mx + b. In essence, x is used as a parameter in this formula, and y is written as a function of x: y = f(x) = mx+b.

Here, we have

The given equation of a line is:

−10x − 12y = −60

10x + 12y = 60

x/6 = y/5 = 1

Hence, the x−intercept is 6 and the y-intercept is 5.

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Answer:

The number of minutes should be 68.

A cell phone plan costs $23.70 monthly for 700 minutes of talk time. It costs an additional $0.06 per minute for each minute over 700 minutes.

Getting e-mail access costs 20% of the price for 700 minutes of talk time. The total cost for all 6 months is $195.12.Equation and number of minutes:The equation is 195.12=6(0.06m+23.70+0.20(23.70))195.12 = 0.36m + 142.2 + 28.4424.48 = 0.36mm = 68 minutes

The area of the floor in the scale drawing will be equal to 150 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Length of the classroom, l = 30 feet and,

The width of the classroom, w = 20 feet.

As per the scale drawing, the length of the classroom, l' = 15 feet

Let the scale width, w' = x feet

As we can see that the original length is twice the scale drawing.

Then, the original width also is twice the scale drawing.

So, w' = 20/2 = 10 feet.

Now, the area of the floor in the scale drawing will be,

A = wl

A = (15)(10)

A = 150 in².  

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The data item in this distribution corresponding to a z-score of -7 will be 290.

The standard score in statistics is the number of standard deviations that a raw score's value is above or below the mean value of what is being observed or measured. Raw scores that are higher than the mean have positive standard scores, whereas those that are lower than the mean have negative standard scores. The Z-score measures how much a particular value deviates from the standard deviation. The Z-score, also known as the standard score, is the number of standard deviations above or below the mean for a given data point. The standard deviation reflects the level of variability within a particular data collection.

Here,

z=(X-μ)/σ

-7=(X-500)/30

-210=X-500

X=290

The data item in this distribution that corresponds to we given z-score

z equals to -7 will be 290.

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The probability that the sample mean is greater than 18 as calculated  is 0.8413.

Given data,

n = 36, sample size

μ = 17, population mean

σ = 6, population standard deviation

when x = 18

z = (18 - 17)/1 = 1

P(x <18) = 0.8413

Therefore , the probability = 0.8413

A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.

While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.

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Answer:

Linear function:  y = x + 7.75

Step-by-step explanation:

A store sells packages of comic books with a poster. We are told that:

Let p be the cost of one poster.

Let c be the cost of one comic book.

Write a system of equations using the given information and the defined variables:

[tex]\begin{cases}p + 4c = 11.75\\p + 11c = 18.75\end{cases}[/tex]

Subtract the first equation from the second equation to eliminate p:

[tex]\begin{array}{crcrcl}&p&+&11c&=&18.75\\-&(p&+&4c&=&11.75)\\\cline{2-6}&&&7c&=&\;\;7.00\\\cline{2-6}\end{array}[/tex]

Solve for c:

[tex]7c=7.00[/tex]

 [tex]c=1.00[/tex]

Therefore, the cost of one comic book is $1.00.

Substitute the found value of c into one of the equations and solve for p:

[tex]\begin{aligned}p+4(1.00)&=11.75\\p+4.00&=11.75\\p&=7.75\end{aligned}[/tex]

Therefore, the cost of one poster is $7.75.

Now we know the cost of one poster and one comic, we can write a linear function that models the cost y of a package containing x number of comic books:

[tex]y = 1.00x + 7.75[/tex]

[tex]y =x + 7.75[/tex]

We are told that another store sells a similar package modeled by a linear function rule with initial value $6.99.  The initial value is the y-intercept of each function, i.e. the cost of the package when zero comics are sold. So the linear function for this package is:

[tex]y = x + 6.99[/tex]

To determine which store has the better deal, we need to compare the y-intercepts (the initial values). The store with the lower initial value provides a better deal because it charges less for the basic package (when the number of comic books is zero).

Since 6.99 is less than 7.75, the other store offers a better deal, as it has a lower initial cost for the basic package.

Answer:

[tex]\Huge \boxed{ \texttt{\bf{y = x + 7.75} }}[/tex]

Step-by-step explanation:

To find the linear function rule that models the cost [tex]\texttt{y}[/tex] of a package containing any number [tex]\texttt{x}[/tex] of comic books, we can use the given information:

Let's denote the cost of a poster as [tex]\texttt{P}[/tex] and the cost of a comic book as [tex]\texttt{C}[/tex]. Then, we can write two equations:

To solve these equations, we can use the method of elimination. Let's use this method to eliminate [tex]$$P$$[/tex]:

Now, substituting the value of [tex]\texttt{C}[/tex] back into equation 1:

Now that we have the cost of a poster (P) and a comic book (C), we can write the linear function rule as:

[tex]\Large \boxed{\texttt{y = x + 7.75}}[/tex]

Now, suppose another store sells a similar package modelled by a linear function rule with an initial value of $6.99. This means that the cost of a poster at the other store is $6.99. Since the cost of a comic book is the same at both stores ($1), the linear function rule for the other store is:

[tex]\Large \boxed{ \texttt{y = x + 6.99}}[/tex]

Comparing the two linear function rules, we can see that the second store has a better deal because the initial cost of a poster is lower ($6.99) compared to the first store ($7.75).

________________________________________________________

Answer:

This is an irrational number.

Step-by-step explanation:

If you see the decimal, it has the values of 1 and 0, but are not constant.

If it were to be 0.010101010... it would be rational.

But this decimal does not look like that, so its irrational.

Hope this helps.

The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93,  Hₐ : p > 0.93.

A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Let 'p' be the population proportion.

Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.

Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some  difference,

Hence, the null and alternative hypotheses for this hypothesis test will be :-  H₀ : p = 0.93

          Hₐ : p > 0.93

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To label the three basket correctly , We have to pull out total two fruits from  all of them

Let Say , We are drawing a fruit from a basket labelled "Mixture"

If this fruit is an apple, then indicate such on the label (Because this basket does not contain Mixture, so if one is apple, all are apples only). We've now discovered that the basket marked "Mixture" solely includes apples.

Therefore , the Correct Label is "apples"

Now, Drawing another fruit from basket labelled  "Oranges," we can see that it either contains solely apples or mixture. The basket marked "Oranges" contains "Mixture," as we already know which basket only contains apples. Put "Mixture" on the label.

Oranges will be the name of the third basket.

The same reasoning holds true if you suppose that you initially chose an orange from the basket marked "Mixture."

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Answer:

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6)  Draw a line to join those 2 points.  The inequality is ≤ that means the solutions are the points on the line and below the line.  This is shown in the pink shading.

y ≤ -3x - 3

Step-by-step explanation:

The graph crosses the y-axis at -3.  The slope is -3.  (0, -3) .  From that point do down vertical 3 spaces and horizontally 1 space.  You will be at the point (1,-6) Draw a line to join those 2 points.  

The inequality is ≤ which means the solutions are the points on the line and below the line.  This is shown in the pink shading.

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The magnitude of AB based on the information is 5.1.

To show that points A, B, and C are colinear, we need to show that they lie on the same line. One way to do this is to find the direction vector of the line passing through A and B, and then check whether point C is on the same line.

The direction vector of the line passing through A and B is given by the vector AB, which is equal to OB - OA. Substituting the given values for OA and OB, we find that AB = (3i - 2i) + (-2j + 3j) = i + j.

To check whether point C is on the same line as A and B, we can find the direction vector of the line passing through C and any one of the other two points.

We can find the direction vector of the line passing through C and A, which is given by the vector CA = OA - OC = (2i + 3j) - (i + 6j + 3k) = i + (-3j - 3k).

Since the direction vectors of the lines passing through A and C and through B and C are both in the same direction, we can conclude that points A, B, and C are colinear.

To find the magnitude of AB, we can use the distance formula:

AB = √((3 - 2)² + (-2 - 3)²) = √(1² + (-5)²) = √(26) = 5.1

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The integers are -47, -11, -6, 12, 20 in order of least to greatest.

A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.

Positive numbers, negative numbers, and zero make up integers. Thus, integers include 0 through 3, as well as -1, -2, and -3. No further parts, such as fractions or decimals, are allowed in integers. Therefore, fractional and decimal numbers like 3 1/2 and -7.5 are NOT integers.

Integer is derived from the Latin integer, which means whole or untouched, from the prefix in (for "not") with tangere ("to touch"). The words "entire" and "integer" are both derived from the same root, which is the French word entire.

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The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6

g(x) = 4x +9.

An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.

The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.

Given,

f(x) = x²+x-6

g(x) = 4x +9

f(g(x))=f(4x+9)

g(f(x))=4(x²+x-6)+9

g(f(x))=4x²+4x-24+9

g(f(x))=4x²+4x-15

Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6

g(x) = 4x +9.

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The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is

(x-4)^ 2+k = 0 using quadratic equation properties .

What is quadratic equation ?

A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Properties of graph of quadratic equation :

1. The shape of curve y = f(x) is a parabola.

2. If a>0, the parabola opens upwards.

3. If a<0, the parabola opens downwards.

4.The coordinates of vertex of parabola in all these cases is

(-b/2a , -D/4a).

The given equation is x^ 2-8x+19=0

a  = 1,

b = -8,

c = 19.

As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.

So, the vertex = (4,3)

The minimum value = 3 at 4.

So, the value of k = 3,

Given equation can be written as x^ 2-8x+16+3 = 0.

                                                      = (x-4)^ 2 +3 = 0.

The option A is correct.

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The acceleration of the dolly-sandbag system is 1.23 m/s²

Given parameters:

The mass of the dolly and actor combined is: M = 94 kg

the mass of the sandbag is: m = 35 kg.

The coefficient of kinetic friction between the dolly and the stage floor is 0.20.

Let the acceleration is a.

Hence, From Newton's 2nd law of motion, we can write that:

ΣF = (m+M) a

mg - μMg = (m+M) a

a = g (m- μM)/ (m+M)

= 9.8 (35 - 0.20 × 94)/(35 + 94)

= 9.8 (16.2)/(129)

= 1.23 m/s².

Hence, the acceleration of the dolly-sandbag system is 1.23 m/s².

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The large percentage obtained above will still not be a cause for celebration, because the observations demand a higher precision in the calculation results being obtained after running a logistic reg-session.

A precise calculation can be referred to or considered as a type of calculation, wherein the final results obtained are completely true and correct. Unlike approximate results, there is no scope of true and fair results in a precise calculation. Usually, rounding-off shall be avoided to obtained precise solutions at the end.

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Senior citizen tickets cost $7, while child tickets cost $3.

A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.

Senior citizen tickets should equal ST.

CT = child tickets

The school sold 11 senior citizen tickets and 12 kid tickets on the first day of ticket sales for a total of $113.

11 senior citizens equals 11ST.

12 children equals 12CT a total $113

11ST + 12CT = $113 ( REFER AS 1 )

On the second day, the school sold 10 senior citizen tickets and 2 kid tickets, bringing in $76.

10 senior citizen =10ST

2 children = 2CT

total 76

10ST + 2CT = $76 ( REFER AS 2 )

So from 1 and 2 we do elimination method

multiply eq 2 with 6 and subtracted from eq 1

60ST + 12CT = 456

That is

(60 -11)ST + (12-12)CT = 456 - 113

49ST = 343

ST = 343/49

ST = $7

the cost of senior citizen ticket is $7

10ST + 2CT = $76

10*7 + 2CT = 76

70 +2CT = 76

2CT = 76 - 70

2CT = 6

CT = $3

the cost of child ticket is $3

Senior citizen tickets cost $7 each, while child tickets cost $3 each

( to recheck from eq 1

7*11 + 3* 12 should be equal to 113

77 + 36 = 113 )

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There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.

A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.

A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this

Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.

Given that,

Total number voters = 80,000

Total number of votes polled = 90%

Thus,

= (90/100) × 80,000

= 72,000

So, total percent of votes received by B if A gets 60% of polled votes.

= 100% - 60%

= 40%

Hence, total number of votes received by B

= (40/100) × 72,000

= 28,800

Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.

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The length of side x in simplest radical form is √128/1 with a rational denominator of 1.

The triangle is given in the question which is a right triangle.

As per the given figure, we can determine the length of side x by the Pythagoras theorem.

According to Pythagoras's theorem,

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

perpendicular²+base² = hypotenuse²

8² + 8² = (x)²

64 + 64 = (x)²

(x)² = 128

x = √128

Hence, the required length of side x of the triangle is √128.

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Answer:

No

Step-by-step explanation:

When the 2 equations are graphed the point (13, 17) is not

a solution to the system of linear equations.

So the answer is no.

If you want to look for the solution**- the solution to the equation is (12, 18)