The length of a rectangle is four times its width.
If the perimeter of the rectangle is 100 m, find Its area.

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).

________________________________________________________

Dependent variable: t (total cost of the pizza)

Independent variable: x (number of extra toppings)

Equation: t = 10.50 + 1.50x

To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:

t = 10.50 + 1.50(3)

t = 10.50 + 4.50

t = 15.00

So the total cost of the pizza with 3 extra toppings is $15.00.

What is Dependent Variables?

The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.

What is Independent Variables?

Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.

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Yes, for all values x ≥ 0. If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other.

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24.07 rounded to the nearest tenth is 24.1

Answer:

27.6•\• is the answer from me

First, we need to find the price that Angel suppliers paid for the construction materials, including the profit made by Annapurna suppliers and the VAT.

The price that Annapurna suppliers sold the materials for was Rs. 4,40,000 + Rs. 4,40,000 * 10% = Rs. 4,84,000.

The VAT that Annapurna suppliers added was Rs. 4,84,000 * 13% = Rs. 62,820.

So, the total price that Angel suppliers paid was Rs. 4,84,000 + Rs. 62,820 = Rs. 5,46,820.

Next, we need to find the price that the constructor paid for the materials, including the profit made by Angel suppliers, the transportation cost, the local tax, and the VAT.

The profit that Angel suppliers made was Rs. 5,46,820 * 10% = Rs. 54,682.

The total price that the constructor paid was Rs. 5,46,820 + Rs. 54,682 + Rs. 5,000 + Rs. 2,500 = Rs. 6,58,002.

The VAT that the constructor should pay is Rs. 6,58,002 * 13% = Rs. 70187.

Therefore, the answer is Rs. 70187.

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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 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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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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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 formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:

Cumulative probability is equal to (number of events * e)/(average number of events per time period).

(Number of events / (-average number of events per time period)!)

In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:

Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.

That amounts to:

Probability total = 1 + 0.05 + 0.0025

which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.

The exponential function to show the growth in y years is P(1.2)^y

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

In this problem, this is an exponential growth since the rate increases.

Let;

The exponential function to represent this will be;

A = P(1 + r)^y

A = P(1 + 0.2)^y

A = P(1.2)^y

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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 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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Using the geometry from the question and using the Pythagorean theorem with the distance provided, The answer is 30.09 miles.

By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

It's formula is:

[tex]h^{2} = p^{2} +b^{2}[/tex]

h1=30500 feet = 5.77 miles

d1= 50 miles

h2= 18000 feet = 3.4 miles

d2= 20 miles

for right angle triangle,

height = h1-h2 = 2.37 miles

distance  = 50-20 = 30 miles

plane flown = [tex]\sqrt{2.37^{2}+30^{2}}[/tex]

=30.09 miles

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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)

                               ......................................................................                                      

Answer:

Base = 10 cm

Height = 6 cm

Step-by-step explanation:

Here is the formula for the area of a triangle.

 [tex]A=\frac{bh}{2}[/tex]

We are given

[tex]A=30[/tex]

[tex]b=h+4[/tex]

Replace all occurrences of [tex]b[/tex] with [tex]h+4[/tex] in each equation.

[tex](h+4)*\frac{h}{2} =30[/tex]

Apply the distributive property.

[tex]h(\frac{h}{2})+4(\frac{h}{2})=30[/tex]

[tex]\frac{h*h}{2}+4(\frac{h}{2})=30[/tex]

Use the power rule to combine exponents.

[tex]\frac{h^2}{2}+4(\frac{h}{2})=30[/tex]

Factor 2 out of 4 .

[tex]\frac{h^2}{2}+2(2)(\frac{h}{2})=30[/tex]

Cancel the common factor.

[tex]\frac{h^2}{2}+2h=30[/tex]

Solve for h.

Multiply each term in  [tex]\frac{h^2}{2}+2h=30[/tex]  by 2 to eliminate the fractions.

[tex]\frac{h^2}{2}*2+2h*2=30*2[/tex]

Simplify each term.

Cancel the common factor of 2.

[tex]h^2+2h*2=30*2[/tex]

[tex]h^2+4h=60[/tex]

Subtract 60 from both sides of the equation.

[tex]h^2+4h-60=0[/tex]

Factor using the AC method.

Consider the form [tex]x^2+bx+c[/tex] . Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex] . In this case, whose product is − 60 and whose sum is 4 .

−6, 10

Write the factored form using these integers.

[tex](h-6)(h+10)=0[/tex]

Set [tex]h-6[/tex] equal to 0 and solve for h.

Then add 6 to both sides of the equation.

[tex]h-6=0\\h=6[/tex]

Set [tex]h+10[/tex] equal to 0 and solve for h.

Then subtract 10 from both sides of the equation.

[tex]h+10=0\\h=-10[/tex]

The final solution is all the values that make [tex](h-6)(h+10)=0[/tex] true.

[tex]h=6,-10[/tex]

Given [tex]b=h+4[/tex]

Replace all occurrences of h with 6 in each equation.

[tex]b=6+4\\b=10\\h=6[/tex]

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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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 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: C

Step-by-step explanation:

Slope is the number right in front of x, which in this case would be -2. So C is the answer.

Creating a table is hard, so I'll try my best. Just pretend the vertical line is connected.

x|y

0|5

1|3

2|1

3|-1

4|-3

Answer: p = 4.5

Step-by-step explanation:

12.4 - 4.5 = 7.9

Answer: p=4.5

Step-by-step explanation:

You do it like this: 12.4=7.9+p

12.4-7.9=p

p=4.5

Answer:

10

Step-by-step explanation:

Using this equation,

l × w × h = v

We can simply substitute the numbers into the equation.

2 × 2 × 2 1/2 =?

(We know that the width is equal to 2 because it is a square.)

2 × 2 = 4,

4 × 2 1/2 = 10

The volume of the storage box is equal to 10.

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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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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The true inequality in the list of options is (a) 6π > 2

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

6π > 2, 7π > 30, 8 - π > 5 and π + 4 < 7

The value of the constant π is 3.142

So, we solve for π in the inequality expressions

A.6π > 2

This gives

π > 2/6

Divide

π > 0.33 -- true

B. 7π > 30

Divide

π > 4.29 -- false

C. 8 - π > 5

This gives

π < 3 -- false

D. π + 4 < 7

This gives

π < 3 -- false

Hence, the true inequality is 6π > 2

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Complete question

Which inequality is true?

A. 6π > 2

B. 7π > 30

C. 8 - π > 5

D. π + 4 < 7

The value of k as calculated from the information provided is -16 , -8 , 8 , 16.

The given equation is,

x² + kx + 15

= ( x + a ) (x + b)

= x² + (a + b ) x + ab

Therefore,

k = a + b

ab = 15

as known , a and b are integers,

15 = ( -1 x -15 ) , ( 1 x 15)

15 = (-3 x -5) , (3 x 5 )

Therefore,

k = -1 -15

= -16

and

k = -3 - 5

=8

The values of k are -16 , -8 , 8 , 16.

The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.

On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. "Z" stands for an integer.

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Population standard deviation, level of significance are same.

Margin of error increased.

With increase in margin of error sample size decreases.

By dividing the population's standard deviation by the sample size and then multiplying the resulting number by the crucial factor, the margin of error—a statistical expression used to estimate how much a result will deviate from the value of the full population—can be determined.

The standard deviation of the sample statistics, if we could take several samples of the same size, is the standard error.

Population standard deviation, level of significance are same.

Margin of error increased.

Margin of error increases leads to decrease in the sample size

as the margin of error is in denominator position in sample size formula. Hence with increase in margin of error sample size decreases.

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