A cubic function of the form u = a * x ^ 3 + b * x ^ 2 + cx + d yields the following table:

x y

oo

- 5

The coefficient a =

,and d= Box.

,b=

,C=

The required amount did she spend on Food is $528.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

We have given;

100% = $2400 which is monthly spend.

Then,

there is 22% spending in food

So,

100% = $2400

1% = $24

22% = $528

Thus, Required spend on Food is $528.

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Answer:

[tex]\frac{597}{283750}+3*10^8[/tex]

Step-by-step explanation:

[tex]((2848*838449)/(294949*3848483))+300,000,000\\or\\\frac{2848*838449}{294949*3848483}+300,000,000\\\\\frac{2.388*10^9}{1.135*10^{12} } +3x10^8\\\\\\\frac{597}{283750}+3*10^8[/tex]

Answer: 31457261583.3

Step-by-step explanation:

B: no, bc the side lengths ans angles arent similar

A square must be a rectangle because it's a four-sided geometric shape with four right angles and congruent sides, but a rectangle doesn't always have congruent sides.

In Mathematics and Geometry, a square can be defined as a type of quadrilateral in which the length of all its four (4) sides are equal in magnitude (congruent) and the sum of all its interior angles is equal to 360 degrees (360°) and it forms a right angle.

In Mathematics and Geometry, a rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles that are formed are right angles.

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Hi there, here's your answer:

We have -1 < x ≤ 2 and -2 ≤ x < 3

Let's first solve both the inequalities one at a time.

Case 1:

-1 < x ≤ 2

The solution set for this inequality is (-1 , 2]

Case 2:

-2 ≤ x < 3

The solution set for this inequality is [-2 , 3)

Now, the values that satisfy both these inequalities can be taken from the solution set of case 1.

Thus, we get a new solution set for the satisfactory values.

New solution set = (0,2]

The required integer values are:

0, 1 and 2.

Hope this helps!

Answer: 0, 1, 2

Step-by-step explanation:

0 is less then 2 and 3 and greater than -1 and -2

Same for 1 and 2, but for 2 in the first equation it is equal but look at these signs [tex]\leq \geq[/tex]

It means equal or less/greater than.

2 is = 2 so it satsifys the first equation.

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Answer:

[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]

Step-by-step explanation:

The surface area of the sphere has formula of [tex]\displaystyle{4\pi r^2}[/tex] where r is radius. Therefore, set the equation:

[tex]\displaystyle{4\pi r^2=156}[/tex]

Divide both sides by 156:

[tex]\displaystyle{\dfrac{4\pir^2}{4}=\dfrac{156}{4}}\\\\\displaystyle{\pi r^2=39}[/tex]

Then divide both sides by [tex]\displaystyle{\pi}[/tex]:

[tex]\displaystyle{\dfrac{\pi r^2}{\pi} = \dfrac{39}{\pi}}\\\\\displaystyle{r^2=\dfrac{39}{\pi}[/tex]

Square root both sides:

[tex]\displaystyle{\sqrt{r^2}=\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{r=\pm\sqrt{\dfrac{39}{\pi}}}[/tex]

However, radius can only be positive. Therefore:

[tex]\displaystyle{r=\sqrt{\dfrac{39}{\pi}}}[/tex]

To find the volume, we have to know that the sphere's volume is:

[tex]\displaystyle{\dfrac{4}{3}\pi r^3}[/tex]

Thus, substitute the value of r in:

[tex]\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \left(\sqrt{\dfrac{39}{\pi}}\right)^3}\\\\\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \dfrac{39}{\pi}\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{\text{V} = 52 \sqrt { \dfrac{39}{\pi}}}[/tex]

Therefore, the volume of sphere is:

[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]

Answer: -3/16

Step-by-step explanation:

When there is a negative exponent like x^-2 it equals 1/(x^2) the negative puts the number as a fraction so continuing...

-12(x^-2) (y^-2) can be rewritten as

-12 (1/x^2) (1/y^2) now we plug in x = -2 and y = 4

-12 (1/(-2^2) (1/(4^2)); -2^2 = 4 , 4^2 = 16

-12 (1/4) (1/16)

-3 (1/16)

= -3/16

Answer: don't no

Step-by-step explanation:

Answer:

13/24

Step-by-step explanation:

First we create a common denominator by multiplying the denominators of 8 and 3 to get 24. Now we convert the two given fractions

[tex] \frac{1}{8} = \frac{3}{24} [/tex]

[tex] \frac{1}{3} = \frac{8}{24} [/tex]

A full circle is 24/24. Now all we do is subtract

[tex] \frac{24}{24} - \frac{8}{24} - \frac{3}{24} = \frac{13}{24} [/tex]

Answer:

13/24

Step-by-step explanation:

1-11/24

=

13/24

Answer:

a= 17* √2

Step-by-step explanation:

a=17*cosec45

Jayden is folding a paper strip of 66 cm into a 6 sided honeycomb. So the length of each side will be 11cm.

Jayden has a paper strip of length 66 cm. He had to make a honeycomb with it. It will have six equal sides. To calculate the length we have to formulate the equation.

Total length = number of sides × length of one side

 66 = 6 × x

Dividing by 6 on both sides,

66÷6 = 6x ÷ 6

11 = x

So the length of the side of honeycomb will be of 11 cm.

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The complete question is as below

Jayden folded a 66cm strip of paper into 6 equal parts to model a honeycomb cell's. Each part was one side of the model. What is the length of one side of the model?

The perimeter of this 19-sided regular polygon is equal to 152 cm.

The side length of this 19-sided regular polygon is equal to 8 cm.

Mathematically, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

Substituting the parameters into the area of a regular polygon formula, we have;

1,816.4 = (19 × s × 23.9)/2

3632.8 = 454.1s

Side length, s = 3632.8/454.1

Side length, s = 8 cm.

In Mathematics, perimeter of a regular polygon can be calculated by using this formula:

Perimeter of regular polygon = number of sides × side length

Perimeter of regular polygon = 19 × 8

Perimeter of regular polygon = 152 cm.

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Complete Question:

Find the perimeter and side length of a 19-sided regular polygon with an apothem of 23.9 cm and an area of 1,816.4 cm.

Answer: Area = 4x^2 + 24x + 32

Step-by-step explanation:

Area = length x width

Length = x + 6 + x + 2 = 2x + 8

Width = x + 4 + x = 2x + 4

area = 2x + 8 * 2x + 4

multiply each term by each term

Area = 4x^2 + 24x + 32

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F(x) = 4x & g(x) = 3x are the two functions which the (f o g)(x) was equal to "12x".

Legislation, a regulation, or a declaration that demonstrates the relationships between the independent and relationship between the factors (the dependent variable). Functions may be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The functions f(x) & g(x) are given, and the task is to determine (f o g) (x).

For the following two functions, (f o g)(x) was identical to "12x":

f(x) = 4x and g(x) = 3x.

Proof :

g(x) = 3x

(f o g)(x) = f(x = 3x) = 4(3x) = 12x

(f o g)(x) = 12x

Hence, f(x) = 4x or g(x) = 3x are the 2 type which the (f o g)(x) was equal to 12x.

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Between the time interval 0 to 1 hour, the greatest average rate of change is 700. Therefore, the option (1) is the correct answer.

The slope or rate of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here,

1) 0 to 1 hour

Consider the coordinate points (0, 0) and (1, 700)

Now, rate = (700-0)/(1-0)

= 700

2) 1 hour to 1.5 hours

Consider the coordinate points (1, 700) and (1.5, 900)

Now, rate = (900-700)/(1.5-1)

= 200/0.5

= 400

3) 2.5 hours to 5 hours

Consider the coordinate points (2.5, 1000) and (5, 1640)

Now, rate = (1640-1000)/(5-2.5)

= 640/2.5

= 256

4) 5 hours to 8 hours

Consider the coordinate points (5, 1640) and (8, 1800)

Now, rate = (1800-1640)/(8-5)

= 160/3

= 53.33

Therefore, the option (1) is the correct answer.

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Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 5 ) and (x₂, y₂ ) = (7, - 5 )

m = [tex]\frac{-5-(-5)}{7-2}[/tex] = [tex]\frac{-5+5}{5}[/tex] = [tex]\frac{0}{5}[/tex] = 0

If the Car drive 15, 000 miles then gas used is 315 galloons.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

In 16.8 galloons of gas the Car can travel 400 miles.

So, if they dive about 15,000 miles then the gas in galloons used

= 16.8/400 x 15000

= 2.1 x 150

= 315 galloons.

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pr(z < 2.3) is =NORMSDIST(2.3) which equals 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

The probability that a standard normal random variable is less than 2.3 can be calculated using the cumulative distribution function (CDF) of the standard normal distribution. This function gives us the probability that a standard normal random variable is less than or equal to a given value.

In Excel, you can use the NORMSDIST function to calculate the CDF of the standard normal distribution. The syntax for this function is:

=NORMSDIST(x)

where x is the value for which you want to calculate the CDF.

In this case, to calculate the probability that a standard normal random variable is less than 2.3, we would use the following formula in Excel:

=NORMSDIST(2.3)

This gives us the result of 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

Note: The cumulative distribution function can also be approximated using tables or calculators that have the function built in. The result obtained using these methods may have some slight differences compared to the result obtained using Excel.

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The statement "F(x) > 0 over the interval (-∞, -4)" is true.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. The addition, subtraction, multiplication, and division of functions are discussed in function algebra. We just perform the same operation for individual functions at the same input for every arithmetic operation of two functions at an input.

Here,

For any value of x less than -4, substituting it into the expression f(x) = x² + 4 will result in a positive value since x² is always positive. For example, if x = -5, then f(x) = (-5)² + 4 = 9 + 4 = 13, which is positive.

So, for all values of x that are less than -4, the function f(x) will have a positive value, making the statement "F(x) > 0 over the interval (-∞, -4)" true.

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Answer:

see below

Step-by-step explanation:

90 x, y, z

x pennies =1/2y

y nickels

z quarters = 3 1/2 y

so 1/2y+y+3 1/2 y =90

total 5y =90

y =18

x=9

z = 63

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3600\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]

[tex]A = 3600\left(1+\frac{0.02}{12}\right)^{12\cdot 18}\implies A=3600(\frac{601}{600})^{216} \implies A \approx 5158.44[/tex]

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ 0.25 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ 0.25}(x-\stackrel{x_1}{5}) \implies y +2= 0.25 (x -5)[/tex]

The inequality used to determine v, the minimum number of visits Taylor needs to earn her first free movie ticket is 75 + 6.5v ≥ 100.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given,

Points for signing up = 75 points

Points for each visit to the movie theater = 6.5 points

Let v be the minimum number of visits Taylor needs to earn her first free movie ticket.

Points earned for v visits = 6.5v

She needs at least 100 points for a free movie ticket.

75 + 6.5v will be the points she earn for a free movie ticket.

This expression must be greater than 100, which is the required points for a free movie.

75 + 6.5v ≥ 100

Hence the inequality representing the situation is 75 + 6.5v ≥ 100.

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The equation of the line parallel to y = 3x - 4 is y + 5 = 3(x+1)

The equation of a line expressed in point slope form is expressed as:

y-y0 = m(x-x0)

where

m is the slope

(x0, y0) is any point on the line

Given the following parameters

(x0, y0) = (-1, -5)

slope of the given line is 3

Substitute

y - (-5) = 3(x-(-1))
y + 5 = 3(x+1)

Hence the required equation of the line is y + 5 = 3(x+1)

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By rounding off, we can determine that Mike thought the difference would be 72 whereas it is actually 72.74.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number.

For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

The crucial figures are preserved when numbers are rounded off.

Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up.

So, Mike calculated 79 as 79.44 and 7 as 6.7, so he calculated the difference as follows:

79 - 7 = 72

Actual figures that differ are:

79.44 - 6.7 = 72.74

Therefore, by rounding off, we can determine that Mike thought the difference would be 72 whereas it is actually 72.74.

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Correct question:

Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be . The actual difference is .

The dimension of the rectangular prism will be x, x + 2, and x + 1.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

The volume of the rectangular prism is given as,

V = x³ + 3x² + 2x

Factorize the equation, then we have

V = x³ + 3x² + 2x

V = x(x² + 3x + 2)

V = x(x² + 2x + x + 2)

V = x[x(x + 2) + 1(x + 2)]

V = x(x + 2)(x + 1)

The dimension of the rectangular prism will be x, x + 2, and x + 1.

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The values of p and q are p = 35 and q = 12

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

Intersecting chords in a circle

To solve this question, we make use of the intersecting chords theorem

This is represented as

q/12 = 35/p

Cross multiply

So, we have the following representation

pq = 35 * 12

From the circle, we have

p > q

So, we can rewrite the equation as

p = 35 and q =12

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Answer:

To find 47% of 900, you can multiply 900 by 0.47, which represents 47% as a decimal:

47% = 47/100 = 0.47

So, 47% of 900 is:

0.47 x 900 = 423

Therefore, 47% of 900 is 423.

Convert 47% to a decimal

= 47% = 47/100 = 0.47

47%= 0.47 × 900

=423

Answer:

4.89

Step-by-step explanation:

6×4 and the root of that is 4.8989794