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Answer:

4x^2+19x-47

Step-by-step explanation:

(4x^2+8x+15)+(x^2-x-27)-(x-5)(x-7)

=(4x^2+8x+15)+(x^2-x-27)-x^2+7x+5x-35

=(4x^2+x^2-x^2) + (8x-x+7x+5x) + (15-27-35)

= 4x^2+19x-47

Hope this helps!

The given expression after simplifying 4x^2+19x-47.

We have given the following expression

\((4x^2+8x+15)+(x^2-x-27)-(x-5)(x-7)\)

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

\(=(4x^2+8x+15)+(x^2-x-27)-x^2+7x+5x-35\)

\(=(4x^2+x^2-x^2) + (8x-x+7x+5x) + (15-27-35)\)

\(= 4x^2+19x-47\)

The given expression after simplifying 4x^2+19x-47.

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Answer:

4

Step-by-step explanation:

Absolute value is just the number without and negative signs, for example, -5 would have an absolute value of 5

Answer:

a) 0.12386 = 12.386% probability that in a year, there will be 3 hurricanes.

b) 5.57 years are expected to have 3 hurricanes, that is, between 5 and 6 years.

c) 5 years is very close to the mean of 5.57, which means that the Poisson distribution works well here.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

The mean number of hurricanes in a certain area is 5.3 per year.

This means that \(\mu = 5.3\)

a. Find the probability that in a year, there will be 3 hurricanes.

This is P(X = 3).

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = x) = \frac{e^{-5.3}*5.3^{3}}{(3)!} = 0.12386\)

0.12386 = 12.386% probability that in a year, there will be 3 hurricanes.

b. in a 45-year period, how many years are expected to have 3 hurricanes ?

0.12386 each year. So, for 45 years:

45*0.12386 = 5.57

5.57 years are expected to have 3 hurricanes, that is, between 5 and 6 years.

c. How does the result from part (b) compare to a recent period of 45 years in which 5 years had 3 hurricanes? Does the Poisson distribution work well here?

5 years is very close to the mean of 5.57, which means that the Poisson distribution works well here.

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

Answer:

C

Step-by-step explanation:

So we have the rational expression:

\(\frac{x^2-11x+30}{x^2-x-30}\)

We can factor the numerator and the denominator:

Numerator:

\(x^2-11x+30\)

Factor:

\((x-5)(x-6)\)

Denominator:

\(x^2-x-30\)

Factor:

\((x-6)(x+5)\)

Substitute:

\(\frac{x^2-11x+30}{x^2-x-30}\\=\frac{(x-6)(x-5)}{(x-6)(x+5)}\)

We can cancel out the (x-6). Thus:

\(=\frac{x-5}{x+5}\)

Our answer is C.

Answer:

cold and hot Is the answer

Linear function Is a function that can be graphed as a solid line discrete or continuous

Linear functions are simply known as functions whose graph is a straight line.

They have one dependent variable and one independent variable.

These functions have either one or two variables without exponents.

Continuous graphs are used to represent functions that are continuous along their entire or whole domain.

Whereas, discrete graphs are used to represent values at specific points along the number line from different directions.

Types of the linear function;

Hence, it is a linear function

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Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.

Volume of the bead = Volume of the sphere - volume of the cylindrical hole

= 4/3π(4³) - π(1²)(8)

= 268.08 - 25.13

Volume of the bead = 242.95 mm³

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Answer:

114.29

Step-by-step explanation:

Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c

Step-by-step explanation:

Answer:

(x+5)² + 4, so c is 5 and d is 4

Step-by-step explanation:

x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.

We need to complete the square to get it in the form

(x + c)² + d

Completing the square uses the form:

\((x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c\)

substitute b = 10 and c = 29 in this form:

\((x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29\)

Simplify further:

\((x + 5) {}^{2} - 25 + 29\)

\((x + 5) {}^{2} + 4\)

c = 5, d = 4

7/3 = 2 1/3

Hope it helps

Answer:

1 2/3

Step-by-step explanation:

divide 3 by 7 you will get a reminder of one and then the two at the top and the three you divide with is your fraction.

Price of downloads of number of movies and songs is given by function g(x) =2x and f(x) = (x/2) +2 respectively , then total cost of the downloads of total 3 movies and 8 songs is equal to 12 dollars.

As given in the function,

Price of downloads of number of movies represented by

g(x) = 2x

where x is the number of movies

Price of downloads of number of songs represented by

f(x) = (x /2) +2  

where x is the number of songs

Total number of downloads

First week

Number of movies downloads = 2

Number of songs downloads =3

Next week

Number of movies downloads = 1

Number of songs downloads = 5

Total movies = 2+1

                    =3

Cost of downloads 3 movies

g(3)= 2(3)

     =6

Total songs =3+5

                  = 8

Cost of downloads8 songs

f(8)= (8/2) +2

     =6

Total cost of the downloads = 6 +6

                                           = 12 dollars

Therefore, price of downloads of number of movies and songs is given by function g(x) =2x and f(x) = (x/2) +2 respectively , then total cost of the downloads of total 3 movies and 8 songs is equal to 12 dollars.

The complete question is :

The price for digital downloads of music is represented by the linear function f(x) shown on the graph. The price for digital downloads of movies is represented by g(x) = 2x, where x is the number of movies downloaded and g(x) is the total cost in dollars. Graph of a line with equation f of x equals one half times x plus 2. The x-axis is labeled Number of Songs, and the y-axis is labeled Price in Dollars.

You download 2 movies and 3 songs the next week you download 1 movie and 5 songs. What is the total cost of the downloads?

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Answer:

C. 7°F

Step-by-step explanation:

The z-score of -1.6 is less than 2.00 but greater than -2.00.

Hence, we can conclude that the value is not unusual.

The correct answer is: -1.6; not unusual.

When we are given a test score of 48.4 on a test that has a mean of 66 and a standard deviation of 11,

we need to find the corresponding z-score and determine whether the value is unusual or not.

The formula for calculating z-score is:

z = (x - μ) / σ

Where, z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the given values in the formula, we get: z = (48.4 - 66) / 11z = -1.6

Therefore, the z-score corresponding to the given value is -1.6.

Now, we need to determine whether this value is unusual or not.

A score is considered unusual if its z-score is less than -2.00 or greater than 2.00.

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Since 1 < x < 5, adding each side by a, where a is negative, gives

a > ax > 5a

and adding b to each side gives

a + b > ax + b > 5a + b

or

5a + b < ax + b < a + b

Since 7 < f(x) < 23, it follows that

5a + b = 7

a + b = 23

Solve for a by eliminating b :

(5a + b) - (a + b) = 7 - 23

4a = -16

a = -4

Solve for b :

-4 + b = 23

b = 27

Triangle ABC has its vertices at points A(3,6), B(-2,-2), and C(6,4)

This triangle was dilated and triangle A'B'C' was determined. The coordinates of one of the vertices of the dilated triangle are A'(1,2)

To perform the dilation, the coordinates of each vertex of the triangle were multiplied by a scale factor "k" following the rule:

Compare the coordinates of the corresponding points A and A' to determine the scale factor used in the dilation:

x-coordinate of A is 3

x-coordinate of A' is 1

Then:

The scale factor used is k=1/3

Answer:

0.865

Step-by-step explanation:

Specific gravity is a ratio of the weight of a substance to the weight of an equal volume of a substance chosen as a standard. The standard for liquid and solids is water while for gas is hydrogen.

Amount of displaced oil = 12.64 g — 9.12 g = 3.52 g

Amount of displaced water = 12.64 g — 8.57 g = 4.07 g

Specific gravity of oil = 3.52 g / 4.07 g = 0.865

Specific gravity is a measure of the amount a substance is more or less

heavier than a standard substance.

Reason:

The mass of the glass plummet in the air, m = 14.35 g

Mass of the glass in water = 11.40 g

Mass of the glass in sulfuric acid = 8.95 g

Required:

The specific gravity of the acid.

Solution:

Mass of water displaced = 14.35 g - 11.40 g = 2.95 g

Mass of the acid displaced = 14.35 g - 8.95 g = 5.4 g

The volume of the sulfuric acid and the water displaced by the glass are

the same, therefore;

Mass of water = 2.95 g

Mass of equal volume of acid = 5.4 g

\(Specific \ gravity = \dfrac{Mass \ of \ acid}{Mass \ of \ equal \ volume \ of water }\)

\(Specific \ gravity \ of \ acid = \dfrac{5.4 \ g}{2.95\ g} \approx 1.83\)

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Given:

There are given that the 35 ft shadow when the sun is at 56 degrees.

Explanation:

To find the tall of the tree, first we need to draw the image:

So,

The image of the given statement is:

Now,

from the given image, we need to find the value of the length of the tree.

So,

To find the length of the tree, we need to use the tan function:

Then,

From the formula of tan function:

Then,

Then,

Final answer:

Hence, the height of the tree is 52 ft.

Answer:

The answer is switch direction

Step-by-step explanation:

since the arrow is pointing to the left:   <--------

and you don't change the symbol, because when it is greater than or equal to or less than or equal to, it's always a closed circle

The total area of the regions between the curves is 4.5 square units

The graph is attached

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

y = x² - 6x + 9 and y = x - 1

With the use of graphs, the curves intersect at

x = 2 and x = 5

So, the area of the regions between the curves is

Area = ∫x² - 6x + 9 - x + 1

This gives

Area = ∫x² - 7x + 10

Integrate

Area =  x³/3 - 7x²/2 + 10x

Recall that x = 2 and x = 5

So, we have

Area = [2³/3 - 7(2)²/2 + 10(2)] - [5³/3 - 7(5)²/2 + 10(5)]

Evaluate

Area = 4.5

Hence, the total area of the regions between the curves is 4.5 square units

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1/2 : 3/4 = 2 : 3 is the answer

Answer:

hope it helped you...! :)

The muralist needs 4 gallons of paint to cover the entire wall with a solid white background.

To calculate the amount of paint the muralist needs to cover the entire wall, we first need to calculate the total area of the wall.

The wall is rectangular, so we can use the formula for the area of a rectangle, which is length times width.

In this case, the length is 80 feet and the height is 20 feet, so the total area is:
80 feet x 20 feet = 1600 square feet
The total area of the wall is the product of its length and height:

Area of wall = Length × Height = 80 ft × 20 ft = 1600 sq ft

Number of gallons of paint needed = Area of wall ÷ Coverage per gallon of paint

Number of gallons of paint needed = 1600 sq ft ÷ 400 sq ft/gal

Number of gallons of paint needed = 4 gallons
Now that we know the total area of the wall, we can divide it by the coverage of each gallon of paint.

The problem states that each gallon covers 400 square feet, so we can divide the total area of the wall by 400 to get the number of gallons needed:
1600 square feet ÷ 400 square feet/gallon

= 4 gallons
Therefore, the muralist needs 4 gallons of paint to cover the entire side wall of the old fire station.

It's worth noting that this calculation assumes that the muralist only needs one coat of paint to cover the wall completely.

Depending on the type of paint and the desired level of coverage, the muralist may need to apply more than one coat, which would require more gallons of paint.

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Answer:

12.50

Step-by-step explanation:

4.52 is roundes to 4.50. Then, 7.99 is rounded to 8. Thus, 4.50 + 8 = 12.50

Answer:

y= -3/5x -2.2

Step-by-step explanation:

you can graph it or solve it mathematically

The names of the functions in the attached figure are:

Functions can be named by their parent functions.

This is so because functions derive their properties from their parent functions.

There are several parent functions, some of them are:

Using the above as a guide, the names of the functions in the attached figure are:

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We have the following:

Answer:21

Step-by-step explanation:

1hr=7

3hr=21

7x3=21

Answer:

21 dollars

Step-by-step explanation:

Hi there!

All you have to do to solve this problem is multiply the amount of money made per hour by the number of hours worked.

In this case, its 7 x 3, which equals 21.

Hope this helped!