Solve the inequality. negative 12 greater than or equal to 24 x

A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).

Degree of the polynomial function is equal to 3.

Zero's of the polynomial function is equal to 2, -3 , 5 .

And f(3) = 6

If 2, -3, and 5 are zeros of f(x), then we can write function as,

f(x) = a(x-2)(x+3)(x-5)

where a is some constant.

To determine the value of a, we can use the fact that f(3) = 6.

Substituting x = 3 into the equation above, we get,

f(3) = a(3-2)(3+3)(3-5)

     = -12a

Here we have,

f(3) = 6, so we can set these two expressions equal to each other and solve for a,

⇒ -12a = 6

⇒ a = -1/2

Now we can substitute this value of a back into the equation for f(x) that we found earlier,

⇒ f(x) = -1/2 (x-2)(x+3)(x-5)

Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).

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Answer:

  5/6 mile

Step-by-step explanation:

The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.

__

Here is the equation for the area of a rectangle.

  A = LW . . . . . area is the product of length and width

When we fill in the area and width, we have ...

  5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland

Solving this equation gives ...

  L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L

  L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division

The length of Sandra's farmland is 5/6 mile.

Answer:

1,208.92613

Step-by-step explanation:

this is the answer

The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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Answer:

Point slope-  y + 8 = − 1 2 ⋅ ( x − 4 )

Slope Intercept Form- y = − 1/ 2 x − 6

Slope- m=-1/2

Step-by-step explanation:

Point slope- y-y₁=m(x-x₁)

Slope Intercept form- y=mx+b\

Slope- rise/run= y2-y1/x2-x1

Answer:

(1) The point estimate for the population mean is 4.925.

(2) Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

(3) Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

(4) As the level of confidence increases, the width of the interval increases.

Step-by-step explanation:

We are given that the following data represent the pH of rain for a random sample of 12 rain dates.

X = 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68.

(1) The point estimate for the population mean is given by;

Point estimate, \(\bar X\) = \(\frac{\sum X}{n}\)

                            = \(\frac{5.20+5.02+ 4.87+5.72+ 4.57+ 4.76+4.99+ 4.74+ 4.56+ 4.80+5.19+ 4.68}{12}\)

                            = \(\frac{59.1}{12}\)  = 4.925

(2) Let \(\mu\) = mean pH of rainwater

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~  \(t_n_-_1\)

where, \(\bar X\) = sample mean = 4.925

             s = sample standard deviation = 0.33

            n = sample of rain dates = 12

            \(\mu\) = population mean pH of rainwater

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, \(\mu\) is ;

P(-2.201 < \(t_1_1\) < 2.201) = 0.95  {As the critical value of t at 11 degrees of

                                               freedom are -2.201 & 2.201 with P = 2.5%}  

P(-2.201 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 2.201) = 0.95  

P( \(-2.201 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(2.201 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

P( \(\bar X-2.201 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+2.201 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

95% confidence interval for \(\mu\) = [ \(\bar X-2.201 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+2.201 \times {\frac{s}{\sqrt{n} } }\) ]

                                      = [ \(4.925-2.201 \times {\frac{0.33}{\sqrt{12} } }\) , \(4.925+2.201 \times {\frac{0.33}{\sqrt{12} } }\) ]  

                                     = [4.715, 5.135]

Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

The interpretation of the above confidence interval is that we are 95% confident that the population mean pH of rainwater is between 4.715 & 5.135.

(3) Now, 99% confidence interval for the population mean, \(\mu\) is ;

P(-3.106 < \(t_1_1\) < 3.106) = 0.99  {As the critical value of t at 11 degrees of

                                               freedom are -3.106 & 3.106 with P = 0.5%}  

P(-3.106 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 3.106) = 0.99

P( \(-3.106 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(3.106 \times {\frac{s}{\sqrt{n} } }\) ) = 0.99

P( \(\bar X-3.106 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+3.106 \times {\frac{s}{\sqrt{n} } }\) ) = 0.99

99% confidence interval for \(\mu\) = [ \(\bar X-3.106 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+3.106 \times {\frac{s}{\sqrt{n} } }\) ]

                                     = [ \(4.925-3.106 \times {\frac{0.33}{\sqrt{12} } }\) , \(4.925+3.106 \times {\frac{0.33}{\sqrt{12} } }\) ]  

                                     = [4.629, 5.221]

Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

The interpretation of the above confidence interval is that we are 99% confident that the population mean pH of rainwater is between 4.629 & 5.221.

(4) As the level of confidence increases, the width of the interval increases as we can see above that the 99% confidence interval is wider as compared to the 95% confidence interval.

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

Answer:

-2.7 < y

Step-by-step explanation:

2.9 < 5.6+y

Subtract 5.6 from each side

2.9-5.6 < 5.6-5.6+y

-2.7 < y

The number of tiles required is 27 tiles. Then the number of boxes of tiles that Tamara needs will be 5.

Let W be the rectangle's width and L its length. Then the rectangle's area will be written as,

Area of the rectangle = L × W square units

The area of the border is given as,

A = 9 x (1/3)

A = 3 square feet

The area of each tile is given as,

a = (1/3) x (1/3)

a = 1 / 9

The number of tiles required is given as,

⇒ A/a

⇒ 9 / (1/3)

⇒ 9 x 3

⇒ 27

The number of boxes of tiles that Tamara needs is given as,

⇒ 27 / 6

⇒ 4.5 ≈ 5

The number of tiles required is 27 tiles. Then the number of boxes of tiles that Tamara needs will be 5.

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The sides of a right triangle that would form a right triangle is 9 m, 40 m, 41 m. 9 yards. 12 yards, 15 yards and 15 miles. 8 miles. 17 miles

An equation is an expression that shows the relationship between two or more numbers and variables.

Pythagoras theorem states that for a right angled triangle, the sides of the triangle are related to each other using the expression:

(hypotenuse side)² = (adjacent side)² + (opposite side)²

The sides of a right triangle that would form a right triangle is 9 m, 40 m, 41 m, because:
41² = 40² + 9²

Also, 9 yards. 12 yards, 15 yards, because:

15² = 9² + 12²

15 miles. 8 miles. 17 miles, because

17² = 15² + 8²

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Answer:

x = 0.6 * 50

Step-by-step explanation:

x = 60% of 50

x = 60% * 50

x = 0.6 * 50

Answer:

60% of 50 = 60 / 100 × 50 = ⅗ × 50 = 150 / 5 = 30

________

x% of y = x / 100 × y = xy / 100

Answer:

\(1.23 \times 10^{14}\)

Step-by-step explanation:

A number written in scientific notation consists of two parts that are multiplied.

The first part is a number that is greater than or equal to 1 and less than 10.

The second part is an integer power of 10.

Start with your number, 123,000,000,000,000.

All the zeros are place holders. To get a number out of it that is greater than or equal to 1 and less than 10, you move the decimal place to just to the right of the 1, like this: 1.23

Now you know very well that 1.23 is much, much smaller than the original number, but if you multiply it by a power of 10, you will get the original number.

To know the exponent of 10 you need to use, count the number of decimal places that the original number changed to become 1.23.

Original number: 123,000,000,000,000.

Notice the decimal place is all the way at the right after the last zero.

The new number is

1.23000000000000

How many places did the decimal place move? 14

Therefore, the answer is

\(1.23 \times 10^{14}\)

Answer:

The margin of error is  \(E = 6.9 \)

The 95% confidence interval is  \( 26.5  <  \mu < 40.3 \)  

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  31

     The mean is  \(\mu = 33.4 \ ng/ml\)

      The standard deviation is  \(\sigma = 19.6 \ ng/ml\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>  \(E = 1.96  *  \frac{19.6  }{\sqrt{31 } }\)

=>  \(E = 6.9 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=> \( 33.4  - 6.9 <  \mu < 33.4  +  6.9 \)

=> \( 26.5  <  \mu < 40.3 \)  

Answer:

-3/4

Step-by-step explanation:

4p+6-3=0

4p+3=0

4p=-3

p= -3/4

Step-by-step explanation:

Heron's formula when all 3 sides (a, b, c) are given :

s = (a + b + c)/2

A = sqrt(s(s-a)(s-b)(s-c))

in our case

s = (34+73+89)/2 = 98

A = sqrt(98(98-34)(98-73)(98-89)) =

= sqrt(98×64×25×9) = sqrt(98)×8×5×3 =

= sqrt(2×49)×120 = sqrt(2)×7×120 =

= sqrt(2)×840 = 1,187.939392... ≈ 1,188 in²

Answer:

The area of a circle with a radius of 5 inches will be 78.54 inches.

Step-by-step explanation:

The formula to find the area of a circle is \(A=\pi r^{2}\)

We know that the radius is 5 inches. Let's plug that into the equation.

\(A=\pi\) × \(5^{2}\)

5 squared is the same as multiplying 5 by itself, which gives us 25. Our equation now looks like:

\(A=\pi\) × \(25\)

In this equation, we'll be rounding pi into 3.14

3.14 × 25 = 78.54

Here's your answer! I hope it's correct ^u^

Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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Answer: m=11

Step-by-step explanation:

Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Answer:

Step-by-step explanation:

-9x - 45 = -7x - 15  (Distribute -0.75 to (12x+60))        (x-8x = -7x)

-30 = 2x   (add 15 to both sides and add 9x to both sides)

-15 = x (divide both sides by 2)

Answer:

  100/9 ≈ 11.11...(repeating)

Step-by-step explanation:

You want the maximum value of 0.3^x on the interval [-2, 2].

The base of 0.3 is less than 1, so you know the function is decreasing. The maximum value will be at the left end of the interval, where x = -2.

  y = (0.3)^-2 = 1/0.09 = 100/9 ≈ 11.11...(repeating)

Answer:

2+5/9 is the answer

If you add 2 to 5/9, that makes the statement true

Answer:

Step-by-step explanation:

Let's use the following variables to solve the problem:

Let's call the number of adult tickets sold "a"

Let's call the number of child tickets sold "c"

Let's call the total cost "C" (in pounds)

From the problem statement, we know the following:

The cost of an adult ticket is £7.70

The cost of a child ticket is £4.20

The total cost of all the tickets sold is C

We can set up an equation based on this information:

C = 7.7a + 4.2c

We also know that the value of C is a whole number greater than 90 and less than 96. So we can write:

90 < C < 96

We need to find the value of C that satisfies both of these conditions. We can start by trying some values of a and c and seeing if they give us a value of C that satisfies the conditions. One way to do this is to use trial and error.

Let's start with a = 10 (meaning 10 adult tickets were sold). We can plug this into our equation and solve for c:

C = 7.7a + 4.2c

C = 7.7(10) + 4.2c

C = 77 + 4.2c

To satisfy the conditions, C must be greater than 90 and less than 96. Let's see if any value of c satisfies these conditions:

90 < C < 96

90 < 77 + 4.2c < 96

Subtract 77 from all parts of the inequality:

13 < 4.2c < 19

Divide all parts of the inequality by 4.2:

3.1 < c < 4.5

Since c must be a whole number, the only possible value is 4. But let's check if this value of c gives us a value of C that satisfies the conditions:

C = 77 + 4.2c

C = 77 + 4.2(4)

C = 94.8

This value of C is very close to 95, which satisfies both conditions (greater than 90 and less than 96). So the value of C is approximately £94.80.

At a cinema a child's ticket costs £4.20 and an adult's ticket costs

£7.70. When a group of adults and children went to see a film, the

total cost was £C, where C is a whole number greater than 90 and

less than 96.

What is the value of C?

Answer:

it should be answer C- the mode of the data is same for both data sets

Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is a function as it passes the vertical line test.

Applying the definition of variation, we have:

1. When x = 36, y = 6.

2. When x = 1, y = 27.

3. It takes 3 seconds for the object to fall 144 feet.

4. Length of a string that vibrates 64 times per second is 48 inches.

Inverse variation is a type of relationship between two variables in which one variable increases while the other decreases, or vice versa, in a way that the product of the two variables remains constant.

In other words, if we have two variables x and y that are inversely proportional, we can write:

x × y = k, where k is a constant.

1. We are given that y varies directly as the square root of x. This means that we can write:

y = k√x

where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 16, y = 4:

4 = k√16

4 = 4k

k = 1

Now we can use this value of k to find y when x = 36:

y = 1√36

y = 6

Therefore, when x = 36, y = 6.

2. We are given that y varies inversely with the cube of x. This means that we can write:

y = k/x³

where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 3, y = 1:

1 = k/3³

1 = k/27

k = 27

Now we can use this value of k to find y when x = 1:

y = 27/1³

y = 27

Therefore, when x = 1, y = 27.

3. We are given that the distance that an object falls varies directly with the square of the time, t, of the fall. This means that we can write:

d = kt²

where d is the distance, k is a constant of proportionality, and t is the time. To find the value of k, we can use the given information that when t = 1, d = 16:

16 = k(1)²

16 = k

k = 16

Now we can use this value of k to find the time it takes for the object to fall 144 feet:

144 = 16t²

9 = t²

t = 3

Therefore, it takes 3 seconds for the object to fall 144 feet.

4. We are given that the rate of vibration of a string under constant tension varies inversely with the length of the string. This means that we can write:

r = k/L

where r is the rate of vibration, L is the length of the string, and k is a constant of proportionality.

To find the value of k, we can use the given information that when L = 24 inches, r = 128 vibrations per second:

128 = k/24

k = 3072

Now we can use this value of k to find the length of a string that vibrates 64 times per second:

64 = 3072/L

L = 48 inches

Therefore, the length of a string that vibrates 64 times per second is 48 inches.

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