A sheet of metal is 9 inches longer than it is wide, and its total area is 252 square inches. Find the dimensions of the sheet of metal.

If w represents the width of the metal sheet, which of the following equations is a model for the given word problem?
A. w^2-9w-252=0
B. w^2-9w+252=0
C. w^2+9w+252=0
D. w^2+9w-252=0

The discrete quantitative variable among the options provided is (a) the number of employees of an insurance company. Discrete variables are numerical variables that can only take on specific, separate values.

Discrete variables typically arise from counting or enumerating items or individuals. In the case of the number of employees of an insurance company, it represents a count of individuals and can only take on whole number values. For example, the number of employees can be 10, 100, 1000, etc., but it cannot take on fractional values or be measured as a continuous range.

On the other hand, options (b), (c), and (d) represent examples of continuous quantitative variables. Continuous variables can take on any value within a certain range and can be measured along a continuous scale. The volume of water released from a dam can be measured in liters or cubic meters, and it can take on any value within that scale, including fractional values. The distance you drove yesterday can also take on any value along the scale of distance, and it can include fractional distances. The Dow Jones Industrial Average represents a continuous variable that can take on any value within the range of the index, which is typically measured in points or as a percentage.

Therefore, the number of employees of an insurance company (option a) is the discrete quantitative variable among the options provided.

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In this problem we have that

The volume of the cone is 60pi cm3

The volume of the cylinder is 180pi cm3

Compare the volumes

Divide both volumes

180pi/60pi=2

that means

the volume of the cylinder is two times the volume of the cone

or

Answer:

35

Step-by-step explanation:

We use trignometry here

Assuming that the angle created between the surface of the sea and the 56feet below line is 90 degrees.

So we use the sin rule

sin90/97 = sin x/56

multiply 56 to the other side

56*sin90/97 = sin x

sin90=1

56/97 = sin x

x= sin^-1 (56/97)

x= 35.3

Round and you get 35

The following proportion by cross multiplying:

( x + 2 ) / 6 = ( x - 4 ) / 3 is -19

Given:

( x + 2 ) / 6 = ( x - 4 ) / 3

( x + 2 )=2(x-4)

x+2=2x-8

x=-10

If the ratio between the first and second amounts is identical to the ratio between the second and third, the three quantities are said to be in continuing proportion. Similarly, the ratio between the first and second amounts in a continuous proportion will be equal to the ratio between the third and fourth.

Consider the following two ratios: a:b and c:d. We shall convert the means of the two specified ratio terms to a single term/number in order to get the ongoing proportion.

This is the LCM of means in general, and for the given ratio, the LCM of b & c is bc. As a result of multiplying the first ratio by c and the second ratio b.

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Answer:

c = 58x

Step-by-step explanation:

A linear equation is an equation in the form of f(x) = mx + c. Where m is the slope and c is the intercept.

Let the price of one guitar lessons be x, then 47guitars will be 47x and 11 guitar lessons will be 11x. All together will be 47x + 11x = 58x.

Thus, the total cost, c, is

c = 58x

Answer:

a.) x=7 or x=-11

b.) x=−2 or x=−8

Step-by-step explanation:

a)  x² + 4x – 77 = 0

Step 1: Factor left side of equation.

(x−7)(x+11)=0

Step 2: Set factors equal to 0.

x−7=0 or x+11=0

x=7 or x=−11

b.) x(x + 4) = -2(3x + 8)

Step 1: Simplify both sides of the equation.

x^2+4x=−6x−16

Step 2: Subtract -6x-16 from both sides.

x^2+4x−(−6x−16)=−6x−16−(−6x−16)

x^2+10x+16=0

Step 3: Factor left side of equation.

(x+2)(x+8)=0

Step 4: Set factors equal to 0.

x+2=0 or x+8=0

x=−2 or x=−8

Answer:

a) {-11, 7}.

b) {-8, -2}

Step-by-step explanation:

a) x^2 + 4x - 77 = 0

To factor this we need 2 numbers whose product is -77 and sum is + 4.

They are + 11 and - 7, so:

( x + 11)(x - 7) = 0

x + 11 = 0 or x - 7 = 0

x = -11,  7.

b) x(x + 4) = -2(3x + 8)

x^2 + 4x = -6x - 16

x^2 + 4x + 6x + 16 = 0

x^2 + 10x + 16 = 0

(x + 2)(x + 8) = 0

x = -8, -2.

Answer:

5.40

Step-by-step explanation:

let X represent the price of a 18 minute phone call

X=18 ×1.80

6

= 5.40

If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

Answer:

25. Yes, it is a function, because none of the x outputs are repeating

Step-by-step explanation:

Hey there!

25). Ans;

It is a function. [ many to one function].

26).Ans; Put all values of "x" in (2x^2+7).

a. f(x) = -2

\( f( - 2)= 2 \times { (- 2)}^{2} + 7\)

So, f(-2)= 15

b. f(x)= -1.

\(f( - 1) = 2 \times ( { - 1)}^{2} + 7\)

So, f(-1)= 9

c. f(x)= 0

\(f(0) = 2 \times ( {0)}^{2} + 7\)

So, f(0)= 7

d. f(x)= 1

\(f(1) = 2 \times {(1)}^{2} + 7\)

So, f(1)= 9

e. f(x)= 2

\(f(2) = 2 \times {(2)}^{2} + 7\)

So, f(2)= 15

f. f(x)= 3.

\(f(3) = 2 \times {(3)}^{2} + 7\)

So, f(3)= 25.

Hope it helps...

Answer:

im out of ideas

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

3^2(2^3+4)/2^2

3^2(8+4)/2^2

3^2(12)/2^2

9(12)/4

108/4

27

Answer:

x = 1

Step-by-step explanation:

x/4 = 8/32

x = 1

Best Regards!

Answer:

X=1 m

X= 0.81 m

Step-by-step explanation:

for the first X you must put in a proportion like this

38:8=4:X

X=(4×8)/38= 1 m

for the second one's you could use Pythagorean theorema

finding the diagonal of the biggest rectangle and you must put the diagonals in proportion whit the 2 sides

32:4=Y:32.9

Y=(32×32.9)/4=4.1 m (diagonal of the smallest rectangle)

\( } \sqrt{ {4.1}^{2} - {4}^{2} } = 0.81m\)

use an other time the Pythagorean theorema and you find the other option

Answer:

H

Step-by-step explanation:

If we look at the green line (x ≥ 3) we know that the solution must be shaded to the right of the line. The only region out of all of our answer choices that satisfies this is H.

An equation that represents the line is Y is (-4/3)x+2 is the solution.

Y = mx+b, where m is the slope and b is the y-intercept, is the formula for a line's slope-intercept (the point on the y-axis where the line crosses it). Replace m with the value you determined for your slope. In our case, the formula might be written as y = 1x+b or y = x+b if the slope value were substituted.

y=(-4/3)

We have two points since x+2 = -1.33x+2:

(3) and (2) are calculated from the graph.

We are aware that the line's equation is

y=mx+b

m=slope

m=(y2-y1)/(x2-x1)

m=(2-(-2))/(0-3)

therefore the slope is what we have

m=4/-3

m=-4/3

-4/3=-1.3333

We must track down "b"

using the example (0,2)

There are

2=m*0+b

2=b

Finally, here is

Y=(-4/3)x+2 is the solution.

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Answer:

(a) Shown below.

(b) Explained below.

Step-by-step explanation:

(a)

The sample space of rolling an 8-sided die twice is as follows:

S = {(1 , 1) , ( 1 , 2) , ( 1, 3) , ( 1, 4 ) , ( 1, 5) , ( 1 , 6 ) , ( 1, 7 ) , ( 1, 8) ,

        (2 , 1) , (2 , 2) , ( 2, 3) , ( 2, 4 ) , ( 2, 5) , (2 , 6 ) , ( 2, 7 ) , ( 2, 8) ,

        (3 , 1) , ( 3, 2) , ( 3, 3) , ( 3, 4 ) , ( 3, 5) , ( 3 , 6 ) , (3, 7 ) , ( 3, 8) ,

        (4, 1) , ( 4 , 2) , ( 4, 3) , ( 4, 4 ) , ( 4, 5) , (4 , 6 ) , (4, 7 ) , (4, 8) ,

        (5, 1) , ( 5 , 2) , ( 5, 3) , (5, 4 ) , ( 5 ,5) , (5, 6 ) , ( 5, 7 ) , ( 5, 8) ,

        (6 , 1) , ( 6 , 2) , ( 6, 3) , (6, 4 ) , ( 6, 5) , (6 , 6 ) , ( 6, 7 ) , ( 6, 8) ,

        (7 , 1) , ( 7 , 2) , ( 7, 3) , ( 7, 4 ) , ( 7 , 5) , ( 7, 6 ) , ( 7, 7 ) , (7, 8) ,

        (8 , 1) , ( 8 , 2) , (8, 3) , ( 8, 4 ) , ( 8, 5) , ( 8 , 6 ) , ( 8, 7 ) , ( 8, 8)}

There are a total of N = 64 elements.

(b)

(i)

The product of the two numbers is a prime number:

Product is a prime number samples:

2 = ( 1, 2)  , ( 2, 1)

3  = ( 1 , 3) , ( 3 , 1)

5 = ( 1, 5) , ( 5 , 1)

7 = ( 1, 7) , ( 7 , 1)

Number of samples, n = 8

P (Product is a prime number) = 8/64 = 1/8 = 0.125.

(ii)

The product of the two numbers is not a perfect square :

Product is not a perfect square samples:

2 =  ( 1, 2)  , ( 2, 1)

3  = ( 1 , 3) , ( 3 , 1)

5 = ( 1, 5) , ( 5 , 1)

6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)

7 = ( 1, 7) , ( 7 , 1)

8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)

10 = ( 2, 5) , ( 5, 2)

12 = (2 , 6) , ( 3 , 4) , ( 4 3)  , ( 6 , 2)

14  = ( 2, 7) , ( 7 , 2)

15 = (3 , 5) , ( 5 , 3)

18 = ( 3, 6) , ( 6 , 3)

20 = ( 4, 5) , ( 5, 4)

21 = ( 3 , 7) , ( 7 , 3)

24 = ( 3 , 8) , ( 4 , 6 ) , ( 6 , 4) , ( 8 , 3)

28 = ( 4 , 7)  , ( 7 , 4)

30 = ( 5 , 6) , ( 6 ,5 )

32 = ( 4 , 8) , ( 8 , 4)

35 = ( 5 , 7) , ( 7 , 5)

40 = ( 5 , 8) , ( 8 , 5)

42 = ( 6 , 7) , ( 7 , 6)

48 = ( 6 , 8) , ( 8 , 6)

56 = ( 7 , 8) , ( 8 , 8)

Number of samples, n = 52

P (Product is not a perfect square) = 52/64 = 0.8125

(iii)

The product of the two numbers is a multiple of 5:

Product is a multiple of 5 samples:

5 = ( 1, 5) , ( 5 , 1)

10 = ( 2, 5) , ( 5, 2)

15 = (3 , 5) , ( 5 , 3)

20 = ( 4, 5) , ( 5, 4)

25 = ( 5 , 5)

30 = ( 5 , 6) , ( 6 ,5 )

35 = ( 5 , 7) , ( 7 , 5)

40 = ( 5 , 8) , ( 8 , 5)

Number of samples, n = 15

P (Product is a multiple of 5 ) = 15/64 = 0.2344.

(iv)

The product of the two numbers is less than or equal to 21:

Product is less than or equal to 21 samples:

1   =  ( 1, 1)

2 =  ( 1, 2)  , ( 2, 1)

3  = ( 1 , 3) , ( 3 , 1)

4 =   (1 , 4) , ( 2, 2) , ( 4, 1)

5 = ( 1, 5) , ( 5 , 1)

6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)

7 = ( 1, 7) , ( 7 , 1)

8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)

9 = ( 3, 3)

10 = ( 2, 5) , ( 5, 2)

12 = (2 , 6) , ( 3 , 4) , ( 4 3)  , ( 6 , 2)

14  = ( 2, 7) , ( 7 , 2)

15 = (3 , 5) , ( 5 , 3)

16  = (2 , 8) , ( 4 , 4) , ( 8 , 2)

18 = ( 3, 6) , ( 6 , 3)

20 = ( 4, 5) , ( 5, 4)

21 = ( 3 , 7) , ( 7 , 3)

Number of samples, n = 40

P (Product is less than or equal to 21) = 40/64 = 0.625.

(v)

The product of the two numbers is divisible by 4 or 6:

Product is divisible by 4 or 6 samples:

4 =   (1 , 4) , ( 2, 2) , ( 4, 1)

6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)

8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)

12 = (2 , 6) , ( 3 , 4) , ( 4 3)  , ( 6 , 2)

16  = (2 , 8) , ( 4 , 4) , ( 8 , 2)

18 = ( 3, 6) , ( 6 , 3)

20 = ( 4, 5) , ( 5, 4)

24 = ( 3 , 8) , ( 4 , 6 ) , ( 6 , 4) , ( 8 , 3)

28 = ( 4 , 7)  , ( 7 , 4)

30 = ( 5 , 6) , ( 6 ,5 )

32 = ( 4 , 8) , ( 8 , 4)

36 = (6 , 6)

40 = ( 5 , 8) , ( 8 , 5)

42 = ( 6 , 7) , ( 7 , 6)

48 = ( 6 , 8) , ( 8 , 6)

56 = ( 7 , 8) , ( 8 , 8)

64 = ( 8 , 8)

Number of samples, n = 42

P (Product is less than or equal to 21) = 42/64 = 0.6563.

Answer:

-1

Step-by-step explanation:

2(3х – 1) > 4х – 6

Distribute

6x -2 > 4x-6

Subtract 4x from each side

6x-2-4x > 4x-6-4x

2x-2 > -6

Add 2 to each side

2x-2+2> -6+2

2x> -4

Divide by 2

2x/2 > -4/2

x > -2

The number is greater than -2

The only number that is greater than -2 is -1

Answer:

  x > -3

Step-by-step explanation:

The function will be increasing where its derivative is positive.

__

  y = x^2 +6x . . . . . given function

  y' = 2x +6 . . . . . . . derivative

The derivative is positive for ...

  2x +6 > 0

  2x > -6

  x > -3 . . . . . domain where the function is increasing

Answer:

Lateral surface: 135.34

surface area: 185.61

Step-by-step explanation:

Lateral surface formula: AL=πrh2+r2

surface area formula: A=πr(r+h2+r2)

As per the angle sum property, the value of x is 125°

Angle sum property:

According to the angle sum property, the sum of interior angles of a triangle is 180°.

Given,

In the given diagram, PQR and SQT are straight line.

Now we need to find the value of x.

As per the angle sum property, we know that the sum of all the angles of the triangle is 180 degrees.

While we equate the given values within this property, we get.

x° + 55° = 180°

x° = 180° - 55°

x° = 125°

Therefore, the value of x is 125°.

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Answer:

15 15 17 17 19 30

Step-by-step explanation:

to ne and to 69 04 16 97 50 27

The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.

It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5

To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.

Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).

Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).

So, the p-value for the given test is 0.067 (rounded to two significant digits).

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Answer:

1= 2,3

2= 6,-2

Step-by-step explanation:

sup real human here,

d starts at 1,3

we move it to the right one to fill x+1 so it would be 2,3

We move it down 6 to fill y-6 so it would not be 2,-3

for 2, it is being moved down 5 and over 5

we see this because the original point is 4,-2 and the new position is -1,3 which would be down 5 over 5 from the original

this would make 1,3 become 6,-2

Answer:

1. plug the point (1, 3) into the expressions: (x+1, y-6)

(1+1, 3-6) = (2, -3)

2. make an expression for the points based on B and B':

B: (4, -2)

B': (-1, 3)

(x-5, y+5) because 4 - 5 = -1, and -2 + 5 = 3

plug in A (1,3):

(1 - 5, 3 + 5) = (-4, 8)

x is greater than eleven thirds.

Inequality are expression that have <, > , ≤ and ≥ .

Therefore,

1 / 5 (5x) + 10 + 5x > 32

Hence,

1 / 5 × 5x + 10 + 5x > 32

x + 10 + 5x >32

combine like terms

x + 10 + 5x >32

x + 5x + 10 > 32

Therefore,

x + 5x + 10 > 32

6x + 10 > 32

subtract 10 from both sides

6x + 10 - 10 > 32 - 10

6x > 22

divide both sides by 6

x > 22 / 6

x > 11 / 3

Therefore, x is greater than eleven thirds.

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The equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12) is y = -5x + 1

A line is the distance between two points

Given the equation of a line expressed as 10x + 2y = -2. Determine the slope

2y = -10x -2

y = -5x - 1

Slope of the line is -5

The equation of a line in point-slope form is y - y1 = m(x-x1)

Substitute the point and the slope of the parallel line

y - 12 = -5(x  - 0)
y - 12 = -5x
y = -5x + 12

Hence the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12) is y = -5x + 12

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Answer:

its d

Step-by-step explanation:

i got it

Answer:

D

Step-by-step explanation:

The value of the iterated integral ∫∫R (5x - 2y) dy dx over the region R given by 0 ≤ x ≤ 6 and 0 ≤ y ≤ x/2 is 81.

The iterated integral ∫∫R (5x - 2y) dy dx over the region R given by 0 ≤ x ≤ 6 and 0 ≤ y ≤ x/2 is:

∫[0,6]∫[0,x/2] (5x - 2y) dy dx

We can integrate with respect to y first:

∫[0,6]∫[0,x/2] (5x - 2y) dy dx = ∫[0,6] [5xy - y^2]⌈y=0⌉⌊y=x/2⌋ dx

= ∫[0,6] [(5x(x/2) - (x/2)^2) - (0 - 0)] dx

= ∫[0,6] [(5/2)x^2 - (1/4)x^2] dx

= ∫[0,6] [(9/4)x^2] dx

= (9/4) * (∫[0,6] x^2 dx)

= (9/4) * [x^3/3]⌈x=0⌉⌊x=6⌋

= (9/4) * [(6^3/3) - (0^3/3)]

= 81

Therefore, the value of the iterated integral ∫∫R (5x - 2y) dy dx over the region R given by 0 ≤ x ≤ 6 and 0 ≤ y ≤ x/2 is 81.

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Answer:19

Step-by-step explanation:

Answer:

\(x=\sqrt{\frac{9}{2}}\)

Step-by-step explanation:

\(a^2+b^2=c^2\\x^2+x^2=3^2\\2x^2=9\\x^2=\frac{9}{2} \\x=\sqrt{\frac{9}{2} }\)