the weights of cars passing over a bridge have a mean of 3550 lb and a standard deviation of 870 pounds. Assume that the weights of cars passing over the bridge or never distributed. Use the empirical rule to estimate the probability that a randomly-selected car going over the bridge will weigh less than 940 lbs
​

Answer:

The common ratio of the geometric sequence is 3

Given that :

GL = 4x - 2

GE = 3x + 2

GK = 2x + 8

we are to find GJ and GE

using the idea of slant angle, lets equate some sides in other to get x

GK = GL

2x + 8 = 4x - 2

collecting like terms

4x - 2x = 8 + 2

2x = 10

divide both sides by 2

2x/2 = 10/2

x = 5

Since GK = GJ

inputing x = 5 into GK

GK = 2x + 8

GK = 2(5) + 8

GK = 10 + 8

GK = 18

since GK = 18, GJ = 18

GE = 3x + 2

recall x = 5

GE = 3(5) + 2

GE = 15 + 2

GE = 17

Therefore,

GJ = 18

GE = 17

Answer:

that divide negative -7 and 84

Step-by-step explanation:

It is being multiplied because 8/-7 is a division expression and you need to do the opposite. Multiplication is the opposite of division.

hope it helps!

The empirical rule, also known as the 68-95-99.7 rule, provides a rough estimate of the percentage of values that fall within a certain number of standard deviations from the mean in a normal distribution.

According to the empirical rule, approximately 68% of the area under a normal curve is within 1 standard deviation of the mean, approximately 95% of the area is within 2 standard deviations of the mean, and approximately 99.7% of the area is within 3 standard deviations of the mean.

To match the probabilities to the range for the empirical rule, we can use the following table:

Within 1 standard deviation of the mean: 68%

Within 2 standard deviations of the mean: 95%

Within 3 standard deviations of the mean: 99.7%

It's important to note that the empirical rule is only an approximation and may not be accurate for all normal distributions.

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The percentage increase in the population of the town is 12%.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Increase in population =  90,000 - 80,000  = 10,000

          Percentage increase = 10,000/80,000 * 100 = 100/8 = 12.5%

Hence the percentage increase in the population of the town is 12%.

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The bias based on the naive forecast method for the given data is 2.0.

To calculate the bias using the naive forecast method, we first need to calculate the average of the time series values. The formula for the naive forecast is simply taking the last observed value as the forecast for the next period.

The time series values given are 13, 19, 8, and 14. To find the average, we sum up these values and divide by the number of values:

Average = (13 + 19 + 8 + 14) / 4

= 54 / 4

= 13.5

Next, we take the last observed value, which is 14, as the forecast for the next period.

Finally, we calculate the bias by subtracting the average from the forecast:

Bias = Forecast - Average

= 14 - 13.5

= 0.5

Rounding the bias to 1 decimal place, we get a bias of 0.5, which can also be expressed as 2.0 when rounded to the nearest whole number.

Therefore, the bias based on the naive forecast method for the given data is 2.0.

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Plotting points in R3 are the techniques that enable one to graph points that exist in 3-dimensional spaces. A point P(x, y, z) in R3 can be plotted by mapping the corresponding coordinates onto the x, y, and z-axes. A point can be defined as a point that does not have any size, length, or width but merely represents a location.

For each point P(x, y, z) given below, let A(x, y, 0), B(x, 0, z), and Clo, y, z) be points in the xy-, xz-, and yz-planes, respectively. Plot and label the points A, B, C, and P in R3 as given below:13a) P(2,2,4): Point P will be located on the coordinate (2,2,4), where the x-axis intercepts the y-axis and the z-axis14a) P(-3,2,4): Point P will be located on the coordinate (-3,2,4), where the x-axis intersects the y-axis and the z-axis. Similarly, we can plot the rest of the points given using the techniques mentioned above.

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To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

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The slope of the line in the graph will be -1.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also a ratio of the rise to the run.

The formula to calculate the slope of the lines is given below:-

m = [y₂  - y₁ ] / [ x ₂ - x₁ ]

The two points from which the line is passing are ( 2,0) and ( 0,2)

( x₁,y₁) = ( 2 , 0 )

( x₂,y₂) = ( 0 , 2 )

m = [ 2 - 0 ] / [ 0 - 2 ]

m = 2 / - 2

m =-1

Therefore, the slope is -1

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The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)

The list of options represents the given parameter

All ordered pairs are relations but not all ordered pair are functions

For an ordered pair to be a function, the following must be true:

The y values on the ordered pair must have  different x values

Using the above as a guide,

This means that the ordered pair in option (b) represents a function

Hence, the ordered pair that is a function is (b)

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The exact value of ||7v - 3w||, where v = -i - 3j and w = 5i - 2j, is 7√59.

To find the exact value of ||7v - 3w||, we first calculate the vector 7v - 3w.

Given v = -i - 3j and w = 5i - 2j, we can substitute these values into the expression and simplify:

7v - 3w = 7(-i - 3j) - 3(5i - 2j)

        = -7i - 21j - 15i + 6j

        = -22i - 15j

Next, we find the magnitude of the vector -22i - 15j using the formula ||a + bi|| = √(a^2 + b^2):

||-22i - 15j|| = √((-22)^2 + (-15)^2)

               = √(484 + 225)

               = √709

               ≈ 7√59

Therefore, the exact value of ||7v - 3w|| is 7√59.

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Answer:

157.5 pounds

Step-by-step explanation:

11.25×12=135 then add 135 to 22.5

Answer:

16 and 4

Step-by-step explanation:

Let (x+y) =20 and (x-y)=12 then:

Isolate for x in each equation

   x=20-y and x=12+y

Set the equations to equal each other since the value of x should be the same for both

   20-y = 12+y

Rearrange so that y is on one side and the numbers are on the other

   8 = 2y

   y= 8/2

   y= 4

Now  substitute the y- value back into either of the original equations

   x+y= 20

   x+4 = 20

Rearrange and isolate  x

   x = 20-4

   x = 16

So the two values are 16 and 4

Hey there! :)

We are given the equation:

\( \displaystyle \large{y - 2 = - 5(x + 6)}\)

First, we have to isolate y-term; add -2 both sides.

\( \displaystyle \large{y - 2 + 2= - 5(x + 6) + 2} \\ \displaystyle \large{y = - 5(x + 6) + 2}\)

Then we simplify the expression; distribute -5 in the x+6.

\( \displaystyle \large{y = - 5x - 30 + 2}\)

Evaluate:

\( \displaystyle \large{y = - 5x - 28}\)

Therefore, y = -5x-28 is equivalent to y-2=-5(x+6)

function of f(2) is f(2) = 3(2) + 15 = 21.

Given the function f(x) = 3x + 15, we want to find the value of f(2). To do this, we substitute 2 in place of x in the function.

When we replace x with 2, we get f(2) = 3(2) + 15.

Now, we simplify the expression by performing the multiplication first. Multiplying 3 by 2 gives us 6.

So, we have f(2) = 6 + 15.

Finally, we perform the addition to get the final result. Adding 6 and 15 gives us 21.

Therefore, f(2) = 21, which means that when we plug in 2 for x in the function f(x) = 3x + 15, the result is 21.

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Answer:

50.24

Step-by-step explanation:

area of circle = πr²

where r = radius

given radius = 4

so area = (3.14)(4)²

==> evaluate exponent

area = (3.14)(16)
==> multiply 3.14 and 16

area = 50.24

b) h = \(tan \theta\)  x 17 is the required equation.

c) The height of the streetlight is 20.4 ft.

The height of the person is 6 ft.

The distance at which the person is standing from the streetlight = 12 ft.

The distance at which the person's shadow appears = 5ft.

a) Hence, we can make the following diagram.

The right triangle below gives a visual representation of the problem. It shows the known quantities and a variable 'h' to indicate the height of the streetlight.

b) Let's now find an equation trigonometric function involving the unknown quantity 'h'.

from the below diagram, we can say that,

\(tan \theta\) = h/base

base= 12+5=17

hence we have, \(tan \theta\) = h/17

h = \(tan \theta\)  x 17 is the required equation.

c) Now we have to find the height of the streetlight.

firstly let's find the value of \(\theta\),

\(\theta\) = tan 6/5.

\(tan^{-1}\)(6/5) = 50.2°

hence, tan 50.2 = h/17

                   1.20 = h/17

                         h= 1.20 x 17

                         h= 20.4 ft.

Hence, the height of the streetlight is 20.4 ft.

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Answer:

NQ = 9cm

Step-by-step explanation:

If you divide 24 with 6, you get 4. So I divide 36 with 4, which gave me 9.

The curve y = 8e^x has maximum curvature at the point (0, 8).there is no point where the second derivative equals zero,

To determine the point of maximum curvature on the curve y = 8e^x, we need to find the second derivative of the function and identify the point where it equals zero. The second derivative represents the rate of change of the slope, or the curvature, of the curve.

First, we find the first derivative of y = 8e^x with respect to x:

dy/dx = 8e^x

Then, we differentiate again to find the second derivative:

d²y/dx² = d(8e^x)/dx = 8e^x

Setting the second derivative equal to zero:

8e^x = 0

Exponential functions, such as e^x, are never equal to zero for any value of x. Therefore, there is no point where the second derivative equals zero, indicating that the curve y = 8e^x does not have any inflection points or points of maximum curvature.

However, we can determine the point where the curvature is the greatest by considering the graph of y = 8e^x. Since the exponential function e^x is always positive, the curve y = 8e^x is always concave up. This means that the curvature is positive throughout the curve, but there is no specific point of maximum curvature.    

In conclusion, the curve y = 8e^x does not have a point of maximum curvature but is always positively curved.  

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Answer:

C. Multiply the bottom equation by 2

Step-by-step explanation:

-2x+ 4y= 10

3x- 2y =-7

We want to multiply the second equation by 2

-2x+ 4y= 10

6x- 4y =-14

------------------

4x +0y = -4

Answer:

C. Multiply the bottom equation by 2

x = - 1

y = 2

Step-by-step explanation:

Multiplying 3x - 2y = - 7 by 2, we get:  

- 2x + 4y = 10

6x - 4y = - 14

____________

4x = - 4

x = - 1

Putting x = - 1 in 3x - 2y = - 7, we get:

3 * (- 1) - 2y = - 7

= - 3 - 2y = - 7

= - 2y = - 7 + 3

= - 2y = - 4

= y = 2

Hope this helps!

The value of the variables are x = 2 and y = 1

From the information given, we have the simultaneous equations are;

y = 6x -11

-2x - 3y = -7

Now, substitute the value of y in equation 1 to equation 2, we get;

-2x - 3(6x -11) = -7

expand the bracket

-2x - 18x + 33 = -7

collect the like terms

-2x - 18x = -7 - 33

Add the values

-20x = -40

Make 'x' the subject

x = 2

Substitute the values

y = 6x -11

y = 6(2) - 11

y = 1

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The equation in point-slope form is y - 5 = (5/3)(x + 5). The general form of the equation is 5x - 3y + 40 = 0.

To find the equation of a line parallel to the given line and passing through the point (-5,5), we can use the point-slope form of a linear equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. First, we need to find the slope of the given line, and then we can substitute the values into the point-slope form to obtain the equation. Additionally, we can convert the equation to the general form, which is Ax + By + C = 0, by rearranging the terms.

The given line has the equation 5x - 3y - 2 = 0. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope. Rearranging the equation gives us:

-3y = -5x + 2

y = (5/3)x - 2/3

From the equation, we can see that the slope of the given line is 5/3. Since the line we want to find is parallel to this line, it will have the same slope.

Now, using the point-slope form with the point (-5,5) and the slope 5/3, we can write the equation:

y - 5 = (5/3)(x - (-5))

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

This is the equation of the line in point-slope form.

To convert it to general form, we can multiply through by 3 to eliminate the fraction:

3y - 15 = 5x + 25

5x - 3y + 40 = 0

This is the equation of the line in general form.

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Answer:

y = 1/5x + 3

Step-by-step explanation:

y = mx + b

m: slope = 1/5

b: y - intercept

(x, y): (-5, 2)

2 = 1/5(-5) + b

2 = -1 + b

add 1 to both sides to get b alone

2 + 1 = -1 + b + 1

3 = b

Answer:

49 units and 7 units per minute

Step-by-step explanation:

If we look at a number line, -66 and -17 are 49 units apart. 49/7 = 7.

Answer:

7.5

Step-by-step explanation:

Since we are given the price for 5 bags of dog food, we have to find the unit rate. Now to do that we divide the price by the amount.

12.50/5= 2.50

now since we have the unit rate, we take that and multiply the price of one by 3 to find the price of 3

2.50x3=7.50

Hope this helps!

Answer: 7.5 bags

Step-by-step explanation:

$12.50 divided by 5 bags= $2.5 per bag

$2.5*3 bags= $7.5

I believe that may be false

Answer:

Step-by-step explanation:

True.

Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.

This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.

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The nearest tenth of a foot, the thickness T of the cantilever at x = 6 feet is 7.6 feet.

The given equation for the bottom edge of the cantilever is y = 2Vx, where V is the height of the cantilever. Therefore, the height of the cantilever is:

V = y / (2x)

At x = 6 feet, the value of y is:

y = 2Vx = 2(3.2) = 6.4 feet

To find the thickness T at x = 6 feet, we can use the Pythagorean Theorem:

T² = b² - y²

where b is the height of the cantilever. We have already calculated V to be 3.2 feet, so:

b = 3.2 + y = 3.2 + 6.4 = 9.6 feet

Substituting these values into the equation for T², we get:

T² = (9.6)² - (6.4)² = 57.76

Taking the square root of both sides, we get:

T ≈ 7.6 feet

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