Assume the normal distribution of data has a mean of 14 and a standard Deviation of 3. use the 65-95-99.7 rule to find the percentage of values that lie below 8

Answer:

3*10=30

10^-6=1^-6. (10 raised to the power of-6)

therefore 3*1^-6=3

is equal to

4.86*10=48.6

10^-4=1^-4

therefore 48.6*1^-4=48.6

Answer:

(tenth root of x to the third power)

see image

Step-by-step explanation:

To do this problem you need to know how to convert radicals to an expression with a fraction exponent(and back to radicals again), ALSO exponent rules for division ALSO subtracting fractions.

Square root x can be written as x^ 1/2

fifth root x can be written as x^ 1/5

When you are dividing expressions with the same base, exponent rules say to SUBTRACT the exponents.

1/2 - 1/5 change to common denominator

5/10 - 2/10

= 3/10

x^1/2 / x^1/5 =

x^ (1/2 - 1/5) =

x^ (5/10-2/10) =

x^ 3/10

Then change back to a radical. Remember "down and out" or "roots are down" and "up, up, up" or "exponents are up"

the number down below goes out (outside) the radical. And the number up top is up and exponents are up, up, up

see image.

x^3/10 =

tenth root (x^3)

see image.

The parabola that has the height and width similar to the Gateway arc, gives;

(a) The quadratic equation of the parabola is presented as follows;

[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]

(b) The completed table is presented as follows;

Width. Height

567. 63.12

478. 225.67

308. 459.2

The shape of a quadratic function is a parabola, which is either upward facing or downward facing

(a) The given dimensions of the arc are;

Height = 625

Width at the base = 598

The points on the parabola are therefore;

(0, 0), (598÷2, 625) = (299, 625), (598, 0)

The equation of the parabola is of the form;

f(x) = a•x² + b•x + c, which gives;

f(0) = 0 = a×0² + b×0 + c = c

c = 0

f(299) = 625 = a×299² + b×299 + 0...(1)

f(598) = 0 = a×598² + b×598...(2

(a×598² + b×598) - 2×(a×299² + b×299) = 0 - 2×625

a•178802 = -2×625

a = -2×625 ÷ 178802

a ≈ -6.991 × 10^(-3)

b ≈ 4.181.

The equation is therefore;

[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]

(b)

The table of values is completed as follows;

When the width is 567 feet, x = 299 - 567÷2 = 15.5

[tex] \displaystyle{f(15.5) = -6.991 × 10^{-3} \times 15.5² + 4.181 \times 15.5 approx 63.12} [/tex]

When the width is 478 feet, x = 299 - 478÷2 = 60

[tex] \displaystyle{f(60) = -6.991 × 10^{-3} \times 60² + 4.181 \times 60 approx 225.67} [/tex]

When the width is 308 feet, x = 299 - 308÷2 = 145

[tex] \displaystyle{f(145) = -6.991 × 10^{-3} \times 145² + 4.181 \times 145 approx 459.2} [/tex]

The table is therefore presented as follows;

Width. Height

567. 63.12

478. 225.67

308. 459.2

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Answer: 24 mph

Step-by-step explanation:

If she can run 12 mph/ 12 miles per hour

She runs for 2 hours

12 · 2 = 24

Answer:

Th

Explanation:

Given the ordered pair (-4, -1), we have that x = -4 and y = -1. Plotting this point, we'll have;

Quadrants are labeled in an anti-clockwise direction with the top right portion of the graph being the 1st quadrant. Looking at the plotted point, we can see that the point is in the 3rd quadrant.

Take into account that dop plots are usefull for small or moderate sized data sets, and also they are suefull for data with big gaps.

Based on the previous description, you can conclude that the best option for a dot plot is:

16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97

in comparisson with the other data sets, the elements of the rest of data sets are closer to each other.

SOLUTION

The equation relating x and y is

The equation connecting x and y is an equation of the form

Since slope is also refers to as changes between two variables,

Hence

Cmparing with the equation given,

Therefore,

The change per minute in the total amount of water in the pond is 27 litres

The starting amount ot water is when the time is at 0 minutes .

Hence, substite x=0 into the equation given and obtain the value of y which stands for the amount of water at the begining.

Therefore,

The starting amount of water is 600 litres

Answer: A) 27 litres B). 600 litres

To find the amount of servings, we just need to divide the entire bar weight by the serving weight. Solving this calculation, we have

SOLUTION

The figure above consists of a triangle and a semi-circle.

Area of the figure = Area the of triangle + Area of the semi-circle

Area of composite figure = 112.5 + 88.3125 = 200.8125

Therefore the Area of the figure = 200.81 squared feet to the nearest hundredth

We have to calculate the average temperature change per hour.

We know that the temperature drops from 48 degrees to -12 degrees in 24 hours.

To calculate the average change, in degrees per hour, we calculate the ratio between the variation of the temperature and the interval of time.

We can expres this as:

Answer: The average change in temperature is -2.5 degrees per hour.

We know,

1 liter=1000 milliter.

So, millilters in 1/5 liters​ is,

Therefore, there are 200 milliters in 1/5 liters.

The algebraic expression for each phrase would be the following:

a. the product of 9 and a number t would be expressed as:

9*t

b. the difference of a number x and 1/2 would be expressed as:

x - 1/2

c. the sum of a number m and 7.1 would be expressed as:

m + 7.1

d. the quotient of 207 and a number n​ would be expressed as:

207 / n

5 to 6 odds means that, out of 11 possible outcomes, odds are that there will be 5 of one kind of outcome and 6 of another kind of outcome.

In this case, you are given 5 to 6 odds, which means that out of 11 possible outcomes you will win a bet 5 times, and lose it 6.

In fraction, it will look like this:

Because of that, the probability of winning the bet is 45.45%, and in a fraction, it is 5/11, which means you will win in 5 out of 11 scenarios.

Congruent Shapes

Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),

All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.

The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.

Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is

xm = (-6+4)/2 = -1

Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:

xm = (-8+6)/2 = -1

For the points R(-4,-6) and D(2,-6):

xm = (-4+2)/2 = -1

For the points Q(-9,-4) and D(8,-4):

xm = (-9+8)/2 = -0.5

Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent

For both shapes to be congruent, the coordinates of Q should have been (-10,-4)

Given:

The population of a town increases by 9 % annually.

The current population is 4,500.

Required:

We need to find the equation that gives the population of the town.

Explanation:

The population can be found by the following equation.

Let now be the current population of the town =4500.

Let Next be the population of the town.

The population can be found by the following equation.

Take the common term now out.

Final answer:

Given the number of sides of a pentagon:

Number of sides = 5

Let's find the sum of the measures of the 5 equal angles.

To find the sum of the measures of interior angles of a polygon, apply the formula:

Where:

n is the number of sides = 5

Thus, we have:

Therefore, the sum of the interior angles of the pentagon is 540 degrees.

ANSWER:

540°

Consider that the domain are the set of x values with a point on the curve.

In this case, based on the grap, you can notice that the domain is:

domain = (-8,2)

domain = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2}

In this case you can observe that the circle has a left limit given by x = -8 (this can be notices by the subdivisions of the coordinate system) and a right limit given by x = 2. That's the reason why it is the interval of the domain.

The range are the set of y values with a point on the curve.

range = (-3,7)

range = {-3,-2,-1,0,1,2,3,4,5,6,7}

In this case, you observe the down and up limits of the circle.

Solution

The final answer

We have the following equation of a hyperbola:

Let's divide all the equations by 4, just to simplify it

Just to make it easier, let's put the term if "x" isolated

Now we can complete squares on both sides, just remember that

Now let's complete it!

We already completed one side, now let's complete the side with y^2, see that we will add 4 again, then

And now we can write it using the standard equation!

And now we can graph it like all other hyperbolas, the vertices will be:

And the foci

Then the foci are

Now we can plot the hyperbola!

When you have an arithmetic sequence you can use the next general formula to get the explicit formula:

Where a(1) is the first term in the sequence, d is the difference between each term in the sequence, and n is the nth term

You have the sequence: 28,38,48,58

The difference in this sequence is d=10

The first term is: a(1)=28

Then:

Without converting the equations to the same form, the property that must be different in the functions is the slope

From the question, the equations are given as

y = x + 5

y + x = 5

From the question, we understand that:

The equations must not be converted to the same form before the question is solved

The equation of a linear function is represented as

y = mx + c

Where m represents the slope and c represents the y-intercept

When the equation y = mx + c is compared to y = x + 5, we have

Slope, m = 1

y-intercept, c = 5

The equation y = mx + c can be rewritten as

y - mx = c

When the equation y - mx = c is compared to y + x = 5, we have

Slope, m = -1

y-intercept, c = 5

By comparing the properties of the functions, we have

Hence, the different properties of the functions are their slopes

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Dave has 17 nickels, 24 dimes and 27 pennies in his piggy bank.

According to the question,

We have the following information:

Dave has 7 more dimes than nickels and 10 more pennies than nickels.

Now, let's take the number of nickels to be x.

So,

Dimes = (x+7)

Pennies = (x+10)

Now, Dave has $3.52 in his piggy bank.

We will convert nickels, dimes and pennies into dollars.

We know that 1 nickel = 0.05 dollars, 1 dime = 0.1 dollars and 1 pennies = 0.01 dollars.

Now, we will convert the given numbers of nickel, dime and pennies into dollars.

x Nickels in dollars = $0.05x

(x+7) dimes in dollars = $0.1(x+7)

(x+10) pennies in dollars = $0.01(x+10)

Now, we will them.

0.05x + 0.1(x+7) + 0.01(x+10) = 3.52

0.05x + 0.1x + 0.7 + 0.01x + 0.1 = 3.52

0.16x + 0.8 = 3.52

0.16x = 3.52-0.8

0.16x = 2.72

x = 2.72/0.16

x = 17

Now, we have:

Number of nickels = 17

Number of dimes = (17+7)

Number of dimes = 24

Number of pennies = (17+10)

Number of pennies = 27

Hence, the number of nickels, dimes and pennies are 17, 24 and 27 respectively.

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If the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] then the domain of the function exists

[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]

The collection of all potential inputs for a function is its domain.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Let the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]

Domain of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] :

[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]

Range of [tex]$\frac{x^3-3 x+1}{8 x-5}:\left[\begin{array}{cc}\text { Solution: } & -\infty < f(x) < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Axis interception points of [tex]$\frac{x^3-3 x+1}{8 x-5}[/tex]

X Intercepts: [tex]$(0.34729 \ldots, 0),(1.53208 \ldots, 0)$[/tex], [tex]$(-1.87938 \ldots, 0)$[/tex],

Y Intercepts: [tex]$\left(0,-\frac{1}{5}\right)$[/tex]

Asymptotes of [tex]$\frac{x^3-3 x+1}{8 x-5}: \quad$[/tex]

Vertical: [tex]$x=\frac{5}{8}$[/tex]

Extreme Points of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]

Minimum [tex]$(-0.54351 \ldots,-0.26422 \ldots)$[/tex]

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Let

x ------> number of switch type A

y -----> number of switch type B

so

Remember that

1 hour=60 min

32 hours=32*60=1,920 minutes

4x+5y=1,920 -------> equation 1

3x+5y=1,740 ------> equation 2

Solve the system of equations

Solve by graphing

using a graphing tool

see the attached figure

Solution is

x=180

y=240

therefore

Given

A circle with a tangent drawn to it forming one side of a triangle

Required

we need to find the diameter of the circle

Explanation

clearly it is a right angled triangle as radius through point of contact is perpendicular to the tangent. let the lenght of missing side be d

Therefore

or

or

or d=16

Answer:

Step-by-step explanation:

-215

Answer:

-215

Step-by-step explanation:

the answer to 11-3x75-1 is -215

As we can see in the graph the object returned to its original position in t=6.

It's not accelarating because acceleration is the second derivate of the position, and the position is determined by a linear equation.

The answer is C.

For the given question, we will use the formula from part (b) to answer part (d)

The given function is as follows:

We will find the number of species (S) When A = 813

so, substitute with A = 813, then find S

Rounding the answer to the nearest 10 species

So, the answer will be:

STEP 1:

We write out the formulas and the necessary values

STEP 2

We substitute the values into the formula

Explanation

The model has the form

Where a=initial amount

y= final amount

K= growth rate constant

t= time

When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.

Therefore, the first solution is

For part b we have 16 hours.

Thus, the answer is 36kg