The ages of rocks in an isolated area are known to be approximately normally distributed with a mean of 7 years and a standard deviation of 1.8 years. Using the normalcdf function on your graphing calculator, what percent of rocks are between 5.8 and 7.3 years old?

To find the money at start let us use an equation

Since he puts $8 per week

Then his rate is 8

Since he has a total of $52 after some weeks

We must find the nearest number to 52 in table 8

Since 6 * 8 = 48 the nearest number to 52 in table 8

Then he did that for 6 weeks

52 = 8(6) + x

Let us find x

52 = 48 + x

Subtract 48 from both sides

52 - 48 = 48 - 48 + x

4 = x

He started with $4

Answer:

81 cm³

Step-by-step explanation:

To find the probability between two z-scores on a normal distribution, we can use a z-score table.

A z-score table gives the probability of a data less than the corresponding z-score, like in the picture:

So, if we want the probability between 1.98 and -1.15, we need to do the following:

Since the normal distribution in symmetric around z = 0, we have that:

And since the whole distribution give a 100% probability, or an area of 1, we have that:

So, in the end, we have:

So, the total probability is:

It is given that the total area of the beach is 100 yd².

We have to find the length x and the width y that the organization shoul use to use the least amount of fencing as possible. it means that we have to find the dimensions for which parameter is leasr.

The perimeter of a rectangle is:

In option 1, the length is 50 yards and the width is 20 yards. then the perimeter will be (using the previous formula) equal to 140.

In option too the perimeter will be 130.

in option 3 the perimeter will be 134.44

and, in option 4 it will be 146.36

Given the following:

a)

b) The critical value is -1.645

Also

c) Conclusion:

We fail to reject the test, since there is no enough evidence to conclude that the proportion of wrong tests is less than 10%

Answer:

answer in image

Step-by-step explanation:

Answer:

(-5, 101) or (1, -7)

Step-by-step explanation:

The gradient of a function is zero when its first differential is zero

Taking first derivative of y = x³ + 6x² - 15x + 1

we get
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}(x^3+6x^2-15x\:+\:1)[/tex]

[tex]= \dfrac{d}{dx}(x^3)+ \dfrac{d}{dx}(6x^2) - \dfrac{d}{dx}(15x)\:+\: \dfrac{d}{dx}(1)\\\\[/tex]

[tex]= 3x^2 + 2(6x) - 15 + 0\\\\\\= 3x^2 + 12x - 15x\\[/tex]

Set this first differential to 0, find the solution set for x

[tex]3x^2 + 12x - 15x =0[/tex]

This is a quadratic equation which will have 2 solutions for x.

First divide throughout by 3
[tex]= > x^2 + 4x - 5 = 0[/tex]

Factor the term:
[tex]= > x^2 + 4x - 5 = 0\\\\== > (x -1)(x + 5) = 0\\== > x - 1 =0 \text { or } x + 5 =0\\\\[/tex]

This means x = 1 or x = -5 is the solution set

To find the y value corresponding to these values of x, plug in each of these x values in the original equation and solve for y

Plug in x = 1 into equation x³ + 6x² - 15x + 1

=> 1³ + 6(1)² - 15(1) + 1

=> 1 + 6 - 15 + 1

=> -7

So one point is (1, -7)

Looking at the choices we can eliminate the first and  last choices

Looking at choices 2 and 3 we see that only one of them has x = -5 which is the other solution value. This is the second choice

So the correct answer is second choice
(-5, 101) or (1, -7)

Note we did not have to go through the pain of computing y for x = -5

Answer:

4

Step-by-step explanation:

Given expression:

[tex](3^{8} \cdot 2^{-5} \cdot 9^{0})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]

Any number to the power of zero is 1:

[tex]\implies (3^{8} \cdot 2^{-5} \cdot 1)^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]

[tex]\implies (3^{8} \cdot 2^{-5})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b \cdot c^d)^p=a^{bp}\cdot c^{dp}:[/tex]

[tex]\implies 3^{(8 \cdot -2)} \cdot 2^{(-5 \cdot -2)} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]

[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{\left(2^{-2}\right)^{4} }{\left(3^{3}\right)^{4} } \cdot 3^{28}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{(-2 \cdot 4)}}{3^{(3\cdot 4)}} \cdot 3^{28}[/tex]

[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{-8}}{3^{12}} \cdot 3^{28}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]\implies 3^{-16} \cdot 2^{10} \cdot 2^{-8} \cdot 3^{-12} \cdot 3^{28}[/tex]

Gather like terms:

[tex]\implies 2^{10} \cdot 2^{-8} \cdot3^{-16} \cdot 3^{-12} \cdot 3^{28}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 2^{(10-8)}\cdot3^{(-16-12+28)}[/tex]

[tex]\implies 2^{2}\cdot3^{0}[/tex]

Any number to the power of zero is 1:

[tex]\implies 2^{2}\cdot 1[/tex]

[tex]\implies 2^2[/tex]

Therefore, the solution is:

[tex]\implies 2^2=2 \times 2=4[/tex]

The measure of all the three angles of a triangle will be 45°, 57° and 78° respectively.

What is Triangle?

A triangle is a three sided polygon , which has three vertices and three angles, whose sum is equal to 180 degree.

Given that;

The sum of measures of the angles of a triangle is 180.

The sum of the measures of the second and third angles is three times the measure of the first angle.

The third angle is 21 more than the second.

Now,

Let the measures of all the three angles are x , y and z.

Since, The sum of measures of the angles of a triangle is 180.

So, we can formulate;

x + y + z = 180°   .... (i)

The sum of the measures of the second and third angles is three times the measure of the first angle.

So, we can formulate;

y + z = 3x   ... (ii)

The third angle is 21 more than the second.

So, we can formulate;

z = 21 + y ... (iii)

Substitute value of z in equation (ii);

y + 21 + y = 3x

3x = 2y + 21

x = 2/3 y + 7

So, We can substitute x = 2/3y + 7 , y = y and z = 21 + y in equation (i), we get;

x + y + z = 180°  

2/3 y + 7 + y + 21 + y = 180

2/3y + 2y + 28 = 180

8/3 y = 180 - 28

8/3 y = 152

y = 152 × 3 / 8

y = 57°

Hence, x = 2/3y + 7

x = 2/3 × 57 + 7

x = 2 × 19 + 7

x = 45°

And, z = 21 + y

z = 21 + 57

z = 78°

Thus, The measure of all the three angles of a triangle will be 45°, 57° and 78° respectively.

Learn more about the triangle visit:

https://brainly.com/question/24382052

#SPJ1

The transformation that is used is a translation of 3 units upwards.

Numerous different coordinate systems can be used to describe geometrical figures.

From the diagram of the graph we can see that the transformation that is used is translation of 3 units upwards.

To learn more about transformation visit:

https://brainly.com/question/11709244

#SPJ1

Answer:

Step-by-step explanation:

y=4x3

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

First, rearrange -3x - 4y = 5 into y = mx + c form.

-3x - 4y = 5

-4y = 3x + 5

y = -3/4x - 5/4

Since parallel lines have the same gradient, equation of line is y = -3/4x + c.

Substitute (4,-2) into the equation to find c.

-2 = -3/4(4) + c

c = 1

Hence, equation of line is y = -3/4x + 1.

Answer:

-2.86, -0.37, 0.19, 0.91, 1.46

Step-by-step explanation:

the negatives will always be the least, hope this helps!

Answer:

140 ounces

Step-by-step explanation:

(8)(2.5)(7) = 140 ounces

∠1 and ∠5 are a pair of corresponding angles.
∠15 and ∠7 are corresponding angles.
∠4 and ∠10 are a pair of alternate interior angles.
∠8 and ∠13 are a pair of co-interior angles.
∠3 and ∠4 are a pair of linear angles.


What are corresponding angles?
When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
What are alternate interior angles?
When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar. These angles indicate whether or not the two provided lines are parallel to one another. When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.
What are alternate exterior angles?
The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.
What are linear pair of angles?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Following the above literature,
∠1 and ∠5 are a pair of corresponding angles since angles are created in matching corners or corresponding corners with the transversal.
∠15 and ∠7 are corresponding angles since angles are created in matching corners or corresponding corners with the transversal.
∠4 and ∠10 are a pair of alternate interior angles.
∠8 and ∠13 are a pair of co-interior angles.
∠3 and ∠4 are a pair of linear angles since pair's total angles are always equal to 180°.

To learn more about this, tap on the link below:
https://brainly.com/question/6752750

#SPJ9

Given the sequence:

1, 1, 2, 6, 24

Let's fill in the sequence.

Here, we can see that the nth term is equal to the pprevious term multiplied by n.

First term: 1 x 1 = 1

Second term: 1 x 2 = 2

Third term: 2 x 3 = 6

Fourth term: 6 x 4 = 24

Fifth term: 24 x 5 = 120

Sixth term: 120 x 6 = 720

Seventh term: 720 x 7 = 5040

8th term: 5040 x 8 =40320

Hence, the sequence is:

1, 1, 2, 6, 24, 120, 720, 5040, 40320

The explicit formula of the sequence is:

For example to find the 6th term, we have:

We can see the 6th term is 720.

For the recursive formula, we have:

ANSWER:

Sequence: 1, 1, 2, 6, 24, 120, 720, 5040, 40320

Explicit formula:

Recursive formula:

We have the function:

We then replace the values of b and c, that is:

From this expression, we have that the solution is 13.

so u need to know

[tex] {p}^{a} \times {p}^{b} = {p}^{a + b} [/tex]

and

[tex] { ({p}^{a} )}^{b} = \: {p}^{a \times b} [/tex]

question :

[tex] { ({p}^{a} )}^{4} \times {p}^{3} = {p}^{11} [/tex]

so we can tell :

[tex] {p}^{(a \times 4) +3 } = {p}^{11} [/tex]

then

[tex](a \times 4 )+ 3 = 11[/tex]

[tex]a = 2[/tex]

the answer is a=2

The constant of proportionality is 12

Number of fresh jars of honey stored by The Busy Bee in 3 hours= 36 jars

Number of fresh jars of honey stored by The Busy Bee in 7 hours= 84 jars

So, In 3 hours = 36 jars

In 1 hour = 36/3 = 12 jars

Similarly, In 7 hours = 84 jars

In 1 hour = 84/7 = 12 jars

So, 12 is the constant number

Let x represent the number of hours and y the total number of jars stored by The Busy Bee after x hours

So, the equation can be formulated as:

y = 12x

Learn more about the constant of proportionality:

https://brainly.com/question/8598338

#SPJ1

Water :60 ounces

Salt solution:60 ounces

Explanation

Step 1

set the equations

Let x represent the amoun of water forthe solution

let y represents the amount of solution ( 40% salt)

so

a)the scientific mixes water with the solution to obtain 120 ounces, so

b)the mixture is 20% salt

so

salt fromwater+salt from solution( 40%) = salt in the solution (20%)

so

hence, the amount of salt solution is 60 ounces

,now to find x, replace the y value in equation (1)

so, water : 60 ounces

therefore, the answer is

Water :60 ounces

Salt solution:60 ounces

I hope this helps you

8x - 3y = -22

y = 5x + 19

Substituting the second equation into the first one:

8x - 3(5x + 19) = -22

8x - 3*5x - 3*19 = -22

8x - 15x - 57 = -22

-7x = -22 + 57

x = 35/(-7)

x =

The missing amount is A. 790 B. 20 C. 90 D. 75 E. 20 F. 275

Subtract non-cash assets from total current assets. This number represents the cash amount on the balance sheet. Below is a simple way to calculate income, capital, and total cost of income: Net Income = Ending Equity  Starting Equity from the Balance Sheet Total Expenses = Net Income  Net Income.

Everything a company owns must come from debt-equity owners or equity so the equation must be balanced. Equity equals the balance sheet total minus all liabilities. All these figures are on the company's balance sheet. For homeowners, equity is the value of the home minus any outstanding mortgage debt or liens.

Learn more about The missing amounts here:-https://brainly.com/question/24188456

#SPJ1

We can divide the hexagon into 6 equilateral triangles, and call the side 'x'. I will draw the situation:

Every line is x because the hexagon is regular (all sides have the same length). Therefore we can find x, because two times x is 18'':

The hexagon has the same area of 6 equilateral triangles with the side equal to x. The formula of the area of an equilateral triangle is:

Therefore the area of the hexagon will be:

Rounding it will be 210 square inches.

The number form of (1 + 1) will be (1 + 1) only.

So, 1 + 1 in number form:

Given (1 + 1) is 2 when we do the sum of it, the number form of 2 will be:

Therefore, the number form of (1 + 1) will be (1 + 1) only.

Kow more about number forms here:

https://brainly.com/question/19169731

#SPJ13

Answer:

x=-10, you would get this by fixing the equation like this (x+10) (x+) =0 then you would have to -10 on both sides and you get -10 as your answer

the prime numbers smaller than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

let's find the sums that give us 50:

3+47=50

7+43=50

13+37=50

19+31=50

so the answer is four different ways.

Answer:

the answer is 66

Step-by-step explanation:

multiply

In this problem we have a vertical parabola open upward

the vertex represents the absolute minimum

Looking at the graph

the vertex is the point (1,-3)

therefore

the function is increasing at the interval (1, infinite)

the function is decreasing at the interval (-infinite, 1)

the absolute minimum is (1,-3)

Step-by-step explanation:

volumes of liquor because these are the ones which have volume and cm can be changed to millimeters

a)

From the information given, the ferris wheel makes a complete rotation in 16 minutes.

A complete rotation is 360 degrees. This means that each angle is

360/12 = 30 degrees

Lets us assume that the starting point is A. As the ferris wheel move towards the highest point at D, the angle covered is 30 + 30 + 30 = 90 degrees

We have the following equations

360 = 16

90 = (90 x 16)/360 = 4

b) Recall, 1 minute = 60 seconds

Thus, 16 minutes = 16 x 60 = 960 seconds

It x