What is the exponential regression equation to best fit the data? Round each value in your equation to two decimal places.
x y
0 14
1 23
2 30
3 58
4 137
5 310

See the attached picture for the solution.

Round the answer as needed.

Answer:

Step-by-step explanation:

This problem models a right triangles, where the hypothenuses is the length of the string, and one leg would be 180ft, which is the difference between the total height from the ground and the pole height (186-6=180). Also, the angle in front of the knowing leg is 60.

As, based on all given values, we can apply trigonometric reasons to the hypothenuse, which is L.

[tex]sin60=\frac{180}{L}\\ L=\frac{180}{sin60}\\ L=\frac{180}{\frac{\sqrt{3} }{2} }\\ L=\frac{360}{\sqrt{3}}=\frac{360}{1.7} \approx 211.8ft[/tex]

Therefore, the length of the kite string is around 211.8 feet.

Answer:

The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)

Step-by-step explanation:

* Lets revise how to change from polar form to rectangular form

- Cartesian Coordinates (x , y) and Polar Coordinates (r , θ)

- Where x = r cosФ , y = r sinФ

* To convert from Polar Coordinates (r , θ) to Cartesian Coordinates (x , y)

 # x = r × cos( θ )

 # y = r × sin( θ )

* In the problem

∵ z = 8 cos72° + 8 sin72°

∴ r = 8

∴ Ф = 72°

∵ x = r cosФ

∴ x = 8 cos72° = 2.5

∵ y = r cosФ

∴ y = 8 sin72° = 7.6

* The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)

Answer:

The volume of the figure is [tex](\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of the cone minus the volume of the square pyramid

step 1

Find the volume of the cone

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=\frac{l\sqrt{2}}{2}\ units[/tex] ----> the diagonal of the square base of pyramid is equal to the diameter of the cone

[tex]h=l\ units[/tex]

substitute

[tex]V=\frac{1}{3}\pi (\frac{l\sqrt{2}}{2})^{2}(l)[/tex]

[tex]V=\frac{1}{6}\pi (l)^{3}\ units^{3}[/tex]  

step 2

Find the volume of the square pyramid

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

we have

[tex]h=l\ units[/tex]

[tex]B=l^{2}\ units^{2}[/tex]

substitute

[tex]V=\frac{1}{3}l^{2}(l)[/tex]

[tex]V=\frac{1}{3}l^{3}\ units^{3}[/tex]

step 3

Find the volume of the figure

[tex]\frac{1}{6}\pi (l)^{3}\ units^{3}-\frac{1}{3}l^{3}\ units^{3}=(\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]

The answer is D.

Hope this helps!

Answer:

D. 3.36

Step-by-step explanation:

Just by intuition, we can see that 3.7 / 1.1 will give a result somewhere around 3.3 (forget the decimal point, think 37 / 11).  That automatically allows you to zoom in on the correct answer, based on the other choices.

But let's verify it too.

3.7 / 1.1 = 3.363636

They ask to round to the nearest hundredth, so 3.363636 becomes 3.36

Answer:

You need 30 total weeks to win at least 65% games

Step-by-step explanation:

Team have played = 20 games

Number of winning games = 3

Let x represents the number of additional weeks.

You have won 3 games per week. Therefore you will win 3x additional games.

We know that 65% = 0.65

Therefore,

3+3x/20+4x = 0.65

By cross multiplication:

3+3x= 0.65(20+4x)

3+3x = 13+2.6x

Combine the like terms:

3x-2.6x = 13-3

0.4x=10

4x/10 =10

4x = 10*10

4x=100

Divide both sides by 4

4x/4 = 100/4

x = 25

since you have already played 5 weeks...you need to play 25+5 = 30 weeks.

Therefore you need 30 total weeks to win at least 65% games....

6*6-(3*3)-(2*2) is the answer

Answer: 17.7 (rounded)

Step-by-step explanation:

53/3= 17.6 ..

17.6 rounded is 17.7

Answer:

result is 17.7

Step-by-step explanation:

Answer:

Because 0 is basically nothing. This would only change if X=-9. In that case , |x| < 0.

Step-by-step explanation:

Im just a sixth grader so..........

Answer:

$1480.24

Step-by-step explanation:

This will be solved by the formula:

[tex]FV=I(1+r)^t[/tex]

Where

FV is the future value (what we are looking for)

I is the initial amount (which is $1000)

r is the rate of interest per period (8% is annual interest, but the period is SEMI-ANNUAL, that's 6 months, half of yearly. So r would be half of 8%, which is 4% or r = 0.04)

t is the times compounding occurs in the whole time (The whole time period is 5 years, but compounding occurs semi-annually, so 5*2 = 10 times. Thus, t = 10)

plugging the info into the formula we will get our answer.

[tex]FV=I(1+r)^t\\FV=1000(1+0.04)^{10}\\FV=1000(1.04)^{10}\\FV=1480.24[/tex]

Answer:

C. $1,480

Step-by-step explanation:

Plato

Answer:

H0: u ≤ 10

Ha: u > 10

A right-tailed test

Step-by-step explanation:

In hypothesis testing there are two types of hypotheses;

The null hypothesis, H0 and the alternative hypothesis, Ha. The null hypothesis is the hypothesis of no difference and as such it always has an equality sign;

=, ≤, ≥

On the other hand the alternative hypothesis complements the null hypothesis meaning that if the null hypothesis is rejected then we take the alternative hypothesis to be true.

In order to identify the null and alternative hypothesis we look out for specific key words that will provide us with information on the type of inequality sign. In this scenario, the coach claims that the average number of fouls committed per game is no more than 10. Since µ represents the team's average number of fouls per game, this statement can be written in mathematical symbols as;

u ≤ 10, that is u is no more than 10; average number of fouls committed per game is no more than 10.

This statement will be our null hypothesis since it contains an equality sign.

H0: u ≤ 10

The complement of this statement will enable us deduce the alternative hypothesis. The complement of this statement can be found in the claim of the second coach who thinks that these players create more fouls, to be specific more than 10 fouls. In mathematical notation this claim can be written as;

u > 10, more than 10 fouls.

This statement will be our alternative hypothesis since it complements the null hypothesis;

Ha: u > 10

The type of significance test to be carried out in hypothesis testing emanates from the inequality sign of the alternative hypothesis. The following are the key points to note, if the alternative hypothesis contains;

≠, then this automatically becomes a two tailed test

<, then this automatically becomes a left tailed test since the inequality sign is pointing towards the left.

>, then this automatically becomes a right tailed test since the inequality sign is pointing towards the right.

Our alternative hypothesis contains >, hence this will be a right-tailed test .

Answer:

Answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

85

A triangle with angles of 30, 60, and 90 degrees is a unique and special type of right triangle known as a 30-60-90 right triangle, which has consistent properties and side ratios in Euclidean geometry.

Yes, a triangle with angles of 30, 60, and 90 degrees is a unique triangle, known as a 30-60-90 right triangle. This classification is based on the fact that in Euclidean geometry, the sum of the angles in any triangle is exactly 180 degrees. Since one of the angles is given as 90 degrees, this indicates it is a right triangle, and the remaining angles must add up to 90 degrees. Given that the other two angles are 30 and 60 degrees, this satisfies the requirement exactly, making it a specific type of right triangle with consistent properties.

For example, the sides of a 30-60-90 triangle are always in the ratio 1:√3:2. The side opposite the 30-degree angle is the shortest; the side opposite the 60-degree angle is √3 times longer; and the hypotenuse, opposite the 90-degree angle, is twice as long as the shortest side. These proportions and the angles create the unique properties of the 30-60-90 triangle, and they can be applied in trigonometric calculations and proofs. This distinct set of angles and side ratios is what makes the 30-60-90 triangle a special and unique case in geometry.

there is no bar graph here

Answer:

2x + 6

Step-by-step explanation:

Each term in the parenthesis is multiplied by the 2 outside, that is

2(x + 3)

= (2 × x) + (2 × 3)

= 2x + 6

Answer:

12

Step-by-step explanation:

Answer:

1:60, 2:120

Step-by-step explanation:

In one serivng there are 60 calories, i.e. 60 calories per serving. This is 1:60, an equivalent is 2:120

1:60, 9:540

Hope this helps!

Answer:

Angle G is smaller than angle P

Step-by-step explanation:

In this problem we know that

MN > HK

therefore

∠P > ∠G

The measure of angle P is greater than the the measure of angle G

Rewrite

∠G < ∠P

The measure of angle G is smaller than the the measure of angle P

Answer:

Angle G is smaller than angle P

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

12 times 12 is 144

Answer:

12.

Step-by-step explanation:

If you were to divide 144 into 12 parts, each part would have 12 pieces. Another way to imagine it would be setting up a fraction (144/12) and then simplifying until you get 12/1.

Answer: [tex]x=\frac{89}{3}[/tex] or [tex]26\frac{2}{3}[/tex]

[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\6x+2-2=180-2\\6x=178[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}6\\\frac{6x}{6}=\frac{178}{6}\\[/tex]

[tex]x=\frac{89}{3}[/tex]

Hope this helps and have a great day!!!

Answer: there are three answers. the exatct, decimal, and mixed. i will give them all!

exact: X= 89/3

decimal: x= 29.6

mixed: x= 29 2/3

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Knowing what place values are, we know that since both of those numbers have the 7 in the tens place, it represents 70.  So both of those number are 70 plus another number (under 10)

Answer:

1

Step-by-step explanation:

1

Answer:b 2(39) +2(75)

Step-by-step explanation:

Because there are four corners of a mattress your going to take the length and width of the mattress and multiply each time to then add them to get the exact size your needing

Answer:

39 × 75

Step-by-step explanation:

Since, the shape of the twin mattress is rectangular,

Given,

The length of the mattress = 75 inches,

Width of the mattress = 39 inches,

Now, the the area of the top of the mattress( which is covered by the quilt) = Area of the mattress

We know that,

The Area of a rectangle =  Length × Width

Hence, the area of the top of the mattress = 75 × 39

= 39 × 75

Third option is correct.

Answer:

6+10=16 That is your length.

Step-by-step explanation:

Answer:

POINTSS

Step-by-step explanation:

I WANT POIITNS

Answer:

192.5 ft²

Step-by-step explanation:

Area of the sector

= (360-100)/360 x π(8.35)²

= 158.195 ft²

Area of the triangle

= 1/2 (8.35)(8.35) sin (100)

= 34.3316 ft²

Area of the shaded part

= 158.195 + 34.3316

= 192.5 ft²

Answer:

(B) -9

Step-by-step explanation:

g(x) = 2x² - 11x

To find g(1), we substitute x = 1 into g(x).

g(x) = 2x² - 11x

g(1) = 2(1)² - 11(1) = 2 - 11 = -9

ANSWER

B) -9

EXPLANATION

The given function is

[tex]g(x) = 2 {x}^{2} - 11x[/tex]

Put x=1 into the given function to obtain;

[tex]g(1) = 2 {(1)}^{2} - 11(1) [/tex]

Simplify to get:

[tex]g(1) = 2 (1) - 11(1) [/tex]

[tex]g(1) = 2 - 11 = - 9[/tex]

The correct choice is B.

Answer:

The distributive property says that when there is a number outside of parenthesis, this means it should be distributed (or multiplied) to the values inside the parenthesis.

So in this situation, 10 x b = 10b

and 10 x 4c = 40 c

so 10(b + 4c) becomes 10b + 40c once the 10 is distributed within the parenthesis.

I hope this helps!

Answer:

They are equivalent expressions because if you use distributive property and multiply 10*b, then multiply 10*4c, you get 10b+40c

Step-by-step explanation:

its 14n+21. 7×2n is 14n, and 3×7 is 21

Answer:

[tex]7(2n+3)=14n+21[/tex]

Step-by-step explanation:

[tex]7(2n+3)=(7*2n)+(7*3)\\\\ 7*2n=14n\\ 7*3=21\\ \\ 7(2n+3)=14n+21[/tex]

Answer:   The area of the triangle is:

____________________________________________________

                         →    "  (4x²  +  6x)  cm³  " .

____________________________________________________

Step-by-step explanation:

____________________________________________________

The formula for the "Area, "A" ; of a triangle is:

 A = (1/2) * (baselength) * (perpendicular height) ;

            →  that is:

            →    A = (1/2) * b * h ;

____________________________________________________

The Area, "A" ; should be in "cubic units" ;  in our case, "cubic centimeters" ;

                                                                                       or;  " cm³ " .

____________________________________________________

 Given:  baselength:  "b" = " 4x "  ;

             perpendicular height:  " h = (2x + 3) " ;

____________________________________________________

 Plug in these values into the equation/formula:

           A = (1/2) * b * h ;

         →  A = (1/2) * (4x) * (2x + 3) ;

                →  (1/2) * 4x = 2x ;

         →  A = 2x (2x + 3)  cm³

____________________________________________________

         →  2x (2x + 3) = ?

____________________________________________________

 Note the "distributive property" of multiplication:

        →  a(b + c) = ab + ac .

____________________________________________________

As such:

         →  2x (2x + 3)  =   2x(2x) + (2x)(3) ;

                                 =    4x²  +  6x  ;   ____________________________________________________

The area of the triangle is:  " (4x² + 6x) cm³ " .

________________________________________________

Hope this helps!

       Best wishes in your academic endeavors

                — and within the "Brainly" community!

____________________________________________________

Irrational because it can not be a whole number

Answer:

6.98%

Step-by-step explanation:

To find relative frequency we divide frequency with the total number participants in that age bracket

Total number of participants age 10-19=172.....................given in the table

The frequence for those who ski at age 10-19=12---------------given in table

Relative frequency= 12/172 = 0.0697

Expressed as a percentage= 0.06976×100 =6.98%

Answer:

The correct answer option is 6.98%.

Step-by-step explanation:

We are given the results of a survey which asked  two age groups which summer sport they most preferred.

We are to find the relative frequency of 10-19 year old who preferred to ski.

For that, we will divide the number of kids aged 10-19 years who prefer to ski by the total number of people who prefer to ski and multiply by 100.

Relative frequency = 12/172 * 100 = 6.98%

Answer:

x = k/(y+z)

Step-by-step explanation:

We need to write a general formula to describe the variation: x varies jointly with the inverse of the sum of y and z

it can be written as

x ∝ 1/(y+z)

or can be written as

x = k/(y+z)

where k is the constant of variation introduced when we remove the ∝ sign.