The table shows the number of flowers in four bouquets and the total cost of each bouquet. A 2-column table with 4 rows. The first column is labeled number of flowers in the bouquet with entries 8, 12, 6, 20. The second column is labeled total cost (in dollars) with entries 12, 40, 15, 20. What is the correlation coefficient for the data in the table? –0.57 –0.28 0.28 0.57

Answer:

Sister is 70

Step-by-step explanation:

John is 39.

8 less than twice his age is

39*2-8 = 70

Answer:

70 years old.

Step-by-step explanation:

Since John's sister is 8 years younger than TWICE his age, we just need to multiply 39*2 which equals 78. Now we just need to subtract 8 which equals 70.

Hope this helps!! <3

Answer:

x = 1

Step-by-step explanation:

Given

[tex]\frac{1}{2}[/tex] : [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{4}[/tex] : x

Multiply all parts by 12 to clear the fractions

6 : 8 = 9 : 12x , simplifying

3 : 4 = 3 : 4x

Thus

4x = 4 ( divide both sides by 4 )

x = 1

Answer:

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Step-by-step explanation:

[tex]\alpha \text{ and } \beta \text{ in Quadrant I}[/tex]

[tex]$\tan(\alpha)=\frac{1}{7} \text{ and } \sin(\beta)=\frac{1}{\sqrt{10}}=\frac{\sqrt{10} }{10} $[/tex]

Using Pythagorean Identities:

[tex]\boxed{\sin^2(\theta)+\cos^2(\theta)=1} \text{ and } \boxed{1+\tan^2(\theta)=\sec^2(\theta)}[/tex]

[tex]$\left(\frac{\sqrt{10} }{10} \right)^2+\cos^2(\beta)=1 \Longrightarrow \cos(\beta)=\sqrt{1-\frac{10}{100}} =\sqrt{\frac{90}{100}}=\frac{3\sqrt{10}}{10}$[/tex]

[tex]\text{Note: } \cos(\beta) \text{ is positive because the angle is in the first qudrant}[/tex]

[tex]$1+\left(\frac{1 }{7} \right)^2=\frac{1}{\cos^2(\alpha)} \Longrightarrow 1+\frac{1}{49}=\frac{1}{\cos^2(\alpha)} \Longrightarrow \frac{50}{49} =\frac{1}{\cos^2(\alpha)} $[/tex]

[tex]$\Longrightarrow \frac{49}{50}=\cos^2(\alpha) \Longrightarrow \cos(\alpha)=\sqrt{\frac{49}{50} } =\frac{7\sqrt{2}}{10}$[/tex]

[tex]\text{Now let's find }\sin(\alpha)[/tex]

[tex]$\sin^2(\alpha)+\left(\frac{7\sqrt{2} }{10}\right)^2=1 \Longrightarrow \sin^2(\alpha) +\frac{49}{50}=1 \Longrightarrow \sin(\alpha)=\sqrt{1-\frac{49}{50}} = \frac{\sqrt{2}}{10}$[/tex]

The sum Identity is:

[tex]\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)[/tex]

I will just follow what the question asks.

[tex]\text{Find the value of }\alpha+2\beta[/tex]

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]\text{I will first calculate }\cos(2\beta)[/tex]

[tex]$\cos(2\beta)=\frac{1-\tan^2(\beta)}{1+\tan^2(\beta)} =\frac{1-(\frac{1}{7})^2 }{1+(\frac{1}{7})^2}=\frac{24}{25}$[/tex]

[tex]\text{Now }\sin(2\beta)[/tex]

[tex]$\sin(2\beta)=2\sin(\beta)\cos(\beta)=2 \cdot \frac{\sqrt{10} }{10}\cdot \frac{3\sqrt{10} }{10} = \frac{3}{5} $[/tex]

Now we can perform the sum identity:

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]$\sin(\alpha + 2\beta)=\frac{\sqrt{2}}{10}\cdot \frac{24}{25} +\frac{3}{5} \cdot \frac{7\sqrt{2} }{10} = \frac{129\sqrt{2}}{250}$[/tex]

But we are not done yet! You want

[tex]\alpha + 2\beta[/tex] and not [tex]\sin(\alpha + 2\beta)[/tex]

You actually want the

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Answer:

ok bye guy................

Answer:

1: 90º

2: 25º

Step-by-step explanation:

Hey there!

Well we know that all the middle angles are 90º right angles,

so we can conclude that angle 1 is 90º.

All the angles in a triangle add up to 180 so we can set up the following,

65 + 90 + x = 180

Combine like terms

155 + x = 180

-155 to both sides

x = 25º

So angle 2 is 25º.

Hope this helps :)

Answer:

Below

Step-by-step explanation:

From the kite you easily notice that 1 is a right angle so its mesure is 90°.

2 is inside a triangle. This triangke has two khown angles: a right one and a 65° one.

The sum of a triangle's angles is 180°.

● (2) + 90+65 = 180

● (2) +155 =180

● (2)= 180-155

●(2) = 25°

Answer:

C

Step-by-step explanation:

In a function, each domain has one range. But a range can have many domains.

Think about it like this:

Patty is eating dinner

Patty is swimming

Both can't happen at the same time.

But:

Patty is eating dinner

Leo is eating dinner

C has two domains of -3, each having different ranges.

Hope that helps, tell me if you need further info. =)

Answer:

C. C{(6,-9),(-3,6),(-3,-7),(-9, -2)}

Step-by-step explanation:

If you see the same x-coordinate used more than once, it is not a function.

Here, you only see this in choice C, where x = -3 for two points. That makes this relation not a function.

Answer:

We reject the students claim because the P-value is less than the significance level.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = 25,235

Alternative hypothesis;Ha; μ > 25,235

Now, let's find the test statistic. Formula is;

t = (x' - μ)/(σ/√n)

We are given;

x' = 27,524

μ = 25,235

σ = 6000

n = 100

Thus;

t = (27524 - 25235)/(6000/√100)

t = 2289/600

t = 3.815

So from online p-value calculator as attached, using t=3.815, DF = 100-1 = 99 and significance level of 0.05, the P-value is gotten as p = 0.000237.

The p-value is less than the significance level of 0.05. Thus,we reject the students claim.

Answer:

126 cm³

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = Al ( A is the cross sectional area and l the length ), thus

V = 21 × 6

   = 126 cm³

Answer:

4.16% is the hourly growth rate

Step-by-step explanation:

What we can do here is to first set up an exponential relationship that relates the present number of bacteria, the initial number of bacteria, the growth rate of the bacteria and the number of hours.

What we want to establish here has a resemblance with the compound interest formula in finance.

Let’s see the initial number of bacteria as the amount deposited, the present number of bacteria as the amount after some months, the growth rate as the monthly percentage while the number of hours works like the number of months.

Mathematically, what we have will be;

P = I(1 + r)^h

where P is the present bacteria number, I is the initial, r is the growth rate while h is the number of hours.

Thus, we have the following values from the question;

P = 1530

I = 1,300

r = ?

h = 4

Substituting these values, we have;

1530 = 1300(1 + r)^4

divide both sides by 1,300

1.177 = (1+r)^4

Find the fourth root of both sides

(1.177)^(1/4) = 1+ r

1.0416 = 1 + r

r = 1.0416-1

r = 0.0416

This in percentage is 4.16%

Answer:

Hey there!

Triangle PQT and RQT are congruent by AAS. AAS means that one side is congruent, and two angles are congruent.

Since these triangles share one side, then the side is congruent.

PR is a straight line, so if angle Q is 90 degrees, then the supplementary angle is also 90 degrees.

Finally, the diagram shows that angles R and P are congruent to each other.

Hope this helps :)

Answer:

           [tex]\bold{a=5\,,\quad b=-4\frac27}[/tex]

Step-by-step explanation:

[tex]5+\frac{2\sqrt3}7+4\sqrt3=5+\frac27\sqrt3+4\sqrt3=5+4\frac27\sqrt3=5-(-4\frac27)\sqrt3[/tex]

Answer:

D. RO

Step-by-step explanation:

Answer:

One

Step-by-step explanation:

y = 3 x - 5.

y = -x + 4.

x=9/4 and y=7/4

1 solution (9/4 , 7/4)

For a system of the equation to be an Independent Consistent System, the system must have one unique solution. The system of the equation has only one solution. Thus, the correct option is A.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

Given the two equations y=3x -5 and y=-x+4. If the two of the equations are plotted on the graph. Then it can be observed from the graph that there is only one intersection between the two lines.

Hence, the system of the equation has only one solution. Thus, the correct option is A.

Learn more about the System of equation:

https://brainly.com/question/128952

#SPJ2

Answer:

4kg

Step-by-step explanation:

...../...../

2kg + half of its weight

so half of its weight = 2kg

so 2kg + 2kg= 4kg the weight of the fish

Answer: y = 2x+1

Step-by-step explanation:

It is the only line with (1,3) as a solution.  A slower algebraic way to solve this would be to plug in 1 for x and 3 for y, then, out of the equations in which it works, plug in -2 for x and -3 for y.  The equation that remains true for both points is the answer.

Hope it helps <3

Answer:

[tex]\boxed{y = 2x + 1}[/tex]

Step-by-step explanation:

The line passes through (1, 3).

The solution of the line is the points it crosses.

x = 1

y = 3

Plug x as 1 and y as 3 in the equation.

y = -2x + 1

3 = -2(1) + 1

3 = -2 + 1

3 = -1 False

Plug x as 1 and y as 3 in the equation.

y = 2x + 1

3 = 2(1) + 1

3 = 2 + 1

3 = 3 True

Plug x as 1 and y as 3 in the equation.

y = x - 1

3 = 1 - 1

3 = 0 False

Plug x as 1 and y as 3 in the equation.

y = -x + 1

3 = -(1) + 1

3 = -1 + 1

3 = 0 False

Answer:

Total number of fruits remaining =  25

Step-by-step explanation:

Let the number of

apples = 4x

bananas = 5x

Therefore

4x-2 / 5x = 2 / 3

Solve for x, cross multiply

3(4x-2) = 2(5x)

12x - 6 = 10 x

2x = 6

x = 3

Apples = 4*3 = 12

Bananas = 5*3 = 15

Apples remaining = 12-2 = 10

Total number of fruits remaining = 10+15 = 25

Answer:

[tex]\boxed{25 \ fruits}[/tex]

Step-by-step explanation:

Let apples be 4x and Bananas be 5x

So, the given condition is:

[tex]\frac{4x-2}{5x} = \frac{2}{3}[/tex]

Cross Multiplying

5x*2 = 3(4x-2)

10x = 12x - 6

Adding 6 to both sides

10x+6 = 12x

12x - 10x = 6

2x = 6

x = 3

Now, Fruits remaining in the bowl are:

=> 4x-2 + 5x

=> 12 - 2 + 15

=> 10+15

=> 25

Answer:

-3

Step-by-step explanation:

[tex]F(x)=-\,(-x)\\f(-3)=-(-(-3))\\f(-3)=-3[/tex]

Answer:

y = StartFraction 5 Over 9 EndFraction

y=5/9

Step-by-step explanation:

Given:

x+6y=20

-x+3y=-15

x+6y=20. (1)

-x+3y=-15 (2)

From (1)

x=20-6y

Substitute x=20-6y into (2)

-x+3y=-15

-(20-6y)+3y = -15

-20+6y+3y = -15

9y=-15+20

9y=5

Divide both sides by 9

9y/9=5/9

y=5/9

y = StartFraction 5 Over 9 EndFraction

Answer:

y=-5/9

Step-by-step explanation:

9y=-5

---------- Divided by 9

9      9  

Y is equal to negative five over 9

Have a good day and stay safe!

Answer: The depth is 12m

Step-by-step explanation:

The area is 350m^2

And the depth in each point of the base is at the same depth D.

Then we have a cuboid.

Now, the volume of a cuboid is equal to:

V= L*W*D

L = lenght, W = width and D = depth.

Such that L*W = area = 350m^2

then we have:

V = D*350m^2

Now we want V = 4200m^3

4200m^3 = D*350m^2

D = (4200/350) m = 12m

The depth is 12m

The 3 pack cost $9.45

3 single cartons would have cost: 3 x 4.20 = $12.60

Difference in cost: 12.60 - 9.45 = $3.15

Percent savings : 3.15/ 9.45 = 0.3333

0.333 x 109 = 33.33%

Round the answer as needed

Answer:

The tower is 73.4 m tall

Step-by-step explanation:

The height of the pole = 2.5 m

The shadow cast by the pole = 1.72 m

Shadow cast by tower = 50.5 m

To find the height of the tower, we proceed by finding the angle of elevation, θ, of the light source casting the shadows as follows;

[tex]Tan\theta =\dfrac{Opposite \ side \ to\ angle \ of \ elevation}{Adjacent\ side \ to\ angle \ of \ elevation} = \dfrac{Height \ of \ pole }{Length \ of \ shadow} =\dfrac{2.5 }{1.72}[/tex]

[tex]\theta = tan ^{-1} \left (\dfrac{2.5 }{1.72} \right) = 55.47 ^{\circ}[/tex]

The same tanθ gives;

[tex]Tan\theta = \dfrac{Height \ of \ tower}{Length \ of \ tower \ shadow} =\dfrac{Height \ of \ tower }{50.5} = \dfrac{2.5}{1.72}[/tex]

Which gives;

[tex]{Height \ of \ tower } = {50.5} \times \dfrac{2.5}{1.72} = 73.4 \ m[/tex]

Answer:

3x + 2y = 12.

Step-by-step explanation:

Two conspicuous points on the graph are at (0, 6), and (4, 0).

That means the slope of the line is (6 - 0) / (0 - 4) = 6 / -4 = -3 / 2.

The intercept of the line is at (0, 6).

This means that the equation of the line is y = -3/2x + 6.

y = -3/2x + 6

Add 3/2x to both sides

3/2x + y = 6

Multiply all terms by 2

3x + 2y = 12

Hope this helps!

Answer:

after 2 seconds

Step-by-step explanation:

Given

h(x) = - x² + 4x + 12

The ball will reach its maximum at the vertex of the parabola

Find the zeros by letting h(x) = 0, that is

- x² + 4x + 12 = 0 ← multiply through by - 1

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

The x- coordinate of the vertex is at the midpoint of the zeros, thus

[tex]x_{vertex}[/tex] = [tex]\frac{-2+6}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Substitute x = 2 into h(x)

h(2) = - 2² + 4(2) + 12 = - 4 + 8 + 12 = 16

The cannonball reaches its maximum height of 16 ft after 2 seconds

Answer:

2 seconds

Step-by-step explanation:

I just did it just trust me. This isn't reated to the answer but I had spagehtti for lunch

Answer:

18- 14+8=3x

4+8=3x

12=3x

12/3=2x/3

x=4

Answer:

2/3, -8, -1/6, 4.

Step-by-step explanation:

Step-by-step explanation:

The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as :

Now, from the given options, the possible choices can be :

A, B, C and E

D can be there because after taking any pair the rational root can't be 3

F can't be possible because an does't have 4 in its factors so denominator cannot be 4.

Answer:

x=60 degrees

Step-by-step explanation:

Formula for angle at x=1/2(240-120)

x=60

Answer:  Perimeter = 6π ≈ 18.84

                         Area = 15π ≈ 47.10

Step-by-step explanation:

This is a composite of a big semicircle with diameter of 10 --> radius (r) = 5

plus a medium semicircle with diameter of 6 --> r = 3

minus a small semicircle with diameter of 4 --> r = 2

Perimeter of a semicircle = [tex]\dfrac{1}{2}(2\pi r)=\pi r[/tex]

[tex]P_{big}=\pi (5)\quad =5\pi\\P_{medium}=\pi (3)\quad =3\pi\\P_{small}=\pi (2)\quad =2\pi\\P_{composite} =5\pi+3\pi -2\pi\\.\qquad \qquad =\large\boxed{6\pi}[/tex]

Area of a semicircle = [tex]\dfrac{1}{2}(\pi r^2)[/tex]

[tex]A_{big}=\dfrac{1}{2}\pi (5)^2\quad =12.5\pi\\\\A_{medium}=\dfrac{1}{2}\pi (3)^2\quad =4.5\pi\\\\A_{small}=\dfrac{1}{2}\pi (2)^2\quad =2\pi\\\\A_{composite} =12.5\pi+4.5\pi -2\pi\\\\.\qquad \qquad =\large\boxed{15\pi}[/tex]

Answer:

option D 25 is the right answer

Answer:  D) 25

Step-by-step explanation:

I graphed the coordinates and partitioned it into four triangles and one rectangle. Then I found the area for each partition.

The sum of the partitions is 25.

Answer:

The center is ( 1,-3) and the radius is 3

Step-by-step explanation:

The equation of a circle can be written in the form

( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius

(x-1)^2 + (y+3)^2= 9

(x-1)^2 + (- -3)^2= 3^2

The center is ( 1,-3) and the radius is 3

Answer:

112 weeks

Step-by-step explanation:

784/7=112

Answer:

112 weeks............

Answer:

Based on the function, the growth rate is 4.5%

Step-by-step explanation:

In this question, we are given the exponential equation and we are told to deduce the growth rate.

Mathematically, we can rewrite the exponential equation as follows;

S(t) = 152(1.045)^t = 152(1 + 0.045)^t

What we see here is that we have successfully split the 1.045 to 1 + 0.045

Now, that value of 0.045 represents the growth rate.

This growth rate can be properly expressed if we make the fraction given as a percentage.

Thus the issue here is converting 0.045 to percentage

Mathematically, that would be;

0.045 = 4.5/100

This makes is 4.5%

So the growth rate we are looking for is 4.5%