Find the value of the linear correlation coefficient r. The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Temperature 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16 Question options

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer: 64cm

Step-by-step explanation:

Answer:

B. 64cm

Step-by-step explanation:

Answer:

A. 35

Step-by-step explanation:

The total amount of movies that the critic rates that we are given is 20. Now they want to figure us to figure it out with 100 movies. 20 times 5 is one hundred. We are supposed to look at the 3 star reviews, which is 7 movies. 7 times 5 is 35. Hope this helps!

Answer:

The answer is option A

Step-by-step explanation:

I have shared a file with the steps if you still can't understand so feel free to contact me through my email. Thanks.

The given cylindrical wind chime of dimensions 16 inches long will not fit inside the box in the shape of rectangular-prism having dimensions 10 inches x 8 inches x 6 inches.

1)shorter than

2) shorter than

3)will not fit.

What is a rectangular-prism?

Rectangular prism also called as cuboid, is a closed three dimensional solid having six faces. This prism has eight vertices or corners and 12 edges. The perimeter of this shape is the total length of 12 edges. The area of this shape is the sum of area of for or six surfaces depending on the given situation.

Given dimensions of cuboid/rectangular prism:

Length=10 inches, height= 6 inches & Width=8 inches

Dimensions of cylindrical wind chime: Length of cylinder = 16 inches

Case I: comparision of diagonal of base of the box & length of wind chime.

Diagonal of base can be found using pythagorean theorem:

Diagonal=\(\sqrt{L^{2} +W^{2} }\)

              =\(\sqrt{(10)^{2} +(8)^{2} }\)

              =\(\sqrt{100+64\\}\)

               =\(\sqrt{164}\)

               =12.8 inches ≠ 16 inches

Diagonal of rectangular prism base shorter than length of wind chime.

Case II:comparision of interior diagonal of the box & length of wind chime.

Interior diagonal of box=\(\sqrt{L^{2} +W^{2} +H^{2} }\)

                                       =\(\sqrt{(10)^{2} + (8)^{2} +(6)^{2} }\)

                                       =\(\sqrt{100+64+36}\)

                                        =\(\sqrt{200}\)

                                        =14.14 inches ≠ 16 inches

Interior Diagonal of rectangular prism is shorter than length of wind chime.

As the wind chime is greater than both the diagonals of cuboid, the chime will not fit into the prism.

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Refer to the complete question attached below.

Answer:

\(\huge\boxed{True\hookleftarrow}\)

Answer:

20 use https://www.calculator.net/triangle-calculator.html

Step-by-step explanation:

Acute Isosceles Triangle

Side a = 1

Side b = 1

Side c = 0.51764

Angle ∠A = 75° = 1.309 rad = 5/12π

Angle ∠B = 75° = 1.309 rad = 5/12π

Angle ∠C = 30° = 0.5236 rad = π/6

C=30°B=75°A=75°b=1a=1c=0.518

Area = 0.25

Perimeter p = 2.51764

Semiperimeter s = 1.25882

Height ha = 0.5  

Height hb = 0.5

Height hc = 0.96593

Median ma = 0.61966  

Median mb = 0.61966

Median mc = 0.96593

Inradius r = 0.1986  

Circumradius R = 0.51764  

Vertex coordinates: A[0, 0] B[0.51764, 0] C[0.25882, 0.96593]

Centroid: [0.25882, 0.32198]

Inscribed Circle Center: [0.25882, 0.1986]

Circumscribed Circle Center: [0.25882, 0.44829]

+ Show Calculation Steps

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Answer:

1/4 divided by 3/8

(write in simplest form)

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

1/3 divided by 5/6

(simplest form)

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

1 3/4 divided by 3

(simplest form)

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

1 3/5 divided by 5/8

(simplest form) (I think its 1)

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

10 divided by 2/5

(simplest form) (I think its 25)

Lesson 7 Dividing Fractions and Mixed Numbers

Unit 4 Operations with Fractions and Rational Numbers

Connections AcademyStep-by-step explanation:

Answer:

Amanda has 8 cousins

Step-by-step explanation:

Let C be the number of cousins Caleb has, A be the number of cousins Amanda has, and R be the number of cousins Ruby has:

\(C=2A\\R=5\\R=C-11\\\\R=C-11\\5=C-11\\16=C\\\\C=2A\\16=2A\\8=A\)

Therefore, Amanda has 8 cousins.

Answer:

Amanda has 8 cousins.

Step-by-step explanation:

Let's use algebraic variables to solve the problem.

Let's assume the number of cousins Amanda has is represented by 'A'.

Since Caleb has twice as many cousins as Amanda, the number of cousins Caleb has is '2A'.

And Ruby has 5 cousins, which is 11 less than what Caleb has, so the number of cousins Caleb has is '5 + 11 = 16'.

Equating the two expressions for the number of cousins Caleb has:

2A = 16

Now we can solve for 'A', the number of cousins Amanda has:

Divide both sides of the equation by 2:

A = 16 / 2

A = 8

Therefore, Amanda has 8 cousins.

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Answer:

adult tickets = 118

student tickets = 354

Step-by-step explanation:

a = number of adult tickets

s = number of student tickets

a + s = 472

3a = s

substitute for s

a + 3a = 472

reduce

4a = 472

divide by 4

4a/4 = 472/4

a = 118

s = 354

Answer:

x= 3√126 /3

Step-by-step explanation:

hope this helps

Answer:

A is the answer brainliest?

Step-by-step explanation:

Answer:

line is negative, so -3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

beep boop beep bap bap slat twan
answer it yo self

local maximum = 0, 8

local minimum, smaller x  value (-9 , -4)

local minimum at larger x value is (6 , 2)

You can easily get these values by tracing the points where they oc cur on the graph that we have

The local maximum x , y is gotten at the mqmaximum vertex on y

the count is from 2, it cuts the graph on y = 8 and x = 0

local maximum = 0, 8

local minimum, smaller x  value

(-9 , -4)

local minimum at larger x value is (6 , 2)

The graph can be seen to increase at (-9, 0) U (6, ∞)

The graph decreases at -∞, -9 and 0 , 6

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The cruise ship's resultant velocity is approximately 22.67 mph, and its direction is approximately 10.2 degrees south of east.

To find the resultant direction, we can use vector addition. Let's represent the southward velocity of the cruise ship as vector A and the eastward velocity of the Gulf Stream as vector B.

Given:

Magnitude of vector A (southward velocity of the cruise ship) = 22 mph

Magnitude of vector B (eastward velocity of the Gulf Stream) = 4 mph

To find the resultant velocity, we add the two vectors together. Since the vectors are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant vector:

Resultant velocity = √(A^2 + B^2) = √(22^2 + 4^2) ≈ 22.67 mph

Now, to find the direction of the resultant vector, we can use trigonometry. The angle between the resultant vector and the south direction can be calculated as:

θ = arctan(B / A) = arctan(4 / 22) ≈ 10.17 degrees

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The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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Total amount raised for the cookies is $75, Option C is correct.

Two or more expressions with an Equal sign is called as Equation.

Given that Cupcakes were sold for two dollars each.

Cookies were sold for $0.50 each.

The members sold a total of 450 items.

Let x be the number of cupcakes and y be number of cookies

x+y=450

Of the items sold 2/3 were cupcakes and the remaining items were cookies.

x = 2/3×450 = 300

Y= 450 - 300 = 150

The total amount raised from the cupcakes is $2× 300 = $600.

The total amount raised from the cookies is $0.50 × 150 = $75.

Hence, total amount raised for the cookies is $75, Option C is correct.

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Answer:

Prepaid expenses are payments made in advance for goods or services that will be received or used in the future. These expenses are considered assets on a company's balance sheet because they provide future economic benefits. Examples of prepaid expenses include rent payments made in advance, insurance premiums, and prepaid service contracts. They are recorded as an asset on the company's balance sheet until the expense is incurred, at which point it is recognized as an expense on the income statement.

Step-by-step explanation:

9514 1404 393

Answer:

  z = 62°

Step-by-step explanation:

You know that ...

  x = (1/2)(y -z)

So ...

  2x = y - z

  z = y - 2x = 160 -2(49)

  z = 62 . . . . degrees

Answer:

13

Step-by-step explanation:

a2+b2=c2

12^2+5^2=c^2

144+25=169

square root of 169

13

Create a can with a 2 cm radius and a 9 cm height using the interactive, this can has a volume of 113.1 cm3.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Since the forms of various three-dimensional objects vary, so do their volumes.

According to our question-

volume of a can is = πr²h + 2πr³

V = Π (4)2*12

113.1 cm3.

Hence, Create a can with a 2 cm radius and a 9 cm height using the interactive, this can has a volume of 113.1 cm3.

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To make a cake :-

Quantity of flour needed = 500 g

Quantity of butter needed = 450 g

Quantity of sugar needed = 470 g

Quantity of mixed fruit needed = 1.8 kg = 1000 g + 800 g

Quantity of eggs needed = 70 × 4 = 280 g

It's weight after adding all the ingredients =

=500 + 450 + 470 + 1000 + 800 + 280

= 3500 g

Mass that got lost while baking the cake :

\( = \frac{12}{100} \: of \: 3500\)

\( = \frac{12}{100} \times 3500\)

\( =\frac{(12 \times 3500)}{100} \)

\( =\frac{42000}{100} \: g\)

\( = 420 \: g\)

Final mass = Initial mass - mass that got lost

\( = 3500 - 420 \: g\)

\( = 3080 \: g\)

∴ The final mass of the cake is 3080 g .

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer: 2v-5/v-7 or 2V-5/7

Step-by-step explanation: