21. a) The average height of sunflowers in a field is 64 in. with a standard deviation of 3.5 in. On a
piece of paper, draw a normal curve for the distribution, including the values on the horizontal
axis at one, two, and three standard deviations from the mean. Describe your drawing in as
much detail as possible, and explain how you came up with each of your labels.
b) If there are 3,000 plants in the field, approximately how many will be taller than 71 in.?
Explain how you got your answer.

Answer:

Step-by-step explanation:

try iproxy from chrome

Answer:droneblocks

Step-by-step explanation:

Answer: 9,585

Step-by-step explanation:

Answer:

$9,585.00

6.5x9000 over 100

Therefore ,  95% confidence interval for the difference in mean mcls levels is 95% C.I = {4.0978 , 3.1423}.

In frequentist statistics, a confidence interval is a range of estimates for an unobserved parameter. The most frequent confidence level is 95%, while other levels, such 90% or 99%, are occasionally used for computing confidence intervals.

Here,

Given:

c= 1.95 M.E = 0.5 ,n=?,C.V=1.96

Using formula,

=> M.E = C.V + [tex]\frac{c}{\sqrt{n} }[/tex]

=> 0.5 = 1.96 + 1.95/[tex]\sqrt{n}[/tex]

=> 0.5 = 3.822/[tex]\sqrt{n}[/tex]  

=> [tex]\sqrt{n}[/tex]  = 3.822/0.5

=> [tex]\sqrt{n}[/tex]  = 7.644

=> n =58.43

=> n ≈ 58

So, n = 64 , [tex]x^{'}[/tex]=3.62,α=1.95

=> u = [tex]x^{'}[/tex] ± C.V * α/[tex]\sqrt{n}[/tex]

=> u = 3.62 ±  1.96 * 1.95/√64

=>  u = 3.62 ± 0.47775

=>  u = 3.62+ 0.47775 = 4.0978

 or u=3.62-0.47775 = 3.1423

95% C.I = {4.0978 , 3.1423}

Therefore ,  95% confidence interval for the difference in mean mcls levels is 95% C.I = {4.0978 , 3.1423}.

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The two points, along with the [x] - intercept are joined are joined.

        [tex]y =log_{e} x[/tex]

We have the following function -

y = log (1/8)x

We can write -

y = log (1/8)x

y = log(x/8)

y = log(x) - log(8)

Refer to the graph attached. The two points, along with the [x] - intercept are joined.

Therefore, the two points, along with the [x] - intercept are joined are joined.

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Article IV Clause 2 of the US Constitution is referred to as the Supremacy Clause. It proves that all other laws and international treaties are subordinate to US federal law.

The United States Constitution's Supremacy Clause declares that the Constitution, federal laws adopted in accordance with it, and treaties signed in accordance with its authority are the "supreme Law of the Land" and supersede any conflicting state laws. According to its provisions, state constitutions are subservient to the supreme law and state courts are obligated by it.

Moreover, federal statutes and treaties must be within the bounds of the Constitution, i.e., they must be in accordance with the enumerated powers of the federal government and must not violate other constitutional restraints on federal power that specify that the federal government only has the authority granted to it by the Constitution.

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By using the fact that the sum of the internal angles must be equal to 360°, we will see that x = 18

Suppose we have a figure of N sides, the sum of the internal angles of that figure will be equal to:

S = (N - 2)*180°

In this case, we have 4 sides, then:

S = (4 - 2)*180° = 360°

Also notice that the figure is symmetrical around the two vertical vertices, then the angle at the left side (the only one that we don't know) also measures 101°, like the one in the right side.

Then we can write the linear equation:

100° + 101° + 101° + (4 + 3x)° = 360°

Now we can try to solve this for x.

(100° + 101° + 101°) + (4 + 3x)° = 360°

302° + (4 + 3x)° = 360°

(4 + 3x)° = 360° - 302°

4 + 3x = 58

3x = 58 - 4 = 54

x = 54/3

x = 18

That is the value of x in the kite.

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No , Dilation doesn't increase the measure of angles

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

The new figure obtained after dilation is called the image and the original image is called the pre-image

We dilate any figure by scale factor.

Dilated figures will always be similar figures.

Similar figures have the same shape, angles with the same measures, and the lengths of corresponding sides have equal ratios. The ratio is the same as the scale factor of the dilation.

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If winners are chosen randomly from the 300 people who bought this lottery, the expected profit of a random person is $0.766..

The expected profit under a probability demand distribution is calculated by multiplying the profit amount by the probability of achieving that profit.

It is denoted as E(X) . We have given that,

A $1 lottery ticket has a number of prizes.

Probability of winning first prize , $10 = p₁ = 3/300 = 1/100

probability of winning a 2nd prize, $50

= p₂= 2/300= 1/150

probability of winning a 3rd prize, $100

= p₃ = 1/300 = 1/300

E = expectation value = ∑ Vᵢpᵢ where Vᵢ = value of prize, pᵢ = probability of winning prize,

E = $10 ×1/100 + $50×1/150 + $100×1/300

=> E = $10/100 + $50/150 + $100/300

Taking LCM as 300 on right hand side,

=> E =( $30+ $100+$100)/300

=> E = $(230/300) = $0.766

So, expected winnings for a person buying one ticket is $0.766..

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Answer:

  P(x) = (x +1)(x -2)(x -4)

  see the 2nd attachment for a graph

Step-by-step explanation:

You want the factors of P(x) = x³ - 5x² + 2x + 8, given that (x+1) is one of the factors. You also want a graph of it.

The quotient from dividing P(x) by the given factor will be a quadratic we can factor to find the other two binomial factors. The first attachment shows that quotient is (x² -6x +8).

To factor this quadratic, we look for factors of 8 that have a sum of -6. They are -2 and -4. Hence the remaining binomial factors are (x -2)(x -4).

The desired product is ...

  P(x) = (x +1)(x -2)(x -4)

The second attachment shows a graph of P(x). The y-intercept is the constant in the equation, 8. The x-intercepts are the values of x that make the factors zero.

The options that are done by translational research or science are given as follows:

c. Take laboratory findings for development for use with patients at the bedside

d. Use clinical research findings to ask new questions for research in the laboratory

e. Discover practical applications for scientific theories and laws.

Translational research is a field of science that studies strategies to convert research results or data into strategies that actually benefit humans.

Hence statements c, d and e are correct, as they all involve strategies that benefit humans.

Statements a and b are incorrect, as:

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With a water flow rate of 2 gallons per minute (gpm), the volume of water after 4 minutes will be 8 gallons of water.

Gallons per minute (gpm) is a measurement of the flow rate of the liquid. Gpm measures how much volume of water is flowing out (in imperial measurement of gallon) of the pipe, shower head, taps, pumps, etc in a given time.

Given that a drum is being filled with a flow rate of 2 gpm and the time given is 4 minutes, we need to figure out the volume of water using a water flow rate gallons per minute (gpm) we will then calculate with the following formula:

Volume = flow rate × time

Volume = 2×4

Volume = 8 gallons

Therefore the drum will be filled with 8 gallons of water after 4 minutes of filling.

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Answer:-2/3

Step-by-step explanation: the rise is 2 and the run is 3

The weight of a randomly selected pack of gum that has a z-score of 3.11 is 54.6 grams

Z-score aids in determining how much the data deviates from the mean. It represents the frequency with which the data is above or below the mean.

Z-scores are calculated using the formula z = (x-)/, where x represents the raw score, the population mean, and the population standard deviation. The z-score is just the raw scoreless population mean, divided by the population standard deviation, as the calculation demonstrates.

According to the formula,

Z = ( X - μ ) / σ

Z being the Z-score,

The data point is X,

The standard variable is, and the mean is.

The z-score of the weight of a randomly chosen pack of gum is 3.11. As a result, this pack of gum weighs 3.11 standard deviations more than the average.

Z = ( X - μ ) / σ

3.11 X 2.4 = X - 47.1

X = 54.6 g

Therefore, choice B is the right one.

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The coefficient of the variable term of the equation A = 4x - 20 is 4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given as

A = 4x - 20

On simplifying the equation , we get

The value of A = 4x - 20

Taking 4 as the common factor of the equation , we get

The value of A = 4 ( x - 5 )

Therefore , the coefficient of the equation A is 4

Hence , The coefficient of the variable term of the equation A = 4x - 20 is 4

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Answer:

X= 121

Step-by-step explanation:

A five sided polygon (Pentagon)= (2n-4) x 90degrees

=(2(5) -4) x90 = (6 x 90)=540 degrees

Hence, x+ 92+135+105 + 87= 540 degrees

x+ 419=540

x= 540-419

x=121

Answer:

200

hope you like it

The slopes of the secant lines do not appear to be approaching a limit.

For each value of x, calculate y and then use the slope formula to find the slope of P Q for the given limit.

x = 2 → y = 0 : Q(2, 0) ⇒ m =0 − 0 / 2 − 1 = 0

x = 1.5 → y ≈ 0.866 : Q(1.5, 0.866) ⇒ m = 0.866 − 0/ 1.5 − 1 ≈ 1.73

x = 1.4 → y ≈ −0.434 : Q(1.4, −0.434) ⇒ m =−0.434 − 0 / 1.4 − 1 = −1.08

x = 1.3 → y ≈ −0.823 : Q(1.3, −0.823) ⇒ m = −0.823 − 0/1.3 − 1 = −2.74

x = 1.2 → y ≈ 0.866 : Q(1.2, 0.866) ⇒ m = 0.866 − 0 / 1.2 − 1 = 4.33

x = 1.1 → y ≈ −0.282 : Q(1.1, −0.282) ⇒ m = −0.282 − 0/1.1 − 1 = −2.82

x = 0.9 → y ≈ −0.342 : Q(0.9, −0.342) ⇒ m = −0.342 − 0/0.9 − 1 = 3.42

x = 0.8 → y = 1 : Q(0.8, 1) ⇒ m = 1 − 0/ 0.8 − 1 = −5

x = 0.7 → y ≈ 0.782 : Q(0.7, 0.782) ⇒ m = 0.782 − 0/0.7 − 1 = −2.61

x = 0.6 → y ≈ 0.866 : Q(0.6, 0.866) ⇒ m = 0.866 − 0 / 0.6 − 1 = −2.17

x = 0.5 → y = 0 : Q(0.5, 0) ⇒ m = 0 − 0 / 0.5 − 1 = 0

Hence, The slopes of the secant lines do not appear to be approaching a limit.

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Answer:

c=8b

Step-by-step explanation:

The number of crayons is equal to 8 times the number of boxes.

The value of angle X is 69.10°

The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Given is a triangle XYZ, with sides 17ft, 8ft and 16ft

cosX = (z²+y²-x²)/2yz

cosX = (17²+8²-16²)/2x17x8

cosX = 97/272

X = cos⁻¹(97/272)

X = 69.10°

Hence, The value of angle X is 69.10°

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Let us discuss the 4 ways to find the slope:

1. The first case is where, you have two points (x1,y1)  and (x2,y2)

These points often may be intercepts of the x and/or y axes.

The equation of the slope is given by-

m= (y2−y1) / (x2−x1).

2. The second condition is where you are given the linear equation that is either in the form or can be manipulated into the form y=mx+b.

Here, the slope is m(the coefficient of x).

3. The third case is when you have a line that is a tangent to another function, you may have (or be able to determine) the slope of the tangent as the derivative of the function. Normally in such cases, the derivative is a function expressed in terms of x and all you need to do is substitute the value of x into this function for the required equation.

4. The fourth case is when you are given a graph as follows-

Here , the slope m = Δy/Δx

Also, note that tan θ = Δy/Δx

Hence, this tan θ is considered as the slope of the line.

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Answer:

[tex]\textsf{a)} \quad y=-4x+19[/tex]

[tex]\textsf{b)} \quad y=\dfrac{1}{4}x+2[/tex]

Step-by-step explanation:

From inspection of the graph, two points on the line are:

Substitute these points in the slope formula to find the slope of the line:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-6}{2-1}=\dfrac{-4}{1}=-4[/tex]

Lines that are parallel have the same slope.

Therefore, a line parallel to the given line has a slope of -4.

To write an equation of the parallel line, substitute the found slope and point (4, 3) into the point-slope formula and rearrange:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=-4(x-4)[/tex]

[tex]\implies y-3=-4x+16[/tex]

[tex]\implies y=-4x+19[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.

Therefore, a line perpendicular to the given line has a slope of ¹/₄.

To write an equation of the parallel line, substitute the found slope and point (4, 3) into the point-slope formula and rearrange:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=\dfrac{1}{4}(x-4)[/tex]

[tex]\implies y-3=\dfrac{1}{4}x-1[/tex]

[tex]\implies y=\dfrac{1}{4}x+2[/tex]

Following are all of the subparts' solutions using the probability formula:

Red ball (A) P: 5/8

(B) P: 7/8 (NOT Yellow)

(C) P(yellow or white): 3/8

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

Probability formula: P(E) = favorable events/Total events

(A) P(red ball):

P(E) = favorable events/Total events

P(E) = 5/8

(B) P(NOT Yellow)

P(E) = favorable events/Total events

P(E) = 7/8

(C) P(white or yellow)

P(E) = favorable events/Total events

P(E) = 3/8

Therefore, the answers to all the subparts using the probability formula are shown:

(A) P(red ball): 5/8

(B) P(NOT Yellow): 7/8

(C) P(white or yellow): 3/8

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10 choose 3 with replacement gives you a mere 220 combinations. A “combination” lock uses permutations, so there would be 1000 possibilities.

What is Combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Mathematically, a combination is a selection of things without regard for order.

The formula for “combination with replacement” is:

   [tex]C^{R} (n,r)=\frac{(n+r-1)!}{r! (n-r)!}[/tex]

10 choose 3 with replacement gives you a mere 220 combinations.

The toss of three identical 10-sided dice would have 220 possible outcomes.

Hence, A “combination” lock uses permutations, so there would be 1000 possibilities.

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}[/tex]  of  [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{2}[/tex]  ×  [tex]\frac{1}{3}[/tex]  =  [tex]\frac{1}{6}[/tex]

Hope this helps! :)

Answer:

= 1/6

Step-by-step explanation:

1/2 0f 1/3

is:

(1/2) (1/3) = (1*1) / (2*3)

= 1/6

Using SAS, it can be shown that the two triangles formed are congruent. Then using SSS the length of the road from the intersection to the first turn can be found to be 200ft. Thus the total length of the tour is 1700ft.

What is congruent triangles?

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

The SAS formula states that if two sides and one angle of two triangle are the same then the triangles are congruent to each other.

Two lines AD, EC intersects each other at the point B . Therefore, ∠ABC = ∠DBE  .

The length of the sides AC = DE, BC = BE .

The triangles ΔABC, ΔBDE  are congruent to each other by the SAS formula.

The SSS formula states that two triangles are congurent to each other if the ratio of corresponding sides of two triangles are the same and vice-versa.

Use the SSS formula in the triangles ΔABC, ΔBDE and simplify to calculate the length of BD.

BD/200 = 300/300

BD/200 = 1

BD = 200  

Therefore, using SSS the length of the road from the intersection to the first turn can be found to be 200ft.

Add the lengths of AB, BD, DE, EB, BC, CA to calculate the total length of the tour.

200 + 200 + 300 + 350 + 350 + 300 = 1700

The total length of the tour is 1700ft.

Hence, using SAS, it can be shown that the two triangles formed are congruent. Then using SSS the length of the road from the intersection to the first turn can be found to be 200ft. Thus the total length of the tour is 1700ft.

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The measure of angle 2 is 61 degrees.

The measure of angle 4 is 119 degrees.

What is triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

In the given triangle the measure of two triangles is given which is 61° and 58°.

We have to solve for the measure of angle 2.

Since, the sum of three angles of triangle's is 180 degrees.

⇒ 61° + 58° + ∠2 = 180°

          119 ° + ∠2 = 180°

                     ∠2 = 180° - 119°

                     ∠2 = 61°

Hence, the measure of angle 2 is 61 degrees.

Now to find measure of angle 4.

Here ∠2 and ∠4 are planer angles and their addition is 180°.

⇒ ∠2 + ∠4 = 180°

61° + ∠4 = 180°

∠4 = 180° - 61°

∠4 = 119°

Hence, the measure of angle 4 is 119°.

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The given ray is a bisector of a given angle.

So, the option (b) is the correct answer.

What is bisector?

Bisection in geometry is the division of an object into two equal or congruent parts, typically by a line, which is then referred to as a bisector. The segment bisector and the angle bisector are the two types of bisectors that are most frequently used.

An angle is divided into two equal parts by a ray known as an angle bisector or angle bisector. For instance, if ray AX divides a 60 degree angle into two equal parts, each measurement will be 30 degrees.

Consider, the given angle.

The given angle is bisects by a ray equally.

Hence, the given ray is a bisector of a given angle.

So, the option (b) is the correct answer.

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Answer:

6+d-1

Step-by-step explanation:

Answer:

2d+4

Step-by-step explanation:

2(3+d-1)

2(3)+2(d)+2(-1)

6+2d-2

2d+4

hopes this helps

The inequalities are among the constraints for this situation include the following;

x + y ≥ 50

x ≥ 5y

y ≤ 30

In order to write a system of inequalities to describe this situation, we would assign variables to the number of key chains and number of thumb drives respectively, and then translate the word problem into algebraic equation as follows:

Based on the information provided, we can logically deduce that there are three (3) inequalities with respect to the constraints for this situation.

Since Sarah needs to make at least (greater than or equal to) 60 gift bags for an event with each gift bag containing at least 1 thumb drive or 1 key chain, we have;

x + y ≥ 50

By using at least 5 times as many key chains as thumb drives, we have;

x ≥ 5y

Lastly, Sarah has 30 thumb drives and 200 key chains;

y ≤ 30

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Answer:

The answer is none its that easy i dont need to explain it

Step-by-step explanation:

your words.

Answer: 2x+3=15 and 81/x-3=6

Step-by-step explanation: