Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Answer:

he made an error, the probability that his homeruns traveled at least 380 feet is 65.54%

Step-by-step explanation:

let´s see the Robinson's calculation:

using the formula for normal distribution:

Z = (x-μ)(σ/[tex]\sqrt{n}[/tex]) [1]

where:

x is raw measurement

μ is the mean

σ is the standar deviation

n is the size of sample

in this case x = 380, μ = 394, σ = 35, n = 1.

then using the equation [1] he calculated the Z score:

[tex]Z = \frac{380-394}{\frac{35}{\sqrt{1}}}\\\\Z = -\frac{14}{35}\\\\Z = -0.4\\\\[/tex]

and it's correct but his answer is wrong because he confuse the term at least.

at least means that the probability be greater than 380 feet, not less than 380 feet.

so he looked the Z score in a table of normal distribution (this table has been attached) and effectively this value is 0.3446. but as I told you this probability is for x < 380.

therefore, the probability that his homeruns traveled at least 380 feet is:

[tex]P(x > 380) = 1 - P(x < 380)\\\\P(x > 380) = 1 - 0.3446\\\\P(x > 380) = 0.6554 \ or \ 65.54 \%[/tex]

please see the table attached.

To rank the company sales by smallest to largest percent of increase, calculate the percent of increase for each company, which in this case is 0% for all companies.

To rank the company sales by smallest to largest percent of increase, we need to calculate the percent of increase for each company. The percent of increase can be found by subtracting the initial value from the final value, dividing that number by the initial value, and then multiplying by 100.

Since all the percent of increase values are 0%, the company sales can be ranked in any order, as there is no change in sales for any of the companies.

The solution is x = (7 - r) / a.

To solve the equation ax + r = 7 for x, follow these steps:

Subtract r from both sides of the equation:

ax + r - r = 7 - r

This simplifies to:

ax = 7 - r

Divide both sides by a:

x = (7 - r) / a

Substitute the value of x back into the original equation to ensure it is correct.

Answer:

133  degrees

Step-by-step explanation:

Given is a picture of a kite DCFE inscribed in circle A

The vertices of the kite D, C, E and F lie on the circle.

A is the centre.

Arc DEF = 266 degrees

This means the subtended angle of arc DEF at the centre = Angle DAF = 266

By theorem on circles, we have central angle of any arc is twice the angle subtended by the arc on the remaining part of the circumference

Hence

Angle DEF = 1/2 angle DAF

i.e. DEF =[tex]\frac{266}{2} =133[/tex]

133 degrees

The measure of the angle will be;

⇒ 60°

The sum of two or more angle is 180 degree then the angle is called the Supplementary angle.

Given that;

The statement is,

''The measure of an angle is 60° less than nineteen times the measure of its supplement.''

Let measure of an angle = x

So, The measure of its supplement = 180° - x

Hence, We can formulate;

⇒ x = (180 - x) - 60°

Solve for x as;

⇒ x = 180 - x - 60

⇒ x + x = 120

⇒ 2x = 120

⇒ x = 120/2

⇒ x = 60°

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Answer:

Area is 2√3 ft².

Step-by-step explanation:

Given,

A right triangle having sides,

a = 2√3 ft,

c = 4 ft,

Where, c is the hypotenuse of the triangle,

If b is the other leg of the triangle,

By the pythagorean theorem,

[tex]c^2=a^2+b^2[/tex]

[tex]4^2=(2\sqrt{3})^2+b^2[/tex]

[tex]16=12+b^2[/tex]

[tex]4=b^2[/tex]

[tex]\implies b = 2[/tex]

Hence, the area of the given triangle is,

[tex]A=\frac{1}{2}\times a\times b[/tex]

[tex]=\frac{1}{2}\times 2\sqrt{3}\times 2[/tex]

[tex]=\frac{4\sqrt{3}}{2}[/tex]

[tex]=2\sqrt{3}\text{ square ft}[/tex]

Answer:

Diameter of the circle K = 20 units

Step-by-step explanation:

Given that : EF = HG

Also, HG = 16 units

⇒ EF = 16 units

Now, any line drawn perpendicular to the chord always bisects the chord

⇒ KI will bisect the chord EF

⇒ EI = 8 units

Now, in ΔEIK using Pythagoras theorem we have :

⇒ EK² = 8² + 6²

⇒ EK² = 100

⇒ EK = 10 units

So, Radius of the circle K = 10 units

Now, Diameter of the circle K = 2 × 10

                                                  = 20 units

Answer:

True

Step-by-step explanation:

By the distance formula,

The distance between two points [tex](a_1, b_1)[/tex] and [tex](a_2, b_2)[/tex] is,

[tex]d=\sqrt{(a_2-a_1)^2+(b_2-b_1)^2}[/tex]

Here, [tex]a_1=3[/tex], [tex]b_1=7[/tex], [tex]a_2=x_1[/tex] and [tex]b_2=y_1[/tex]

Thus, the distance would be,

[tex]d=\sqrt{(x_1-3)^2+(y_1-7)^2}[/tex]

= the square root of [tex](x_1 - 3)^2 + (y_1 - 7)^2[/tex]

Answer:

0.098415

Step-by-step explanation:

The way the question is worded is odd and you should probably actually include “don’t grow into a healthy plant” or something. You can use the binomial distribution. Suppose ∼Bin(6,0.1)  so the probability that k trees don’t grow into a healthy plant is

Pr( = ) = (6 / ) 0.16^ 0.9^6−

Then the probability that two don’t grow into healthy plants is

Pr( = 2) = (6/2) 0.1^2 0.9^4

this is equal to 0.098415

To calculate the probability of exactly 4 out of 7 seeds failing to grow, use the binomial probability formula with n = 7, p = 0.10, and k = 4. The calculation involves combinations and exponentiation.

The question is asking for the probability of exactly 4 seeds out of 7 failing to grow. Given that each seed has a 90% chance of growing into a healthy plant, which means each seed has a 10% (1 - 0.90) chance of not growing. To solve this, we can use the binomial probability formula: P(X = k) = C(n, k) * (pk) * ((1 - p)n - k), where n is the number of trials, p is the probability of success, and k is the exact number of successes. In this case, n = 7, p = 0.10 and k = 4. So, we get:

P(X = 4) = C(7, 4) * (0.104) * (0.907 - 4)

The calculation of this probability requires the use of combinations and exponentiation, providing the specific likelihood of having exactly 4 seeds out of 7 not growing into a healthy plant.

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Answer:

the answer is TRUE.

Step-by-step explanation:

we can coclude that the three-dimensional geometry is more or less the extension of a two-dimensional geometry as many of the same principles imply.

two points determine a straight line no matter whether the points are two-dimensional or three-dimensional.

hence the following statements holds true that the rules of two dimensional geometry can be applied to three dimensional solids.

Answer:

The answer is false.

Step-by-step explanation:

Answer:

14 units

Step-by-step explanation:

both points have the same y-coordinate, so therefore, the line is horizontal from x = -9 and x = 5 9        (plus I did the 5.05 math quiz segment two 6th grade)

Answer:

answer is A

Step-by-step explanation:

Answer:

Arc length = 5.23 cm  

Step-by-step explanation:

Given : Radius = 5 cm

             Angle = [tex]\theta=\frac{\pi}{3}[/tex]

To find : Arc length(A)

Solution: The formula of arc length is

                 A = radius × angle(in radian)

                [tex]A= 5\times\frac{\pi}{3}[/tex]

                          ⇒[tex]\frac{5\pi}{3}[/tex]

                      A  ⇒15.70/3 = 5.23 cm

To solve the problem, denote the number of brown shoes as x, and the black shoes as 2x, as the store has twice as many black shoes. The total number of shoes is x + 2x = 66. Solving this gives us x (brown shoes) as 22.

The subject is concerning a mathematical problem involving ratios. In the given problem, it is stated that the shoe store has twice as many black shoes as brown shoes, and the total number of shoes is 66. Here's a step-by-step process to solve it:

Therefore, there are 22 brown shoes in the store.

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The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign. So in the expression ∑4i = 0(5)(1/3)i will be the same as:

∑4i = 0(5)(1/3)i

= (1/3)⁰ + (1/3)¹ + (1/3)² + (1/3)³ + (1/3)⁴ + (1/3)⁵

= 364/243

Answer:

[tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]

Step-by-step explanation:

we have to write the sum using summation notation of the following series:

2-12+72-432+...

which could also be written as:

2+(-12)+72+(-432)+...

We observe that first term=2

second term=2×-6

Third term=2×-6×-6

Fourth term=2×-6×-6×-6

nth term=[tex]2\times (-6)^{n-1}[/tex]

Hence, the series sum=   [tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]