what is the height of the flag pole?

The probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3 is 0.7295

Binomial Distribution

The binomial distribution is the sum of a series of multiple independent and identically distributed Bernoulli trials. In a Bernoulli trial, the experiment is said to be random and can only have two possible outcomes- success or failure.

In a binomial distribution the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.

Mean rate of lost time accident = 0.3 per day

probability that the number of lost-time accidents occurring over a period of 7 days will be no more than 3.

n = 7

Using binomial distribution formula :

P(x ≤3)

Probability of success (p) = 0.3

1 - p = 1- 0.3 = 0.7

nCx * p^x * (1 - p)^(n-x)

Using the binomial probability distribution calculator to save computation time :

P(x ≤3) = P(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)

P(x ≤3) = 0.0403 + 0.1556 + 0.2668 + 0.2668

P(x ≤3) = 0.7295

0.7295

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Answer:

60

Step-by-step explanation:

both triangles are 30 60 90, angle G is made up of 2 30 degree angles

30 plus 30 is 60

The number of seconds will it take the ball to hit the ground will be 2.078 seconds.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.

As per the given,

h(t)=-16t² + 14t + 40

The time when the ball hit the ground h(t) = 0

-16t² + 14t + 40 = 0

-8t² + 7t + 20 = 0

8t² - 7t - 20 = 0

t = (7 ± 26.25)16

t = 2.078 seconds

Since time can never be negative thus, 2.078 seconds will be correct.

Hence "The number of seconds will it take the ball to hit the ground will be 2.078 seconds".

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The perpendicular bisector of the line is option c)

The bisector of the angle YXZ is option B)

The perpendicular from point Z to the line XY is option G)

What is perpendicular bisector?

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

We are asked to find the perpendicular bisector on the line XY

Now this means a segment dividing segment XY in two equal parts and intersecting XY at right angle

Hence This description match with option C)

Hence The perpendicular bisector of the line is option c)

Similarly,

The bisector of Angle YXZ will be the line which divides the angle in two equal parts

This description matches with option B)

Hence the correct option is option B)

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Answer:

128 4/7

Step-by-step explanation:

100%-30%=70%

90=.7X

900=7X

128 4/7=X

Answer:

5 cms

Step-by-step explanation:

This is assuming that it is equilateral and that n is the length of one side

In this experimental design, the y variable is the testosterone levels.

A variable is defined as any symbol or letter that is used to express an unknown quantity. There are two types of variables: the dependent variable (y variable) and the independent variable ( x variable).

An independent variable (x variable) is the variable which causes the change in another variable.

A dependent variable (y variable) is the result or effect of that change in the dependent variable.

If we are interested in what happens to testosterone levels as the men age in adult men ages 18 years and older, then the x variable is the age and the y variable is the testosterone levels.

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There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

H0:p1=0.5,p2=0.3,p3=0.2

Ha:At least one proportion is different from the stated proportions.

Null hypothesis indicate that proportions are same as stated.

Product observed(fo) pi Expected(fe) (fo-fe)^2/fe

Whole 74 0.5 154.50 41.943

Universal 71 0.3 92.70 5.080

Annuities 164 0.2 61.80 169.010

Total 309 1 309 216.033

Expected value for the number of customers who prefer Whole Life=309*0.5=154.50

Expected value for the number of customers who prefer Universal Life=309*0.3=92.70

Test statistic:

Chi square=216.033

df=3-1=2

critical Chi square value=CHIINV(0.01,2)=9.210

Reject the null hypothesis

Therefore, There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

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The probability which motor cycle owns for sample is 0.0001

What is Sample ?

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

Given,

p= 14% or 0.14

p bar = 20% or 0.20

n=500

The mean of the sample distribution of p bar is equal to the population proportion p

µp = p =0.14

The standard deviation of sample distribution of p bar is

σp = [tex]\sqrt{p(1-p}/n[/tex]

= [tex]\sqrt{0.14(1-0.14}/500[/tex]

= 0.0155177

the z score is the value decreased by the mean, divided by the standard deviation:

z =x- µ/σ

= 0.20-.014/0.0155177

=3.87

so the corresponding probability will be

P(p>20%) = P(z>3.87) = P(Z<-3.87) = 0.0001

The likelihood that a motorcycle is present in the sample is 0.0001.

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Answer:

[tex]120^{\circ}[/tex]

Step-by-step explanation:

Using the exterior angle theorem, [tex]x=50^{\circ}+70^{\circ}=120^{\circ}[/tex].

Answer:

Step-by-step explanation:

we know the inside total angles for triangle is 180 degrees.

We are given the two internal angles as 70 and 50 degrees.

So the equation can be written as

70+50+y = 180

y= 60

Also, we know that straight line is 180 degrees.  Now we can write the second equation as follow:

60+x = 180

x = 120 degrees

A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Next, we would determine the translation rule as follows;

ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)

ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)

ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)

Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).

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Step-by-step explanation:

the surface area is the combination of

the base (square) area

the 4 side (triangle) areas.

the base area is : 10×10 = 100 in²

the area of a triangle is

baseline × height / 2

we know the baseline of each of the 4 triangles (10 in) and we know the height (14 in).

one triangle area is

10×14/2 = 70 in²

we have 4 of these triangles (each side of the pyramid) :

4×70 = 280 in²

the total surface area of the pyramid is

100 + 280 = 380 in²

Order of Operations: BPEMDAS

Functions

Compounded Interest Rate Formula:
[tex]\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^t[/tex]

Let's compile what we know (what we are given).

An investment of $500 means that our principle amount P equals 500.

2.8% nominal yearly interest means that our rate r equals 0.028.

Compounded quarterly means that our compounded rate n equals 4.

So, we have:

[tex]\displaystyle\begin{aligned}P & = 500 \\r & = 0.028 \\n & = 4 \\\end{aligned}[/tex]

In order to find an equation that models the final amount A in terms of t years, we can simply substitute in our known variables:

∴ our equation that models the amount A the investment is worth t years after the principle has been invested is:

[tex]\displaystyle \boxed{ A = 500(1.007)^t }[/tex]

___

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___

Topic: Algebra I

Unit: Interest Rate Formulas

A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.96}{2} =0.02[/tex]

Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex] .

So it is z with a p value of 1-0.02 = 0.98, so z= 2.055

Now, find the margin M as such

[tex]M = Z*\frac{\sigma }{\sqrt{n} }[/tex]

In which [tex]\sigma[/tex]  is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

[tex]\sigma = 40 , M = 10\\\\M = Z*\frac{\sigma}{\sqrt{n} } \\\\10 = 2.055*\frac{40}{\sqrt{n} } \\\\\sqrt{n} = 8.22\\\\n= 67.6[/tex]

Hence , a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

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The flux = 0

According to the divergence theorem, the volume integral of the divergence of a vector point function "F" taken over the volume "V" encompassed by the surface "S" is equal to the surface integral of the normal component of F taken over the closed surface "S." As a result, the divergence theorem is symbolically represented as:∬ v ∫ ▽ F → .

The sphere is presumably closed, so we can use the divergence theorem.

▽ F  =d(xy)/dx + d(yz)/dy + d(zx)/dz

▽ F =x + y + z

Now convert to spherical coordinates:

x=ρsinφcosθ,

y=ρsinφsinθ,

z=ρcosφ

The flux is then given by the volume integral for the radius 6

[tex]\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} = 36 }[/tex]   f.ds = [tex]\int\limits\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} < =36 }[/tex] (x+y+z) dv

Thus the flux = 0

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Answer: A+B+C=π⇒A+B=π−C

Step-by-step explanation: I think not sure hope this helps :)

Answer:

I'm sure the answer is 125

Step-by-step explanation:

Hope it helps ; )

Answer:

3r < = 4r - 6

3r - 4r < = -6

-r < = -6

r > = 6........it is 6 and 7

Step-by-step explanation:

Answer:

your answer would be 6, and 7.

Step-by-step explanation:

The value of x for the given linear equation; 3 ( −4x + 5 ) = 12 is; 1 / 4.

It follows from the task content that the value of x in the given linear equation; 3 ( −4x + 5 ) = 12 is to to be determined.

Since the given expression is;

3 ( −4x + 5 ) = 12

By the distributive property; we have;

-12x + 15 = 12

-12x = 12 - 15

-12x = -3

x = -3 / -12

x = 1/4.

Therefore, the required value of x in the given linear equation is; 1 / 4.

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Answer:

See below

Step-by-step explanation:

This is the slope formula.  Do they give you two points?  If they give you two points like (2,3 ) and (5,7)  You subtract the y's over the subtraction of the x's

An ordered pair is in the form (x,y)  

So in the example that I give the y's are 7 and 3 and the x's are 5 and 2

[tex]\frac{7-3}{5-2}[/tex] = [tex]\frac{4}{3}[/tex]

I am thinking that they gave you two points and they want you to find the slope.

Answer:

Step-by-step explanation:

Ok so this is how to find slope of a line that passes through 2 points.

(x1,y1) and (x2,y2)

and to find the slope of the line (m) you have to do (y2-y1)/(x2-x1)

you just have to plug in the points

No, this correspondence is not a function because a function is a relation between two sets of values in which each value of the first set corresponds to exactly one value in the second set.

In this case, there is no information given about the correspondence, so it is impossible to determine if it is a function or not.

A function is a special type of relation in which each value of the first set, sometimes referred to as the domain, is associated with exactly one value in the second set, called the range. A function must satisfy the property of functional uniqueness, meaning that each element of the domain is associated with exactly one element in the range. If a correspondence fails to meet this requirement, then it is not a function. Without knowing any more information about the correspondence, it is impossible to determine if it is a function or not.

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Answer:

10

Step-by-step explanation:

0 in the 0nes place but less than 12. more than 6. so it has to be 10.

Answer: 6 hours

Step-by-step explanation:

The question asks how long until they meet.

First, you add 1.5 miles per hour and 2 miles per hour to get 3.5 miles per hour.

Then you divide 21/by 3.5 which gets you how many hours it takes for them to meet.

Which means 21/3.5 is 6 hours.

In the distribution system, the water  main sizes most commonly in use up to 3.65m to  tiny 12.7mm.

Water pipes come in a variety of sizes, from enormous mains with a diameter of up to 3.65 m to tiny 12.7 mm pipes used to supply individual outlets within a building.

Any pipe or tube intended to deliver drinking water to consumers is referred to as a water pipe. Depending on the situation, water may be treated either before distribution or at the point of use (POU). Water is typically treated before distribution in well-thought-out water distribution networks, and occasionally it is also chlorinated, to prevent recontamination on the way to the end user.

Polyvinyl chloride (PVC), cast iron, copper, steel, and, in older systems, concrete or fired clay are materials frequently used to build water pipes. Long runs of water pipe can be joined together using flange, nipple, compression, or soldered joints (SCOTT 2011).

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The value of x and y are (11.66,5)

Given that,

3x-30=y-----------1

7y-6=3x-----------2

Now, putting the value of equation 1 in equation 2 we get

⇒7(3x-30)-6=3x

⇒21x-210=3x

⇒21x-3x=210

⇒18x=210

⇒x=11.66

now put the value of x in equation 1 we solved earlier we get

⇒3×11.66-30=y

⇒35-30=y

⇒y=35-30

⇒y=5

Therefore the value of x is 11.66 and the value of y is 5

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Answer:

To find the equation of the altitude from point A to side BC, we can use the formula for the equation of a line in point-slope form, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

We can find the slope of the line by using the formula for the slope of a line between two points:

m = (y2 - y1)/(x2 - x1)

We can use this formula to find the slope of line BC, which is the line connecting points B and C. Substituting the coordinates of these points into the formula gives us:

m = (2 - (-2))/(2 - 6) = 4/-4 = -1

Next, we can use the point-slope form of the equation of a line to find the equation of the altitude from point A to line BC. Substituting the coordinates of point A and the slope of line BC into the point-slope formula gives us:

y - 1 = -1(x + 2)

This is the equation of the altitude from point A to line BC.

Step-by-step explanation:

SELF EXPLANATORY

Answer: 312=(2)(2)(2)(3)(13)

Step-by-step explanation:

312  |  2

156  |  2

78   |  2

39   |  3

13    | 13

Hence, 312=(2)(2)(2)(3)(13)

The probability that the first is red and the second is white is 4/21 or 0.190476.

The total number of marbles in the jar is 4 red, 7 white and 10 blue. This means there is a total of 21 marbles.

The probability of selecting a red marble first is 4/21 (4 out of 21 marbles are red).

The probability of selecting a white marble second is 7/20 (7 out of the remaining 20 marbles are white).

The probability of selecting a red marble first and a white marble second is 4/21 x 7/20 = 28/420 = 4/60 = 0.190476

The probability of selecting two marbles at random from the jar is calculated by multiplying the individual probabilities of selecting each marble. The probability of selecting the first marble is 4/21 (4 out of 21 marbles are red) and the probability of selecting the second marble is 7/20 (7 out of the remaining 20 marbles are white). Thus, the probability of selecting a red marble first and a white marble second is 4/21 x 7/20 = 28/420 = 4/60 = 0.190476.

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Answer: x=-3/28

Step-by-step explanation:

isolate x alone and move all other numbers to the right

-2/3x+3/7-(3/7)=1/2-3/7

-2/3x= 1/14

-2/3(-3/2)+x=1/14*-3/2

x=-3/28