Kapil's robot starts 70cm from its charging base. It faces the base, then turns 60 degrees clockwise, as shown. Finally, the robot moves 50cm. After moving, how far is the robot from the charging base? Do not round during your calculations. Round your final answer to the nearest centimeter.

Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we have that the parameters are given as follows:

[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].

The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{35 - 34}{0.4}[/tex]

Z = 2.5

Z = 2.5 has a p-value of 0.9938.

0.9938 = 99.38% probability that the average of these members is less than 35.

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Answer:

1

Step-by-step explanation:

216 is term 1
36 is term 2
6 is term 3
1 is term 4

Answer:

to solve this you need to find out what number n is to make it equal 28.

Step-by-step explanation:

19+3 =22 so 3 is not it

19+9=28

answer is 9

hopefully this is right and this gets to you on time

Answer:

err Im not sure if this is a multiple-choice but n=3

Step-by-step explanation:

3(n) + 19 is 28 meaning you have to find what multiplies with 3 to get 9 because 19+9 is 28
Hope this helps

Using the given information in the diagram, we have proven that sin(B)/b = sin(C)/c

From the question, we are to prove that sin(B)/b=sin(C)/c

Consider the right triangle with sides a, c, and h

Using SOH CAH TOA, we can write that

sin(B) = h/c

∴ h = c × sin(B) --------- (1)

Also,

Consider the other right triangle

Using SOH CAH TOA, we can write that

sin(C) = h/b

∴ h = b × sin(C) ---------- (2)

Equate equations (1) and (2)

That is,

c × sin(B) = b × sin(C)

This can then be expressed as

sin(B)/b = sin(C)/c

Hence, the given expression is proven as shown above

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Answer:

Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of qp where p and q are integers and q =0.

Answer:

7.5

Step-by-step explanation:

10 is to 8 as    x is to 6

10/8  = x/6

6 (10/8) = x = 7.5

Answer:

Step-by-step explanation:

The two triangles are similar because the corresponding angle in each is equal to the angle corresponding angles in the other.

Put in simpler language. ΔAEB ~ ΔADC by parallel lines properties. If that's the case 10/(10 + 8) = x/(x + 6)

Equation

AE/AD = AB/AC                  Substitute values

Solution

10/(10 + 8) = x/(x + 6)           Cross Multiply

10*(x + 6) = x* (10 + 8)          Combine

10*(x + 6) = 18x                     Remove the Brackets

10x + 60 = 18x                      Subtract 10x from both sides

8x = 60                                 Divide by 8.

x = 60/8

x = 7.5

Answer: A

Answer:

  B.  0.95

Step-by-step explanation:

The probability that the value of the random variable is in the given range is the area under the normal probability distribution curve over that range. The value of this area is conveniently provided by any number of calculators, apps, or spreadsheets. It can also be determined using the "empirical rule" that tells you the probability over certain normalized ranges.

__

A standard normal probability density function (PDF) has a mean of 0 and a standard deviation of 1. The range in this problem can be normalized to some number of standard deviations above or below the mean. The mean is given as 46, and the standard deviation is given as 22.

In this problem, the lower limit of the range is ...

  z = (2 -46)/22 = -2

standard deviations from the mean.

Similarly, the upper limit is ...

  z = (90 -46)/22 = +2

standard deviations from the mean.

The empirical rule tells us that 95% of the area of the PDF lies between -2 and +2 standard deviations from the mean.

  P(2 < X < 90) ≈ 0.95

_____

Additional comment

The empirical rule for other ranges is ...

  ± 1 standard deviation: 68%

  ±2 standard deviations: 95%

  ±3 standard deviations: 99.7%

The 2nd dot plot in the attachment represents the dot plot that has the same sample mean as the population mean

The dot plot that completes the question is added as an attachment.

Start by calculating the mean of the data plot using:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

Substitute the values on the dot plot

[tex]\bar x = \frac{2*1+3*3+4*2+5+6*3+7*5+8*2+9*4+11*2+12*2}{25}[/tex]

[tex]\bar x = 7[/tex]

This means that the population mean of the dot plot is 7

Next, we create another dot plot that has the same mean as 7.

There are no direct rules to this, so we make use of the trial by error method.

After several attempts, we have the following frequency table:

Data point      Frequency

2                                  1

3                                  2

4                                  0

5                                  4

6                                  5

7                                  2

8                                  5

9                                  0

10                                 2

12                                 3

The mean of the frequency table is:

[tex]\bar x = \frac{2 * 1 + 3 * 2 + 4 * 0 + 5 * 4 + 6 * 5 + 7 * 2 + 8 * 5 + 9 * 0 + 10 * 2 + 12 * 3}{1+2+0+4+5+2+5+0+2+3}[/tex]

Evaluate

[tex]\bar x = \frac{168}{24}[/tex]

Evaluate the quotient

[tex]\bar x = 7[/tex]

This means that the sample mean is 7 (same as the population mean)

Lastly, we represent the frequency table using a dot plot (the 2nd dot plot in the attachment)

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Answer:

3.287 Customers

Step-by-step explanation:

Interarrival time (a) = 60 seconds per minute / 190 customers per minute = 0.316 seconds.

Utilization = p / (a × m) = 2 / (0.316 × 8) = 0.792.

Number in queue = Tq / a = 1.038 / 0.316 = 3.287 customers.

Answer:

-3

Step-by-step explanation:

g(-3) = -2x+3x

-2(-3) +3(-3)

6+-9 = -3

give brainliest please

hope this helps :)

Answer:

just commenting so you can give the other guy brainliest !

Step-by-step explanation:

Answer:

3.9m x 4.8m

Step-by-step explanation:

1 cm = 1.5m

→ Multiply both sides by 2.6

2.6 cm = 3.9m

→ Multiply from the original statement, both sides by 3.2

3.2 cm = 4.8 m

→ Combine them

3.9m x 4.8m

The expected number of adults that believe ufos are watching earth is 4

The given parameters are:

p = 48%

Sample size, n = 8

The expected number of adults that believe ufos are watching earth is calculated as:

E(x) = np

This gives

E(x) = 8 * 48%

Evaluate

E(x) = 3.84

Approximate

E(x) = 4

Hence, the expected number of adults that believe ufos are watching earth is 4

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Answer:

the value of b to 2

The value of b changes to 2.

The correct option is C.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

We have,

Equation: h(x) = -x + 5

Now, using the slope intercept form

y = mx + b

From which we get

m = -1 and b=5

Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get

y = -x+5 -3

y = -x +2.

Here y-intercept is 2.

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Answer:

one

Step-by-step explanation:

When a system of equations is graphed, the solution is the coordinate that is plotted at the intersection of the two lines.

If the two lines cross once, there is only one solution.

If the two lines are on top of each other then there are infinitely many solutions.

If the two lines are parallel ( and never touch ) then there are no solutions

By looking at the graph we notice the two lines intersect once. So we can conclude that there is only one solution.

Answer:

(-2, -2)

Step-by-step explanation:

the solution of the system of equation put simply is the point of intersection between the 2 lines

hence, the answer is (-2,-2)

Using the Law of Cosines,

[tex]c^{2}=2^{2}+4^{2}-2(2)(4)(\sin 30^{\circ})\\\\c^{2}=12\\\\c=2\sqrt{3}[/tex]

Using the Law of Sines,

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}\\\\\frac{\sin A}{2}=\frac{\sin 30^{\circ}}{2\sqrt{3}}\\\\\frac{\sin A}{2}=\frac{1}{4\sqrt{3}}\\\\\sin A=\frac{1}{2\sqrt{3}}\\\\A=\boxed{\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]

So, as angles in a triangle add to 180 degrees,

[tex]B=180^{\circ}-30^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)\\\\B=\boxed{150^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]

Answer:

Irrational

Step-by-step explanation:

[tex]\sqrt{9}= 3[/tex]

3 × √3 = 3√3 which is irrational

Hope this helped and brainliest please

Product is multiplication:

√3 x √9 = 3√3 = 5.19615....

Because the fraction does not end, it is not rational.

Answer: Irrational

The function of the curve is an exponential function. So, the function would be y = e^x.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

Their usual form is specified below. They are written in several such equivalent forms.

For example, [tex]y^x[/tex]

where a is a constant is an exponential function.

We can see that the curve of the function is decreasing constantly.

Thus, the function of the curve is an exponential function. So, the function would be y = e^x.

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Answer:

2.33

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

The total perimeter of the chicken coop if the length of one side is 3√5 yards is; 15√5 yards.yards

We are told that Isabelle had a five sided chicken coop in her yard and that the length was equal in all the sides.

Now, we need to find the total perimeter of the chicken coop.

The length of one side of the coop from online sources is 3√5 yards.

Since the coop is 5 sided, it means that it is a pentagon and we know that;

Perimeter of a pentagon = 5a

Where a is length of one side of the pentagon. Thus;

Perimeter = 5 x 3√5

Perimeter = 15 √5 yards

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The value of the complete equation is 5.1.

We have given the equation,

15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore we have,

[tex]15.3/3=15+0.3 \ tenths/3\\=5+0.1 \ tenths\\=5.1[/tex]

Therefore the value of the complete equation is 5.1.

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The variable that is most likely to have a positive correlation with the number of swimsuits purchased is the temperature changing outside.

Correlation measures the relationship between two variables. When there is a positive correlation, it means that the two variables move in the same direction. If one of the variables increases, the other variable increases. If one of the variables decreases, the other variable decreases.

When it is summer, it is expected that the number of swimsuits bought would increase. When it is winter, it is expected that the number of swimsuits bought would decrease.

Here are the options:

A. The number of swimsuit cover-ups the store has in stock

B. The number of sand castles built by store customers

C. The temperature outside changing

D. The number of minutes it takes the store's employees to get to work

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Answer:

Polynomial

Step-by-step explanation:

⇒ It cannot be option 1 as y does not vary with an exponent

⇒ It cannot be option 2 as y does not relate to any logarithmic values of x

⇒ It cannot be a option 4 as there no irrational numbers under a root

⇒ Therefore it is a polynomial, as it is written in the form : y = ax³ + bx² + cx + d (cubic polynomial)

Answer:

15) 3.2

17) 13.4

Step-by-step explanation:

To find the missing lengths, you need to use the Pythagorean theorem:

a² + b² = c²

In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.

You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".

15)    a = 4.1     c = 5.2

a² + b² = c²                                    <----- Pythagreom Theorem

(4.1)² + b² = (5.2)²                          <----- Plug values in for "a" and "c"

16.81 + b² = 27.04                         <----- Raise numbers to the power of 2

b² = 10.23                                      <----- Subtract 16.81 from both sides

b = 3.2                                           <----- Take the square root of both sides

You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".

17)   a = 4.4      b = 12.7

a² + b² = c²                                      <----- Pythagreom Theorem

(4.4)² + (12.7)² = c²                           <----- Plug values in for "a" and "b"

19.36 + 161.29 = c²                          <----- Raise numbers to the power of 2

180.65 = c²                                      <----- Add

13.4 = c                                            <----- Take the square root of both sides

[tex] {5}^{3} \: \times \: {5}^{ - 5} [/tex]

[tex] {5}^{ - 2} [/tex]

[tex] \boxed{ {a}^{ - n} \: = \: \frac{1}{ {a}^{n} } }[/tex]

[tex] {5}^{ - 2} \: = \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]

[tex]\text{Option C.} \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]

The drain rate is constant and thus equal to the average drain rate over the entire 4.5 hour period. This rate is

[tex]\dfrac{0 \,\mathrm L - 180 \,\mathrm L}{4.5 \,\rm h} = -40 \dfrac{\rm L}{\rm h}[/tex]

which is to say, water flows from the tank at a rate of 40 L/h.

The value of the composite function (p + q)(2) is 1

The function expression is given as:

(p + q)(2)

As a general rule

(p + q)(x) = p(x) + q(x)

Substitute 2 for x

(p + q)(2) = p(2) + q(2)

From the table, we have:

p(2) = 3 and q(2) =-2

So, we have:

(p + q)(2) = 3 - 2

Evaluate

(p + q)(2) = 1

Hence, the value of the composite function (p + q)(2) is 1

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Answer: (p+q)(2)=1

Step-by-step explanation:

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