How are you suppose to simplify a^-n ?

Answer:

[tex] 6.7 -0.674 *1.1 =5.96[/tex]

[tex] 6.7 +0.674 *1.1 =7.44[/tex]

Step-by-step explanation:

Let X the random variable that represent the  head breadths of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(6.7,1.1)[/tex]  

Where [tex]\mu=6.7[/tex] and [tex]\sigma=1.1[/tex]

We want the range of the middle 50% values on the distribution. Since the normal distribution is symmetrical we know that in the tails we need to have the other 50% and on each tail 25% by symmetry.

We can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

The critical values that accumulates 0.25 of the area on each tail we got:

[tex] z_{crit}= \pm 0.674[/tex]

And if we solve x from the z score we got:

[tex] x = \mu \pm z \sigma[/tex]

And replacing we got:

[tex] 6.7 -0.674 *1.1 =5.96[/tex]

[tex] 6.7 +0.674 *1.1 =7.44[/tex]

Answer:

0.68

Explanation:

The question is incomplete without the tables. Find attached the table used in solving the question.

group 20-24 25-34 35-44 45-54 55-64 65-74 75+ respectively

Probability 0.004 0.006 0.14 0.29 0.32 0.17 respectively

This is a probability of complementary events. The sum of the two complementary events = 1

Hence, the probability of selecting a man with the disease that is not between the ages of 55 and 64 + the probability of selecting a man with the disease that is between the ages of 55 and 64 = 1

The probability of selecting a man with the disease is not between the ages of 55 and 64 = 1- probability of selecting a man with the disease is between the ages of 55 and 64

Let Pr(between 55 and 74) = probability of selecting a man with the disease is between the ages of 55 and 64

From the table, Pr(between 55 and 74) = 0.32

The probability of selecting a man with the disease is not between the ages of 55 and 64 = 1 - 0.32

The probability of selecting a man with the disease is not between the ages of 55 and 64 = 0.68

Answer:

Step-by-step explanation:

A

All the factors of the function f (x) = x³ - 2x² - 68x - 120 are,

⇒ (x - 10) (x + 6) (x + 2)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ f (x) = x³ - 2x² - 68x - 120

Here, We have;

⇒ f (-2) = 0

Hence, This function have a factor (x + 2).

Now, After divide the function f (x) = x³ - 2x² - 68x - 120 by (x + 2), we get;

⇒ ( x³ - 2x² - 68x - 120 ) ÷ (x + 2)

⇒ x² - 4x - 60

⇒ (x - 10) (x + 6)

Hence, All the factors of the function f (x) = x³ - 2x² - 68x - 120 are,

⇒ (x - 10) (x + 6) (x + 2)

Learn more about the mathematical expression visit:

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The complete question is this,

If f(–2) = 0, what are all the factors of the function f (x) = x cubed minus 2 x squared minus 68 x minus 120? Use the Remainder Theorem. (x + 2)(x + 60) (x – 2)(x – 60) (x – 10)(x + 2)(x + 6) (x + 10)(x – 2)(x – 6)

Answer:

$504 a week

Step-by-step explanation:

Answer:

a. The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residentstravel per day is 88

b. The 95% confidence interval for the difference between the two population means is (0.58171,7.21829)

Step-by-step explanation:

a. According to the given data we have the following:

Buffalo residents mean=22.5

Standard deviation=8.4

n=50

Boston residents mean=18.6

Standard deviation=7.4

n=40

Hence, the point estimate is the difference of the means=22.5-18.6=3.9

The standard error=√((s1∧2/n1)+((s2∧2/n2))=√((8.4∧2/50)+(7.4∧2/40))=1.67

Therefore, the difference of miles=n1+n2-2=50+40-2=88

The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residentstravel per day is 88.

b. The critical value of t at 95% confidence level and DoF=88 is 1.987

The interval:(x1-x2)+ (critical value* std error)

=3.9-(1.987*1.67),3.9+(1.987*1.67)

Difference between mean=(0.58171,7.21829)

The 95% confidence interval for the difference between the two population means is (0.58171,7.21829)

Answer:

hope this helps you

Answer:

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Angle θ is in standard position and (4,4) is a point on the terminal side of θ.

[tex]\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}[/tex]

Now, secant is the inverse of cosine.

Therefore:

[tex]\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

Hello!

The variable "X: Full scale IQ score of an adult" follows a normal distribution with mean μ= 100 and standard deviation σ= 15

The claim is that the county's residents are smarter than the national average, symbolically: μ > 100

To test this a researcher took a sample of n=100 residents that took the test and recorded an average of X[bar]= 105

The hypotheses are:

H₀: μ ≤ 100

H₁: μ > 100

α: 0.05

p-value: 0.0004

Using the p-value approach, the decision rule is as follows:

p-value ≤ α, reject the null hypothesis.

p-value > α, do not reject the null hypothesis.

The p-value is less than the significance level so the decision is to reject the null hypothesis.

At a 5% significance level, you can conclude that the average full-scale IQ score of the Smart County residents is higher than the national average.

I hope this helps!

Answer:

Given diameter: r = d / 2 , Given area: r = √[A / (4 * π)] , Given volume: r = ³√[3 * V / (4 * π)] , Given surface to volume ratio: r = 3 / (A/V) .

Step-by-step explanation:

So, do that!

Answer:

36pi

Step-by-step explanation:

i already did it and it was correct.

Answer:

d) 0.135% of total arrivals were much more delayed than others.

e) 0.135% of total flights arrived much earlier than scheduled compared to others.

Step-by-step explanation:

With the question not totally complete, we will solve the available parts as well as possible.

d) How many arrivals were much more delayed than others (i.e., positive outliers with z-score of time difference > 3)?

P(z > 3)

Using the normal distribution table

P(z > 3) = 1 - P(z ≤ 3) = 1 - 0.99865 = 0.00135 = 0.135% of total arrivals were much more delayed than others.

e) How many flights arrived much earlier than scheduled compared to others (i.e., negative outliers with z-score of time difference < -3)?

P(z < -3)

Using the normal distribution table

P(z < -3) = 0.00135 = 0.135% of total flights arrived much earlier than scheduled compared to others.

Hope this Helps!!!

Answer:

17

Step-by-step explanation:

the amount of visits given by the problem is:

[tex]v=10[/tex]

and we have that the equation that relates the number of visits with the total cost is:

[tex]c=v+7[/tex]

where [tex]c[/tex] is the total cost for [tex]v[/tex] number of visits.

We plug into this equation the known value of visitors:

[tex]c=10+7[/tex]

and we solve this expression:

[tex]c=17[/tex]

the total cost for 10 visitors is 17.

Answer:

No. There is not enough evidence to support the claim that the boxes of dog food are being under filled (P-vaue=0.027).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the boxes of dog food are being under filled.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=32\\\\H_a:\mu< 32[/tex]

The significance level is 0.02.

The sample has a size n=200.

The sample mean is M=31.7.

The standard deviation of the population is known and has a value of σ=2.2.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{2.2}{\sqrt{200}}=0.156[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{31.7-32}{0.156}=\dfrac{-0.3}{0.156}=-1.928[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.928)=0.027[/tex]

As the P-value (0.027) is bigger than the significance level (0.02), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the boxes of dog food are being under filled.

Answer:

12 trips

Step-by-step explanation:

Given;

Dimension of cone shapef pile of earth;

height h = 12 ft = 4 yards

diameter d = 30 ft = 10 yards

radius r = d/2 = 10/2 = 5 yards

The volume of a cone V;

V = (1/3)πr^2 h

Substituting the given values;

V = (1/3) ×π × 5^2 × 4 cubic yards

V = 104.72 cubic yards

Given that a dump truck have a capacity of 9 cubic yards.

Vc = 9 cubic yards

Number of trips it will take is;

N = Volume of earth pile/truck capacity

N = V/Vc

Substituting the values;

N = 104.72/9

N = 11.64

N ≈ 12 trips

Therefore, the truck will make 12 trips

Answer:

A

Step-by-step explanation:

Answer:

Option (2). [tex]2\frac{1}{4}[/tex]

Step-by-step explanation:

The given expression is [[tex]-5\frac{1}{4}-(-7\frac{1}{2})[/tex]]

We can rewrite the fractions as,

[tex]-5\frac{1}{4}[/tex] = [tex]-(5+\frac{1}{4})[/tex]

[tex]-7\frac{1}{2}=-(7+\frac{1}{2})[/tex]

Now we will substitute the fractions in the expression,

[tex][-(5+\frac{1}{4})]-[-(7+\frac{1}{2})][/tex]

= [tex]-(5+\frac{1}{4})+(7+\frac{1}{2})[/tex]

= (-5 + 7) + [tex](-\frac{1}{4}+\frac{1}{2})[/tex]

= 2 + [tex]\frac{2-1}{4}[/tex]

= 2 + [tex]\frac{1}{4}[/tex]

= [tex]2\frac{1}{4}[/tex]

Therefore, Option (2). will be the answer.

Question:

Write an inequality to represent the situation.

A light bulb is programmed to turn on

when the temperature in a terrarium is

72°F or cooler.

Answer:

t ≤ 72⁰F

Step-by-step Explanation:

Given this situation, we can write an inequality to represent the temperature in a terrarium at which the light bulb is programmed to turn on as follows:

t ≤ 72⁰F

where, t is the temperature of the terrarium, the sign "≤" implies that at a temperature of 72⁰F and below (i.e. colder would mean temperature below 72⁰F), the light bulb should turn on, as programmed.

Invariably, the inequality "t ≤ 72⁰F" mean the light bulb would turn on if the temperature of the terrarium is less than or equals 72⁰F.

Answer:

Cost of the land = $90,900

Step-by-step explanation:

Cash Paid for the construction = $79,000

Cost of demolition of the old warehouse = $8,000

Salvage (i.e Proceeds from the salvaged materials) = $1,660

Additional Expenditure before construction began

Attorney's fee = $1,160

Real estate broker's fee = $4,400

Architect's fee = $8,660 ( Note that this will be capitalized to building cost)

Driveways and parking lot = $13,800 ( Note that this is capitalized to land improvements)

Sum of additional expenditure = Attorney's fee + Real estate broker's fee

Sum of the additional expenditure = 1160 + 4400

Sum of the additional expenditure = $5,560

Cost of the land = Cash paid + cost of demolition + Additional expenditure - salvage

Cost of the land = 79000 + 8000 + 5560 - 1660

Cost of the land = $90,900

Answer:

Amount to be reported as the cost of the land = $ 91,400

Step-by-step explanation:

Payment of Real Estate= $ 79,000

Building Demolished  $ 8000

Gains on Sale of materials = ($1660)

Attorney’s fee for work concerning the land purchase, $1160

Broker's fee       $4,400

Amount to be reported as the cost of the land = $ 91,400

Broker's fee is included in the purchase of land . Gains on the sale of salvaged materials is deducted  from the cost of land because it is of the building demolished.  Architect's fee is not also included in the cost of land but in the construction costs.

Answer:

HL

Step-by-step explanation:

Both triangles are right triangles as shown by the right angle marks in the figure.

Two corresponding legs are congruent as shown.

The diagonal is congruent to itself, and it is the hypotenuse of both right triangles.

Answer: HL

Answer:

The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm

P(155.6 < x⁻ < 156.2) = 0.174 cm

Step-by-step explanation:

Given sample size 'n' = 11 steel rods

Mean of the Population = 155.1 cm

Standard deviation of the Population = 2.2 cm

Given x⁻ be the random variable of Normal distribution

Let x₁⁻ =  155.6 cm

[tex]Z_{1} = \frac{x^{-} _{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{155.6-155.1}{\frac{2.2}{\sqrt{11} } } = 0.7541[/tex]

Let  x₂⁻ =  156.2 cm

[tex]Z_{2} = \frac{x^{-} _{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{156.2-155.1}{\frac{2.2}{\sqrt{11} } } = 1.659[/tex]

The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm.

P(x⁻₁ < x⁻ <x⁻₂) = P(Z₁ < Z <Z₂)

                       = P(Z <Z₂) - P(Z<Z₁)

                      = 0.5 +A(1.629) - (0.5 +A(0.7541)

                      = A(1.629) - A(0.7541)

                      = 0.4474 - 0.2734

                      = 0.174

Conclusion:-

The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm = 0.174

Answer:

1/6

Step-by-step explanation:

There are 6 CD

P( song from 6th ) = number of CD's that are 6th/ total

                                = 1/6

Answer:

first option

Step-by-step explanation:

Given 2 secants to a circle from an external point, then

The product of the external part and the whole of one secant is equal to the external part and the whole of the other secant, that is

PQ(RP) = PS(TP)

Answer:

Step-by-step explanation:

The two force F1 and F2  are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

[tex]v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j[/tex]

The unit vector in the direction of force will be

[tex]\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}[/tex]

The magnitude of the force is 40lb, so the force will be

[tex]F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)[/tex]

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

[tex]v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k[/tex]

[tex]\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}[/tex]

The magnitude of the force is 60lb, so the force will be

[tex]F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)[/tex]

The resultant of the two forces is

[tex]F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k[/tex]

The magnitude force will be

[tex]|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68[/tex]

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

[tex]\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469[/tex]

The angle formed by F and y axis

[tex]\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=[/tex]

The angle formed by F and z axis

[tex]\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359[/tex]

Answer:

4/5

Step-by-step explanation:

Since there are 100 people, and 20 people say their favorite flower was the tulip, we can make a fraction of the people who like tulip.

20/100=2/10=1/5

There are the people who's favorite flower is tulip. However, the question asks what fraction of the people say their favorite flower is NOT tulip.

Take 1 as the entire people surveyed, and subtract:

1-1/5= 4/5

Therefore 4/5 of the people surveyed says their favorite flower is NOT tulip.

Answer:

-2 (5) + 3

- 10 + 3

= -7

Answer:

f(-3)=3

Step-by-step explanation:

We know that f(x)=-2x-3. In order to find f(-3), we simply need to substitute x with -3.

Thus, we have:

=-2(-3)-3

=6-3

=3

Answer:

3

Step-by-step explanation:

f(x)=-2x-3

Let x=-3

f(-3)= -2(-3) -3

     = 6-3

    = 3

Answer:

Step-by-step explanation:

From the information given :

The null hypothesis [tex]H_o : \sigma = 60[/tex]

The alternative hypothesis  [tex]Ha : \sigma \neq 60[/tex]

Given that:

the sample size n = 21

sample standard deviation s = 68

population standard deviation σ = 60

a) The level of significance [tex]\alpha =0.01[/tex]

b) The chi-square statistics can be calculated as:

[tex]\bar X = \dfrac{(n-1)s^2}{\sigma^2}[/tex]

[tex]\bar X = \dfrac{(21-1)68^2}{60^2}[/tex]

[tex]\bar X = \dfrac{(20)4624}{3600}[/tex]

[tex]\bar X = 25.69[/tex]

The degree of freedom is :

= n - 1

= 21 - 1

= 20

Answer:

5/8 is about 1/2. 2/6 is about 0.

Step-by-step explanation:  2/6 is about 0 because 2 is close to 0. If the numerator is  close to 0 and the denominator is not close to 0 then the benchmark is going to be 0. If the numerator is about half of the denominator then the benchmark is going to be 1/2. If the numerator and denominator is close to each other than the benchmark is going to be 1.

Answer:

Part 1

Type II error

Part 2

No ; is not ; true

Step-by-step explanation:

Data provided in the question

Mean = 100

The Random sample is taken = 43 students

Based on the given information, the conclusion is as follows

Part 1

Since it is mentioned that the classes are successful which is same treated as a null rejection and at the same time it also accepts the alternate hypothesis

Based on this, it is a failure to deny or reject the false null that represents type II error

Part 2

And if the classes are not successful so we can make successful by making type I error and at the same time type II error is not possible

Therefore no type II error is not possible and when the null hypothesis is true the classes are not successful

The according to the dot plot, the true statement is: the data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game

A data distribution that is left-skewed is negatively skewed. This means that the long tail goes in the negative direction of the number line, with most of the values being concentrated on the right side.

The dot plot given is left-skewed, which means it is negatively-skewed.

Therefore, the according to the dot plot, the true statement is:

The data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game

Learn more about left-skewed data on:

https://brainly.com/question/3252860

Answer:

c

The data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game.

Step-by-step explanation:

swag

Answer:

20 trips

Step-by-step explanation: