Which line is parallel to the line that passes through the points (1, 7) and (-3, 4)? A. B. C. D.

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:

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)

Question:

For the following exercise, determine the range (possible values) of the random variable. A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.

Answer:

Possible values are all integers from 1 to 491.

{1,2,...........491}

Step-by-step explanation:

Given:

Total number of machined parts = 500

Number that do not conform to customers requirements = 10

Number that conforms to customers requirements = 500 - 10 = 490

Since, parts are selected successively, without replacement, until a nonconforming part is obtained, the range of the random variable (number of parts selected) here will be all integers from 1 to 491 ie {1,2,...........,491}.

Here, we have a total of 490 conforming parts, and 10 non conforming parts, there must be a non-conforming part among 491 selections, considering the fact that total number of parts are 500

There will be one non-confirming part in the 491 selections and this can be determined by using the given data.

Given :

Given that the total number of parts is 500 that contains 10 that do not conform to customer requirements. So, the total number of parts that conform to customer requirements is (500 - 10) 490.

It is also given that parts are selected successively, without replacement, until a nonconforming part is obtained so, the range of the random variables is [1,491]

So, there will be one non-confirming part in the 491 selections.

For more information, refer to the link given below:

https://brainly.com/question/23044118

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:

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:

[tex] f(t) = 6000 (\frac{1}{2})^t^/^3 [/tex]

Step-by-step explanation:

Let's take the equation:

[tex] y = y_0 e^-^k^t[/tex]

Given the initial population of bacteria = 6000,

[tex] y = 6000e^-^k^t[/tex]

Population of bacteria after 3 hours is 3000.

y(3) = 3000

Thus,

[tex] 6000e^-^k^3 = 3000[/tex]

[tex] e^-^k^3 = \frac{3000}{6000}[/tex]

[tex] e^-^k^3 = \frac{1}{2}[/tex]

[tex] (e^-^k)^3 = \frac{1}{2}[/tex]

[tex] e^-^k= (\frac{1}{2})^1^/^3[/tex]

Let's substitute [tex] (\frac{1}{2})^1^/^3 [/tex] for [tex] e^-^k[/tex] in [tex] y = 6000e^-^k^t [/tex]

Therefore, we have:

[tex] 6000e^-^k^t [/tex]

[tex] = 6000 [(\frac{1}{2}) ^1^/^3]^t[/tex]

[tex] = 6000 [\frac{1}{2}] ^t^/^3 [/tex]

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:

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:

[tex] Range = 60-5=55[/tex]

In order to find the variance and deviation we need to find the mean with this formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex] \bar X =36.07 [/tex]

Now we can find the variance with the following formula:

[tex]s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]

And replacing we got:

[tex] s^2=357.610[/tex]

And the standard deviation would be:

[tex] s = \sqrt{357.610}= 18.911[/tex]

For this case since the range observed is large is better to use a measure of variation in order to check the spread of the values and take a decision useful

Step-by-step explanation:

For this case we have the following dataset:

60 58 55 53 47 45 44 43 25 25 20 18 7 5

We can find the range with this formula:

[tex] Range = Max-Min[/tex]

And replacing we got:

[tex] Range = 60-5=55[/tex]

In order to find the variance and deviation we need to find the mean with this formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex] \bar X =36.07 [/tex]

Now we can find the variance with the following formula:

[tex]s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]

And replacing we got:

[tex] s^2=357.610[/tex]

And the standard deviation would be:

[tex] s = \sqrt{357.610}= 18.911[/tex]

For this case since the range observed is large is better to use a measure of variation in order to check the spread of the values and take a decision useful

Answer: 96°

Step-by-step explanation:

Sum of angles of a triangle = 180°

3 + 8 + 4 = 15

The biggest angle is 8/15 * 180 = 96°

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:

[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:

N = 35 × 34^6

N = 54,068,154,560

Step-by-step explanation:

Given;

The license plate have 7 characters.

Each character can be a capital letter, or a digit except for 0.

There are 26 capital letters

And there are 9 digits excluding 0

The total number of possible entries in each character is;

26+9 = 35

The number of license plates in which no two adjacent characters are the same are;

For no two adjacent characters of the license plate not to be the same that is no two characters that follow each other can be the same, the number of possible entries in the adjacent characters apart from the first character would be reduced by one.

N = 35 × 34 ×34×34×34×34×34

N = 35 × 34^6

N = 54,068,154,560

Therefore, there are 54,068,154,560 possible license plates

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:

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:

Step-by-step explanation:

We have to perform one sample proportion test. To do so we have to proceed through following steps.

(1) We have to collect data about vehicle sales in last 20 years.

(2) Using random number table or random number generator or otherwise we have to select sample of vehicles from the list of sale. In this step, we have to keep an eye on the fact that sample is to be selected from all years (all of 20). Using stratified random sampling by dividing vehicles sold over different years is an effective way to do so. That means, we may divide vehicles sold into 20 homogeneous strata over 20 years and select sample from each strata.

(3) After selecting sample of vehicles we have to communicate to corresponding vehicle owners to gather information about that particular vehicle.

(4) We have to note number of vehicles which are still on the road.

Suppose, we have selected  n vehicles as sample and after communicating we found that \tiny r of those are still on the road.

We have to test for null hypothesis [tex]H_0:p=0.80[/tex]

against the alternative hypothesis [tex]H_1 \neq 0.80[/tex]

Our test statistic is given

[tex]z=\frac{\hat p - p_0}{\sqrt{p_0(1-p_0)/n} }[/tex]

here,

[tex]\hat p =\frac{r}{n}[/tex]

[tex]p_0 =0.80[/tex]

[tex]z=\frac{r/n-0.80\sqrt{n} }{0.40} \\\\=2.5(\frac{r}{n} -0.8)\sqrt{n}[/tex]

We then calculate corresponding p-value.

We reject our null hypothesis if [tex]\text{p-value}<\alpha[/tex] , level of significance.

According to our obtained p-value and level of significance we proceed to certain conclusion.

Answer:

a

Step-by-step explanation:

the slope is negative bec it's going from the top left to the bottom right corner(if I was negative the line would be going from the bottom left to the too right) then your y-intercept( the point that hits y when x is zero) is 120

Answer:

The correct answer would be A, y = -4/3x + 120

Step-by-step explanation:

Let us start with the y-intercept, the y-intercept is 120. The graph shows that the y-intercept is positive, but the slope is negative. B, C, D, and E are not correct due to the mis use of signs, a wrong slope, and a wrong y-intercept.

if u want to prove me wrong, then go ahead.

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:

brainly.com/question/1859113

#SPJ2

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:

a. Yes

b. No

Step-by-step explanation:

In a hypothesis​ test, the null hypothesis is in fact true.

a. Is it possible to make a Type I​ error?

Yes, it is possible to make a type I error because a type I error typically occurs if the null is rejected when it is actually true.

b. Is it possible to make a Type II​ error?

It is not possible to make a type II error because the condition for a type II error is that the null is in fact not true but we fail to reject it.

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:

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:

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

Answer:

H(3)=39

Step-by-step explanation:

H(3) =10 (3) + 9

=30 +9

=39

Hope this helps...

Answer:

y-2=0

Step-by-step explanation:

In y=mx+b

m=(y2-y1)/(x2-x1) [2]

Or another way of thinking about it is rise over run.

define point (-1,2) as x1,y1

define point (5,2) as x2,y2

substitute into formula [2]

m=(2-2)/(5-(-1))

We know that 2-2=0 therefore the slope (m) is 0

y=0x+b

Or simply

y=b

to solve for b we substitute into the formula any of the points

2=b for y1

or 2=b for y2

b=2

therefore y=2

to convert it into general form make the equation equal 0

y-2=0

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:

$117

Step-by-step explanation:

Given that:

They buy these books for $105 each and sell them to unsuspecting undergraduates at $222 each

Marginal Profit = Marginal Revenue – Marginal Cost.

Marginal Profit = $222 - $105

Marginal Profit = $117

the marginal profit for a single elementary statistics book $117

For the remaining unsold books in the middle of the semester he bundles them up and sells to vendor in another country for $40 each for which he suffers a marginal loss of $105 - $40 = $65 each

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.

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.