A parking lot for a new ice cream stand has an area of 5000 square yards. The length of the lot is 50 yards longer than its width. Determine algebraically the dimensions of the parking lot, in yards.

Answer:

Correct option: first one

"StartFraction P minus 2 l Over 2 EndFraction = w"

Step-by-step explanation:

First we start from the perimeter equation:

P = 2*l + 2*w

Then, we need to solve for w, so we need to isolate it.

The first step is subtracting 2*l from both sides of the equation:

P - 2*l = 2*w

Then, we divide both sides by 2:

w = (P - 2l) / 2

So the correct option is the first one:

"StartFraction P minus 2 l Over 2 EndFraction = w"

Answer:

Its the first one

Step-by-step explanation:

i got it right on edge

Answer:

41.41°  

Step-by-step explanation:

In ∆ABC below, the legs are 4 and the base is 6.

So, the legs are ⅔ the length of the base.

In ∆CBD,

cosB = BD/BC = 3/4 = 0.75

B = arccos 0.75 = 41.41°

The base angles are each 41.41°

The measure should be 41.41°  

Since In ∆ABC , the legs should be 4 and the base should be 6.

Now

the legs are two-third the length of the base.

Also,

In ∆CBD,

cosB [tex]= BD\div BC = 3\div 4 = 0.75[/tex]

So,

B = arccos 0.75 = 41.41°

Therefore, we can concluded that The base angles are each 41.41°

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Answer:

a) Experiment

b) Proportion of subjects infected. Quantitative

c) Null hypothesis failed to be rejected. P-value=0.101.

There is not enough evidence to support the claim that the RV infection rate of subjects using hand sanitizer is significantly lower.

d) The  95% confidence interval for the difference between proportions is (-0.223, 0.047).

As we can see, the value 0 (meaning no difference between the proportions) is included in the interval. This can be interpreted the sam wat that the hypothesis test: at 95% confidence, we can not assurre that there is significant difference between the proportions.

Step-by-step explanation:

a) This is an experiment, as the groups are designed by the researcher. The individuals are then asigned randomly to one of both groups.

b) The response variable is the proportion of subjects infected. This variable is quantitative, as is a sum of positive cases divided by the total amount of subjects in the group.

c) This is a hypothesis test for the difference between proportions.

The claim is that the RV infection rate of subjects using hand sanitizer is significantly lower.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

The significance level is 0.05.

The sample 1 (HL+ group), of size n1=116 has a proportion of p1=0.4224.

[tex]p_1=X_1/n_1=49/116=0.4224[/tex]

The sample 2 (Control group), of size n2=96 has a proportion of p2=0.5104.

[tex]p_2=X_2/n_2=49/96=0.5104[/tex]

The difference between proportions is (p1-p2)=-0.088.

[tex]p_d=p_1-p_2=0.4224-0.5104=-0.088[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{49+49}{116+96}=\dfrac{98}{212}=0.4623[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4623*0.5377}{116}+\dfrac{0.4623*0.5377}{96}}\\\\\\s_{p1-p2}=\sqrt{0.0021+0.0026}=\sqrt{0.0047}=0.0688[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.088-0}{0.0688}=\dfrac{-0.088}{0.0688}=-1.28[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=P(z<-1.28)=0.101[/tex]

As the P-value (0.101) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the RV infection rate of subjects using hand sanitizer is significantly lower.

d) We want to calculate the bounds of a 95% confidence interval.

For a 95% CI, the critical value for z is z=1.96.

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4623*0.5377}{116}+\dfrac{0.4623*0.5377}{96}}\\\\\\s_{p1-p2}=\sqrt{0.0021+0.0026}=\sqrt{0.0047}=0.0688[/tex]

Then, the margin of error is:

[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.0688=0.1348[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.088-0.1348=-0.223\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.088+0.1348=0.047[/tex]

The  95% confidence interval for the difference between proportions is (-0.223, 0.047).

As we can see, the value 0 (meaning no difference between the proportions) is included in the interval. This can be interpreted the sam wat that the hypothesis test: at 95% confidence, we can not assurre that there is significant difference between the proportions.

Answer:

6.3 ft

Step-by-step explanation:

The perimeter of a parallelogram is given by

P = 2(l+w)

49.6 = 2 (18.5 +t)

Divide by 2

49.6/2 = 2/2 (18.5 +t)

24.8 = 18.5+t

Subtract 18.5

24.8-18.5 = t

6.3 = t

Answer:

a) test statistic, [tex]t_{s} = -4.20[/tex]

b) P-value = 0.0001

c) It can be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years

Step-by-step explanation:

There are 40 trading days, therefore, sample size, n = 40

Calculate the Sample mean:

[tex]\bar x = \frac{\sum x}{n} \\\bar x = \frac{4.153 +4.6228 + ...+...+5.4563}{40}\\\bar x = 5.5945[/tex]

Get the null and alternative hypothesis:

Null hypothesis, [tex]H_{0} : \mu = 7.52[/tex]

Alternative hypothesis, [tex]H_{a} : \mu \neq 7.52[/tex]

Calculate the sample standard deviation:

[tex]SD = \sqrt{\frac{\sum (x - \bar x)^{2} }{n - 1} } \\SD = \sqrt{\frac{(4.1531-5.5945)^{2} + (4.6228-5.5945)^{2}+...+ (5.4563-5.5945)^{2}}{39} } \\SD = \sqrt{\frac{327.6161}{39} } \\SD = 2.8983[/tex]

a) Calculate the test statistic:

[tex]t_{s} = \frac{\bar{x} - \mu}{SD/\sqrt{n} } \\t_{s} = \frac{5.5945 -7.52}{2.8983/\sqrt{40} }\\t_{s} = -4.20[/tex]

b) Calculate the P-value

Getting the P-value using the excel function:

P-value = (=T.DIST.2T(|ts|, df))

P-value = (=T.DIST.2T(4.20, 39))

P-value = 0.0001

c) If the level of significance, [tex]\alpha = 0.05[/tex]

The P-value (0.0001) < α(0.05), the null hypothesis is rejected.

It can therefore be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years

Answer:

  ∠W = 81°

Step-by-step explanation:

Triangle OGD is isosceles, so angle OGD has the same measure as angle ODG, 17°.

Triangle OGF is isosceles, so angle OGF has the same measure as angle OFG, 49°.

Angle DGF is the difference between angle OGF and angle OGD:

  ∠DGF = 49° -17° = 32°

External angle W is equal to the sum of remote internal angles DGF and OFG:

  ∠W = 32° +49°

  ∠W = 81°

Answer:

(a) The average baggage-related revenue per passenger is $15.70.

(b) The standard deviation of baggage-related revenue is $19.95.

(c) The expected revenue for 120 passengers is $1,884.

Step-by-step explanation:

Let the random variable X represent the baggage-related revenue per passenger.

It is provided that the baggage fees is $25 for the first bag and $35 for the second.

The probability model is:

    X :   0         25      60

P (X) : 0.54    0.34    0.12

(a)

Compute the average baggage-related revenue per passenger as follows:

[tex]E(X)=\sum {X\times P (X)}[/tex]

         [tex]=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70[/tex]

Thus, the average baggage-related revenue per passenger is $15.70.

(b)

Compute the standard deviation of baggage-related revenue as follows:

[tex]E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\[/tex]

[tex]SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}[/tex]

           [tex]=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95[/tex]

Thus, the standard deviation of baggage-related revenue is $19.95.

(c)

Compute the expected revenue for 120 passengers as follows:

[tex]E(R)=n\times E(X)[/tex]

        [tex]=120\times 15.7\\\\=1884[/tex]

Thus, the expected revenue for 120 passengers is $1,884.

Answer:

It will take 1.47 hours for the horse and clown to collide

Step-by-step explanation:

They are driving toward each other, in opposite directions.

So to find their speed of approximation, we add their speeds.

19 mph + 15 mph = 34 mph.

This means that each hour, they are 34 miles closer.

How long it takes for them to find each other if they are 50 miles apart?

1 hour - 34 miles

x hours - 50 miles

[tex]34x = 50[/tex]

[tex]x = \frac{50}{34}[/tex]

[tex]x = 1.47[/tex]

It will take 1.47 hours for the horse and clown to collide

Solution,

Diameter=16.8 cm

Radius=16.8/2=8.4 cm

Area of circle=pi r^2

= 3.142*(8.4)^2

=3.142*70.56

=221.69952 cm^2

hope it helps

Good luck on your assignment

Answer:

The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error 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 quesstion:

[tex]\sigma = 1.5, n = 22[/tex]

So

[tex]M = 1.645*\frac{1.5}{\sqrt{22}} = 0.53[/tex]

The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.

Answer:

[tex][0,Z_n][/tex]

Step-by-step explanation:

Z = the sales tax percentage for a randomly selected amazon purchase, where n = the total number of possible sales tax percentages for online purchases

Since Amazon is an online purchase, The set of possible values for the variable is a positive real number. It is a positive real number that must be within [tex]Z_n[/tex]. It cannot exceed the tax percentage for online purchases that can be found in Amazon. [tex]Z_n[/tex] is a set of online purchases that can be found on Amazon, therefore the set of possible values for the variable is [tex][0,Z_n][/tex]

Answer:

26 remainder 2

Step-by-step explanation:

5 - 3 =2

2 + 78 = 80

80 ÷ 3

3 can go into 8 twice remaining with 2

2 goes across to 0

3 can go into 20 6 times because 3×6= 18

so 3 into 20 is 6 remainder of 2

answer= 26 remainder of 2

Answer:

[tex]= 26 \frac{3}{2} \\ [/tex]

Step-by-step explanation:

[tex]5 - 3 + 78 \div 3 \\ 2 + 78 \div 3 \\ 80 \div 3 \\ = 26 \frac{3}{2} [/tex]

hope this helps you

Answer:

49.97% probability of getting one child of each sex

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a couple’s first child is a boy is 0.512.

This means that [tex]p = 0.512[/tex]

The will have two children:

This means that [tex]n = 2[/tex]

(a) What is the probability of getting one child of each sex?

This is P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{2,1}.(0.512)^{1}.(0.488)^{1} = 0.4997[/tex]

49.97% probability of getting one child of each sex

Answer:

1

Step-by-step explanation:

We need to points

(-1,0) and (0,1)

The slope is found by

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

m = (1-0)/(0- -1)

   = (1-0)/(0+1)

   = 1/1

The slope is 1

Answer:

1

Step-by-step explanation:

The slope is rise/run and can be found by counting how many units up and over you must go from one point on the line to another.

Therefore the answer is

1

Answer:

positive

Step-by-step explanation:

the higher the temp the higher the number of ice creams sold

The association would be positive between the variables.

Given that,
Recorded the daily high temperature and the daily amount of ice cream sold by an ice cream vendor at your favorite beach this summer, starting on Memorial Day weekend and ending on Labor Day weekend.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
As the temperature increases, people will love to eat the ice cream more, which increase the sales of the ice cream which implies that the association would be positive between the variable.

Thus, the association would be positive between the variables.

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Answer:

The equilibrium point for the product (x,y) = (50,2300)

Step-by-step explanation:

The equilibrium point refers to the point in the demand and supply curves where we have the quantity demanded equals the quantity supplied at a particular price.

From the question, we can identify the following;

S(x) = 300 + 40x

D(x) = 4300 - 40x

Now, at the equilibrium point, S(x) = D(x)

This means that;

300 + 40x = 4300 -40x

80x = 4300-300

80x = 4000

x = 4000/80 = 50

Now, we input the value of x into any of the equation of the demand and supply to get the quantity.

Let’s use S(x) = 300 + 40x = 300 + 40(50) = 300 + 2000 = 2,300

The equilibrium point for the product (x,y) = (50,2300)

Answer:

80cm

Step-by-step explanation:

i worked it out like this

2x4=8

then that means

20x4=80

Answer:

80 is the answer

Answer:

b) Dependent sample

Step-by-step explanation:

Given:

Sample size, n = 1400

The average sleep of the respondents in weekdays = 6.5 hours

The average sleep of the respondents in weekends = 7.2 hours

% with eight or more hours of sleep on​ weekdays = 20%

% with eight or more hours of sleep on​ weekends = 43%

Required: To Check if the samples on weekdays and weekends are independent or dependent.

When samples are independent, it means one sample does not influence the other and vice versa, while samples are said to be dependent if the outcome of one test influences the outcome of the other. The tests might be from a similar population or from various populations.

In this case, the sample gathered are from similar population because same sample is used for both weekdays and weekends. Therefore, we can say the sample is a paired sample.

The samples on weekdays and weekends are dependent since same people are used, also since sleep on weekdays and sleep on weekends may influence each other.

Answer:

Step-by-step explanation:

DO YOU MEAN :

[tex]4x + 5y = 7\\ 3x - 2y = -12\\Multiply-equation 1 -by -the-coefficient-of-x-in-equation-2\\multiply-equation-2 -by-the-co-efficient -of x -in-equation- 1\\\\3(4x + 5y = 7)\\4( 3x - 2y = -12)\\\\12x +15y=21\\12x -8y=-48[/tex]

Answer:

The critical value of t =3.012

Step-by-step explanation:

Solution

Recall that:

Bruce a store owner put together information on random sales of = 14 days

A significant level of =0.5%

The mean revenue per day = 65 dollars

Now,

We find he critical values using the partial t-table stated above

Thus,

The degree of freedom is given below:

n -1 = 14

14-1 =13

For a 0.005 level and right tailed test and with a 13 degree of freedom, the critical value of t =3.012.

Answer:

3

Step-by-step explanation:

1+1= 2 + -2=0 + 3 = 3

Answer:

[tex]3[/tex]

Step-by-step explanation:

[tex](1 + 1 -2 +3)[/tex]

[tex]1+1-2+3[/tex]

[tex]2+1[/tex]

[tex]=3[/tex]

Answer:

Step-by-step explanation:

Obviously, factors can be written in any order. So, there are multiple answers to this question.

1. x^2 -2x -15 = (x -5)(x +3) . . . . (a, b, c, d) = (1, -5, 1, 3)

__

2. 2x^2 -6x -36 = 2(x^2 -3x -18) = 2(x -6)(x +3) . . . . (a, b, c, d) = (2, -12, 1, 3)

__

3. 4x^2 +10x +4 = 2(2x^2 +5x +2) = 2(2x +1)(x +2) . . . . (a, b, c, d) = (4, 2, 1, 2)

Answer:

16/25

Step-by-step explanation:

4/10=40/100

24/100=24/100

40+24=64

64/100

16/25

Answer:

16/25

Step-by-step explanation:

Answer:

hope this helps, take care and stay safe

Step-by-step explanation:

you can do this by timing 6.5 by 2 which = 13. if you get stuck on questions like this, do the rewind effect, that is when you do the opposite of the question, which is what i did above, you can check this in 2 ways, on a calculator (if of course you are allow) or do the question again by using what you have work out, so 13 divide by 2 = 6.5.

The number 13 is divided by 2 to give the number 6.5.

Used the concept of divide which states that,

The division method is used to distribute a group of things into equal parts. The division is just the opposite of multiplications.

To find the number that is divided by 2 to give the number 6.5

Let us assume that the number = x

Hence, it can be written as,

x ÷ 2 = 6.5

x/2 = 6.5

Multiply both sides 2;

x = 2 × 6.5

x = 13

Therefore, the number of the given condition is 13.

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Assuming [tex]A'[/tex] denotes the complement of the set [tex]A[/tex], i.e. all elements in the universal set that do not belong to [tex]A[/tex], then we can prove this in general.

To establish equality between two sets, you need to show that they are both subsets of one another.

Let [tex]x\in(A\cup B)'[/tex].

By definition of set complement, this means [tex]x\not\in A\cup B[/tex].

By definition of set union, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].

By definition of complement, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].

By definition of set intersection, [tex]x\in A'\cap B'[/tex].

Therefore [tex](A\cup B)'[/tex] is a subset of [tex]A'\cap B'[/tex], because membership of some arbitrary element in the first set directly implies membership in the second set.

Let [tex]x\in A'\cap B'[/tex]. The proof follows similarly as above.

By definition of intersection, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].

By definition of complement, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].

By definition of union, [tex]x\not\in(A\cup B)[/tex].

By definition of complement, [tex]x\in(A\cup B)'[/tex].

Therefore [tex]A'\cap B'[/tex] is a subset of [tex](A\cup B)'[/tex].

And hence both sets are equal, regardless of what the sets may be.

Answer:

if x=ky, where k is constant.

value of x

45/3=k3/3

15=k, constant is 15

value of x when y =6

x=ky

x=15(6)

x=80

Answer:

The total amount in 7 years is: $958.62

Step-by-step explanation:

Recall the formula for compound interest:

[tex]A=P\,(1+\frac{r}{n} )^{n\,t}[/tex]

where:

A is the Accrued value (total in the account including accumulated interest), and in our case the unknown.

P is the Principal (amount initially deposited), and in our case $700.

r is the annual percent rate (but in decimal form) in our case 0.045

n is the number of compoundings done per year, and in our case 12 since it is compounded monthly

t is the time in years of the deposit.

Then the formula becomes:

[tex]A=P\,(1+\frac{r}{n} )^{n\,t}\\A=700\,(1+\frac{0.045}{12} )^{12\,*\,7}\\A=958.61657[/tex]

which can be rounded to the cents: $958.62

Answer:

a idk

Step-by-step explanation:

Answer:

The Answer is D on Edge

Step-by-step explanation:

Answer:

D is the answer

Step-by-step explanation: