What is the optimal solution for the following problem?

Minimize

P = 3x + 15y

subject to

2x + 4y ? 12

5x + 2y ? 10

and

x ? 0, y ? 0.

(x, y) = (2, 0)

(x, y) = (0, 3)

(x, y) = (0, 0)

(x, y) = (1, 2.5)

(x, y) = (6, 0)

Answer:

The rent should be $ 390 or $ 410.

Step-by-step explanation:

Given,

The original monthly rent of an apartment = $350,

Also, the original number of apartment that could be filled = 90,

Let the rent is increased by x times of $ 10,

That is, the new monthly rent of an apartment =( 350 + 10x ) dollars

Since, for each $10 per month increase there will be two vacancies with no possibility of filling them.

Thus, the new number of filled apartments = 90 - 2x,

Hence, the total revenue of the firm = ( 90 - 2x )(350 + 10x ) dollars,

According to the question,

( 90 - 2x )(350 + 10x ) = 31,980

[tex]90(350)+90(10x)-2x(350)-2x(10x)=31980[/tex]

[tex]31500+900x-700x-20x^2=31980[/tex]

[tex]-20x^2+200x+31500-31980=0[/tex]

[tex]20x^2-200x+480=0[/tex]

By the quadratic formula,

[tex]x=\frac{200\pm \sqrt{(-200)^2-4\times 20\times 480}}{40}[/tex]

[tex]x=\frac{200\pm \sqrt{1600}}{40}[/tex]

[tex]x=\frac{200\pm 40}{40}[/tex]

[tex]\implies x=\frac{200+40}{40}\text{ or }x=\frac{200-40}{40}[/tex]

[tex]\implies x=6\text{ or } x =4[/tex]

Hence, the new rent of each apartment, if x = 6, is $ 410,

While, if x = 4, is $ 390

Answer:

Given an unguided connected graph, an extension tree of this graph is a subgraph which is a tree that connects all vertices. A single graph may have different extension trees. We can mark a weight at each edge, which is a number that represents how unfavorable it is, and assign a weight to the extension tree calculated by the sum of the weights of the edges that compose it. A minimum spanning tree is then an extension tree with a weight less than or equal to each of the other possible spanning trees. Generalizing more, any non-directional graph (not necessarily connected) has a minimal forest of trees, which is a union of minimal extension trees of each of its related components.

Answer:

He drove approximately 478.78 km

Step-by-step explanation:

We know that,

Distance = Speed × time,

Given,

Time taken by john in driving = 3.5 hours,

His average speed = 85 mph,

So, the total distance he drove = 3.5 × 85 = 297.5 miles,

Since, 1 miles = 1.60934 km,

Thus, the total distance he drove = 1.60934 × 297.5 = 478.77865 km ≈ 478.78 km

Answer:

7257600

Step-by-step explanation:

Number of freshmen in the student council= 4

Number of sophomores in the student council= 5

Number of juniors in the student council= 6

Number of seniors in the student council= 7

Ways of choosing council members

⁴C₂×⁵C₂×⁶C₂×⁷C₂

[tex]^4C_2=\frac{4!}{(4-2)!2!}\\=\frac{24}{4}=6\\\\^5C_2=\frac{5!}{(5-2)!2!}\\=\frac{120}{12}=10\\\\^6C_2=\frac{6!}{(6-2)!2!}\\=\frac{720}{48}=15\\\\^7C_2=\frac{7!}{(7-2)!2!}\\=\frac{5040}{240}=21[/tex]

⁴C₂×⁵C₂×⁶C₂×⁷C₂=6×10×15×21=18900

Ways of lining up the four classes=4!=1×2×3×4=24

Ways of lining up members of each class=2⁴=2×2×2×2=16

Pictures are possible if each group of classmates stands​ together

⁴C₂×⁵C₂×⁶C₂×⁷C₂×4!×2⁴

=18900×24×16

=7257600

There are 453600 possible different pictures

The given parameters are:

Freshmen = 4

Sophomores = 5

Juniors = 6

Seniors = 7

Two council members are to be selected from each group.

So, the number of ways this can be done is:

n = ⁴C₂×⁵C₂×⁶C₂×⁷C₂

Apply combination formula, and evaluate the product

n = 18900

Each group are to stand together.

There are 4! ways to arrange the 4 groups.

So, the total number of pictures is:

Total = 4! * 18900

Evaluate the product

Total = 453600

Hence, there are 453600 possible different pictures

Read more about combination at:

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Answer:

Step-by-step explanation:

Given that n =30, x bar = 375 and sigma = 81

Normal distribution is assumed and population std dev is known

Hence z critical values can be used.

For 95% Z critical=1.96

Margin of error = [tex]1.96(\frac{81}{\sqrt{30} } )=29[/tex]

Confidence interval = 375±29

=(346,404)

B) 99% confidence

Margin of error = 2.59*Std error =38

Confidence interval = 375±38

=(337, 413)

C) For 90%

Margin of error = 20

Std error = 20/1.645 = 12.158

Sample size

[tex]n=(\frac{81}{12.158} )^2\\=44.38[/tex]

Atleast 44 people should be sample size.

To determine the confidence intervals for the average kilowatt-hours, a formula is used that includes the sample mean, Z-values, population standard deviation, and sample size. For a 95% confidence level, the interval is 324.95 to 425.05 kWh, and for a 99% confidence level, the interval is 311.01 to 438.99 kWh. To have a confidence level of 90% with a maximum error amount of 20kWh, the minimum sample size required is approximately 35 households.

A. Determine the interval of 95% confidence for the average kilowatt-hours for the population:

To determine the interval of 95% confidence, we can use the formula:

95% confidence interval = sample mean ± (Z-value) * (population standard deviation / √sample size)

Substituting the given values, we have:

95% confidence interval = 375 ± (1.96) * (81 / √30) = 324.95 to 425.05 kWh

B. Determine the 99% confidence interval:

Using the same formula, but with a Z-value of 2.57 (corresponding to 99% confidence), we have:

99% confidence interval = 375 ± (2.57) * (81 / √30) = 311.01 to 438.99 kWh

C. Minimum sample size for a confidence level of 90% and an error amount of 20kWh:

To determine the minimum sample size, we can rearrange the formula for the confidence interval and solve for the sample size:

Sample size = ((Z-value) * (population standard deviation / error amount))^2

Substituting the given values, we have:

Sample size = ((1.645) * (81 / 20))^2 = 34.64 or approximately 35 households

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Answer:Explained Below

Step-by-step explanation:

The given equation is similar to an ellipse which is in the form of

[tex]\frac{x^2}{a^2}[/tex]+[tex]\frac{y^2}{b^2}[/tex]=1

where

2a=length of major axis

2b=length of minor axis

Here after rearranging the given equation we get

[tex]\frac{x^2}{\frac{144}{9}}[/tex]+[tex]\frac{y^2}{\frac{144}{16}}[/tex]=1

[tex]\frac{x^2}{16}[/tex]+[tex]\frac{y^2}{9}[/tex]=1

[tex]\frac{x^2}{4^2}[/tex]+[tex]\frac{y^2}{3^2}[/tex]=1

therefore its origin is (0,0)

and vertices are[tex]\left ( \pm4,0\right )[/tex]&[tex]\left ( 0,\pm3\right )[/tex]

We can find origin by checking what is with x in the term [tex]\left ( x-something\right )^{2}[/tex]

same goes for y

for [tex]\left ( x-2\right )^{2}[/tex] here 2 is the x  coordinate of ellipse

and for vertices Each endpoint of the major axis is vertices and each endpoint of minor axis is co-vertices

Answer:

The answer is 105.5 kcal/slice of bread.

Step-by-step explanation:

The kcal per gram of:

Now, you have:

If we multiply the amount of components by his kcal:

Now gram/gram = 1, and we can cancel the grams in the equation:

Finally, the result of the kcal of the slice bread is:

Answer: There was population of  22808 in 2000.

Step-by-step explanation:

Since we have given that

Population was in 2002 = 25,570

According to question, the population in 2002 was 10% more than 2001.

So, the population in 2001 was

[tex]25570=P_1(1+\dfrac{r}{100})\\\\25570=P_1(1+\dfrac{10}{100})\\\\25570=P_1(1+0.1)\\\\25570=P_1(1.01)\\\\\dfrac{25570}{1.01}=P_1\\\\25316.8\approx 25317=P_1[/tex]

Now, we have given that

In 2001, the population in a town was 11% more than it was in 2000.

So, population in 2000 was

[tex]25317=P_0(1+\dfrac{r}{100})\\\\25317=P_0(1+\dfrac{11}{100})\\\\\25317=P_0(1+0.11)\\\\25317=P_0(1.11)\\\\P_0=\dfrac{25317}{1.11}\\\\P_0=22808[/tex]

Hence, there was population of  22808 in 2000.

Answer:   0.1342

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

[tex]P(x)=1-e^{\frac{-x}{\lambda}}[/tex], where [tex]\lambda [/tex] is the mean of the distribution.

Given : [tex]\lambda =20[/tex]

Then , the probability that the battery will last between 10 and 15 hours is given by :-

[tex]P(10<x<15)=P(15)-P(10)\\\\=1-e^{\frac{-15}{20}}-(1-e^{\frac{-10}{20}})\\\\=-e^{-0.75}+e^{-0.5}=0.13416410697\approx0.1342[/tex]

Hence, the probability that the battery will last between 10 and 15 hours = 0.1342

The probability that the battery will last between 10 and 15 hours is 18.13%.

In order to find the probability that the battery will last between 10 and 15 hours, we need to use the exponential distribution. The exponential distribution is defined by the formula P(X

For this problem, the mean is 20, so λ = 1/20. Plugging in the values, we get P(10

Therefore, the probability that the battery will last between 10 and 15 hours is 18.13%.

Looks like the integral is

[tex]\displaystyle\iint_R2(x+1)y^2\,\mathrm dA[/tex]

where [tex]R=[0,1]\times[0,3][/tex]. (The inclusion of [tex]y=3[/tex] will have no effect on the value of the integral.)

Let's split up [tex]R[/tex] into [tex]mn[/tex] equally-sized rectangular subintervals, and use the bottom-left vertices of each rectangle to approximate the integral. The intervals will be partitioned as

[tex][0,1]=\left[0,\dfrac1m\right]\cup\left[\dfrac1m,\dfrac2m\right]\cup\cdots\cup\left[\dfrac{m-1}m,1\right][/tex]

and

[tex][0,3]=\left[0,\dfrac3n\right]\cup\left[\dfrac3n,\dfrac6n\right]\cup\cdots\cup\left[\dfrac{3(n-1)}n,3\right][/tex]

where the bottom-left vertices of each rectangle are given by the sequence

[tex]v_{i,j}=\left(\dfrac{i-1}n,\dfrac{3(j-1)}n\right)[/tex]

with [tex]1\le i\le m[/tex] and [tex]1\le j\le n[/tex]. Then the Riemann sum is

[tex]\displaystyle\lim_{m\to\infty,n\to\infty}\sum_{i=1}^m\sum_{j=1}^nf(v_{i,j})\frac{1-0}m\frac{3-0}n[/tex]

[tex]\displaystyle=\lim_{m\to\infty,n\to\infty}\frac3{mn}\sum_{i=1}^m\sum_{j=1}^n\frac{18}{mn^2}(j-1)^2(i-1+m)[/tex]

[tex]\displaystyle=\lim_{m\to\infty,n\to\infty}\frac{54}{m^2n^3}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}j^2(i+m)[/tex]

[tex]\displaystyle=\frac92\lim_{m\to\infty,n\to\infty}\frac{(3m-1)(2n^3-3n^2+n)}{mn^3}[/tex]

[tex]\displaystyle=\frac92\left(\lim_{m\to\infty}\frac{3m-1}m\right)\left(\lim_{n\to\infty}\frac{2n^3-3n^2+n}{n^3}\right)=\boxed{27}[/tex]

Answer:

20 percent

Step-by-step explanation:

Total number of pieces in a puzzle = 500

No. of pieces in first container = 220

No. of pieces in second container = 180

Let no. of pieces in the third container  be x.

We get,

[tex]220+180+x=500[/tex]

On adding 220 and 180, we get

[tex]400+x=500[/tex]

On transposing 400 to RHS, we get

[tex]x=500-400=100[/tex]

Percentage of pieces in the third container = (no. of pieces in third container/total no. of pieces in a puzzle) [tex]\times 100[/tex]

[tex]=\frac{100}{500}\times 100=\frac{10000}{500}=20[/tex]

Therefore, percentage of pieces in the third container = 20 percent

Answer:

Because they have never had to express one quantity in terms of another. The idea of such a relationship is completely new, as is the vocabulary for expressing such relationships.

Step-by-step explanation:

"Function" is a simple concept that says you can relate two quantities, and you can express that relationship in a number of ways. (ordered pairs, table, graph)

The closest experience most students have with functions is purchasing things at a restaurant or store, where the amount paid is a function of the various quantities ordered and the tax. Most students have never added or checked a bill by hand, so the final price is "magic", determined solely by the electronic cash register. The relationship between item prices and final price is completely lost. Hence the one really great opportunity to consider functions is lost.

Students rarely play board games or counting games (Monopoly, jump rope, jacks, hide&seek) that would give familiarity with number relationships. They likely have little or no experience with the business of running a lemonade stand or making and selling items. Without these experiences, they are at a significant disadvantage when it comes to applying math to their world.

[tex]A\cap B=\{x:x\in A \wedge x\in B\}[/tex]

[tex]\large\boxed{A\cap B=\{a,c\}}[/tex]

Answer:

[tex]a=2 \quad \text{and} \quad b=-2[/tex]

Step-by-step explanation:

Take [tex]a=2 \quad \text{and} \quad b=-2[/tex], note that

[tex]2=(-1)\cdot(-2)[/tex]

hence b divides a. On the other hand, we have that

[tex]-2=(-1)\cdot2[/tex]

which tells us that a divides b. Moreover, [tex]a=2 \neq -2=b[/tex].

By Stokes' theorem, the integral of the curl of [tex]\vec F[/tex] across [tex]S[/tex] is equal to the integral of [tex]\vec F[/tex] along the boundary of [tex]S[/tex], call it [tex]C[/tex]. Parameterize [tex]C[/tex] by

[tex]\vec r(t)=2\cos t\,\vec\imath+2\sin t\,\vec\jmath[/tex]

with [tex]0\le t\le2\pi[/tex]. So we have

[tex]\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S=\int_C\vec F\cdot\mathrm d\vec r[/tex]

[tex]=\displaystyle\int_0^{2\pi}(10\sin t\cos 0\,\vec\imath+e^{2\cos t}\sin0\,\vec\jmath+2\cos t\,e^{2\sin t}\,\vec k)\cdot(-2\sin t\,\vec\imath+2\cos t\,\vec\jmath)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}-20\sin^2t\,\mathrm dt[/tex]

[tex]=\displaystyle-10\int_0^{2\pi}(1-\cos2t)\,\mathrm dt=\boxed{-20\pi}[/tex]

The problem makes use of Stokes' theorem to evaluate a given field over a hemisphere. We established the boundary curve of the surface and described it using a vector equation.

This problem can be solved using Stokes' theorem which asserts that the magnetic field flux through a surface is related to the circulation of the field encircling that surface. Stokes' theorem can be written in this form ∫ S curl F · dS = ∫ C F · dr. Given the field F(x, y, z) = 5y cos(z) i + ex sin(z) j + xey k and the hemisphere S defined by x² + y² + z² = 4, z ≥ 0, we need to look for its boundary curve C. C here is the circle in the xy-plane defined by x² + y² = 4, z = 0. We can describe this boundary using a vector equation r(t) = 2 cos(t) i + 2 sin(t) j + 0k with 0 ≤ t ≤ 2π.

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Answer:  (16%, 24%)

Step-by-step explanation:

The confidence interval for proportion is given by :-

[tex]p\pm E[/tex]

Given : Significance level : [tex]\alpha=1-0.95=0.05[/tex]

The proportion of the respondents answered "crime and violence." : p=0.20

Margin of sampling error : [tex]E=\pm0.04[/tex]

Now, the 95% confidence interval for the proportion of the population that would respond "crime and violence" to the question asked by the pollsters is given by :-

[tex]0.20\pm 0.04\\\\=0.20-0.04,\ 0.20+0.04\approx(0.16,0.24)[/tex]

In percentage, [tex](16\%,24\%)[/tex]

Hence, the 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters =(16%, 24%)

The 95% confidence interval for the population that would answer "crime and violence" to the poll question, given a sample proportion of 20% and a margin of error of 4%, is between 16% and 24%.

This question is about constructing a confidence interval based on poll data, a mathematical and statistical concept. The poll indicates that 20% of respondents believe the most pressing issue in the country today is "crime and violence", with a margin of error of ±4%. A 95% confidence interval for the population proportion can be constructed by adding and subtracting the margin of error from the sample proportion.

So in this case, we can calculate the low and high end of the interval as follows:

So, we can be 95% confident that the true population proportion that would respond "crime and violence" to the question lies somewhere between 16% and 24% based on this poll.

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Answer:

24 ways

Step-by-step explanation:

Two different events

1) flip a spinner with 4 different colors regions.

2) tossing a die with 6 outcomes

to calculate number of colored dots possible

note here both action are independent of each other

by the principal of counting we can say

if an act is performed in m ways and another act can be performed in n ways the both the act simultaneously can be performed in [tex]m\times n[/tex] ways.

here act 1 has m=4 ways and act n= 6 ways

hence number of ways of getting colored dots = [tex]4\times6[/tex] ways

= 24 ways

The total number of possible outcomes when flipping a spinner with 4 differently colored regions and tossing a die is 24, calculated by multiplying the number of possible outcomes from the spinner (4) and the die (6).

The subject of the question is the calculation of possible outcomes in a probability scenario involving a spinner and a die. A spinner with 4 differently colored areas can give 4 outcomes (red, white, blue, green), and tossing a die can result in 6 outcomes (1, 2, 3, 4, 5, 6).

To find the total number of possible outcomes, we simply multiply the number of possible outcomes from the spinner and the die: 4 (from the spinner) times 6 (from the die).

So, there are 24 color-dot outcomes possible when flipping a spinner with 4 differently colored areas and tossing a die.

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Answer:

I'm going to write both of these because maybe you have a fill in the blank question. I don't know.

[tex](x-4)^2+(y-5)^2=9^2[/tex]

Simplify:

[tex](x-4)^2+(y-5)^2=81[/tex]

Step-by-step explanation:

[tex](x-h)^2+(y-k)^2=r^2[/tex] is the equation of a circle with center (h,k) and radius r.

You are given (h,k)=(4,5) because that is the center.

You are given r=9 because it says radius 9.

Let's plug this in.

[tex](x-4)^2+(y-5)^2=9^2[/tex]

Simplify:

[tex](x-4)^2+(y-5)^2=81[/tex]

Answer:

(x-4)^2 + (y-5)^2 = 9^2

or

(x-4)^2 + (y-5)^2 =81

Step-by-step explanation:

The equation for a circle is (x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

(x-4)^2 + (y-5)^2 = 9^2

or

(x-4)^2 + (y-5)^2 =81

Answer:

Gold - $33, Silver - $5, Copper - $0.02

Step-by-step explanation:

Let $x be the price of one gram of gold, $y - price of 1 g of silver and $z - price of 1 g of copper.

1. The first alloy is​ 75% gold,​ 5% silver, and​ 20% copper, so in 100 g there are 75 g of gold, 5 g of silver and 20 g of copper.  If 100 g of the first alloy costs ​$2500.40​, then

75x+5y+20z=2500.40

2. The second alloy is​ 75% gold,​ 12.5% silver, and​ 12.5% copper, so in 100 g there are 75 g of gold, 12.5 g of silver and 12.5 g of copper.  If 100 g of the first alloy costs ​$2537.75​, then

75x+12.5y+12.5z=2537.75

3. The third alloy is​ 37.5% gold and​ 62.5% silver, so in 100 g there are 37.5 g of gold and 62.5 g of silver .  If 100 g of the first alloy costs ​$1550.00​, then

37.5x+62.5y=1550.00

Solve the system of three equations:

[tex]\left\{\begin{array}{l}75x+5y+20z=2500.40\\75x+12.5y+12.5z=2537.75\\37.5x+62.5y=1550.00\end{array}\right.[/tex]

Find all determinants

[tex]\Delta=\|\left[\begin{array}{ccc}75&5&20\\75&12.5&12.5\\37.5&62.5&0\end{array}\right] \|=28125\\ \\

\Delta_x=\|\left[\begin{array}{ccc}2500.40&5&20\\2537.75&12.5&12.5\\1550.00&62.5&0\end{array}\right] \|=928125\\ \\

\Delta_y=\|\left[\begin{array}{ccc}75&2500.40&20\\75&2537.75&12.5\\37.5&1550&0\end{array}\right] \|=140625\\ \\

\Delta_z=\|\left[\begin{array}{ccc}75&5&2500.40\\75&12.5&2537.75\\37.5&62.5&1550\end{array}\right] \|=562.5\\ \\[/tex]

So,

[tex]x=\dfrac{\Delta_x}{\Delta}=\dfrac{928125}{28125}=33\\ \\\\y=\dfrac{\Delta_y}{\Delta}=\dfrac{140625}{28125}=5\\ \\\\z=\dfrac{\Delta_z}{\Delta}=\dfrac{562.5}{28125}=0.02\\ \\[/tex]

Answer:

  The probability of success is 1/2.

Step-by-step explanation:

The histogram of a binomial distribution has a mode of n×p. For that to be n/2, the value of p must be 1/2.

Answer:

$15

Step-by-step explanation:

He had $20 and he spent [tex]\frac{3}{4}[/tex] of that in baseball cards, that is

[tex]20*\frac{3}{4}= \frac{20*3}{4} = \frac{60}{4} = 15.[/tex]

So, he spent $15 in baseball cards.

Answer:

No down payment = $73 267; 10 % down payment = $81 408

Step-by-step explanation:

1. With no down payment

The formula for a maximum affordable loan (A) is

A = (P/i)[1 − (1 + i)^-N]

where  

P = the amount of each equal payment

i = the interest rate per period

N = the total number of payments

Data:

     P = 500

APR = 2.83 % = 0.0283

      t = 15 yr

Calculations:

You are making monthly payments, so

i = 0.0283/12 = 0.002 358 333

The term of the loan is 15 yr, so

N = 15 × 12 = 180

A = (500/0.002 3583)[1 − (1 + 0.002 3583)^-180]

= 212 014(1 - 1.002 3583^-180)

= 212 014(1 - 0.654 424)

= 212 014 × 0.345 576

= 73 267

You can afford to spend $73 267 on a home.

2. With a 10 % down payment

Without down payment, loan = 73 267

With 10 % down payment, you pay 0.90 × new loan

           0.90 × new loan = 73 267

New loan = 73267/0.90 = 81 408

With a 10 % down payment, you can afford to borrow $81 408 .

Here’s how it works:

Purchase price =  $81 408

Less 10 % down =    -8 141

                 Loan = $73 267

And that's just what you can afford.

Answer:

251.28 cubic feet

Step-by-step explanation:

The height of the cylinder is 9.7 ft.

The base length is 7 feet. So, the radius(R) = [tex]\frac{7}{2} = 3.5 feet[/tex]

The length of 4 feet cylinder cut out. So, the radius of the cut cylinder (r) = [tex]\frac{4}{2} = 2 feet[/tex]

We have to find the volume of solid cylinder figure without cutting part.

= Volume of the whole cylinder - Volume of the hole cut

We know that volume of a cylinder is [tex]\pi *r^2*h[/tex]

Using this formula,

= [tex]\pi *R^2*h - \pi *r^2*h[/tex]

= [tex]\pi h [R^2 - r^2][/tex]

Here π = 3.14, R = 3.5, r = 2 and h = 9.7

Plug in these values in the above, we get

= [tex]3.14*9.7 [3.5^2 - 2^2]\\= 30.458[12.25 - 4]\\= 30.458[8.25]\\= 251.2785 ft^3[/tex]

When round of to the nearest hundredths place, we get

So, the volume of solid cylinder figure not including cut out= 251.28 cubic feet

The inside angle is half the outside angle.

2x +2 = 76 /2

2x +2 = 38

Subtract 2 from each side:

2x = 36

Divide both sides by 2:

x = 36 /2

x = 18

The answer is B.

Answer:

This is a stem leaf data, in which the stem generally stands for the "tens" place value while the leaf stands for the "ones" place value.

Expand the data, and find the median by finding the middle number:

10, 13, 16, 20, 21, 23, 27, 27, 28, 29, 30, 32, 33, 33, 33, 33, 38, 39, 46, 46, 46, 48

There are 22 numbers in all. To find the Median when there is a even amount of numbers, Find the two middle numbers, and find the mean of the two numbers:

(32 + 30)/2 = (62)/2 = 31

31 is your answer.

~

Answer:

A. 6.5

Step-by-step explanation:

First we find the average  [tex]\bar{x}[/tex] of the 9 data:

[tex]\bar{x} =\frac{\sum_{x=1}^{n}x_{i}}{n}[/tex]

Where n is the data number, that in this case is 9.

[tex]\bar{x} =\frac{1+ 2+ 11+ 8+ 16+ 16+20+ 16+ 18}{9}=12\\[/tex]

The formula of the standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=\sqrt{\frac{\sum_{x=1}^{n}(x_{i}-\bar{x})^{2}}{n}}[/tex]

We replace the data and find the value of the standard deviation:

[tex]\sigma=\sqrt{\frac{(1-12)^{2}+(2-12)^{2}+(11-12)^{2}+(8-12)^{2}+(16-12)^{2}+(16-12)^{2}+(20-12)^{2}+(16-12)^{2}+(18-12)^{2}}{9}}[/tex]

[tex]\sigma=\sqrt{\frac{(-11)^{2}+(-10)^{2}+(-1)^{2}+(-4)^{2}+(4)^{2}+(4)^{2}+(8)^{2}+(4)^{2}+(6)^{2}}{9}}=6,54[/tex]

We approximate the number and the solution is 6,5

Answer:

12 cm²

Step-by-step explanation:

Length of rectangle = 5.6 cm

Width of rectangle = 2.1 cm

Area of rectangle = Length of rectangle×Width of rectangle

⇒Area of rectangle = 5.6×2.1

⇒Area of rectangle = 11.76 cm²

11.76 has 4 significant figures in order to write this term in 2 significant terms we round of the term

The last digit in the decimal place is 6. Now, 6≥5 so we round the next digit to 8 we get

11.8

Now the last digit in the decimal place is 8. Now, 8≥5 so we round the next digit to 2 we get

12

∴ Hence the area of the rectangle when rounded to 2 significant figures is 12 cm²

Final answer:

To find the number of adults in the family, we need to solve the system of equations. By multiplying the first equation by 2 and subtracting it from the second equation, we can eliminate x and solve for y. Substituting the value of y back into the first equation, we can solve for x. The number of adults in the family is 3.

Explanation:

To find the number of adults in the family, we need to solve the system of equations:

Equation 1: 8x + 4y = 32

Equation 2: 16x + 12y = 72

We can solve this system by first multiplying Equation 1 by 2 to make the coefficients of x in both equations the same. This gives us:

Equation 1 (multiplied by 2): 16x + 8y = 64

Next, we can subtract Equation 1 (multiplied by 2) from Equation 2 to eliminate x:

Equation 2 - Equation 1 (multiplied by 2): (16x + 12y) - (16x + 8y) = 72 - 64

Simplifying the equation, we get:

4y = 8

Dividing both sides by 4, we find:

y = 2

So, there are 2 children in the family. Substituting this value back into Equation 1, we can solve for x:

8x + 4(2) = 32

8x + 8 = 32

8x = 24

Dividing both sides by 8, we find:

x = 3

Therefore, there are 3 adults in the family.

Answer: 0.1061

Step-by-step explanation:

Given : An insurance company found that 9% of drivers were involved in a car accident last year.

Thus, the probability of drivers involved in car accident last year = 0.09

The formula of binomial distribution :-

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

If seven (n=7) drivers are randomly selected then , the probability that exactly two (x=2) of them were involved in a car accident last year is given by :-

[tex]P(X=2)=^7C_2(0.09)^2(1-0.09)^{7-2}\\\\=\dfrac{7!}{2!5!}(0.09)^2(0.91)^{5}=0.106147867882\approx0.1061[/tex]

Hence, the required probability :-0.1061

Answer: 0.0031

Step-by-step explanation:

Binomial distribution formula :-

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of x successes in the n independent trials of the experiment and p is the probability of success.

Given : A binomial probability experiment is conducted with the given parameters.

[tex]n=9,\ p=0.8,\ x\leq3[/tex]

Now, [tex]P(x\leq3)=P(3)+P(2)+P(1)+P(0)[/tex]

[tex]=^9C_3(0.8)^3(1-0.8)^{9-3}+^9C_2(0.8)^2(1-0.8)^{9-2}+^9C_1(0.8)^1(1-0.8)^{9-1}+^9C_0(0.8)^0(1-0.8)^9\\\\=\dfrac{9!}{3!6!}(0.8)^3(0.2)^6+\dfrac{9!}{2!7!}(0.8)^2(0.2)^7+\dfrac{9!}{1!8!}(0.8)(0.2)^8+\dfrac{9!}{0!9!}(0.2)^9=0.003066368\approx0.0031[/tex]

Hence,  [tex]P(x\leq3)=0.0031[/tex]