The average size of single-family homes in the U.S. is 2,390 square feet. A random sample of 100 homes in California yielded the mean of 2,507 square feet and the standard deviation of 257 square feet. Do the sample data provide sufficient evidence to conclude that the mean size of California homes exceeds the national average? Test using significance level of 0.01. (7 Points)

Answer:

[tex]\displaystyle \frac{118}{125}[/tex]

Step-by-step explanation:

Trigonometry

Calculate

[tex]\sin (3\sin^{-1}(2/5))[/tex]

We use the formula for the sine of triple angle:

[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]

And recall:

[tex]\sin \sin^{-1}x=x[/tex]

For this problem, we set:

[tex]x=\sin^{-1}(2/5)[/tex]

Thus:

[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]

[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]

[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]

Answer:

6 mph

Step-by-step explanation:

the cars acceleration was

6mph

Answer:

 Standard error (S.E) =  0.048  ≅ 0.05

Step-by-step explanation:

Explanation:-

Given  sample size 'n'=76

Given the dean who randomly selects 76 students and finds that 58 out of 76 are receiving financial aid.

Sample proportion

                         [tex]p = \frac{x}{n} = \frac{58}{76} = 0.7631[/tex]

The standard error is determined by

                     [tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]

                     [tex]S.E = \sqrt{\frac{0.763(0.2369}{76} }[/tex]

  Standard error is 0.048  ≅ 0.05

Answer for #5:

L=2,6,f=-2,6 ,m=3,1 ,g=-3,1 ,n=6,3 ,h=-6,3

Answer:

b

Step-by-step explanation:

Answer:

132

Step-by-step explanation:

132

Step-by-step explanation:

First, find how many beats are in a minute by creating a proportion:

\frac{11}{5} = \frac{x}{60}

Cross multiply and solve for x:

5x = 660

x = 132

So, there are 132 beats in one minute.

This means the constant of proportionality is 132.

Answer:

132

Step-by-step explanation:

9514 1404 393

Answer:

  f(x) = x³ -5x² +2x +8

Step-by-step explanation:

If the function has a zero of p, then it has a factor of (x-p). The polynomial of least degree will only have factors corresponding to the given zeros:

  f(x) = (x -(-1))(x -2)(x -4)

  = (x +1)(x -2)(x -4)

  = (x² -x -2)(x -4)

  f(x) = x³ -5x² +2x +8

Answer:

16428 oranges

Explanation:

Total yield = number of trees × number of oranges in each tree

Initial yield = 600×24= 14400 oranges

To find the equation needed, let x = additional trees and y= total yield

Number of trees = 24 +x

Number of oranges in each tree = 600-12x

Equation of total yield y= (24+x)(600-12x)

y= 14400-288x+600x-12x²

y= -12x²+312x+14400

Using a graphing calculator, from the graph drawn for this quadratic equation, we notice that it is a parabola. Therefore to find the maximum value, we should find the maximum point which is at the vertex of the parabola, we use the formula x= -b/2a

A quadratic equation is such: ax²+bx+c

Therefore x =-312/2×-12

x= -312/-24

x= 13

So we can conclude that in order to maximise oranges from the trees, the person needs to plant an additional 13 trees. Substituting from the above:

24+x=24+13= 37 trees in total

y= -12x²+312x+14400= -12×13²+312×13+14400= -2028+4056+14400

=16428 oranges in total yield

The number of trees that gives the most yield is 37

The given parameters are:

Represent the additional number of trees with x.

So, we have:

The equation that represents the total yield (y) becomes

[tex]y = (24 + x) \times (600 - 12x)[/tex]

Expand

[tex]y= 14400-288x+600x-12x\²[/tex]

Evaluate the like terms

[tex]y= 14400+312x-12x\²[/tex]

Rewrite as:

[tex]y= -12x\²+312x+14400[/tex]

Differentiate

[tex]y'= -24x+312[/tex]

Set to 0

[tex]-24x+312 = 0[/tex]

Solve for x

[tex]-24x=-312[/tex]

[tex]x=13[/tex]

Recall that:

Trees per acre = 24 + x

This gives

[tex]Trees = 24 + 13[/tex]

[tex]Trees = 37[/tex]

Hence, the number of trees that gives the most yield is 37

Read more about quadratic functions at:

https://brainly.com/question/11631534

Answer:

2 books

Step-by-step explanation:

8 x 6 = 48

Step-by-step explanation

2.5 cups = 5servings

x cups = 8servings

2.5*8 = 5*x

20 = 5x

divide both sides by the coefficient of x

20/5 = 5x/5

4 = x

i.e x = 4

It's like walking but faster, so you go faster like sonic lol.

Answer: (7t)/(y+v)

All work is in the picture below:

Answer:

B. Function F is odd

Step-by-step explanation:

If a function is odd, then -f(x) = f(-x), for all values of x.

For such function an origin symmetry is obtained just like the image uploaded.

Also, for such function, there is an equal distance between f(x) and f(-x), just like the image uploaded (d₁ = d₂).

Thus, the correct option is "B"

Step-by-step explanation:

Triangles WXY and RPY are congruent.

Since letters X and P are both the 2nd letter in their respective triangles, angle X = angle P (A).

Answer:

“A systematic arrangement” of data in rows and columns is called Table.

Explanation: A table is used to arrange data in rows and columns

Answer:

y=4 and x=0

Step-by-step explanation:

4(5y-20)+3y=12

20y-80+3y=12

23y-80=12

23y=92

y=4

Substitute y as 4 to get x.

Answer:

y=4

x=0

Step-by-step explanation:

4x + 3y = 12

X - 5y =-20

Multiply second equation by 4

4x + 3y = 12

4x - 20y = - 80

Subtract

23y = 92

y = 92/23

y =4

Put the value in first equation

4x + 12 =12

So 4x = 0

Therefore x= 0

Answer:

6/7

Step-by-step explanation:

you already have a common denominator, so 4/7 plus 2/7 is 6/7

Answer:

[tex]\boxed{\frac{6}{7} }[/tex]

Step-by-step explanation:

[tex]\frac{4}{7} + \frac{2}{7}[/tex]

[tex]= \frac{4 + 2}{7}[/tex]

[tex]= \frac{6}{7}[/tex]

Answer:

40+2+0.1

Step-by-step explanation:

Answer:

Ethan sold more

Step-by-step explanation:

2/3 and 1/4

Simplify to 8/12 and 4/12

8/12 is more

Answer:

4 x [tex]\frac{3}{2}[/tex] = 6

Step-by-step explanation:

The division equation would be 4 divided by 2/3, but that is equal to 4 x 3/2 = 6.

Hope it helps! (I'm so sorry if it's wrong).

Answer:

2.66

Step-by-step explanation:

2/3 of 4 is the same as:

2/3 * 4 = (2/3) * (4/1)

By the rules for multiplying fractions, this is (2*4) / (3*1) = 8/3

8/3 is 2.66

Answer:

2. unlikely

Step-by-step explanation:

The probability of rolling a 2 is 1/6, 0r 0.1666...  .

Probabilities and their meanings:

0   -   impossible

between 0 and 0.5   -   from unlikely to almost as likely as not

0.5   -   as likely as not

between 0.5 and 1   -   from as likely as not to almost certain

1   -   certain

This probability is 0.1666... which is in the category from 0 to 0.5. It is closer to 0 than to 0.5, so although it is not impossible, it is unlikely.

Answer: 2. unlikely

Step-by-step explanation:

f(x) = x

g(x) =3x

point if intersection

f(x) =g(x)

x = 3x

Answer:

3,510

Step-by-step explanation:

3,511.1 is closer to 3,510 than it is to 3,520

Answer:

yellow 9/25

yellow and green is 14/25

Using it's concept, it is found that the probabilities are given as follows:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 9 out of 25 are yellow, then 5 out of 24 will be green, hence:

P(yellow, then green) = 9/25 x 5/24 = 45/(25 x 24) = 0.075 = 7.5%.

For both blue, we have that they are, respectively, 6 out of 25 and 5 out of 24, hence:

P(both blue) = 6/25 x 5/24 = 30/(25 x 24) = 0.05 = 5%.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ2

Answer: x = -2/3

[tex]\frac{x}{x+2}- \frac{4}{x-2}=1\\\\<=>\frac{x(x-2)}{(x+2)(x-2)}-\frac{4(x+2)}{(x+2)(x-2)}=1\\\\\\<=>\frac{x(x-2)-4(x+2)}{(x-2)(x+2)}=1\\\\\\=>x(x-2)-4(x+2)=(x-2)(x+2)\\\\\\<=> x^{2} -2x-4x-8=x^{2} -4\\\\\\<=>-6x-8=-4\\\\\\<=>-6x=8-4\\\\\\<=>-6x=4\\\\\\<=>x=-4/6=-2/3[/tex]

Step-by-step explanation:

Step-by-step explanation:

x+y=17 (First equation)

x-y=3 (Second equation)

Solving Equation (i)

x+y=17

x=17-y(First equation)

Putting value of x in equation (ii)

x-y=3

x=3+y

17-y=3+y

17=3+y+y

17=3+2y

2y=17-3

y=14/2

y=7

Putting value of y in equation(i)

x=17-y

x=17-7

x=10