A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000. To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245. Can you conclude that the mean monthly rent in the city is less than $1000

Answer:

8 ten dollar bills

20 fifty dollar bills

Step-by-step explanation:

x = number of 10 dollar bills

y = number of 50 dollar bills

x+y = 28

10x+50y = 1080

Multiply the first equation by -10

-10x -10y = -280

Add this to the second equation

-10x -10y = -280

10x+50y = 1080

-----------------------

 40y = 800

Divide by 40

40y/40 = 800/40

y = 20

Now find x

x+y =28

x+20 = 28

x = 28-20

x= 8

Answer:

Does the answer help you

Answer:

Option d (7.84 or less) is the right alternative.

Step-by-step explanation:

Given:

[tex]\sigma^2=1936[/tex]

[tex]\sigma = \sqrt{1936}[/tex]

   [tex]=44[/tex]

Random sample,

[tex]n = 121[/tex]

The level of significance,

= 0.95

or,

[tex](1-\alpha) = 0.95[/tex]

        [tex]\alpha = 1-0.95[/tex]

[tex]Z_{\frac{\alpha}{2} } = 1.96[/tex]

hence,

The margin of error will be:

⇒ [tex]E = Z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )[/tex]

By putting the values, we get

        [tex]=1.96(\frac{44}{\sqrt{121} } )[/tex]

        [tex]=1.96(\frac{44}{11} )[/tex]

        [tex]=1.96\times 4[/tex]

        [tex]=7.84[/tex]    

Answer:

Since points T, R, and P are all present on plane B, the answer is A.

Points T, R, and P define plane B

We have given that,

A. plane B

B. line e

C. line segment PR⎯⎯⎯⎯⎯⎯⎯

D. plane M

We have to determine the Points T, R, and P, define

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.

Since points T, R, and P are all present on plane B, the answer is A

Points T, R, and P define plane B.

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Answer:

Step-by-step explanation:

The reasons for each statement are inside the parentheses

1. <1 and <2 are complementary (given)

2. m<1 + m<2 = 90° (definition of complementary angles)

3. m<2 = 74° (given)

4. m<1 + 74° = 90° (Substitution)

5. m<1 = 16° (Subtraction property of equality)

This is gotten by subtracting 74° from both sides as follows:

m<1 + 74° - 74° = 90° - 74°

m<1 = 16°

Answer:

graph C

Step-by-step explanation:

Amanda needs to have a score higher than 86 on her final.

That means she can't get lower than 86 (Obviously) but not even an 86.

It has to be higher than 86 for her to pass

Let x represent Amanda's score

[tex]x>86[/tex]

Bolded dots on graphs mean that she can have a 86 but if it's not a bolded dot she can have either higher or lower

Just keep that in mind

The answer will be C. because it describes Amanda's score higher than 86

Answer:

c

Step-by-step explanation:

Answer:

650 calls

Step-by-step explanation:

so since you have 18$ per month plus 5 cents per call you would do

18+0.5n(n represent the number of calls)= the total fee of $50.50 cents.

thus,now you need to figure out how much the phone calls were without the monthly fee so you would do:

50.50-18=32.50

so 32.50 is the price of all the phone calls

then you divide 32.50 by 0.05 which equals to 650

meaning that n=650

hope I helped!

Answer:

D.

Step-by-step explanation:

The required inequality is given as x ≥ 100 as the water boils at 100°C and above, Option B is correct.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
As given in the question,
Water boils at 100°C and above,
So let x be the temperature of the water,
And according to the condition,
x ≥ 100° C

Thus, the inequality x ≥ 100 is shown in option B.

Thus, the required inequality is given as x ≥ 100 as the water boils at 100°C and above, and Option B is correct.

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Answer:

[tex]y \: \alpha \: {x}^{3} \ \\ y \: = k {x}^{3} \\ where \: y = 7 \: and \:x = 3 \\ y = k {x}^{3} \\ 7 = k ( {3)}^{3} \\ 7 = 27k \\ k = \frac{7}{27} \\ \\ so \: \: y = \frac{7}{27} {x}^{3} \\ \\ y = \frac{7}{27} {4}^{3} \\ y = \frac{448}{27} [/tex]

the required value of y at x = 4 is 16.64.

Given that,
y varies directly as the cube of x. When x = 3, then y = 7.To determine the y when x = 4.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.

Here,
y is directly proportional to the cube of x i.e
y ∝ x³
y = kx³   - - - - - (1)
where k is proportionality constant,
At x = 3 y = 7
7 = k (3)³
7 / 27 = k
k = 0.26
Put k in equation 1

y = 0.26 x³
Now at x = 4
y = 0.26 * 4³
y = 0.26 * 64
y =  16.64

Thus, the required value of y at x = 4 is 16.64.

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The required equation of the line is y = [x]+2

From the graph shown, we can see that the line dotted points forms a straight line. We are to find the required equation of the line formed.

The formula for calculating the equation of a straight line is expressed as

y = mx+b where

m is the slope b is the y-intercept

Get the slope 'm'

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the coordinate points (2, 0) and (4, 2)

[tex]m=\frac{2-0}{4-2}\\m=\frac{2}{2}\\m=1[/tex]

Get the y-intercept 'b'

Substitute m = 1 and (2, 0) into y = mx+b as shown;

[tex]2=1(0)+b\\2=0+b\\b=2[/tex]

Get the required equation. Recall that y = mx+b, hence;

[tex]y = 1x + 2\\y=x+2[/tex]

Hence the required equation of the line is y = [x]+2

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Answer:

The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )

Step-by-step explanation:

Conducting an F-test to determine association between race and average age at marriage

step 1 : State the hypothesis

H0 : ц1 = ц2 = ц3

Ha : ц1 ≠ ц2 ≠ ц3

step 2 : determine the mean square between

Given mean value of all groups = 23.33

SS btw = 113*(25.39 - 23.33)² +  904*(22.99 - 23.33)² + 144*(23.89 - 23.33)^2            = 113(4.2436) + 904(0.1156) + 144(0.3136)

= 629.1876

hence:  df btw = 3 - 1 = 2

             df total = 1161 - 1 = 1160

              df within = 1160 - 2 = 1158

              SS within = 36.87*1158 = 42695.46

Therefore the MS between =  629.19 / 2 = 314.60

The F-ratio = 314.59 / 36.87 = 8.53

using the values for Btw the P-value = 0.00021

The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )

9514 1404 393

Answer:

  26 players to start; 21 players after 5 withdrew

Step-by-step explanation:

We are told that the withdrawing players did not play against each other, so the total number of games they played was 5×2 = 10. Then the number of games played by the remaining players was 220 -10 = 210. When n players play each other, they play a total of n(n -1)/2 games. Here, that total is 210, so we have ...

  n(n -1)/2 = 210

  n^2 -n = 420 . . . . . . . . .multiply by 2

  (n -1/2)^2 = 420.25 . . . . add 0.25 to complete the square

  n = 1/2 +√420.25 = 0.5 +20.5 = 21 . . . . . square root and add 1/2

The number of participating players after 5 withdrew was 21. There were 26 players to start.

Answer:

0.03

Step-by-step explanation:

Using the z-distribution, it is found that the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).

The confidence interval is:

[tex]\overline{x} \pm zs[/tex]

In which:

In this problem, we are given that z = 2.576, s = 0.0407. The sample mean is the difference of the proportions, hence:

[tex]\overline{x} = \frac{28}{162} - \frac{82}{272} = -0.129[/tex]

Then, the bounds of the interval are given by:

[tex]\overline{x} - zs = -0.129 - 2.576(0.0407) = -0.234[/tex]

[tex]\overline{x} + zs = -0.129 + 2.576(0.0407) = -0.024[/tex]

The 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).

More can be learned about the z-distribution at https://brainly.com/question/25890103

9514 1404 393

Answer:

  69.1 ft

Step-by-step explanation:

The diameter of the circle is 24 ft. The length of the arc is more than twice the diameter, so cannot be less than about 50 ft. The only reasonable choice is ...

  69.1 ft

__

The circumference of the circle is ...

  C = 2πr = 2(3.14)(12 ft) = 75.36 ft

The arc length of interest is 330° of the 360° circle, so is 330/360 = 11/12 times the circumference.

  s = (11/12)(75.36 ft) = 69.08 ft ≈ 69.1 ft

Answer:D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve for y:

[tex]2y-3x=10\\2y=3x+10\\y=\frac{3}{2} x+5[/tex]

Therefore:

y = 3/2x + 5

m = 3/2

b = 5

Graph below courtesy of Desmos.

Answer:

2×2×3×3

Step-by-step explanation:

Answer:

2×2×3×3

Step-by-step explanation:

36=3×12

12=3×4

4=2×2

=3×3×2×2

Hope this helps! <3

Answer:

C

Step-by-step explanation:

C is the only function that have a consistent decrease while A is a trigonometric function, B is a non linear function, D is an exponential function

Answer:

3

Step-by-step explanation:

2(4x-3)-8=4+2x

8x - 6 - 8 = 4 + 2x

8x - 2x = 4 + 6 + 8

6x = 18

x = 18/6

x = 3

Answer:

[tex]2(4x - 3) - 8 = 4 + 2x \\ 2 \times 4x + 2 \times - 3 - 8 = 4 + 2x \\ according \: to \: bodmas \: first \: \times then + or - \\ so \\ 8x - 6 - 8 = 4 + 2x \\ 8x - 14 = 4 + 2x \\ 8x - 2x = 4 + 14 \\ 6x = 18 \\ x = \frac{18}{6} \\ x = 3 \\ thank \: you[/tex]

Recall that

[tex]\sin(x)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex]

Differentiating the power series series for y(x) gives the series for y'(x) :

[tex]y(x)=\displaystyle\sum_{n=0}^\infty a_nx^n \implies y'(x)=\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]

Now, replace everything in the DE with the corresponding power series:

[tex]y'-2xy = 6\sin(3x) \implies[/tex]

[tex]\displaystyle\sum_{n=0}^\infty (n+1)a_{n+1}x^n - 2\sum_{n=0}^\infty a_nx^{n+1} = 6\sum_{n=0}^\infty(-1)^n\frac{(3x)^{2n+1}}{(2n+1)!}[/tex]

The series on the right side has no even-degree terms, so if we split up the even- and odd-indexed terms on the left side, the even-indexed [tex](n=2k)[/tex] series should vanish and only the odd-indexed [tex](n=2k+1)[/tex] terms would remain.

Split up both series on the left into even- and odd-indexed series:

[tex]y'(x) = \displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} + \sum_{k=0}^\infty (2k+2)a_{2k+2}x^{2k+1}[/tex]

[tex]-2xy(x) = \displaystyle -2\left(\sum_{k=0}^\infty a_{2k}x^{2k+1} + \sum_{k=0}^\infty a_{2k+1}x^{2k+2}\right)[/tex]

Next, we want to condense the even and odd series:

• Even:

[tex]\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2k+2}[/tex]

[tex]=\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2(k-1)+1}x^{2k}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2k-1}x^{2k}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty \bigg((2k+1)a_{2k+1} - 2a_{2k-1}\bigg)x^{2k}[/tex]

• Odd:

[tex]\displaystyle \sum_{k=0}^\infty 2(k+1)a_{2(k+1)}x^{2k+1} - 2\sum_{k=0}^\infty a_{2k}x^{2k+1}[/tex]

[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2(k+1)}-2a_{2k}\bigg)x^{2k+1}[/tex]

[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1}[/tex]

Notice that the right side of the DE is odd, so there is no 0-degree term, i.e. no constant term, so it follows that [tex]a_1=0[/tex].

The even series vanishes, so that

[tex](2k+1)a_{2k+1} - 2a_{2k-1} = 0[/tex]

for all integers k ≥ 1. But since [tex]a_1=0[/tex], we find

[tex]k=1 \implies 3a_3 - 2a_1 = 0 \implies a_3 = 0[/tex]

[tex]k=2 \implies 5a_5 - 2a_3 = 0 \implies a_5 = 0[/tex]

and so on, which means the odd-indexed coefficients all vanish, [tex]a_{2k+1}=0[/tex].

This leaves us with the odd series,

[tex]\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1} = 6\sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}[/tex]

[tex]\implies 2(k+1)a_{2k+2} - 2a_{2k} = \dfrac{6(-1)^k}{(2k+1)!}[/tex]

We have

[tex]k=0 \implies 2a_2 - 2a_0 = 6[/tex]

[tex]k=1 \implies 4a_4-2a_2 = -1[/tex]

[tex]k=2 \implies 6a_6-2a_4 = \dfrac1{20}[/tex]

[tex]k=3 \implies 8a_8-2a_6 = -\dfrac1{840}[/tex]

So long as you're given an initial condition [tex]y(0)\neq0[/tex] (which corresponds to [tex]a_0[/tex]), you will have a non-zero series solution. Let [tex]a=a_0[/tex] with [tex]a_0\neq0[/tex]. Then

[tex]2a_2-2a_0=6 \implies a_2 = a+3[/tex]

[tex]4a_4-2a_2=-1 \implies a_4 = \dfrac{2a+5}4[/tex]

[tex]6a_6-2a_4=\dfrac1{20} \implies a_6 = \dfrac{20a+51}{120}[/tex]

and so the first four terms of series solution to the DE would be

[tex]\boxed{a + (a+3)x^2 + \dfrac{2a+5}4x^4 + \dfrac{20a+51}{120}x^6}[/tex]

Answer:

m∠F = 45°

Step-by-step explanation:

Notice the lengths of the given sides and the right angle. This is enough information to prove that this is a 45-45-90 triangle, or just basically a square cut diagonally.

Regardless if even just one side is given for a 45-45-90 triangle, all 45-45-90 triangles have one thing in common. The sides that form the right angle are equivalent and the hypotenuse is equal to one of the sides that form the right angle times the square root of two. I'm aware that it sounded confusing, as I'm awful at explaining, so just look at the picture I've attached instead of trying to understand my explanation that seemed like trying to learn a second language.

Look at the picture. See that FD = x times that square root of 2 and that DE = x. Now look back at your picture. It's connecting, now isn't it?

Now that we know that this is indeed a 45-45-90 triangle, we can confirm that m∠F = 45°

Answer:

Step-by-step explanation:

10 = 2*5

35 = 5*7

40 = 2*2*2*5

The number 5 is common to all three  factorisations

So the HCF = 5.

Continued division:

10 and 35:

 10) 35(3

       30

          5)10(2

              10

                0

- so the HCF of 10 and 35 is 5.

10 and 40:

10)40( 4

     40

        0  

So the HCF of 10 and 40 is 10

We found HCF of 10 and 35 is 5 so:

HCF of 10, 35 and 40 is HCF of 5 and 10 which is 5.  

Answer:

554.7

Step-by-step explanation:

The pay=25.8*14+(25.8)*5*1.5=554.7

Answer:

A = 800, B = 200, C = 400 Andy D = 400

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

70 because as the number of trials increase, the actual ratio of outcomes will converge on the expected ratio.

Answer:

1 and 5 sevenths of a bag

Step-by-step explanation:

2/7 males half to it takes 4/7 to make a full one multiply 4 by 3 and you get 12/7 so that makes 1 and 5/7

Answer:

The angles are 45 and 135

Step-by-step explanation:

The two angles form a straight line, which is 180 degrees

c+ 3c = 180

4c = 180

Divide by 4

4c/4 =180/4

c = 45

3c = 3(45) = 135

The angles are 45 and 135

Answer:

45 and 135 ...

Answer:

The expected number of offspring is 2

Step-by-step explanation:

The given parameters can be represented as:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.24} & {0.25} & {0.19} & {0.17} & {0.15} \ \end{array}[/tex]

Required

The expected number of offspring

This implies that we calculate the expected value of the function.

So, we have:

[tex]E(x) = \sum x * P(x)[/tex]

Substitute known values

[tex]E(x) = 0 * 0.24 + 1 * 0.25 + 2 * 0.19+ 3 * 0.17 + 4 * 0.15[/tex]

Using a calculator, we have:

[tex]E(x) = 1.74[/tex]

[tex]E(x) = 2[/tex] --- approximated

Answer:

I think the answer is B. 65%