what is the constant of proportionality for 4y=16

Answer:

0.0668 or 6.68%

Step-by-step explanation:

Variance (V) = 10,000

Standard deviation (σ) = √V= 100

Mean score (μ) = 500

The z-score for any test score X is:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = 650:

[tex]z=\frac{650-500}{100}\\z=1.5[/tex]

A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]

The probability is 0.0668 or 6.68%

The probability that he or she will make a score of 650 or more is 0.0668.

Let X = Scores made on a certain aptitude test by nursing students

X follows normal distribution with mean = 500 and variance of 10,000.

So, standard deviation = [tex]\sqrt{10000}=100[/tex].

z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].

The probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]

Learn more: https://brainly.com/question/14109853

Answer:

Step-by-step explanation:

The formula of a slope:

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

We have

[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]

Substitute:

[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]

The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:

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

We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:

[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]

[tex]=\dfrac{14}{7}=2[/tex]

The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!

Complete Question

If w'(t) is the rate of growth of a child in pounds per year, what does

[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  represent?

a) The change in the child's weight (in pounds) between the ages of 4 and 7.

b) The change in the child's age (in years) between the ages of 4 and 7.

c) The child's weight at age 7.

d) The child's weight at age 4. The child's initial weight at birth.

Answer:

The correct option is  option a

Step-by-step explanation:

From the question we are told that

       [tex]w'(t)[/tex] represents the rate of growth of a child in   [tex]\frac{pounds}{year}[/tex]

So      [tex]{w'(t)} \, dt[/tex]  will be in  [tex]pounds[/tex]

Which then mean that this  [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  the change in the weight of the child between the ages of  [tex]4 \to 7[/tex] years

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer:

(0,-2)

Step-by-step explanation:

The y-intercept is simply when the function touches or crosses the y-axis.

We're told that the graph crosses the y-axis at -2. In other words, the y-intercept is at -2.

The ordered pair would be (0,-2)

Answer:

49.923 mph

Step-by-step explanation:

we know that the car traveled 133 miles in h hours at an average speed of x mph.

That is, xh = 133.

We can also write this in terms of hours driven: h = 133/x.

If x was 30 mph faster, then h would be one hour less.

That is, (x + 30)(h - 1) = 133, or h - 1 = 133/(x + 30).

We can rewrite the latter equation as h = 133/(x + 30) + 1

We can then make a system of equations using the formulas in terms of h to find x:

h = 133/x = 133/(x + 30) + 1

133/x = 133/(x + 30) + (x + 30)/(x + 30)

133/x = (133 + x + 30)/(x + 30)

133 = x*(133 + x + 30)/(x + 30)

133*(x + 30) =  x*(133 + x + 30)

133x + 3990 = 133x + x^2 + 30x

3990 = x^2 + 30x

x^2 + 30x - 3990 = 0

Using the quadratic formula:

x = [-b ± √(b^2 - 4ac)]/2a  

= [-30 ± √(30^2 - 4*1*(-3990))]/2(1)  

= [-30 ± √(900 + 15,960)]/2

= [-30 ± √(16,860)]/2

= [-30 ± 129.846]/2

= 99.846/2  -----------  x is miles per hour, and a negative value of x is neglected, so we'll use the positive value only)

= 49.923

Check if the answer is correct:

h = 133/49.923 = 2.664, so the car took 2.664 hours to drive 133 miles at an average speed of 49.923 mph.

If the car went 30 mph faster on average, then h = 133/(49.923 + 30) = 133/79.923 = 1.664, and 2.664 - 1 = 1.664.

Thus, we have confirmed that a car driving 133 miles at about 49.923 mph would have arrive precisely one hour earlier by going 30 mph faster

Answer:

The answer is 15.6/31 or 1/2

Step-by-step explanation:

The data in the question is sufficient to find an answer for it.

1. I look at the temperature and rainfall chart for Brighton, United Kingdom.

2. Check for rainy season and dry season.

3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.

4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.

The number of rainfall days is 15.6 and we know there are 31 days in July.

If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5

Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.

In fraction, 0.5 = 1/2

Answer:

the probability that one parachute of the  five parachute is damaged is 0.156

Step-by-step explanation:

From the given information;

Let consider X to be the altitude above the  ground that a parachute opens

Then; we can posit that the probability that the parachute is damaged is:

P(X ≤ 100 )

Given that the population mean μ = 155

the standard deviation σ = 30

Then;

[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]

[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]

[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]

From standard normal tables

[tex]P(X \leq 100 ) = 0.0334[/tex]

Hence; the probability of the given parachute damaged is 0.0334

Let consider Q to be the dropped parachute

Given that the number of parachute be n= 5

The probability that the parachute opens in each trail be  p = 0.0334

Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334

The probability mass function is:

Q [tex]\sim[/tex] B(5, 0.0334)

Similarly; the event that one parachute is damaged is :

Q ≥ 1

P( Q ≥ 1 ) = 1 - P( Q < 1 )

P( Q ≥ 1 ) = 1 - P( Y = 0 )

P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )

P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = 1 -  0.8437891838

P( Q ≥ 1 ) = 0.1562108162

P( Q ≥ 1 ) [tex]\approx[/tex] 0.156

Therefore; the probability that one parachute of the  five parachute is damaged is 0.156

Answer:

In Table C, y vary inversely with x.

1×18 = 18

2×9 = 18

3×6 = 18

18 = 18 = 18

Step-by-step explanation:

We are given four tables and asked to find out in which table y vary inversely with x.

We know that an inverse relation has a form given by

y = k/x

xy = k

where k must be a constant

Table A:

x     |      y

1     |      3

2     |     9

3     |    27

1×3 = 3

2×9 = 18

3×27 = 81

3 ≠ 18 ≠ 81

Hence y does not vary inversely with x.

Table B:

x     |      y

1     |     -5

2     |     5

3     |    15

1×-5 = -5

2×5 = 10

3×15 = 45

-5 ≠ 10 ≠ 45

Hence y does not vary inversely with x.

Table C:

x     |      y

1     |      18

2     |     9

3     |     6

1×18 = 18

2×9 = 18

3×6 = 18

18 = 18 = 18

Hence y vary inversely with x.

Table D:

x     |      y

1     |      4

2     |     8

3     |    12

1×4 = 4

2×8 = 16

3×12 = 36

4 ≠ 16 ≠ 36

Hence y does not vary inversely with x.

Answer:

[tex] S.A = 246.6 in^2 [/tex]

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface area

[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]

[tex] = 81 + 18*9.2 [/tex]

[tex] = 81 + 165.6 [/tex]

[tex] S.A = 246.6 in^2 [/tex]

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

33800

Step-by-step explanation:

100 x 338 = 33800

Answer:

33800

Step-by-step explanation:

338x10=3380 then 3380x10=33800

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Good luck with your assignment...

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer:

The probability that no more than 70% would prefer to start their own business is 0.1423.

Step-by-step explanation:

We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let [tex]\hat p[/tex] = sample proportion of people who prefer to start their own business

The z-score probability distribution for the sample proportion is given by;

                               Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion who would prefer to start their own business = 72%

            n = sample of 18-29 year-olds = 600

Now, the probability that no more than 70% would prefer to start their own business is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%)

       P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.07) = 1 - P(Z < 1.07)

                                                                       = 1 - 0.8577 = 0.1423

The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.

Answer: 680

Step-by-step explanation:

When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Given: Total participants = 17

From these, a group of 3 participants is to be tested under a special condition.

Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]

[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]

Hence, there are 680 groups of 3 participants can  be chosen,.

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

Answer: Pi multiplied by the diameter of the circle

Step-by-step explanation:

Answer:

The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].

Answer:

cars are dum

Step-by-step explanation:

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Answer:

(H1, T1)

Step-by-step explanation:

Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).

Answer:

D. (H1, T1)

Step-by-step explanation:

Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is

D. (H1, T1)

Answer:

z(c)  = - 1,64

We reject the null hypothesis

Step-by-step explanation:

We need to solve a proportion test ( one tail-test ) left test

Normal distribution

p₀ = 63 %

proportion size  p = 51 %

sample size  n = 114

At 5% level of significance   α = 0,05, and with this value we find in z- table z score of z(c) = 1,64  ( critical value )

Test of proportion:

H₀     Null Hypothesis                        p = p₀

Hₐ    Alternate Hypothesis                p < p₀

We now compute z(s) as:

z(s) =  ( p - p₀ ) / √ p₀q₀/n

z(s) =( 0,51 - 0,63) / √0,63*0,37/114

z(s) =  - 0,12 / 0,045

z(s) = - 2,66

We compare z(s) and z(c)

z(s) < z(c)      - 2,66 < -1,64

Therefore as z(s) < z(c)  z(s) is in the rejection zone we reject the null hypothesis

Answer:

8lb of the cheaper Candy

17.5lb of the expensive candy

Step-by-step explanation:

Let the cheaper candy be x

let the costly candy be y

X+y = 25.5....equation one

2.2x +7.3y = 25.5(5.7)

2.2x +7.3y = 145.35.....equation two

X+y = 25.5

2.2x +7.3y = 145.35

Solving simultaneously

X= 25.5-y

Substituting value of X into equation two

2.2(25.5-y) + 7.3y = 145.35

56.1 -2.2y +7.3y = 145.35

5.1y = 145.35-56.1

5.1y = 89.25

Y= 89.25/5.1

Y= 17.5

X= 25.5-y

X= 25.5-17.5

X= 8

Answer:

Part A- 6

Part B- 3

Part C- 3/22100

Step-by-step explanation:

Part A-

Use the permutation formula and plug in 3 for n and 2 for k.

nPr=n!/(n-k)!

3P2=3!/(3-2)!

Simplify.

3P2=3!/1!

3P2=6

Part B-

Use the combination formula and plug in 3 for n and 2 for k.

nCk=n!/k!(n-k)!

3C2=3!/2!(3-2)!

Simplify.

3C2=3!/2!(1!)

3C2=3

Part C-

It is given that the total number of three-card hands that can be dealt from a deck of 52 cards is 22100. Use the fact that the probability of something equals the total successful outcomes over the sample space. In this case the total successful outcomes is 3 and the sample space is 22100.

I believe the answer is 3/22100

I honestly suck at probability but I tried my best.

Answer: The length of the line B'C" is 1 unit.

Step-by-step explanation:

Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.

If A (2,2), B= (4,3) and C=(6,3).

Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]

Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]

[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]

Length of image = scale factor x length in original figure

B'C' = 0.5 × BC

= 0.5 × 2

= 1 unit

Hence, the length of the line B'C" is 1 unit.

Add the top and bottom numbers together, divide that by 2 then multiply by the height.

15.3 + 19.5 = 34.8

34.8/2 = 17.4

17.4 x 11.1 = 193.14

Answer is 193.1 m^2

Answer:

a. p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]  

b.0.6 ±  1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]  

c. { -1.96 ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ 1.96} = 0.95  

Step-by-step explanation:

Here the total number of trials is n= 1000

The number of successes is p` = 600/1000 = 0.6. The q` is 1 - p`= 1- 0.6 = 0.4

The degree of confidence is 95 %  therefore z₀.₀₂₅ = 1.96 ( α/2 = 0.025)

a.  The formula used will be

p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]       ( z with the base alpha by 2 (α/2 = 0.025))

b. Putting the values

0.6 ±  1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]  

c. Confidence Interval in Interval Notation.

{ -1.96 ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ 1.96} = 0.95  

{ -z( base alpha by 2) ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ z( base alpha by 2)  } = 1- α

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

Answer:16.1%

Step-by-step explanation:

Answer:

The investment needs the rate of growth to be approximately 16.1%.

Step-by-step explanation:

Answer: Price-earnings ratio= 22.0

Step-by-step explanation:

Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90

To find: price-earnings ratio

Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]

Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]

⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]

Hence, the price-earnings ratio= 22.0