Peter won £75 as a prize.He gave 4/5 of the prize money as a present to Roger and Bethan.Roger and Bethan shared the present in the ratio 2:3 .work out how much they each got​

Answer:

C the one with the 12

so the 3 turn into 1/3 now 1/3 times 1/4 = 1/12

now turn the 1/12 into the outside of the sign

Step-by-step explanation:

Answer:

Step-by-step explanation:

if a straight line with a slop [tex]m[/tex] pass through point [tex]P(x_o, y_o)[/tex] it's equation is:

[tex]y-y_o=m(x-x_o)\\\\y-(3)=-4(x-(-1))[/tex]

[tex]y=-4x-4+3\\\\y=-4x-1[/tex]

Answer:

Since there are 2 sides, a front & back, and a top & bottom, you must find the surface area of each of those 3 surfaces and multiply by 2.

Step-by-step explanation:

The formula would be:

Top & Bottom - 5 × 4 (multiply by 2 for top AND bottom)

Front & Back - 5 × 7 (multiply by 2 for front AND back)

Sides - 4 × 7 (multiply by 2 for BOTH sides)

___________________________________________________

Once you find the 3 surface areas, add the areas all together for the total. (I did not show the answer because that is for you to do on your own.)

Ex. Top & Bottom + Front & Back + Sides

Answer:

166 is the answer.

When using GeoGebra, I'm getting the regression curve to be roughly

h(t) = 1.67*(1.4)^t

I'm not sure how your teacher got 1.64 instead of the 1.67, but it's fairly close. So it seems like choice B is the best answer for the first part.

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Once we know the regression equation, we plug in t = 14 to find that,

h(t) = 1.64*(1.4)^t

h(14) = 1.64*(1.4)^(14)

h(14) = 182.236911939151

h(14) = 182.2

If 14 days have gone by, then we estimate the height is roughly 182.2 inches.

Compared to what the table says, which is 190 inches, we see that we have an underestimate. The error is about 190-182.2 = 7.8 which is under 10.

Answer: Choice C

The model under-predicts the actual height by less than 10 inches

Answer:

[tex] \cos(A + B) = \cos A \cos B - \sin A \sin \: B \\ but : \cos \: A = \sqrt{1 - ({ \frac{3}{5} })^{2} } = \frac{4}{5} \\ : \sin B = \sqrt{1 - {( \frac{ - 12}{13} })^{2} } = \frac{5}{13} \\ \therefore \cos(A + B) = ( \frac{4}{5} )( \frac{ - 21}{13} ) - ( \frac{3}{5} )( \frac{5}{13} ) \\ = \frac{ - 84}{65} - \frac{3}{13} \\ = \frac{ - 99}{65} \\ = - 1.52[/tex]

Answer:

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 54% of the registered voters in a country are Democrats. Sample of 770.

This means that:

[tex]p = 0.54, s = \sqrt{\frac{0.54*0.46}{770}} = 0.01796[/tex]

What is the probability that the sample proportion of Democrats will be greater than 52%?

This is 1 subtracted by the p-value of Z when X = 0.52. So

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.52 - 0.54}{0.01796}[/tex]

[tex]Z = -1.11[/tex]

[tex]Z = -1.11[/tex] has a p-value of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Answer:

85º and 95º

Step-by-step explanation:

supplementary angle total 180

(8x – 3) + (7x + 18)  = 180

Combine like terms

15x + 15 = 180

15x = 165

x = 11

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

8x – 3

8(11) - 3

88 - 3

85º

7x + 18

7(11) + 18

77 + 18

95º

Answer:

I'm not sure if you have the question quite right.  Whenever you multiply x and y by something, it is a dilation.  So 3 of those are dilations.  If you add or subtract something from x, it is a translation.

Hope that helps.

Step-by-step explanation:

Answer: Yes since its + (-5/12) each time

Step-by-step explanation:

Answer:

The last one, (1/2)^2 < 2/3 < 0.75

Step-by-step explanation:

So lets try to put each number in the same form, and see what their values are.

Lets start with (1/2)^2

This is squaring the 1 and 2 in 1/2. 1^2 is 1. 2^2 is 4. So its now:

1/4

Lets look at the others:

2/3

Lets just give it a common denominator. To do this, lets find the lowest number that both 3(from 2/3) and 4(from 1/4) go into. This is also known as the LCM.

This will be 12.

Since 3(from 2/3) goes into 12 4 times, we multipy both numerator and denominator of 2/3 by 4:

4*2=8, 3*4=12:

8/12

Since 4(from 1/4) goes into 12 3 times, we multiply both the numerator and denominator by 3:

1*3=3, 4*3=12:

3/12

So lets just go over what we know so far:

(1/2)^2 = 3/12

2/3 = 8/12

Now lets find our last value:

0.75

When converted into fraction form, we will get:

3/4

We already have a LCM, which is 12, that goes into this.

The denominator goes into 12 3 times, so again, we multiply numerator and denominator in this:

3*3=9, 4*3=12:

9/12

So:

(1/2)^2 = 3/12, 2/3 = 8/12, and 0.75 = 9/12

3/12 is smaller than 8/12, and 8/12 is smaller than 9/12. This can be written as:

3/12 < 8/12 < 9/12

And this basically means that:

(1/2)^2 < 2/3 < 0.75

This is the last answer in your answer list.

Hope this helps!

Answer:

3

9

21

Step-by-step explanation:

For the first one use the law of total probability

B=A∩B+A'∩B

12=9+A∩B

A∩B= 3

For this one you should use demorgans law and the union formula

(A'∩B')=(AUB)'

AUB= A+B-A∩B

6+12-3=15

15'= 24-15 = 9

For this one use demorgans law again

(A'UB')=(A∩B)'

(A∩B)'= 24-A∩B= 24-3= 21

Answer:

if 25c + 15d = 0, then d = -25/15c

Step-by-step explan

just yes, that

9514 1404 393

Answer:

 5

Step-by-step explanation:

Put the numbers where the letters are and do the arithmetic.

  5(3) -2(5) = 15 -10 = 5

Answer:

5

Step-by-step explanation:

5m - 2n

Where, we have given ; m = 3 & n = 5

plug the value in the equation

Answer:

A) 1.7 inches of lumber is left.

Answer:

(x+1)(3x+2) is the answer

Answer:

Step-by-step explanation:

3x^2+5x+2

3x^2+(3+2)x+2

3x^2+3x+2x+2

3x(x+1)+2(x+1)

(3x+2)(x+1)

===============================================

Explanation:

When you list out the perfect squares, notice that 49 and 64 are on that list.

These are values we focus on because 49 < 52 < 64

We'll apply the square root to all three sides

[tex]49 < 52 < 64\\\\\sqrt{49} < \sqrt{52} < \sqrt{64}\\\\7 < \sqrt{52} < 8\\\\[/tex]

This shows that [tex]\sqrt{52}[/tex] is between 7 and 8

A calculator helps confirm this

[tex]\sqrt{52} \approx 7.2111\\\\[/tex]

Answer:

The answer is "[tex]0.99999340657 \sim 1[/tex]".

Step-by-step explanation:

[tex]Sucess \ probability \ (p) = 94\% \ or\ 0.94\\\\Sample\ numbers\ n = 14\\[/tex]  

Using formula:

[tex]P(X=r)= ^n C_r \times p^r \times (1-p)^{n-r}[/tex]

 Let

[tex]\to r=8,9,10,11,12,13 \ or\ 14\\\\[/tex]

Substituting the value for all r:

 [tex]P(X=8)= 0.00008540547\\\\P(X=9)= 0.00089201264\\\\P(X=10)= 0.00698743233\\\\P(X=11)= 0.03980719025\\\\P(X=12)= 0.15591149513\\\\P(X=13)= 0.37578668058\\\\P(X=14)= 0.42052319017\\[/tex]

Therefore,

[tex]P(X>7)= P(X=8)+P(X=9)+....P(X=14)\\\\= 0.99999340657 \sim 1.[/tex]

Answer:

C) 1/16

Step-by-step explanation:

2*2*2*2=16

Therefore, 2^(-4)=1/16.

Answer:

C) [tex]\frac{1}{16}[/tex]

Step-by-step explanation:

2⁻⁴

2⁴ = 2 × 2 × 2 × 2 = 16

[tex]\frac{1}{16}[/tex]

Answer:

23.5 degree stands tap of the floor

Answer:

100 in 10 theaters. 100÷10=10 44÷4=11

Answer:

4.54 x 1010

Hope this helps!

Answer:

I think it's a square or maybe a rhombus?

Step-by-step explanation:

Answer:

5.9 years.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

Mean of the population is [tex]\mu = 5.9[/tex]

If a sampling distribution is created using samples of the ages at which 69 children begin reading, what would be the mean of the sampling distribution of sample means?

By the Central Limit Theorem, the same population mean, of 5.9 years.

Answer:

[tex]A(2,4)<-3,-2)A'(-1,2)>A''(-4,8)[/tex]

[tex]B)(5,2)-> B'(2,0)->B''(8,0)[/tex]

[tex]C(3,1)->C'(0,-1)->C''(0,-4)[/tex]

[tex](x,y)->(x-3,y-2)->([(x-3)*4],[(y-2)*4])[/tex]

Answer:

Brand A

Step-by-step explanation:

Because it has the most returns, therefore, it is the brand that is most likely to be returned.

Answer: Brand B

Step-by-step explanation:

use ratios for each brand to find the probability of each being returned