3 Lizzie buys 3 clocks for a total cost of £50 at a car boot sale.
She sells 2 of the clocks for £22 each and the other clock for £20
Lizzie thinks she has made a profit of over 30% of the cost of the clocks.

Answer:

4104.807

Step-by-step explanation:

4269÷1.04

=4104.807

Answer:

4104.8

Step-by-step explanation:

To solve this problem, the easiest approach is to set up a proportion. Use the following general format;

[tex]\frac{currenncy_1}{currency_2}=\frac{balance_1}{balance_2}[/tex]

This will allow one to describe the relationship between the different currency values. Substitute in the given information and solve;

[tex]\frac{currenncy_1}{currency_2}=\frac{balance_1}{balance_2}[/tex]

[tex]\frac{canadian}{australian}=\frac{balance_1}{balance_2}[/tex]

[tex]\frac{1}{1.04}=\frac{x}{4269}[/tex]

Cross products,

[tex]\frac{1}{1.04}=\frac{x}{4269}[/tex]

[tex](1)(4269)=(1.04)(x)\\4269=1.04x[/tex]

Inverse operations,

[tex]4269=1.04x\\4104.8\approx x[/tex]

Answer: 12 dollars

Step-by-step explanation:

2x3x2=12

Easy math

Answer:

4/3

Step-by-step explanation:

Substitute in 4.

(1/3)4

Multiply

4/3

I hope this helps!

Answer:

$224.932

Step-by-step explanation:

Note: The question is not complete

say the rate is 10%

Given data

Initial depostite= $212

TIme= 6years

rate= 10%

the expression for the compound interest is given as

A=P(1+r)^t

substitute

A=212(1+0.1)^6

A=212(1.01)^6

A=212*1.061

A= $224.932

Hence the final amount at the rate of 10% is $224.932

Answer:

the second graph is correct

Step-by-step explanation:

Answer:

5000

Step-by-step explanation:

Add the number of adults first: 27+23=50

Then multiply the number of adults by 100 for the fee.

50*100 = 5000

Answer:

within the two days a total of 5000$ where collected in the two days

Solution:

R= 100 per adult

1 adult = 100

27(R)+ 23(R) = 27(100)+ 23(100)

27(100)+23(100) =5000

or add both 27 and 23 and multiple by 100

50•100 = 5000

Answer:

X<-2551.5

Step-by-step explanation:

-2x<5112-9

-2x/-2<5103/-2

x<-2551.5

The median of the following set of values is equals to 17.

Median represents the middle value of the given data when arranged in a particular order. The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

We are given that the median of the following set of values

7, 21, 19, 15, 19, 14, 15, 19

Line them up in order first.

7, 14, 15, 15, 19, 19, 19, 21

Here the middle value are 15 and 19.

The median is 15 and 19. OR 17,

Therefore, 15 + 19 = 34/2 which equals to 17.

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Answer:

Sin = 7/25

Cos = 24/25

Tan = 7/24

Step-by-step explanation:

The ratio for sin is opposite/hypotenuse, cos is adjacent/ hypotenuse, and tan is opposite/ adjacent.

Given:

The graph of a line.

To find:

The equation for the given line.

Solution:

From the given graph, it is clear that the line passes through the points (0,-5) and (5,0). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-5)=\dfrac{0-(-5)}{5-0}(x-0)[/tex]

[tex]y+5=\dfrac{5}{5}(x)[/tex]

[tex]y+5=x[/tex]

Subtract 5 from both sides.

[tex]y+5-5=x-5[/tex]

[tex]y=x-5[/tex]

Therefore, the equation of the given line is [tex]y=x-5[/tex].

Answer:

B. Pie chart.

Step-by-step explanation:

In this question, the students are asked what political party they belong. The best display format would be one in which the graph can be divided into parts, or percents, according to the percentage of students belonging to each political party. The graph that best describes this, distributing a group into parts, is a pie chart, and thus, the correct answer is given by option b.

Scatterplot is used when two variables correlate together, that is, there is a relationship between them, which we don't have between the number, or proportion of students belonging to each political party. Stemplot are used when there is a high number of quantitative data, which we do not have here.

Answer:

7

Step-by-step explanation:

28-3(7)

The 7th term of the given sequence 28 - 3n is 7.

A sequence is an ordered list of elements with a specific pattern.

According to the given question.

We have a sequence 28 - 3n.

So, for finding the value 7th term of the sequence substitute n = 7 in

28 - 3n.

Therefore, the 7th term of the given sequence

= 28 - 3(7)

= 28 - 21

= 7

Hence, the 7th term of the given sequence 28 - 3n is 7.

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Answer:

Step-by-step explanation:

P(4,3), Q(4,1), S(-1,3), R(-1,1)

[tex]Distance =\sqrt{(x_{2}-x_{1})^{2}+(y_{2} -y_{1})^{2}}\\\\PQ= \sqrt{(4-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-2)^{2}}\\\\\=\sqrt{4}\\\\=2 \ units\\\\\\QS=\sqrt{(-1-4)^{2}+(3-1)^{2}}\\\\=\sqrt{(-5)^{2}+(2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\ units\\\\\\SR =\sqrt{(-1-[-1])^{2}+(1-3)^{2}}\\\\=\sqrt{(-1+1)^{2}+(-2)^{2}}\\\\=\sqrt{0+4}\\\\= \sqrt{4}\\\\= 2 \\\\\\PR = \sqrt{(-1-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-5)^{2}+(-2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\\\\[/tex]

PQRS is a rectangle

Area= length *breadth

       = 2 * √29

       = 2√29 sq.units

Answer:

1. 3

2. D

3. KE

4. B

5. A

Step-by-step explanation:

those should be your answers

Answer:

1. 3

2. D

3. E and K

4. B

5. A

negative integers lie on the negative side of the number line(usually having a minus sign in front of them)

positive ones lie on the positive side( usually have no signs in front of them)

Answer:

.

Step-by-step explanation:

.

[tex]4\pi[/tex]

Step-by-step explanation:

[tex]C = 2\pi r,\:\:\:\:r = 4[/tex]

The circumference of the circle of radius 4 is [tex]8\pi[/tex]. Since we are dealing with only half of the circle, the arc length is then half the circumference or [tex]4\pi[/tex].

Answer:

Just Between Friends

The percentage of consignors who receive a check for more than $370 is:

= 16%.

Step-by-step explanation:

Mean of consignor check, μ = $480

Standard deviation, σ = $110

Value of check received, x > $370

Solution: find the z-score to determine the percentage of consignors who receive a check for more than $370:

z = (x-μ)/σ

z= ($370 - $480)/$110

z = -$110/$110

z = -1.00

Percentage of consignors who receive a check for more than $370

= 0.15866

= 0.16

= 16%

Answer:

False

Step-by-step explanation:

f'(x) would be a negative number. Hence less than zero.

Answer:

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

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.

Mean life of 82 months with a standard deviation of 7 months.

This means that [tex]\mu = 82, \sigma = 7[/tex]

Sample of 71

This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]

What is the probability that the mean monitor life would be greater than 83.8 months?

1 subtracted by the p-value of Z when X = 83.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]

[tex]Z = 2.17[/tex]

[tex]Z = 2.17[/tex] has a p-value of 0.985.

1 - 0.985 = 0.015

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Answer:

There are 824 deer in the preserve.

Step-by-step explanation:

Since to determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose, and later, 316 deer are caught, 158 of them are tagged, to determine how many deer are in the preserve you must perform the following calculation:

316 = 100

158 = X

158 x 100/316 = X

50 = X

50 = 412

100 = X

824 = X

Therefore, there are 824 deer in the preserve.

Answer:

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]

Required

The domain

There are no undefined points such as denominator of x or square roots.

Hence, the domain is:

[tex]-\infty < x < \infty[/tex]

9514 1404 393

Answer:

  9.  c. 1

  10.  c. y = 15/x

Step-by-step explanation:

The equation for inverse variation can be written as ...

  y = k/x

The value of k can be determined from given values of x and y. Multiply by x to get ...

  k = xy

Solving for x, you get ...

  x = k/y

___

9. k = (1/7)(49) = 7

  x = k/y = 7/7

  x = 1

__

10. k = (3)(5) = 15

  y = 15/x

Answer:

1) Isosceles

2) Acute

3) Right angled

4( Obtuse

5) Equilateral

Answer:

"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

Step-by-step explanation:

Let be the following system of linear equations:

[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)

[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)

[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)

1) We eliminate [tex]y[/tex] by adding (1) and (2):

[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]

[tex]6\cdot x +2\cdot z = 24[/tex] (4)

2) We eliminate [tex]y[/tex] by adding (1) and (3):

[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]

[tex]9\cdot x -4\cdot z = 36[/tex] (5)

Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

Graph B is the best graph that represents the linear equation

Answer:

m=2b=1y=2x+1

just enter it

Answer:

0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%

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]

A film distribution manager calculates that 5% of the films released are flops.

This means that [tex]p = 0.05[/tex]

Sample of 572

This means that [tex]n = 572[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.05[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{572}} = 0.0091[/tex]

What is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%?

1 subtracted by the p-value of Z when X = 0.06. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.06 - 0.05}{0.0091}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643

1 - 0.8643 = 0.1357

0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%

Answer:

467 voters

Step-by-step explanation:

Given

See attachment for complete question

Required

Sample size at 95% confidence interval

From the attachment, we have:

[tex]p = 65\% = 0.65[/tex]

[tex]E = 4.33\% = 0.0433[/tex]

[tex]CL = 0.95[/tex]

[tex]\alpha = 0.05[/tex] i.e. 1 - CL

First, we calculate the critical level

At [tex]CL = 0.95[/tex] and [tex]\frac{\alpha}{2}[/tex]

[tex]z^* = 1.96[/tex] --- the critical level

So, we have:

[tex]n = p * (1 - p) * (\frac{z^*}{E})^2[/tex]

[tex]n = 0.65 * (1 - 0.65) * (\frac{1.96}{0.0433})^2[/tex]

[tex]n = 0.65 * (1 - 0.65) * (45.3)^2[/tex]

[tex]n = 0.65 * 0.35 * 2052.1[/tex]

[tex]n = 466.9[/tex]

[tex]n = 467[/tex] --- approximated

Answer:

2 Quadrilateral DEFG was shifted up 6 units.

Step-by-step explanation:

trust me cuz when there is ' its not the orginal shape

[tex]f(x)=\sqrt{x} -2[/tex] is the correct option

Answer:

BH/2

Step-by-step explanation:

For the area of the triangle, (BH)/2. B=base and H=height