. Joe has some pocket money. He spends three-quarters of it. He has fifty pence left. How much pocket money did he have?​

Answer:

-68

Step-by-step explanation:

Subtract 18 from each side of the equation.

a + 18 = -50

    -18    -18

Turn -50 - 18 into -50 + (-18) because you need to add the opposite.

a = -50 + (-18)

a = 68

Answer:

Step-by-step explanation:

The answer is C. 5x + 15 because the 5 outside the parentheses () is supposed to multiply by what's inside the parentheses. So multiply 5 and x and 5 and 3 (5 * X = 5x) (5 * 3 = 15).

Answer:

y=0.3x-2

Step-by-step explanation:

first find the gradient

m=y2-y1/x2-x1

m=0-(-2)/6-0

m=0.3

then use this equation

y-y1=m(x-x1)

y-(-2)=0.3(x-0)

y+2=0.3x-0

y=0.3x-2

Answer:

because the answer of 0.3 times 0.9 is 0.27

Step-by-step explanation:

Answer: 0.27

Step-by-step explanation: When you multiply 0.3 x 0.9 you get 0.27

Answer:

1 i.e. n

Step-by-step explanation:

The mean of the sampling distribution is still 810 grams, which is the same as the population mean. The standard deviation of the sampling distribution is 4 grams.

The mean of the sampling distribution for the average weight of a simple random sample can be considered an unbiased estimator of the population mean. In this case, since the population mean is 810 grams, the mean of the sampling distribution remains the same.

The standard deviation of the sampling distribution, on the other hand, is influenced by the sample size. The formula for the standard deviation of the sampling distribution of the sample mean is given by the population standard deviation divided by the square root of the sample size. In this case, the population standard deviation is 40 grams, and the sample size is 100. Therefore, the standard deviation of the sampling distribution is calculated as 40 grams divided by the square root of 100, which is 4 grams.

In summary, the mean of the sampling distribution for the average weight of simple random samples of 100 children born with ELBW is 810 grams, and the standard deviation is 4 grams.

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Answer:

2ab

Step-by-step explanation:

6ba + 2ab = 2ab(3+1)

= 2ab (4)

so, the common factor = 2ab

Answer:

2ab

Step-by-step explanation:

The wwwwwwwwwwwwwwwwwwwwwww

Answer:

the the the rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Step-by-step explanation:

312.5 μCi is equivalent to 0.3125 mCi.

Conversion factors refer to a relationship between the value in one unit to the value in another unit. It is used to convert a quantity expressed in one unit to another unit.

The following conversion factors are needed to convert 312.5 μCi to millicuries (mCi):1 mCi = 1000 μCiUsing the above conversion factor, we can write the given value of 312.5 μCi as:312.5 μCi = (312.5/1000) mCi= 0.3125 mCi

Therefore, the value of 312.5 μCi can be converted to millicuries (mCi) using the above conversion factor. We can rearrange the formula as shown below.312.5 μCi × 1 mCi / 1000 μCi= (312.5/1000) mCi= 0.3125 mCi

Therefore, 312.5 μCi is equivalent to 0.3125 mCi. The calculation can be summarized in a sentence as follows: To convert 312.5 μCi to millicuries (mCi), we use the conversion factor 1 mCi = 1000 μCi.

The calculation shows that 312.5 μCi is equivalent to 0.3125 mCi. The answer can be expressed as follows: 312.5 μCi = 0.3125 mCi.

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The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

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

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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A lower degree of significance should be selected if the cost of a Type I error is substantial.

The level of significance chosen for the hypothesis test is equivalent to the likelihood of making a type I error. Therefore, there is a 5% probability that a type I mistake could happen if the threshold of significance is 0.05.

Two things can lead to type 1 errors : poor research methods and random chance. No random sample, whether it be an A/B test or a pre-election survey, can ever accurately represent the population it is meant to characterize.

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As a result, 315 pupils attended the school play.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The first equation in the system is given by the total number of attendees:

c + a = 330

The second equation is given by the number of children being 21 times the number of adults:

c = 21a

We can use substitution to find the value of a and then find the value of c. Substituting the second equation into the first equation, we get:

21a + a = 330

Combining the two terms on the left-hand side, we have:

22a = 330

Dividing both sides by 22, we have:

a = 15

So there were 15 adults in attendance at the school play. To find the number of children, we can use the second equation:

c = 21a = 21 * 15 = 315

So there were 315 children in attendance at the school play.

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Answer:

6

Step-by-step explanation:

first, look at the first two coefficents, (12,6) 6 can divide 12 and 6 obviously didvides itself so we can day the gcd(12,6) is 6. now look at the last two coefficents (6,18). Similarly we can see that the gcd here is also 6.

finally, look at 12 and 18, neither divide each other so we can try dividing them by our most common gcd so far 6. this yields 2,3. niehter can be simplified further so we can conlcude the gcd of this monomials is 6

To calculate the probabilities, we need to use the concept of binomial probability.

For a fair coin being tossed 5 times:

(a) Probability of getting five heads:

The probability of getting a head in a single toss is 1/2.

Since each toss is independent, we multiply the probabilities together.

P(Head) = 1/2

P(Tails) = 1/2

P(Five Heads) = P(Head) * P(Head) * P(Head) * P(Head) * P(Head) = \((1/2)^5\) = 1/32 ≈ 0.03125

So, the probability of obtaining five heads is approximately 0.03125 or 3.125%.

(b) Probability of getting four heads:

There are five possible positions for the four heads.

P(Four Heads) = (5C4) * P(Head) * P(Head) * P(Head) * P(Head) * P(Tails) = 5 * \((1/2)^4\) * (1/2) = 5/32 ≈ 0.15625

So, the probability of obtaining four heads is approximately 0.15625 or 15.625%.

(c) Probability of getting one head:

There are five possible positions for the one head.

P(One Head) = (5C1) * P(Head) * P(Tails) * P(Tails) * P(Tails) * P(Tails) = 5 * (1/2) * \((1/2)^4\) = 5/32 ≈ 0.15625

So, the probability of obtaining one head is approximately 0.15625 or 15.625%.

For a fair die being thrown eight times:

(a) Probability of a 6 occurring six times:

The probability of rolling a 6 on a fair die is 1/6.

Since each roll is independent, we multiply the probabilities together.

P(6) = 1/6

P(Not 6) = 1 - P(6) = 5/6

P(Six 6s) = P(6) * P(6) * P(6) * P(6) * P(6) * P(6) * P(Not 6) * P(Not 6) = \((1/6)^6 * (5/6)^2\) ≈ 0.000021433

So, the probability of rolling a 6 six times is approximately 0.000021433 or 0.0021433%.

(b) Probability of a 6 never happening:

P(No 6) = P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) = \((5/6)^8\) ≈ 0.23256

So, the probability of not rolling a 6 at all is approximately 0.23256 or 23.256%.

(c) Probability of an odd number of 6s:

To have an odd number of 6s, we can either have 1, 3, 5, or 7 6s.

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

\(P(One 6) = (8C1) * P(6) * P(Not 6)^7 = 8 * (1/6) * (5/6)^7P(Three 6s) = (8C3) * P(6)^3 * P(Not 6)^5 = 56 * (1/6)^3 * (5/6)^5P(Five 6s) = (8C5) * P(6)^5 * P(Not 6)^3 = 56 * (1/6)^5 * (5/6)^3P(Seven 6s) = (8C7) * P(6)^7 * P(Not 6) = 8 * (1/6)^7 * (5/6)\)

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

Calculate each term and sum them up to find the final probability.

After performing the calculations, we find that P(Odd 6s) is approximately 0.28806 or 28.806%.

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The amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

Given,

Two waves are described by:

3₁ (2, 1) = (0.30) sin(5z - 200t)] and

g (z,t) = (0.30) sin(52-200t)

+ =]

where OA A, 0.52 m and v= 40 m/s

OB A=0.36 m and

v= 20 m/s OC

A=0.60 m and

v= 1.2 m/s OD.

A = 0.24 m and

v= 10 m/s

DE A=0.16 m and

= 17 m/s

The amplitude of a wave is the distance from its crest to its equilibrium. The amplitude of the resultant wave is calculated by adding the amplitudes of the individual waves and is represented by A.

The expression for the resultant wave is given by f(z,t) = 3₁ (2, 1) + g (z,t)

= (0.30) sin(5z - 200t)] + (0.30) sin(52-200t)

+ =]

f(z,t) = (0.30) [sin(5z - 200t) + sin(52-200t)

+ =]

Therefore, A = 2(0.30) = 0.60 m/s

The speed of a wave is given by the product of its wavelength and its frequency. The wavelength of the wave is the distance between two consecutive crests or troughs, represented by λ. The frequency of the wave is the number of crests or troughs that pass through a given point in one second, represented by f.

Speed = λf

The wavelengths of the given waves are OA = 0.52 m,

OB = 0.36 m,

OC = 0.60 m,

OD = 0.24 m,

DE = 0.16 m

The frequencies of the given waves are OA :

v = 40 m/s,

f = v/λ

= 40/0.52

= 77.0 Hz

OB : v = 20 m/s,

f = v/λ

= 20/0.36

= 55.6 Hz

OC : v = 1.2 m/s,

f = v/λ

= 1.2/0.60

= 2.0 Hz

OD : v = 10 m/s,

f = v/λ

= 10/0.24

= 41.7 Hz

DE : v = 17 m/s,

f = v/λ

= 17/0.16

= 106.25 Hz

The speed of the resultant wave is the sum of the speeds of the individual waves divided by the number of waves. Therefore,

Speed of the resultant wave = (40 + 20 + 1.2 + 10 + 17)/5

= 17.64 m/s

Hence, the amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

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The amplitude of the resultant wave and its speed are to be determined.

Let's use the formula of the resultant wave, where,

A is amplitude, f is frequency, v is velocity and λ is wavelength of the wave.

A = \([(OA^2 + OB^2 + OC^2 + OD^2 + DE^2 + 2(OA)(OB)(cosθ) + 2(OA)(OC)(cosθ) + 2(OA)(OD)(cosθ) + 2(OA)(DE)(cosθ) + 2(OB)(OC)(cosθ) + 2(OB)(OD)(cosθ) + 2(OB)(DE)(cosθ) + 2(OC)(OD)(cosθ) + 2(OC)(DE)(cosθ) + 2(OD)(DE)(cosθ))]^{1/2\)

where, cosθ = [λ1/λ2] and λ1, λ2 are the wavelength of the two waves.

The velocity of the wave is given by the relation v = fλ

We can calculate the velocity of the resultant wave by using the above formula and calculating the value of wavelength of the wave.

Here, we are given λ for each wave. Speed = 40 m/s

Amplitude of the resultant wave= \([ (0.52^2 + 0.36^2 + 0.6^2 + 0.24^2 + 0.16^2 + 2(0.52)(0.36) + 2(0.52)(0.6) + 2(0.52)(0.24) + 2(0.52)(0.16) + 2(0.36)(0.6) + 2(0.36)(0.24) + 2(0.36)(0.16) + 2(0.6)(0.24) + 2(0.6)(0.16) + 2(0.24)(0.16) )]^{1/2\)

=\([ (0.2704 + 0.1296 + 0.36 + 0.0576 + 0.0256 + 0.3744 + 0.624 + 0.2496 + 0.1664 + 0.1296 + 0.0864 + 0.0576 + 0.144 + 0.096 + 0.0384) ]^{1/2\)

=\([ (2.2768) ]^{1/2\)

= 1.51 m/s

Therefore, the amplitude of the resultant wave is 1.51 m/s and the speed of the wave is 1.51 m/s.

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Answer:

-3k + 10

Step-by-step explanation:

you have to combine -8 and 2 because they are like terms, but since -8 is being subtracted from -3k the minus sign and the negative sign basically combine to make a positive sign so it would make it -3k + 8 + 2 which gives you -3k + 10

Answer: Heyaa! ~

Your Answer is... − 3k+10

Step-by-step explanation:

Hopefully this helps you! ~

Answer: $16

Step-by-step explanation:

reduce by 20% means cutting from 100% and leftover with 80% of original

                                            100%-20%=80%

original price: $20×100%=$20

after reduction: $20×(100%-20%)=$16

Answer:

16

Step-by-step explanation:

First find the discount

20 * 20%

20 * .20

4

Subtract this from the price

20 -4

16

The new price is 16

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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\(x = 0.45d + 4\)

Answer:

  y = 5x +7

Step-by-step explanation:

Using the hint, we have ...

  y -(-3) = 5(x -(-2)) . . . . . m = 5, (x1, y1) = (-2, -3)

  y = 5x +10 -3 . . . . . eliminate parentheses, add -3

  y = 5x +7

The value of x in the equation \(1331x^{3} - 216 = 0\) is \(-\frac{6}{11}\), the correct option is A.

To solve for x in the given equation, we can first isolate the variable term by adding 216 to both sides of the equation, which gives:

\(\frac{1331x^{3} }{3} = -216\)

Next, we can divide both sides of the equation by 1,331 to obtain:

\(x^{3} = - \frac{216}{1331}\)

We can simplify this expression by finding the prime factorization of both numbers. We can write 216 as 2³× 3³ and 1,331 as 11 × 11 × 11. Substituting these values, we get:

x³ = - (2³ × 3³) ÷ (11³)

x³ = - (8 ÷ 1331) × (27)

x³ = - 216 ÷ 1331

The result of taking the cube root of both sides is:

x = \(-( \frac{216}{1331})^{1/3}\)

x = \(- \frac{6}{11}\)

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Answer:

Sure. Here are the steps on how to construct a confidence interval at a 95% confidence level for the mean amount spent on a child's last birthday gift:

Identify the sample size, n. In this case, n=13.

Identify the sample mean,  

x

ˉ

. In this case, $\bar{x} = $36.

Identify the sample standard deviation, s. In this case, $s = $15.

Identify the t-critical value, t. The t-critical value is the value that cuts off 2.5% of the distribution in each tail, leaving 95% of the distribution in the middle. To find the t-critical value, we need to know the degrees of freedom, df. The degrees of freedom are calculated as df=n−1. In this case, df=13−1=12.

We can find the t-critical value using a t-distribution table. The t-distribution table shows the t-critical values for different degrees of freedom and different confidence levels. For a 95% confidence level and 12 degrees of freedom, the t-critical value is 2.179.

Calculate the confidence interval. The confidence interval is calculated as follows:

$\bar{x} \pm t \cdot \frac{s}{\sqrt{n}}$

In this case, the confidence interval is:

$36 \pm 2.179 \cdot \frac{15}{\sqrt{13}} = (27.28, 44.72)$

Therefore, a 95% confidence interval for the mean amount spent on a child's last birthday gift is $27.28 to $44.72.

Step-by-step explanation:

The area of shaded part in the figures are

1. 7.07cm²

2. 19.54cm²

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

The area of a sector is expressed as:

A= tetha/360 × πr²

Area of the shaded part = area of big sector - area of small sector.

1. area of big sector = 90/360 × 3.14 × 5²

= 7065/360

= 19.63cm²

area of small sector = 90/360 × 3.14 × 4²

= 12.56cm²

area of shaded part = 19.63 - 12.56

= 7.07cm²

2. Area of big sector = 40/360 × 3.14 × 9²

= 28.26cm²

area of small sector = 40/360 × 3.14 × 5²

= 8.72

area of shaded part = 28.26-8.72

= 19.54cm²

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To find the volume multiply all 3 numbers together.

2 1/2 x 1 1/2 = 3 3/4

3 3/4 x 3 = 11 1/4

The volume is 11 and 1/4 cubic units

The z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.

The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the data value, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (80 - 52) / 9 = 3.11 (rounded to two decimal places)

Therefore, the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.

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The z-score for a data value of 80 in this data set is approximately 3.1.

Calculate the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9.

To find the z-score, follow these steps:

Identify the data value (x), mean (µ), and standard deviation (σ).

In this case, x = 80, µ = 52, and σ = 9.

Use the z-score formula:

z = (x - µ) / σ

Plug in the values:

z = (80 - 52) / 9

Perform the calculations:

z = 28 / 9

Round the answer to the nearest tenth: z ≈ 3.1

So, the z-score for a data value of 80 in this data set is approximately 3.1.

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Given:

Total number of hours = 70 hours

Amount he charges (base fee) = $75

Amount he charges per hour =

Answer:

a=9

Step-by-step explanation:

Use the pythagorean theorem

a^2+(5.6)^2=(10.6)^2

a^2+31.36=112.36

a^2=81

a=9

The inverse Laplace transform of F(s) = 5040s^7 - 8s is f(t) = 5040t^7 - 8.

To find the inverse Laplace transform of F(s), we need to apply the inverse Laplace transform to each term separately.

For the term 5040s^7, we can use the inverse Laplace transform property: L^-1{as^n} = (n!/s^(n+1)). Applying this property, we have:

L^-1{5040s^7} = (7!/s^(7+1)) = 5040/(s^8)

For the term -8s, we can again use the inverse Laplace transform property: L^-1{as} = -a. Applying this property, we have:

L^-1{-8s} = -(-8) = 8

Combining both terms, we get the inverse Laplace transform of F(s):

f(t) = L^-1{5040s^7 - 8s} = 5040/(s^8) + 8 = 5040t^7 - 8

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