Dermot bakes 420 cakes.
He bakes only vanilla cakes, banana cakes and lemon cakes. 120 of the cakes are vanilla cakes.
35% of the cakes are banana cakes.
Work out the number of lemon cakes Dermot bakes. PLEASEE I NEED NOW

By squaring the deviations from the mean, we make them positive numbers, and the sum of the squared deviations will also be a positive number.

In mathematics and statistics, deviation refers to the difference between a value and a reference value or an expected value. More specifically, deviation is a measure of how far a set of numbers is spread out from their average value or the central point.

By squaring the deviations from the mean, we make them positive numbers, and the sum of the squared deviations will also be a positive number. This is because squaring any number makes it positive, regardless of whether the original number was positive or negative.

Additionally, squaring the deviations before summing them up allows us to give more weight to larger deviations from the mean. This is because squaring a larger deviation will result in a much larger value than squaring a smaller deviation, which helps to highlight the effect of outliers or extreme values in the data set.

The sum of the squared deviations is used in many statistical calculations, including calculating the variance and standard deviation of a data set, which are measures of the spread of the data.

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Answer:

2.5 cups

Step-by-step explanation:

\(\frac{2}{12} =\frac{x}{15}\) (x is the amount of cups of zucchini you will need to feed 15 people)

This proportion is showing that 2 cups of zucchini can feed 12 people, and we will use it to find how much zucchini we will need to feed 15 people.

Cross multiply

30 = 12x

divide both sides by 12 to isolate x

\(\frac{30}{12}\) = x

2.5 = x

That is your answer

- Kan Academy Advance

Answer:

8 bagels

Step-by-step explanation:

This is a remainder division problem. We need to divide 719 by 9 and find the remainder.

First off, 9 is bigger than 7, so we need to move to the next digit. How many times does 9 go into 71? 9 times 7 is 63! That's the closest smaller number we can get, so I will write a 7 in the long division problem above the 1. I will subtract 63 from 71 to get 8.

      7

9 | 719

   -63

       8

Now, the 9 can be brought down, making our 8 into an 89. How many times does 9 go into 89? 9 times 9 is 81! That's the closest we can get! I will write a 9 by the 7 above the 9 in 719, and write 81 below the 89. Subtracting these leaves us with a remainder of 8.

      79

9 | 719

  -63 ↓

      89

      -81

         8

This means that the bagels were sent in 9 equal shipments of 79 bagels each, and the baker was left with 8 bagels!

The absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5

The given parameters are:

Minimum = 70 mg/dL

Maximum = 99 mg/dL

Calculate the mean using:

Mean = (Minimum + Maximum)/2

This gives

Mean = (70 + 99)/2

Evaluate

Mean = 84.5

Calculate the range using

Range = Maximum -Minimum

This gives

Range = 99 - 70

Evaluate

Range = 29

The absolute value equation that represents the minimum and maximum normal glucose levels is

|x - Mean| = Range/2

So, we have:

|x - 84.5| = 29/2

Evaluate

|x - 84.5| = 14.5

Hence, the absolute value equation that represents the minimum and maximum normal glucose levels is |x - 84.5| = 14.5

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Answer:

24

Step-by-step explanation:

We can make the equation

225+50x=1425

=

50x=1200

=

x=24

The four equilibria of  differential equation  x' = sin(2x) whose interval is x € [0, 3π/2] are:  x = kπ/2 for k = 0, 1, 2, 3 . The equilibria at x = π/2 and x = 3π/2 are unstable, and the equilibria at x = 0 and x = π are stable.

To find the equilibria, we need to set x' = 0 and solve for x. Thus, sin(2x) = 0, which implies 2x = kπ where k is an integer. Therefore, x = kπ/2 for k = 0, 1, 2, 3. These are the four equilibria of the differential equation.

To determine the stability of the equilibria, we need to examine the sign of x' near each equilibrium. We know that sin(2x) is positive for x in the intervals (kπ/2, (k+1)π/2) where k is an even integer, and negative for x in the intervals (kπ/2, (k+1)π/2) where k is an odd integer.

Thus, for x near x = kπ/2 where k is even, x' is positive, which means that x will increase and move away from the equilibrium. Similarly, for x near x = kπ/2 where k is odd, x' is negative, which means that x will decrease and move away from the equilibrium.

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The expected value of the insurance policy can be calculated by multiplying the payout amount by the probability of survival and subtracting the premium paid. By multiplying the payout amount by the probability of survival, we get $300,000 * 0.999544 = $299,863.20.

Expected value = (Payout amount * Probability of survival) - Premium

In this case, the payout amount is $300,000, the probability of survival is 0.999544, and the premium paid is $270.

Expected value = ($300,000 * 0.999544) - $270 = $299,863.20 - $270 = $299,593.20

Therefore, the expected value of this policy to the insurance company is $299,593.20.

The expected value represents the average amount of money the insurance company expects to make from selling this policy to a 20-year-old female for one year. It takes into account the payout amount, the probability of survival, and the premium paid by the insured.

In this case, the insurance company expects to receive a premium of $270 from the policyholder. The payout amount, which is the coverage provided by the policy, is $300,000. However, the insurance company also considers the probability of survival, which is 0.999544. This means that there is a very high chance that the insured individual will survive the year and the insurance company will not have to pay out the coverage amount.

This represents the expected payout to the insurance company if the insured individual survives the year.

To calculate the expected value, we subtract the premium paid from the expected payout: $299,863.20 - $270 = $299,593.20. This is the expected value of the policy to the insurance company.

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when the period of a sine function doubles, the frequency is halved (reduced by a factor of 1/2).

When the period of a sine function doubles, it means that the length of one complete cycle of the sine function has doubled.

The frequency of a sine function is defined as the number of cycles per unit of time.

If the period doubles, it means that the time it takes for one cycle of the sine function has increased.

Therefore, the frequency of the sine function decreases because fewer cycles occur within a given unit of time.

Mathematically, the relationship between period (T) and frequency (f) is given by:

f = 1 / T

If the period doubles (T' = 2T), the corresponding frequency (f') can be found by substituting T' into the equation:

f' = 1 / T'

   = 1 / (2T)

   = 1/2 * (1 / T)

   = 1/2 * f

So, when the period of a sine function doubles, the frequency is halved (reduced by a factor of 1/2).

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Given :

Martin drinks 1/4 of a litre of juice each day.

Juice costs £3.60 for a 2 litre carton and £2.00 for a 1 litre carton.

To Find :

Martin buys enough juice to last for 2 weeks (14 days).

What is the lowest price Martin can pay for this juice.

Solution :

Amount of litre used in 14 days is :

V = 14× ( 1/4 )

V = 3.5 liter

Lowest price to pay is :

P = 2 × Cost of one 2 L carton

P = £(2 × 3.60)

P = £7.2

The lowest price Martin can pay for this juice is £7.2 .

Hence, this is the required solution.

The y-intercept is 3.75, and the equation of the line of best fit is

y = 1.5x + 3.75, and after 13 months, 23 matches could be won.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}\)

Part A:

As we can see in the graph, the line crosses the y-axis at a certain point between 3 and 4.5.

So the y-intercept lies between 3 and 4.5

We can take the middle of these two values to get the approximate value of the y-intercept.

b = (3+4.5)/2 = 3.75

We know the line of the best fit is:

y = mx + b

y = mx + 3.75

b is the y-intercept and m is the slope of a line

Plug the point (9, 18) in the equation to get the value of m:

18 = 9m + 3.75

m = 1.5

y = 1.5x + 3.75

Plug x = 13 months in the above equation:

y = 1.5(13) + 3.75

y = 23.25 ≈ 23 number of matches that could be won

Thus, the y-intercept is 3.75, and the equation of the line of best fit is

y = 1.5x + 3.75, and after 13 months, 23 matches could be won.

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The ratio of the number of jackets to the number of sweaters is 1:4.

According to the question,

The ratio of the number of shirts to the number of trousers = 4:5

∴ Let the number of shirts be 4x and that of trousers be 5x.

The ratio of the number of jackets to the number of shirts = 3:8

∴ Let the number of jackets be 3y and that of the shirts be 8y.

The ratio of the number of sweaters to the number of trousers = 6:5

∴ Let the number of sweaters be 6z, and that of trousers be 5z.

Now,

Number of shirts = 4x = 8y

                           ⇒ x = 2y.               (1)

Number of trousers = 5x = 5z

                            ⇒ x = z                 (2)

From eq.(1) and eq.(2), we get,

x = 2y = z

⇒ z = 2y                                              (3)

But, from above, we have, the number of sweaters = 6z

                                                                                     = 6 × 2y    {from eq.(3)}

                                                                                     = 12y

∴ The ratio of the number of jackets to the number of sweaters = 3y ÷ 12y

                                                                                                    = 1:4

Hence, the ratio of the number of jackets to the number of sweaters is 1:4.

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Answer:

The ratio of the number of jackets to the number of sweaters is 1/4.

Step-by-step explanation:

Let's assign variables to the quantities mentioned in the problem:

Let S be the number of shirts.

Let T be the number of trousers.

Let J be the number of jackets.

Let W be the number of sweaters.

We are given the following ratios:

The ratio of shirts to trousers: S/T = 4/5

The ratio of jackets to shirts: J/S = 3/8

The ratio of sweaters to trousers: W/T = 6/5

We need to relate these variables using the given information to find the ratio of jackets to sweaters (J/W).

First, let's simplify the given ratios:

S/T = 4/5 can be rewritten as S = (4/5)T

J/S = 3/8 can be rewritten as J = (3/8)S

W/T = 6/5 can be rewritten as W = (6/5)T

Now, substitute these expressions into the ratio we are trying to find:

J/W = (J/S)/(W/T)

= [(3/8)S]/[(6/5)T]

= [(3/8)(4/5)T]/[(6/5)T]

= (3/8)(4/5)/(6/5)

= (3/8)(4/6)

= (3/8)(2/3)

= 6/24

= 1/4

Therefore, the ratio of the number of jackets to the number of sweaters is 1/4.

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Answer:

error= 0.1/2, 0.05

4.8 + 0.05 = 4.85

6.3 + 0.05 = 6.35

4.85 x 6.35 = 30.7975 cm (when rounded, gives 30.80 cm).

Step-by-step explanation:

The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

\(Ax + By + C = 0\)

Equation of Straight Line or Slope:

\(y = mx+b\)

Point-slope form:

\(y-y_{1} = m(x-x_1)\)

Slope when 2 points are given:

\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)

Quadratic Equation:

\(Ax^2 + Bx +C = 0\)

When lines are parallel:

Slope of both lines are equal. \(m_1 = m_2\)

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).

Work Formula:

Total Work Done = Number of Days \(\times\) Efficiency

where Efficiency is inversely proportional to Time Taken.

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Five million four thousand three hundred can be written in standard form as 5,004,300.

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Answer:

The number five million four thousand three hundred can be written in standard form as `5,004,300`. In scientific notation, it can be written as `5.0043 x 10^6`.

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The probability that the sample proportion will be less than 0.1 is 1.0000.

To find the probability that the sample proportion will be less than 0.1 when a direct mail company samples 276 people and the true proportion is 0.06, we can use the normal approximation for the binomial distribution. Here are the steps:

1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution.
  μ = n * p = 276 * 0.06 = 16.56
  σ = √(n * p * (1 - p)) = √(276 * 0.06 * 0.94) ≈ 3.94

2. Convert the sample proportion to a z-score.
  z = (x - μ) / σ = (0.1 * 276 - 16.56) / 3.94 ≈ 7.01

3. Use a z-table or calculator to find the probability corresponding to this z-score. Since we want the probability that the sample proportion is less than 0.1, we look up the area to the left of the z-score.
  P(z < 7.01) ≈ 1.0000 (almost certain)

The probability that the sample proportion will be less than 0.1 when 276 people are sampled is approximately 1.0000, or almost certain.

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Answer:

0.007 kg

Step-by-step explanation:

There are 25 packets

Each packet contains 4 biscuits.

The total number of biscuits = 4 * 25

The total number of biscuits = 100

100 biscuits = 0.7 kg

1 biscuit is 0.7 kg / 100

1 biscuit is 0.007 kg

If you are not sure of this, put it in a calculator.

Just out of curiosity  note that 1 kg = 1000 grams

0.007 kg = 0.007 * 1000 = 7 grams each.

use 0.007 as your answer.

Answer:

A) x=9

Step-by-step explanation:

48-12=36.

36/4=9

More detailed explanation:

4x+12=48

    -12    -12

     4x = 36

     /4     /4

     x   =    9

The solution of the equation is, x = 9.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The equation is,

⇒ 4x + 12 = 48

Now, We can solve the equation for value of x as;

⇒ 4x + 12 = 48

Subtract 12 both side, we get;

⇒ 4x + 12 - 12 = 48 - 12

⇒ 4x = 36

Divide by 4;

⇒ 4x/4 = 36/4

⇒ x = 9

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Answer:

the quotient of a number y and negative three point six is less than six point five.

Answer: Yes

If you notice, you can actually see that each number is multiplied by 5:

Hope this helps you!

The angle formed by the intersection of the tangents is as follows:

m∠PQR = 49 degrees

The tangent PQ and QR intersect at point Q.  Therefore, the measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs.

Hence, let's find the angle Q as follows;

m∠PQR = 1 / 2( m∠PSR - m∠PR)

Therefore,

m∠PSR  = 360 - 131 = 229 degrees

Hence,

m∠PQR = 1 / 2 (229 - 131)

m∠PQR = 1 / 2 × 98

m∠PQR = 49 degrees

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Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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Answer:

The domain of y = cos x is the set of all real numbers.

Therefore, the correct option is O A. All real numbers.

Step-by-step explanation:

The domain of y = cos x is the set of all real numbers.

Therefore, the correct option is O A. All real numbers.

The probability of selecting a black marble followed by a red marble with replacement is option A: 4.7%.

Based on the question, for one to calculate the probability of selecting a black marble followed by a red marble, we need to look at the two independent events which are:

So, the probability of selecting a black marble on the first draw is:

2 black marbles out of a total of 16 marbles (6 red + 3 yellow + 2 black + 5 pink)

= 2/16 approximately 1/8.

Based on the fact that the marble is replaced, the probabilities for each draw will have to remain the same.

So, the probability of selecting a red marble on the second draw =  6 red marbles out of a total of 16 marbles

= 6/16

= 3/8.

To know the probability of both events occurring, we need to multiply the sole probabilities:

P(black marble and then red marble) = P(black marble) x  P(red marble)

= (1/8) x (3/8)

= 3/64

So one can Convert the probability to a percentage, and it will be:

P(black marble and then red marble) = 0.047

                                                               = 4.7%

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see text below

A bag contains 6 red, 3 yellow, 2 black, and 5 pink marbles. What is the probability of selecting a black marble followed by a red marble? The first one is replaced.

4.7%

12.5%

78.3%

75%

Cable television is a form of television programming that is delivered to subscribers through a coaxial or fiber-optic cable network. It typically offers a wide range of channels and programming options, including news, sports, movies, and TV shows.

For the residents of Oak Vista, cable television is a mandatory service that is included in their monthly rent or housing fees. This means that all residents are required to pay $60 per month for the cable TV service, regardless of whether they use it or not. This is known as a bundled service, where a single fee is charged for multiple services or products.

The reason for the mandatory cable TV service is likely due to the fact that the apartment complex has a contract with a cable TV provider, and the cost of the service is spread across all residents. Additionally, offering a bundled service can be a way for the complex to offer a lower overall price for cable TV, since the cost is spread across a larger group of people.

While some residents may not want or need cable TV, the mandatory fee means that they must pay for the service regardless. However, some complexes may offer alternative options or allow residents to opt-out of the service for a reduced fee.

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Answer:   x = 39/10     y = 29/5

Answer:

(17,25)

Step-by-step explanation:

To find the solution to the system, solve with elimination.

Equation 1.

−4x + 3y =7

Equation 2.

5x − 2y =35

To cancel out the y-variable, multiply the first equation by 2, and the second equation by 3.

2(−4x + 3y =7)

-8x+6y=14

3(5x − 2y =35)

15x-6y=105

Combine both equations.

-8x+6y=14

15x-6y=105

7x=119

x= 17

Plug in x into the first equation to solve for y.

-8x+6y=14

-8(17)+6y=14

-136+6y=14

6y=150

y=25

Answer:

-4

Step-by-step explanation:

as x goes up one y goes down 4

slope is change in y over change in x

-4/1=-4

The slope of the linear function represented by the table is -6.

To find the slope of the linear function represented by the table, we can use the formula for slope:

Slope (m) = (change in y) / (change in x)

Let's calculate the slope using two points from the table. We'll choose the points (-1, 2) and (2, -16):

(change in y) = -16 - 2 = -18

(change in x) = 2 - (-1) = 3

Slope (m) = (-18) / (3) = -6

Therefore, the slope of the linear function represented by the table is -6.

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The line we want is given by the vector equation

L(t) = (4i + 3j - k) t + (5i + 2.5j + 3.1k)

L(t) = (4t + 5) i + (3t + 2.5) j + (-t + 3.1) k

As parametric equations, we write

x(t) = 4t + 5

y(t) = 3t + 2.5

z(t) = -t + 3.1

The concrete required to make the tank be 27.4122 m³.

Given, a concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick.

External diameter = 10 m

Height = 3 m

Thickness = 0.3 m

External radius = 5 m

Internal radius = 5 - 0.3 = 4.7 m

Volume = πh(e.r² - i.r²)

Volume = (3.14)(3)(5² - 4.7²)

Volume = 9.42(9.7)(0.3)

Volume = 27.4122 m³

Hence, the concrete required to make the tank be 27.4122 m³.

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