Zachary has mangos and papayas in a ratio of 41:5. How many mangos does he have if he has 50 papayas?

Step-by-step explanation:

when multiplying factors of the same base, we can simply add the exponents.

when dividing, we subtract.

so,

z⁹xz⁶/z⁷ = xz^(9+6-7) = xz⁸

If the vector a = x + iy, then the complex conjugate of vector a is x - iy where x is the real part and b is the imaginary part.

A number that may be expressed as (a + ib), where a denotes the real component, b denotes the imaginary part, and I denotes a fictitious number called iota, which is equivalent to the root of -1. In mathematics, a conjugate is created by flipping the sign of one of a binomial's terms.

A complex number's reflection about the horizontal axis (real axis) on Arcand's plane is represented by the conjugate of that complex number.

Another definition of a complex conjugate or conjugate of a complex number is a complex number having the same real component as the original number and the opposite sign of the imaginary part while maintaining the same magnitude, i.e., the original complex number's 'i' changes to the conjugate's '-i'.

Let a = x + iy

Complex conjugate of a is

a* = x - iy

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When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean and vice-versa.

What is mean absolute deviation?

The ratio of the sum of all absolute values of deviation from the central measure to the total number of observations is known as the mean absolute deviation.

We find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data.

The mean absolute deviation reveals how dispersed or concentrated a group of data is around the mean. This is the data's variation.

When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean. Data points are more closely packed around the mean when the mean absolute deviation is lower.

Hence, this way the mean absolute deviation is used to compare data sets.

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Answer:

19.2 inches

Step-by-step explanation:

The arc length,s, can be calculated using the formula s=r*c, where r is the radius of the circle and c is the central angle in radians. So, for a circle with a radius of 8 inches and a central angle of 2.4 radians, the arc length would be s=8 inches*2.4 radians =19.2 inches

The arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.

What is the arc length?

Arc length is a measure of the distance along a curved line segment of a circle or a curve. It represents the length of a portion of the circumference of a circle, or the distance between two points on a curved line. In mathematical terms, it is defined as the integral of the magnitude of the velocity vector along the curve. The formula for the arc length of a circle depends on the radius r and the central angle θ (measured in radians) that cuts off the arc. It is given by

s = r * θ

In this case, the radius r is 8 inches, and the central angle θ is 2.4 radians. Plugging in these values, we get:

s = 8 * 2.4 = 19.2 inches

Hence, the arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.

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The number of pies made by 1 peck of apples is 5.25.

What is the Unitary method?

A quantity's unit value must first be determined in order to solve a problem for two different quantities of the quantity. The unitary approach is the name of this technique.

Due to that,

One bushel of apples weighs 42 pounds.

There are four pecks in a bushel.

Additionally, two pounds of apples are needed to produce one pie.

The following unitary method can be used to tackle the provided problem:

One peck weighs 42/4, or 10.5 pounds.

Since one pie only requires two pounds.

Pie can be made from 1 pound.

Therefore, 10.5 pounds or one peck can yield 5.25 pies (10.5 0.5).

Thus, 5.25 pies can be made from one peck of apples.

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Number of seconds it takes the object to travel the entire length of the path is 15 seconds.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, the object travels 1/20 of the length of the path in 3/4 seconds.

1/20 is a tiny portion of the length that needs to be traveled.  

20/20 is the whole length.  

If 1/20 gets traveled in 3/4 of a second, multiply 3/4 by 20.

That is, 20(3/4) = 15 seconds

Therefore, number of seconds it takes the object to travel the entire length of the path is 15 seconds.

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The graphed quadratic equation, in vertex form, is:

y = 3*(x - 2)^2 - 5

So the correct option is C.

Remember that for a quadratic equation with a leading coefficient a and a vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we can see that the vertex is at the point (2, -5), replacing that we will get:

y = a*(x - 2)^2 - 5

We also can see that the parabola passes through (0, 7), then we can replace that to get:

7 = a*(0 - 2)^2 - 5

7 = 4a - 5

7 + 5 = 4a

12/4 = a

3 = a

The quadratic equation is:

y = 3*(x - 2)^2 - 5

The correct option is C.

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45 divided by 3 is 15. The solution has been obtained by using long division.

What is long division?

When splitting huge numbers, the task is divided into several sequential steps using the long division approach. The dividend is divided by the divisor, just like in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

Using long division, we get    

   1 5  

3 | 45

-  3              (Multiplying 3 by 1, we get 3)

    1 5            (Bringing down the next number of the dividend)

-  1 5            (Multiplying 3 by 5, we get 15)

    0  

Hence, 45 divided by 3 is 15.

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Volume = a3, where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.

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The ratio of red to green to blue to yellow marbles is, 3 : 5 : 2 : 6

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Give that,

A jar contains,

three red, five green, two blue, and six yellow marbles

the ratio of red to green to blue to yellow marbles = ?

The ratio can be written as,

⇒ 3 : 5 : 2 : 6

Hence, the ratio of balls is 3 : 5 : 2 : 6

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Answer:

(3y-2)(y+4)Ω

Step-by-step explanation:

real simple

Answer: 15.5^2 - 7.2^2 = 240.25 - 51.84= 188.41

188.41 square root is 13.7262522197 or 13.7

Step-by-step explanation: Hope this helps!! :))

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

Given data :

a )

There are 7 people from the CS department and 5 people from the math (M) department who could serve on the committee, so there are a total of 12 people.

department that could serve on a 4-person committee

b) probability that the only people serving on the committee are from the cs department :

The general probability formula can be expressed as: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or. P(A) = f / N

 = 5 / 7

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To calculate the measures of spread for Mrs. Hampton's class data, you need to calculate the range, interquartile range (IQR), variance, and standard deviation.

The range is the difference between the highest and lowest values. To calculate the IQR, you must first find the quartiles of the data set.

The variance is the sum of the squared difference between each data value and the mean, divided by the number of data values. Finally, the standard deviation is the square root of the variance. To justify your response, you can explain how each of these measures of spread can provide insight into the data set, such as showing the spread of values or the degree of variation.

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It is used the observational study. A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Now, According to the question:

"Information available from the question"

A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Statisticians often refer to the "levels of measurement" of a variable, a measure, or a scale to distinguish between measured variables that have different properties. There are four basic levels: nominal, ordinal, interval, and ratio.

In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

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Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

Let us write down some of the parameters and statistics that are given in the question.

Population mean thickness

μ=4mm.

Population standard deviation

σ=1.1mm.

Random sample size

n=100.

Let the random normal variable

¯X denote the average thickness of the sample.

Then according to the Central Limit Theorem,

¯X

follows a normal distribution with mean

μ¯X=μ=4

and standard deviation

σ¯X=σ√n=1.1√100=1.110=0.11.

Then we can convert ¯X

into its standard normal form ¯Z

using the following transformation:

¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)

Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need

P(¯X<3.91).

Using (2) we get

P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)

Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

which is our answer.

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Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

Let us write down some of the parameters and statistics that are given in the question.

Population mean thickness

μ=4mm.

Population standard deviation

σ=1.1mm.

Random sample size

n=100.

Let the random normal variable

¯X denotes the average thickness of the sample.

Then according to the Central Limit Theorem,

¯X

follows a normal distribution with mean

μ¯X=μ=4

and standard deviation

σ¯X=σ√n=1.1√100=1.110=0.11.

Then we can convert ¯X

into its standard normal form ¯Z

using the following transformation:

¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)

Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need

P(¯X<3.91).

Using (2) we get

P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)

Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

which is our answer.

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If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage.

A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.

Two numbers or measurements are compared to form a ratio. The quantities being compared are referred to as the terms of the ratio. A ratio divides two amounts into equal parts, with the dividend or antecedent serving as the unit of comparison and the divisor or unit of comparison serving as the unit of comparison.

To make a cake, I combined 750g of flour, 250g of butter, and 300g of sugar.

a) 250/750 = 1/3 = 1 : 3

b) 750/300 = 15/6 = 5/2 = 5 : 2

c) 250/300 = 5/6 = 5 : 6

If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.

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Answer: 66.2°F

Step-by-step explanation: (19°C × 9/5) + 32 = 66.2°F

Answer is 66.2°F.

How to calculate 19 °C in °F?

The base formula for this c to f converter is

Fahrenheit = (19 °C x 9/5) + 32

                 = 66.2°F

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The simplification of the expression gives 3 + √3

Simplification of an expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression

Surds are represented by square roots of non-perfect squares and are expressed using the radical symbol (√). For example, √2 is a surd, as it cannot be expressed as a finite decimal or a fraction.

√3(√3 - 1) =  (√3)*√3 + (√3)*1

                 = 3 + √3

Therefore, the expression can be simplified as 3 + √3

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Bias results from random variation and will always be present, while bias results from samples that do not represent the population. Bias can usually be reduced when the sample size is larger.

Bias is an error that occurs in statistical studies when the results are not representative of the true population. Bias can occur when the sample size is too small, or when the sample does not accurately reflect the population. This means that even if the study is perfectly designed, bias will still exist. Additionally, bias can result from samples that do not represent the population. For example, if a study is conducted on a population that is predominantly male, then the results may be biased towards male behavior. Finally, bias is usually reduced when the sample size is larger. This is because a larger sample size provides for more accurate results, as there is less of a chance that random variation will affect the data. Therefore, increasing the sample size is a helpful way to reduce bias in a study.

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The timeline which correctly organizes the founding of important world religions are;

Judaism, Buddhism, Christianity, and Islam

The correct answer choice is option B.

Chronological order is the order of events from the first to the last.

Christianity was founded about 2,000 years ago.

Islam was founded about 1,400 years ago.

Hinduism was founded about 3,500 years ago.

Buddhism was founded about 2,500 years ago.

Judaism was founded about 4,000 years ago

Arrangements from the first to the last;

Therefore, the important world religions are in the order; Judaism, Hinduism, Buddhism, Christianity and Islam.

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The true mean study time is likely between 19.6 and 21.6 hours per week .The higher the confidence level, meaning that we can be more sure that the true mean study time is within the given range.

The margin of error is an important statistic that helps measure the accuracy of a survey. It is calculated by multiplying the standard deviation by the z-score for the given confidence level. A 90% confidence level has a z-score of 1.645, a 96% confidence level has a z-score of 1.96, and a 99% confidence level has a z-score of 2.58. Using this information, the margin of error for a survey of 225 students with a mean study time of 20.6 and a standard deviation of 2.7 is approximately 1.0. This means that the true mean study time is likely between 19.6 and 21.6 hours per week. The higher the confidence level, the higher the margin of error, meaning that we can be more sure that the true mean study time is within the given range.

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The mass in grams of 0. 450 moles of magnesium sulfate, MgSO4 in grams is 54.2.

The mole, which is 6.0221023 molecular entities, is the basic unit of a substance. One mole of a substance is equivalent to that substance's molecular weight.

The link between moles and molar mass means that the quantity of moles in a material is equal to the product of its mass and molecular mass.

The molar mass of magnesium sulphate is:

Magnesium = 24

Oxygen = 16 x 4 = 64

Sulphate = 32

Thus, the mass of magnesium sulphate is = 24 + 64 + 32 = 120 grams.

Now, moles is equal to:

Moles = given mass/molecular mass

Putting the values:

moles = given mass / 120

0.450 x 120 = given mass

Given mass = 54g.

Thus, the given mass of the magnesium sulphate is 54 g.

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The derivative of the natural log of y is (1/y)(dy/dx). The derivative is performed with respect to x.

What is a natural logarithm?

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equal to 2.718281828459.

Given function is log y.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative.

Generally derivative or the changes of the function is found with respect to x.

Assume that

z = log y

Differentiate with respect to x:

dz/dx = d(log y)/dx

Applying the formula of drivative d(ogx)/dx = 1/x:

dz/dx = (1/y)(dy/dx)

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The coordinates of A= are also (-3,4). The answer to the query is determined by the coordinates of the second endpoint B. (x, y). The midpoint's coordinates can be calculated using the formula below:

The following are b's coordinates: B= (-7,-8) (-7,-8)

We are given the midpoint's coordinates as M= (-5,-2).

Furthermore, A='s coordinates are (-3,4). The solution to the question depends on the coordinates of the second endpoint B.

the coordinates of B (x, y). The following formula can be used to determine the midpoint's coordinates:

[tex]$& x_m=\frac{x_a+x_b}{2} \\[/tex]

[tex]$& y_m=\frac{y_a+y_b}{2}[/tex]

We know xa = -3 and xm = -5. Solve the first equation for x b :

[tex]$2 x_m=x_a+x_b \Rightarrow x_b=2 x_m-x_a[/tex]

Substituting:

[tex]$& x_b=2 \cdot(-5)-(-3)=-10+3 \\[/tex]

[tex]$& x_b=-7[/tex]

We can solve the second equation for xb and get:

[tex]$y_b=2 y_m-y_a[/tex]

Since ya = 4 and ym = -2, then:

[tex]$& y_b=2 \cdot(-2)-(4)=-4-4 \\[/tex]

[tex]$& y_b=-8[/tex]

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Assuming the point (x, y) is in the indicated quadrant, the given ratio are as follows;

Quadrant II, x/y is a negative ratio.

Quadrant III, y/x is a positive ratio.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Now, we can determine the whether the given ratios are positive or negative:

Quadrant II, x/y = -x/y (negative ratio).

Quadrant III, y/x = -y/-x (positive ratio).

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Answer: 10

Step-by-step explanation:

a2 + b2 =c2

(5 x 5) + (9 x 9) = c2

25 + 81 = 106

Root of 106 = 10.295630141

Round to the nearest tenth

Answer:  Decreasing, if it "Halves (cuts in half)". If it was increasing, it would probably say double.

Step-by-step explanation:

So, if it was being cut in half every two days, we would only be counting days 2, 4, and 6.

So days 2, it would be cut in half, and go from 500 to 250. Day 4, it would go from 250 to 125. The day 6, it would go from 125 to 62.5.

In 6 days, the investment will be worth $62.50

Mean and median measures of central tendency would be affected if the outlier 11 was added to the data set.

As per the given data, the data set is 27, 20, 34, 37, 21, 42, and 39.

Mean of the data is the sum of all observations divided by the total number of observations.

Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39}{7}[/tex]

Mean = [tex]$\frac{220}{7}[/tex]

Mean = 31.42

The median of the data for an odd number of observations is the middlemost term.

First, arrange the data in ascending order.

20, 21, 27, 34, 37, 39, 42

Middlemost term = 34.

The mode of the data is the most repeated data.

As no number is repeated there will be no mode.

As given 11 is added to the data set.

Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39+11}{8}[/tex]

Mean = [tex]$\frac{231}{8}[/tex]

Mean = 28.8

The median of the data for an even number of observations is the average of the middle two terms.

First, arrange the data in ascending order.

11, 20, 21, 27, 34, 37, 39, 42

Median = [tex]$\frac{27+34}{2}[/tex]

Median = [tex]$\frac{61}{2}[/tex]

Median = 30.5

For the new data set also there will be no mode as there are no repeated numbers.

Comparing old and new values there is a change in the values of mean and median.

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