The letter represented by the star symbol is 1.
We can start by using the rules of arithmetic. Since each symbol represents a different digit, we can represent the symbols with the numbers 0 to 9. Then we can write the equation as an algebraic expression and solve for the star symbol.
Let's assign the value of the letter represented by the star symbol to x.
A + B = 10x + x = 11x
We know that the maximum value for the result of the addition (C) is 18 (9 + 9) and that the maximum value for 11x is 990 (90 * 11), so x cannot be greater than 9.
Let's try the lowest value for x, which is 0.
A + B = 10 * 0 + 0 = 0
Since 0 cannot be a digit in A or B, x cannot be 0.
Let's try the next value for x, which is 1.
A + B = 10 * 1 + 1 = 11
Since 11 is a valid result of the addition, x = 1 is a solution.
Therefore, the letter represented by the star symbol is 1.
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The complete question is:
In the following addition problem, different letters represent different digits, and equal letters represent equal digits. Find the value of the letter represented by the star symbol. A + B = C
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Which measures of central tendency would be affected if the outlier 11 was added to the following set? Thank you to whoever answers this.
27, 20, 34, 37, 21, 42, 39
A mean, median, and mode
B mean and mode
C mean and median
D mean only
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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what three statements about bias are true
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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What is 19 °C in °F?
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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what is the complex conjugate of vector a ?
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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What is the mass in grams of 0. 450 moles of magnesium sulfate, MgSO4?
grams
Your answer should be rounded to three significant figures. Do not include units in your answer.
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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Find the scale factor of Figure A to Figure B.
A- 5:9
B- 7:18
C- 9:5
D- 18:7
The scale factor of Figure A to Figure B is A- 5:9
How to determine the scale factorFrom the question, we have the following parameters that can be used in our computation:
Figure A and Figure B
The scale factor of Figure A to Figure B is calculated as
Scale factor = Figure B : Figure A
Substitute the known values in the above equation, so, we have the following representation
Scale factor = 20 : 36
Evaluate
Scale factor = 5 : 9
Hence, teh scale factor is 5 : 9
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Please help trying to answer it can be with or without step with step
suppose that the point (x, y) is in the indicated quadrant. decide whether the given ratio is positive or negative. recall that in quadrant i, is positive or negative?
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.
What is a quadrant?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:
Quadrant I: both x and y are positive.Quadrant II: x is negative while y is positive.Quadrant III: both x and y are negative.Quadrant IV: x is positive while y is negative.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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Find the length of segment EF
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:
What is meant by coordinate?A point or shape's location in a two-dimensional plane can be found using coordinates, which are a pair of numbers. The terms "x-coordinate" and "y-coordinate" are used to define a point's location on a 2D plane. Coordinates are always stated in brackets with a comma separating the two numbers. Coordinates are ordered pairs of numbers where the first number represents the point on the x axis and the second number represents the point on the y axis.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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To bake a cake, 750g of flour i added to 250 of butter and 300g of ugar. F
ind the ratio of (a) butter to flour (b) flour to ugar (c) butter to ugar
If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.
What is meant by ratios?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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A crypto investment halves every 2 days. Is this an example of an increasing or decreasing relation?
How much will their investment be worth after 6 days if the account had $500 to begin with?
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
Root 3 (root 3 - 1) expand and simplify the following.
The simplification of the expression gives 3 + √3
How to simplify a surd expression?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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when the increase in demand is greater than the decrease in supply, the equilibrium price _____ and the equilibrium quantity _____.
Answer:
increasedeacreasesWhen the increase in demand is greater than the decrease in supply, the equilibrium price rises and the equilibrium quantity increases.
What is economic equilibrium?
Economic equilibrium, as used in economics, is a state in which forces such as supply and demand are in balance and where, in the absence of external influences, the values of economic variables will remain constant.
The equilibrium quantity rises if the rise in demand outweighs the fall in supply. The equilibrium quantity falls if the rise in demand is smaller than the fall in supply. Equilibrium price rises in each scenario.
The supply and demand curves move in opposition to one another. However, the supply curve shifted to the left while the demand curve shifted to the right (signalling a rise in demand) (indicating a decrease in supply).
In the case increase in demand > decrease in supply
In this instance, the supply curve's leftward movement is proportionally less than the rightward change of the demand curve. So, the price and the equilibrium quantity both increase.
Therefore, the equilibrium price and quantity increases.
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A Parabola is graphed below. What is the vertex form of the parabola?
A. y=( x - 3 )² + 5
B. y= -5 ( x - 2 )² - 3
C. y= 3 ( x - 2 )² - 5
D. y= -1 ( x - 3 )² + 5
The graphed quadratic equation, in vertex form, is:
y = 3*(x - 2)^2 - 5
So the correct option is C.
What is the vertex form of the parabola?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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A survey of 225 students showed the mean number of hours spent studying per week was 20. 6 and the standard deviation was 2. 7. Assuming a 90% confidence level, the margin of error is approximately a 4-column table has 2 rows. The first column has entries confidence level (percentage), z-score. The second column has entries 90, 1. 645. The third column has entries 96, 1. 96. The fourth column has entries 99, 2. 58.
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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What is 45 divided by 3 using long division?
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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Determine whether an observational study or an experimental study is used.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
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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determine the value of s , the arc length (measured in inches) cut off in a circle with a radius of 8 inches by an angle with a measure of 2.4 radians.
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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21.1.4 Quiz: Thinking Chronologically
Question 5 of 5
Which timeline correctly organizes the founding of important world religions?
O A
B.
О с.
O D.
World Religions
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.
·
← PREVIOUS
Buddhism
Judaism
Christianity
Hinduism
Judaism
Buddhism
Judaism
Islam
Christianity
Christianity
Islam
Christianity
Islam
Islam
Hinduism
Judaism
The timeline which correctly organizes the founding of important world religions are;
Judaism, Buddhism, Christianity, and Islam
The correct answer choice is option B.
Which timeline correctly organizes important world religion?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;
JudaismHinduismBuddhismChristianityIslamTherefore, the important world religions are in the order; Judaism, Hinduism, Buddhism, Christianity and Islam.
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How to Calculate the Volume of a Cube: Formula & Practice ?
Volume = a3, where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.
How do you determine a cube's volume? The Volume Calculator.Multiplying the length, breadth, and height yields the volume calculation formula.The fact that each of these measurements for a cube has the exact same measurement is good news.Any side's length can therefore be multiplied by three.Volume = side * side * side follows from this.Volume = a3, where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.By multiplying the edge value by itself three times, one can determine the volume of a cube.For instance, if an edge is 5 inches long, the volume is 53.Remember that a cube's volume and all of its corners are the same size.To learn more about volume of a cube refer
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[tex]z^{9} x z^{6} / z^{7}[/tex]
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
How do you use the mean absolute deviation to compare data sets?
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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I need help with my homework
Answer:
Step-by-step explanation: First you need to know the powers, the power of a number says how many times to use the number in a multiplication. Therefore, you should be able to multiply that by ur number.
Calculate the measures of spread for Mrs. Hampton’s class data. Justify your response by describing the process used to find each measure. 20 points for who ever answers
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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factorise 3y^2+10y-8
Answer:
(3y-2)(y+4)Ω
Step-by-step explanation:
real simple
Valeria drew a scale drawing of a house and its lot. The scale of the drawing was
12 centimeters : 7 meters. The actual length of the front patio is 21 meters. How long is the
patio in the drawing?
centimeters
The length of the patio in the drawing, according to the scale of the drawing of 12 cm : 7 m, is 36 cm.
A scale is defined to be the ratio between the size of a given original object and a new object, which is its representation but is either smaller or bigger. It refers to the relative size of an object. Sometimes it is called a scale factor.
We are given a scale of the drawing of 12 cm : 7 m. Also, the actual length of the front patio is 21 m. To find the length of the patio in the drawing, we'll use algebra.
First, we write an equation that contains the scale of the drawing and the ratio of the actual length of the front patio to the length of the patio in the drawing, which is unknown still so we use a variabel x:
12 cm / 7 m = x / 21 m
Note that we're asked to find the length of the patio in the drawing in centimeters, so we'll then need to convert from meters to centimeters. Remember that 1 meter is defined to be equal to 100 centimeters.
12 cm / (7 · 100) = x / (21 · 100)
12 cm / 700 cm = x / 2,100 cm
Finally, let's solve for x.
12 / 700 = x / 2,100
3 / 175 = x / 2,100
6,300 = 175x
175x = 6,300
x = 36
Since x = 36 and it represents the length of the patio in the drawing, it then is equal to 36 centimeters.
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a jar contains three red, five green, two blue, and six yellow marbles. what is the ratio of red to green to blue to yellow marbles?
The ratio of red to green to blue to yellow marbles is, 3 : 5 : 2 : 6
What is the ratio?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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a factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. a simple random sample of 100 sheets of glass is to be measured, and the sample mean thickness of the 100 sheets x is to be computed. we know the random variable x has approximately a normal distribution because of the group of answer choices law of large numbers. central limit theorem. law of proportions. fact that probability is the long run proportion of times an event occurs. normality of the population distribution.
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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The shortest side of a right triangle is 7.2 centimeters long and the longest side is 15.5 centimeters long.
What is the length, to the nearest tenth of a centimeter, of the third side? (1 point)
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!! :))
Find the length of the third side. If necessary, round to the nearest tenth.
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