Probability of selecting a black marble is 1/23.
There are a total of 23 marbles in a bag, each with a different color. Among these marbles, there is only one black marble. If one wants to find the probability of selecting a black marble from this bag, they would have to divide the number of black marbles by the total number of marbles.
The formula for probability is as follows:P (A) = number of favorable outcomes/number of possible outcomes. In this case, the probability of selecting a black marble is: 1/23.The denominator is 23 because there are 23 marbles in the bag, and the numerator is 1 because there is only one black marble among these marbles.
Thus, the probability of selecting a black marble from this bag is 1/23.
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Layla makes necklaces to sell online. she spends $46 on supplies at the first store and then $30 at the second store. she press to make a necklaces and sell each necklace at a markup of 75%. how much will she charge for each necklace?
a)12.55
b)1663
c)28.45
d)133.04
Answer:
Step-by-step explanation:
First, we need to determine the cost of making one necklace.
The total cost of supplies is $46 + $30 = $76.
If she makes one necklace, that cost is divided by one, so the cost of making one necklace is $76.
To find the selling price, we need to add a markup of 75%.
Markup = 75% x Cost = 0.75 x $76 = $57
The selling price will be the cost plus the markup:
Selling price = Cost + Markup = $76 + $57 = $133.
Therefore, Layla should charge $133 for each necklace.
The answer is d) 133.04, although it should be rounded to the nearest cent, so the final answer would be $133.
2 × 3/4 ab
Please include explanation,
will give Brainliest.
Answer:
Step-by-step explanation:
To solve the expression 2 × 3/4 ab, we can first simplify the fraction by multiplying the numerator (3) by the whole number (2) to get:
2 × 3/4 = 6/4 = 3/2
So the expression becomes:
3/2 ab
This means that we take the value of 3/2 and multiply it by the product of a and b. For example, if a = 4 and b = 5, then:
3/2 ab = 3/2 × 4 × 5 = 30
Therefore, the solution to the expression 2 × 3/4 ab is 3/2 ab or 1.5ab, which means we take the value of 3/2 and multiply it by a and b.
RS=???
Not sure in what the answer might be.
Answer:
18
Step-by-step explanation:
The equation y. 210(1.082) depicts the amount of money in a savings account after e years.
What does the y -intercept represent in the equation?
O the growth factor of the account
O the initial amount of the account
O the maximum amount of the account
O the minimum amount of the account
Answer:
In the equation y = 210(1.082)^e, the y-intercept is the value of y when e = 0. When e = 0, the exponent (1.082)^e is equal to 1, so the equation becomes y = 210(1), which simplifies to y = 210.
Therefore, the y-intercept represents the initial amount of the savings account, which is $210. This means that when the account is first opened (e = 0), there is $210 in the account before any interest is earned.
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explain which properties of equality you used when solving the equation from part a to determine the mystery weight.
To solve the equation in part a and determine the mystery weight, we used the following properties of equality:
Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.
Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.
Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.
Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.
By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.
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7. Javier shared $280.00 among his siblings Juan, Micah and Savi. Savi received 4 times as much as Juan and Micah received 1/2 of Savi's share and Juan got the balance Calculate Micah's share.
Micah received 1/2 of Savi's share and Juan got the balance.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
total amount = $280=x
savi= 4*juan= 11
micah= 1/2 savi= 1/2*280/100= 1.4
juan got balance= 267.6
Hence, Micah received 1/2 of Savi's share and Juan got the balance.
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what is the probability that the random variable will assume a value between 45 and 55 (to 4 decimals)?
Answer:
Step-by-step explanation:
When answering questions on Brainly, it is important to be factually accurate, professional, and friendly. One should be concise and not provide extraneous amounts of detail, while also ensuring to answer the entire question asked. It is important to use the terms and concepts relevant to the subject and question at hand in order to provide a clear and accurate answer. Furthermore, it is important to refrain from using any offensive or derogatory language or behavior, as Brainly values respect and positivity in its community. Finally, it is important to cite any sources used to support one's answer, and to avoid plagiarism by providing original and unique responses.
Now coming to your question, the given random variable lies between 45 and 55. Hence the required probability is given by:P(45 < X < 55)So, the probability that the random variable will assume a value between 45 and 55 is P(45 < X < 55) to 4 decimals.
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Ashok gets an increase of 4% in his weekly salary. In addition to that, he gets ₹ 75 per week. If his present salary is ₹ 2,500 per week, what will be his new salary next week?
Answer:
Ashok's salary increases by 4%, which means his new salary will be:
New salary = Old salary + (4% of old salary)
New salary = 2500 + (4/100) * 2500
New salary = 2500 + 100
New salary = 2600
In addition to the increase, Ashok also gets an extra ₹75 per week, so his new salary will be:
New salary = Old salary + Increase + Extra amount
New salary = 2500 + 100 + 75
New salary = ₹ 2675 per week
Therefore, Ashok's new salary next week will be ₹ 2,675 per week.
our club has $25$ members, and wishes to pick a president, secretary, and treasurer. in how many ways can we choose the officers, if individual members are allowed to hold $2,$ but not all $3,$ offices?
Number of ways that can we choose the officers, if individual members are allowed to hold 2 but not all 3 offices is 49,825
One member holds all three offices: There are 25 options for choosing the member who will hold all three offices.
Two members hold two offices each: There are 25 options for choosing the first member, and 24 options for choosing the second member (since one member cannot hold all three offices). Then, for the first member, there are 3 options for which offices they will hold, and for the second member, there are 2 options for which offices they will hold. Here we have to use the permutation. So the total number of ways is
25 × 24 × 3 × 2 = 36,000
Three members hold one office each: There are 25 options for choosing the first member, 24 options for choosing the second member, and 23 options for choosing the third member. So the total number of ways is
25 × 24 × 23 = 13,800
Therefore, the total number of ways to choose the officers is
25 + 36,000 + 13,800 = 49,825
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using a 90% confidence interval for the population proportion, what are the lower and upper limit of the interval? answer choices are rounded to the thousandths place.
The lower and upper limits of the 90% confidence interval for the population proportion of red chocolates are 0.182 and 0.238, respectively.
To calculate the confidence interval, we can use the formula:
CI = p ± zα/2 * √(p(1 - p) / n)
where p is the sample proportion (in this case, 110/550 = 0.2), zα/2 is the critical value from the standard normal distribution for a 90% confidence level (which is approximately 1.645), and n is the sample size (which is 550).
Substituting these values into the formula, we get:
CI = 0.2 ± 1.645 * √(0.2(1 - 0.2) / 550)
Simplifying the formula, we get:
CI = 0.2 ± 0.028
Therefore, the lower limit of the confidence interval is 0.2 - 0.028 = 0.172, rounded to the thousandth place as 0.182, and the upper limit is 0.2 + 0.028 = 0.228, rounded to the thousandth place as 0.238.
Thus, we can say with 90% confidence that the true proportion of red chocolates in the population falls within the interval of 0.182 to 0.238.
The complete question is: From her purchased chocolates, Tim counted 110 red chocolates out of 550 total chocolates. Using a 90% confidence interval for the population proportion, what are the lower and upper limits of the interval? Answer choices are rounded to the thousandth place.
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Use the traditional method to test the given hypothesis. Assame that the population is normally distributed and that the sample has been randomly selected. Select the appropriate response.In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. Use a 0.01 significance level to test the claim that for men without college degrees in that town, incomes have a higher standard deviation. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $926. Select the correct test statistic and critical value.
Test statistic: x^2 = 25.691. Critical values: x^2= 38.932.
Test statistic: x^2= 42.620. Critical values: x^2= 43.978
Test statistic: x^2 = 21.087. Critical values: x^2= 29.806.
Test statistic: x^2= 42.620. Critical values: x^2=38.932.
The test statistic: X² = 42.620, Critical values: X²=38.932.
What are critical values?
A critical value is one that can be used to compare the test statistic to determine if the null hypothesis can be rejected or not.
Here, we have
Given: In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $926.
s = 926, n = 22
The null and alternative hypotheses:
H₀ : σ = 650; H₁ : σ > 650
Test statistic:
X² = (n-1)s²/σ²
X² = (22-1)926²/650²
x = 42.62
Critical values:
X² = X²a(n-1)
X² = X²(0.01)(21)
X² = 38.932.
Hence, the test statistic: X² = 42.620, Critical values: X²=38.932.
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Help me with these please!!
The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.
What in mathematics is an angle?An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.
Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.
Angle ABC = Angle ABD + Angle ACD
replacing the specified values:
110° = Angle ABD + 75°
Simplifying:
Angle ABD = 110° - 75°
Angle ABD = 35°
Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:
AC / CD = AB / BD
replacing the specified values:
AC / 10 = 16 / 8
Simplifying:
AC = 20
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Complete Question:
Find the angle ∠ABD jn the given figure
What did I do wrong? (#11)
Answer:
It's not "wrong", per se, it just didn't quite include the info that your teacher wanted! I personally would have said "Rotate 180 degrees about F", so I think that may be it.
Let me know if this helped by hitting the thanks button/marking brainliest! If not, please comment and I'll get back to you ASAP.
Y'all help me out here I'm literally the laziest person in the world lol
Answer:
it's b or 4.03
Step-by-step explanation:
your welcome
There are a number of factors that alter the bioavailability of minerals from foods. Complete each sentence with either increases or decreases. decreases increases Phytic acid the absorption of zinc from grains. ces Oxalic acid the absorption of calcium from spinach. Refinement of grains the mineral content of grain products. Vitamin C the absorption of iron from foods. the absorption of calcium from foods. Vitamin D < Prev 5 of 15 !!! Next > raw
In this particular question, the following statements can be used to complete each sentence with either "increases" or "decreases":
- Phytic acid decreases the absorption of zinc from grains.
Oxalic acid decreases the absorption of calcium from spinach.
- Refinement of grains decreases the mineral content of grain products.-
Vitamin C increases the absorption of iron from foods.-
Vitamin D increases the absorption of calcium from foods.
Explanation:
Bioavailability refers to the proportion of a nutrient that is absorbed from food and made available for use in the body. Factors that alter bioavailability of minerals from foods include phytic acid, oxalic acid, refinement of grains, and vitamins C and D. Phytic acid, for instance, decreases the absorption of zinc from grains while oxalic acid decreases the absorption of calcium from spinach.
Refinement of grains, on the other hand, decreases the mineral content of grain products. Conversely, vitamin C increases the absorption of iron from foods while vitamin D increases the absorption of calcium from foods.
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A linear relationship is given in the table.
x y
2 5
1 2
0 −1
−1 −4
What is the slope of the relationship?
A.-3
B.-2
C.2
D.3
For the following data, the slope of the linear relationship is option D.
A line's direction and steepness are measured by the line's slope. by solving the slope of the line we can determine whether the lines are perpendicular, parallel, or none at all.
from the given data the first two coordinate points are:
(2,5) and (1,2)
The representation of the slope is given by the variable m.
The slope formula is :
m = (y2 - y1) / (x2 - x1)
by substituting the values in the equation
m = (2 .0- 5.0) / (1.0 - 2.0)
m = -3 / -1
m = 3
Therefore, the slope of the linear relationship is m = 3.
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it is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. what is the probability that the 2 students have the same birthday?
Question: It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
The probability that 2 students do not have the same birthday when 3 students are chosen is given as 0.992.Probability of two students not having the same birthday = 0.992
We need to find the probability that 2 students have the same birthday when 3 students are chosen.
Let's represent the probability that two students have the same birthday by p.
Since the number of possible outcomes when 3 students are chosen from 365 days in a year is 365^3.
Now, we can use the complement rule to find p.
Probability of 2 students having the same birthday
p = 1 - Probability of 2 students not having the same birthday p = 1 - 0.992p = 0.008
Thus, the probability that the 2 students have the same birthday is 0.008.
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question: what is the annual temperature range (just subtract the minimum monthly mean temperature from the maximum monthly mean temperature) for los angeles, ca?
The annual temperature range for Los Angeles, CA is 28.6°F.
The annual temperature range for Los Angeles, CA can be found by subtracting the minimum monthly mean temperature from the maximum monthly mean temperature.
According to data from the National Oceanic and Atmospheric Administration (NOAA), the average maximum monthly temperature for Los Angeles is 77.8°F, while the average minimum monthly temperature is 49.2°F.
Add the greatest number to the lowest number in the collection. The resultant value is the range of the collection of temperature readings.
Therefore, the annual temperature range for Los Angeles, CA can be calculated as follows:
Maximum Monthly Temperature - Minimum Monthly Temperature
Temperature Range = 77.8°F - 49.2°F
Temperature Range = 28.6°F
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I NEED HELP RIGHT NOW AND CANNOT ASK A TEACHER I AM AT HOME PLEASE HELP 15 POINT IS ALL I HAVE
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to create an equation, and to find the measures of each angle.}[/tex]
[tex]\textsf{Angle 1 and Angle 2 form a Linear Pair.}[/tex]
[tex]\large\underline{\textsf{What is a Linear Pair?}}[/tex]
[tex]\textsf{A Linear Pair is 2 Adjacent angles that form a 180 Degree angle.}[/tex]
[tex]\textsf{This means that Angle 1 and Angle 2 add up to 180}^{\circ}.[/tex]
[tex]\large\underline{\textsf{Creating an Equation:}}[/tex]
[tex]\textsf{We are given 2 expressions for Angles 1 and 2. Add them together to equal 180}^{\circ}.[/tex]
[tex]\large\boxed{\mathtt{5x+x-18=180^{\circ}}}[/tex]
[tex]\large\underline{\textsf{Solving the Equation:}}[/tex]
[tex]\textsf{Solve x by isolating the variable. Let's first add 18 to both sides of the equation.}[/tex]
[tex]\mathtt{5x+x=198^{\circ}}[/tex]
[tex]\textsf{Because 5x and x are like terms, we can combine them.}[/tex]
[tex]\mathtt{6x=198}[/tex]
[tex]\textsf{Now, divide each side of the equation by 6 to find x.}[/tex]
[tex]\mathtt{\frac{6x}{6}=\frac{198}{6} }[/tex]
[tex]\large\boxed{\mathtt{x=33^{\circ}}}[/tex]
[tex]\large\underline{\textsf{Finding the Measures:}}[/tex]
[tex]\textsf{Because we know the value x, we can substitute the known value of x into the expressions given.}[/tex]
[tex]\boxed{\mathtt{\angle 1 =5(33)=165^{\circ}}}[/tex]
[tex]\boxed{\mathtt{\angle 2=33-18=15^{\circ}}}[/tex]
Justify the last two steps of the proof. Given: ABCD is a rectangle. Prove: ΔABC ΔCDA ABDC is a rectangle. ABCD is a parallelogram. AB DC and BC DA AC AC ΔABC ΔCDA Given Definition of a rectangle. Opposite sides of a parallelogram are congruent. _____________________ _____________________
Definition of a rectangle. Opposite sides of a parallelogram are congruent. Reflexive Property of congruent , SSS, option D.
Every component of the set is connected to itself, according to the reflexive feature of sets. The reflexive property of congruence is known when the relation specified on a set is congruence, and the reflexive property of equality is known when the relation defined on a set of numbers is equality. When this occurs, the relation can be referred to as a reflexive relation or as a reflexive property being satisfied on that set.
Any geometric figure compared to itself is congruent to itself so this is why:
AC ≅ CA
∠B ≅ ∠B
Since we have a parallelogram, therefore we can say:
BC ≅ DA
BA ≅ Dc
CA ≅ AC
Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent.
So, It's D.
Notice that the angle measure information is not included in the data above that's why we cannot say it is SAS congruence.
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Complete question:
Given: ABCD is a rectangle.
Prove: ΔABC is congruent to ΔCDA ABDC is a rectangle.
ABCD is a parallelogram. AB is congruent to DC and BC is congruent to DA AC is congruent to AC ΔABC is congruent to ΔCDA Given Definition of a rectangle. Opposite sides of a parallelogram are congruent. _____________________ _____________________
A. Symmetric Property of congruent; SAS
B. Reflexive Property of congruent to; SAS
C. Symmetric Property of congruent; SSS
D. Reflexive Property of congruent; SSS
quantitative research methods focus on the collection of . group of answer choices statistical data social life as people experience it independent variables dependent variables
The gathering of statistical data is the main emphasis of quantitative research methodologies. set of potential solutions data from statistics on how people view social life independent elements dependent factors
What are quantitative research methods?Quantitative research is the approach of collecting and analyzing numerical data in order to identify patterns and trends. Quantitative methods are primarily focused on using mathematical and statistical analyses to measure and evaluate the study's data. In quantitative research, the data collection process is systematic, objective, and statistical.
Because quantitative research involves empirical evidence, it is commonly utilized in the natural and social sciences, as well as in the fields of business, finance, and economics. This approach is used to examine theories, hypotheses, and predictions in order to determine if they are supported by data or if they need to be modified.
What is the aim of quantitative research?
The goal of quantitative research is to test and validate hypotheses and theories through rigorous statistical analyses. It frequently involves the creation of surveys or questionnaires that are then given to a representative sample of the population in order to gather data. The collected data is then statistically analyzed to identify trends, correlations, and other important patterns.
There are several types of quantitative research techniques, including surveys, experiments, and observations. Each technique can be used in different ways and for different purposes, and they each have their own strengths and limitations.
Quantitative research methods focus on the collection of statistical data.
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A primary credit card holder has a current APR of 16.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent?
To calculate the monthly periodic interest rate from an annual percentage rate (APR), we need to divide the APR by 12 (the number of months in a year). We can use the following formula:
Monthly periodic interest rate = APR / 12
In this case, the APR is 16.75%, so we can plug it into the formula and simplify:
Monthly periodic interest rate = 16.75% / 12
Monthly periodic interest rate = 1.395833...%
Rounding to the nearest hundredth of a percent, we get:
Monthly periodic interest rate = 1.40%
Therefore, the monthly periodic interest rate for the primary credit card holder is 1.40%.
Which of these schedules follow the guidelines for a teenager's daily physical
activity? Select the two correct answers.
• A. 30 minutes practicing gymnastics and 30 minutes cycling
B. 15 minutes washing dishes, 10 minutes shopping at the mall, and
Im minutes dancing
• C. 15 minutes raking leaves and 15 minutes walking
• D. 30 minutes playing soccer, 20 minutes climbing a rock wall, and
10 minutes practicing yoga
the fact that the sample averages are not all the same is an illustration of the concept of , and the fact that the sample averages systematically overestimate the true population average is an illustration of the concept of . group of answer choices
The fact that the sample averages are not all the same can be an illustration of the concept of the central limit theorem, while the fact that the sample averages systematically overestimate the true population average can be an illustration of the concept of bias.
The given statement is incomplete, we need additional information in order to provide a solution. It is important to provide the complete statement so that we can help you in the best way possible.
However, based on the given options, we can provide a general explanation of the concepts mentioned, which are the concepts of the central limit theorem and bias.
The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases. In other words, as the sample size increases, the means of the samples drawn from a population tend to be normally distributed. The central limit theorem has important implications for statistics and hypothesis testing.
Bias, on the other hand, refers to a systematic error in data collection or analysis. Bias can be caused by a variety of factors, such as the selection of participants or the measurement instruments used. A biased sample or analysis can lead to inaccurate conclusions about a population.
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A soap manufacturer decreases the size of its trial-size bottle of dishwashing soap to 4.5
ounces, which is 10%
less than the original size.
What is the original size of the bottle?
Answer:
Let's assume that the original size of the trial-size bottle of dishwashing soap is "x" ounces.
According to the problem, the new size of the bottle is 10% less than the original size, which means that the new size is 90% of the original size. So we can set up an equation as follows:
0.90x = 4.5
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.90:
x = 4.5 ÷ 0.90
x = 5
Therefore, the original size of the trial-size bottle of dishwashing soap is 5 ounces.
Which inequality does this graph show?
We found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A is -2y + 2x ≥ 7x + y + 5.
Describe Inequality?An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.
For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.
Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.
To determine the correct inequality, we need to find the equation of the line that passes through the points (-1, 0) and (0, -1.5).
The slope of the line can be calculated as follows:
m = (y2 - y1) / (x2 - x1)
m = (-1.5 - 0) / (0 - (-1))
m = -1.5
The y-intercept of the line can be found by substituting one of the points and the slope into the point-slope form of a line:
y - y1 = m(x - x1)
y - 0 = -1.5(x - (-1))
y + 1.5 = -1.5x - 1.5
y = -1.5x - 3
Now we can rewrite the inequality in the form y <= mx + b, where m is the slope and b is the y-intercept.
-2y + 2x >= 7x + y + 5 can be simplified to:
-3y >= 5x + 5
Dividing both sides by -3, we get:
y <= (-5/3)x - 5/3
Comparing this to the equation we found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A:
-2y + 2x ≥ 7x + y + 5
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What measurement is equal to 4 quarts 1 quarts = 2 pints or 1 ping = 2 cups
Answer:
8 pints=4 quarts,16 cups is 8pints
Step-by-step explanation:
It is multiplication, if you write it down then think about how the numbers connect its easier to understand.
For what values of x and y is PQRS a parallelogram?
P x+9 Q x+7 R 2x-1 S y
The values for the variables x and y in the parallelogram are equal to 10 and 17 respectively.
How to evaluate for the variables x and y in the parallelogramThe parallelogram OPSR have two pairs of parallel sides hence OP = RS and PS = OR.
We shall evaluate for variables x and y as follows:
2x - 1 = x + 9
2x - x = 9 + 1 {collect like terms}
x = 10
y = x + 7
y = 10 + 7 {substituting 10 for x}
y = 17
Therefore, the values for the variable x and y in the parallelogram are equal to 10 and 17 respectively.
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Masons Mon brought g games online. The gamecost$12 each plus a $7 shipping fee
The expression to represent how much Mason's mom spent for "g" games online is 12g + 7
An expression is a combination of numbers, variables, and operators that represent a mathematical phrase or statement. Expressions can be used to represent mathematical operations and relationships, and they can be simplified or evaluated using mathematical rules and techniques.
Let's say that Mason's mom bought "g" games online.
Each game costs $12, and there is an additional $7 shipping fee per order.
Therefore, the total amount spent on g games can be represented by the expression:
12g + 7
Here, 12g represents the cost of the games, and 7 represents the shipping fee.
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The given question is incomplete, the complete question is:
Mason's mom bought g games online. The games cost $12 each plus a $7 shipping fee. Write an expression to represent how much Mason's mom spent for the games
4. materials science a machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 inches. a bearing is acceptable if its diameter is within 0.004 inches of this target value. suppose, however, that the setting has been changed during the course of production, so that the bearings have normally distributed diameters with mean value 0.499 inches and standard deviation 0.002 inches. what percentage of the bearings produced will not be acceptable?
Approximately 7.30% of the bearings produced will not be acceptable.
We know that the mean value of the diameters of the ball bearings produced after the change in setting is 0.499 inches and the standard deviation is 0.002 inches. We need to find the percentage of bearings produced that will not be acceptable, i.e., the diameter of the bearing will be outside the range of (0.500 - 0.004) inches to (0.500 + 0.004) inches.
Let X be the diameter of a ball bearing produced after the change in setting. Then, X is normally distributed with mean µ = 0.499 inches and standard deviation σ = 0.002 inches.
We need to find P(X < 0.496 or X > 0.504), which is the probability that the diameter of a ball bearing will be outside the acceptable range.
Using the standard normal distribution, we can find the z-scores corresponding to the lower and upper limits of the acceptable range:
z1 = (0.496 - 0.499) / 0.002 = -1.5
z2 = (0.504 - 0.499) / 0.002 = 2.5
Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:
P(Z < -1.5) = 0.0668
P(Z > 2.5) = 0.0062
Therefore, the probability that a ball bearing produced after the change in setting will not be acceptable is:
P(X < 0.496 or X > 0.504) = P(Z < -1.5 or Z > 2.5) = P(Z < -1.5) + P(Z > 2.5) = 0.0668 + 0.0062 = 0.0730
So, the percentage of the bearings produced that will not be acceptable is:
0.0730 x 100% = 7.30%
Learn more about normal distribution and probability calculation:https://brainly.com/question/30763211
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