The equivalent expression using associative property is; 5×(3×12).
Given expression is; [(5 × 3) × 12]
The associative property is a property of addition and multiplication that allows the grouping of numbers or variables without changing the result.
For addition: (a + b)+c = a+(b + c)
For multiplication: (a × b) ×c = a × (b × c)
In simpler terms, it means that you can add or multiply a set of numbers in any order, and still get the same result.
Therefore, the equivalent expression to [(5 × 3) × 12] using only the associative property would have the same operands but a different grouping. One possibility would be;
[(5 × 3) × 12] = [5 × (3 × 12]
Both expressions simplify to 180.
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Circles - Circumference - Question 11
For the given problem, a.)The unicycle covers 1.885 meters, in one revolution of wheel. b.) The wheel must rotate 53 times to cover distance of 100 metres.
How to calculate distance covered by wheel in one rotation?a.) The circumference of a unicycle's wheel is determined by
[tex]\qquad \qquad C = \pi d\\ \text {where, d is the diameter of the wheel. }[/tex]
As a result, the unicycle moves C metres when the wheel revolves once.
Now, on substituting d = 60 cm and π= 3.14.
We obtain,
[tex]C\approx 188.5 cm = 1.885 m[/tex] (∵ 1m = 100cm)
As a result, when the wheel revolves once, the unicycle goes 1.885 metres.
How to calculate number of rotation required by wheel?b.) Now, Distance covered in one rotation by wheel = [tex]C = 1.885 m[/tex]
To travel 100 metres, wheel need to rotate = 100/C times.
As a result, the number of full rotations necessary is:
[tex]100/C = 100/1.885 = 53.0504 \;rotations[/tex]
Thus, To traverse 100 metres, the wheel must rotate 53.04 times or 53 times( in nearest whole number )
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A group of 8 students was asked, "How many hours did you watch television last week?" Here are their responses.
13, 16, 15, 11, 11, 4, 6, 19
Find the median and mean number of hours for these students.
If necessary, round your answers to the nearest tenth.
(a) Median: hours
(b) Mean:
hours
X
Xx
5
Ś
Answer:
Median: As this is a set of 8, add the two numbers which are in the middle (11 and 13) and then divide them by two.
Mean: Add all of the numbers in the set and then divide the answer by the total number of the numbers in the set, which is 8.
REMINDER: DO NOT use your calculator or an app to obtain normal curve areas such as you would for finding a p-value. Use the table in your formula packet. DO NOT use another method or the difference in precision may cause you to lose points.
An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of n=84
�
=
84
college students students found 31 who had brown eyes.
Consider testing
H0:p=.45
�
0
:
�
=
.45
Ha:p≠.45
�
�
:
�
≠
.45
(a) The test statistic is z
�
=
(b) P-value =
Answer:
Step-by-step explanation:
A randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.
What is statistics?
Statistics is the science of collecting, organizing, analyzing, and interpreting data. It involves describing, summarizing, and making inferences about a given set of data. Statistics is used to make decisions in various fields, such as business, economics, medicine, psychology, and engineering. Statistical methods are used to help scientists understand the behavior of complex systems, to analyze the relationships between different variables, and to test hypotheses. Additionally, statistics can be used to draw conclusions from data, to identify patterns, to estimate probabilities, and to make predictions.
In order to establish causality, the best type of study to conduct is a randomized controlled trial (RCT). An RCT is a type of experiment designed to establish a cause-and-effect relationship between variables. This study involves randomly assigning individuals to different experimental groups, and then comparing the outcomes between the groups. This helps to determine the effects of a particular treatment or intervention on a population.
For example, if we wanted to study the effects of a new medication on a particular condition, we would create two groups of people – one group would receive the medication and the other would receive a placebo. We would then measure the outcomes of the two groups to see if the medication has an effect on the condition. This type of study helps to establish a causal relationship between the treatment and the outcome, as the randomization helps to control for other confounding factors that could influence the results.
Therefore, a randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.
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(a) The test statistic is z = -1.788 and (b) P-value = 0.0734.
Hypothesis testing:Hypothesis testing is a statistical method used to make decisions about a population based on a sample of data.
The process involves setting up a null hypothesis (H₀) and an alternative hypothesis (Hₐ), collecting data from a sample, calculating a test statistic based on the sample data, and using the test statistic to determine whether to reject or fail to reject the null hypothesis
Here we have
An article published in the Washington Post claims that 45 percent of all Americans have brown eyes.
A random sample of n = 78 college students found 30 who had brown eyes. Consider testing = H₀: p =0 .45 Hₐ:p + 0.45
(a) The test statistic can be calculated using the formula:
z = (p' - p) / √(p(1-p) / n)
where p' is the sample proportion, p is the hypothesized proportion under the null hypothesis, and n is the sample size.
In this case, the hypothesized proportion is p = 0.45, the sample proportion is p' = 30/78 = 0.3846 (rounded to four decimal places), and the sample size is n = 78. Therefore:
z = (0.3846 - 0.45) / √(0.45 × 0.55 / 78)
z = -1.788
So the test statistic is z = -1.788.
(b) To find the p-value, we need to look up the area in the standard normal distribution table corresponding to the test statistic z = -1.788. The area to the left of z = -1.788 is 0.0367 (rounded to four decimal places). Since this is a two-tailed test (Ha: p > 0.45), we need to double this area to get the p-value:
p-value = 2 × 0.0367
p-value = 0.0734 (rounded to four decimal places)
Therefore,
(a) The test statistic is z = -1.788 and (b) P-value = 0.0734.
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Complete Question:
REMINDER: DO NOT use your calculator or an app to obtain normal curve areas such as you would for finding a p-value. Use the table in your formula packet. DO NOT use another method or the difference in precision may cause you to lose points. An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of n = 78 college students found 30 who had brown eyes. Consider testing = H₀: p= 0.45 Hₐ:p + 0.45 (a) The test statistic is z = -1.161 (b) P-value =
Lester got $50 for his birthday, so his mom took him to the bank to open a savings account. Going forward, Lester also plans to deposit all of his income into his savings account each week. He has two sources of weekly income: his $10 allowance and the $15 he makes from delivering newspapers
Answer: (11) Julius asks Rachel if she would like to sell her boat. Rachel privately has no interest in selling her boat and believes that Julius can't afford her boat anyway. Rachel says, "I'd sell my boat to you for $20,000." To Rachel's surprise, Julius responds "Ok, it's a deal." Rachel does not want to sell the boat to Julius for any price. Julius and Rachel have:
Billy wants to estimate the percentage of students who live more than three miles from the school. He wants to create a 95% confidence interval which has an error bound of at most 3%. How many students should be polled to create the confidence interval?
z0.10 z0.05 z0.025 z0.01 z0.005
1.282 1.645 1.960 2.326 2.576
The percentage with a 95% confidence interval that has an error bound of at most 3%.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, if there are 20 red marbles out of 100 marbles in a jar, we can say that the percentage of red marbles is 20%. Similarly, if a store offers a 10% discount on a $50 item, the discounted price would be $45.
Percentages are commonly used to represent proportions or rates in various contexts, such as finance, and science. They allow us to easily compare and communicate numbers on a standardized scale, making it easier to interpret and analyze data.
To estimate the required sample size, we need to use the following formula:
n = (z*σ / E)^2
where:
n is the sample size we need to estimate the percentage with the desired error bound
z is the z-score for the desired level of confidence (95% in this case), which is 1.96
σ is the standard deviation of the population (unknown)
E is the desired margin of error, which is 3% of the percentage we are trying to estimate
Since we do not know the standard deviation of the population, we can use a conservative estimate of 0.5 (which gives the largest possible sample size).
Substituting the values we have:
n = (1.96 * 0.5 / 0.03)^2
n = 1067.11
So we would need to poll at least 1068 students to estimate the percentage with a 95% confidence interval that has an error bound of at most 3%.
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Sketch the graph of the following system of equations and label at least 3 points on each graph. At what point do the equations intersect ?
x + y = 4
2x + 3y = 18
PLEASE HELP TIMED QUIZ!! 25 POINTS!
The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.
The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.
The point of intersection is (-6, 10).
We have,
To sketch the graph of the system of equations:
x + y = 4
2x + 3y = 18
We can start by solving each equation for y:
y = -x + 4
y = (-2/3)x + 6
Then, we can plot a few points on each graph by choosing values of x and solving for y.
Here are three points for each graph:
x + y = 4:
x = -4, y = 8: (-4, 8)
x = 0, y = 4: (0, 4)
x = 4, y = 0: (4, 0)
2x + 3y = 18:
x = 0, y = 6: (0, 6)
x = 3, y = 4: (3, 4)
x = 9, y = 0: (9, 0)
To plot the graphs, we can use these points and draw a straight line through each set of three points.
The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.
The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.
To find the point of intersection, we can solve the system of equations:
x + y = 4
2x + 3y = 18
One way to solve this system is to use substitution.
We can solve the first equation for x:
x = 4 - y
Then we can substitute this expression for x into the second equation and solve for y:
2(4 - y) + 3y = 18
8 - 2y + 3y = 18
y = 10
Now that we know that y = 10, we can substitute this value into either equation to solve for x:
x + y = 4
x + 10 = 4
x = -6
So the point of intersection is (-6, 10).
Thus,
The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.
The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.
The point of intersection is (-6, 10).
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find the value of x
3x + 7 = 19
give full solution
Answer:
hope it helps
Step-by-step explanation:
The given equation is as follows:
3x + 7 = 19
To solve for x, we need to isolate x on one side of the equation.
First, we can start by subtracting 7 from both sides of the equation to get rid of the constant term:
3x + 7 - 7 = 19 - 7
Simplifying, we get:
3x = 12
Next, we can find x by dividing both sides of the equation by 3:
3x/3 = 12/3
Simplifying, we get:
x = 4
Therefore, the solution to the equation 3x + 7 = 19 is x = 4.
Using simplification of equations, we can find the value of x to be = 4.
Define equations?Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol. It'll be regarded as a term.
This is the equation that is provided:
3x + 7 = 19
We must isolate x on one side of the equation in order to find its value.
To eliminate the constant term, we can begin by deducting 7 from both sides of the equation:
3x + 7 - 7 = 19 - 7
To put it simply, we obtain
3x = 12.
Then, by multiplying both sides of the equation by 3, we can determine x:
3x/3 = 12/3
To put it simply, we obtain x = 4.
Consequently, x = 4 is the answer to the equation 3x + 7 = 19.
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HELP ASAP !! Thanks
Step-by-step explanation:
First, let's find the area of the rectangular sides using the dimensions given.
16 x 7 = 112 [tex]in^2[/tex]
112 is just for one rectangle. We need to find the area for 3 rectangles.
112 x 3 = 336 [tex]in^2[/tex]
Now, we need to find the area of the triangle. Using the formula let's find the area.
bh/2
7 x 8/2
56
Our answer is 56 as we find the area of two triangles and 28 x 2 equals 56. To find the prism's total area, we have to add the areas altogether.
56 + 336 =
Answer: 392 [tex]in^2[/tex]
Samira is playing a board game.
She rolls a fair six-sided dice numbered 1 to 6.
She wants to find how many times she is likely to roll the dice before she gets a 6.
She uses a computer simulation to roll a dice 100 times.
Here are her results:
Numbers of rolls to get 6......... Frequency
1........................................................16
2........................................................14
3........................................................13
4..........................................................9
More than 4.....................................48
Complete each sentence with the correct number.
Samira is likely to get a 6 after ..... rolls approximately 1 out of 10 times.
There is approximately a ...... % chance that Samira will roll the dice more than 4 times to get a 6.
(NOTE: THIS IS A BETTER VERSION OF ambreennk12's QUESTION)
Answer:
Step-by-step explanation:Answer 1 person found it helpful Davis Holmes These outcomes are only estimates of the real odds because they relied on Samara's 100 trials. The measured rates should approach the actual odds as she keeps rolling the dice.Which four kinds of probability are there?Mathematics' study of chance events is known as probability, and there are four major kinds of probability: axiomatic, classical, observational, and subjective.After three tries, Samira is expected to receive a 6.There is approximately a 9% chance that Samira will roll the dice more than 4 times to get a 6.Frequency:1: 162: 143: 134: 9more than 4: 48Note: These results are based on Samira's 100 trials, so they are only an estimate of the actual probabilities. As she continues to roll the dice more times, the observed frequencies should approach the true probabilities.To know more about Probability
There are 148 cars in front of a department store. If each car has 4 wheels, estimate the number of wheels in front of the store by rounding the larger number to the nearest ten.
convert 300° to radius
Answer:
radians = degrees x π/180
Therefore, to convert 300 degrees to radians, we have:
radians = 300 x π/180
radians = 5π/3
So, 300 degrees is equal to 5π/3 radians.
Assume you own a wood house in the country that is worth $200,000, using the
table below, what would be your annual premium to insure.
Annual Premium per $100 of coverage
Brick
Area
rating
City
0.39
Suburb 0.45
Rural
0.6
Steel
|Mixed
Wood
Building Contents Building Contents Building
Contents
Building |
Contents
0.43
|05
054
0.55
0.52
0.56
0.63
0.72
0.69
0.71
0.8
0.89
0.65
0.74
0.91
0.66
0.76
0.83
0.85
1
1.02
• $1,320
• $1,660
• $2,000
О $2,500
Based on the given table, the annual premium per $100 of coverage for a wood house in the country would be 0.74.
To calculate the annual premium for the $200,000 house, we first need to determine the coverage amount. Assuming a coverage of 80% of the house's value, the coverage amount would be:
Coverage amount = 80% of $200,000 = $160,000
Next, we can calculate the annual premium as follows:
Annual premium = (Coverage amount / $100) x Annual premium per $100 of coverage
= ($160,000 / $100) x 0.74
= $1,184
Therefore, the annual premium to insure the $200,000 wood house in the country would be $1,184.
18 mm cylinder surface area
Where we use division in real life?? Give Examples
Answer: You might want to know how many 24 apples are, individually, also being an accountant, mathematician, scientist, all require Math and math follows PEMDAS [Parenthesis, exponents, multiplication, division, addition, subtraction.] normally.
Step-by-step explanation:
Also, if you multiple something let's say 378x54 and get 20,412 and let's say you want to divide this huge number to a smaller number you can divide from 2 all the way up! Mathematics is not just something we have to learn, it's also something we can use!
A salesperson had 360,000 dollars in sales last year, which is 40% of the sales she had this year. Which equation could be used to determine x, the salesperson’s total amount of sales, in dollars, for this year?
Answer: [tex]0.4x=360,000[/tex]
Step-by-step explanation:
From the problem it can be seen that 360,000 is 40% of the sales she got this year. So, 40% of her sales is 360,000.
40% of x is mathematically 0.4 times x.
Therefore the equation you could use is: [tex]0.4x=360,000[/tex]
If you want to solve this for x, simply divide 0.4 from both sides to get x by itself.
[tex]x=(\frac{360,000}{0.4})=900,000[/tex]
So this year she made 900,000 dollars.
Which statement is true?
A.The given sides and angles cannot be used to show similarity by either the SSS or SAS similarity theorems.
B.The given sides and angles can be used to show similarity by the SSS similarity theorem only.
C.The given sides and angles can be used to show similarity by the SAS similarity theorem only.
D.The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems
The triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.
Given that:
The diagram is shown.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The ratio of the corresponding sides of the triangle ΔFGH and ΔLJK is given as,
FG / JL = HF / LK = GH / JK
32/8 = 36/9 = 48/12
4 = 4 = 4
The ratio of the corresponding side will be equal. Then the triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.
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The brain volumes (cm³) of 20 brains have a mean of 1106.2 cm³ and a standard deviation of 126.6 cm³. Use the given standard thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of
Step-by-step explanation:
cutive Function Test aimed at elderly individuals be a useful tool?
Using the standard thumb, we can say that any brain volume that falls outside the range of 878.6 cm³ to 1333.8 cm³ is significantly low or significantly high. Therefore, any brain volume below 878.6 cm³ or above 1333.8 cm³ would be considered significantly low or significantly high.
As for whether a Brain Executive Function Test aimed at elderly individuals would be a useful tool, the information given is not enough to answer that question. The Brain Executive Function Test is a cognitive assessment tool that measures various cognitive skills such as attention, problem-solving, working memory, and decision-making. The usefulness of this test depends on the purpose of the assessment and the population being tested. The given information only provides brain volume data of 20 brains and does not give any indication of the age or cognitive status of the individuals. Therefore, it is not possible to determine whether a Brain Executive Function Test aimed at elderly individuals would be useful based on this information alone.
A 40-year-old man in the U.S. has a 0.24% risk of dying during the next year . An insurance company charges $290 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar.
The answer is 46 dollars
Assuming that x \neq -3, simplify (8x - 4)(x + 3) - (4x - 44)(2x + 6).
Answer: Your answer is 504 or if you want it differently it's 84x+252
Hope it helped :D
1) Nikoli rolls a number cube and lets A = {1, 2, 3, 4) and B = [5, 6) represent two different events.
Which term best describes these events?
O uniform
O theoretical
O approximated
O complementary
The probability term that best describes these events is D. complementary.
What are complimentary events ?Complementary events are those that cannot occur simultaneously and are mutually exclusive and exhaustive in probability, meaning that their probabilities add up to 1. Nikoli rolls a number cube with six possible outcomes in this scenario: 1, 2, 3, 4, 5, and 6.
Because events A and b have no common outcomes and their union encapsulates all outcomes that could result from rolling a number cube, they are complimentary events.
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Which of the following proportions is false?
find the surface area of the right prism.
8 ft
2 ft
3 ft
Answer: 92 ft²
Step-by-step explanation:
To find the surface area of a right prism, we will find the area of each side and add them together. We have three sets of two congruent sides. We will write an equation representing the area of these sides, set it equal to the surface area, and solve by simplifying.
2(8 ft * 3 ft) + 2(3 ft * 2 ft) + 2(8 ft * 2 ft) = Surface Area
2(24 ft²) + 2(6 ft²) + 2(16 ft²) = Surface Area
48 ft² + 12 ft² + 32 ft² = Surface Area
92 ft² = Surface Area
regrisson for the equation
Answer:
A. Quadratic
Step-by-step explanation:
The equation y=x^2+7x-15 is a quadratic equation. It might be the result of a quadratic regression.
_____
The descriptors "linear," "quadratic," "exponential," and "power" describe the sort of equation that is used to try to match the data. Quadratic regression returns a quadratic equation.
In a class of 70 students, 10 students passed mathematics, biology or chemistry, 30 pass mathematics, 30 pass biologi, and 25 pass mathematics if 11 pass mathematics or biology 10 pass biology and chemistry and 7 pass mathematics and. Chemistry how many pass all three subjects
Answer:
We can use a Venn diagram to visualize the information given in the problem.
Let M, B, and C represent the sets of students who pass mathematics, biology, and chemistry, respectively. We are given the following information:
|M| = 10 (the number of students who pass mathematics)
|B| = 30 (the number of students who pass biology)
|C| = 25 (the number of students who pass chemistry)
|M ∩ B| = 11 (the number of students who pass both mathematics and biology)
|B ∩ C| = 10 (the number of students who pass both biology and chemistry)
|M ∩ C| = 7 (the number of students who pass both mathematics and chemistry)
|M ∩ B ∩ C| = ? (the number of students who pass all three subjects)
We know that:
| M ∪ B ∪ C | = |M| + |B| + |C| - |M ∩ B| - |B ∩ C| - |M ∩ C| + |M ∩ B ∩ C|
Substituting the given values:
| M ∪ B ∪ C | = 10 + 30 + 25 - 11 - 10 - 7 + |M ∩ B ∩ C|
Simplifying:
| M ∪ B ∪ C | = 37 + |M ∩ B ∩ C|
We also know that:
| M ∪ B ∪ C | = 70 (the total number of students)
Substituting the value:
70 = 37 + |M ∩ B ∩ C|
Simplifying:
|M ∩ B ∩ C| = 33
Therefore, 33 students pass all three subjects.
Step-by-step explanation:
pls mark branliest i beggggg u
In the diagram below, what is the approximate length of the minor arc XY?
X
NO
23 cm 120°
OA. 36 cm
B. 48 cm
O C. 72 cm
OD. 24 cm
SUBMIT
Since the angle at the center of the circle is 120 degrees, the angle subtended by the minor arc XY at the center of the circle is also 120 degrees.
The circumference of a circle with radius r is given by 2πr, where π is the constant pi (approximately equal to 3.14).
The total circumference of the circle is 2π(23 cm) ≈ 72.4 cm.
Since the minor arc XY subtends an angle of 120 degrees at the center of the circle, it will have a length that is 120/360 = 1/3 of the total circumference.
Therefore, the approximate length of the minor arc XY is (1/3)(72.4 cm) ≈ 24.1 cm.
So the closest option to this value is option D, 24 cm.
Answer: A. 48 cm
Step-by-step explanation:
I just did it :)
Is it .3 or .4. Confused how to get answer.
Answer:
(b) 0.4
Step-by-step explanation:
You want the experimental probability that Antonia will make both of her next two free throw attempts.
Experimental probabilityThe "experimental" probability is the fraction of times the outcome of interest occurred in the trials used for the experiment.
Here, Antonia made both free throws in trials 2, 5, 9, and 10 of the ten trials, so her record for making both free throws is 4 out of 10 trials. We are to assume this 4/10 ratio is the probability that the next 2 attempts will result in Antonia making both free throws.
The experimental probability of making both free throws is 0.4, choice B.
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PLEASE HURRY DUE TONIGHT
Mary is babysitting a 4-year-old. The little boy wants to play in the kiddie pool in the backyard. Mary knows that using the hose that is near the kiddie pool will take 30 minutes to fill up. The little boy has already asked 17 times if the pool is ready but she hasn't even turned on the water yet. Mary also knows that the hose from the front yard works faster and can fill the pool in 1/2 the time as the hose in the back yard. If she can use both hoses at the same time, how long will it take for the pool to fill up?
(PLEASE SHOW YOUR WORK)(I saw other people get 7.5 min and 75 min but those answers are incorrect.)
A. 5 minutes
B. 10 minutes
C. 22.5 minutes
Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.
To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).
The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.
We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.
Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.
To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)
Density = 600g / 600 cubic feet = 1g/cubic foot
Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.
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can someone help me on number 1
The perimeter and the area of the rectangle are given as follows:
P = 10.4 inches.A = 22.4 in².How to calculate the perimeter and the area of a rectangle?Considering dimensions l and w, the perimeter of the rectangle is given as follows:
P = 2(l + w).
The dimensions in this problem are of 7 in and 3.2 in, hence the perimeter is given as follows:
P = 2(7 + 3.2)
P = 10.4 inches.
The area of a rectangle is given as follows:
A = lw.
Hence:
A = 7 x 3.2
A = 22.4 in².
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Find the inverse of the matrix: A = 4 2 3 2 Step 1: Calculate the determinant: 4 2 3 2 =
The inverse of the matrix A by getting its determinant value is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]
The matrix is equal to,
A = [tex]\left[\begin{array}{ccc}4&2\\3&2\end{array}\right][/tex]
To find the inverse of a matrix,
we first need to calculate its determinant of the matrix A we have,
|A| = [tex]\left|\begin{array}{ccc}4&2\\3&2\end{array}\right|[/tex]
⇒ |A| = 4(2) - 2(3)
= 8 - 6
= 2
Now we can proceed to find the inverse of A.
Set up the matrix of cofactors.
The matrix of cofactors C is obtained by replacing each element of A with its corresponding cofactor,
which is the determinant of the submatrix obtained by deleting the row and column that contain that element.
For our matrix A, we have,
C = [tex]\left[\begin{array}{ccc}2&-3\\-2&4\end{array}\right][/tex]
Transpose the matrix of cofactors.
The transpose of a matrix is obtained by flipping its rows and columns. For our matrix C, we have.
[tex]C^{T} = \left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]
Divide by the determinant.
The inverse of A is obtained by dividing the transpose of the matrix of cofactors by the determinant of A.
For our matrix A, we have,
A⁻¹ = [tex]C^{T}[/tex] / |A|
[tex]C^{T} = (1/2)\left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]
[tex]C^{T} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]
Therefore, the inverse of the matrix A is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]
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The relation T = 190 (1/2)^t/10 can be used to determine the length of time, t, and hours that milk of a certain fat content will remain fresh . T is the storage temperature in degrees Celsius.
(a) what is the freshness half-line of milk? 
(b) how long will milk keep fresh at 22°C?
(c) how long will milk keep fresh at 4°C?
The the freshness half-line of milk is 10h, (b) The milk keep fresh at 22°C for 31.1h (c) The milk keep fresh at 4°C for 55.7h
What is storage temperature?Recal that Storage temperature refers to the temperature at which food product is stored immediately after preparation and maintained at a safe holding temperature until it is dispensed to the customer
The given relation is T = 190 (1/2)^t/10
a. From the relation, T = 190 (1/2)^t/10
So the freshness half life of milk is 10 hours
b. 22 = 190 (1/2)^t/10
t = 10log₁/₂(190/22) = 31.1 hours
c. = 190 (1/2)^t/10
t= 10log₁/₂(190/22 = 55.7 hours
Milk can keep fresh for 55.7 hours at 4°C
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