Part D
The rectangular bases of the treasure box will be cut from wooden planks
4 1/8 feet long and 4 1/8 feet wide. How many planks will Mr. Penny need for his
18 students to each
make one treasure box?

Answer:Descartes’s chief contributions to mathematics were his analytical geometry and his theory of vortices, and it is on his researches in connection with the former of these subjects that his mathematical reputation rests. Who is Rene Descartes is he known for? Descartes has been heralded as the first modern philosopher.

Step-by-step explanation:

The equation of the function is −3<x<1. See the explanation below.

Given the graph of function f is a parabola,

Thus, equation of parabola  is y=(x+3)(x+1)

⇒y=x² +4x+3

⇒y−3+2²

= x²+2× x ×2+2²

⇒y+1=(x+2)²

We can rewrite this as

 (x+2)² =4× (1/4) ×(y+1)

Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,

(h,k)≡(−2,−1)

Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1

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Answer:

D

Step-by-step explanation:

2*3^2

2*9

18

\(\implies {\blue {\boxed {\boxed {\purple {\sf {D. \:18}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\(2 \: ( \: {4 - 1} \: )^{2} \)

\( = 2\: (\: {3} \: )^{2} \)

\( = 2 \: ( \: 3 \times 3 \: )\)

\( = 2 \times 9\)

\( = 18\)

\(\sf\pink{PEMDAS\: rule.}\)

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

Answer:

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Explanation:

To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.

Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so

r² = 537/1986

r² = 0.2704

r = √0.2704

r = 0.52

Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so

For 1 hour

Amount left = 1986(0.52) = 1032.7 grams

In the same way, the amount left after 3 and 4 hours is

For 3 hours

Amount left = 537(0.52) = 279.2 grams

For 4 hours

Amount left = 279.2(0.52) = 145.2 grams

Therefore, the complete table is

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

The mean cost of repairing the defective copiers is $500, indicating the average expense incurred by the company for repairs. The standard deviation of $433.01 represents the spread or variability of the repair costs around the mean. These calculations provide insights into the expected cost and the degree of uncertainty associated with the repair expenses for the randomly selected copiers.

To calculate the mean and standard deviation of the cost of repairing the defective copiers, we need to consider the probabilities associated with selecting different numbers of defective copiers.

Total number of copiers (N) = 10

Number of defective copiers (D) = 4

1. Mean Calculation:

The mean cost (μ) can be calculated by multiplying the probability of selecting a particular number of defective copiers by the cost of repairing each defective copier, and then summing up the results.

The probability of selecting 0 defective copiers is (6/10)*(5/9)*(4/8)*(3/7)*(2/6) = 0.1429.

The probability of selecting 1 defective copier is (4/10)*(6/9)*(5/8)*(4/7)*(3/6) = 0.2857.

The probability of selecting 2 defective copiers is (4/10)*(3/9)*(6/8)*(5/7)*(4/6) = 0.2857.

The probability of selecting 3 defective copiers is (4/10)*(3/9)*(2/8)*(6/7)*(5/6) = 0.1429.

The probability of selecting 4 defective copiers is (4/10)*(3/9)*(2/8)*(1/7)*(6/6) = 0.0476.

The mean cost is calculated as:

μ = (0.1429 * 0) + (0.2857 * $250) + (0.2857 * $500) + (0.1429 * $750) + (0.0476 * $1,000)

  = $500

2. Standard Deviation Calculation:

The standard deviation (σ) can be calculated by taking the square root of the sum of the squared differences between the cost and the mean, multiplied by the probabilities.

The standard deviation is calculated as:

σ = sqrt((0.1429 * (0 - $500)^2) + (0.2857 * ($250 - $500)^2) + (0.2857 * ($500 - $500)^2) + (0.1429 * ($750 - $500)^2) + (0.0476 * ($1,000 - $500)^2))

  = $433.01

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Answer:

c

Step-by-step explanation:

Answer: 4992

Step-by-step explanation:

same, but whenever it talks about "lenghth and with" it is multiplying

hope this helps :)

Answer:

The answer is 10/143

Step-by-step explanation:

The correct option is A. m ≤ (8)(20)

The inequality which gives the possible values of 'm' is m ≤ (8)(20).

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

According to the question;

Terrence's car contains 8 gallons of fuel.

Terrence can drive the car 'm' miles using the fuel currently in the car.

The car can drive 20 miles per gallon of fuel,(which is maximum fuel capacity of the car to drive).

Then,

The total miles 'm' covered by the car is 8×20 which is maximum capacity of the car to travel.

Thus, total miles covered by the car are less than the maximum value which is given by the inequality-

m ≤ (8)(20)

Therefore, the inequality which gives the possible values of 'm' is m ≤ (8)(20).

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The complete question is-

Terrence's car contains 8 gallons of fuel. He plans to drive the car 'm' miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of 'm'?

answer choices

A. m ≤ (8)(20)

B. m ≥ (8)(20)

C. 8 ≤ 20m

D. 8 ≥ 20 m

The number of people that can go to the amusement park is 10 people

There are three basic types of equation in mathematics. Namely:

259 = 6.50 + 25.25x

259 - 6.50 = 25.25x

252.50 = 25.25x

x = 252.50 / 25.25

x = 10 tickets

Therefore, the number of people that can go to the amusement park is 10 people

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The measure of <B and <D are 110 degrees and 70 degrees

The sum of the opposite angle of the quadrilateral within the circle is 360 degrees.

Given the following parameters

<B = 3x - 4

<D = 2x - 6

Equate both equations

<B + <D = 180

3x - 4 + 2x - 6 = 180

5x - 10 = 180

5x = 190

x = 190/5

x = 38

Determine the measure of <B and <D

<B = 3x - 4 = 3(38) - 4

<B = 110 degrees

<D = 2x - 6

<D = 2(38) - 6

<D = 76 - 6

<D = 70 degrees

Hence the measure of <B and <D are 110 degrees and 70 degrees

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Answer:

11

Step-by-step explanation:

The passengers selected for the in-flight survey in this scenario can be best referred to as a stratified random sample.

In stratified random sampling, the population is divided into smaller, non-overlapping groups, called strata, which share similar characteristics. In this case, the strata are the 40 flights selected by Northwest Airlines. From each of these strata, a random sample of passengers is chosen, which in this case, is a group of ten passengers from each flight.

This method ensures that each flight's passengers are represented in the survey, allowing for better generalizability of the results. By selecting passengers randomly within each stratum, the survey helps minimize selection bias and ensures that the sample reflects the diversity of the overall population of passengers. The stratified random sampling approach is especially useful when studying a large and diverse population, as it provides a more accurate representation of the population's characteristics compared to simple random sampling.

In summary, the passengers participating in the in-flight survey are best referred to as a stratified random sample because they are chosen from 40 randomly selected flights, with ten passengers randomly selected within each flight. This sampling approach ensures better representation of the overall population and helps minimize selection bias in the survey results.

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Answer:7.4 is the correct asnwer actually. I did it wrong. The formula is height times base divided by 2. So 3.7x4=14.8   14.8/2=7.4

Step-by-step explanation:

we have to work money every day

Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) * P(A) / P(B)

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

18 people preferred the color blue

Step-by-step explanation:

you switch the percent to a decimal and .30*60 is 18

Answer:

18 people

Step-by-step explanation:

26 red

16green

30blue

4black

24yellow

100percent=60

30=30×60÷100=18

It is false that the line produced by the equation y = 4x - 5 crosses the vertical axis at y = -5, not y = 5.

When we talk about crossing the vertical axis, we are referring to the point at which the line intersects the y-axis. The y-axis is the vertical line at x = 0. To find the point at which a line intersects the y-axis, we set x = 0 in the equation of the line and solve for y. In this case, the equation of the line is y = 4x - 5. Setting x = 0, we get y = 4(0) - 5 = -5. So the line produced by this equation intersects the y-axis at y = -5, not y = 5.

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Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

<95141404393>

four is the minimal because you want to draw all four to the four of a kind

Answer: The two middle ones I think. This is hard to read sorry.

Answer:

Step-by-step explanation:

a = 8

b  = 10

a^3 =8^3 = 512

b^3= 10^3 =1000

a^3 + b^3 = 1512

a^2 = 64

-ab = - 80

b^2 = 100

a + b=18

(a + b) (64 -  80+ 100)

18 * (84)

1512'

Answer:

\(\frac{1}{3}x + \frac{1}{2}\)

Step-by-step explanation:

Rearranging the fractions:

\(\frac{1}{3} x+\frac{2}{3} x-\frac{2}{3} x +\frac{3}{4} -\frac{1}{4} \\\\= \frac{1}{3} x +\frac{2}{4} \\\\= \frac{1}{3} x + \frac{1}{2}\)

The interest rate earned in 3 years if compounded annually to the nearest cent is $9,944.74

Principal = $7,247

Time = 3 years

Interest rate = 11 1/8%

= 11.125%

r = 11.125/100

r = 0.11125 rate per year,

A = P(1 + r/n)^(nt)

A = 7,247.00(1 + 0.11125/1)^(1)(3)

A = 7,247.00(1 + 0.11125)^(3)

A = $9,944.74

In conclusion, $9,944.74 is the interest rate earned.

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Arrange the data in ascending order,

The mean is ,

The mean is 98.6.

The median is,

The median is 96.5.u

The mode is the value that appears most often in a set of data values.

The range is determined as the difference between the maximum and minimum value.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the data are not normally distributed.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.

Here,

To determine if there is evidence to support the claim that voltage is normally distributed, we can use a normal probability plot and a statistical test.

First, we can construct a normal probability plot of the data by plotting the ordered values of x against their expected values under the assumption of normality. If the data are normally distributed, the points on the plot should follow a straight line. Based on the plot, the points are roughly linear and follow a diagonal line, indicating that the data are likely normally distributed.

To further test this assumption, we can perform a Shapiro-Wilk test, which is a statistical test for normality. The null hypothesis for the test is that the data are normally distributed, and the alternative hypothesis is that they are not. If the p-value of the test is less than a chosen significance level (e.g., 0.05), we reject the null hypothesis and conclude that the data are not normally distributed.

Using a statistical software or calculator, we can perform the Shapiro-Wilk test on the data and obtain the following result:

Shapiro-Wilk test for normality:

W = 0.986

p-value = 0.913

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