Luke is completing a science experiment at home. He bought two hibiscus plants for his experiment. One of the plants was 5 cm tall. Each week he measured and recorded the
height of the plant, H, in cm. After collecting data for several weeks, he determined that the height of the plant, H, in cm, could be represented by the function H (t) = 5 +0.5t,
where t is the number of weeks since he purchased the plant.
Part A
What is the value of H(4)?
Part B
What does H (2) = 10 mean in this situation?
The height of the plant was 2 cm after 10 weeks.
The height of the plant was 7 cm after 4 weeks.
The height of the plant was 4 cm after 7 weeks.
The height of the plant was 10 cm after 2 weeks.

Answer:

  (tables, chairs) = {(2, 12), (3, 8), (4, 6), (6, 4), (8, 3), (12, 2)}

Step-by-step explanation:

Divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Each of these (except 1 and 24) can be a number of tables:

  2 tables, 12 chairs each

  3 tables, 8 chairs each

  4 tables, 6 chairs each

  6 tables, 4 chairs each

  8 tables, 3 chairs each

  12 tables, 2 chairs each

13 degrees mPQT = 1 degree in internal angle .

An illustration of an internal angle?

mPQR=25 degrees , mRQT=11 degrees.

mPQT=PQR-RQT

MPQT=25-11=13 degrees

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If the cost of college tuition in 2010 was $6016 and in 2014 was $9139, then the average rate of change in tuition during this time period was $781/year. Do you agree or disagree​?

To find the average rate of change during this time period, you need to divide the amount, in dollars, of the difference between the years and divide it by the number of years the time period was.

In 2010, the cost of the tuition was $6,016. In 2014, the cost of the tuition was $9,139. First, you need to subtract to find the difference in tuition.

\(9,139-6,016=3,123\)

The increase in tuition for this time period is $3,123. Now, you need to find the number of years it took to increase by $3,123.

\(2010 \rightarrow2014 = 4 \text{ years}\)

That means it took four years to increase by $3,123. Lastly, you need to find the average rate of change. You can find this by dividing the amount of dollars(the tuition increased by) by the number of years it took to increase.

\(\frac{\text{amount of dollars}}{\text{number of years}} = \frac{\$3,123}{4} = \$780.75\)

That means the average rate of change during this time period was $780.75. Rounded to the nearest whole number, it would be $781. Therefore, you can agree that the average rate of change during this time was $781/year.

Answer:

I Agree

Step-by-step explanation:

That seems like a fair advantage for people planning to go to college!

Answer:

(A) There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.

(B) Saturday has the highest percentage of traffic accidents.

Step-by-step explanation:

(A)

The Chi-square goodness of fit test would be used to determine if the proportion of traffic accidents is the same for each day of the week.

The hypothesis for the test can be defined as follows:

H₀: The proportion of traffic accidents is the same for each day of the week.

Hₐ: The proportion of traffic accidents is not same for each day of the week.

Assume that the significance level of the test is, α = 0.05.

The Chi-square test statistic is given by:

\(\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}\)

Compute the values in Excel.

The expected frequency for all the days is 60.

The Chi-square test statistic value is, 14.333.

Compute the p-value using the Excel function "=CHISQ.DIST.RT(14.33,6)".

p-value = 0.0262

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

The p-value is less than 0.05.

The null hypothesis will be rejected.

Conclusion:

There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.

(B)

Compute the percentage of traffic accidents occurring on each day of the week as follows:

\(\text{Sunday}=\frac{66}{420}\times 100\approx 16\%\\\\\text{Monday}=\frac{50}{420}\times 100\approx 12\%\\\\\text{Tuesday}=\frac{53}{420}\times 100\approx 13\%\\\\\text{Wednesday}=\frac{47}{420}\times 100\approx 11\%\\\\\text{Thursday}=\frac{55}{420}\times 100\approx 13\%\\\\\text{Friday}=\frac{69}{420}\times 100\approx 16\%\\\\\text{Saturday}=\frac{80}{420}\times 100\approx 19\%\)

Saturday has the highest percentage of traffic accidents.

The notation which is the most appropriate notation when calculating conditional probabilities is option B.

The appropriate notation for calculating conditional probabilities is often denoted using the vertical bar symbol "|". This symbol represents "given" or "conditional on."

In a mathematical expression, the conditional probability of event A given event B is written as P(A | B), where "P" stands for probability. This notation indicates that the probability of event A occurring is being calculated assuming that event B has already occurred.

Thus option B is correct.

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Answer:

11 parts equal $4.95

Step-by-step explanation:

Answer:

2:3

hope this help you....

Answer:

true

Step-by-step explanation:

3n3n3p0mdo98rueu33

Answer:

14

Step-by-step explanation:

Steps shown in the image

\(-5x^2+3x = -3x^2 +3x -50\\\\\implies 5x^2-3x^2 +3x-3x -50 =0\\\\\implies 2x^2 -50 =0\\\\\implies x^2 -25 = 0\\\\\implies x^2 = 25\\\\\implies x = \pm5\\\\\text{Hence}~ x = 5~ \text{or}~ x = -5\)

Answer:

X = 5, —5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

\(\\ \sf\longmapsto Force=Mass\times Acceleration \)

\(\\ \sf\longmapsto Force=1(12)\)

\(\\ \sf\longmapsto Force=12N\)

Let,

The value of mass be 1 kg.

Given,

Acceleration = 12 m/s²

Now,

As we know, Force = mass × acceleration ( F = m × a )

F = 1 × 12

F = 12

Therefore, the new net force is 12.

_______________________________

Additional Comment:

F means Force.

Answer: 0.35

Step-by-step explanation:

Times 7 = 2. 45kg

Answer:

16 + 2x

Step-by-step explanation:

9514 1404 393

Answer:

  (a, b) = (4, 8)

Step-by-step explanation:

Writing both equations in general form, we have ...

  6a -5b +16 = 0

  9a -7b +20 = 0

__

We can make a little array of the numbers in the equations:

  \(\left[\begin{array}{cccc}6&-5&16&6\\9&-7&20&9\end{array}\right]\)

Note that the first column is repeated at the end.

Now, we can "cross multiply" and form the differences of products in adjacent columns:

  d1 = (6)(-7) -(9)(-5) = 3 . . . . . . left 2 columns

  d2 = (-5)(20) -(-7)(16) = 12 . . . . . middle 2 columns

  d3 = (16)(9) -(20)(6) = 24 . . . . . right 2 columns

Then the solutions to these equations are the solutions to ...

  1/d1 = a/d2 = b/d3

  a = d2/d1 = 12/3 = 4

  b = d3/d1 = 24/3 = 8

The values of a and b are 4 and 8, respectively.

_____

Additional Comment

There are a number of ways to solve linear equations. This is similar to what you would get by doing "elimination". It is also similar to Cramer's Rule and Vedic math techniques. The number of math operations is about the same*. Once you learn the technique, it is fairly fast and requires no decision-making. My other favorite method is using a graphing calculator.

__

* This method uses 6 multiplications, 3 subtractions, 2 divisions. In the general case of "elimination", where the coefficients are not "nice" (as here), you would perform 7 multiplications, 4 subtractions and 2 divisions. This method is less work when the coefficients don't cancel easily.

Answer: 11176ft.

Step-by-step explanation:

The cost of the carpet will be $2,335.5.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The dimensions of the carpet are;

⇒ 15 feet by 18 feet

Now,

The area of the carpet = 15 x 18

                                   = 279 feet²

                                   = 270 / 3 yards²

                                   = 90 yards²

Since, The carpet costs = $25.95 per square yard.

Hence, The carpet cost for 90 yards² = 90 x $25.95

                                                          = $2,335.5

Thus, The cost of the carpet will be $2,335.5.

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62 square yards is the area of the figure.

Area is the measure of a region's size on a surface and the area of a plane region or plane area refers to the area of a shape

In the given figure there are three rectangle in that two are smaller rectangles squares.

The rectangle has length of 10 yd and width of 5 yd.

Area of rectangle (Large)=10×5

=50 square yds

The side length of smaller rectangle is 3 yards and width is 2 yd

Area of rectangle (small)=3×2

6 square yds.

As there are two smaller rectangles, then area will be 2(6)=12 yards.

Now total area = 50+12

=62 square yards.

Hence, the area of the figure is 62 square yards.

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Answer:

40

Step-by-step explanation:

100/2.5=40

part a.

The equation that has the variable in the correct place to match the given situation is: Sunday's mile

part b

the Mansour family drove 210 miles on Sunday.

An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign =..

We have that the equation that has the variable in the correct place to match the given situation is: Sunday's mile

Sunday's miles = Total miles - Friday's miles - Saturday's miles

Sunday's miles = 687 - 313 - 164

Sunday's miles = 210

In conclusion, the Mansour family drove 210 miles on Sunday.

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The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Answer:

3

: The term that completes the product so that it is the difference of squares is 3.

The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

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The value of the test statistic rounded to two decimal places is equal to 5.05.

In Mathematics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

For a claim that most adults would erase all of their personal information online if they could, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p ≤ 0.5.

Ha: p > 0.5.

Mathematically, the test statistic for the z-test of a population proportion can be calculated by using this mathematical expression;

\(z=\frac{\hat{p} \;- p}{\sqrt{\frac{p(1\;-p)}{n } } }\)

Where:

Substituting the given parameters into the formula, we have;

z = (0.61 - 0.5)/√(0.5(1 - 0.5)/526)

z = (0.11)/√(0.5(0.5)/526)

z = (0.11)/√(0.25/526)

z = 0.11/0.0218

z = 5.05.

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The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

We have,

To calculate the probabilities of rolling specific totals with a pair of dice, we need to consider all possible combinations of numbers on each die.

Probability of rolling a total of 9:

There are four combinations that can result in a total of 9: (3, 6), (4, 5), (5, 4), and (6, 3).

Since each die has six sides, there are 6 * 6 = 36 equally likely outcomes when rolling two dice.

The probability of rolling a total of 9 is 4/36, which can be simplified to 1/9.

Probability of rolling a total of 10:

There are three combinations that can result in a total of 10: (4, 6), (5, 5), and (6, 4).

The probability of rolling a total of 10 is 3/36, which can be simplified to 1/12.

Probability of rolling a total of 11:

There are two combinations that can result in a total of 11: (5, 6) and (6, 5).

The probability of rolling a total of 11 is 2/36, which can be simplified to 1/18.

Thus,

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

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1) The study design used is a quasi-experimental nonequivalent control group design.

2) The threats to internal and external validity include selection bias, maturation, history, testing, and instrumentation, with the most serious threat being selection bias for internal validity and generalizability for external validity.

3) To improve the design, a randomized controlled trial design with a larger and more representative sample, multiple measures of awareness and preference, and a comparison group could be used.

1) The design being used in this study is a quasi-experimental design, specifically a nonequivalent control group design. There are two groups, a before and after group, but they were not randomly assigned to each condition, and there was no control group to compare the results.

2) There are several threats to internal and external validity in this study, including,

Selection bias: There was no random assignment to conditions, which may lead to systematic differences between the two groups.

Maturation: The changes in preference and awareness may be due to natural changes over time rather than the advertising campaign.

History: Events outside of the study may have influenced the results.

Testing: Respondents may have answered the same or differently in the before and after survey simply because they had already taken the survey before.

Instrumentation: Changes in the survey instrument or administration may have affected the results.

The most serious threat to internal validity is selection bias, as there may be systematic differences between the before and after groups that are not due to the advertising campaign. The most serious threat to external validity is generalizability, as the sample was drawn from readers of a single trade magazine and may not be representative of the larger population.

3) To improve the design, several changes could be made. First, a randomized controlled trial design could be used, with random assignment to an experimental and control group. This would help address the selection bias threat. Second, a longer-term study could be conducted to rule out the maturation threat. Third, a larger sample size and a more representative sample could be obtained to improve external validity. Fourth, multiple measures could be used to assess awareness and preference, such as behavioral measures and surveys from different sources. Finally, a comparison group could be used to control for history and testing threats.

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Answer:

s-6

Step-by-step explanation:

difference means subtract

s-6

Answer:

Step-by-step explanation:

considering A). hemisphere diameter = 48 yd

volume of hemisphere = (2/3)*pi*(r)^3

the radius of hemisphere = diameter/2 = 48/2 = 24 yd

hence, the volume of hemisphere = (2/3)*pi*(24)^3  yd^3

taking pi = 3.14

volume = 28938.24 yd^3 approximately volume = 28940 yd^3

considering B). Circumference of a great circle = 26 m

circumference of sphere = 2*pi*r

therefore r = 4.14 m

volume of sphere = (4/3)*pi*(r)^3

volume of sphere = 297.077 m^3

Answer:

24. A. 28952.9 yd²

B. 297.2 m³

Step-by-step explanation:

24.

A.

diameter=48 yd

radius (r)=diameter/2=48/2=24yd

We have

Volume of Hemisphere= ⅔*πr³=⅔*π*r³

Substituting value

Volume of Hemisphere=⅔*π*24³=28952.9 yd³

B.

Circumference of great circle=2πr=26m

2πr=26

r=26/(2π)

r=4.14

Now

Volume of sphere = 4/3*πr³

Volume of sphere=4/3*π*4.14³=297.2 m³

Answer:

$60

Step-by-step explanation:

since every year, she receives $5 more than the last, then on her twelfth birthday, you'll have to multiply 5 by 12 to get 60.

Answer:

6

Step-by-step explanation: