In this rectangle, the base is 1 cm more than the height. The area of the rectangle is 100 cm². Using a trial and improvement method, find the value of h, correct to 1 decimal place. You must show all of your working

Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

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The value of x and y are 10 and 10√3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Here the hypotenuse is 20 and the opposite to angle 30 is x and the adjacent is y

Therefore;

sin30 = x/20

1/2 = x/20

2x = 20

x = 20/2 = 10

cos 30 = y/20

√3/2 = y/20

2y = 20√3

y = 20√3/2

y = 10√3

therefore the value of x and y are 10 and 10√3

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The asked probabilities are 1/3, 6/7 and 50/71.

Given that are events we need to find the required probability,

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability (Event) = Favorable Outcomes/Total Outcomes = x/n

There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The probability is classified into theoretical probability and experimental probability.

so,

Probability = favorable outcomes / total outcomes

1) P(Morgan is a vocalist) = 9/27 = 1/3

2) P(Angela is not a guitarist) = 18/21 = 6/7

3) P(Gina is a vocalist) = 50/71

Hence the probabilities are 1/3, 6/7 and 50/71.

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Answer:

the answer is B 6t and t are like terms

Answer:

Here are the correct answers:

B. gram

C. milligram

The probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

What is probability?

Probability is a way to gauge how likely or unlikely something is to happen. It measures the degree of ambiguity surrounding the result of a single event or a series of related occurrences. Typically, probability is stated as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certain or guaranteed event.

To determine the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, we need information about the distribution of baseball weights. Without specific information about the distribution, it is challenging to provide an exact probability.

However, assuming the weights of baseballs follow a normal distribution with a known mean and standard deviation, we can provide a general guideline for calculating the probability using the Central Limit Theorem.

Let's assume the mean weight of a baseball is μ grams, and the standard deviation is σ grams. Since we don't have the exact values, we'll need to make some assumptions. Let's say the mean weight of a baseball is 150 grams, and the standard deviation is 5 grams.

The average weight of the 16 baseballs follows a normal distribution with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ/[tex]\sqrt[1]{n}[/tex]).

In this case, the mean is 150 grams, and the standard deviation is 5 grams divided by the square root of 16 (since we have 16 baseballs). The square root of 16 is 4.

The standard deviation of the average weight is 5 grams / 4 = 1.25 grams.

Now, we want to calculate the probability that the average weight is more than 147 grams. To do this, we can convert it into a standard normal distribution by subtracting the mean (150 grams) and dividing by the standard deviation (1.25 grams).

The z-score for 147 grams is (147 - 150) / 1.25 = -2.4.

Using a standard normal distribution table or calculator, we can find the probability associated with a z-score of -2.4. Let's assume it is P(Z < -2.4) = 0.0082.

However, since we are interested in the probability that the average weight is more than 147 grams, we need to consider the area to the right of the z-score (-2.4). This is equal to 1 - P(Z < -2.4).

Therefore, the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

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Check the picture below.

Answer:

Variance is a measure of variability which describes the average degree of spread in the data about the mean.

Step-by-step explanation:

The 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

To calculate the 95.44% confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's determine the critical value. Since the confidence level is 95.44%, we need to find the z-score that corresponds to a tail probability of (1 - 0.9544)/2 = 0.0228. Looking up this value in the standard normal distribution table or using a statistical calculator, we find that the z-score is approximately 2.17.

Next, we need to determine the standard deviation of the population. Since we don't have that information, we'll use the sample standard deviation as an estimate. Let's assume the sample standard deviation is 5 minutes.

Now we can calculate the confidence interval:

Confidence Interval = 22.3 ± (2.17) * (5 / sqrt(20))

Calculating the expression inside the parentheses:

= 22.3 ± (2.17) * (5 / sqrt(20))

= 22.3 ± 2.17 * (5 / 4.472)

= 22.3 ± 2.17 * 1.118

Calculating the confidence interval:

Lower Limit = 22.3 - (2.17 * 1.118)

Upper Limit = 22.3 + (2.17 * 1.118)

Lower Limit = 22.3 - 2.42706 ≈ 19.87294

Upper Limit = 22.3 + 2.42706 ≈ 24.72706

Therefore, the 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

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The tax allowance for a person with two kids and no dependent relative earning 180,000 naira per month before tax is 34,375 naira.

The tax allowance is calculated by first determining the individual's annual income before tax, which in this case is 2,160,000 naira (180,000 x 12 months). Next, the individual's personal allowance of 1,500,000 naira is subtracted from their annual income.

The resulting figure is 660,000 naira, which is then multiplied by 5% to give a tax allowance of 33,000 naira. An additional 375 naira is added to this figure for each child, resulting in a total tax allowance of 34,375 naira for an individual with two kids and no dependent relative earning 180,000 naira per month before tax. This tax allowance reduces the individual's taxable income, thereby reducing the amount of tax they would be required to pay.

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The proportion of students that choose nachos is given as follows:

0.3333.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The proportion of students choosing nachos is the probability that a single student choose nachos.

Out of 33 students, 11 choose nachos, hence the proportion is given as follows:

11/33 = 1/3 = 0.3333.

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The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:

155ºF.

The temperature function is defined as follows:

[tex]T(t) = T_a + (T_0 - T_a)e^{-kt}[/tex]

Considering the surrounding and initial temperature, we have that the function is given as follows:

[tex]T(t) = 69 + 135e^{-kt}[/tex]

The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:

[tex]185 = 69 + 135e^{-1.5k}[/tex]

[tex]e^{-1.5k} = \frac{116}{135}[/tex]

[tex]k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}[/tex]

k = 0.1011.

Hence:

[tex]T(t) = 69 + 135e^{-0.1011t}[/tex]

Hence the temperature after 4.5 minutes is given as follows:

[tex]T(4.5) = 69 + 135e^{-0.1011 \times 4.5}[/tex]

T(4.5) = 155ºF.

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Answer:

------------------

The angle formed by two secants is half the difference of the intercepted arc measures:

Substitute values and solve for x:

Answer:

4 days

Step-by-step explanation:

first, figure out how many cars are produced in a day. since there are 7 days in a week, and 1400 cars are produced in a week, divide 1400 by 7. 1400/7 equals 200. so, if 200 cars produced each day, then:

200x= 800 (x = days)

200x/200 = 800/200

So, 4 days.

Answer:

The RN should set up the infusion pump to deliver 125 mL/hour.

To calculate the infusion rate, we can use the following formula:

Infusion rate = Volume / Time

In this case, the volume is 1000 mL and the time is 8 hours. Plugging these values into the formula, we get the following:

Infusion rate = 1000 mL / 8 hours

Infusion rate = 125 mL/hour

Therefore, the RN should set up the infusion pump to deliver 125 mL/hour.

It is important to note that this is just the calculated rate. The actual rate may vary slightly depending on the type of infusion pump and the settings that are used.

Step-by-step explanation:

The approximate probability that "x" will be within 0.5 of population mean is (c) 0.3026.

We use "Central-limit-theorem" to find probability that "x" will be within 0.5 of population mean. According to the central limit theorem, the distribution of sample means approaches a "Normal-Distribution" with mean μ and standard deviation σ/√(n), where μ = population mean, σ = population standard deviation, and n = sample size,

In this case, we have, sample-size of (n) = 49, population mean (μ) = 43, and population "standard-deviation" of (σ) = 9.

So, standard-deviation of sample mean distribution is:

standard deviation = σ/√(n) = 9/√(49) = 1.2857,

To find the probability that x will be within 0.5 of the population mean, we need to standardize the interval using the standard deviation of the sample mean distribution,

z = (x - μ)/(σ/√n) = (43 + 0.5 - 43)/(1.2857) = 0.3892,

The probability that "x" will be within 0.5 of the population mean is the area under the standard normal distribution curve between z = -0.3892 and z = 0.3892.

P(-0.3892 < Z < 0.3892) = P(Z < 0.3892) - P(Z < -0.3892)

= 0.6513 - 0.3487

= 0.3026

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Suppose that a random sample of size 49 is to be selected from a population with mean 43 and standard-deviation 9. What is the approximate probability that "x" will be within 0.5 of the population mean?

(a) 0.5026

(b) 0.6974

(c) 0.3026

(d) 0.6053

Possible committees contain at least one member of each class is 5235.

Number of freshman = 3

Number of sophomores = 4

Number of juniors = 4

Number of seniors = 5

Total = 3 + 4+ 4 + 5 = 16

Number of committees of five members of the council would contain at least one member of each class is given by = total - Number of possibility without freshmen - Number of possibility without sophomores - Number of possibility without juniors - Number of possibility without seniors

= [tex](\left \116 \atop 5\right. ) - (\left \413 \atop 5\right. ) -(\left \112 \atop 5\right. )-(\left \112 \atop 5\right. )-(\left \111 \atop 5\right. )[/tex]

= 8568 - 1287 - 792 - 792 - 462

= 5235

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Answer: Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).

Step-by-step explanation:

Let's first find the coordinates of the midpoint of AC, which will be the coordinates of point B if AB:BC is 1:2.

The x-coordinate of the midpoint = (x-coordinate of A + x-coordinate of C) / 2 = (-5 + 4) / 2 = -0.5

The y-coordinate of the midpoint = (y-coordinate of A + y-coordinate of C) / 2 = (4 - 5) / 2 = -0.5

So the midpoint of AC is B(-0.5, -0.5).

Now we can find the coordinates of A by using the midpoint formula:

The x-coordinate of A = (2 * x-coordinate of B + x-coordinate of C) / 3 = (2 * (-0.5) + 4) / 3 = 1.17

The y-coordinate of A = (2 * y-coordinate of B + y-coordinate of C) / 3 = (2 * (-0.5) - 5) / 3 = -2.17

So the coordinates of point A are (1.17, -2.17).

Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).

Based on the results of the 40 trials, the estimated probability of randomly choosing a red cube from the bag is 2/5 in its simplified form.

     To arrive at this answer, we can use the formula for probability: Probability of an event = Number of favorable outcomes / Total number of outcomes. In this case, the favorable outcome is selecting a red cube, and the total number of outcomes is 40 (since a cube is selected and put back in the bag before each trial). We know that a red cube was selected 16 times out of 40 trials, so the number of favorable outcomes is 16. Thus, the probability of selecting a red cube is 16/40, which simplifies to 2/5. Therefore, based on the results of the 40 trials, the estimated probability of randomly choosing a red cube from the bag is 2/5.

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The volume of the cylinder is 29.78 inches cube.

The volume of the cone is  9.93 inches cube.

The figure above is a sphere, cylinder and a cone. The volume of the figure can be represented as follows:

volume of a sphere = 4 / 3πr³

where

20 = 4 / 3 × π × r³

cross multiply

4r³π = 60

r³π = 15

r = ∛15 / π

r = ∛4.78

r = 1.68 inches

volume of a cylinder = πr²h

where

volume of a cone = 1 / 3 πr²h

where

Therefore, let's find the volume of the cylinder and cone with the following information.

Hence,

volume of the cylinder = π × (r)² × 2r

volume of the cylinder = 2(1.68)³π

volume of the cylinder = 29.78 inches cube

Therefore,

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × 3.14 × r² × 2r

volume of the cone = 1 / 3 × 3.14 × 2(1.68)³

volume of the cone = 29.77744896 / 3

volume of the cone = 9.93 inches cube

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Answer: 50 1/3

Step-by-step explanation: (30 X 5 +4) divided by 3 = 50 1/3

Answer:

y= 32

Step-by-step explanation:

Answer:

The answer for y is 32

Step-by-step explanation:

-3=-11+√2y

-3+11=√2y

8=√2y

square both sides

8²=√2y²

64=2y

divide both sides by 2

2y/2=64/2

y=32

The equation which is equivalent to 3x - 12 = -9 is 3(x - 4) { -9

3x - 12 = -9

The equation is divided into two parts; right part and left part

From the left part; find the common factor of 3x and 12 which is 3

So,

3(x - 4) = -9

3x - 12 = -9

Add 12 to both sides

3x = -9 + 12

3x = 3

divide both sides by 3

x = 3/3

x = 1

Hence, the value of x based on the given equation is 2

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The mean distance thrown is approximately 37.31 feet. the Average distance thrown by the heavy ball.

To find the mean of the distances thrown from the stem-and-leaf plot, we need to add up all the distances and divide by the total number of throws.

From the stem-and-leaf plot, we can see that there are 13 throws in total.

To add up the distances, we can use the key to interpret the plot: for example, the number "31" means that one throw went 3.1 feet. Using this method, we can find the following distances:

20, 22, 25, 31, 33, 34, 41, 41, 45, 50, 56, 67, 71

Adding up these distances, we get a total of 485.

To find the mean, we divide by the total number of throws:

mean = 485/13 ≈ 37.31

Therefore, the mean distance thrown is approximately 37.31 feet.  the average distance thrown by the heavy ball.

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After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.

First, find the value of the investment when it is compounded periodically, 12 times a year.

The formula is:

= Amount invested x ( 1 + rate ) ^ number of periods

= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰

= $ 53, 678. 16

If compounded annually, the value would be :

= 9, 000 x ( 1 + 9 % ) ²⁰

= $ 50, 439. 69

The difference is :

= 53, 678. 16 - 50, 439. 69

= $ 3, 238. 47

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The length of the tangent x is 11.2 units.

Given is circle with radius 8.4 units and a tangent with x units, we need to find the length of the tangent,

Since we know that the tangents are perpendicular to the circle, so to find the length,

Using Pythagoras theorem,

Hypotenuse is 5.6+8.4 = 14 units,

So,

14² = 8.4² + x²

x = √196 - 70.56

x = 11.2

Hence the length of the tangent x is 11.2 units.

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Answer:

87

Step-by-step explanation:

beause

Answer:

48%

Step-by-step explanation:

Let x equal the percent

25x = 12

25x/25 = 12/25

x =0.48

0.48 = 48%