P ( rolling a composite number and the coin landing on heads and tails )

The sum of the arithmetic series of 28 + 28.4 ...+ 42 is 1260.

An arithmetic series is a sequence of numbers in which each term is obtained by adding a constant difference, called the common difference, to the preceding term.

To resolve this issue, we can utilise the following formula for the sum of an arithmetic series:

S = (n/2) * (a₁ + aₙ)

When n is the number of terms, a1 is the first term, and an is the nth term, S is the series total.

To find the number of terms, we need to figure out the pattern of the series. The common difference (d) is expressed as follows:

d = 28.4 - 28 = 0.4

To get from 28 to 42, we need to add (42 - 28)/0.4 = 35 terms.

So the number of terms is:

n = 35 + 1 = 36

The first term is a₁ = 28, and the last term is aₙ = 42.

Now we can plug these values into the formula:

S = (n/2) * (a₁ + aₙ)

= (36/2) * (28 + 42)

= 18 * 70

= 1260

Therefore, the sum of the arithmetic series is 1260.

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Answer: D. 33

Step-by-step explanation:

Total 84 students, are needed to guarantee that there are two students expected to graduate in the same year who have the same major.

We have undergraduate students at a college. Students belong to 4 groups (depending on year ) and 21 different majors. Total different majors for choice

= 21

We have to determine number of students needed to guarantee that there are two students expected to graduate in the same year who have the same major. Using the combinations, total different combinations possible for student having a particular major and year = 21× 4 = 84

By Pigeon Hole principle, if there is n boxes and m objects then atleast one box must contain more then one object. Here, we have 84 different Buckets . The 85th object ( 84 + 1 = 85) makes sure

bucket has 2 objects. The 85 is required number of students to that atleast one Year and 21 students in same year and same major.

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Decreasing the circumference of a tire by 20% would increase the number of rotations required to travel a given distance.

What is Circumference ?

Circumference is the distance around the outside of a circle or a curved object. It is the measurement of the boundary line or the perimeter of the circular object. The circumference of a circle is calculated using the formula C = 2πr, where "C" is the circumference, "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14159.

The number of rotations of a tire depends on its circumference, which is the distance around the outside of the tire. If the circumference of a tire decreased by 20%, it means that the distance around the outside of the tire would be 20% less than it was before. This would cause the tire to cover less ground in each rotation, which would result in an increase in the number of rotations needed to travel a given distance. Specifically, the number of rotations would increase by 20% for the same distance traveled, as the tire would need to rotate more times to cover the same distance due to the reduced circumference.

Therefore, decreasing the circumference of a tire by 20% would increase the number of rotations required to travel a given distance.

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Answer:

x = y + 3

Step-by-step explanation:

y = x - 3 ( add 3 to both sides )

y + 3 = x , that is

x = y + 3

The cost of 3.25m lace would be $22.75

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

we are given 0.8m of lace costs $5.60

now, we can find cost of 1m of lace

so, we have to divide both sides by 0.8

1 m of lace cost [tex]=5.60\div0.8[/tex]

1 m of lace cost [tex]=7[/tex]

so, we will also get

[tex]3.25\div0.8 = 4.0625[/tex]

Now multiply that by 3.25

[tex]3.25 \times 7 = 22.75[/tex]

So, the cost of 3.25m lace is $22.75

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Answer:

Step-by-step explanation:

x^2-2xz+xy-2yx^2+xy-xz-yz =x^2+xy+xy-yz-2xz-xz-2yx^2

=x^2+xy+xy-yz-2xz-xz-2yx^2

=x^2+2xy-yz-3xz-2x^2y

The answer is option b. confidence coefficient.

To explain this, let's start by defining interval estimation. Interval estimation is a statistical method used to estimate an unknown population parameter (such as the population mean or proportion) by constructing a range of values, called a confidence interval, that contains the true value of the parameter with a certain level of confidence.

The level of confidence refers to the percentage of times that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated. For example, a 95% confidence level means that if we were to repeat the interval estimation procedure many times, we can expect to obtain a confidence interval that contains the true population parameter 95% of the time.

The confidence coefficient, on the other hand, is the probability that a particular confidence interval actually contains the true value of the population parameter. It is the complement of the significance level, which is the probability of making a Type I error (rejecting a true null hypothesis). For example, if we have a 95% confidence level, then the confidence coefficient is 0.95, and the significance level is 0.05.

Therefore, the confidence coefficient represents the probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated. It is a measure of how confident we are that the estimated interval contains the true population parameter.

In conclusion, the confidence coefficient is a crucial concept in interval estimation that reflects the probability of obtaining a confidence interval that includes the true population parameter. It provides a measure of the reliability and accuracy of the interval estimation procedure and helps researchers interpret the results of their analyses.

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a. The necessary assumptions are the population variances are equal and combine the two sample variances into one.

b. The null and alternative hypotheses are defined.

c. The sample sizes are equal, and the sample standard deviations are approximately equal, we can safely assume equal variances and pool the sample variances.

d. The value of test statistic is 3.15 and p value is 0.05.

e. The mean diameter of bearings from machine 2 is greater than that of machine 1 at a 5% level of significance.

To begin the hypothesis test, the manager needs to state the null and alternative hypotheses. The null hypothesis (H0) is the statement of "no difference" between the mean diameters of bearings from the two machines. The alternative hypothesis (Ha) is the statement that the mean diameter of bearings from machine 2 is greater than that of machine 1.

In symbols,

H0: μ1 = μ2 (where μ1 is the mean diameter of machine 1 and μ2 is the mean diameter of machine 2) and

Ha: μ2 > μ1.

Before conducting the hypothesis test, we need to check some assumptions.

The next step is to calculate the test statistic and p-value. We use a t-test to compare the means of two independent samples. The test statistic is calculated as:

t = (x₁ - x₂) / [s_p x √(2/n)]

where x₁ and x₂ are the sample means, s_p is the pooled standard deviation, and n is the sample size.

Plugging in the numbers, we get:

t = (3.355 - 3.302) / [0.050 x √(2/50)] = 3.15

Using a t-distribution table with 98 degrees of freedom (n₁ + n₂-2), we find that the p-value associated with a t-value of 3.15 is less than 0.01.

Finally, we need to state our conclusion based on the p-value. Since the p-value is less than our significance level of 0.05, we reject the null hypothesis.

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A control chart that measures variables measures characteristics that can be measured on a continuum of value like weight and volume.

Control diagrams are a measurable instrument used to screen and control processes over the long haul. They are utilized to follow factors that can be estimated on a consistent scale, like weight, volume, temperature, or time. These factors are not discrete, yet rather fall along a reach or continuum of values. By plotting information over the long haul on a control graph, a cycle can be observed to guarantee that it stays inside a predetermined scope of OK variety. The control diagram gives a visual portrayal of the cycle information, permitting process proprietors to recognize when the interaction is crazy or when it might require remedial activity. Generally, control outlines that action factors assist with guaranteeing the nature of the cycle yield by empowering process proprietors to distinguish and address issues before they bring about deformities or mistakes.

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Answer:

36 coins

Step-by-step explanation:

10 percent is 18 coins. so just double that.

Answer:

Step-by-step explanation:

Total coin Eva has = 180

20% of her coins are represented by 20% of the 180

= 20/100 * 180

=0.2 * 180= 36

36 coins represent 20% of Eva's coins.

A percentage is a number or ratio that represents a fraction of 100. It is used to describe numbers. It is a dimensionless quantity. A percentage is denoted by the % symbol.

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Mihir's daily basic energy requirement is 8424 (kl/day).

How to find BMI body mass index or BER from body mass?

As the formula to find daily BER is given below,

[tex]Daily\ BER\ = 5.4 \times 24 \times body\ mass[/tex]

body mass = 65 kg

Therefore, put body mass, to find BER,

[tex]Daily\ BER\ = 5.4 \times 24 \times 65\\Daily\ BER\ = 8424\ (kl/day)[/tex]

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Mihir's daily basic energy requirement is 7,776 kJ/day.

A person's BMI is calculated by dividing their weight in kilograms (or pounds) by their square of height in meters (or feet). A high BMI may indicate excessive body fat. BMI measures weight categories that could lead to health issues, but it does not assess a person's health or body fat percentage.

to calculate Mihir's daily basic energy requirement using the formula:

Daily BER (kl/day) = 5.4 x 24 hours x body mass (kg)

We can substitute the given values to get:

Daily BER (kl/day) = 5.4 x 24 hours x 65 kg

Daily BER (kl/day) = 7,776 kJ/day

Therefore, Mihir's daily basic energy requirement is 7,776 kJ/day.

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Answer:

First, we can calculate the discount from the sale. The sweater costs $65.99, and with a 40% discount, the price is reduced by:

$65.99 x 0.40 = $26.40

So the sale price of the sweater is:

$65.99 - $26.40 = $39.59

Next, we can apply Carson's $10 coupon to the sale price:

$39.59 - $10 = $29.59

Therefore, Carson pays $29.59 for the sweater after the discounts.

To calculate the total discount that Carson receives, we can first find the amount of the 40% discount on the sweater, which is:

40% of $65.99 = 0.4 x $65.99 = $26.40

Then, we can add the additional $10 coupon discount to get the total discount:

$26.40 + $10 = $36.40

Therefore, the total discount that Carson receives on the sweater is $36.40.

To find the final price that Carson pays after the discounts, we can subtract the total discount from the original price:

$65.99 - $36.40 = $29.59

Therefore, Carson pays $29.59 for the sweater after the discounts.

Answer:

If u mean 312 inches then the answer is 12480in^3

Step-by-step explanation:

To solve volume do LxWxH which is Length times width time height.

An equation in slope-intercept form of the line that passes through (-3, 2) and (-2, - 5) is: C. y = -7x - 19.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-5 - 2)/(-2 + 3)

Slope (m) = -7/1

Slope (m) = -7

At data point (-3, 2), a linear equation in slope-intercept form for this line can be calculated as follows:

y - y₁ = m(x - x₁)

y - 2 = -7(x + 3)

y = -7x - 21 + 2

y = -7x - 19

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Jamal spends a total of $44 on lunch for his family, including tax and tip.

Algebraic expression can be defined as combination of variables and constants.

The total cost of the drinks is 4 x $1.75 = $7.

The total cost of the sandwiches is 4 x $7.50 = $30.

So, the subtotal before the tip is $7 + $30 = $37.

Since the prices include tax, we can directly add the tip to the subtotal to get the total amount Jamal spends:

Total cost = Subtotal + Tip = $37 + $7 = $44.

Therefore, Jamal spends a total of $44 on lunch for his family, including tax and tip.

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Answer:

109°

Step-by-step explanation:

Given:

arc QS = 65°

∠QRS = 44°

Find: arc PS -

.

∠QRS = arc PS - arc QS

arc PS = ∠QRS + arc QS

arc PS = 44° + 65° = 109°

Answer:

Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions.

The formula one-half(a° - b°) is derived from the fact that the exterior angle of a triangle is equal to one-half the difference between the measures of the two remote interior angles.

The formula that would be used to find the measure of angle 1 is one-half(a° - b°). This formula applies to a situation where angle 1 is an exterior angle of a triangle, and a° and b° are the measures of the two remote interior angles of the triangle that are adjacent to angle 1. The exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Mathematically, this can be expressed as:

angle 1 = a° - b°

To find the measure of angle 1 using the formula one-half(a° - b°), we would simply plug in the known values of a° and b°, and perform the necessary arithmetic operations.

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Answer:

D: Left side

Step-by-step explanation:

The probability that a randomly selected part is not defective is 47/50.

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here Total number of parts machine makes = 50

Number of parts defective out of 50 = 3

Then number of parts not defective out of 50 = 50-3 = 47.

Now using probability formula:

Probability = No of favorable item/ Total no of item

Now probability that a randomly selected part is not defective is,

= 47/50.

Hence the probability that a randomly selected part is not defective is 47/50.

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As a result, the product property can be used to manipulate and equation statements containing 2xy, as well as to express 2xy in terms of its factors.

An equation is a statement that shows the equality between two mathematical expressions. It is a fundamental concept in mathematics and is used to describe relationships between quantities.

The purpose of an equation is to find the value of the unknown variable(s) that make the equation true. This is typically done by applying algebraic operations to manipulate the equation, with the goal of isolating the variable on one side of the equal sign.

[tex]2xy = 2 * x * y[/tex]

[tex]2xy = 2x * y = 2y * x = x * 2y = y * 2x = x * y * 2[/tex]

[tex]4x^2y * 3xy^2 = (4 * x * x * y) * (3 * x * y * y)[/tex]

[tex]= 12 * x^3 * y^3[/tex]

As a result, the product property can be used to manipulate and simplify statements containing 2xy, as well as to express 2xy in terms of its factors.

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The length 53.1°, 90°, and 39.9°,vertical length: 3/5 ,length of vertical: 4/5 1 hypotenuse.

Angle is a geometric concept that describes the relative difference between two straight lines or planes that meet at a common point. It is measured in degrees, radians or grads, and is often represented by the symbol θ. An angle can be acute, right, obtuse, straight, reflex, or full. Angles can be used to measure the size of a triangle, to calculate the area of a figure, and to determine the position of a point in a coordinate system.

We possess that

Angle = 53.1°

Vertical length = 3/5 (this is the adjacent cathetus)

Vertical length equals 4/5 (this is the opposite cathetus)

We can use it to check this.

tg(angle) = adjacent/opposite:

tg(53.1) = 1.33

and

(4/5)/(3/5) = 4/3 = 1.33

This makes sense, then.

Using the relationship, we can now identify the hypotenuse:

Sin(angle) = the antipode or hypotenuse

sin(53.1) = (4/5)/H

H = (4/5)/sin(53.1) = 1

Hence, there is always a 90° angle in a triangle or rectangle.

We may get the final angle using the fact that the sum of a triangle rectangle's three interior angles is always 180 degrees.

A + 53.1° + 90° = 180°

A = 90° - 53.1° = 36.9°

Now that we have located every missing part of the triangle.

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The coordinates of the image is at

The coordinates of the image is solved by applying the translation rule which is

(x, y) → (x + 6, y - 4)

This is applied as follows

preimage coordinates    translation        image coordinates

(-9, 2)                 →             (-9 + 6, 2 - 4) → (-3, -2)

(-9, 4)                 →             (-9 + 6, 4 - 4) → (-3, 0)

(-7, 4)                 →             (-7 + 6, 4 - 4) → (-1, 0)

(-5, 2)                →             (-5 + 6, 2 - 4) → (1, -2)

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The cost of 1800 bricks is $7,386.76. The cost of 1800 bricks, each measuring 7 1/4 in by 21 1/4 in by 3 1/4 in and weighing 0.06 ounces per cubic inch, can be calculated as follows:

First, we need to find the volume of one brick by multiplying its three dimensions:

Volume of one brick = 7.25 in x 21.25 in x 3.25 in = 526.0156 cubic inches

Next, we can find the weight of one brick by multiplying its volume by its weight per cubic inch:

Weight of one brick = 526.0156 cubic inches x 0.06 ounces/cubic inch = 31.56094 ounces

The total weight of 1800 bricks can be found by multiplying the weight of one brick by 1800:

Total weight of 1800 bricks = 31.56094 ounces/brick x 1800 bricks = 56,809.6928 ounces

Finally, we can find the cost of the bricks by multiplying their total weight by the cost per ounce:

Cost of 1800 bricks = 56,809.6928 ounces x $0.13/ounce = $7,386.76

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Answer:

621.09 mm²

Step-by-step explanation:

Area of pentagon = [tex]\frac{(perimeter) (apothem)}{2}[/tex]

Let's solve

[tex]\frac{(5 times 19) times 13.08}{2}[/tex] = 621.09 mm²

So, the answer is 621.09 mm²

Answer: 8.58 cm²

Step-by-step explanation:

The area of the central triangle bounded by each of the sides can be computed as ...

 A = (1/2)r²sin(α) . . . . where α is the central angle, 360°/5 = 72°  

There are 5 such triangles, so the area of the pentagon is

A = (5/2)(1.9 cm)²sin(72°) ≈ 8.58 cm²

To complete her journey Ann needs to run for (120/3) = 40 minutes in order to travel at an average speed of 5 km/h.

We can start by using the formula:

average speed = total distance ÷ total time

Let's first calculate the total distance Ann covers:

distance walked = speed x time = 4 km/h x (8 km / 4 km/h) = 8 km

distance run = speed x time

Let's call the time Ann runs for "t". Then:

distance run = 8 km/h x (t/60) h = (8t/60) km

Total distance = distance walked + distance run = 8 km + (8t/60) km = (480 + 8t) / 60 km

Now, let's find the total time:

total time = time walked + time run

time walked = distance ÷ speed = 8 km ÷ 4 km/h = 2 h

time run = t/60 h

total time = 2 h + t/60 h = (120 + t)/60 h

Now we can substitute the values we have found into the formula for average speed:

5 km/h = [(480 + 8t)/60 km] ÷ [(120 + t)/60 h]

Simplifying the right-hand side, we get:

5 km/h = (480 + 8t) / (120 + t)

Multiplying both sides by (120 + t), we get:

600 + 5t = 480 + 8t

Subtracting 480 and 5t from both sides, we get:

120 = 3t

Therefore, Ann has to run for (120/3) = 40 minutes to have an average speed of 5 km/h over her complete journey.

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The total amount of energy used by the computer is:

0.4 kW × 20.7 h = 8.28 kWh

The cost of the energy used is:

8.28 kWh × $0.08/kWh = $0.6624

Therefore, it costs $0.66 to use the computer.

A computer in a house uses 0.4 kilowatt for 20.7 hours. If electricity costs $0.08 per kilowatt-hour, how much does it cost (in dollars, to the penny) to use the computer? use exact numbers; do not estimate.

The cost of using the computer for 20.7 hours can be found by multiplying the electricity used per hour by the cost per kilowatt-hour.

That is,Cost = Power (kilowatts) × Time (hours) × Cost per kilowatt-hour (dollars)Given that the power used by the computer is 0.4 kilowatts and the time it was used is 20.7 hours, we can find the total cost of using the computer by substituting the values in the above equation.Cost = 0.4 kilowatts × 20.7 hours × $0.08 per kilowatt-hourCost = 0.4 × 20.7 × 0.08Cost = $0.06624Therefore, it costs $0.06624 to use the computer.

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According to the figure the value of x is

The value of x is solved using the intersecting secant tangent theorem

The theorem have the formula

12^2 = 9 * (9 + x)

solving for x

144 = 81 + 9x

9x = 63

9x / 9 = 63 / 9

x = 7

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