In PQR, Q= 76, PQ = 18, and QR = 27
Please find angle P, T and PR for 5

The correct answer is c. Line graphs show the change in one or more variables progressively across time.

Histograms show the distribution of data, pie charts show the proportions of a whole, bar charts compare categories or groups, and diagrams show the relationships between different elements.

The correct answer is c. Line graphs show the change in one or more variables progressively across time

A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics. Frequency, which can be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data.

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Line graphs show the change in one or more variables progressively across time. C

A line graph is a type of chart that displays data as a series of data points connected by straight lines.

The horizontal axis of the graph typically represents time, while the vertical axis represents the value of the variable being measured.

By connecting the data points with lines, a line graph can show the trend or pattern of change in the variable over time.

Line graphs are commonly used in fields such as economics, finance, and science to visualize trends in data over time.

They can be used to identify patterns, compare different variables, or forecast future trends.

In contrast, histograms, pie charts, bar charts, and diagrams are different types of charts that are used to display data in different ways.

Histograms are used to show the distribution of data within a single variable, while pie charts and bar charts are used to compare different categories or groups of data.

Diagrams are used to represent complex systems or relationships, often using visual symbols or icons to represent different components.

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The distance between Reeta and the school when the cyclists arrive the home for this case is found to be 2 km

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example, if it is asked to increase some items by 4, then you can add 4 in that item to increase it by 4. If something is, for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert descriptions to mathematical expressions.

How to find the speed of an object?

If the object is going linearly, and at a constant speed, then the speed of that object is given by the distance it travelled to the time it took to travel that distance.

If the object travelled D distance in T units of time, then that object's speed is

\(Speed = \dfrac{D}{T}\)

Given that:

Suppose at time 0 hours, all three people departed from school (on that Monday).

After 't' hours, suppose the cycle gets punctured.

Then, as the cycle was going by 20 km/hour speed, so in 't' hours, it must have covered d kilometres (suppose),

then we get:

\(S =\dfrac{D}{T}\)

\(20=\dfrac{d}{t}\)

d = 20t

This distance is measured from school. But we know that this distance is 4 km, so we get:

20t = 4

t  =  1 / 4

The remaining 1 km (as the home is 5 km away from school and 4 km is already travelled) is walked by Cyclists. And walking speed is 5 km/hour, so let they take T hours to travel that 1 km walking, then we get:

5 =  1 / T

t = 0.2 hours

So, the total time cyclists took to reach home from school is: 0.2+0.2=0.4 hours

Reeta is walking that whole 5 km.

The time the cyclist reached home, Reeta had walked for 0.4 hours as they had started at the same time, and it took cyclists 0.4 hours to reach home.

Thus, we have:

Time is taken 0.4 hours, speed of Reeta = walking speed= 5 km/hour, then we get:

D = S x T

D = 5 x 0.4 = 2 km

So Reeta was 2 km away from school when cyclists reached home on that Monday.

Thus, the distance between Reeta and the school when the cyclists arrive at the home for this case is found to be 2 km

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Answer:

Height of the tree is 78.11 feet.

Step-by-step explanation:

By applying the tangent rule in the right triangle formed,

Since, tanθ = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(32)° = \(\frac{h}{125}\)

h = 125(tan32°)

h = 125(0.62487)

h = 78.109

  ≈ 78.11 ft

Height of the tree will be 78.11 feet.

The measure of arc BC in circle E, inscribed in triangle BCD with angle DBC measuring 51 degrees, is 102°.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Since BD is a diameter, angle DBC is a right angle, and the intercepted arc BC is a semicircle. Therefore, the measure of arc BC is 180°.

However, we are given that angle DBC measures 51 degrees. In an inscribed triangle, the measure of an angle is equal to half the measure of its intercepted arc. So, angle DBC is half the measure of arc BC, which means arc BC measures 2 times angle DBC, or 2 * 51° = 102°.

Hence, the measure of arc BC is 102°.

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Inscribed circle E is formed by triangle BCD, with BD as the diameter. DC and CB are secants, and angle DBC is 51 degrees. We need to find the measure of arc BC.

When a triangle is inscribed in a circle, the measure of an angle formed by two secants that intersect on the circle is half the measure of the intercepted arc.

In this case, angle DBC is 51 degrees, which means the intercepted arc BC has twice that measure. Therefore, the measure of arc BC is 2×51=102 degrees.

To understand why this relationship holds, we can use the Inscribed Angle Theorem. According to this theorem, an angle formed by two chords or secants that intersect on a circle is equal in measure to half the measure of the intercepted arc.

In our scenario, angle DBC is formed by secants DC and CB, and it intersects the circle at arc BC. According to the Inscribed Angle Theorem, angle DBC is equal to half the measure of arc BC.

Hence, if angle DBC is 51 degrees, the measure of arc BC is twice that, which gives us 102 degrees.

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The angle subtended at the center of the arc is 102⁰

Recall that to find the length of an arc on a circle, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.  If the central angle is measured in degrees, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.

Lenght of arc = A/360 *2пr

A = angle at center = ?

п = 22/7 r = radius = 840 feet

⇒1500 = A/360  2 *22/7 * 840

1500 = 36960A/2520

3780000= 36960A

making A the subject we have

3780000/36960 = A

A = 102.27

A= 102⁰

The angle is 102⁰

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Answer: Depends how long he's in school and how far away it is from his house.

Step-by-step explanation:

To solve for the angles that satisfy the equation 9 tan 0+13= 2 tan 0 + 6, we need to first simplify the equation. We can start by moving all the terms involving tan 0 to one side of the equation and the constant terms to the other side. This gives us: 7 tan 0 = -7

Next, we can isolate tan 0 by dividing both sides by 7: tan 0 = -1 Now we can find the angles that satisfy this equation by using a calculator or reference table to find the angle whose tangent is -1. This angle is -45 degrees or 315 degrees, since the tangent function has a period of 180 degrees and the tangent of an angle in the second quadrant is negative. Therefore, the two angles that satisfy the equation are -45 degrees and 315 degrees.
To find all angles that satisfy the given equation, 9tan(θ)+13 = 2tan(θ)+6, first isolate the tan(θ) term:
9tan(θ) - 2tan(θ) = 6 - 13 7tan(θ) = -7 tan(θ) = -1 Now, use the arctangent function to find the principal angle (in degrees) that corresponds to a tangent value of -1: θ = arctan(-1) ≈ -45° Since tangent has a period of 180°, we can find all angles between 0° and 360° by adding multiples of 180° to the principal angle: θ1 = -45° + 180° = 135 θ2 = -45° + 360° = 315°
So, the angles that satisfy the equation are approximately 135° and 315°.

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The optimal solution for the given problem is P = 57, achieved at (x, y) = (4.5, 3).

To solve this problem using Excel's Solver add-in, we need to set up the objective function and the constraints.

Objective function:

Maximize P = 3x + 8y

Constraints:

2x + 4y ≤ 20

6x + 3y ≤ 18

x ≥ 0, y ≥ 0

Step 1: Open Excel and set up the spreadsheet as follows:

In cell A1, enter "x"

In cell B1, enter "y"

In cell C1, enter "P"

In cell A2, enter "0" (initial guess for x)

In cell B2, enter "0" (initial guess for y)

In cell C2, enter the formula "=3*A2+8*B2" (objective function)

Step 2: Set up the constraints:

In cell A3, enter "2"

In cell B3, enter "4"

In cell C3, enter "<="

In cell D3, enter "20"

In cell A4, enter "6"

In cell B4, enter "3"

In cell C4, enter "<="

In cell D4, enter "18"

Step 3: Add the Solver add-in:

Go to the "Data" tab, click on "Solver" (found in the "Analysis" group)

Set the objective cell to C2 and select "Max" as the goal

Set the variable cells to A2:B2

Click on the "Add" button to add the constraints

Select A3:D4 as the constraint range

Click on "OK" to close the Add Constraint window

Click on "Solve" to find the optimal solution

:

After solving the problem using Excel's Solver add-in, the optimal solution is found to be P = 57, which is achieved when x = 4.5 and y = 3. This means that to maximize P, we should set x to 4.5 and y to 3, while ensuring that the constraints 2x + 4y ≤ 20 and 6x + 3y ≤ 18 are satisfied.

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Therefore, the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4) is -30 degrees.

An ellipse is a geometric shape that resembles a stretched or squished circle. It can be defined as the set of all points in a plane, such that the sum of the distances from two fixed points, called the foci, is constant. An ellipse has two axes, a major axis and a minor axis, which intersect at the center of the ellipse. The length of the major axis is twice the distance from the center to one of the foci, while the length of the minor axis is twice the distance from the center to one of the points where the ellipse intersects the major axis. Ellipses have many applications in mathematics, physics, and engineering. They are used to model the orbits of planets and satellites, as well as the paths of objects in electric and magnetic fields. They are also used in optics to describe the shape of lenses and mirrors, and in statistics to model data distributions.

Here,

To determine the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4), we first need to find the equation of the tangent line to the ellipse at the point (0,4).

To do this, we take the derivative of the equation of the ellipse with respect to x and evaluate it at the point (0,4):

d/dx (x² + 3y²) = 2x + 6y(dy/dx)

At the point (0,4), we have x = 0 and y = 4, so the equation becomes:

0 + 6(4)(dy/dx) = 0

Solving for dy/dx, we get:

dy/dx = 0

This means that the tangent line to the ellipse at the point (0,4) is a horizontal line passing through the point (0,4).

Now we can find the angle at which the ellipse is seen from the point M (0,4) by finding the angle between the horizontal tangent line and the line connecting the point M to the origin. This angle is given by:

tan θ = (y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) = (0,4) is the point M and (x₂, y₂) is the point where the tangent line intersects the x-axis.

Since the tangent line is horizontal, it intersects the x-axis at the point (±2√3, 4), which are the x-intercepts of the ellipse. Choosing the positive x-intercept, we have:

x₂ = 2√3

y₂ = 0

Substituting these values into the formula for the tangent, we get:

tan θ = (0 - 4)/(2√3 - 0) = -2/2√3 = -1/√3

Taking the inverse tangent of both sides, we get:

θ = -30 degrees

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Answer:

a.Equation :y=40-2.5x

b.straight, decreases, the same

Step-by-step explanation:

To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

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Answer:

If Maria uses 2 parts cream and 3 parts milk, then for every 2 parts of cream, she uses 3 parts of milk.

Since she uses 8 liters of cream, we can find the total volume of mixture by finding the equivalent volume of milk that she used.

To find the equivalent volume of milk, we multiply the volume of cream by the ratio of milk to cream:

8 liters * (3 parts milk) / (2 parts cream) = 12 liters

So Maria used 8 liters of cream and 12 liters of milk for a total volume of 20 liters.

Answer:

y-axis is located 4 units from point M

Explanation:

Given that the point M is located at;

we want to find what is located 4 units from M.

Points A,B and C are all more than 4 units point M.

Point M is 6 units from the x-axis.

Point M is 4 units from the y-axis.

Therefore, y-axis is located 4 units from point M

Answer:

1

Step-by-step explanation:

A rational number between 3.623623 and 0.484848 is 1.

Answer:

Remember: rational numbers are numbers that can be written as fractions and decimals that either terminate or repeat. Here are some rational numbers:

0.5, 3/4, 1, 1.5...3, 3.5

Step-by-step explanation:

BRAINLIEST, PLEASE!

Answer:

x=14 and y=37

Step-by-step explanation:

The sample size which is required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03 is equals to the 382.

We have provide that the state education commission wants to draw an estimate on the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Population proportion, p = 0.21

confidence level = 85%

Margin of error = 0.03,

We have to determine the sample size. For determining sample size for estimating a population propotion, using the below formula,

n = (Zα/2)² ×p×(1-p) / MOE²

where MOE is the margin of error

Using the distribution table, Zc for 85% for confidence level where α = 0.15 or α/2 = 0.075 equals to the 1.439.

Substituting all known values in formula we

n = 1.439² × 0.21( 0.79)/ (0.03)²

=> n = 382.2336 ~ 382

Hence, required sample size is 382.

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Answer:

45

Step-by-step explanation:

small brain

Answer:

The answer is. 4.5x10^-4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent would be positive. Hope this helps!

Answer:

Step-by-step explanation:

The amount of water that was in the cooler initially is dependent on the amount of water in the cooler now(that is, what is remaining). And also, the rate of which water was being used. If the rate at which water was being used was 10 liter/hour, this means that an 11 liter cooler would remain 1 liter after an hour. Because 10 liters must have been used within the said hour.

Answer:

10 liters

Step-by-step explanation:

The sample is a stratified sample.

A stratified sample is a sampling method in which a population is separated into distinct, non-overlapping subpopulations, or strata, and a random sample is taken from each stratum.

This is frequently utilized when the population contains subpopulations with distinct characteristics, and the researcher wants to guarantee that these subpopulations are adequately represented in the sample.

Likewise, in the provided scenario of the electronics store, the store will first separate the customers who purchased a computer over the past two years and then take 100 receipts through a random number generator to question customers about high-speed Internet rates.

This way, it can ensure that all customers are adequately represented in the sample and the information it receives is not biased.

A stratified sample is a sampling technique used in statistics and research to ensure that the sample accurately represents the different subgroups or strata within a population. It involves dividing the population into distinct subgroups or strata based on certain characteristics or variables and then selecting a sample from each stratum.

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The initial value problem calculator is a tool used to calculate differential equations.

An instrument for solving ordinary differential equations with initial conditions is an initial value problem calculator. Finding a function that solves a given differential equation and a set of initial conditions is the goal of this calculator, a particular kind of differential equation problem. The differential equation, the beginning conditions, and other pertinent parameters are entered into the calculator, which then generates a solution that fulfils the initial conditions.

Usually, the answer is provided as a function that specifies how the system behaves over time. In disciplines like physics, engineering, and economics, where differential equations are regularly employed to represent dynamic systems, these calculators are widely used. They can be helpful for obtaining an understanding of a system's behavior and for predicting its upcoming trends

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Answer:

\(-9x-10y\)

Step-by-step explanation:

\(10yi^2-9x \\ \\ =10y(-1)-9x \\ \\ =-9x-10y\)

The probability that there will be at least 4 typos on page 301 is 0.847

To solve this problem, we need to make some assumptions. Let's assume that the number of typos on each page follows a Poisson distribution with a mean of 6 typos per page, and that the number of typos on one page is independent of the number of typos on any other page.

Under these assumptions, we can use the Poisson distribution to calculate the probability of observing a certain number of typos on a given page.

Let X be the number of typos on page 301. Then X follows a Poisson distribution with a mean of 6 typos per page. The probability of observing at least 4 typos on page 301 can be calculated as follows

P(X ≥ 4) = 1 - P(X < 4)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

Using the Poisson distribution formula, we can calculate the probabilities of each of these events

P(X = k) = (e^-λ × λ^k) / k!

where λ = 6 and k is the number of typos. Thus,

P(X = 0) = (e^-6 × 6^0) / 0! = e^-6 ≈ 0.0025

P(X = 1) = (e^-6 × 6^1) / 1! = 6e^-6 ≈ 0.015

P(X = 2) = (e^-6 × 6^2) / 2! = 18e^-6 ≈ 0.045

P(X = 3) = (e^-6 × 6^3) / 3! = 36e^-6 ≈ 0.091

Plugging these values into the equation above, we get

P(X ≥ 4) = 1 - (e^-6 + 6e^-6 + 18e^-6 + 36e^-6)

≈ 0.847

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Answer:

s=  -5

Step-by-step explanation:

have a good day

Answer:

Step-by-step explanation:

subtract 28 on both sides that will cancel the 28

-35 = 7s, divide both sides by 7, this cancels the 7

- 5 = s

s=-5

The simplified expression is 2cos²(x) + sinx - 1 = 0

The expression we will be simplifying is

=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.

To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:

(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)

Simplifying this expression using the distributive property, we get:

(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)

Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:

1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1

Similarly, for the second fraction, we can use the same identity to obtain:

1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1

Substituting these values back into the original expression, we get:

1 + 1 = 2sinx/(sin⁴x - cos⁴x)

Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:

sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ

Substituting this back into the expression, we get:

2 = 2sinx/(sin²ˣ - cos²ˣ)

Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):

2 = -2sinx/cos(2x)

Multiplying both sides by -cos(2x), we get:

-2cos(2x) = 2sinx

Dividing both sides by 2, we get:

-cos(2x) = sinx

Using the double-angle formula for cosine, we get:

-2cos²(x) + 1 = sinx

Simplifying this expression, we get:

2cos²(x) + sinx - 1 = 0

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The p-value for the test that the coin is biased for heads is 0.097.

To calculate the p-value for the test that the coin is biased for heads, we can use the binomial distribution and the concept of a one-tailed test.

In this case, the null hypothesis is that the coin is fair and unbiased. The alternative hypothesis is that the coin is biased for heads.

Let's define:

- n = number of coin tosses = 60

- x = number of times the coin lands on heads = 35

- p = probability of getting heads on a single toss under the null hypothesis (fair coin) = 0.5

We can calculate the expected number of heads under the null hypothesis by multiplying the number of tosses by the probability of heads:

Expected number of heads = n * p = 60 * 0.5 = 30

Next, we can use the binomial distribution to calculate the probability of getting 35 or more heads out of 60 tosses, assuming the null hypothesis is true:

P(X ≥ 35) = P(X = 35) + P(X = 36) + ... + P(X = 60)

To calculate this sum, we can use the normal approximation to the binomial distribution since n is large (n = 60) and p is not too close to 0 or 1. The normal approximation relies on the mean and standard deviation of the binomial distribution.

Mean (μ) = n * p = 60 * 0.5 = 30

Standard deviation (σ) = sqrt(n * p * (1 - p)) = sqrt(60 * 0.5 * 0.5) = sqrt(15) ≈ 3.873

Now, we can standardize the observed value of heads (x = 35) using the mean and standard deviation:

z = (x - μ) / σ = (35 - 30) / 3.873 ≈ 1.29

Using the z-table provided, we can find the p-value associated with z = 1.29. The closest value in the table is 0.903, corresponding to z = 1.3.

Since we're performing a one-tailed test (testing for bias towards heads), the p-value is the area under the curve to the right of the observed value. Therefore, the p-value is approximately 1 - 0.903 = 0.097.

Rounding the p-value to three decimal places, we find that the p-value for the test that the coin is biased for heads is 0.097.

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Answer:

the original price would be $800

Step-by-step explanation:

800-75% = 200

just use a calculator

Answer: 27

Step-by-step explanation: in order to find out the LCM, you have to list out the multiples of 9 ( 9: 9, 18, 27, 36, etc.) and 27 ( 27: 27, 54, etc). Then you find the least common multiple which in this case is 27.