Work out the sum of the interior angles of a pentagon.​

Answer:

m∠1 = 43°

m∠2 = 17°

m∠3 = 120°

m∠4 = 60°

m∠5 = 60°

m∠6 = 60°

m∠7 = 17°

m∠8 = 120°

m∠9 = 43°

Step-by-step explanation:

If ΔABC is an isosceles triangle, m∠1 = m∠9 since the base angles of an isosceles triangle are equal.

\(\implies m \angle 1 = m \angle 9\)

\(\implies (4x+3)^{\circ}=(9x-47)^{\circ}\)

\(\implies 4x+3=9x-47\)

\(\implies 50=5x\)

\(\implies x=10\)

Substitute the found values of x into the expressions for ∠1 and ∠9:

\(\implies m \angle 1 = 4(10)+3=43^{\circ}\)

\(\implies m \angle 9 = 9(10)-47=43^{\circ}\)

If ΔDBE is an equilateral triangle, all three interior angles are congruent.

\(\implies m \angle 4 = m \angle 5 = m \angle 6\)

Interior angles of a triangle sum to 180°.

\(\implies m \angle 4 = m \angle 5 = m \angle 6 = \dfrac{180^{\circ}}{3}=60^{\circ}\)

Angles on a straight line sum to 180°.

\(\implies m \angle 3 + m \angle 4 = 180^{\circ}\)

\(\implies m \angle 3 + 60^{\circ} = 180^{\circ}\)

\(\implies m \angle 3 = 120^{\circ}\)

Similarly:

\(\implies m \angle6 + m \angle 8 = 180^{\circ}\)

\(\implies 60^{\circ}+m \angle 8= 180^{\circ}\)

\(\implies m \angle 8 = 120^{\circ}\)

Interior angles of a triangle sum to 180°.

\(\implies m \angle 1+ m \angle 2+ m \angle 3 = 180^{\circ}\)

\(\implies 43^{\circ}+ m \angle 2+ 120^{\circ} = 180^{\circ}\)

\(\implies m \angle 2 = 17^{\circ}\)

Similarly:

\(\implies m \angle 7+ m \angle 8+ m \angle 9 = 180^{\circ}\)

\(\implies m \angle 7 + 120^{\circ}+ 43^{\circ} = 180^{\circ}\)

\(\implies m \angle7 = 17^{\circ}\)

Based on the ratio of the number of boys to the number of girls in choir, 5:4, the number of boys is 35.

The ratio refers to the relative size of a value, variable, or number to another.

Ratios are the quotients of a number or value and another value, which is the denominator.

As fractional values, ratios can be expressed in fractions, decimals, or percentages.

The ratio of boys to girls = 5:4

The sum of ratios = 9 (5 + 4)

The total number of students in the choir = 63

The number of boys = 35 (63 x 5/9)

The number of girls = 28 (63 x 4/9)

Thus, we can conclude that there are 35 boys and 28 girls in the choir.

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Question:

Mr. & Mrs. Martin drove 200 miles in September. They drove 2 times as many miles in November as they did in September. They drove 2 times as many miles in October as they did in November. How many miles did Mr. & Mrs. Martin drive in October?

Answer:

200 miles x 2 = 400 miles in September  400 x 2 = 800 in october

Answer:

2

Step-by-step explanation:

4/2=2

ANSWER

6a

EXPLANATION

The order of operations is always the same:

0. Parenthesis

1. Exponents (include powers and roots)

2. Multiplications and divisions

3. Additions and subtractions

Let's take a look at the given expression. We have two terms - which are separated by a minus sign. In the first term there's a parenthesis so we have to solve what's inside first. Note that what's inside the parenthesis is just a number, no operation to be done. Therefore for the first step we have:

Now, again in the first term there's an exponent in the denominator. We have no exponents in the second term. Solving 2³ = 8:

The third operations to solve are multiplications and divisions. We have many of those, but since we have a variable a, it is convenient if we solve the division first in the first term:

And the division of the second term:

Therefore after solving the third operations we have:

Now we do the subtraction. As mentioned before, there's a variable involved so to solve the subtraction we have to combine like terms. In this case, both terms contain the variable so we take it as common factor:

And solve the operation inside the parenthesis:

Hence, the expression simplifies to 6a

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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Answer:

$15.69

Step-by-step explanation:

multiply the retail price by 1.06 to get the price after taxes.

find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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Answer:

y = -1/2x + 1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,1) (4, -1)

We see the y decrease by 2 and the x increase by 4, so the slope is

m = -2/4 = -1/2

Y-intercept is located at (0,1)

So, our equation is y = -1/2x + 1

Answer:

251.2

Step-by-step explanation:

The formula for the volume of a cylinder is \(\pi r^2h\). Plugging in your measurements...

Height = 20 inches.

Radius = 2 inches.

The volume is \(\pi2^2h\).

Simplification...

\(\pi2^220 = \pi4(20)= 4\pi 20\).

\(\pi\) ≈ \(3.14\)

3.14 * 4 = 12.56

12.56*20 = 251.2

Answer:

Therefore A is the answer.

Step-by-step explanation:

As the triangle is proportional. One of them is enlarged of the other.

So lets find the equal sides:

here x is QP so it is similar to JK, if the other sides are equal:

and

Here in A,

if cross multiplied,

x = (8*5)/10

x = 4

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

Answer:

8

Step-by-step explanation:

Answer:

133,860

Step-by-step explanation:

The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".

* No we have our key elements:

- Starting amount = 145,500

- Rate of change = 8%

* We will get the "8%" of the number 145,500

- Firstly, "8%" means 8/100

- So, 0.08 will be our new rate of change.

* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.

- 145,500 × 0.08 = 133,860 ; the same as

145,500 × 8/100 = 133,860

Answer:

1. nonlinear

2. linear

Step-by-step explanation:

Answer:

  k = 110

Step-by-step explanation:

You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.

The area of a circle is given by the formula ...

  A = πr²

Then the area of the outer circle is ...

  A = π(14 cm)² = 196π cm²

The area of the inner circle is ...

  A = π(8 cm)² = 64π cm²

The area of the whole donut is the difference of these areas:

  whole donut area = (196 -64)π cm² = 132π cm²

The shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...

  shaded area = (300°/360°)×whole donut area

  shaded area = 5/6 × 132π cm² = 110π cm²

Comparing this to the expression kπ cm², we see that ...

  k = 110

Answer:

An airplane cruises 1 kilometer in 1/12 of a minute. What is its cruising speed?200

Answer:

damm just had the same question holl up

Step-by-step explanation:

Answer:

The probability of them being in the right order would be a fraction of 1/7

A graph of the image of the figure after a reflection across the x-axis is shown below.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

By applying a reflection over or across the x-axis to triangle GLQ, we have;

(x, y)                →      (x, -y)

G (3, 4)             →      (3, -(4)) = G' (3, -4)

L (1, 2)                →     (1, -(2)) = L' (1, -2).

Q (4, -1)              →      (4, -(-1)) = Q' (4, 1)

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The graph of the relation can be seen in the image at the end, there we can see that the relation is a function.

A function is a relation where each input is mapped into a single output, where the notation is (input, output).

The inputs go on the horizontal axis and the outputs on the vertical axis.

Here we have the following relation:

(-5,-1), (-4,1), (-3,3), (-1,5), (1,7)

The graph of these points can be seen on the image below. There you can see that there are no two points on the same vertical line, that means that the relation is a function.

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The mass, in grams, of substance Y is given the mass of substance x is 1.22 x 10^-6

Standard form is used to condense big numbers into smaller numbers. In order to write a number in standard form, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

In order to determine the mass, multiply 6.10 by 2 and add 2 to -7

6.10 x 2 = 12.2 = 1.22 x 10^-6

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Answer:2

Step-by-step explanation:

In the middle equation on the left side, if you let x = 3/2, then the term containing A vanishes and you can solve for B :

12*(3/2) - 25 = A (2*(3/2) - 3) + B

18 - 25 = A * (3 - 3) + B

B = -7

which makes the last option the correct answer.

Answer:

D

Step-by-step explanation:

edge 2021

The mean, mean deviation mode, median standard deviation, and coefficients of variation, CV, are as follows;

1. The mean deviation about the mean, median mode are;

2.653, 3.709, and 3.709, respectively

The coefficients of variation are;

0.364, 0.337, 0.337, respectively

The variance is about 9.462

The standard deviation is about 3.076

2. Section A has a higher relative dispersion than section B

3. City 2

4. a. Mean ≈ 43.85

b. Mode 40 - 54 inches

c. Median ≈ 45.16

The variance ≈ 125.8056

Standard deviation ≈ 11.216

Coefficient of variation ≈ 0.268

The coefficient of variation of a data quantifies or is a measure of the variability of the values in the set of data.

The mean for the data can be calculated as follows;

Mean  = (3×10 + 6×15 + 11×25 + 2×6 + 4×4 + 10×3 + 5×2 + 7×8 + 8×9 + 9×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 7.29

The median is the 86/2 value = 43rd value

10 + 15 + 25 = 50

Therefore, the median is in the class with a frequency of 25, which is 11

The mode of the data, which is the value with the highest frequency in the data set is 11

The mean deviation from the mean is therefore;

(|3 - 7.29|×10 + |6 - 7.29|×15 + |11 - 7.29| ×25 + |2 - 7.29| ×6 + |4 - 7.29| ×4 + |10 - 7.29| ×3 + |5 - 7.29| ×2 + |7 - 7.29|×8 + |8 - 7.29| ×9 + |9 - 7.29| ×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 2.653

The coefficient for the mean deviation about the mean is therefore; 2.653/7.29 ≈ 0.364

The mean deviation about the median is therefore;

(|3 - 11|×10 + |6 - 11|×15 + |11 - 11| ×25 + |2 - 11| ×6 + |4 - 11| ×4 + |10 - 11| ×3 + |5 - 11| ×2 + |7 - 11|×8 + |8 - 11| ×9 + |9 - 11| ×4)/(10+15+25+6+4+3+2+8+9+4)

The mean deviation about the median = 319/86 ≈ 3.709

The coefficient ≈ 3.709/11 ≈ 0.337

The median = The mean deviation about the mode ≈ 3.709

The coefficient is about 0.337

The variance = (10×(3 - 7.29)² + 15×(6 - 7.29)² + 25×(11 - 7.29)² + 6×(2 - 7.29)² + 4×(4 - 7.29)² + 3×(10 - 7.29)² + 2×(5 - 7.29)² + 8×(7 - 7.29)² + 9×(8 - 7.29)² + 4×(9 - 7.29)²)/(10+15+25+6+4+3+2+8+9+4) ≈ 9.462

The standard deviation, s ≈ √(9.462) ≈ 3.076

2. The coefficient of variation, CV, can be used to compare the variability of the datasets comprising of different scales as follows;

CV = Standard deviation/( The mean of the data)

Therefore; CV for section A = 23/79 ≈ 0.2911

CV for section B = 11/64 ≈ 0.172

The higher CV value for section A indicates that the scores of section A have a higher relative dispersion than the scores for the section B

3. The consistency values can be obtained by finding the standard deviation for the values in the data for each city, using a web based tool as follows;

City 1; Mean = 23

Variance = 50/4

Standard deviation, City 1 = (√(50))/2 = 5·√2/2

City 2; Mean = 21.8

Sample variance = 2.2

Standard deviation, City 2 = √(2.2) ≈ 1.483

City 3; Mean = 29.2

Sample variance = 18.7

Standard deviation, City 3 = √(18.7) ≈ 4.324

The standard deviation of city 2, which is the smallest compared tom the other cities, indicates that the City 2, has the most consistent temperature

4. The mean of the data obtained from the data using the midpoint of the data, is; Mean = ∑fx/∑f

Therefore; The mean obtained using an online tool is; 43.85

The mode is the data that occurs most frequently, which is the data with the value; 40 - 54 inches

The median is the value at the middle of the data set, which is the value with a frequency of 53, and in the interval 40 - 54 inches

The median is; 39.5 + (54.5 - 39.5) × (50 - 30)/53 ≈ 45.16

The standard deviation found for the grouped data, using an online tool is as follows;

Variance, σ² ≈125.8056

The standard deviation, σ ≈ √(125.8056) ≈ 11.216

The coefficient of variation is; 11.216/41.83 ≈ 0.268

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The probability that a red card is drawn at least once by the third draw is 0.88.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let, a card is drawn from a standard deck of 52 cards and then placed back into the deck.

In a standard 52 card deck the red cards are 26.

So,

P(red) =  n(red cards) / n(total cards)

          = 26 / 52

P(red) = 0.50

Now, X ≈ Bin (n = 3, P = 0.50)

P(X = x) = (n  x) p^x (1 - p)^n-x

(n  x) = \(\frac{n!}{x!(n-x)!}\)

P(X ≥ 1) = 1 - P(X < 1)

            = 1 - P(X = 0)

            = 1- (3  0)(0.5)^0(0.5)^3

            = 1 - 0.125

             = 0.875

P(X ≥ 1)  = 0.88

Hence, the probability that a red card is drawn at least once by the third draw is 0.88.

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Answer:

a) P = 0.274925

b) required confidence interval = (0.2705589, 0.2793344)

c) FALSE

d) FALSE

e) TRUE

f) There is still probability that he would win. And it would be highly unusual if he wins assuming that the true population proportion is 0.274925.

Step-by-step explanation:

a)

PROBABILITY

since total number of simulations is 40,000 and and number of times Donald Trump wins an Electoral College majority in the 2020 US Presidential Election is  10,997

so the required Probability will be 10,997 divided by 40,000

P = 10997 / 40000 = 0.274925

b)

To get 95% confidence interval for the parameter in question a

(using R)

>prop.test(10997,40000)

OUTPUT

1 - Sample proportion test with continuity correction

data: 10997 out of 40000, null probability 0.5

x-squared = 8104.5, df = 1, p-value < 2.23-16

alternative hypothesis : true p ≠ 0.5

0.2705589  0.2793344

sample estimate

p

0.274925

∴ required confidence interval = (0.2705589, 0.2793344)

c)

FALSE

This is a wrong interpretation of a confidence interval. It indicates that there is 95% chance that the confidence interval you calculated contains the true proportion. This is because when you perform several times, 95% of those intervals would contain the true proportion but as the confidence intervals will vary so you can't say that the true proportion is in any interval with 95% probability.

d)

FALSE

Once again, this is a wrong interpretation of a confidence interval. The confidence interval tells us about the population parameter and not the sample statistic.

e)

TRUE

This is a correct interpretation of a confidence interval. It indicates that if we perform sampling with same sample size (40000) several times and calculate the 95% confidence interval of population proportion for each of them, then 95% of these confidence interval should contain the population parameter.

f)

The simulation results obtained doesn't always comply with the true population. Also, result of one simulation can't be taken for granted. We need several simulations to come to a conclusion. So, we can never ever guarantee based on a simulation result to say that Donald Trump 'Won't' or 'Shouldn't' win.

There is still probability that he would win. And it would be highly unusual if he wins assuming that the true population proportion is 0.274925.

Answer:

24

6

3

4.50

Step-by-step explanation:

3 x 8

1.5 x 4

.5 x 6

1.5 x3