Write a proof that shows that the distance of point c from endpoint a is the same as the distance of point c from endpoint b, or in other words prove that ca=cb.

The formula for the n-th term is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

For a geometric sequence where the first term is a₁ and the common ratio is r, the formula for the n-th term is:

aₙ = a₁*(r)⁽ⁿ⁻¹⁾

Here we know that the first term is a₁ = 3 and the common ratio is r = 1/2.

Then the formula for the n-th term of the sequence is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

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Answer:

60%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

9/15=.6

.6 as a percent is 60%

Answer:

620

Explanation:

When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Calculation of the number of elk:

Since the population is 7,750.

The random sample is 50.

So here be like

= 620

hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

Yes

Step-by-step explanation:

The area of a square is equal to the length squared.

So, the length of one side of the original floor is √400 which equals 20.

If you increase the length by 1, the area of the dance floor is 21 squared.

21 * 21 is certainly a rational number.

Answer:

Step-by-step explanation:

I think so, yes.

The area of a square is A = s*s where s is the length of the side

s^2 = 400

sqrt(s^2) = sqrt(400)

s = 20

If you increase each dimension by one foot you get 21 * 21 for the area of the new ballroom.

The result is rational. That's because the square root was rational when you found 20.

Area = 21 * 21 = 441 which is rational.

Answer:

21 is the correct answer because

Answer:

They found the slope of the same line. This is because 2/6 is equal to 1/3.

The value of x which is the length of the base of the triangle in the question is; 29 meters

A triangle is a three sided polygon, with three interior angles.

Please find attached the possible diagram in the figure, (created with MS Word), which is a question from a mathematics textbook posted on the internet

The diagram indicates that the altitude or height of the triangle = 8 meters

The specified area of the triangle is; A = 261 square meters

The base length of the triangle = x

The formula for the area of a triangle, A, is; A = (1/2) ×Base length × Height

Therefore;

A = 261 m² = (1/2) × x × 18 m

x = 261 m² ÷ ((1/2) × 18 m) = 29 m

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-2 1/5

at least I think so lol

The number of simple events in this experiment is 16.

The correct answer to the given question is option c.

The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.

The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.

Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

Therefore, the number of simple events in this experiment is 16, which is option (c).

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Answer:

10 Quarters and 5 dimes

Step-by-step explanation:

10 Quarters = $2.50

5 dime = $0.50

Answer:

20 dimes and 4 quarters

Step-by-step explanation:

So, a dime is 10 cents and a quarter is 25

So, let's say you have x dimes and y quarters

X+Y=24 (total amount of coins)

Also,

10x+25y= 300 (cents)

I just put the 3 dollars into cents

Now, you have a system of equations and we should solve it:

X+y=24 ----x=24-y

10x+25y=300

So substitute x in the 2nd equation

10(24-y)+25y=300

240-10y+25y=300

240+15y=300

15y=60

y=4

Now that you know the amount of quarters, you can just say that you will have 20 dimes since 24-4=20

So, 4 quarters and 20 dimes

Check:

20 dimes=2 dollars

4 quarters= 1 dollar

correct

Answer:

x equals 10

Step-by-step explanation:

trrrdvhdhdudjrnrfbfhfsdnrbrhf HRT b4

Flipping the bulbs is an illustration of sequence and patterns

19 bulbs would remain on.

The sequence of turning the bulbs off and on, would change the state of the bulbs until the 380th process.

While changing the state of the bulbs, the bulb at the perfect square positions would remain on.

There are 19 perfect square numbers between 1 and 380 (inclusive)

Hence, 19 bulbs would remain on.

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The required algebraic representation for a rotation 180° clockwise is -x, -y. Option D is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

here,
When rotation 180° clockwise takes place then the sign of the coordinate is reversed as if it is positive then it becomes negative and vice versa.

So the algebraic representation for a rotation 180° clockwise of (x, y) is (-x, -y).

Thus, the required algebraic representation for a rotation 180° clockwise is -x, -y. Option D is correct.

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Answer:Linear Algebra Examples ... Linear Algebra. Solve by Substitution y=x+3 , y=2x-1 ... Eliminate the equal sides of each equation and combine. ... Subtract 1 1 from 8 8 . ... The solution to the system of equations can be represented as a point.

Step-by-step explanation:

Answer: what grade u in?

Step-by-step explanation:

Answer:

165 students or the sophomore class of 220 are not athletic.

Step-by-step explanation:

60/240 = .25 This means that 25% of the class is athletic.  That would mean and .75 or 75% are not athletic.

220 x .75 = 165

To determine the value of β, we need to analyze the rolling motion of the cylindrical object and apply the principles of conservation of energy and rotational motion.

Conservation of energy:

Initially, the object has gravitational potential energy due to its height, which is converted into kinetic energy as it rolls down the ramp and onto the floor. The equation for conservation of energy is:

M * g * H = (1/2) * M * v^2 + (1/2) * I * ω^2

where:

M is the mass of the object

g is the acceleration due to gravity

H is the initial height

v is the linear velocity of the object

I is the rotational inertia of the object

ω is the angular velocity of the object

Rolling motion:

For a rolling object, the linear velocity and angular velocity are related by:

v = R * ω

where R is the radius of the object.

Expression for rotational inertia:

The rotational inertia (I) of the object is given by:

I = β * M * R^2

where β is a constant that depends on the object's mass distribution.

Now, let's proceed with the calculations:

From the given information, we have:

H = 0.95 m

h = 0.12 m

d = 0.475 m

Using conservation of energy, we can equate the initial potential energy to the final kinetic energy:

M * g * H = (1/2) * M * v^2 + (1/2) * I * ω^2

Substituting the expressions for v and I from the rolling motion and rotational inertia equations:

M * g * H = (1/2) * M * (R * ω)^2 + (1/2) * (β * M * R^2) * ω^2

Simplifying the equation:

g * H = (1/2) * R^2 * ω^2 * (1 + β)

Rearranging the equation to isolate β:

β = (2 * g * H) / (R^2 * ω^2) - 1

Now, we need to determine the values of g, H, R, and ω in order to calculate β.

Please provide the values for the acceleration due to gravity (g), the initial height (H), the radius of the object (R), and the angular velocity (ω), so we can continue with the calculation.

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Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

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H₀: The mean number of sunny days per year in Sunnytown is 300. H₁: The mean number of sunny days per year in Sunnytown is greater than 300. Type I error: Rejecting H₀ when it is true. Type II error: Failing to reject H₀ when it is false. Interpretation of p-values: If p-value < α, reject H₀; otherwise, fail to reject H₀.

Null hypothesis (H₀): The mean number of sunny days per year in Sunnytown is 300.

Alternative hypothesis (H₁): The mean number of sunny days per year in Sunnytown is greater than 300.

Type I error: Rejecting the null hypothesis when it is true, i.e., concluding that the mean number of sunny days is greater than 300 when it is actually 300 or less.

Type II error: Failing to reject the null hypothesis when it is false, i.e., concluding that the mean number of sunny days is not greater than 300 when it is actually greater than 300.

Interpreting p-values:

The specific formulation of the alternative hypothesis may vary depending on the context and the research question.

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Answer:

12,713 lbs

Step-by-step explanation:

1 ton = 2,000 lbs

So,

6(2,000) + 713 = 12,713 lbs

Answer:

24

Step-by-step explanation:

use a calculator for these type of problems next time!

the answer to this equation would be 24x

it's answer is square metre because SI unit of area is square and in most of the case area of garden is given as metre

Answer:

C. 3

y = 3x - 4

Step-by-step explanation:

y = 3x - 2

Slope stays 3 because they are parallel.

y - 5 = 3(x - 3)

y - 5 = 3x - 9

y - 5 + 5 = 3x - 9 + 5

y = 3x - 4

Step-by-step explanation:

y= 3x-4

hopefully that is helpful

Answer: £1342.5

Step-by-step explanation:

y = a(1 + R)^n

y = 1290(1 + 0.005)^8

y ≈ 1342.51

∴ £1342.5

Answer:

Step-by-step explanation:

I'm assuming this is linear and that there is no special on a larger order of wings. To find the unit price of each piece, divide $28.80 by 16 to get that each piece cost $1.80 (that's a lot for a single chicken wing. That better be one BIG chicken...). To find the cost of 9 wings, multiply 9 by $1.80 to get $16.20

The rule of three is a way to solve problems of proportionality between three known values and one unknown. It establishes a relationship of linearity, proportionality, between the values involved.

Chicken Wings             Price

     16------------------------$28.80

      9-----------------------------x

First, multiply the number of wings purchased by the given price, divided by the number of wings purchased.

We solve

Answer: 9 wings would cost a total of $16.2

Answer: 48

Step-by-step explanation:

We need to find the least common multiple of 12 and 16.

Finding the prime factorizations of 12 and 16,

\(12=2^{2} \times 3\\\\16=2^{4}\)

Thus, the least common multiple is \(2^{4} \times 3=\boxed{48}\)

Answer:

The reporter surveyed 60 girls.

Step-by-step explanation:

From the information given, you can use a rule of three to find the amount of girls that the reporter surveyed which is 100% given that 39 girls represent 65%:

65%  →  39

100% →    x

x=(100*39)/65

x=60

According to this, the answer is that the reporter surveyed 60 girls.

a. €410 is equivalent to approximately £295.20.

b. The £ to € exchange rate is approximately €1 = £1.39.

a. To convert €410 to £, we can use the exchange rate of €1 = £0.72.

€410 * (£1/€1) = £410 * (€1/£1) * (£0.72/€1) = £410 * £0.72 = £295.20

Therefore, €410 is equivalent to £295.20.

b. To determine the £ to € exchange rate, we can take the reciprocal of the given € to £ exchange rate.

£1/€1 = (1/€1)/(1/£1) = £1/€1 = £1/(€1/£1) = £1/£0.72 ≈ €1.39

Therefore, the £ to € exchange rate is approximately €1 = £1.39.

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