if you add two obtuse angles do they sometimes make supplamentary angles?

Answer:

3rd option

Step-by-step explanation:

The sum to infinity of a geometric sequence is

S = \(\frac{a}{1-r}\)

where a is the first term and r the common ratio

The expression inside the summation is

6 \((\frac{1}{3}) ^{n-1}\)

which is in the form of the nth term of a geometric sequence

with a = 6 and r = \(\frac{1}{3}\) , then

S = \(\frac{6}{1-\frac{1}{3} }\) ← expression required

  = \(\frac{6}{\frac{2}{3} }\)

  = 9

Answer:

C I took the quiz

Step-by-step explanation:

Answer:

0 hours: 24 miles

1 hours: 17.6 miles

2 hours: 11.2 miles

3 hours: 4.8 miles

Step-by-step explanation:

The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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The definite integral in this problem has the value given as follows:

B. 42.

The definite integral in the context of this problem is given as follows:

\(\int_0^2 (x^7 + 5) dx\)

Applying the power of x integral rule, the result of the integral is given as follows:

\(\frac{x^8}{8} + 5x\)

At x = 2, the numeric value of the integral is given as follows:

\(\frac{2^8}{8} + 5(2) = 42\)

At x = 0, the numeric value of the integral is given as follows:

0.

(as both terms involve a multiplication by x and x = 0).

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

42 - 0 = 42.

Hence option B is the correct option in the context of this problem.

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Answer:

  1282 miles

Step-by-step explanation:

You have a rectangle with sides 365 and 276 miles, and you want to know the perimeter. (This is an approximation of the state of Wyoming.)

The perimeter of a rectangle is the sum of its side lengths. The formula is ...

  P = 2(L +W)

  P = 2(365 +276) = 2(641)

  P = 1282

The perimeter of Wyoming is about 1282 miles.

Answer:

D. y= 0.3x2

Step-by-step explanation:

In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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The surface area of the rectangle is 44 square centimeters.

Let's solve the problem step by step:

Given:

Width of the rectangle = w

Length of the rectangle = w + 7

To find the surface area of the rectangle, we need to calculate the product of the length and width.

Surface area = Length × Width

Surface area = (w + 7) × w

Additionally, it's mentioned that the surface area is equal to 7 times the sum of the width and 4 cm:

Surface area = 7 × (w + 4)

Now we can equate the two expressions for the surface area:

(w + 7) × w = 7 × (w + 4)

Expanding and simplifying the equation:

w² + 7w = 7w + 28

Bringing all terms to one side:

w² + 7w - 7w - 28 = 0

Simplifying further:

w² - 28 = 0

Now we can solve this quadratic equation for w using factoring, completing the square, or the quadratic formula.

Factoring the equation:

(w - 4)(w + 7) = 0

Setting each factor equal to zero:

w - 4 = 0 --> w = 4

w + 7 = 0 --> w = -7 (not a valid width)

Since width cannot be negative, the valid solution is w = 4.

Therefore, the width of the rectangle is 4 cm.

To calculate the surface area, we substitute the width back into the expression:

Surface area = (w + 7) × w = (4 + 7) × 4 = 11 × 4 = 44 cm²

Hence, The surface area of the rectangle is 44 square centimeters.

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Answer:   D

d. because they are not subtracted(C), the two fractions do not add up to 13(B), and the number is not equal to 2(A).

Answer:

5 packages of biscuits and 9 packages of bread.  

Step-by-step explanation:

18x5 = 90, and 9 x 10 = 90. If we use the least common denominator, then it would look like this:

18, 36, 54, 72, 90, 108, 126, 144, 162, 180

10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Out of the two multiplication lines, the one common part about it would be 90, which is 5 away from the start for 18, and 9 away from the start for 10.

hope it helped

Answer:

5 packs of biscuits

9 packs of bread

Step-by-step explanation:

To find out how many of each one, you have to find their least common multiple:

18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180

10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

18*5 = 90

5 packs of biscuits

10*9 = 90

9 packs of bread

Answer:

The length of the border is approximately 4 feet.

Step-by-step explanation:

Since the garden has a circular border we can apply the formula for the circle's length, which is shown below:

\(length = 2*\pi*radius\)

Where the radius is half the diameter. The diameter is the distance between two points in the circle going through the center, therefore for this garden the diameter is 1.2 feet and the radius is 0.6 feet. Applying this to the formula gives us:

\(length = 2*\pi*0.6\\length = 1.2*\pi\\length = 3.8\)

The length of the border is approximately 4 feet.

Answer:

x < 16 ft

Step-by-step explanation:

Perimeter = x

If it is less than 16, the equation is:

x < 16

-Chetan K

Answer:

C. 14%

Step-by-step explanation:

We know that Dallas's wage increased from $9 to $10.25.

Let's say the percent increase is x. Then we write the expression:

9 + x * 9 = 10.25

Divide by 9 from both sides:

1 + x = 10.25 / 9 ≈ 1.14

Subtract 1 from both sides:

x = 1.14 - 1 = 0.14

Since x is a percent, that means x = k/100, where k is an integer. So we have:

x = k/100 = 0.14

Multiply both sides by 100:

k = 0.14 * 100 = 14%

The answer is thus C.

~ an aesthetics lover

Answer:

Step-by-step explanation:

\(Original\:price = \$9\\New\:price =\$10.25\\\\Increase = 10.25-9\\Increase = 1.25\\\\Increase \: \% = \frac{Increase}{Original \:price} \:\times 100\\\\= \frac{1.25}{9} \times 100\\\\= \frac{125}{9}\\ \\= 13.888\\= 14\%\)

Answer:

y = 163°

Step-by-step explanation:

Vertically opposite angles are equal. So, y = 163°

Also, the points u give for the question is halved for the person who writes the answer. So, I will get 10 points, not 20. Anyways, Cheers!

Answer:

Step-by-step explanation:

There are but a few rules we have to follow when completing the square. However, they are very important rules so we have to be careful. First and foremost, the coefficient on the x-squared term HAS to be a positive 1. If it is not, we have to manipulate the function so it is a positive 1. Then we take half the linear term, square it and add it to both sides (and sometimes this can be very tricky. It is tricky here, so pay attention.)

We begin by separating the x terms from the constant by setting the parabola equal to 0 and moving the constant:

\(-x^2-2x=5\)

The coefficient on the x-squared is a negative 1, so we factor out the negative:

\(-(x^2+2x)=5\)

The linear term is 2. We take half of 2 which is 1, square 1 to get 1 and add it into the left side. BUT don't forget that we have a -1 out front of the ( ) refusing to be ignored. It is a multiplier. That means that we didn't add in a +1, we added in -1(1) which is -1. That is what we add to the right side:

\(-(x^2+2x+1)=5-1\) which simplifies to

\(-(x^2+2x+1)=4\)

The reason for this process is that by completing the square you create a perfect square binomial on the left. We rewrite the parabola in terms of that perfect square binomial:

\(-(x+1)^2=4\) which simplifies to

\(-(x+1)^2-4=y\)

From this you can now determine that the vertex of the parabola is (-1, -4)

A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled.

A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled. In the finite element method (FEM), the PDE is discretized into a set of algebraic equations, and the source term appears in each of these equations.

Specifically, for each algebraic equation resulting from the discretization of the PDE, the source term contributes to the coefficient of the dependent variable on the left-hand side of the equation, and it is taken to the right-hand side of the equation. The resulting coefficient and right-hand side term are then used to construct the corresponding row of the global coefficient matrix and the right-hand side vector, respectively.

Therefore, the source term affects all algebraic equations in the finite element method and is an essential component of the mathematical model. Changing the source term will affect the solution obtained from the ANSYS solver and can result in a different physical behavior of the system being modeled.

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9514 1404 393

Answer:

  $120

Step-by-step explanation:

Let c represent the original price of the calculator. Then the amount Justin spent was ...

  (6.20 +c)(1 -0.15) = 107.27

  6.20 +c = 107.27/0.85 . . . . . divide by the multiplier on the left

  c = 126.20 -6.20 . . . . . . . . . . subtract 6.20

  c = 120

The original price of the calculator was $120.

The no-arbitrage price today of a 5-year $1,000 US Treasury note with a 2% coupon rate and a 4.25% yield to maturity is approximately $908.44, closest to option B: $900.53.

To determine the no-arbitrage price of a 5-year $1,000 US Treasury note with a coupon rate of 2% and a yield to maturity (YTM) of 4.25%, we can use the present value of the future cash flows.First, let's calculate the annual coupon payment. The coupon rate is 2% of the face value, so the coupon payment is ($1,000 * 2%) = $20 per year.The yield to maturity of 4.25% is the discount rate we'll use to calculate the present value of the cash flows. Since the coupon payments occur annually, we need to discount them at this rate for five years.

Using the present value formula for an annuity, we can calculate the present value of the coupon payments:PV = C * (1 - (1 + r)^-n) / r,

where PV is the present value, C is the coupon payment, r is the discount rate, and n is the number of periods.

Plugging in the values:PV = $20 * (1 - (1 + 0.0425)^-5) / 0.0425 = $85.6427.

Next, we need to calculate the present value of the face value ($1,000) at the end of 5 years:PV = $1,000 / (1 + 0.0425)^5 = $822.7967.

Finally, we sum up the present values of the coupon payments and the face value:No-arbitrage price = $85.6427 + $822.7967 = $908.4394.

Rounding to the penny, the no-arbitrage price is $908.44, which is closest to option B: $900.53.

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Answer:

53.79%

Step-by-step explanation:

Answer:

8/11

Step-by-step explanation:

In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:

P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.

Calculating the electric flux through a surface is most straightforward if the electric field is constant and perpendicular to the surface. Hence the correct statement to fill in the blanks is "The electric field is constant and perpendicular to the surface."

The electric flux through a surface is a measure of the total electric field passing through that surface. It depends on the strength and orientation of the electric field lines relative to the surface.

When the electric field is constant and perpendicular to the surface, the calculation of electric flux becomes more straightforward. In this case, the electric field lines are parallel to the surface, and their strength remains constant across the surface.

With a constant and perpendicular electric field, the electric flux can be calculated using the formula:

Electric Flux = Electric Field Strength × Surface Area × Cos(θ),

where θ is the angle between the electric field and the surface normal. Since the electric field is perpendicular to the surface, the angle θ becomes 0 degrees, and the cosine of 0 degrees is 1.

Thus, when the electric field is constant and perpendicular to the surface, the calculation of electric flux simplifies to:

Electric Flux = Electric Field Strength × Surface Area.

This simplification makes the determination of electric flux more straightforward and easier to compute.

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Answer:

105 for all of them

Step-by-step explanation:

1) take 180-75, because of opposite angles.

105

2)again, 105 because we know the opposite angle is 75

3)105

again, opposite angles.

The solution is Option C.

The height of the wall to the top of the ladder is 15 feet

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Let the height of the wall be represented as h = AB

Now , Larry liens a 16 foot ladder against a wall

So , the hypotenuse of the triangle AC = 16 feet

And , the base is 5 feet away from the wall

So , the base of the triangle BC = 5 feet

The height of the wall h is given by the Pythagoras theorem ,

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

AC² = AB² + BC²

16² = AB² + 5²

On simplifying the equation , we get

Subtracting 5² on both sides of the equation , we get

AB² = 16² - 5²

AB² = 256 - 25

AB² = 231

Taking square root on both sides of the equation , we get

AB = 15.19

AB ≈ 15 feet

Therefore , the value of h is 15 feet

Hence , the height of the wall is 15 feet

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Answer:

-13

Step-by-step explanation:

f(x)=2x-7

f(-3)=2(-3)-7=-6-7=-13

The null hypothesis (H0) when testing for normality is:

H0 states that the values are sampled from a population that follows a normal distribution.

When testing for normality, the null hypothesis (H0) assumes that the data in the sample is derived from a population that follows a normal distribution. In other words, it assumes that the underlying population from which the sample is taken is normally distributed.

The purpose of testing for normality is to assess whether the data deviates significantly from a normal distribution. By assuming the null hypothesis, we aim to determine whether there is enough evidence to reject it and conclude that the data does not follow a normal distribution.

The other statements provided in the answer choices are not directly related to the null hypothesis when testing for normality. Statements such as "there is not statistically significant difference between two samples" or "if the data is normal, we can be certain that the data in different samples are similar" are not specific to testing for normality.

The null hypothesis (H0) when testing for normality states that the values are sampled from a population that follows a normal distribution. This hypothesis is tested using various statistical tests and techniques to assess the normality assumption of the data.

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The area bounded by the curve y = 8 − x³ and the x-axis is 15.5 square units.

The area bounded by the curve y = 8 − x³ and the x-axis is illustrated below. We need to determine the region's bounds and the integral to solve for the area.We need to determine the x-intercepts of the curve y = 8 − x³. Because the curve passes through the origin, it must have at least one x-intercept.

To find x, we set y = 0, 0 = 8 − x³, x³ = 8, x = 2.

The region is bounded by the curve y = 8 − x³, the x-axis, and the lines x = 0 and x = 2.

We have:∫₀² (8 - x³) dx

The area is calculated as follows:∫₀² (8 - x³) dx= [8x - (1/4) x⁴]₀²= (8(2) - (1/4)(2⁴)) - (8(0) - (1/4)(0⁴))= 15.5 square units

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a) z-scores for Mississauga-Erindale: Z = (143,361 - 102,639.28) / 21,855.384 ≈ 1.865 and for Parkdale-High Park: Z = (102,142 - 102,639.28) / 21,855.384 ≈ -0.023
b) The citizens might feel underrepresented in the House of Commons as their votes have less weight compared to those in smaller ridings.

a) To compare the z-scores for these ridings, we need to use the formula:

z-score = (x - μ) / σ

where x is the population of the riding, μ is the mean population of all ridings, and σ is the standard deviation of all ridings.

For Mississauga-Erindale:

z-score = (143,361 - 102,639.28) / 21,855.384 = 1.87

For Parkdale-High Park:

z-score = (102,142 - 102,639.28) / 21,855.384 = -0.02

Therefore, Mississauga-Erindale has a z-score of 1.87, which means its population is above the mean population of all ridings by 1.87 standard deviations. Parkdale-High Park has a z-score of -0.02, which means its population is almost exactly at the mean population of all ridings.

b) The citizens of Mississauga-Erindale could argue that their riding is overrepresented in the House of Commons. This is because their population is above the mean population of all ridings by almost 2 standard deviations, which means they have more political influence per person compared to other ridings. However, it's important to note that the electoral district boundaries are redrawn every 10 years based on population changes, so the population of each riding may change over time.
a) To compare the z-scores for Mississauga-Erindale and Parkdale-High Park, we need to calculate the z-scores for each riding using the given mean and standard deviation. The formula for calculating z-scores is:

Z = (X - μ) / σ

For Mississauga-Erindale:
Z = (143,361 - 102,639.28) / 21,855.384 ≈ 1.865

For Parkdale-High Park:
Z = (102,142 - 102,639.28) / 21,855.384 ≈ -0.023

b) The citizens of Mississauga-Erindale could argue that their representation in the House of Commons is unfair because their riding has a significantly larger population compared to the average riding size. The z-score of 1.865 indicates that the population of Mississauga-Erindale is approximately 1.865 standard deviations above the mean, meaning it is larger than a majority of other ridings. Consequently, the citizens might feel underrepresented in the House of Commons as their votes have less weight compared to those in smaller ridings.

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