8 coins are tossed simultaneously, find the chance of obtaining at least six heads​

Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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Amount to be repaid for Bank A is $2,696.625 and Amount to be repaid for Bank B is $2,741.25. However, I will choose Bank B because it offers a lower interest rate.

The formula to calculate the simple interest is;

I = PRT

Where;

P is principal

R is rate

T is time

Now, we are given that;

Bank A;

Principal amount; P = $2550

Interest rate; R = 11.5% = 0.115

Time; t = 6 months = 0.5 years

Thus;

I = (2550 * 0.115 * 0.5)

I = $146.625

Amount to be repaid = 2550 + 146.625

Amount to be repaid = $2,696.625

Bank B;

Principal amount; P = $2550

Interest rate; R = 7.5% = 0.075

Time; t = 12 months = 1 year

Thus;

I = (2550 * 0.075 * 1)

I = $191.25

Amount to be repaid = 2550 + 191.25 = $2,741.25

Thus, bank B offers a more favorable interest rate and as such would be the preferred bank.

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Answer:

25%

Step-by-step explanation:

Answer = difference/Originalx100

Answer=15/60=0.25x100=25%

The size of angle y in the quadrilateral is 130 degrees.

A quadrilateral is a polygon with 4 sides and angles. The quadrilateral above is a kite. The sum of angles in a quadrilateral is 360 degrees.

Therefore, let's find the angles in the quadrilaterals as follows:

y + y + 70 + 30 = 360(sum of angles in a quadrilateral)

2y + 100 = 360

2y = 360 - 100

2y = 260

divide both sides by 2

y = 260 / 2

y = 130 degrees

Therefore, the size of y is 130 degrees.

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Answer:

Step-by-step explanation:

Function f(x)=|x| is transformed to create function g(x)=|x+4|+3. What transformations are performed to function f to get function g? Select each correct answer.

Function f is translated 4 units to the right.

Function f is translated 3 units to the left.

Function f is translated 4 units down.

(this one is correct) Function f is translated 3 units up.

Function f is translated 4 units up.

(this one is correct) Function f is translated 4 units to the left.

Function f is translated 3 units to the right.

Function f is translated 3 units down.

The diameter of the hemisphere is 39.1918 feet.

The surface area of a hemisphere is given by the formula:

Surface Area = 2πr²

We have,

surface area of the hemisphere is 768π square feet,

So, 2πr² = 768π

Dividing both sides of the equation by 2π, we get:

r² = 384

To find the diameter, we need to double the radius.

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

r = √384

r ≈ 19.5959

Now, Diameter ≈ 2 x 19.5959 ≈ 39.1918

Therefore, the diameter of the hemisphere is 39.1918 feet.

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Answer:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

Answer:12

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The  97% confidence interval is  \(1528  <  \mu <  1612 \)

b

Option A and  Option D  are correct

Step-by-step explanation:

From the question we are told that

     The sample size is n =  119

     The  sample  mean is \(\$ 1570\)

    The  population standard deviation is  \(\sigma  =  \$ 211\)

    Generally given that the confidence level is  97% then the level of significance is mathematically represented as

      \(\alpha = (100 - 97 )\%\)

=>    \(\alpha = 0.03\)

From the normal  distribution table  the critical value  of  \(\frac{\alpha }{2}\) is  

     \(Z_{\frac{\alpha }{2} } =  2.17\)

Generally the margin of error is mathematically represented as

     \(E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }\)

    \(E =  2.17*  \frac{211}{\sqrt{ 119 } }\)

=>   \(E =   41.98 \)

Generally the 97% confidence interval is mathematically represented as

     \(\= x  - E  <  \mu <  \= x  + E\)

=>    \(1570  - 41.98  <  \mu <  1570  + 41.98 \)

=>    \(1528  <  \mu <  1612 \)

Generally looking at confidence interval we see that the width is dependent on the size of the margin of error.

Generally the margin error is directly proportional to the  critical value of  \(\frac{\alpha }{2}\) which increases when the confidence level increases and vise versa

Also the margin error is inversely proportional to the square root of  sample size

Hence to reduce the width of the confidence interval we need to lower the confidence level  and increase the sample size

The given expression is:

It is required to find the value of the expression when y=8.

To do this, substitute y=8 into the expression and evaluate:

The answer is 13.

Answer:

rational numbers and irrational numbers

Step-by-step explanation:

A graph of this quadratic equation x² + x - 6 = 0 is shown below.

The solutions to the equation x² + x - 6 = 0 are (-3, 0) and (2, 0).

In Mathematics, the graph of a quadratic function always form a parabolic curve or arc because it is u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive one (1) and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function x² + x - 6 = 0 is positive one (1), we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts (-3, 0) and (2, 0). Also, the value of the quadratic function f(x) would be minimum at -6.25.

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When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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The measure of the angle formed by the plane's path and the road from city J to city K is approximately 57.2 degrees.

To find the measure of the angle formed by the plane's path and the road from city J to city K, we can use the trigonometric concept of tangent.

In right triangle JKL, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, we are interested in finding the angle formed by the plane's path and the road from city J to city K. Let's denote this angle as θ.

The tangent of angle θ can be calculated as:

tan(θ) = Opposite / Adjacent

Using the given information, the opposite side is KL with a length of 15.1 miles, and the adjacent side is LJ with a length of 9.4 miles.

tan(θ) = 15.1 / 9.4

Using a calculator or approximation, we find:

tan(θ) ≈ 1.60638

To find the measure of angle θ, we can take the inverse tangent (arctan) of the calculated value:

θ ≈ arctan(1.60638)

Using a calculator or inverse tangent table, we find:

θ ≈ 57.2°

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The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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The quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.

What is a quadratic equation?

Any algebraic equation that can be expressed in standard form as where x represents an unknown value and where a, b, and c represent known values, where a 0 is a quadratic equation.

We know that the standard form of a quadratic equation is represented as: a\(x^{2}\) + bx + c = 0.

Here, we are given a = 4, b = -8 and c = -60.

On substituting these values, we get

⇒ a\(x^{2}\) + bx + c = 0

⇒ 4\(x^{2}\) - 8x - 60 = 0

On dividing both sides by 4, we get

⇒ \(x^{2}\) - 2x - 15 = 0

Hence, the quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.

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Answer:

The 99​% confidence interval estimate of the percentage of girls born is (74.37%, 85.63%).

Usually, 50% of the babies are girls. This confidence interval gives values considerably higher than that, so the method to increase the probability of conceiving a girl appears to be very effective.

Step-by-step explanation:

Confidence Interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

For this problem, we have that:

\(n = 335, \pi = \frac{268}{335} = 0.8\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a pvalue of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{335}} = 0.7437\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{335}} = 0.8563\)

For the percentage:

Multiplying the proportions by 100.

The 99​% confidence interval estimate of the percentage of girls born is (74.37%, 85.63%).

Usually, 50% of the babies are girls. This confidence interval gives values considerably higher than that, so the method to increase the probability of conceiving a girl appears to be very effective.

Answer:

Option D: [-5,9]

Step-by-step explanation:

We know that the range of a function calls for the interval of numbers of the y coordinate. By looking at the graph you can see that the lowest point is -5 and the highest point is 9. Because these two points have closed circles the answer will use brackets and not parentheses. Therefore [-5,9].

un cuadrilátero es un polígono con cuatro aristas y cuatro vértices

Los elementos o características de un cuadrilátero son los siguientes:

4 vértices: puntos de intersección de los lados que conforman el cuadrilátero.

4 lados: segmentos que unen los vértices contiguos.

2 diagonales: segmentos cuyos extremos son dos vértices no contiguos.

4 ángulos interiores: el determinado por dos lados contiguos.

4 ángulos exteriores: el determinado por la prolongación de uno de los lados sobre un vértice y el contiguo en el mismo vértice.

Un incentro, centro de la circunferencia inscrita.

La suma de sus ángulos interiores es igual a 360º

Los cuadriláteros se clasifican según el paralelismo de sus lados, sus longitudes y sus ángulos interiores:

Paralelogramo: sus lados opuestos son paralelos.

Cuadrado: todos sus lados son iguales, todos sus ángulos interiores son rectos, sus diagonales son iguales y perpendiculares entre sí, tiene una circunferencia inscritas y otra circunscrita, además todos los cuadrados son semejantes entre sí .

Rombo: todos sus lados son iguales, cada par de ángulos agudos y obtusos son opuestos, sus diagonales son distintas y perpendiculares entre sí, son bisectrices, tiene una circunferencia inscrita.

Rectángulo: sus lados opuestos son iguales dos a dos y los paralelos, todos sus ángulos interiores son rectos, sus dos diagonales son iguales pero no son perpendiculares entre sí y tiene una circunferencia circunscrita.

Romboide: sus lados opuestos son iguales dos a dos, cada par de ángulos agudos y obtusos son opuestos, sus dos diagonales son de distinta longitud y no son perpendiculares entre sí.

Trapecio: En geometría, se llama trapecio a un cuadrilátero que tiene dos lados no consecutivos paralelos llamados bases del trapecio, y el segmento perpendicular entre las dos bases y su propia longitud son llamadas altura del trapecio

Trapezoide: En geometría euclídea plana, un trapezoide es un cuadrilátero convexo sin lados paralelos.

Ejemplos de cuadriláteros:

The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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The doctor had the opinion about the boy that it world

hare been better is he had velict

The trigonometric measures in the given right triangle are as follows:

a) tan(30º) = x/20.

b) x = 11.54.

c) tan(60º) = 20/x.

The relations in a right triangle are presented as follows:

For item a, the tangent of the angle of 30º is calculated as follows:

tan(30º) = opposite leg/adjacent leg = x/20.

The actual value of the tangent of 30º is of 0.577, hence the solution for x is calculated as follows:

tan(30º) = x/20

0.577 = x/20

x = 20 x 0.577

x = 11.54.

For the angle of 60º, the opposite and adjacent legs are exchanged relative to the angle of 30º, hence the tangent is calculated as follows:

tan(60º) = 20/x.

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Answer:

B. Line

Step-by-step explanation:

It is a line passing through the origin and rising to the right. The angle between the line and the x axis = pi/3 radians.

Answer:

8/15

Step-by-step explanation:

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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