The second side a triangle is 4 inches longer than the first side. The third side of the triangle is 3 inches longer than the second side. If the perimeter of the triangle is 101 inches, find the length of the third side of the triangle.

Answer:

b. 120°

Step-by-step explanation:

K is any point outside of the circle with center M.

KJ and KL are tangents to the circle at points J and L respectively drawn from point K.

MJ and ML are radii of the circle with center M.

Since, tangent is perpendicular to the radius of the circle.

\( \therefore m\angle MJK = m\angle MLK = 90\degree \\\)

Since, measure of central angle of a circle is equal to the measure of its corresponding minor arc.

\( \therefore m\angle JML = m\widehat {(JL)} \\

\therefore m\angle JML = 60\degree \\\)

Since, JKLM is a quadrilateral. Hence by angle sum postulate of interior angles of quadrilateral JKLM, we have:

\( m\angle JML + m\angle MJK + m\angle MLK \\+ m\angle JKL= 360\degree \\

\therefore 60\degree +90\degree +90\degree +m\angle JKL= 360\degree \\

\therefore 240\degree +m\angle JKL= 360\degree \\

\therefore m\angle JKL= 360\degree-240\degree \\

\huge \purple {\boxed {\therefore m\angle JKL= 120\degree}} \\\)

The measure of angle JKL is 120 degrees and the correct choice is B.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

We are given that K is any point outside of the circle with center M.

Since KJ and KL are tangents to the circle at points J and L respectively drawn from point K. also MJ and ML are radii of the circle with center M.

We know that measure of central angle of a circle is equal to the measure of its corresponding minor arc.

Given, JKLM is a quadrilateral.

The angle sum postulate of interior angles of quadrilateral JKLM, we have:

Angle JKL + 90 + 60 + 90 = 360

Angle JKL = 360 - 240

Angle JKL = 120

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Answer:

a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.

b) 0.076 = 7.6% probability that the sample will contain at least three defectives

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

Sample of 20 items is selected from the machine.

This means that \(n = 20\)

5% defectives

This means that \(p = 0.05\)

(a) the normal approximation to the binomial

The mean is:

\(\mu = E(X) = np = 20*0.05 = 1\)

The standard deviation is:

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747\)

The probability is, using continuity correction, \(P(X \geq 3 - 2.5) = P(X \geq 2.5)\) , which is 1 subtracted by the pvalue of Z when X = 2.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2.5 - 1}{0.9747}\)

\(Z = 1.54\)

\(Z = 1.54\) has a pvalue of 0.9382

1 - 0.9382 = 0.0618

0.0618 = 6.18% probability that the sample will contain at least three defectives.

(b) the exact binomial tables

This is:

\(P(X \geq 3) = 1 - P(X < 3)\)

In which

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358\)

\(P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377\)

\(P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189\)

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924\)

\(P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076\)

0.076 = 7.6% probability that the sample will contain at least three defectives

In fraction 5 / 6 the number of the groups of 1²/₃ is only 1.

The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given that there are two fractions 5/6 and 1²/₃. The group will be calculated as,

Fraction =  1²/₃ = 5 / 3

Fraction = 5 / 6 = ( 5 / 3 ) x ( 1 /2 )

Here in the above fraction of 5 / 6 there is only one 5 / 3 or 1²/₃.

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Answer:

equation for perpendicular bisector passing through CB is;

y=⁴/³– 5/30

The equation of the rule that relates x and y is y = 2x - 6.

Anything on one side of the equals sign in a calculation must equal anything on the other side of the equals sign. So long as we maintain the balance on both sides of the equals symbol, we can do whatever we want to an equation.

We can create a system of equations using the provided values (8, 10) and (9, 12) in order to determine the rule that connects x and y. One approach is as follows:

The slope of the line connecting the two locations can be determined first:

m = (y2 - y1)/(x2 - x1) = (12 - 10)/(9 - 8) = 2/1 = 2

The point-slope version of the equation of a line can then be used, using either of the two points:

y - y1 = m(x - x1)

For example, using the first point (8, 10):

y - 10 = 2(x - 8)

Simplifying:

y - 10 = 2x - 16

y = 2x - 6

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( a ) The null hypothesis, represented by \(H_{0}\), should be equivalent to 0.6 pounds per square inch, considering it normally is predicted to be equivalent to the population parameter, which, in this case, is 0.6 psi ( pounds per square inch. ) The alternative hypothesis on the other hand contradicts the null hypothesis, and as the manager feels the pressure has been reduced, the alternative hypothesis points that the pressure is less than 0.6 psi -

\(H_0: stigma = 0.7,\\H_a: stigma < 0.7\)

stigma is represented by the sign ( σ )

( b ) Now if you were to reject the null hypothesis when true, that would lead to a type I error. That would mean that to reject the fact that σ = 0.7, and accept that σ < 0.7, even though σ = 0.7 is true, would make a type I error.

_______

( c ) A type II error is quite the opposite. Accepting the null hypothesis while rejecting the alternative hypothesis would make a type II error.

From the information given and using error concepts, it is found that:

a)

The null hypothesis is \(H_0: \sigma = 0.6\)

The alternative hypothesis is \(H_1: \sigma < 0.6\)

b) It would mean a conclusion that the standard deviation is of less than 0.6 psi when in fact it is not.

c) It would mean a conclusion that the standard deviation not significantly less than 0.6 psi when in fact it is.

At the null hypothesis, we test if the standard deviation is of 0.6 psi, that is:

\(H_0: \sigma = 0.6\)

At the alternative hypothesis, we test if variability has been reduced, that is, if the standard deviation is of less than 0.6 psi, hence:

\(H_1: \sigma < 0.6\)

Item b:

A Type I error happens when a true null hypothesis is rejected, hence, it would mean a conclusion that the standard deviation is of less than 0.6 psi when in fact it is not.

Item c:

A Type II error happens when a false null hypothesis is not rejected, hence, it would mean a conclusion that the standard deviation not significantly less than 0.6 psi when in fact it is.

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Answer:

hope this helps

The solution is 3,27,680

The geometric progression is given by aₙ = a ( r )ⁿ⁻¹ , where r = 4 is the common ratio and after 8 hours a₈ = 3,27,680

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the first term of the geometric sequence be a₁ = 20

Let the second term a₂ = 80

So , the common ratio r = second term / first term

On simplifying the equation , we get

Common ratio r = 80/20

Common ratio r = 4

Now , the explicit formula for the GP is

aₙ = a ( r )ⁿ⁻¹ , where n is the number of hours

aₙ = 20 ( 4 )ⁿ⁻¹

So , after 8 hours ,

Substitute the value of n = 8 in the equation , we get

a₈ = 20 ( 4 )ⁿ⁻¹

a₈ = 20 ( 4 )⁷

a₈ = 3,27,680

Therefore , the value of a₈ = 3,27,680

Hence , the equation is aₙ = 20 ( 4 )ⁿ⁻¹

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Answer:

0.6

Step-by-step explanation:

-4.5-5.1=0.6

Answer:

Step-by-step explanation:

\(v =( 7 \times 6 \times 1) + (3 \times 2 \times 1) \\ v = 42 + 6 \\ v = 48 \: {cm}^{3} \)

I hope that is useful for you :)

9514 1404 393

Answer:

  a) about 113°

  b) about 16.6 m

Step-by-step explanation:

a) Half of the angle through which Tarzan swings is the angle in a right triangle with hypotenuse 30 m and opposite side 25 m. That half-angle is then ...

  sin(α/2) = 25/30 = 5/6

  α/2 = arcsin(5/6)

  α = 2×arcsin(5/6) ≈ 112.895° ≈ 113°

Tarzan will need to swing through an angle of about 113°.

__

b) The side adjacent to that half-angle is the height of the vine attachment above the riverbank. It can be found using the Pythagorean theorem.

  h = √(30² -25²) = √275 ≈ 16.583

The top of the vine needs to be about 16.6 m above the riverbank so Tarzan stays above the water.

Answer:

0.53125

Step-by-step explanation:

17/32 equals 0.53125

Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25

The variance is the difference between the numbers in a set of data, to put it simply. Each number's variability is a statistical statistic that indicates how far off from the mean and from each other number in the set it is.

Here,

Given : mean = 10

varience = 3

Using chebyshevs inequality we have

P(|X-u| ≥ k)≤ \(\sigma^{2}\)/\(k^{2}\)

hence we can have,

=> P(X>15)  ≤ 3/\(5^{2}\)

=> P(X>15)  ≤ 3/25

Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25

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The correct image include the following: B. Green: image A.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.

In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.

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Answer:

C

Step-by-step explanation:

 2

+2

-----

 4

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer: -5, 6

Step-by-step explanation:

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

thirteen minus four equals eight.

or

Thirteen subtracted by four will equal eight

best of luck

Step-by-step explanation:

Answer: I have 18 balloons. I give my friend 4 balloons. How many balloons do i have?

I put it in the most simplest word problem. Hope this helps

Answer:

Step-by-step explanation:

I answer for what I understand,

the question is really confused.

(60 + 15) + 3 - 2(4) + 23 =

75 + 3 - 8 + 23 =

78 - 8 + 23 =

70 + 23 =

93

Answer:

Step-by-step explanation:

Add 60 and 15

Cube 2

Divide 75 by 3

Multiply 2 by 4

Subtract 8 and 25

Add 17 and 8

Answer:

21

Step-by-step explanation:

Two small triangles are similar, so

y : 3 = 7 : y

y² = 21

\(y=\sqrt{21}\)

In question 6, the standard divisor, the standard quota, the lower quota, and the upper quota for Conner are 67.8, 3.024, 3, and 4, respectively.

In question 7, the number of seats for the counties A, B, C, D, and E is 14, 6, 18, 4, and 13, respectively.

We have two apportionment problems.

In question 6, the number of candies is 25. The number of pages read by Shaun, Conner, Antonio, and Isaac is 655, 205, 480, and 355, respectively. The total number of pages is 1695.

The standard divisor is 1695/25 = 67.8.

The standard quota for Conner is 205/67.8 = 3.024.

The lower quota for Conner is rounding down the standard quota, i.e., 3.

The upper quota for Conner is rounding up the standard quota, i.e., 4.

In question 7, the number of seats is 55. The population in counties A, B, C, D, and E is 349000, 159000, 471000, 110000, and 326000, respectively. The total population is 1415000.

The standard divisor is 1415000/55 = 25727.27.

The number of seats for county A is 349000/25727.27 = 14.

The number of seats for county B is 159000/25727.27 = 6.

The number of seats for county C is 471000/25727.27 = 18.

The number of seats for county D is 110000/25727.27 = 4.

The number of seats for county E is 326000/25727.27 = 13.

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Answer:

0.0625 is the answer.

Hope it helps you!!!

The motion of the dolphin, evaluated using the kinematic equations and Newton's second law of motion are;

Mathematically, Newton's second law of motion states that force is the product of mass and acceleration.

The mass of the dolphin = 230 kg

Height to which the dolphin leaps = 6.4 m

The distance the drag brings the dolphin to a stop = 6.4 meters

First part;

The time it takes the dolphin to stop can be found from the equation;

At the water surface;

m·g·h = 0.5·m·v² (conservation of energy)

g·h = 0.5·v²

v² = 2·g·h

Therefore;

v² = 2 × 9.81 × 6.4 = 125.568

In the water, the initial velocity is v, the velocity at 1.5 meters depth is u, we get;

u² = v² - 2·a·s

Therefore;

v² = 2·a·s

a = v²/(2·s)

a = 125.568/(2 × 1.5) = 41.856

a = 41.856 m/s²

v = u - a·t

t = (u - v)/a

Therefore;

t = (√(125.568))/41.856 ≈ 0.268

The time it takes the dolphin to stop is about 0.268 seconds

Second part

Newton's second law of motion states that force is directly proportional to the rate of change of momentum produced

Mathematically

Force = Mass × Acceleration

Force on the dolphin, F = 230 kg × 41.856 m/s²= 9626.88 N

The possible parts of the question, obtained from a similar question are;

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The solution set of the quadratic inequality x² - 5 < 0 is - √5 < x < √5

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

The quadratic inequality is:

x^2-5<0

Express properly

x² - 5 < 0

Add 5 to both sides of the inequality

x² < 5

Take the square root of both sides

x < ±√5

Expand the inequality expression

- √5 < x < √5

Hence, the solution is - √5 < x < √5

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Answer:

Step-by-step explanation:

A= A0 e(r.t)

A= 20 e( 0.9*16)

A= 35,881,495.45

So bc they want to round to the nearest whole number

A= 35,881,495 the epidemiologist will find bacteria

Answer:

6710886067

Step-by-step explanation:

Answer:15

Step-by-step explanation:1) 1/2

2) 3/5

3)4

D) 8

5) 16

plz branliest

Answer:

x would be equal to 6

Step-by-step explanation:

24 would be divided by 4 because it's 4x

Answer:

x = 24 ÷ 4 or 24/4

Step-by-step explanation:

In order to isolate the variable, you multiply both sides by the reciprocal of 4, which is 1/4.