How do i solve this??

The probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

This is a binomial distribution problem, where we have n = 15 trials and the probability of success (a patient having hyperextending joints) is p = 0.2.

A. To find the probability that exactly 5 of the 15 patients have hyperextending joints, we can use the formula for the binomial probability mass function:

P(X = 5) = (15 choose 5) * 0.2^5 * 0.8^10

where (15 choose 5) is the number of ways to choose 5 patients out of 15. Using a calculator, we get:

P(X = 5) = 0.188

So the probability that exactly 5 of the 15 patients have hyperextending joints is 0.188, or about 18.8%.

B. To find the probability that no more than 7 of the 15 patients have hyperextending joints, we need to add up the probabilities of having 0, 1, 2, ..., 7 patients with hyperextending joints. We can use the cumulative distribution function (CDF) of the binomial distribution:

P(X ≤ 7) = Σ(P(X = k)) for k = 0 to 7

Again, using a calculator, we get:

P(X ≤ 7) = 0.985

So the probability that no more than 7 of the 15 patients have hyperextending joints is 0.985, or about 98.5%.

C. To find the probability that more than 7 of the 15 patients have hyperextending joints, we can use the complement rule:

P(X > 7) = 1 - P(X ≤ 7)

We already know from part (B) that P(X ≤ 7) = 0.985, so:

P(X > 7) = 1 - 0.985 = 0.015

Therefore, the probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

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The radius of the circle is 9 units. The center of the circle is at (5, 0).

The given equation is (x – 5)²y² = 81.

To identify the radius and center of this circle, we can rewrite the equation in standard form.

First, let's divide both sides by 81 to get (x – 5)²y²/81 = 1.

Next, we can take the square root of both sides to eliminate the squared terms.

This gives us the equation (x – 5)/9 · y/3 = 1.

The standard form of a circle is (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius.

Comparing this form to our equation, we can see that (x – 5)/9 and y/3 correspond to (x – h) and (y – k), respectively.

Therefore, we can solve for h and k by setting (x – 5)/9 = 0 and y/3 = 0, respectively.

This gives us h = 5 and k = 0, so the center of the circle is (5, 0). Finally, we can solve for the radius r by noting that the

distance from the center (5, 0) to the edge of the circle is 3 units in the x-direction and 9 units in the y-direction.

Therefore, the radius of the circle is 9 units, and we can express our final answer as:

The radius of the circle is 9 units. The center of the circle is at (5, 0).

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Answer:

15

Step-by-step explanation:

The factors of 15 are 1,3,5,15

The factors of 30 are 1,2,3,5,6,10, 15, 30

The largest factor that both of these numbers share is 15

The measures of angles in a rhombus are m∠2=130, m∠3=50 and m∠4=50.

Angle measure is a term used in geometry to describe the size of an angle. It is usually expressed in degrees, which is a unit of measurement for angles. A degree is defined as 1/360th of a complete revolution around a circle.

In the rhombus, m∠1 =130

In a rhombus, opposite angles are congruent.

The angle opposite to angle 1 is angle 2.

so m∠1 =m∠2

m∠2= 130 degrees

Other pair of opposite angles are also congruent.

so m∠3=m ∠4

We know that the sum of 4 angles = 360

m∠1+m∠2+m∠3+m∠4=360

130+130+m∠3+m∠4=360

260+m∠3+m∠4=360

m∠3+m∠4=360-260

m∠3+m∠3=100

2m∠3=100

m∠3=50

Now, m∠3=50

m∠4=50

Therefore, m∠2=130, m∠3=50 and m∠4=50

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The measure of diagonal DB in the given square is 5√2.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles.

Using Pythagoras theorem of right triangle

DB² = DC² + BC²

Here given that

DC = BC

Then

DB² = DC² + DC²

DB² = 5² + 5²

DB² = 25 + 25

DB² = 50

DB = √50

DB = 5√2

Thus, the measure of diagonal DB in the given square is 5√2

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The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.

Given, The weight of the chain per foot = 2 pounds

Total length of the chain = 20 feet

The chain is hanging from a winch 20 feet above ground level.

The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is to be determined.

The force required to lift the chain is equal to the weight of the chain. Therefore, the force needed is F = 2 × 20 = 40 pounds. The work done is the product of force and distance.

Therefore, Work done = force × distance= 40 × (20 − 10)= 400 foot-pounds

Thus, the work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.

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D = Dan's share

P = Paul's share

[tex]\stackrel{D}{11}~~ : ~~\stackrel{P}{5}\qquad \implies \qquad \cfrac{D}{P}=\cfrac{11}{5}\implies D=\cfrac{11P}{5}[/tex]

now Dan decides to give Paul £39, so that means that Dan has £39 less whilst Paul has £39 more, so the new shares will be D - 39 and P + 39, and that puts them in a 1 : 1 ratio.

[tex]\stackrel{D-39}{1}~~ : ~~\stackrel{P+39}{1}\qquad \implies \qquad \cfrac{D-39}{P+39}=\cfrac{1}{1}\implies D-39=P+39 \\\\\\ \stackrel{\textit{substituting from the 1st eqution}}{\left(\cfrac{11P}{5} \right)-39~~ = ~~P+39}\implies \cfrac{11P}{5}=P+78\implies 11P=5P+390 \\\\\\ 6P=390\implies P=\cfrac{390}{6}\implies \boxed{P=65}[/tex]

Alexander would need to make monthly payments of $430 for the next 8 months to pay off his credit card debt.

To calculate the monthly payment that Alexander needs to make, we can use the formula for the present value of an annuity, which is:

[tex]PMT=PV*(r*(1+r)^n)/(1+r)^n-1)[/tex]

Where:

PMT = Monthly payment

PV = Present value of the debt

r = Monthly interest rate

n = Total number of payments

First, we need to calculate the monthly interest rate. The annual interest rate is 16.8%, which means the monthly interest rate is 16.8%/12 = 1.4%.

Next, we can calculate the total number of payments that Alexander needs to make over 8 months.

n = 8

Now, we can plug in the values:

[tex]PMT = 3200*\frac {(0.014*(1+0.014)^8)}{((1+0.014)^8-1)}[/tex]

This works out to approximately $430 per month (rounded to the nearest dollar).

Therefore, Alexander would need to make monthly payments of $430 for the next 8 months to pay off his credit card debt.

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An angle measurement, m∠BOC = 60° degrees where O is the center of the corcle.

What is an angle?

Since the ΔABC has three similar sides, we know that it is an equilateral triangle, meaning that all three angles are equal and each angle measures 60°.

Since A, B, and C are points on a circle with O as the center, we know that each of the distances OA, OB, and OC is equal to the radius of the circle.

Let's call this radius r.

Since ΔABC is equilateral, we know that each side has length r. We can also draw radii from the center O to points A, B, and C to form three congruent triangles AOB, BOC, and COA, each with two sides of length r and one angle of 60°.

Since the sum of the angles in a triangle is 180° degrees, each of the other two angles in each of these congruent triangles must measure 60° as well.

Thus, we see that ∠BOC is one of the angles in the isosceles ΔBOC, which has two angles of 60° and a third angle x, which we want to find.

We can use the fact that the sum of the angles in a triangle is 180° to find x:

x + 60 + 60 = 180

Simplifying, we get:

x = 60

Therefore, angle BOC measures 60°

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Complete question is:  m∠BOC = 60° degrees where O is the center of the corcle.

The angles are vertical and the value of x  from the angles (4x -25) and 75 can be expressed as 25.

A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees. When two lines join to form an angle, say X=45°, the opposite angle is also 45°, for instance.

From the fiqure we can see that the angles the vertically opposite angles, base on this condition we can form the equation as;

(4x-25)=75

4x=(75+25)

4x=100

x=100/4

x=25

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Answer:42.8571429%

Step-by-step explanation:

His GPS tracker got 7 miles while he actually ran 10. 10 - 7 = 3. Then you divide 3 by 7 which is [tex]\frac{3}{7}[/tex] and that is around 42.8571429%.

The length of segment A'E' of the new formed pentagon is 5 units.

We are given that:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

From the attached graph, we see that the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A- (0, 0)

E- (0, 2)

The length of the segment AE is:

AE = √((2-0)² + (0 - 0)²)

AE = √2²

AE = 2

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;

Length of segment A'E' = 5/2 × Length of segment AE

Thus;

Length of segment A'E' = 5/2 × 2

Length of segment A'E' = 5 units.

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Complete question is:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

Find the length of the line segment A'E'.

The calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

A manager of a sports club maintains data about the main sport in which members participate and their ages.

To verify if there is a connection between the age of a member and their sport preference, a test of independence is performed on 651 sports club members who were randomly selected at a 5% level.200 Words:

Test of independence: Test of independence is a statistical method that helps to determine if there is a connection between two groups, and if there is, what is the magnitude of the relationship.

A test of independence is performed using the chi-square statistic.

The null hypothesis in this test is that there is no relationship between the two group S.

We will use a chi-square test to determine whether there is a connection between the age of the member and the sport in which they participate.

Hypotheses:

Null hypothesis: There is no link between the age of a member and the sport in which they participate.

Alternate hypothesis: There is a relationship between the age of a member and the sport in which they participate.

Level of significance = 5%.

Step 1: Prepare the contingency table for observed values

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  25  30  20  10  15 20-29 years  20  50  35  30  25 30-39 years  15  40  40  35  30 40-49 years  10  35  25  25  20 Over 50 years  5  15  10  15  10

Step 2: Calculate the marginal frequencies.

Age  Basketball  Football  Hockey  Soccer  Other Total Under 20 years  25  30  20  10  15 100 20-29 years  20  50  35  30  25 160 30-39 years  15  40  40  35  30 160 40-49 years  10  35  25  25  20 115 Over 50 years  5  15  10  15  10 55 Total 75  170  130  115  100 651

Step 3: Compute the expected frequencies.

The predicted frequency for each group is (row total) * (column total) / total number of observations.

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  11.5  26.1  19.9  17.7  15 20-29 years  30.9  70.1  53.4  47.5  40.1 30-39 years  30.9  70.1  53.4  47.5  40.1 40-49 years  21.3  48.2  36.8  32.7  27.6 Over 50 years  9.4  21.4  16.4  14.6  12.3

Step 4: Calculate the test statistic:

We will use a chi-square test statistic to determine whether the null hypothesis should be accepted or rejected.

Chi-square test formula is:χ2 = Σ (Observed frequency – Expected frequency)2 / Expected frequency.

Degrees of freedom = (Number of rows – 1) * (Number of columns – 1)

χ2 = (25-11.5)2 / 11.5 + (20-30.9)2 / 30.9 + (15-30.9)2 / 30.9 + (10-21.3)2 / 21.3 + (5-9.4)2 / 9.4 + (30-26.1)2 / 26.1 + (50-70.1)2 / 70.1 + (40-70.1)2 / 70.1 + (35-48.2)2 / 48.2 + (15-21.4)2 / 21.4 + (20-19.9)2 / 19.9 + (35-53.4)2 / 53.4 + (40-53.4)2 / 53.4 + (25-36.8)2 / 36.8 + (10-16.4)2 / 16.4 + (15-14.6)2 / 14.6 + (15-32.7)2 / 32.7 + (25-27.6)2 / 27.6 + (10-12.3)2 / 12.3χ2 = 15.16

Degrees of freedom = (5-1) * (4-1) = 12

Step 5: Determine the p-value:

The p-value is determined by looking up the chi-square value and the degrees of freedom in the chi-square table.

The p-value is the probability of obtaining a result as extreme as or more extreme than the calculated value if the null hypothesis is true.

We will use a 5% level of significance.

Since the calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

There is evidence to suggest that the age of a member is related to the sport in which they participate.

In other words, the age of a member and their sport preference are not independent.

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Answer:

a) v.h=v*cos(63)=7.26 m/s

b) v.v=v*sin(63)=14.26 m/s

c) t=v.v/g=14.26/9.8=1.46 s since time the body takes to go upward is defined by the acceleration due to gravity and the vertical component of the speed

d) h=1/2*gt^2=7.15 m

e) T=2t=2.92 s

f) R=v.h*t=7.26*1.46=10.6 m since horizontal displacement is defined by the horizontal component of the speed only.

Step-by-step explanation:

Hope this helps! =D

Mark me brianliest! =D

To calculate the amount of money Joe will have in 3 years, we can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the amount of money Joe will have in 3 years

P = the principal amount = $2500

r = the annual interest rate = 9% = 0.09 (expressed as a decimal)

n = the number of times the interest is compounded per year (assuming annual compounding, n = 1)

t = the number of years = 3

Plugging in these values, we get:

A = $2500(1 + 0.09/1)^(1*3)

= $2500(1.09)^3

= $2500(1.29503)

= $3237.58 (rounded to two decimal places)

Therefore, Joe will have $3237.58 in 3 years.

Answer:

5.2 feet

Step-by-step explanation:

436.8/7/12 feet

The bank made $100 in profit from the loan.

What is simple interest?

Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on.

If John had to pay back $321 in total and the original loan was $221, then the bank made $100 in interest from John.

Interest = Amount John had to pay - Original Loan

Interest = 321 - 221

Interest = $100

So, the bank made $100 in profit from the loan.

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Answer:

v<-4/35. If you want interval notation it is (-infinity, -4/35)

Step-by-step explanation:

Answer:

first find constant term

y=kx

32=k(4)

32/4=4k/4

k=8

find value of y when x=5

y=kx

y=8×5

y=40

The required ratio of the time to rotate first and next 2 revolution is given by option 2. (√2+1) : 1.

Merry go round starts from rest.

Let us assume that the initial angular velocity and displacement are zero. Final angular velocity after 2 revolutions is ω.

This implies,

ω₀ = 0 rad/s.

For first two revolutions of the merry go round we have,

θ = 2×2π rad

⇒ θ = ω.t₁ + 1/2 × α × t₁²

⇒ 2×2π = 0×t₁ + 1/2 × α × t₁²

⇒t₁² = 8π/α

⇒ t₁ = √(8π/α)

For first four revolutions of the merry go round we have,

θ = 4×2π rad

⇒ θ = ω.t₂ + 1/2 α.t₂²

⇒ 4×2π = 0×t₂ + 1/2 × α × t₂²

⇒ t₂² = 16π/α

⇒t₂ = √(16π/α)

Time taken for 3rd and 4th revolution of the merry go round is equals to,

t₃ = t₂ - t₁

Substitute the values we get,

⇒ t₃ = √(16π/α) - √(8π/α)

⇒t₃ = (√2-1) √(8π/α)

Ratio of time to rotate first 2 revolutions and next 2 revolutions is written as ,

t₁/t₃ = √(8π/α) / [(√2-1)√(8π/α)]

⇒ t₁/t₃  = 1/(√2-1)

Multiply and divide by the conjugate of √2-1 is equals to,

⇒ t₁/t₃  = 1/(√2-1) × (√2+1)/(√2+1)

⇒ t₁/t₃  = √2+1

Therefore, ratio of time to rotate first 2 revolutions & next 2 revolutions is  equals to option 2. (√2+1) : 1.

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The above question is incomplete, the complete question is:

A merry go round rotates from rest with constant angular acceleration `α` . Ratio of time to rotate first 2 revolutions & next 2 revolutions is

1) 1:1

2) (√2+1):1

3) √2:1

4) 1:√2

The equation of the polynomial function in standard form is P(x) = x³ + 6x² - 7x - 60

Given that we have the following

zeros = -5,-4,and 3

The polynomial function in standard form is calculated as

P(x) = (x - zeros)

So, we have

P(x) = (x + 5)(x + 4)(x - 3)

Opening the brackets, we have the following equation

P(x) = x³ + 6x² - 7x - 60

Hence, the polynomial is P(x) = x³ + 6x² - 7x - 60

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In linear equation, 6499 ft CD, the height of the plane from the ground, to the nearest foot.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.

in the triangle ACD

sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1

in the triangle BCD

sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2

equation 1=equation 2

sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD

sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]

BD=15979 ft

in the triangle BCD

cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491

BC=17491 ft

    =  BC is 17491 ft

Part 2) Find CD, the height of the plane from the ground, to the nearest foot.

CD=sin24*BD        ( remember equation 2)

BD=15979 ft

CD=sin24*15979 -----------> CD=6499 ft

     =  CD is 6499 ft

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An equation is modeled. The value of x makes the equation true is -1.

Equation:

Conditional comparisons apply only to specific values ​​of variables. An equation consists of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Usually the right side of the equation is assumed to be zero. If this is accepted, it does not reduce the generality, since it can be done by subtracting the right side from the two sides.

According to the Question:

5x + 6 = 1

5x = -5

x = -1

Complete Question:

An equation is modeled. What value of x makes the equation true?

(1) 1

(2) 7

(3) -5

(4) -1

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The possible triangle whose vertices are given by the lattice points with positive integer coordinates less than 5 is 20.

To solve this, we apply principles of permutation and combination to count the number of possible triangles that can be formed from the given set of lattice points.

Here are the different ways of arranging the lattice points with lattice point coordinates less than 5:

If we want to choose any three lattice points, we can pick the first point from the 20 given in the table above.

Then, we can pick the second point from those lattice points that lie strictly above and strictly to the right of the first point.

For the third point, we can only pick lattice points lying above and to the right of the line segment connecting the first two points.

So, there are 20 possible triangles whose vertices are positive integer coordinates less than five.

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Answer:

x = 4, y = -14

Step-by-step explanation:

1. x + y = -10 and -3x - y = 2

2. y= -10 - x > plug in for y > -3x - (-10 - x) = 2

3. solve for x > -3x + 10 + x = 2

-2x + 10 = 2 > -2x = -8 > x= 4

4. plug x into original equation > 4 + y = -10 > y = -14

Answer:

x = 11

Step-by-step explanation:

3x + 5x + 2 =90

(3x + 5x) + (2) = 90

8x + 2 = 90

8x + 2 -2 = 90 -2

8x = 88

8x/8 = 88/8

x = 11

Step-by-step explanation:

According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex zeros (counting multiplicities).

The degree of the polynomial f(x) = 5x^6+2x^3−4x + 1 is 6, which means that it is a sixth-degree polynomial. Therefore, it has exactly 6 complex zeros (counting multiplicities).

Note that the zeros may be real or complex, and they may not all be distinct. To find the exact number of zeros and their values, we would need to use additional methods such as factoring, the rational zeros theorem, or numerical methods.

Answer:

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root. In the case of the polynomial function f(x) = 5x^6+2x^3−4x + 1, it is a sixth-degree polynomial function, which means it has at most six complex roots. However, the Fundamental Theorem of Algebra does not tell us the exact number of roots, nor does it tell us whether the roots are real or complex.

To determine the number of real roots of the function f(x), we can use the Intermediate Value Theorem or graph the function to find the number of times it crosses the x-axis. However, determining the number of complex roots requires more advanced techniques, such as the use of the Fundamental Theorem of Algebra in combination with the Factor Theorem, Rational Root Theorem, or other methods.

Therefore, based on the Fundamental Theorem of Algebra alone, we can say that the function f(x) = 5x^6+2x^3−4x + 1 has at least one complex root, but we cannot determine the exact number or nature of the roots without additional analysis.

if it has a diameter of 10, that means its radius is half that or 5.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=16 \end{cases}\implies V=\pi (5)^2(16)\implies V=400\pi[/tex]

Answer: The answer is A, 400π m3

Step-by-step explanation:

A house with value at 210000 correct to 2 significant figures. The lowest possible value of the house is equals to the £205000.

The second significant figure of a number is the digit after the first significant figure. This is true even in case of the digit is zero. We have a house is valued at £210000 correct to 2 significant figures. So, it is bounded question. Since, two significant figures is correct then there is error in 10000 range in £210000. The rounded up value is £2.10 × 10⁵. Steps to determine these bounds

here x = £210000, y = 10000

Since 2 significant digits are correct,

is about 10,000 of £210,000. The lowest possible number rounded to 2 significant digits in the £210,000 range is £205,000, because anything below that looks like £204....that doesn't round up to £21. Hence required value is £205000.

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