Of all ladies over the age of 50, 72% report that they color their hair to hide their gray. What is the probability

that under 70% color their hair in a group of 85 older women?

Answer: D or #4: None of the above

Step-by-step explanation: Since the longest angle is 13 x has to be around half because its a 47 degree angle if we round it would be 6 so D

The surface areas of the figures are 336, 82 and 836

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

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

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The surface area of the prisms are

1. 336 cm²

2. 82 m²

3. 836 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as;

SA = 2B +pH

where B is the base area , p is the perimeter and h is the height.

1. SA = 2B +ph

B = 1/2 × 6 × 8

= 24 m²

p = 6+8+10 = 24m

h = 12m

SA = 2 × 24 + 24 × 12

= 48 + 288

= 336 cm²

2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)

= 2( 6+21+14)

= 2( 41)

= 82 m²

3. SA = 2πr( r +h)

= 2 × 3.14 × 7( 7 + 12)

= 44( 19)

= 836 cm²

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The total height of the flyer at any time after deploying the wingsuit would be;

y = -3x + 200 + (-4.9t² + 420),

Now, Based on the given information, we can use the two functions to determine the height of the wingsuit flyer at a particular time.

During the freefall, the height of the flyer can be calculated using the function

y = -4.9x² + 420.

Let's say the flyer falls freely for t seconds before deploying the wingsuit.

Therefore, the height at the moment of deploying the wingsuit would be,

y = -4.9t² + 420.

After deploying the wingsuit, the height of the flyer is given by the function

y = -3x + 200.

We can combine these two functions to get the total height of the flyer at any given time after deploying the wingsuit.

So, the total height of the flyer at any time after deploying the wingsuit would be;

y = -3x + 200 + (-4.9t² + 420),

where x is the time after deploying the wingsuit and t is the time of freefall before deploying the wingsuit.

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Answer:

9x ≥ 81

Step-by-step explanation:

Given

Total = $81 (atleast)

Required

Represent as an inequality

Let the number of weeks he x

If he saves $9 in a week, then he will save $9x in weeks

From the question we understand that he needs at least $81

At least, in inequality means ≥

So, the inequality is:.

9x ≥ 81

To estimate the probability of hitting the bullseye at least 100 times in 2000 throws, we can use the binomial distribution formula. The probability of hitting the bullseye in a single throw can be calculated by finding the ratio of the areas of the bullseye and the entire dartboard.

The area of the bullseye (radius 1) is A_bullseye = π * 1^2 = π square units. The area of the entire dartboard (radius 5) is A_dartboard = π * 5^2 = 25π square units. Therefore, the probability of hitting the bullseye in a single throw is p = A_bullseye / A_dartboard = π / 25π = 1/25.

Now, we use the binomial distribution formula: P(X >= 100) = 1 - P(X < 100), where X is the number of bullseye hits. To calculate P(X < 100), we need to sum the probabilities from X = 0 to X = 99.

P(X < 100) = Σ [C(n, k) * p^k * (1-p)^(n-k)], for k = 0 to 99

Where n = 2000 (total throws), k = number of bullseye hits, and C(n, k) is the binomial coefficient (combinations of n elements taken k at a time).

Computing the above sum and subtracting it from 1 gives us the probability of hitting the bullseye at least 100 times. Due to the large number of calculations, using software or an online calculator can be helpful to compute this probability.

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The solution is, the simplification of the equation is :

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

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

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

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Answer:

b. infinite solutions

Step-by-step explanation:

\(-\frac{1}{2}x+\frac{1}{2}y=-1\\\\\textsf{subtract} \ -\frac{1}{2}y \ \textsf{from both sides:}\\\\\implies -\frac{1}{2}x=-1-\frac{1}{2}y\\\\\textsf{mulitply both sides by -2:}\\\\\implies x=2+y\\\\\textsf{subtract} \ y \ \textsf{from both sides:} \ x-y=2\)

Therefore, the graphs are the same.

If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

Answer:

There's one solution (2,0)

Hope this helps!

Answer:

3

Step-by-step explanation:

1. 54÷6 =9

2. (12-4)=8

3. 9-8 = 1

4. 1+2 = 3

5. I hope this helps it's pretty simple oh and 3 is your anansw.Also you can you your calculator

Answer:

a=72\(\frac{2}{3}\)

Step-by-step explanation:

56/6*(12-4)+2=n

56/6*8+2-2=n-2

56/6*8/8=(n-2)/8

x=9\(\frac{1}{3}\)

x=(n-2)/8

y=74\(\frac{2}{3}\)

y=n-2=a

a=72\(\frac{2}{3}\)

Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

The value of DE is 6 units long.

Since triangles ABC and DEF are similar, we know that their corresponding sides are proportional. In other words, the ratio of any corresponding side lengths in the two triangles is the same.

We can use this fact to set up the following proportion:

DE/BA = EF/BC

Substituting the given values, we get:

DE/9 = 12/18

Simplifying the right side of the equation, we get:

DE/9 = 2/3

To solve for DE, we can cross-multiply:

DE = 9 x 2/3 = 6

Therefore, DE is 6 units long.

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Answer: SAS

Step-by-step explanation:

There are two pairs of congruent angles and the pair of angles formed by these sides are congruent.

\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)

In the given figure, one angle and two adjacent sides of Triangle AFB is equal to corresponding angle and sides of the Triangle DFC.

So, we can conclude that,

Triangle AFB and Triangle DFC are congruent by :

\( \qquad \large \sf {Conclusion} : \)

Answer:

its a such a hard questions i think you should ask to you're teacher ?

Value of cosθ will be cosθ = (√2)/2 after using Pythagorean Identity.

The Pythagorean Identity states that sin²θ + cos²θ = 1. We can use this identity to find cosθ given that sinθ = (√2)/2 and θ terminates in Quadrant I.

Since sinθ = (√2)/2 and θ terminates in Quadrant I, we can draw a right triangle with angle θ in Quadrant I, opposite side equal to √2, adjacent side equal to 1, and hypotenuse equal to √3.

Using the Pythagorean Theorem, we can find the length of the hypotenuse as:

h² = a² + b²

√3² = 1² + (√2)²

3 = 1 + 2

3 = 3

So, the length of the hypotenuse is √3.

Now, we can use the Pythagorean Identity to find cosθ:

sin²θ + cos²θ = 1

Substituting sinθ = (√2)/2:

(√2/2)² + cos²θ = 1

Simplifying:

2/4 + cos²θ = 1

1/2 + cos²θ = 1

cos²θ = 1 - 1/2

cos²θ = 1/2

Since θ terminates in Quadrant I and sinθ is positive, we know that cosθ is also positive. Therefore, taking the positive square root of both sides, we get:

cosθ = √(1/2) = (√2)/2

So, cosθ = (√2)/2.

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The data modelling function is Price required to recoup printing expenses is equal to 0.1 * (numbers of yearbooks sold) + 45.

A yearbook is a collection of images and text that is issued by an organisation once a year to remember and highlight the happenings at a particular school during the previous academic year. Yearbooks were used in elementary, middle, high, and college and university settings throughout the 20th century.

Using the information in the table,

\(n = 5\)

Σ\(x = 1175\)

Σ\(y = 145\)

Σ\((xy) = 41000\)

Σ\((x^2) = 287500\)

When these values are inserted into the formula,

\(m = (541000 - 1175145) / (5*287500 - 1175^2)\)

\(= -0.1\)

Therefore, the slope of the linear function is \(-0.1\).

\(b = y - mx\)

where we can use any of the data points. Let's use\((250, 20)\)

\(b = 20 - (-0.1*250)\)

\(= 45\)

Therefore, the y-intercept of the linear function is \(45\).

\(y = -0.1x + 45\)

Therefore,

Price needed to cover the costs of printing \(= -0.1*\)(number of yearbooks sold) \(+ 45\).

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Answer:

A. True.

Step-by-step explanation:

To get the standard error of the mean, you need to do the sample standard deviation over the square root of the number of samples, n.

In this case, n = 100. The standard deviation is 12. To get the SAMPLE standard deviation, you do the population standard deviation over the square root of n. That is 12 / sqrt(100) = 12 / 10 = 1.2.

So, to get the standard error: 1.2 / sqrt(100) = 1.2 / 10 = 0.12.

The standard error of the mean is, indeed, 0.12, so the statement is A. True.

Hope this helps!

Answer:

We know we have to pay $75 per weel plus $0.25 for each mile we traveled, from that, if we call x the miles we have travelled, the total cost would be:

\(C = 75 + 0.25x\)

As each mile we travel costs $0.25. Now that we have that expression, they ask us how many miles did we travel if we had to pay $96.25.

The only thing we have to do is replacing the C (our total cost) per $96.25 and solve the equation we get:

\(96.25=75+0.25x\)

\(96.25-75=0.25x\)

\(21.25=0.25x\)

\(\frac{21.25}{0.25} = x\)

\(85 = x\)

We hve traveled 85 miles.

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

Given that there is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds.will register a weight greater than 80 pounds

When a body is submerged in a water an upward force acts on the body known as buoyant force which is equal to weight of the water displaced by the body. Since water exerts Buoyant force on the body and according to Newton's third law there must be equal and opposite force exerted by the body on the water. This additional force equal and opposite to the Buoyant force will cause the reading of the scale to increase. Therefore the scale will register a weight greater than 80 pounds due to Newton’s Third Law.

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The complete question is :

There is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds. When a metal cube is submerged tied to a string end into the container, which of the following statements accurately describes the result?

The cube’s density must be provided to predict what will happen

The scale will remain at 80 pounds until the cube is floating on top of the water fully submerged.

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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The nth term of the given Quadratic Sequence is n² + 2n.

Given, a sequence of numbers i.e. 3, 8, 15, 24, 35

Now, we have to find the nth term of this quadratic sequence

Let, the quadratic sequence be defined as,

f(x) = ax² + bx + c

Now, as we have f(1) = 3

So, a + b + c = 3 ... (1)

also, we have f(2) = 8

So, 4a + 2b + c = 8 ... (2)

also, we have f(3) = 15

So, 9a + 3b + c = 15 ... (3)

On solving Eq (1) & (2), we get

3a + b = 5 ... (4)

also, On solving Eq (3) & (2), we get

5a + b = 7 ... (5)

Now, on solving Eq (4) & (5), we get

2a = 2

a = 1

On substituting the value of 'a' in Eq. (5), we get

b = 2

So, the quadratic sequence be f(x) = x² + 2x.

Hence, the Quadratic Sequence f(x) = x² + 2x and the nth term be

n² + 2n.

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

2x

Step-by-step explanation:

because it's2 so two ok carRy on

The value of a is 9.

A factor of polynomial P(x) is any polynomial which divides evenly into P(x).

For finding the factor of a polynomial we will perform following steps:

According to the given question.

We have a cubic polynomial \(x^{3} -4x^{2} +ax -2a\)

Also, x - 3a is a factor of the given polynomial.

⇒ \(x - 3 = 0\)

⇒\(x = 3\)

⇒ 3 is the one solution of the given cubic polynomial.

If 3 is the one solution of the cubic polynomial then it must satisfy the equation (i).

So, substitute the value of x in the given polynomial.

\((3)^{3} -4(3)^{2} + a (3) - 2a = 0\)

⇒\(27 -4(3)^{2} +a(3) -2a=0\)

⇒\(27 - 36 + 3a - 2a= 0\)

⇒\(-9 + a = 0\)

⇒ \(a = 9\)

Therefore, the value of a is 9.

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The inverse function of f(x) is:

\(g(x) = \sqrt[3]{(x +1)/64}\)

Here we have the function:

\(f(x) = 64*x^3 -1\)

We want to find the inverse, we will say that is of the form:

\(g(x) = \sqrt[3]{a*x + b}\)

If we evaluate f(x) on g(x), we get:

\(f(g(x)) = 64*(\sqrt[3]{ax + b})^3 - 1\\ \\f(g(x)) = 64*(ax + b) - 1\)

If these are inverses, that must be equal to x:

\(64*(ax + b) - 1 = x\\\\64*a*x + 64*b - 1 = x\\\)

Then:

64*a = 1

a = 1/64

64*b - 1 = 0

b = 1/64

So the inverse function is:

\(g(x) = \sqrt[3]{(x +1)/64}\)

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x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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The value of A4 for the given condition if a1=6 and an=2an-1 is 48.

A1 = 6 means a(1) == 6

This is the first term of the sequence. Then you have the “rule” or the “closed form” of the sequence,

which is: an = 2an - 1 for n>1,

Should be written like this: a(n) == 2 × (an - 1) for n>1.

Now,  It says that for any n>1, you should do this:

a(2) - that is the 2nd term is:

a(2) == 2 * (an - 1).

But (an -1) means “the term before this one”, which is the first term.

So, a(2) ==2 × 6 == 12, which is the 2nd term.

The 3rd term will be: a(3) == 2 × 12 = 24.

And the 4th term will be:

a(4) == 2 × 24 = 48.

So,the sequence will be:

6 , 12, 24, 48.

Thus, If a1=6 and an=2an-1, then the value of A4 under the indicated circumstance is 48.

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Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

Answer:

101

Step-by-step explanation:

\(\log a=-8\\\\10^{\log a}=10^{-8}\\\\a=10^{-8}\)

\(\log b=-9\\\\10^{\log b}=10^{-9}\\\\b=10^{-9}\)

\(\log c=-9\\\\10^{\log c}=10^{-9}\\\\c=10^{-9}\)

\(\displaystyle \log\frac{a^2}{b^5c^8}=\log\frac{(10^{-8})^2}{(10^{-9})^5(10^{-9})^8}=\log\frac{10^{-16}}{(10^{-9})^{13}}=\log\frac{10^{-16}}{10^{-117}}=\log(10^{-16-(-117)})=\log(10^{101})=101\)

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

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Answer:

the second answer

juzt find the scale factors of the two numbers given (120 and 96).

Step-by-step explanation:

Using proportions, it is found that Gene's speed was of 25 miles per hour, as he was 30 miles faster over a period of 6 hours.

A proportion is a fraction of a total amount.

At 8 a.m. Anne left Austin and headed south at 20 mph, hence when Gene left at 10 a.m., she was 40 mph ahead.

At 4 p.m., that is, 6 hours after Gene left, the distance was of 10 miles, that is, Gene was 30 miles faster in 6 hours, so the difference in the speeds is given by:

d = 30/6 = 5 mph.

Since Anne's speed is of 20 mph, Gene's is given by:

v = 20 + 5 = 25 mph.

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