What is the positive solution to the equation y=6x^2-54?
What is the negative solution to y=½x^2+x-12?

Answer:

To write the equation y - 7 = 8(x + 2) in slope-intercept form, we need to solve for y:

y - 7 = 8(x + 2)

Distribute the 8:

y - 7 = 8x + 16

Add 7 to both sides:

y = 8x + 23

Now, we have the equation in the form y = mx + b, where m is the slope and b is the y-intercept. Therefore, the slope of the line is 8, and the y-intercept is 23.

The slope-intercept form of the equation is: y = 8x + 23.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]y-7=8(x+2)[/tex]

[tex]y-7=8x+16[/tex]       (expanded brackets)  

[tex]y=8x+23[/tex]              (+7 both sides)

Solution: [tex]y=8x+23[/tex]

Answer: { (-1/2)x - 1, -2 ≤ x ≤ 4

Step-by-step explanation:

Let's start with the first line:

The line passes through two points: (-5, 8) and (-2, 2). The hollow circle at (-5, 8) indicates that this point is not included in the graph, while the closed circle at (-2, 2) indicates that this point is included.

We can find the slope of the line using the two points:

slope = (change in y) / (change in x) = (2 - 8) / (-2 - (-5)) = -6 / 3 = -2

Using point-slope form, we can write the equation of the line as:

y - 2 = -2(x - (-2))

Simplifying:

y - 2 = -2x - 4

y = -2x - 2

Next, let's consider the second line:

The line passes through two points: (-2, -2) and (4, -5). The hollow circle at (-2, -2) indicates that this point is not included in the graph, while the closed circle at (4, -5) indicates that this point is included.

We can find the slope of the line using the two points:

slope = (change in y) / (change in x) = (-5 - (-2)) / (4 - (-2)) = -3 / 6 = -1/2

Using point-slope form, we can write the equation of the line as:

y - (-2) = (-1/2)(x - (-2))

Simplifying:

y + 2 = (-1/2)x + 1

y = (-1/2)x - 1

Now we can write the piecewise function:

f(x) = { -2x - 2, -5 ≤ x < -2

{ (-1/2)x - 1, -2 ≤ x ≤ 4

This piecewise function represents the two lines graphed on the given axes, where the first line is defined for x values between -5 and -2 (inclusive on -2 but not on -5), and the second line is defined for x values between -2 and 4 (inclusive on both).

Answer:

america

Step-by-step explanation:america!!

Here are the factored expressions for the given expressions:

Factored expression: 3(2r^2 - rs - s^2)

Factored expression: x(2x + 3)(3x - 4)

Factored expression: 8mn^2(m - n)(m - 3n)

To factor these expressions, we need to find the common factors among the terms in each expression and factor them out.

6r^2 - 3rs - 3s^2

First, we notice that all three terms have a common factor of 3. We can factor it out:

3(2r^2 - rs - s^2)

The quadratic expression inside the parentheses cannot be factored further using integers, so the factored expression is:

3(2r^2 - rs - s^2)

6x^3 - x^2 - 12x

In this expression, we can factor out x:

x(6x^2 - x - 12)

Now, we can factor the quadratic expression inside the parentheses:

x(2x + 3)(3x - 4)

So, the factored expression is:

x(2x + 3)(3x - 4)

8m^3n^2 - 32m^2n^3 + 24mn^4

In this expression, we can factor out 8mn^2:

8mn^2(m^2 - 4mn + 3n^2)

Now, we can factor the quadratic expression inside the parentheses:

8mn^2(m - n)(m - 3n)

So, the factored expression is:

8mn^2(m - n)(m - 3n)

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Answer:

To draw a line graph, you need to plot your data on the graph. For example, if you have the data for the number of cars produced in a year, you would plot the number of cars on the Y-axis and the year on the X-axis. Then, you would trace both lines to the point where they intersect and place a dot on the intersection. You would repeat this process for each year and then connect the dots with a line.

Accοrding tο the given infοrmatiοn, a linear relatiοnship between time and pοpulatiοn οccurs when the change in pοpulatiοn οver a given periοd is cοnstant οr prοpοrtiοnal tο the pοpulatiοn size at the beginning οf the periοd.

In a graph, a linear relatiοnship is a pattern in which the pοints οn a scatter plοt tend tο fall alοng a straight line. A linear relatiοnship means that there is a cοnstant rate οf change between twο variables, such that when οne variable increases by a certain amοunt, the οther variable increases οr decreases by a cοnstant amοunt as well.

A situatiοn in which a city's pοpulatiοn grοws at a cοnstant rate οver time wοuld exhibit a linear relatiοnship between time and pοpulatiοn. As time passes, the pοpulatiοn wοuld increase by a fixed amοunt. This is an example οf linear grοwth, and it cοuld be mοdeled by a linear equatiοn such as P = mt + b, where P is the pοpulatiοn, m is the slοpe (the rate οf grοwth), t is time, and b is the initial pοpulatiοn at time t=0.

Similarly, if a pοpulatiοn is decreasing by a fixed percentage each year, then the relatiοnship between time and pοpulatiοn will alsο be linear. As time passes, the pοpulatiοn will decline by a cοnstant percentage οf the previοus year's pοpulatiοn.

In general, a linear relatiοnship between time and pοpulatiοn οccurs when the change in pοpulatiοn οver a given periοd is cοnstant οr prοpοrtiοnal tο the pοpulatiοn size at the beginning οf the periοd.

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Answer:

To find the intersection points between the two functions, we need to solve the equation:

cos(2x) + 2 = sin(x) + 3

Rearranging, we get:

cos(2x) = sin(x) + 1

Using the identity cos(2x) = 1 - 2sin^2(x), we can rewrite the equation as:

1 - 2sin^2(x) = sin(x) + 1

Simplifying, we get:

2sin^2(x) - sin(x) = 0

Factoring out sin(x), we get:

sin(x)(2sin(x) - 1) = 0

This gives us two solutions: sin(x) = 0 and sin(x) = 1/2.

For sin(x) = 0, we get the values x = 0, π, and 2π.

For sin(x) = 1/2, we get the values x = π/6 and 5π/6.

Out of these solutions, only π/2 and 3π/2 are in the interval [0, 2π), so the intersection points are:

f(π/2) = cos(2(π/2)) + 2 = 1 + 2 = 3

g(π/2) = sin(π/2) + 3 = 1 + 3 = 4

f(3π/2) = cos(2(3π/2)) + 2 = 1 + 2 = 3

g(3π/2) = sin(3π/2) + 3 = -1 + 3 = 2

Therefore, the answer is: x equals pi over 2 and 3 times pi over 2.

Step-by-step explanation:

The functions f (x) = cos 2x + 2 and g(x) = sin x + 3 intersect at x = π/2, x = 7π/6, x = 3π/2, and x = 11π/6 in the interval [0, 2π).

In order for the functions f (x) = cos 2x + 2 and g(x) = sin x + 3 to intersect, the two equations must equal each other. Hence:

cos 2x + 2 = sin x + 3

By subtracting 2 from both sides of the equation, we are left with:

cos 2x = sin x + 1

This equation can be solved by applying the trigonometric function properties. However, in order to avoid any potential confusion, it can be much easier to use an online graphing tool to find the points of intersection. In the interval [0, 2π), the solutions are x = π/2, x = 7π/6, x = 3π/2, and x = 11π/6.

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Answer: 210

Step-by-step explanation:

The value of 14x15 is 210.

If an art teacher ordered 26 sets for class and there are 100 markers in each set, then the total number of markers is:

26 x 100 = 2600

Therefore, there would be 2600 markers in 26 sets.

Answer:

Rs 183.75

Step-by-step explanation:

1: 24.5

7.5/1 = 7.5

7.5*24.5 = 183.75

Answer: To compute the volume of a prism, we need to know the area of the base and the height of the prism. Assuming that the prism has a rectangular base, the formula for the volume of the prism is:

Volume = Area of Base × Height

Let's assume that the length and width of the rectangular base are both equal to 2d (since we don't have specific dimensions). The height of the prism is also equal to d, as given.

When d = 1:

The area of the base is 2d × 2d = 4 square units

The height is d = 1 unit

Therefore, the volume is:

Volume = Area of Base × Height = 4 × 1 = 4 cubic units

When d = 2:

The area of the base is 2d × 2d = 8 square units

The height is d = 2 units

Therefore, the volume is:

Volume = Area of Base × Height = 8 × 2 = 16 cubic units

When d = 1/2:

The area of the base is 2d × 2d = 1 square unit

The height is d = 1/2 unit

Therefore, the volume is:

Volume = Area of Base × Height = 1 × (1/2) = 1/2 cubic units

So, the volume of the prism is 4 cubic units when d=1, 16 cubic units when d=2, and 1/2 cubic units when d=1/2.

Step-by-step explanation:

The level of the liquid is dropping at a rate of 9/(4π) inches per second when the liquid is 1 inch deep.

We are given that the filter is in the shape of a vertex-down cone, with a height of 6 inches and a diameter of 4 inches at its open (upper) end. We are also given that the liquid drips out the bottom of the filter at a constant rate of 3 cubic inches per second.

Let's let h be the height of the liquid in the cone, and let V be the volume of the liquid in the cone.

The volume of a cone is given by the formula:

V = (1/3)πr²h,

where r is the radius of the cone. Since the diameter of the cone at its open end is 4 inches, the radius is 2 inches. Thus, we have:

V = (1/3)π(2²)h = (4/3)πh.

Now, we need to find dh/dt, the rate at which the height of the liquid is dropping, when the liquid is 1 inch deep. Since the liquid is dripping out of the filter at a constant rate of change 3 cubic inches per second, we have:

dV/dt = -3.

Taking the derivative of the equation for V with respect to t, we get:

dV/dt = (4/3)π dh/dt.

Substituting -3 for dV/dt, and substituting 1 for h, we get:

-3 = (4/3)π dh/dt.

Solving for dh/dt, we get:

dh/dt = (-3)/(4/3)π = -9/(4π) inches per second.

Therefore, the level of the liquid is dropping at a rate of 9/(4π) inches per second when the liquid is 1 inch deep.

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The direction and magnitude of the resultant force is 7,870.1 lbs at 5.3 ° south of west.

We can start by breaking down the forces into their x and y components:

The force of 3700 lbs pulling west has an x-component of -3700 lbs and a y-component of 0 lbs.

The force of 4200 lbs pulling 10° north of west has an x-component of -4200 cos(10°) lbs and a y-component of 4200 sin(10°) lbs.

The x-component of the resultant force is;

Fx = -3700 lbs - 4200 cos(10°) lbs

Fx = -7,836.19 lbs

The y-component of the resultant force is;

Fy =  4200 sin(10°) lbs

Fy = 729.32 lbs

To find the magnitude and direction of the resultant force, we can use the Pythagorean theorem and inverse tangent function:

The magnitude of the resultant force is;

F = √(Fx² + Fy²)

F = √ (-7836.19² + 729.32²)

F = 7,870.1 lbs

The direction of the resultant force is;

θ = arc tan (Fy/Fx)

θ = arc tan (729.32 / 7836.19)

θ = 5.3⁰

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Answer:

(i) To find the actual area of the field represented on the map by a rectangle 6 cm long and 4 cm wide, we need to first convert the dimensions of the rectangle to actual units. Since the scale of the map is 1:20,000, this means that 1 cm on the map represents 20,000 cm in actuality.

The length of the rectangle on the map is 6 cm, so its actual length is:

6 cm x 20,000 cm/cm = 120,000 cm

Similarly, the width of the rectangle on the map is 4 cm, so its actual width is:

4 cm x 20,000 cm/cm = 80,000 cm

The actual area of the rectangle is then:

Actual area = actual length x actual width

Actual area = 120,000 cm x 80,000 cm

Actual area = 9,600,000,000 cm^2

Therefore, the actual area of the field represented on the map by a rectangle 6 cm long and 4 cm wide is 9,600,000,000 cm^2.

(ii) To convert the actual area to hectares, we need to divide by 10,000 m^2/ha, since 10,000 m^2 is equal to 1 hectare.

Actual area in hectares = (9,600,000,000 cm^2) / (10,000 m^2/ha)

Actual area in hectares = 960,000 m^2 / 10,000 m^2/ha

Actual area in hectares = 96 hectares

Therefore, the area of the field in hectares is 96 hectares.

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The effect of changing the sample sizes on the interval would depend on the relative size of the populations. Generally, a larger sample size will lead to a more precise interval, but if population X is much larger than population Y, then the size of the interval will not be affected much by the change.

If a random sample of 52 is selected from population x, and a random sample of 63 is selected from population y and when all other things remain constant, such a change in sample sizes will cause the margin of error to decrease.

When the sample size increases, the standard error of the mean decreases as well. Since the margin of error is directly linked to the standard error of the mean, this is the case. As a result, when the sample size is raised, the margin of error decreases.

The margin of error is a statistical concept that reflects the degree of uncertainty in a sample estimate. As a result, when the margin of error decreases, the precision of the results increases. As a result, when the sample size is increased, the data becomes more accurate.

So, when all other factors remain constant, an increase in sample size produces a more accurate result.

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Answer:

4

Step-by-step explanation:

k(2/9)=4

not 8

:)

The angle measure directly affects the length of the side opposite that angle in a triangle.

The larger the angle, the longer the side opposite it, and the smaller the angle, the shorter the side opposite it.

It appears that the student question is asking about the relationship between angle measures and the side opposite that angle.

This is a concept from triangle properties, specifically the Angle-Side relationship.
To answer this question, let's follow these steps:
1. Identify the angle in question.
2. Observe the side opposite the angle.
3. Determine the relationship between the angle measure and the side length.
Step 1: Identify the angle in question
The student question mentions an angle measure, but it is not clearly specified.

However, we can still discuss the general relationship between angle measures and the side opposite that angle in a triangle.
Step 2: Observe the side opposite the angle
In a triangle, each angle has a side that is directly opposite to it.

For example, in a triangle ABC, angle A is opposite to side BC, angle B is opposite to side AC, and angle C is opposite to side AB.
Step 3: Determine the relationship between the angle measure and the side length

This relationship is essential in understanding the properties of triangles and can be helpful in solving various geometry problems.
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Ordering the probabilities from most likely to occur to least likely to occur:

P(football, then volleyball) = 1/49

P(volleyball, then volleyball) = 1/25

P(baseball, then football, then volleyball) = 3/1000

P(baseball, then football, then football) = 5/2944

P(event) = (number of ways the event can occur) / (total number of possible outcomes)

P(volleyball, then volleyball) if the ball is replaced after the first selection:

The probability of selecting a volleyball on the first draw is:

P(volleyball on first draw) = 10/50 = 1/5

Since the ball is replaced after the first selection, the probability of selecting a volleyball on the second draw is also 1/5. Therefore:

P(volleyball, then volleyball) = P(volleyball on first draw) * P(volleyball on second draw) = 1/5 * 1/5 = 1/25

P(baseball, then football, then volleyball) if the balls are replaced after each selection:

The probability of selecting a baseball on the first draw is:

P(baseball on first draw) = 15/50 = 3/10

Since the ball is replaced after each selection, the probability of selecting a football and a volleyball on the second and third draw respectively is also 1/10. Therefore:

P(baseball, then football, then volleyball) = P(baseball on first draw) * P(football on second draw) * P(volleyball on third draw) = 3/10 * 1/10 * 1/10 = 3/1000

P(baseball, then football, then football) if the balls are not replaced after each selection:

The probability of selecting a baseball on the first draw is:

P(baseball on first draw) = 15/50 = 3/10

Since the ball is not replaced after the first selection, the probability of selecting a football on the second draw is:

P(football on second draw) = 5/49

Since the ball is not replaced after the second selection, the probability of selecting a football on the third draw is:

P(football on third draw) = 4/48

Therefore: P(baseball, then football, then football) = P(baseball on first draw) * P(football on second draw) * P(football on third draw) = 3/10 * 5/49 * 4/48 = 5/2944

P(football, then volleyball) if the ball is not replaced after the first selection:

The probability of selecting a football on the first draw is:

P(football on first draw) = 5/50 = 1/10

Since the ball is not replaced after the first selection, the probability of selecting a volleyball on the second draw is:

P(volleyball on second draw) = 10/49

Therefore: P(football, then volleyball) = P(football on first draw) * P(volleyball on second draw) = 1/10 * 10/49 = 1/49

Ordering the probabilities from most likely to occur to least likely to occur:

P(football, then volleyball) = 1/49

P(volleyball, then volleyball) = 1/25

P(baseball, then football, then volleyball) = 3/1000

P(baseball, then football, then football) = 5/2944

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The answer for the first triangle is 1 triangle(s) and the answer for the second triangle is 0 triangle(s).

According to the given measures, for the triangle with m∠E = 64°, g = 9, and e = 10, only 1 distinct triangle can be formed. In this case, the given angle is opposite the longest side, and hence one distinct triangle can be formed.

On the other hand, for the triangle with m∠J = 129°, k = 8, and j = 3, no distinct triangle can be formed as the given angle is greater than 90 degrees, which violates the triangle inequality theorem.

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Final cost of the item with an original price of $23 and a discount of 15% is $19.5 for given expression.

To calculate the final cost of an item that has a discounted price of 15%, we can use the expression p - 0.15p, where p is the original price of the item. Simplifying:

p - 0.15p = 0.85p

This means that the final cost of the item will be 85% of the original price.

If original price of the item is $23, substitute value into expression to find final cost:

0.85 x $23 = $19.55

Final cost of item with an original price of $23 and a discount of 15% is $19.55.

It's important to note that this calculation assumes that the discount is applied before any taxes or other fees. If there are additional costs associated with the item, such as sales tax, shipping, or handling fees, these should be added to the final cost separately.

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R'(-6, 0), S'(-1, 3), T'(2, -2), and U' are the vertices of the converted square R'S'T'U' (-3, -5).

A transformation in arithmetic is the process of altering the positioning, scale, form, or alignment of a polyhedron. You can think of transformations as functions that translate coordinates from one system to another, which might or might not be the same.

In mathematics, there are various different kinds of transformations, including: Translation: A figure is modified when it is moved a particular distance in one direction without affecting its symmetry or size. Reflection:

A transformation called a reflection flips an image across a line known as the line of reflective thinking. The image appears as just a mirror image of the original figure because the figure is projected across this line.

given

Applying the given transformation to each vertex of the original square RSTU will allow us to graph the transformed square R'S'T'U.

Vertex R'(-6, 0) changes from R(-2, 1):

-4 = -2 - 4, and -1 = 1 - 1

S(3, 4) converts to S'(-1, 3) at the vertex.

-1 = 3 - 4, and 2 = 4 - 1

Transformation of vertex T(6, -1) to T'(2, -2):

2 = 6 - 4, and -1 = -1 - 1

Vertex U(1, -4) changes to U'(-3, -5) because -3 = 1 - 4 and -4 = -4 - 1

R'(-6, 0), S'(-1, 3), T'(2, -2), and U' are the vertices of the converted square R'S'T'U' (-3, -5).

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question is -

Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU?

(–5, –3)

(3, –3)

(–1, –6)

(4, –9)

Answer:xplanation:

the additive inverse of a number is the opposite of the number. It is the amount you add to equal zero. 5 + -5 = 0 so -5 is the additive inverse of 5.

-2/3 + 2/3 =0 so 2/3 is the additive inverse of -2/3

Answer:

25?

Step-by-step explanation:

sorry if this is wrong

So, Isaac should pour 81 cubic inches of mixture into the pan.

Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

The volume of an object or substance can be determined by measuring its length, width, and height (in the case of a solid object), or by measuring the amount of space it occupies (in the case of a liquid or gas).

In mathematical terms, the volume of an object is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height. For irregularly shaped objects, the volume may be determined by displacement - that is, by measuring the amount of water or other fluid displaced by the object when it is immersed in the fluid.

To find the volume of the mixture that Isaac should pour into the pan, we need to find the volume of the pan itself and subtract the volume of the space that needs to be left empty.

The pan is in the shape of a rectangular prism, so its volume is:

V_pan [tex]= l *w * h = 9 in. * 9 in. * 2 in. = 162 in^{3}[/tex]

To leave room for the casserole to rise, Isaac should only fill the pan to a height of 1 inch. So, the volume of the space that needs to be left empty is:

V_empty [tex]= l *w * h = 9 in. * 9 in. * 2 in. = 81 in^{3}[/tex]

Therefore, the volume of the mixture that Isaac should pour into the pan is:

V = V_pan - V_empty[tex]= 162 in^{3} - 81 in^{3} = 81 in^{3}[/tex]

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Answer:

tan(sin^-1(-1)) is undefined.

The inverse sine function returns a value between -pi/2 and pi/2, and since sin(-pi/2) = -1, sin^-1(-1) = -pi/2. However, at -pi/2, the tangent function is undefined since it results in a vertical asymptote.

Banks and financial institutions offer card loans to people who do not apply for them for a variety of reasons, including to extend credit to those with a high risk of default, to attract potential customers, and to build customer loyalty.

A loan is an agreement between a borrower and a lender in which the borrower receives an amount of money (principal) from the lender, and agrees to repay the lender with interest. The terms of the loan usually specify the repayment period, interest rates, and fees associated with the loan. Examples of loans include mortgages, student loans, car loans, and personal loans.

Card loans are a type of revolving credit that allow people to borrow money from a bank or financial institution and then pay it back, with interest, over time. Banks and financial institutions offer card loans to people who do not apply for them for a variety of reasons.

First, card loans are offered to those who are considered high credit risks, such as those with no prior credit history or a low credit score. By offering card loans, banks and financial institutions can extend credit to these individuals and help them establish a credit history. The loan may come with a higher interest rate than those offered to individuals with good credit, but it can still be beneficial for those who need access to credit.

Second, card loans are often offered as a way to entice potential customers to open accounts with the bank or financial institution. Banks may offer a low introductory interest rate and other incentives, such as rewards or cash back, to encourage new customers to open an account with them.

Finally, banks and financial institutions may offer card loans to help build customer loyalty. When customers use a bank's card for their purchases and pay off their balance each month, they may become more likely to use the bank's other services in the future.

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Complete questions as follows-
Why, do you think, do banks and financial institutions offer card loans to people that do not apply for it?

We need to find the measure of angle m∠2.

Given that AB∥DE, C is the point of intersection of line AE and line DB, m∠1 = 80°, and m∠2 : m∠3 = 2 : 3.

Step 1: Identify the alternate interior angles. Since AB∥DE, we know that ∠1 and ∠2 are alternate interior angles.

Step 2: Use the property of alternate interior angles. The property of alternate interior angles states that if two parallel lines are cut by a transversal, the alternate interior angles are congruent. Therefore, m∠1 = m∠2.

Step 3: Substitute the given values. We know that m∠1 = 80°, so m∠2 = 80°. Hence, the measure of angle 2 (m∠2) is 80°.

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Answer: 1. 3(17-y)

Step-by-step explanation: multiply 3 to 17 and y, which you get (51) and (3). Subtract it to get 48, which is equivalent to 60 - 3y - 9 = 48

if it's wrong, i'm sorry

hope this helps!!

The probability that a randomly selected adult does not meet the "US-military"  standards is 16%.

The "IQ-scores" follow a normal distribution having mean = 100 and  standard deviation = 15.

In order to find the probability that a randomly selected adult does not meet US-military enlistment standards (which is an IQ score of less than 85),

We need to find the area under the normal-distribution curve to the left of 85,

Using the z-score formula, we can convert the IQ score of 85 to a standard score (z-score):

⇒ z = (x - μ)/σ,

Where x = IQ score, μ = mean, and σ = standard deviation.

Substituting the values,

We get,

⇒ z = (85 - 100)/15 = -1,

The area to left of -1 in a standard normal distribution table, we get approximately 0.1587 = 15.87% ≈ 16%.

Therefore, the required probability is 16%.

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Answer:

8 students are in the Environmental Club

Step-by-step explanation:

Answer: 5% of 160 is 8, so there are 8 students in the environmental club.

Step-by-step explanation: