IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=IQ of an individual. Round all answers to two decimal places.
A. X ~ N( ____ , ______ )
B. Find the probability that a randomly selected person's IQ is over 105.
C. A school offers special services for all children in the bottom 3% for IQ scores. What is the highest IQ score a child can have and still receive special services?
D. Find the Inter Quartile Range (IQR) for IQ scores.
Q1: ______
Q3: ______
IQR: ______

The point e. x = 5, y = 0 satisfies the two linear constraints simultaneously. We have two linear constraints which are given as;

2x + 5y ≤ 10 (Equation 1)

10x + 6y ≤ 42 (Equation 2)

We need to find the point which satisfies both equations. Let us plug in the values one by one to check which one satisfies the two equations simultaneously.

a. x= 6, y = 2

In Equation 1:2x + 5y = 2(6) + 5(2) = 17

In Equation 2:10x + 6y = 10(6) + 6(2) = 66

Thus, this point does not satisfy equations 1 and 2 simultaneously.

b. x=6, y=4

In Equation 1:2x + 5y = 2(6) + 5(4) = 28

In Equation 2:10x + 6y = 10(6) + 6(4) = 72

Thus, this point does not satisfy equations 1 and 2 simultaneously.

c. x=2, y = 1

In Equation 1:2x + 5y = 2(2) + 5(1) = 9

In Equation 2:10x + 6y = 10(2) + 6(1) = 26

Thus, this point does not satisfy equations 1 and 2 simultaneously.

d. x=2, y = 6

In Equation 1:2x + 5y = 2(2) + 5(6) = 32

In Equation 2:10x + 6y = 10(2) + 6(6) = 52

Thus, this point does not satisfy equations 1 and 2 simultaneously.

e. x = 5, y = 0

In Equation 1:2x + 5y = 2(5) + 5(0) = 10

In Equation 2:10x + 6y = 10(5) + 6(0) = 50

Thus, this point satisfies both equations simultaneously.

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The null hypothesis would not be rejected and the researcher would fail to find statistical significance at the chosen alpha level of .05.

If a researcher sets the alpha level at .05 and obtains a p-value of .06, it means that the p-value is greater than the chosen significance level. The alpha level, also known as the significance level, represents the threshold for determining whether the results are statistically significant or not.

In hypothesis testing, the null hypothesis assumes that there is no significant difference or relationship between variables.

If the p-value is less than or equal to the alpha level, it suggests that there is enough evidence to reject the null hypothesis and conclude that there is a significant difference or relationship.

However, if the p-value is greater than the alpha level, as in this case with a p-value of .06, it means that the observed data does not provide sufficient evidence to reject the null hypothesis.

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Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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Justin"s heart rate decreased 3 beats per minute for each of next 4 minutes

Let his heart rate be be 1

For the first minutes

1 minute his heart rate was 1 - 3 = -2

This is because the heart rate is decreasing 3 beats per minutes

2minutes later, his heart beat will be -2 -3

-2 - 3 = -5

3 minutes later, his heart beat will be -5 - 3

-5 - 3 = -8

4 minutes later, -8 - 3

-8 - 3 = -11

Change = Final heart beat - initial heart beat / initial heart beat

Change = -11 -2 / -2

Change = -13/-2

Change = 13/2

= 6.5

Answer:

7/8+4 there you go I'm help that I help you

To find the slope intercept form, solve the equation for y.

Solve the equation for x:

Answer:

The value of b is 5 times the value of a.

Step-by-step explanation:

The rule that describes the pattern in the table is that the value of b is 5 times the value of a.

Option A is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The table shows two sets of values, a and b, where b is obtained by multiplying a by 5.

For example, when a = 1, b = 5, and when a = 2, b = 10.

This pattern continues throughout the table.

Therefore,

The rule that describes the pattern in the table is that the value of b is 5 times the value of a.

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Considering the factors of time and cost, strategic alliances generally emerge as the quickest and cheapest way to develop a global strategy. (option c)

Strategic alliances involve partnerships or collaborations between companies from different countries, with the goal of leveraging each other's strengths to achieve mutual benefits.

By sharing resources, knowledge, and networks, companies can expand their global presence more efficiently and cost-effectively. Strategic alliances can enable faster market entry and access to new markets by leveraging the partner's existing infrastructure, distribution channels, and customer base.

Moreover, pooling resources can help reduce costs and risks associated with global expansion.

Therefore, strategic alliances can be a relatively quicker and cheaper way to develop a global strategy, as they provide an opportunity to tap into existing capabilities and market presence of the alliance partner.

Hence the correct option is (c).

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Step-by-step explanation:

the answer is in the above image

Answer:

\(-12^{2}\) + 9a - 5

Step-by-step explanation:

combine like terms :

-7\(a^{2}\) - 5\(a^{2}\) = -12\(a^{2}\)  

+3a - (-6a) = 9a    

-9 - (-4) = -5          

Answer:

x = 50°

Step-by-step explanation:

Recall that for a triangle, the exterior angle is equal to the sum of its two remove interior angles (also see attached for reference).

in our case, the exterior angle is given as 105° and its two remote interior angles are x and 55°

therefore

105° = 55° + x

x = 105° - 55°

x = 50°

Answer:

B. 50°

Step-by-step explanation:

Answer:

-100

Step-by-step explanation:

(-5)^2- (-5)^3=

25-125= -100

Hey there!

plug in the value of w and solve:

(-5)²-(-5)³

25-(-125)

25-125

-100

Hence, -100 is the answer.

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:-)

Using the point-slope form of a linear equation, the equation of the line passing through point Q(x,y) with slope m -1/2 is: y = -1/2x + (Qy + 1/2Qx).

what is perpendicular lines?

In geometry, two lines are said to be perpendicular if they intersect each other at a right angle (90 degrees). This means that the angles formed at the point of intersection are equal to 90 degrees.

A. To write an equation of the line that is parallel to line f (y=2) and passes through point Q, we know that parallel lines have the same slope. Therefore, the slope of the new line will also be 2. Using the point-slope form of a linear equation, the equation of the line passing through point Q(x,y) with slope m=2 is:

y - y1 = m(x - x1)

y - Qy = 2(x - Qx)

y - Qy = 2x - 2Qx

y = 2x + (Qy - 2Qx)

B. To write an equation of the line that is parallel to line g (y=2x-1) and passes through point P, we know that parallel lines have the same slope. Therefore, the slope of the new line will also be 2. Using the point-slope form of a linear equation, the equation of the line passing through point P(x,y) with slope m=2 is:

y - y1 = m(x - x1)

y - Py = 2(x - Px)

y - Py = 2x - 2Px

y = 2x + (Py - 2Px)

C. To write an equation of the line that is perpendicular to line f (y=2) and passes through point Q, we know that the slope of the new line will be negative reciprocal of slope of f, which is -1/2. Using the point-slope form of a linear equation, the equation of the line passing through point Q(x,y) with slope m=-1/2 is:

y - y1 = m(x - x1)

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

y - Qy = -1/2x + 1/2Qx

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

D. To write an equation of the line that is perpendicular to line g (y=2x-1) and passes through point Q, we know that the slope of the new line will be negative reciprocal of slope of g, which is -1/2.

Therefore,Using the point-slope form of a linear equation, the equation of the line passing through point Q(x,y) with slope m=-1/2 is:

y - y1 = m(x - x1)

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

y - Qy = -1/2x + 1/2Qx

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

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(a) To find the value of c that makes f(x,y) a probability density function, we need to ensure that the double integral of f(x,y) over the entire plane equals 1.

Thus, we have:

Integral from -infinity to infinity of Integral from -infinity to infinity of c(1-x-y) dxdy = 1

Solving this integral gives us:

c = 2

Thus, c = 2 makes f(x,y) a probability density function.

(b) To find the expected values of X and Y, we need to calculate the double integrals of xf(x,y) and yf(x,y) over the entire plane, respectively. Thus, we have:

E(X) = Integral from -infinity to infinity of Integral from -infinity to infinity of x(2(1-x-y)) dxdy = 1/3

E(Y) = Integral from -infinity to infinity of Integral from -infinity to infinity of y(2(1-x-y)) dxdy = 1/3

(c) To determine if X and Y are independent, we need to check if the joint distribution f(x,y) can be factored into the product of the marginal distributions of X and Y, respectively. Thus, we have:

f(x,y) = 2(1-x-y)

f_X(x) = Integral from -infinity to infinity of f(x,y) dy = 2(1-x) for 0<x<1, and 0 otherwise

f_Y(y) = Integral from -infinity to infinity of f(x,y) dx = 2(1-y) for 0<y<1, and 0 otherwise

Multiplying f_X(x) and f_Y(y) together, we get:

f_X(x)*f_Y(y) = 4(1-x)(1-y) for 0<x<1 and 0<y<1, and 0 otherwise

Since f(x,y) does not factor into the product of the marginal distributions f_X(x) and f_Y(y), X and Y are not independent.

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To reject the null hypothesis, the calculated Chi-square value should be equal to or greater than the critical value of 7.82.

To determine the required calculated value to reject the null hypothesis using a one-way Chi-square test, we need to refer to the Chi-square distribution table or use statistical software.

In this case, since there are 4 flavors of yogurt, the degrees of freedom for the Chi-square test would be (4-1) = 3.

At the 0.05 level of significance, the critical value from the Chi-square distribution table with 3 degrees of freedom is approximately 7.82.

Therefore, the correct answer is:

D. Equal to or greater than 7.82

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Answer:

every option but the first one

Step-by-step explanation:

5 and 7 are verticals meaning they have the same angle degree

7 and 4 are supplementary angles meaning the sum of them = 180

1 and 7 are corresponding meaning they have the same angle degree

18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

Answer:

70

Step-by-step explanation:

solution

total balls: 100

red balls:70

blue balls: 30

balls picked:5

Now,

probability of all picked balls being red: 70

Answer: 70



Step-by-step explanation:

The probability of picking a red ball on a single draw is 70/100 = 0.7 since there are 70 red balls out of 100 total balls.

With replacement means that after each draw, the ball is placed back into the pool, so the total number of balls remains the same.

Therefore, the probability of picking all five red balls can be calculated as follows:

P(5 red balls) = (0.7)^5 = 0.16807

So the probability of picking all five red balls with replacement is approximately 0.16807 or 16.807%.

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When comparing variables x and y that are in the list '(AB), the comparison function we use is EQ.

Here's an explanation:

In Lisp, the EQ operator compares whether the two arguments are the same memory location.

EQV, on the other hand, checks whether the two values being compared are equivalent to each other.

For example, EQV will return true for two identical strings, while EQ will not.

The comparison function that should be used to compare variables x and y, which are both in the list '(AB), is EQ.

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Answer:

oi bruv

Step-by-step explanation:

Answer: Q1.=145, Q2.=20

Step-by-step explanation:

two supplementary angles equal 180

1. 180-35=145

2 . complementary angles , both add up to 90

90-70=20

Answer:

13.3041346957 Ft. ( Or 13.30 Ft. )

Step-by-step explanation:

Formula: A^2 + B^2 = C^2

Substitution: 9^2 + 6^2 = 117

√177 = 13.3041346957

13.3041346957 ( Rounded ( Hundredths Place ) = 13.30 Ft .

The f(5) for the given function f(x) is equal to 29.

We have,

f(x) = {x³     x< -3

         2x² -9   -3≤x<4

          5x+ 4       x≥4}

To determine f(5) for the function f(x), we need to evaluate the function at x = 5.

Let's consider the different cases based on the given piecewise definition of f(x):

For x < -3:

Since 5 is not less than -3, this case does not apply to the value we are evaluating.

For -3 <= x < 4:

Again, 5 does not fall within this range. Therefore, this case also does not apply.

For x >= 4:

Since 5 is greater than or equal to 4, this case applies. In this case, the function is defined as 5x + 4. So, substituting x = 5 into this equation, we get:

f(5) = 5(5) + 4

f(5) = 25 + 4

f(5) = 29

Therefore, f(5) for the given function f(x) is equal to 29.

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Check the picture below.

Answer: each store gets 787 pairs and 1 is left over

Step-by-step explanation:Divide 4723 by 6

SOLUTIONS

Using a desmos graphing to graph the function

This is the concept of transformations, given the function given by f(x)=1/10(10)^x, when the function is reflected along the y-axis the new function will be given by f(x)=1/10(10)^(-x). This will mirror the original function.

The reflection will be

a. The initial size of the bacteria colony is 1 gram.

b. The growth rate for this bacteria colony is 25% per day.

c. The size of the bacteria colony after t days is given by the equation S(t) = 1 * e^(0.25t) grams.

d. To find when the colony size reaches 5 grams, we need to solve the equation 5 = 1 * e^(0.25t) for t. Taking the natural logarithm of both sides and rearranging, we get t = ln(5)/0.25 ≈ 8.7 days.

e. The doubling time for this colony is approximately 2.77 days, which is found by solving the equation 2 = 1 * e^(0.25t) for t. Taking the natural logarithm of both sides and rearranging, we get t = ln(2)/0.25 ≈ 2.77 days.

The law of uninhibited growth states that the growth rate of a population is proportional to its size, and there are no limiting factors that affect the growth. In this problem, the size of the bacteria colony is modeled using an exponential function, where the initial size of the colony is 1 gram and the growth rate is 25% per day.

To find the size of the colony after a certain number of days, we can substitute the given value of t into the equation S(t) = 1 * e^(0.25t). For example, after 5 days, the size of the colony is S(5) = 1 * e^(0.25*5) ≈ 2.28 grams.

To find when the colony size reaches a certain value, we need to solve the exponential equation S(t) = 1 * e^(0.25t) = A, where A is the desired size. Taking the natural logarithm of both sides and rearranging, we get t = ln(A)/0.25. For example, to find when the colony size reaches 5 grams, we solve the equation 5 = 1 * e^(0.25t) for t and get t = ln(5)/0.25 ≈ 8.7 days.

The doubling time is the time it takes for the population to double in size. In this case, we need to solve the exponential equation 2 = 1 * e^(0.25t) for t. Taking the natural logarithm of both sides and rearranging, we get t = ln(2)/0.25 ≈ 2.77 days.

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Putting the considered items in order from most expensive to least expensive item gives the order as shown by: Option b. Blender, ink, hat, heater

Markup is the amount that will be increased in the original price of the considered thing.

Markdown is the amount that will be decreased from the original price of the considered thing.

Think of "up" and "down" as increasing and decreasing prices respectively.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

For this case, the base prices and the chage in price is given as:

Item                Base Price                    Change Direction

Blender            $29.73                           9% Markdown

Hat                   $14.16                             77% Markup

Ink                    $20.17                            27% Markup

Heater             $28.46                           22% Markdown

Calculating the resultant price:

Resultant price = 29.73 - 9% of 29.73

\(P= 29.73 - \dfrac{29.73}{100}\times 9\\\\P = 27.0543 \: \: \text{dollars}\)

Resultant price = 14.16 + 77% of 14.16

\(P= 14.16+\dfrac{14.16}{100}\times 77\\\\P = 25.0632\: \: \text{dollars}\)

Resultant price = 20.17 + 27% of 20.17

\(P= 20.17+\dfrac{20.17}{100}\times 27\\\\P = 25.6159\: \: \text{dollars}\)

Resultant price = 28.46 - 22% of 28.46

\(P= 28.46- \dfrac{28.46}{100}\times 22\\\\P = 25.0448 \: \: \text{dollars}\)

Thus, putting the considered items in order from most expensive to least expensive item gives the order as shown by: Option b. Blender, ink, hat, heater

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Answer:

to establish a point from which to measure future distance

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

We are given that

\(f(x)=0.1x^4-0.5x^3-3.3x^2+7.7x-1.99\)

We have to find the positive value of b.

\(\lim_{x\rightarrow b}f(x)=2\)

\(\lim_{x\rightarrow b}(0.1x^4-0.5x^3-3.3x^2+7.7x-1.99)=2\)

\(0.1b^4-0.5b^3-3.3b^2+7.7b-1.99=2\)

\(0.1b^4-0.5b^3-3.3b^2+7.7b-1.99-2=0\)

\(0.1b^4-0.5b^3-3.3b^2+7.7b-3.99=0\)

\(10b^4-50b^3-330b^2+770b-399=0\)

Let

\(g(b)=10b^4-50b^3-330b^2+770b-399\)

Using Discartes' rule of sign

There are number of sign changes are 3.

Therefore, the positive real roots are 3 or 1.

\(g(-b)=10b^4+50b^3-330b^2-770b-399\)

There are number of sign changes are  1 .

Therefore, negative real roots  are 1.

When negative root is 1 .Then , positive real roots are 3 because total number of roots are 4.

Hence, positive values of b=3