A random sample of 487 nonsmoking women of normal weight (body mass index between 19.8 and 26.0) who had given birth at a large metropolitan medical center was selected. It was determined that 7.2% of these births resulted in children of low birth weight (less than 2500 g) Calculate a confidence interval (C) using a confidence level of 99% for the proportion of all such births that result in children of low birth weight.

Answer:

$0.56, or 56¢.

Step-by-step explanation:

According to the picture, there are two dimes, two nickels, a penny, and a quarter.

A penny is worth $0.01.

A nickel is worth $0.05.

A dime is worth $0.10.

A quarter is worth $0.25.

2(0.1) + 2(0.05) + (0.01) + (0.25) = 0.2 + 0.1 + 0.01 + 0.25 = 0.3 + 0.26 = 0.56.

So, Vivian is using $0.56, or 56¢, to buy a toy. That's a cheap one!

Hope this helps!

Given:

The expressions are:

\(2x(x^2-6x+3)\)

\(2a^2(5b^2+3ab+6a+1)\)

To find:

The product of each expression.

Solution:

According to the distributive property of multiplication over addition, we get

\(a(b+c)=ab+ac\)

The first expression is:

\(2x(x^2-6x+3)\)

Using distributive property of multiplication over addition, we get

\(2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)\)

\(2x(x^2-6x+3)=2x^3-12x^2+6x\)

Therefore, the product of \(2x(x^2-6x+3)\) is \(2x^3-12x^2+6x\).

The second expression is:

\(2a^2(5b^2+3ab+6a+1)\)

Using distributive property of multiplication over addition, we get

\(2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)\)

\(2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2\)

Therefore, the product of \(2a^2(5b^2+3ab+6a+1)\) is \(10a^2b^2+6a^3b+12a^3+2a^2\).

Answer:

104degrees

Step-by-step explanation:

From the given diagram, line LJ bisects KN, hence arcKL = arcHJ

Given

arHJ = 4x

arc KJ = x+39

Equating both

4x = x+39

4x - x = 39

3x = 39

x = 39/3

x = 13

Since arcHK = arcHJ + arcKJ

arcHK = x+39+4x

arcHK = 5x+39

arcHK = 5(13) + 39

arcHK = 65+39

arcHK = 104degrees

Hence the measure of arcHK is 104degrees

Answer:

2 distance

Step-by-step explanation:

you solve it and see it's easy know first try I will do it

from Chicago to Atlanta is 700 miles, so in plain-vanilla shipping costs for that will be $240 per every 100 lbs.

if we're shipping 2,000 lbs, hmmm that's 2000/100 = 20, so 100 lbs 20 times, so our plain-vanillla cost will be 20 * 240 = 4800 bucks.

Now, we're Da Bomb, and hell, why not, let's ship it on a 3-5 day, but that has a Premium of an extra 20%, hmmm that means our cost using 3-5 days service is 4800 + 20%.

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 4800}}{\left( \cfrac{20}{100} \right)4800}\implies 960~\hfill \underset{final~cost}{\stackrel{4800~~ + ~~960}{5760}}\)

The relative frequency of heads is reasonably close to 40%.Mr. Clark's claim about the theoretical probability is likely to be false. This means that the theoretical probability of tails is most likely 0.60.

The relative frequency is the ratio of the number of times an event occurred to the total number of trials. In this case, the relative frequency of heads is 0.38 and tails is 0.62.The theoretical probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Here, Mr. Clark claims that the coin is weighted so that the probability of heads is 40%. Therefore, the theoretical probability of heads is 0.40.However, the relative frequency of heads after 200 trials is only 0.38, which is reasonably close to 0.40. Hence, the relative frequency of heads is reasonably close to 40%.

Mr. Clark's claim about the theoretical probability of heads is likely to be false because the relative frequency of heads is less than the theoretical probability of heads (0.38 < 0.40).Therefore, the theoretical probability of tails is 1 - 0.40 = 0.60 because the coin is fair, so the probabilities of heads and tails should add up to 1. Thus, the theoretical probability of tails is most likely 0.60.

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Answer:

12

Step-by-step explanation:

He is running 12

There is no association between the chicken preferences and rice preferences. Option C

There is an association between two variables when they both decrease or increase simultaneously. In many cases, the association between the variables can be shown using the correlation coefficient when the relationship is plotted on Cartesian coordinates.

If we look at the table, we can see that there is no association between the chicken preferences and rice preferences because because the proportion of chicken and rice eaters to all chicken eaters is lower than all rice eaters to all eaters; and because the proportion of chicken and rice eaters to all rice eaters is lower than all chicken eaters to all eaters.

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In the preceding equation, x has the value -2/11.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality. Usually, it only has one variable and an equal sign. as in 2x - 4 Equals 2.

Equations can be categorized as identities or conditional equations.

6x+2x-17+6x-1-3x+20=0

14x-3x=18-20

11x=-2

x= -2/11

Therefore, in the preceding equation, x has the value -2/11.

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The interval that contains the root of f(x) = 2x − x3 + 0.5 is [-2, -1].

To find which interval contains the root of the equation f(x) = 2x − x3 + 0.5, we can use the intermediate value theorem. This theorem states that if a function is continuous on a closed interval [a, b], and takes on values f(a) and f(b) at the endpoints, then for any value y between f(a) and f(b), there exists a value c in [a, b] such that f(c) = y.

In this case, we can evaluate f(x) at the endpoints of the intervals [-2, -1], [-1, 0], [0, 1], and [1, 2], as follows

For [-2, -1]: f(-2) = -11.5 and f(-1) = 1.5
For [-1, 0]: f(-1) = 1.5 and f(0) = 0.5
For [0, 1]: f(0) = 0.5 and f(1) = 1.5
For [1, 2]: f(1) = 1.5 and f(2) = -11.5

From this, we can see that the function changes sign from negative to positive in the interval [-2, -1], which means there must be a root in this interval. We can also see that the function is positive throughout the interval [1, 2], so there cannot be a root in this interval. The intervals [-1, 0] and [0, 1] do not change sign, so we cannot conclude whether or not there is a root in these intervals.

Therefore, the interval that contains the root of f(x) = 2x − x3 + 0.5 is [-2, -1].

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Answer:

b

Step-by-step explanation:

The t-statistic has 17 degrees of freedom. If the sample size had been 2, the t-statistic would have 1 degree of freedom.

A The t-statistic has 17 degrees of freedom In a t-test, the degrees of freedom (df) represent the number of independent observations available for estimating the population parameters. For a sample of size n, the degrees of freedom in a t-test are calculated as n - 1. In this case, the sample size is 18, so the degrees of freedom for the t-statistic would be 18 - 1 = 17.

b) If the sample size had been 2, the t-statistic would have 1 degree of freedom.

Similarly, if the sample size were 2, the degrees of freedom for the t-statistic would be 2 - 1 = 1. The reason for this is that when the sample size is small, the t-distribution becomes highly influenced by the limited number of observations, resulting in fewer degrees of freedom

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Answer:

-162

Step-by-step explanation:

Answer:

-162

Step-by-step explanation:

because -162 is negative

Answer:

Step-by-step explanation:

sum of ngles of triangle=180

90+39+A=180

129+a=180

A=180-129

apply the some rule:

since 39 = opp/hyp

sin39=16/c

sin 51 = opp/hyp

sin51=a/25.42415166

(a) The exact perimeter is 4√2 ft

(b) An approximation of the perimeter to the nearest tenth of a foot is 5.7 ft.

Given the area of the painting is 2 ft².

To find the perimeter of the painting, we need to find the side of the square painting and then the perimeter of the square painting.

(a) Calculation of exact perimeter:

Let the side of the square painting be a.

Perimeter of the square painting = 4a. (Since all the sides are equal)Area of the painting = a² = 2 ft²

Taking square root on both sides, we get,a = √2 ft

Therefore, the perimeter of the painting = 4a= 4 √2 ft

Therefore, the exact perimeter of the painting is 4 √2 ft.

(b) Calculation of approximation of the perimeter:

Given, √2 ≈ 1.414We have already found that, a = √2 ft

Therefore, the perimeter of the painting = 4a≈ 4 × 1.414 ft≈ 5.656 ft

Therefore, an approximation of the perimeter to the nearest tenth of a foot is 5.7 ft (rounded off to one decimal place).

Hence, the required answers are (a) 4√2 ft and (b) 5.7 ft.

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Therefore, the answer is DNE.

The function \(f(x) = { 2x + 2, x < 9 936 - 2x, x > 9\)

We need to find the limit of f(x) as x approaches 9- (left-hand limit).

Let's first find the right-hand limit:\(lim x→9+ f(x)= lim x→9+ (936 - 2x) = 936 - 2(9) = 918\)

Now, let's find the left-hand limit:\(lim x→9- f(x) = lim x→9- (2x + 2)= 2(9) + 2= 20\)

As the left-hand limit is not equal to the right-hand limit, the limit does not exist.

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A relationship between a causal variable and a dependent variable within one value of another causal variable is known as a conditional relationship.

A relationship between a causal variable and a dependent variable within one value of another causal variable is known as a conditional relationship or a moderated relationship. In this type of relationship, the relationship between the causal variable and the dependent variable is not fixed, but instead depends on the level or value of the moderating variable.

For example, let's say we want to investigate the relationship between exercise and weight loss, and we suspect that age may moderate this relationship. In other words, we think that the relationship between exercise and weight loss may be different for different age groups. We might find that for younger people, exercise is a strong predictor of weight loss, while for older people, exercise has little to no effect on weight loss. In this case, age is the moderating variable that affects the relationship between exercise and weight loss.

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How to draw a circle: place the needle of your compass at the centre coordinate. Then extend the pencil tip to the given length of the radius

If you follow these steps, you will get the following graphs:

Hope it helps!

We know that:

Let's plot the circles one by one.

Circle A:

Finding x and y:

Substitute the radius and the coordinates in the equation:

Plot the equation on the graph to obtain circle A.

~Refer to attachment #1~

Circle B:

Finding x and y:

Substitute the radius and the coordinates in the equation:

Plot the equation on the graph to obtain circle B.

~Refer to attachment #2~

Answer:

D

Step-by-step explanation:

Answer:

a c e f

Step-by-step explanation:

its simple

Answer:

C, E, F

Step-by-step explanation:

A:

ratio of lengths of sides = (9 m)/(3 m) = 3

Any rectangle in which the lengths of two adjacent sides is 3:1 is a scaled version.

B: 10/4 = 2.5, not 3

C: 13.5/4.5 = 3, this works

D: 8/2 = 4, not 3

E: 18/6 = 3, this works

F: 4.5/1.5 = 3, this works

Answer: C, E, F

Answer:

\(T_n=(4-n)\text{log}_a(3)+\text{log}_a(2)\)

Step-by-step explanation:

nth term of an A.P. is given by the explicit formula,

\(T_n=a+(n-1)d\)

Here, 'a' = First term

n = number of term

d = common difference

For an A.P. given as,

\(\text{log}_a(54),\text{log}_a(18),\text{log}_a(6),....\)

First term 'a' of the given A.P. = \(\text{log}_a(54),\)

Common difference 'd' = \(T_2-T_1\)

                                       = \(\text{log}_a(18)-\text{log}_a(54)\)

                                       = \(\text{log}_a(\frac{18}{54})\)

                                       = \(\text{log}_a(\frac{1}{3})\)

                                       = \(-\text{log}_a(3)\)

\(T_n=\text{log}_a(54)+(n-1)[-\text{log}_a(3)]\)

    \(=\text{log}_a(54)-(n-1)\text{log}_a(3)\)

    \(=\text{log}_a(3^3\times 2)-(n-1)\text{log}_a(3)\)

    \(=\text{log}_a(3^3)+\text{log}_a(2)-(n-1)\text{log}_a(3)\)

    \(=3\text{log}_a(3)+\text{log}_a(2)-(n-1)\text{log}_a(3)\)

    \(=3\text{log}_a(3)+\text{log}_a(2)-n\text{log}_a(3)+\text{log}_a(3)\)

    \(=4\text{log}_a(3)+\text{log}_a(2)-n\text{log}_a(3)\)

    \(=(4-n)\text{log}_a(3)+\text{log}_a(2)\)

The gradient of `g(x,y)` is `[7, -36]` evaluated at point `P(-2,1)`.

Given function: `g(x,y) = x² − 4x²y − 5xy²`.

To find the gradient of the given function, we need to find its partial derivatives with respect to x and y.

Step-by-step explanation: Let's find the partial derivative of `g(x,y)` with respect to `x`.

To do that, differentiate `g(x,y)` with respect to `x` by treating `y` as a constant.

g(x,y) = `x² − 4x²y − 5xy²`∂g/∂x = `2x − 8xy − 5y²`

This is the partial derivative of `g(x,y)` with respect to `x`.

Let's now find the partial derivative of `g(x,y)` with respect to `y`. To do that, differentiate `g(x,y)` with respect to `y` by treating `x` as a constant.

g(x,y) = `x² − 4x²y − 5xy²`∂g/∂y = `-4x² − 10xy`

This is the partial derivative of `g(x,y)` with respect to `y`.

The gradient of `g(x,y)` is the vector of its partial derivatives.

Therefore, the gradient of `g(x,y)` is given by:

grad `g(x,y)` = ∇`g(x,y)` = [∂g/∂x, ∂g/∂y]

On substituting the partial derivatives of `g(x,y)` obtained earlier, we get:

grad `g(x,y)` = ∇`g(x,y)` = [2x − 8xy − 5y², -4x² − 10xy]

Now, we need to evaluate the gradient of `g(x,y)` at point `P(-2, 1)`.

Substitute `x = -2` and `y = 1` in the gradient we obtained to find the gradient at `P(-2,1)`.

grad `g(-2,1)` = [2(-2) − 8(-2)(1) − 5(1)², -4(-2)² − 10(-2)(1)]

grad `g(-2,1)` = [-4 + 16 - 5, -16 + (-20)]

grad `g(-2,1)` = [7, -36]

Hence, the gradient of `g(x,y)` is `[7, -36]` evaluated at point `P(-2,1)`.

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Answer: the probability is 1/221

Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.

Let's define the decision variables:

Let C represent the number of chairs produced.

Let T represent the number of tables produced.

Objective function:

The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:

Profit = 150C + 750T

Constraints:

Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:

5C + 3T ≤ 240

Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:

4C + 20T ≤ 700

Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:

C ≥ 0

T ≥ 0

Now, we can solve the linear programming problem to find the optimal solution:

Maximize: Profit = 150C + 750T

Subject to:

5C + 3T ≤ 240 (Labor constraint)

4C + 20T ≤ 700 (Material constraint)

C ≥ 0

T ≥ 0

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Answer:

a.

\(h=\dfrac{2A}{b}\)

b.

A = 220 mm²

b = 20 mm

\(h=\dfrac{2 \cdot 220}{20}=22 \: {mm}\)

Answer:

A=1/2bh

2*A=1/2bh*2

2A/b=bh/b

h=2A/b

b)h=2(220)/20

height=22mm

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3x equals 36

x equals 12

The algebraic expression that represents the given phrase is b + 15 = 180.

The algebraic expression that represents the phrase "the sum of the number of boys and 15 girls is 180" is:b + 15 = 180Explanation:Let's assume that the number of boys is "b".

According to the question, the total number of students in the class can be calculated by adding the number of boys (b) to the number of girls (15) which is equal to 180 students.Using algebra,

we can write this statement as an equation: b + 15 = 180Hence, the algebraic expression that represents the given phrase is b + 15 = 180

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The complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'

In this question, we have been given some information about lines a, b, k and m.

We need use this information and determine which lines in the figure are parallel.

We have been given angle 2 is supplementary to angle 3.

We know that, the sum of the angles on the same side of the transversal which are inside the two parallel lines is always 180°

Also, supplementary angles are the angles whose sum is 180°

i.e., ∠2 + ∠3 = 180°

From above we conclude that, the lines and b are parallel and line k would be the transversal.

Therefore, the complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'

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