Graph the Exponential Function y = log5 (x) by plotting the Horizontal Intercept and one other point

To calculate the confidence interval (CI) for the proportion of all births that result in children of low birth weight, we can use the formula for estimating the proportion with a given confidence level.

Given:

Sample size (n) = 487

Proportion of low birth weight births (cap on p) = 0.072 (7.2%)

Confidence level = 99% (α = 0.01)

To calculate the confidence interval, we can use the formula:

CI = cap on p ± Z * sqrt((cap on p * (1 - cap on p)) / n)

where Z is the z-score corresponding to the desired confidence level.

Step 1: Calculate the z-score.

For a 99% confidence level, the z-score is 2.58 (obtained from standard normal distribution tables).

Step 2: Calculate the margin of error.

Margin of error = Z * sqrt((cap on p * (1 - cap on p)) / n)

= 2.58 * sqrt((0.072 * (1 - 0.072)) / 487)

Step 3: Calculate the confidence interval.

CI = cap on p ± Margin of error

Now, substituting the values into the formula:

Margin of error ≈ 2.58 * sqrt((0.072 * 0.928) / 487)

≈ 2.58 * sqrt(0.066816 / 487)

≈ 2.58 * sqrt(0.000137345)

CI = 0.072 ± Margin of error

= 0.072 ± 2.58 * sqrt(0.000137345)

Finally, we can calculate the confidence interval:

Lower limit = 0.072 - (2.58 * sqrt(0.000137345))

Upper limit = 0.072 + (2.58 * sqrt(0.000137345))

Lower limit ≈ 0.072 - 2.58 * 0.01171

≈ 0.072 - 0.03018

≈ 0.04182

Upper limit ≈ 0.072 + 2.58 * 0.01171

≈ 0.072 + 0.03018

≈ 0.10218

Therefore, the 99% confidence interval for the proportion of all births resulting in children of low birth weight is approximately 0.04182 to 0.10218.

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After 6 years the population of goats on the small island reaches 1000.

It is the rate of increases of population per individual in the population. The term related to time period and entire population.

given, initial population of goat on the smallest island, N° =2,

after t years the population of goats on this island, N= 1000

the maximum goat carrying capacity of this island, K= 1500

per capita growth rate, r = 0.5 per year

now, we use logistic growth equation, dN/dt = r×N[(K-N)/K]

                                                           dN/dt = 0.5×1000{1500-1000)/1500}

                                                                    dN/dt= 166.67

                                                             ∫dN/166.67 = ∫dt

                                                         by integrating both sides

                                               N/166.67 = t+c , where c is the

                                                     integration constant

                                                    at time t=0, N°=2

                                                        c= 0.012

                                                 N/166.67 =t+0.12

                                    as N=1000 , t= 5.99 years

hence, after 6 years the population of goat on the island reaches 1000.

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Answer:

the bigger box

256cm² = 16cm (each side)

the smallest box

64cm²= 8cm (each side)

calculate

16cm-8cm

=8cm

8cm÷2

final answer :-

4 cm

HOPE THIS HELPS

Answer: 6

Step-by-step explanation:

From the question, we are informed that a factory uses 1/8 of a barrel of raisins in each batch of granola bars and that the factory used 3/4 of a barrel of raisins yesterday.

To calculate the number of batches of granola bars that the factory made yesterday, we divide 3/4 by 1/8. This will be:

= 3/4 ÷ 1/8

= 3/4 × 8/1

= 24/4

= 6

The company made 6 batches of granola bars

It is worth noting that there are many other possible choices for a and b that satisfy ab=0. This is because there are many ways to construct matrices with a row or column of zeros, and many ways to choose the nonzero entries in the other positions.

To find nonzero 2x2 matrices a and b such that ab=0, we need to find matrices a and b whose product is the zero matrix. A matrix multiplication is a combination of dot products between rows and columns of the two matrices. In order for the product of two matrices to be zero, one or both of the matrices must have a row of zeros or a column of zeros.

One way to construct such matrices is to set one of the matrices to have a row of zeros and the other to have a column of zeros. Let a be a matrix with a row of zeros and b be a matrix with a column of zeros, but with a nonzero entry in a different position. For example, we could choose:

a = [0 0; 1 0]

b = [0 1; 0 0]

Then, the product ab is:

ab = [0 0; 1 0] * [0 1; 0 0] = [0 0; 0 0]

So, we have found two nonzero 2x2 matrices a and b such that ab=0.

It is worth noting that there are many other possible choices for a and b that satisfy ab=0. This is because there are many ways to construct matrices with a row or column of zeros, and many ways to choose the nonzero entries in the other positions.

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Answer: l think it's none of the others

Step-by-step explanation:

(a)The moment generating function of a random variable X is expected value of e^(tX) .(b) The mean of Y will be the sum of the means of X₁, X₂, and X₃ .(c)The CDF gives the probability that the random variable<=specific value.

(a) The moment generating function of a random variable X is defined as the expected value of e^(tX). For independent random variables, the mgf of the sum is equal to the product of their individual mgfs. In this case, the mgf of Y can be calculated as the product of the mgfs of X₁, X₂, and X₃. (b) The distribution of Y can be obtained by convolving the probability density functions (PDFs) of X₁, X₂, and X₃. Since X₁, X₂, and X₃ are normally distributed, the sum Y will also follow a normal distribution.

The mean of Y will be the sum of the means of X₁, X₂, and X₃ and the variance of Y will be the sum of the variances of X₁, X₂, and X₃. (c) To find the probability P(Y < W), we need to evaluate the cumulative distribution function (CDF) of Y at the value W. The CDF gives the probability that the random variable is less than or equal to a specific value

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Answer:

2b + 88 = 180

Step-by-step explanation:

The angles given in the figure forms a straight line and their sum is equal to 180°.

So the answer is the equation given in the last option represents the relationship between the angles.

Answer:

2.23

Step-by-step explanation:

tune able to find the area you should x one side by the other side to find the area 2.23 * 2.23 equals close to 5 square feet

Answer:

(X,Y)=( \(\frac{4}{3}\) ,\(\frac{25}{9}\))

Step-by-step explanation:

Answer:

x = 1 1/3 and y = 2 7/9

Step-by-step explanation:

Subtract the two equations:

\(5x + 3y = 15\\2x + 3y = 11\)

3x = 4

divide both sides by 3

x = 4/3

Substitute this into the equation 5x + 3y = 15

\(5(\frac{4}{3} ) + 3y = 15\\\frac{20}{3} + 3y = 15\\3y = 8\frac{1}{3} \\y = 2\frac{7}{9}\)

Answer:

Probability ≈ 0.1071

Step-by-step explanation:

Consider steps below;

\(Total Possible Outcomes - 8C5,\\\\8! / 5! ( 8 - 5 )!,\\1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 / ( 1 * 2 * 3 * 4 * 5 )( 1 * 2 * 3 ),\\\\6 * 7 * 8 / 6 = Combinations - 56,\\\\\)

\(Number Of Outcomes - 6C5,\\\\6! / 5! ( 6 - 5 )!,\\1 * 2 * 3 * 4 * 5 * 6 / ( 1 * 2 * 3 * 4 * 5 ) ( 1 ),\\720 / 120 * 1,\\\\Outcomes - 6\)

\(Conclusion ; Solution - 6 / 56 = ( About ) 0.1071\\Hope That Helps!\)

Solution; Probability ≈ 0.1071

The answer of the given question based on Algebric notation is when x=4 and y=2, the value of 3x + 5y is 22.

An expression is combination of numbers, variables, and mathematical operations like addition, subtraction, multiplication, division, exponentiation, and others. Expressions can be simple or complex, and they can be used to represent a wide range of mathematical concepts, such as equations, inequalities, functions, and formulas. For example, "3x + 5y" is an expression that involves the variables x and y, and the operations of multiplication and addition.

In algebra, expressions are often used to represent relationships between variables, and to solve problems by manipulating the expressions to obtain a desired result.

To find the value of 3x + 5y when x=4 and y=2, we simply substitute these values into the expression and evaluate:

3x + 5y = 3(4) + 5(2) = 12 + 10 = 22

Therefore, when x=4 and y=2, the value of 3x + 5y is 22.

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Find 3x + 5y when x=4 and y=2 (algebric notation)?

Answer:

2

Step-by-step explanation:

First you need to get both fractions with a common denominator, so get 3/4 into a fraction with 8 as the denominator.  Multiply the top and bottom by 2, you get 6/8.  Now you divide the total distance by the distance from the water station, and you get 48/24, simplify and this is equal to 2.

The critical numbers of the function s(t) = 3t⁴ - 20t³ - 6t² are: t = -0.193 (smallest value), t = 0, and t = 5.193 (largest value).

To find the critical numbers of the function s(t) = 3t⁴ - 20t³ - 6t², we first need to find the derivative of the function and then set it equal to zero.

Step 1: Find the derivative of s(t):
s'(t) = d/dt(3t⁴ - 20t³ - 6t²)

Using the power rule, we get:
s'(t) = 12t³ - 60t² - 12t

Step 2: Set the derivative equal to zero and solve for t:
12t³ - 60t² - 12t = 0

Factor out the greatest common factor (12t):
12t(t² - 5t - 1) = 0

Now we have two factors to find the roots:
12t = 0 and t² - 5t - 1 = 0

From the first factor, we get t = 0.

For the second factor, use the quadratic formula to solve for t:
\(t=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\)

In this case, a = 1, b = -5, and c = -1:
\(t=\frac{-(-5) \pm \sqrt{(-5)^2-4 (1) (-1)}}{2 (1)}\)
\(t=\frac{1}{2}(5 \pm \sqrt{29})\)

Now we have three critical numbers:
t = 0
\(t=\frac{1}{2}(5 \pm \sqrt{29})\)

Rounded to three decimal places:
t = -0.193 (smallest value)
t = 0
t = 5.193 (largest value)

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Answer:

x=8

Step-by-step explanation:

You need to isolate the variable.

6x+7=55

Subtract 7 from both side.

6x=48

Divide both sides by 6.

x=8

I hope this helps!

pls ❤ and give brainliest pls

Answer:

x=8

Step-by-step explanation:

For the equation 6x+7=55 subtract 7 from both sides of the equation to get 6x=55-7  55-7 =48 so now you have 6x=48 you need to  isolate the variable x by divide both sides by 6 so 6x/6=48/6 you are left with x=8.

Answer: 0.12

x is the number which is chosen

The number of ways to choose x from 1 to 100 is 100 (ways)

because x  is divisible by 8​ => x ∈ {8; 16;...; 96}

=>  the number of terms divisible by 8 from 1 to 100 is (96 - 8)/8 + 1 = 12

the number of ways to choose x which is divisible by 8​ is 12 (ways)

=>  the probability that x is divisible by 8​ is 12/100 = 0.12

Step-by-step explanation:

Answer:

a) 110° (D)

b). 70° (A)

Step-by-step explanation:

Opposite angles in a parallelogram are equal to each other.

Hence: ∠M = ∠R

32x - 18 = 25x + 10

Rearrange

7x = 28

x = 4

To find ∠M, sub x = 4 into the expression

32(4) - 18

= 110°

∠M and ∠Q are supplementary angles, meaning they add up to 180°

Hence: ∠Q + 110 = 180

∠Q = 180 - 110

∠Q = 70°

Answer:

If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix. ( A )

Step-by-step explanation:

A and B been n*n matrices the true statement would be ;  If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix.

Although other options can be true for some matrices but they are not always true for every kind matrices but option A is always true

Answer:

it's is the last one 1 out of 6

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{0}}}}}\)

Step-by-step explanation:

\( \sf{1 - 3x = 1 - x}\)

Move x to left hand side and change it's sign

Similarly, move 1 to right hand side and change it's sign

\( \dashrightarrow{ \sf{ - 3x + x = 1 - 1}}\)

Collect like terms

\( \dashrightarrow{ \sf{ - 2x = 0}}\)

Divide both sides by -2

\( \dashrightarrow{ \sf{ \frac{ - 2x}{ - 2} = \frac{ 0}{ - 2}}} \)

Calculate

\( \dashrightarrow{ \sf{ x = 0}}\)

Hope I helped!

Best regards! :D

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

  A(1, 0), B(3, 0), P(0, 3), Q(2, -1)

Step-by-step explanation:

Points A and B are the x-intercepts of the graph. The values of x at those points are values that make the value of y be zero. The zero product rule tells you these must be the values that make the factors of y = 0.

  x -1 = 0   ⇒   x = 1

  x -3 = 0   ⇒   x = 3

This means ...

  A = (1, 0)

  B = (3, 0)

__

The value of y at the y-intercept is the value when x=0:

  y = (0 -1)(0 -3) = 3

  P = (0, 3)

__

The x-coordinate of the vertex is on the line of symmetry, halfway between the x-intercepts.

  Qx = (1 +3)/2 = 2

The y-coordinate of the vertex is the value of y for that value of x.

  y = (2 -1)(2 -3) = (1)(-1) = -1

The coordinates of Q are ...

  Q = (2, -1)

_____

Additional comment

A graphing calculator can help you with questions like this.

To find the conjunctive form of a propositional formula directly from a disjunctive form for its complement, you can follow these steps:

Start with the disjunctive form of the complement. The disjunctive form consists of multiple clauses joined by logical OR operators.

Identify each clause in the disjunctive form. Each clause represents a combination of literals (variables or their negations) joined by logical AND operators.

Convert each clause into its negated form. Negate each literal within the clause by applying De Morgan's laws. For example, if a clause has the form (A OR B), its negation would be (NOT A AND NOT B).

Combine the negated clauses using logical AND operators. Join all the negated clauses together using logical AND operators to form the conjunctive form. This means that each negated clause becomes a term in the conjunctive form.

Simplify the conjunctive form if possible. Apply any applicable simplification rules to reduce the size or complexity of the formula, such as eliminating redundant terms or applying logical equivalences.

The resulting expression in conjunctive form represents the original propositional formula. It consists of multiple terms joined by logical AND operators, where each term represents a negated clause from the disjunctive form.

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Answer:

(8.7×100)cm=870cm

870cm/20cm=43.5

so 43 20cm can be cut

Answer:

Answer C, Arthur will pay about $918 less in interest if he chooses the 3-year loan.

Step-by-step explanation:

(370.53 x 12) x 3 = 13,339.08

(237.61 x 12) x 5 = 14,256.60

14,256.60 - 13,339.08 = 917.58 (then round up)

Answer:

B

Step-by-step explanation:

let's represent the width with x, if we represent the width with x then that makes the length x+4. Therefore the perimeter would be 2x+2(x+4)=48

Answer:

25

Step-by-step explanation:

multiply then add hoped that helped

Answer:

25 and 9

Step-by-step explanation:

Answer:

  none of the above

Step-by-step explanation:

All of these abbreviations represent postulates that can be used to prove congruence. The HL postulate only applies to right triangles, but all of the others apply to any shape triangle.

All can be used to show congruence.