Left-handed people are rare. Suppose a researcher conducts a survey of 30 people and finds that 4 of them are left handed. (a) Construct a 95% confidence interval to estimate the true proportion of left-handed people in the population. Also, interpret the interval. (b) Research suggests that 11% of the population are left-handed. Assess this claim using your answer from (a). (c) Suppose another researcher conducts a similar sur vey of 61 people and finds that 10 of them are left handed. Use a 95% confidence interval compare the results of the two Tsurveys. What difference is there (if any)?

Mathematics is a fundamental subject in education that is essential in the development of an individual’s critical thinking and problem-solving skills. It is one of the primary subjects that are taught in elementary schools and must be taught appropriately for children to understand and gain the required skills. One true statement about mathematics teaching in elementary schools is that it should be student-centered.

Teachers should focus on the child's understanding, individual learning abilities and styles, and progress.The learning experience should not be centered on the teacher but on the students. Teachers should also make the subject engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject. Besides, teachers should develop a personalized learning approach that allows students to learn and understand the subject at their own pace while creating opportunities for individual and group learning. Through such learning approaches, students can develop the required mathematical concepts and competencies such as critical thinking, problem-solving, and decision-making skills that will be beneficial in their future endeavors.

In elementary schools, mathematics teaching should be student-centered. It should be engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject.

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Log(1), log(-1), log(i) and ii are all numbers written in the form a + bi. Log(1) = 0; log(-1) = undefined; log(i) = 0.5i; ii = -1; a = -1 and b = 0 because the number is in the form a + bi.

Given numbers are;• log(1)• log(-1)• log(i)• iiFor all numbers written in the form a + bi, we must find a and b. Here's how to do it: log(1)In this case, the log is taken in base 10. The result of this is 0. So, we have: log(1) = 0Therefore, a=0 and b=0 because the number is not in the form a + bi. log(-1)In this case, the log is taken in base 10. The result of this is undefined. This is because there is no power to which we can raise 10 to get -1. So, we have: log(-1) = undefinedTherefore, a=undefined and b=undefined because the number is not in the form a + bi. log(i)In this case, the log is taken in base 10. The result of this is 0.5iπ. So, we have: log(i) = 0.5iπTherefore, a=0 and b=0.5π because the number is in the form a + bi. iiIn this case, we are finding the square of i. i is a complex number given as i = 0 + 1i. Therefore, we have: i2 = (0 + 1i)2= (0)2 + 2(0)(1i) + (1i)2= -1This is because i2 = -1. Now, we can write ii as: ii = i × i= (0 + 1i) × (0 + 1i)= 0 + 0i + 0i + 1i2= -1So, we have: ii = -1Therefore, a=-1 and b=0 because the number is in the form a + bi.

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Answer:

a=671000

Step-by-step explanation:

woah

The formula for the number of internet host computers as an exponential function of t is: n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t) and the values of a and k in the model are k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million

a. To find the values of a and k, we can use the information given in the question. Let n(0) be the number of host computers in July 1998, which is 35.3 million. Let n(7) be the number of host computers in July 2005, which is 352.1 million. We can use these values to solve for a and k.

n(0) = a × e^(k0) = a

n(7) = a × e^(k7)

Dividing the second equation by the first equation, we get:

n(7) / n(0) = e^(k×7)

Taking the natural logarithm of both sides, we get:

ln(n(7) / n(0)) = k×7

Therefore, k = (1/7) × ln(n(7) / n(0)) and a = n(0) = 35.3 million.

Therefore, the formula for the number of internet host computers as an exponential function of t is:

n(t) = 35.3 × e^((1/7) × ln(n(7) / 35.3) × t)

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The given integral is evaluated as ∫ (15cos(x)/(5-sin(x))) dx = 15ln|5 - sin(x)| + C.

Given definite integral:

∫ (15cos(x)/(5-sin(x))) dx

Let's use the substitution method.

Let u = 5 - sin(x). We need to find du/dx.

Differentiating u = 5 - sin(x) partially with respect to x:

du/dx = cos(x)

Therefore, dx = du/cos(x).

Substituting these expressions in the given integral:

∫ (15cos(x)/(5-sin(x))) dx = ∫ (15cos(x)/u) (du/cos(x)) = 15∫ (1/u) du

Using the Power Rule of Integration, the integral evaluates to:

15∫ (1/u) du = 15ln|u| + C = 15ln|5 - sin(x)| + C

Thus, the given integral is evaluated as ∫ (15cos(x)/(5-sin(x))) dx = 15ln|5 - sin(x)| + C.

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Answer:

B.

Step-by-step explanation:

Answer is b

lmk if im wrong

(answer got deleted, lost my brainliest :(. )

Answer:

Number of Nickels is 12

Number of Dimes is 9

Number of Quarters is 15

Step-by-step explanation:

Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.

That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.

Let number of nickels be N

Let number of dimes be D

Let number of quarters be Q

Then

N + D + Q = 36 .................................(1)

- There are three fewer quarters than nickels.

This implies that

N = Q - 3 ..............................................(2)

Or

Q = N + 3 .............................................(3)

- There are six more dimes than quarters.

This implies that

Q = D + 6 .............................................(4)

Comparing (3) with (4), we see that

N + 3 = D + 6

N - D = 6 - 3

N - D = 3 ................................................(5)

Using (3) in (1)

N + D + (N + 3) = 36

2N + D = 36 - 3

2N + D = 33 ..........................................(6)

Solving (5) and (6) simultaneously

From (5): D = N - 3

From (6): D = 33 - 2N

=> N - 3 = 33 - 2N

N + 2N = 33 + 3

3N = 36

N = 36/3 = 12..........................................(7)

Using (7) in (6)

2(12) + D = 33

24 + D = 33

D = 33 - 24

D = 9 ........................................................(8)

Using (7) and (8) in (1)

12 + 9 + Q = 36

21 + Q = 36

Q = 36 - 21 = 15.......................................(9)

Therefore,

Number of Nickels, N = 12

Number of Dimes, D = 9

Number of Quarters, Q = 15

Step-by-step explanation:

This is an equation for a LINE.....ANY point on the line will satisfy this equation....so there are INFINITE solutions.

The number of discount tickets was sold is 139.

The linear equation of two variables is the equation where the highest degree of two variables is 1.

Here given that the organizer receives 2884 by selling tickets.

The number of tickets sold is 430

The full price of one ticket is 8.

The discount price of ticket is 4.

Let the number of full price ticket sold is x and the number of discount ticket sold is y.

Then the total price will be = (the price of full price ticket* number of tickets) + (number of discount ticket sold*discount price of one ticket)

= 8x+4y

From the above it is clear that 8x+4y=2884 ------equation 1

total number tickets are = x+y

⇒ x+y =430 -------equation 2

multiplying 8 in equation 2 will be

8x+8y=3440

then subtracting equation 1 from the above equation

8x+8y -(8x+4y)=3440-2884

⇒4y=556

⇒y=556/4

⇒y=139

Therefore the number of discount tickets sold is 139.

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Step-by-step explanation:

huh??????????????????

The equation of the sphere in standard form 16x2 + 162 + 1622 = 96x - 24 - 128 is \((x - 3)^2 + y^2 + z^2 = (81sqrt(17) / 2)^2\)

To write the equation of the sphere in standard form, we need to rearrange the terms so that the variables are on one side and the constant is on the other side.

The standard form of the equation of a sphere is:

\((x - h)^2 + (y - k)^2 + (z - l)^2 = r^2\)

where (h, k, l) is the center of the sphere and r is the radius.

So, let's start by rearranging the terms in the given equation:

\(16x^2 + 162 + 162^2 - 96x + 24 + 128 = 0\)

We can simplify the constants on the left side:

\(16x^2 - 96x + 162^2 + 24 + 128 = 0\)

Now we can complete the square for the x terms:

\(16(x^2 - 6x + 9) + 162^2 + 24 + 128 - 16(9) = 0\)

\(16(x - 3)^2 + 162^2 + 24 + 128 - 144 = 0\)

\(16(x - 3)^2 + 162^2 + 8 = 0\)

Finally, we can divide both sides by 16 to get the equation in standard form:

\((x - 3)^2 + (y - 0)^2 + (z - 0)^2 = (-1/2)162^2 - 1/2(8)\)

The center of the sphere is (3, 0, 0), and the radius is the square root of the constant term on the right side:

\(r = sqrt[(-1/2)162^2 - 1/2(8)] = 81sqrt(17) / 2\)

Therefore, the equation of the sphere in standard form is:

\((x - 3)^2 + y^2 + z^2 = (81sqrt(17) / 2)^2\)

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Answer:

7 \(\frac{1}{2}\) units

Step-by-step explanation:

the distance is the absolute value of the difference of the numbers, that is

| - 2 \(\frac{1}{2}\) - 5 | = | - 7 \(\frac{1}{2}\) | = 7 \(\frac{1}{2}\)

or

| 5 - (- 2 \(\frac{1}{2}\) ) | = | 5 + 2 \(\frac{1}{2}\) | = | 7 \(\frac{1}{2}\) | = 7 \(\frac{1}{2}\)

The probability that the flip results in a head is given as Pr[H] = 23. Therefore, the probability that the flip results in a tail is Pr[T] = 1 - Pr[H] = 1 - 23 = 13.

Let A be the event that a white marble is selected. We need to find the conditional probability Pr[H|A], i.e., the probability that the flip resulted in a head given that a white marble was selected.

Using Bayes' theorem, we have:

Pr[H|A] = (Pr[A|H]*Pr[H]) / Pr[A]

Pr[A|H] is the probability of selecting a white marble given that the flip resulted in a head. This is given by (9/25), since there are 9 white marbles out of 25 in the first urn.

Pr[A] is the total probability of selecting a white marble, which can be found using the law of total probability:

Pr[A] = Pr[A|H]*Pr[H] + Pr[A|T]*Pr[T]

= (9/25)*0.23 + (1/11)*0.13

= 0.0888 + 0.0118

= 0.1006

Pr[A|T] is the probability of selecting a white marble given that the flip resulted in a tail. This is given by (1/11), since there is only 1 white marble out of 11 in the second urn.

Therefore,

Pr[H|A] = (9/25 * 0.23) / 0.1006 = 0.6508

Hence, the probability that the flip resulted in a head given that a white marble was selected is 0.6508 (or approximately 0.65).

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To find the interest rate on the investment for 8 years is equal to 0.7%

Given the following data:

To find the interest rate on the investment for 8 years:

Mathematically, compound interest is given by the formula:

\(A = P(1 + r)^{t}\)

Where;

Substituting the given parameters into the formula, we have;

\(6872.74 = 4000(1 + r)^{8}\\\\(1 + r)^{8}=\frac{6872.74}{4000} \\\\(1 + r)^{8}=1.7182\\\\1+r=\sqrt[8]{1.7182} \\\\1+r =1.07\\\\r=1.07-1\\\\r=0.7\)

Interest rate, r = 0.7%

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Answer:

Step-by-step explanatio the way the question is phrased Is confusing

Answer:

the correct answer is -6

Answer: 3n+2

Step-by-step explanation:

The percent of the second fruit salad is strawberries should be 10%.

= 25% - 15%

= 10%

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Answer:

7 . 8.9

8 . 19.5

9 . 9.9

10 .12.6

Step-by-step explanation:

7.x=11tan39

8.x=28cos46

9.x=8tan51

10.x=31sin24

side opposite of mentioned angle is opposite

longest side in triangle is hypotenuse

the side subtended by the angle is the adjacent

The length of the curve defined by the parametric equations x = (-12/y)(2t+1)^(3/2) and y = t, where 0 ≤ t ≤ 16, is given by (3/t) [ (2/3)(33^(3/2)) + 32 ].

To find the length of the curve defined by the parametric equations x = (-12/y)(2t+1)^(3/2) and y = t, where 0 ≤ t ≤ 16, we can use the arc length formula for parametric curves.

The arc length formula is given by:

L = ∫[a,b] √((dx/dt)² + (dy/dt)²) dt

Let's calculate the derivatives first:

dx/dt = (-12/y)(3/2)(2t+1)^(1/2) * 2

dy/dt = 1

Substituting these derivatives into the arc length formula, we have:

L = ∫[0,16] √((-12/y)(3/2)(2t+1)^(1/2) * 2)² + 1² dt

L = ∫[0,16] √(36/y²)(2t+1) + 1 dt

L = ∫[0,16] (6/y)√(2t+1) + 1 dt

To simplify the integral, we need to evaluate the integral of √(2t+1). Let's make a substitution u = 2t+1, then du = 2dt:

L = ∫[0,16] (6/y)√u + 1 dt

L = ∫[1,33] (6/y)√u + 1 (du/2)

L = (6/y) ∫[1,33] (√u + 1) (du/2)

L = (3/y) ∫[1,33] (√u + 1) du

Integrating (√u + 1) with respect to u, we get:

L = (3/y) [ (2/3)(u^(3/2)) + u ] evaluated from 1 to 33

L = (3/y) [ (2/3)(33^(3/2)) + 33 - (2/3)(1^(3/2)) - 1 ]

L = (3/y) [ (2/3)(33^(3/2)) + 32 ]

Finally, substituting y = t, we have:

L = (3/t) [ (2/3)(33^(3/2)) + 32 ]

Therefore, the length of the curve is (3/t) [ (2/3)(33^(3/2)) + 32 ] (simplified form).

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9514 1404 393

Answer:

  tables A, B, E are proportional relationships

Step-by-step explanation:

Finding the rate of change involves finding the ratio of the difference of adjacent y-values to the difference of adjacent x-values. For this many tables and points, I find that to be exceptionally tedious, so I let a spreadsheet do the work.

For the four points, there are three ratios. In the attachment, each ratio is between the point on the same line and the point on the next line. Two conditions are required for the table to be proportional:

The green color identifies tables that are proportional.

Answer:

5 T

Step-by-step explanation:

It is the only one remotely close to the weight of a pick-up truck.

Answer:

Its 25%

Step-by-step explanation:

The percent population that will grow in a decade is 28% option (3) 28% is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

We have:

\(\rm P(t) = 2,500(1.025)^t\)

Plug t = 10

\(\rm P(10) = 2,500(1.025)^{10}\)

P(10) = 3200

Percent grow = [(3200 - 2500)/2500]×100

Percent grow = 28%

Thus, the percent population that will grow in a decade is 28% option (3) 28% is correct.

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The three expressions ∂r/∂y − ∂q/∂z, ∂p/∂z − ∂r/∂x, and ∂q/∂x − ∂p/∂y represent the components of the curl of the vector field F. So, the curl of the given vector field F can be expressed as Curl(F) = (∂r/∂y − ∂q/∂z)i + (∂p/∂z − ∂r/∂x)j + (∂q/∂x − ∂p/∂y)k.

Using the given values of p, q, and r, we can find the partial derivatives of each component with respect to x, y, and z. Then, we can substitute these values into the expression for the curl to obtain the final answer. So, evaluating the partial derivatives and substituting into the expression for the curl gives Curl(F) = (-48xyz)i + (24x^2z - 24xy^2)j + (16xy - 16yz^2)k.

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Answer:

1 apple

Step-by-step explanation:

2-1=1

Have a great day or night wharever you are!

The number of apples you will have left if your sister takes away one is; 1 apple

We are told that you have 2 apples.

Now, if you have 2 it means that anyone taken away from you would be subtracted from the one that you have.

This means that;

Number of apples you have left if your sister takes one is; 2 - 1 = 1 apple.

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Answer:

Set your calculator to degree mode.

The figure is not shown. Please sketch it to confirm my answer.

tan(20°) = h/92

h = 92×tan(20°) = about 33.49 feet

Answer:

Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

A linear regression model is one that conforms to the algebraic equation y=mx+b. The slope is B, and the y-intercept is m. The previous clause is usually referred to as an "mathematical equation having two variables because both y and x are unique parameters. Two variables make up bivariate linear equations. Linear equations have a variety of applications, all of which have a zero outcome. Y=mx+b, where m stands for the gradient and b for the y-intercept, is the formula for a linear equation.

Here,

Given : 55=0.1(m-500)+50

where m is the number of minute

=> 55=0.1(m-500)+50

=> 55=0.1m-50+50

=>55=0.1m-0

=>55-0=0.1

=>55=0.1

=>0.1=0.1

=>550=m

Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

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Answer:

a. 2/20 or 10%

b. Theoretically 2 out of every 20 times the spinner is spun, it will be blue.

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

P=4/18=2/9