Which graph represents the function f(x) = -2sin(x) +37

The 95% confidence interval is (22.8876, 49.1124)..

To find the 95% confidence interval for the difference in means between two populations, we can use the formula:

CI = (x1 - x2) ± z*(SE)

where x1 and x2 are the sample means of the two populations, SE is the standard error, z is the critical value from the standard normal distribution corresponding to the level of confidence.

Substituting the given values into the formula, we have:

CI = (264 - 228) ± 1.96*(6.69)

Simplifying this expression, we have:

CI = 36 ± 13.1124

Therefore, the 95% confidence interval for the difference in means between the two populations is (22.8876, 49.1124).

This means that we are 95% confident that the true population difference in means falls between 22.8876 and 49.1124. We can interpret this interval as a range of plausible values for the population difference in means, based on the sample data.

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The properties of the exponents are solved and the expression is given by the relation ( 2s )⁻¹ = 1 / 2s

Given data ,

Let the expression be represented as A

Now , the value of A is

( 2s )⁻¹ = 1 / 2s

From the laws of exponents , we get

m⁻ᵃ = ( 1 / mᵃ )

So , on simplifying , we get

( 2s )⁻¹ = 1/ ( 2s )

On further simplification , we get

1/ ( 2s ) = ( 2s )⁻¹

Hence , the expression is ( 2s )⁻¹ = 1/ ( 2s )

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The complete question is attached below :

Use properties of exponents to verify that ( 2s )⁻¹ = 1/ ( 2s ) are equivalent.

Answer: the area of the triangle is 150 cm².

Step-by-step explanation:

To solve this problem, we need to use the formula for the area of a triangle:

Area = (1/2) x base x height

From the diagram, we can see that the base of the triangle is 20 cm and the height is 15 cm. Plugging these values into the formula, we get:

Area = (1/2) x 20 cm x 15 cm

Area = 150 cm²

Therefore, the area of the triangle is 150 cm².

The cord will begin to stretch after approximately 1.46 seconds.

h(t) = -16t^2 + V0t + h0

149 = h0 - h(t)

Substituting h0 = 241 and h(t) = -16t^2 + V0t into this equation, we get:

149 = 241 - (-16t^2 + V0t)

we get:

16t^2 - V0t - 92 = 0

4(16)(-92) / (2(16)

t = sqrt(1856) / 32

Using a calculator, we get:

t ≈ 1.46 seconds

Therefore, the cord will begin to stretch after approximately 1.46 seconds.

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Answer:

Step-by-step explanation:

2344

The requried, experimental probability is 0.1. Option B is correct.

To find the experimental probability that an arrangement will consist entirely of balloons that are the same color, we need to count the number of times that Ethan got an arrangement where all four balloons were the same color and divide that by the total number of trials.

Looking through the data, we can see that the following trials had all four balloons the same color:

rrrr

bbbb

yyyy

So, out of 30 trials, there were 3 trials where all four balloons were the same color. Therefore, the experimental probability is:

3/30 = 0.1

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Answer:

c

Step-by-step explanation:

After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.

So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)

The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.

The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:

Midpoint of JK: (1, -4)

Midpoint of J'K': (4, 1)

The slope of the vector: 3/5

(x₁ + x₂)/2, (y₁ + y₂) /2

Point-slope formula: y - y₁ = m(x - x₁)

Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)

Applying simplification , we get: y = (- 3/5)x - 1.2

To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:

y - 1 = (7/3)( x - 4)

Apply simplification , we get: y = (7/3)x - 17/3

To evaluate the intersection point, we can solve the system of equations:

y =(- 3/5)x - 1.2 = (7/3)x - 17/3

Evaluating for x and y, we get x = -6 and y = -1.

Therefore, the center of rotation is (-6, -1).

√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)

Distance between image points and center of rotation

√( ( 6 - (-6))² + ( 3 - (-1))² = 13

The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).

The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':

Angle of vector: arctan(5/3) = 59.04 degrees

Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

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Answer:  A) £7.49

               B) £2.25

Step-by-step explanation:

Step 1:

Let the cost of a football be [tex]f[/tex]and the cost of a tennis ball be [tex]t[/tex].

Step 2:

Write the 2 equations we have from the given information:

[tex]2f + 3t = 21.73[/tex] [tex] \textsf{(from the cost of 2 footballs and 3 tennis balls)} [/tex]

[tex]5f + 7t = 53.20[/tex] [tex] \textsf{(from the cost of 5 footballs and 7 tennis balls)} [/tex]

Step 3:

Solve for one variable in one of the equations. For example, we can solve for [tex]f[/tex]in the first equation:

Step 4:

Substitute this expression for [tex]f[/tex] into the second equation and solve for [tex]t[/tex]:

So, the cost of a tennis ball is £2.25.

Step 5:

Substitute this value of [tex]t[/tex] into the expression for [tex]f[/tex] and solve for [tex]f[/tex]:

So, the cost of a football is £7.49

Step 6:

Therefore, the cost of a football is £7.49 and the cost of a tennis ball is £2.25.

The quadratic equation representing the new patio area after adding a decorative tile of width x all the way around is: 0 = 4x^2 + 44x - 60

Options A and E are correct.

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.

Since the area of the new patio is given as 180 square feet, we can create a quadratic equation to represent the new patio area:

Area = length × width

180 = (12 + 2x) × (10 + 2x)

After we expand, the answer is given as 0 = 4x^2 + 44x - 60

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Answer:

78.947%

Step-by-step explanation:

It says A OR B, so:

5/19 + 6/19 + 4/19

11/19 + 4/19

15/19 = approx. 0.78947 = 78.947%

The area of a sector is 8.75 [tex]m^{2}[/tex].

A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

where r is the radius, and θ is the central angle.

Given a circle whose area is 45 sq. m.; then;

area of a circle = π[tex]r^{2}[/tex]

45 = π[tex]r^{2}[/tex]

r = [tex]\sqrt{\frac{45}{\pi } }[/tex]

Then,

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

                  = ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]

                  = [tex]\frac{7}{36}[/tex]*π*45/π

                  = [tex]\frac{7}{36}[/tex]*45

                  = 8.75 sq. m.

The area of the sector is 8.75 [tex]m^{2}[/tex].

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Answer: $1856

Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856

Answer:

[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]

[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]

The couple needs to deposit about $554.49 each month end until they retire to reach their goal.

To find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:

FV = PMT * [((1 + r)^n - 1) / r]

We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:

PMT = FV / [((1 + r)^n - 1) / r]

We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:

PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]

PMT ≈ 554.49

Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 [tex]S_{n}[/tex]​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is [tex]a_{1}[/tex] = 4000, second term is [tex]a_{2}[/tex] = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

[tex]d = a_{2} - a_{1} = 5000 - 4000 = 1000[/tex]

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and [tex]S_{n}[/tex] = 165000 in “ [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] “ which can be represented as:

Determining, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex]

⇒ 165000 = [tex]\frac{n}{2}[/tex] [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + [tex]1000n^2[/tex]

⇒ [tex]1000n^2[/tex] + 7000n - 330000 = 0

⇒ [tex]1000n^2[/tex] ( [tex]n^2[/tex] + 7n - 330 ) = 0

⇒  [tex]n^2[/tex] + 7n - 330 = 0

⇒ [tex]n^2[/tex] + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)

A vector is a physical quabntity thet has both magnitude and direction.

To find  the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows

Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),

Let A = (8, -6) and B = (-1, 5)

So, AB = B - A

= (-1, 5) - (8, -6)

= (-1 - 8), (5 - (-6))

= (-9, 5 + 6)

= (-9, 11)

So, the vector in component form is (-9, 11)

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The money invested by the teacher to have at least 125,000 in her account after 40 years of a 6.95% annual interest rate compounded continuously is 7755. Hence, the right solution to the question is option D

Compound interest is given by

A = P[tex](1+r)^t[/tex]

where A is the amount

P is the principal

r is the rate of interest

t is the time

Given in the question,

A = $125,000

r = 6.95% or 0.0695

t = 40 years

P is to be found

A = P[tex](1+r)^t[/tex]

125000 = P [tex](1 + 0.0695)^{40[/tex]

125000 = P * [tex]1.0695^{40[/tex]

125000 = 16.118P

P = 7755

The teacher should invest $7755 initially.

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The required posterior mean prevalence is closest to 0.47.

We can use Bayes' theorem to find the posterior distribution of the prevalence parameter, given the data and the Beta prior:

posterior ∝ likelihood x prior

where the likelihood is given by the binomial distribution:

likelihood = P(observing 4 cases out of 10 | prevalence)

and the prior is a Beta distribution with parameters α = β = 10:

prior = Beta(α=10, β=10)

We can calculate the posterior distribution by multiplying the likelihood and prior, and then normalizing:

posterior = Beta(α=14, β=16)

where the posterior Beta distribution has parameters α=14 (10 + 4) and β=16 (10 + 10 - 4).

The posterior mean of a Beta distribution with parameters α and β is:

posterior mean = α / (α + β)

Plugging in the values of α and β from the posterior distribution, we get:

posterior mean = 14 / (14 + 16) = 0.467

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Answer:

[tex]a(1) = 144[/tex]

[tex]a(n) = 144{( - \frac{1}{6} )}^{n - 1} [/tex]

[tex]a(n) = - \frac{1}{6} a(n - 1)[/tex]

Answer:

12 packages of water

5 packages of cheese sticks

Step-by-step explanation:

The LCM (least common multiple) of 5 and 12 is 60.

w = # of pkgs of water

c = # of pkgs of cheese sticks

5w = 12c = 60

w = 60/5 = 12

c = 60/12 = 5

Answer:

Quick internet search:

The area of each square would be 36 square inch.

We have,

Area of sheet = 12 square inches

So, the area of square to be cut

= 12in × 12in

= 144 square in

Now, number of squares=4

So, area of each square =144÷4

                                        =36 square inches

Thus, the side of each square is

= 36/4

= 6 inch

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Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

Answer:

linear

Step-by-step explanation:

have a good day God bless :)

Answer:

69

Step-by-step explanation:

(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)

x - 28 = 41

x = 69

An example of simple random sampling is given as follows:

C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.

Samples may be classified as:

Hence the samples for this problem are classified as follows:

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The radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis is 27[tex]a^{\frac{3}{2}[/tex].

To find the radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³[tex])^{\frac{3}{2}[/tex]) + 4x²/(9a⁴(x³-a³[tex])^{\frac{1}{2}[/tex])

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³[tex])^{\frac{3}{2}[/tex]) + 4a²/(9a⁴(a³-a³[tex])^{\frac{1}{2}[/tex]) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27[tex]a^{\frac{3}{2}[/tex]

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Answer:

3/5

Step-by-step explanation:

opposite/hypotenuse

21/35

Simplify by dividing by 7 on the numerator and denominator

3/5

A. The value of the standardized test statistic is -2.391.

B. The rejection region for the standardized test statistic is t <-2.160.

C. The decision for the hypothesis test is to reject the null hypothesis.

Employing a t-distribution table or calculator along with 13 degrees of freedom (n1 + n2 - 2) enables us to ascertain the rejection region for the t-statistic at an α=0.025 level of significance (two-tailed test):

Rejection Region: t < -2.160 or t > 2.160

Given that -2.391 falls in the rejection region, we repudiate the null hypothesis. At the α=0.025 level of significance, we are provided sufficient evidence to support that those who consistently partake in exercise generally have a lower resting heart rate than those who do not.

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