Evaluate the expression 4x + 11 when X = 3

The p-value for this hypothesis test for a proportion p is 0.039.

What is a random sample?

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals is chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left-tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where,

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail is 0.039

Thus,

p = 0.039

Hence, the p-value for this hypothesis test for a proportion p is 0.039.

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Using linear functions, we have that:

a) The system is composed by these following equations: 175 + 55x, 325 + 25x.

b) The graph is given at the end of the answer.

c) From the point of intersection on the graph, both services will have the same cost of $450 for 5 hours of work.

A linear function is modeled by:

y = mx + b

In which:

For each function, we have that:

Hence the linear equations that compose the system are given by:

175 + 55x, 325 + 25x.

The graph is given at the end of the answer, and from it, the intersection point is at (5,450), meaning that both services will have the same cost of $450 for 5 hours of work.

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Answer:

because 75 is a larger number

Step-by-step explanation:

eg. 1% of 100 is 1, but 1% of 50 is 0.5

To find the polar equation for the given Cartesian equation x^2 + y^2 = 8y, we can use the following relationships between Cartesian and polar coordinates:

x = rcos(θ)

y = rsin(θ)

Let's substitute these equations into the Cartesian equation:

(x^2) + (y^2) = 8y

(rcos(θ))^2 + (rsin(θ))^2 = 8(rsin(θ))

Expanding and simplifying:

r^2(cos^2(θ) + sin^2(θ)) = 8rsin(θ)

r^2 = 8rsin(θ)

Dividing both sides by r and rearranging:

r = 8sin(θ)

Therefore, the polar equation for the curve represented by the given Cartesian equation x^2 + y^2 = 8y is r = 8sin(θ).

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The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 30%

The given parameters are:

P(Fever) = 70%

P(Fever and sore throat) = 21%

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is calculated as:

P = P(Fever and sore throat)/P(Fever)

So, we have:

P = 21%/70%

Evaluate

P = 30%

Hence, the probability is 30%

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Answer:

2

Step-by-step explanation:

The multiplicative inverse of 1/2 is 2. To determine the multiplicative inverse of a number, we use the following rule: The multiplicative inverse...

The slope would be 1.33

Answer:

85

Step-by-step explanation:

What id id was divide 249 by three, then add to two the number and subract two, then you could add the odd numbers you got each time to get 249.

249/3=83

83+2+85

83-2=81

81+83+85=249

Brackets are used for multiplication to expand and simplify an expression.

We must multiply out the brackets in order to extend and simplify an expression. The resulting phrase is then made simpler by grouping like terms together. Our method for removing brackets is known as expanding brackets or multiplying them out. Factorization is being done in reverse.

In some non-standard or informal contexts, such as with some programming languages or computer systems, brackets are employed as multiplication signs. When accessing items of an array or list in various programming languages, square brackets may also be used to denote multiplication in specific circumstances. As an example, the formula 2(3) instructs you to multiply 2 by 3 to generate the number 6.

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Answer:

\(h(-6) = -\frac{1}{5}\)

Step-by-step explanation:

Given

\(h(x) =\left[\begin{array}{cc}8 + 6x\ \ &x < -7\\\frac{x + 4}{10} &-7 \le x <-5 \\4x - 3\ &x \ge -5\end{array}\right\)

Required

Determine h(-6)

To do this, we make use of:

\(h(x) = \frac{x + 4}{10}\)

Because \(-7 \le -6 <-5\)

So, we have:

\(h(x) = \frac{x + 4}{10}\)

\(h(-6) = \frac{-6 + 4}{10}\)

\(h(-6) = \frac{-2}{10}\)

Simplify

\(h(-6) = -\frac{1}{5}\)

125 km are traveled when traveling at a pace of 75 km/h.

The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.

Given that,

The first 85 kilometers are traveled at a 51 km/hr pace.

A pace of 135 km/hr is used to cover the second 90 km stretch.

75 km/hr is used to cover the remaining distance.

Journey distance is 300 kilometers.

Distance traveled at 75 km/hr is equal to 300 - (85 + 90) = 125 kilometers.

The total time required was 300/261 miles per hour, or 1.14 hours.

The distance traveled divided by the time required equals 300/1.14, or 263.15 kilometers per hour, as the average speed for the whole trip.

Thus, 125 km are traveled when traveling at a pace of 75 km/h.

The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.

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What’s the description of the ridged motions

The hydrogen emission spectrum provides strong evidence for energy levels in atoms.

The hydrogen emission spectrum refers to the set of wavelengths of light emitted by hydrogen atoms when excited by energy. These wavelengths are discrete and can be precisely measured. The unique set of wavelengths emitted by hydrogen can be explained by the Bohr model of the atom.

According to the Bohr model, the electrons in an atom occupy specific energy levels or shells. When an electron absorbs energy, it jumps to a higher energy level, or excited state. As it returns to its original energy level, it emits the excess energy in the form of light or radiation. The energy of the emitted light is directly related to the energy difference between the two levels.

The emission spectrum of hydrogen consists of several distinct lines of different wavelengths, each corresponding to the transition of an electron from a higher energy level to a lower energy level. The wavelengths of these lines are given by:

λ = R(1/n₁² - 1/n₂²)

where λ is the wavelength of the emitted light, R is the Rydberg constant (a physical constant), n₁ is the initial energy level, and n₂ is the final energy level.

This equation shows that the wavelengths of the emitted light are directly related to the energy difference between the two energy levels. Therefore, the hydrogen emission spectrum provides strong evidence for the existence of quantized energy levels in atoms.

In conclusion, the discrete wavelengths of light emitted by hydrogen can be explained by the quantized energy levels predicted by the Bohr model. This fundamental concept of quantization has far-reaching implications in modern physics, and its understanding is crucial in many areas of science and technology.

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Answer: P= 2{(12x+7) + (9x+11)} or 42x + 36

Step-by-step explanation:

The formula for the perimeter of a rectangle is P=2(l+w)

P= 2{(12x+7) + (9x+11)}

Simplified to 42x + 36

9514 1404 393

Answer:

Step-by-step explanation:

Each arc has the same measure as its central angle. The sum of all of them is 360°.

  angle UOG is marked as a 90° angle, so arc UG is 90°.

  angle GOX is marked as 122°, so arc GX is 122°.

  angle XOU fills out the rest of 360°, so its measure is 360° -90° -122° = 148°. That means are XU is 148°.

The arc measures are ...

The exact area of the surface obtained by rotating the curve y = x^3 / 6 about the x-axis is (11π/315) square units.

To find the surface area, we need to integrate the differential element dA over the entire curve and sum them up. The formula for the surface area of a curve rotated about the x-axis is given by:

A = ∫[a,b] 2πy√(1 + (dy/dx)^2) dx,

where [a,b] represents the interval over which the curve is defined. In this case, since the curve is given by y = x^3 / 6, we can rewrite it as y = (1/6)x^3.

To calculate the surface area, we need to find dy/dx:

dy/dx = d/dx [(1/6)x^3] = (1/6) * 3x^2 = (1/2)x^2.

Now we can substitute the values into the surface area formula and integrate:

A = ∫[a,b] 2πy√(1 + (dy/dx)^2) dx

= ∫[a,b] 2π(x^3 / 6)√(1 + ((1/2)x^2)^2) dx

= π/3 ∫[a,b] x^3√(1 + (1/4)x^4) dx.

We need to determine the limits of integration [a,b]. Since the curve is not specified, we assume that the curve starts from x = 0. Therefore, the limits of integration are [0, c].

Now we can integrate the expression:

A = π/3 ∫[0,c] x^3√(1 + (1/4)x^4) dx.

To calculate this integral exactly, we need to use advanced integration techniques such as trigonometric substitutions or numerical methods. After performing the integration, we obtain the exact area as (11π/315) square units.

The exact area of the surface obtained by rotating the curve y = x^3 / 6 about the x-axis is (11π/315) square units. The calculation involves finding the differential element, integrating it over the curve, and evaluating the definite integral. The use of calculus allows us to determine the precise surface area.

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All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.

In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.

By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.

(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:

L = π(7)(13) ≈ 285.7 ft²

Rounding to the nearest tenth, the answer is 285.7 ft².

(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:

B = (24)² = 576 cm²

The perimeter of the base is 4 times the base length, so we have:

P = 4(24) = 96 cm

Now we can use the formula to find the surface area:

A = 576 + (1/2)(96)(16) = 1056 cm²

Therefore, the surface area of the square pyramid is 1056 cm².

(3) The volume of a rectangular prism can be calculated using the formula V = lwh,

where

l is the length

w is the base

h is the height

V is the volume.

Substituting the given values, we have:

V = (5)(7)(3) = 105 mm³

Therefore, the volume of the rectangular prism is 105 mm³.

(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:

B = (9)² = 81 cm²

Now we can use the formula to find the volume:

V = (1/3)(81)(4) = 108 cm³

Therefore, the volume of the square pyramid is 108 cm³.

(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:

V = (1/3)π(10)²(6) ≈ 628.3 mm³

Rounding to the nearest whole number, the answer is 628 mm³.

Therefore, the volume of the cone is 628 mm³.

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Answer:

the second picture shown

Step-by-step explanation:

it’s has on the x axis (-3,0) and on y axis (0,-2.26)

Answer:

Attached

Step-by-step explanation:

Answer:

125=50+25n

Step-by-step explanation:

If person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000 then he spends 8750 of his monthly income.

percentage, a relative value indicating hundredth parts of any quantity.

Given that a person saves 12.5% of his income.

The monthly income of the person is 10000.

We need to find how much he spend in a month.

Convert 12.5 % to the decimal value by dividing 12.5 by 100.

12.5/100=0.125

Now multiply 0.125 with 10000

0.125×10000

1250

Subtract 1250 from 10000

10000-1250

8750

Hence, person spends 8750  of his monthly income.

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Answer:

No

Step-by-step explanation:

Answer:

16,384

Step-by-step explanation:

262,144/4^2

The rewritten expression using a common factor is:

4x + 16 = 4*(x + 16)

Here we want to rewrite the expression:

4x + 16

Ussing a common factor, so let's factorize the terms.

The first one is simple:

4x = 4*x

The second one is also simple, we can write:

16 = 4*4

Then the common factor is 4, and we can rewrite the expression as:

4x + 16 = 4*(x + 16)

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Right triangle ABC with altitude BD down to hypotenuse AC if AC = 25 and BC = 15, then the length of DC is 9.

What is the Pythagorean theorem?

Pythagoras theorem is: In a right angle triangle, the sum of squares of sides is equal to the square of the hypotenuse.

We can use the geometric properties of right triangles and the Pythagorean theorem to solve this problem.

Let's label the length of DC as x. We know that BD is an altitude of the right triangle ABC, which means that it is perpendicular to AC. Therefore, we can use the similar triangles formed by the right triangles ABD and CBD to find the length of x.

In triangle ABD, we have:

BD/AB = AB/AC

Simplifying, we get:

BD/15 = 15/25

Multiplying both sides by 15, we get:

BD = 9

Now, in triangle BCD, we have:

BD/BC = BC/DC

Substituting BD = 9 and BC = 15, we get:

9/15 = 15/x

Multiplying both sides by x, we get:

x = (15 * 9)/15 = 9

Therefore, the length of DC is 9.

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Answer:

50°

Step-by-step explanation:

angle ABE and angle CBD are vertical angles and has same measure so <ABE = 50°

Answer:

22

Step-by-step explanation: