A random sample is taken and the sample size is 25. the sample is normally distributed, the sample mean is 80, and the standard deviation is 5.5. find a 90% confidence interval for the population mean.

In terms of l?

TSA

LSA

Answer:

[tex]\sf SA=54\pi\:\:\:cm^2[/tex]

Step-by-step explanation:

Surface Area of a Cone

[tex]\sf SA=\pi r l+\pi r^2[/tex]

where:

Given:

Substitute the given values into the formula and solve for SA:

[tex]\implies \sf SA=\pi (3)(15)+\pi (3)^2[/tex]

[tex]\implies \sf SA=45\pi+ 9 \pi[/tex]

[tex]\implies \sf SA=54\pi\:\:cm^2[/tex]

Therefore, the surface area of the cone in terms of pi is:

[tex]\sf SA=54 \pi\:\:\:cm^2[/tex]

Answer:

Step-by-step explanation:

Let k: y = a₁x + b₁ and l: y = a₂x + b₂. Then

We have the euation of a line in point slope form:

Convert to the slope intercept form:

y - 4 = 2(x - 6)

y - 4 = 2x - 12

y - 4 + 4 = 2x - 12 + 4

y = 2x - 8

The slope is m₁ = 2.

Let y = m₂x + b.

The lines is perpendicular. Therefore:

2m₂ = -1     |divide both sides by 2

The line passes through the point (-3, -5).

Substitute to the point slope equation:

y - (-5) = -1/2(x - (-3))

y + 5 = -1/2(x + 3)

The statements and reasons that complete the proof are:

4. ∠SPQ ≅ ∠TQR [alternate interior angles theorem]

5. ΔPQS ≅ ΔQRT [ASA congruence theorem]

When two pairs of corresponding angles and one pair of included sides of two triangles are congruent, they are congruent triangles based on the ASA congruence theorem.

We are given the following:

QT ≅ PS [a pair of congruent sides]

∠T ≅ ∠S [a pair of congruent angles]

Thus, since QT is parallel to PS, therefore:

∠SPQ ≅ ∠TQR [alternate interior angles theorem]

Therefore, we can now state that  ΔPQS ≅ ΔQRT based on the ASA congruence theorem.

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Answer:

HOW IS THAT EASY??!?!?!?!?!?

Step-by-step explanation:

The statements and reasons that complete the proof are:

4. ∠SPQ ≅ ∠TQR [alternate interior angles theorem]

5. ΔPQS ≅ ΔQRT [ASA congruence theorem]

What is the ASA Congruence Theorem?

When two pairs of corresponding angles and one pair of included sides of two triangles are congruent, they are congruent triangles based on the ASA congruence theorem.

We are given the following:

QT ≅ PS [a pair of congruent sides]

∠T ≅ ∠S [a pair of congruent angles]

Thus, since QT is parallel to PS, therefore:

∠SPQ ≅ ∠TQR [alternate interior angles theorem]

Therefore, we can now state that  ΔPQS ≅ ΔQRT based on the ASA congruence theorem.

Answer:

B

Step-by-step explanation:

We see the graph of y=x², so eliminate A.

Since the second graph opens downwards, the coefficient of x² must be negative, so eliminate C.

Also, the axis of symmetry is x = 0, so eliminate D.

This leaves us with B

Answer:

People surveyed: 79

a) p(s) = 46/79

b) p(snv) = 13/79

c) p(suv) = 96/79

hope this helps, and tell me if you get it right! It's prob wrong though, im bad at venn diagrams (×_×)⌒☆

Answer:An algorithm is a set of instructions for solving a problem or accomplishing a task.

Step-by-step explanation:

Any series of well defined steps that shows a procedure for solving a given type of problem is called an algorithm.

Step-by-step explanation:

Answer:

  if the ratio allowance/chores is constant, it is proportional

Step-by-step explanation:

The values x and y are directly proportional if they satisfy the equation ...

  y = kx

for some constant k, the constant of proportionality.

__

If the relation that produces ordered pairs (chores, allowance) is directly proportional, all of the ratios (allowance)/(chores) will have the same value: the constant of proportionality (k).

If the ratios are not constant, Carlos's allowance is not directly proportional to the number of chores he completes.

From unit conversion, it is found the following results:

6km ≈ 3.73 mi

2.5 L≈ 0.66 gal

90 lb ≈ 40.82 kg

Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others.  Because of this, it is important to know converting them.

For solving this question you need some information as:

1 km = 0.621371 mi ( unit for length and distance)

1 L = 0.2641722 gallons (unit for volume)

1 lb = 0.453592 kg (unit for mass)

Therefore,

           1 km --------  0.621371 mi

           6 km --------  x mi

           x= 6* 0.621371

           x=3.73 mi

Thus, 6km ≈ 3.73 mi.

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Answer:

C) When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.

Step-by-step explanation:

The Inscribed Similar Triangles Theorem states that if an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other.

The answers are given below:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

1. (cos x. cos y)(tan x + tan y) = sin (x+ y)

  (cos x. cos y)(tan x + tan y)

= cos x. cos y (sinx/ cos x + sin y/ cos y)

= sin x cos y + sin y cos x

= sin (x+ y)    [ sin ( x +y)]= sin x cos y + sin y cos x

= RHS

3. [tex]-\sin ^2\left(x\right)-\cos \left(2x\right)=0[/tex]

Using identity

[tex]-\cos ^2\left(x\right)=0[/tex]

cos ² x=0

Applying [tex]x^{n} =0[/tex] then x=0

So, cos x =0

General solution will be [tex]x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].

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La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.

Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:

Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:

Nota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:

Opciones:

A. Multiplicar (6)(4)

B. Multiplicar (7.5)(4.5)

C. Multiplicar (9)(6)

D. Multiplicar (9.5)(4.5)

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The answer is g(x) = 3x - 6

Answer:

A = -12

Step-by-step explanation:

A   put in -2 for 'x' in the equation to find value

       2(-2)  - y = 8       add 4 to both sides

              -y = 12

               y = -12              

        I think YOU can now find B and C  with this method !

Answer:

Using the concept of linear equations, we find that we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze.

Step-by-step explanation:

Let x = amount of 20% antifreeze

Let y = amount of 70% antifreeze

Given that the total amount of antifreeze is 80 gallons

So, x + y = 80

Also given that the purity of the total antifreeze is 60%.

0.65x + 0.90y = 0.70(x + y)

65x + 90y = 70(x + y)

Simplify and solve the system of equations

65x + 90y = 70x + 70y      

65x -70x+ 90y-70y = 0    

-5x + 20y = 0      

Now we have the following system of equations:

x + y = 50

-5x + 20y = 0

Multiply the first equation by 5 to get opposite coefficients for x;  

add the equations to eliminate x

5x + 5y - 5x + 20y = 250

25y = 250

y = 10              

Since the total mixed gallons is 50,

x = 50 - 10 = 40

So we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze

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The square for the  equation:  [tex]y=2x^{2} + 12x +1[/tex] is [tex]y=2(x+3)x^{2} -17[/tex]

The square for the  equation:  [tex]y=4x^{2} +48x-10[/tex] is [tex]y=4(x+6)x^{2} -154[/tex]

a)

[tex]y=2x^{2} +12x +1[/tex]

[tex]y = 2[(x^{2} + 6x)] + 1[/tex] ( taking common)

[tex]y = 2[(x+3)^{2} - 9] + 1[/tex] ( adding and subtracting 9 to make a square term

[tex]y = 2(x+3)^{2} - 18 + 1[/tex] ( multiplying by 2)

[tex]y=2(x+3)x^{2} -17[/tex]

b)

[tex]y=4x^{2} +48x-10[/tex]

[tex]y = 4[(x^{2} + 12x)] - 10[/tex]  (taking 4 common)

[tex]y = 4[(x+6)^{2} - 36)] - 10[/tex] (adding and subtracting 36)

[tex]y = 4(x+6)^{2} - 144 - 10[/tex](multiplying by 4)

[tex]y=4(x+6)x^{2} -154[/tex]

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Answer:

  (a)  Horizontal line test

Step-by-step explanation:

A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.

The inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.

If the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to pass.

A function will have an inverse function if it passes the Horizontal Line Test.

__

Additional comment

The attached graph shows a function (red curve) that does not pass the horizontal line test. Its inverse relation is the green curve, which you can see is not a function. It does not pass the vertical line test.

The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.

Answer:

A , B , D

Step-by-step explanation:

Answer:

Area of a triangle = 1/2 * base * height

here ,

base = 120 ft

height = 25 ft

Area = 1/2* 120*25

= 60 * 25

= 1500 ft²

Answer 2

Answer:

1/2 * base * height

so 1/2 * 25 * 120

= 1500

Answer:

Just simply input in your calculator arcsin of -5/6. Arcsin is the sign that looks like sin to the power of -1, even though it doesn't mean sin to the power of -1. This comes out to 303.6 degrees. So, it actually isn't in quadrant 3, it's in quadrant 4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

basically all you do is

Answer:

18.1cm

Step-by-step explanation:

Please refer to the attached photo for a better understanding. Apologies for the terrible drawing.

First we will find the length of BE by using pythagoras' Theorem.

[tex]c^{2} =a^{2} +b^{2} \\AB^{2} =BE^{2} +EA^{2} \\16^{2} =BE^{2} +7^{2} \\256=BE^{2} +49\\BE^{2} =256-49\\BE=\sqrt{207} cm[/tex]

We will leave BE as it is as it is not the final answer.

Since we know CD = BE,

CD = [tex]\sqrt{207} cm[/tex]

Now from the photo, draw a line from C to A or A to C, you will see another triangle.

Now we will use Pythagora's Theorem again to find AC.

[tex]AC^{2} =AD^{2} +DC^{2} \\AC^{2} =11^{2} +(\sqrt{207}) ^{2} \\AC^{2} = 121+207\\AC^{2} =328\\AC=\sqrt{328} \\=18.1cm (1dp)[/tex]

Answer:

75

Step-by-step explanation:

Note that

[tex]x^2 - y^2 = (x - y) (x + y)[/tex]

and

[tex]x^2 + 2xy + y^2 = (x + y)^2[/tex]

Then their LCM is [tex]\boxed{x + y}[/tex].

The possible values of x are 5 and -1/12

Given that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x

The ratio is given as:

2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1

Express as fraction

[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]

Cross multiply

4x^2 -4x + 1 = 16x^2 + x  -64x - 4

Collect like terms

-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0

Evaluate the like terms

-12x^2 + 59x + 5 = 0

Divide through by -1

12x^2 - 59x - 5 = 0

Expand

12x^2  + x - 60x - 5 = 0

Factorize

x(12x + 1) - 5(12x + 1) = 0

Factor out 12x + 1

(x - 5)(12x + 1) = 0

Expand

x  - 5 = 0 or 12x + 1 = 0

Solve for x

x = 5 or x = -1/12

Hence, the possible values of x are 5 and -1/12

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The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

We are given the logarithmic functions:

log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),

and we are asked to find the value of the logarithmic function log₄7.

On subtracting (i) from (ii), we get:

log₄21 - log₄3 = 2.196 - 0.792.

Using the quotient law of logarithms, according to which:

logₓa - logₓb = logₓ(a/b), we can write the above equation as:

log₄(21/3) = 1.404,

or, log₄7 = 1.404.

Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

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Answer:

A.

1.404

Step-by-step explanation:

Triangle ABC was rotated 90° around the point, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.

Triangle ABC was rotated 90° around the point B, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.

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