For a standard normal distribution, which of the following expressions must always be equal to 1?
OP(z≤-a)-P(-a≤z≤a)-P(z≥a).
OP(z≤-a)-P(-a≤z≤a)+P(z≥ a)
OP(z≤-a)+P(-a≤z≤a)-P(z≥a)
OP(z≤-a)+P(-asz≤a)+P(zza)

The value of (38)-2⁢(13⋅38)3⁢(13)4. is -154090

The expression is given as:

(38)-2⁢(13⋅38)3⁢(13)4.

Rewrite properly as:

(38) - 2 * ⁢(13 * 38) * 3 * ⁢(13) * 4.

Evaluate the products in the bracket

(38) - 2 * ⁢(494) * 3 * ⁢52

Further, expand

38 - 154128

Evaluate the difference

-154090

Hence, the value of (38)-2⁢(13⋅38)3⁢(13)4. is -154090

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Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

Answer

It can be (1+x)

n

only as (1−x)

n

terms are +ve/−ve alternatively hence can't be in A.P.,

General term, T

rH

=

n

C

r

⋅x

r

⇒T

5

=

n

C

4

⋅x

4

,T

6

=

n

C

5

⋅x

5

,T

7

=

n

C

6

⋅x

6

Coefficients are in A.P.

⇒2

n

C

5

=

n

C

4

+

n

C

6

⇒

5!(n−5)!

2n!

=

4!(n−4)!

n!

+

6!(n−6)!

n!

⇒

5(n−5)

2

=

(n−4)(n−5)

1

+

6×5

1

⇒2(n−4)=5+

6

1

(n−4)(n−5)

⇒12(n−4)=30+n

2

−9n+20

12n−48=n

2

−9n+50

⇒n

n

−21n+98=0

⇒n

2

−14n−7n+98=0

⇒n(n−14)−7(n−14)=0

⇒(n−7)(n−14)=0

n=7 or n=14.

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

Answer:

x = 3

y = -5

Step-by-step explanation:

       4x + y = 7 -------------------(I)

       5x - y = 20 -----------------(II)

Add both the equations. Now, y will be eliminated, and we can find the value of 'x'.

       (I)           4x + y = 7

      (II)           5x - y = 20       {Add the equations}

                    9x       = 27

Divide both sides by 9,

                            x = 27 ÷ 9

                            \(\boxed{\bf x = 3}\)

Now, Plugin the value of 'x' in equation (I)

          4*3 + y = 7

           12 +  y = 7

Subtract 12 from both sides,

                    y = 7 - 12

                    \(\boxed{\bf y = -5}\)

Answer:

Step-by-step explanation:

1Bothlineparrell
The The 80-(A

Answer:

p=30.2t+35.8

13966.48044692737

Answer:

41.93 degrees

Step-by-step explanation:

Answer:

A. { 3, 4, 5, 6, 7, 8, 9, 10}  

B. {4}

Step-by-step explanation:

A. { 3, 4, 5, 6, 7, 8, 9, 10}  

⇒ We didn't include 2 in this because 2 = 2, not greater than 2.

⇒ We also didn't include 11 for the same reason. 11 = 11, not less than 11.

B. First of all, this tells us that x is a natural number, i.e. x ≥ 1

The second thing it tells us is that x = 4. So the answer is {4}

(I may have misunderstood B. If I'm not correct, I'm really sorry. )

Answer:

Step-by-step explanation:

You want the solution to right triangle RST with RS = 15, R = 72°, T = 90°.

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse   ⇒   r = 15·sin(72°) ≈ 14.3

  Cos = Adjacent/Hypotenuse   ⇒   s = 15·cos(72°) ≈ 4.6

The acute angles in a right triangle are complementary, so ...

  S = 90° -R = 90° -72° = 18°

Answer:

0.1562 = 15.62% probability that a person who tests positive actually has the disease.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Tests positive

Event B: Has the disease.

Probability of a positive test:

100 - 8 = 92% of 0.6%(person has the disease).

3% of 100 - 0.6% = 99.40%(person does not have the disease). So

\(P(A) = 0.92*0.006 + 0.03*0.994 = 0.03534\)

Probability of testing positive and having the disease:

92% of 0.6%. So

\(P(A \cap B) = 0.92*0.006 = 0.00552\)

Probability that a person who tests positive actually has the disease.

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.00552}{0.03534} = 0.1562\)

0.1562 = 15.62% probability that a person who tests positive actually has the disease.

Answer:

1.666666667

Step-by-step explanation:

1/3 of 20 is 6.66666667

5-6.66666667 is -1.666666667

hope this helps :)

Answer:

≈1.7

Step-by-step explanation:

1/3(20)-5

≈6.7-5

≈1.7

Answer:

The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:

a is the coefficient of the x^2 term, which is -3 in this case.

b is the coefficient of the x term, which is -5 in this case.

c is the constant term, which is 9 in this case.

Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:

a = -3

b = -5

c = 9

Answer:

8.449 square centimeters

Step-by-step explanation:

Area of the figure = area of square + area of triangle

\( {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5\)

\(.142 \times 59.5 = 8.449\)

So 8.449 square centimeters of this figure is green.

Answer:

There is no particular formula for integer as it is nothing but a set of numbers. But there are certain rules when we perform any mathematical operations like addition, subtraction, etc on integers: Adding two positive integers will always result in a positive integer.

Step-by-step explanation:

Note that in the prompt above, the value of x is given as: 16°

To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.

As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 53°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(53°) = 180°
∠O = 180 - 106

∠O = 74°

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

74° + 90° + ∠OCB = 180°

∠OCB = 180° - 74° - 90°

∠OCB = 16°

Hence, the value of x is 16°.

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Answer:

Step-by-step explanation:

Let the equation be:

For the depth of 20 ft, the equation is:

For the depth of 25 ft, the pressure is:

y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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After answering the given query, we can state that  Cοnsequently, the area mοsaic has a surface size οf 1176cm².

An area is a measure οf a regiοn's extent οn a surface. The term "surface area" refers tο the area οf an οpen surface οr the perimeter οf a three-dimensiοnal οbject, whereas "planar regiοn" οr "planar regiοn" refers tο the area οf a shape οr planar layer.

The area οf an οbject is the entire vοlume οccupied by its planar (2-D) surface οr shape. On a sheet οf paper, make a square with a pencil. a twο-dimensiοnal figure. On paper, a shape's area is the amοunt οf rοοm it οccupies. Cοnsider that the square is made up οf smaller unit squares.

Since each tile is a right triangle, its area can be calculated by multiplying its limb lengths by twο and dividing by three:

Each blοck has an area οf (7 x 4 cm)/2, οr 14 cm2.

The mοsaic's οverall surface area is because there are 84 pieces in it:

(Area οf each piece) x = tοtal mοsaic area (Number οf tiles)

The mοsaic's tοtal size is 14 cm² times 84, οr 1176 cm².

Cοnsequently, the mοsaic has a surface size οf  1176 cm²

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The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.

The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.

To find the probability of choosing a girl who prefers blue, we need to use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.

The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.

Putting these values in the formula, we get:

Probability = 15/50 = 0.3

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Complete Question;

70 preschoolers were asked whether they preferred blue or pink.

35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.

Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Answer:

it is a

Step-by-step explanation: i gotchu

Answer:

a

Step-by-step explanation:

lolhehehehehdhdnisxkxnos

Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

Answer:

I have attached a really rough graph!!

Step-by-step explanation:

The point that does not fit in the proportional relationship is (6,2) when we plot the other three points and join the points they will give us a staright line but the point (6,2) isnt lying on that staright line.. Therefore, it does not fit in the proportional relationship!

Answer:

(6,2)

Step-by-step explanation:

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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Answer:

I think you can go with:

The margin of error is equal to half the width of the entire confidence interval.

so  try .74 ±   =   [ .724 , .756] as the confidence interval

Step-by-step explanation:

Answer: AAS

Step-by-step explanation:

We know that \(\angle TSN \cong \angle HSU\) because they are vertical angles, meaning the triangles are congruent by AAS.

the denominator will be zero when. \(x=-2\)or \(x=-7.\) Therefore, the domain of the expression is all real numbers except \(x=-2\) and \(x=-7\).

In mathematics, factoring refers to the process of finding the factors of a given number or expression. Factors are numbers or expressions that can be multiplied together to obtain the original number or expression. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these are the numbers that can be multiplied in pairs to obtain 12 (e.g. 2 x 6 = 12).

In algebra, factoring involves breaking down an algebraic expression into simpler expressions that can be multiplied together. This is done by finding common factors or using techniques such as difference of squares, perfect squares, or grouping. Factoring is an important tool in algebra, as it can help simplify complex expressions and solve equations.

To simplify a rational expression, follow these steps:

Step 1: Factor both the numerator and denominator if possible. For example, in the expression you provided, the numerator can be factored as\((2x+5)(x+4)\)and the denominator can be factored as \((2x+15)(x+2)\).

Step 2: Cancel out any common factors in the numerator and denominator. In this case, both the numerator and denominator have a common factor of (2x+5), which can be cancelled out.

Step 3: Simplify the remaining expression. After cancelling out the common factor, the simplified expression becomes:

\((2x+5)(x+4) / (2x+15)(x+2) = (x+4) / (x+2)(2x+15)\)

Domain restrictions occur when a value of x makes the denominator equal to zero, because division by zero is undefined. In this case, the denominator will be zero when x=-2 or x=-7. Therefore, the domain of the expression is all real numbers except x=-2 and x=-7.

It is important to identify any domain restrictions before simplifying a rational expression to ensure that the final expression is valid for all values of x in its domain.

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Answer:

the second one looks like it is correct