How would you write the phrase below as an algebraic
expression?
3 decreased by a number times 2
O 3x+2
3-2x
2x-3
O 2(3)-x

The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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Answer:

1. 56

2. 56

Step-by-step explanation:

edge 2021

The measure of the arcs of the circle is given by

a) The difference of arc measures mAC - mDE = 56°

b) The measure of angle 2(∠ABC ) = 56°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

θ/360 * πr²

where;

θ is the central angle of the sector

r is radius

Now, looking at the given options we can say that the only one that represents the area of the sector is;

A = n/360 * πr²

where n is the central angle of the sector'

Given data ,

Let the measure of the arcs of the circle be

The measure of angle ∠ABC = 28°

The measure of arc mAC = 80°

The measure of arc mDE = 24°

So , the difference of arc measures mAC - mDE = 80 - 24

The difference of arc measures mAC - mDE = 56°

And , measure of angle 2(∠ABC ) = 56°

Hence , the measures of arcs of circle is solved

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Answer: he drives 273 miles for 7 hours

Step-by-step explanation:

Answer:

\(\displaystyle f^{-1}(x)=\frac{6x-60}{5}\)

Step-by-step explanation:

Inverse function

Given the function

\(\displaystyle f(x)=\frac{5}{6}x+10\)

We find its inverse following the procedure below:

\(\displaystyle y=\frac{5}{6}x+10\)

\(6y=5x+60\)

\(5x=6y-60\)

\(\displaystyle x=\frac{6y-60}{5}\)

\(\displaystyle y=\frac{6x-60}{5}\)

\(\boxed{\displaystyle f^{-1}(x)=\frac{6x-60}{5}}\)

This is the inverse function

The equation y = y − σ y3 is used in the study of the stability of fluid flow to analyze the behavior of the deviation of the fluid flow from its equilibrium state and determine whether the flow will remain stable or become unstable and potentially turbulent.

The equation y = y − σ y3 is used in the study of the stability of fluid flow. The equation occurs when we are examining the stability of a fluid flow system. In this case, the variable y represents the deviation of the fluid flow from its equilibrium state, and σ is a parameter that represents the strength of the nonlinear term in the equation.

The stability of fluid flow is an important concept in fluid dynamics, as it determines whether a flow will remain stable or become unstable and potentially turbulent. The equation y = y − σ y3 is used to examine the stability of a fluid flow system by analyzing the behavior of the deviation of the fluid flow from its equilibrium state.

If the deviation of the fluid flow from its equilibrium state is small, then the equation y = y − σ y3 will have a stable solution, and the fluid flow will remain stable. However, if the deviation of the fluid flow from its equilibrium state is large, then the equation y = y − σ y3 will have an unstable solution, and the fluid flow will become unstable and potentially turbulent.

In conclusion, the equation y = y − σ y3 is used in the study of the stability of fluid flow to analyze the behavior of the deviation of the fluid flow from its equilibrium state and determine whether the flow will remain stable or become unstable and potentially turbulent.

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

As the level of significance increases, the probability of making a type II error decreases.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

If the level of significance of a hypothesis test is raised from 0.05 to 0.1, the probability of a type II error will decrease.

Type II error occurs when we fail to reject a null hypothesis that is actually false. It is the probability of accepting a false null hypothesis. By increasing the level of significance, we are making it easier to reject the null hypothesis, which in turn decreases the probability of accepting a false null hypothesis.

Hence, as the level of significance increases, the probability of making a type II error decreases.

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Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

The domain of the given function is (5, -∞) and the range of the function is (-1, -∞)

Follow these steps to see a function's domain and range in a graph:

For the domain, the function is starting from x =5 and goes to x= infinity.

For the range, the maximum value of the function is starting from y =-1  and the minimum value is y = -∞ .

Therefore, the domain of the given function is (5, -∞) and the range of the function is (-1, -∞)

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a). We have proved all the given conditions.

b). It is true that condition 3 holds for all regular languages L1 and L2.

(a) Regular languages L1 and L2 can be suggested as follows:

Let \(L_1={0^{(n+1)} | n\geq 0}\)

and

\(L_2={1^{(n+1)} | n\geq 0}\)

We have to prove three conditions:1. L1 ⊈ L2:

The given languages L1 and L2 both are regular but L1 does not contain any string that starts with 1.

Therefore, L1 and L2 are distinct.2. L2  L1:

The given languages L1 and L2 both are regular but L2 does not contain any string that starts with 0.

Therefore, L2 and L1 are distinct.3. (L1 ∪ L2)* = L1* ∪ L2*:

For proving this condition, we need to prove two things:

First, we need to prove that (L1 ∪ L2)* ⊆ L1* ∪ L2*.

It is clear that every string in L1* or L2* belongs to (L1 ∪ L2)*.

Thus, we have L1* ⊆ (L1 ∪ L2)* and L2* ⊆ (L1 ∪ L2)*.

Therefore, L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Second, we need to prove that L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Every string that belongs to L1* or L2* also belongs to (L1 ∪ L2)*.

Thus, we have L1* ∪ L2* ⊆ (L1 ∪ L2)*.

Therefore, (L1 ∪ L2)* = L1* ∪ L2*.

Therefore, we have proved all the given conditions.

(b)It is true that condition 3 holds for all regular languages L1 and L2.

This can be proved by using the fact that the union of regular languages is also a regular language and the Kleene star of a regular language is also a regular language.

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This is true, we can verify that the equation n(A∪B)=n(A)+n(B) holds for the given disjoint sets A={a,e,i,o,u} and B={g,h,k,l,m}.

Since A and B are disjoint sets, meaning they have no common elements, we can say that A∩B=∅. Therefore, the equation n(A∪B)=n(A)+n(B) becomes:
n({a,e,i,o,u,g,h,k,l,m}) = n({a,e,i,o,u}) + n({g,h,k,l,m})
Counting the elements, we see that n({a,e,i,o,u,g,h,k,l,m})=10, n({a,e,i,o,u})=5, and n({g,h,k,l,m})=5.
Substituting these values back into the equation, we get:
10 = 5 + 5
Hi! To verify the equation n(A∪B) = n(A) + n(B) for the given disjoint sets A = {a, e, i, o, u} and B = {g, h, k, l, m}, we first need to find the union of sets A and B.
Since A and B are disjoint (meaning they have no elements in common), the union of A and B, denoted as A∪B, simply combines the elements of both sets. So, A∪B = {a, e, i, o, u, g, h, k, l, m}.
Now, let's find the number of elements (n) in each set:
n(A) = 5 (as there are 5 elements in set A)
n(B) = 5 (as there are 5 elements in set B)
n(A∪B) = 10 (as there are 10 elements in the union of A and B)
Now, we can verify the equation:
n(A∪B) = n(A) + n(B)
10 = 5 + 5

The equation holds true for the given disjoint sets A and B.

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Both \(f(x) = -x^2\) and \(f(x) = -2x^3 + 5x^2 - 3x + 7\) approach negative infinity as x approaches infinity.

As x approaches infinity, the dominant term of the function determines its behavior. In the case of \(f(x) = -x^2\), the term \(x^2\) becomes infinitely large and negative, causing the entire function to approach negative infinity. Similarly, in the case of \(f(x) = -2x^3 + 5x^2 - 3x + 7\), the term \(-2x^3\) dominates and becomes infinitely negative as x approaches infinity, causing the entire function to approach negative infinity. This is because the negative exponent on \(x^3\) causes the value of the term to become increasingly negative as x increases without bound.

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Answer:

4071.5 in^2

Step-by-step explanation:

The surface area of a sphere of radius r is A = 4πr²

In this case, with r = 18 in, A = 4π(18 in)² = 4071.5 in²

The thing that I notice about the two triangles in terms of their size and shape is that they  that is the triangles tend to appear to be of the same size and shape.

Congruent triangles are known to be triangles that are said to have both the same shape and also of the same size for the two triangles.

Note that in the case above, we need to understand that the factors of a triangle are composed of 3 angles and the 3 facets and when you put the three together following the description given, a Congruent triangle will be formed.

Therefore, The thing that I notice about the two triangles in terms of their size and shape is that they  that is the triangles tend to appear to be of the same size and shape.

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Answer:

x = 10/-3

Step-by-step explanation:

-3x - 9 = 2 - 1

-3x - 9 = 1

-3x = 1 + 9

-3x = 10

x = 10 / -3

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Answer:The answer is 1/6

Step-by-step explanation:1/8 miles in 3/4 minutes

then, that means in 1 minute ( 1 min = 3/4 * 4/3) Emma will ride a distance of (1/8)*(4/3)= (1*4)/(8*3)= 1/6.

The answer is 1/6 (in 1 min she will ride 1/6 miles).

The kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.

The potential energy of the roller coaster at the top of the hill can be calculated as:

PE = mgh

where m is the mass of the car and its passengers, g is the acceleration due to gravity \((9.8 m/s^2\)), and h is the height of the hill (62 m). Thus, we have:

PE =\((1088 kg)(9.8 m/s^2)(62 m) = 670,720 J\)

At the bottom of the hill, all of the potential energy has been converted to kinetic energy. The kinetic energy of the roller coaster can be calculated as:

\(KE = (1/2)mv^2\)

where v is the speed of the roller coaster at the bottom of the hill. Thus, we have:

\(KE = (1/2)(1088 kg)(33 m/s)^2 = 594,576 J\)

Therefore, the kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.

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The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

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The equation (dot product form) for the hyperplane in Rⁿ that contains the point y = (-4, 3, -1, 4) and has the normal vector D = (-3, -4, -2, 1)ᵀ is given by the equation -3x₁ - 4x₂ - 2x₃ + x₄ = -32.

This equation represents the hyperplane in n-dimensional space. The dot product of the vector D and the variable vector x, minus the dot product of D and the point y, is set equal to a constant (-32 in this case) to define the hyperplane.

To find the equation of the hyperplane in dot product form, we use the equation D·x = D·y, where D is the normal vector, x is the variable vector of the hyperplane, and y is a point on the hyperplane.

In this case, the point is y = (-4, 3, -1, 4) and the normal vector is D = (-3, -4, -2, 1)ᵀ. Plugging these values into the equation, we get:

(-3)x₁ + (-4)x₂ + (-2)x₃ + (1)x₄ = (-3)(-4) + (-4)(3) + (-2)(-1) + (1)(4) = -32

Thus, the equation for the hyperplane in dot product form is -3x₁ - 4x₂ - 2x₃ + x₄ = -32. This equation defines the hyperplane that contains the given point and has the given normal vector in n-dimensional space.

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Answer:

3. 2 6 30          6. 8:5

   3 9 45

Step-by-step explanation:

The values of a,b,c,d for \(2x^3-6x^2-36x=2x(ax+b)(cx+d)\) are given by 1, -6, 1, 3 respectively.

Given the equation is,

\(2x^3-6x^2-36x=2x(ax+b)(cx+d)\)

factorizing the left hand expression we get,

\(2x^3-6x^2-36x\\=2x(x^2-3x-18)\\=2x(x^2-6x+3x-18)\\=2x[x(x-6)+3(x-6)]\\=2x(x+3)(x-6)\)

So, 2x(x-6)(x+3) = 2x(ax+b)(cx+d)

So, a=1, c=1, b= - 6, d=3

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Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

The closest point to y in the subspace w spanned by u1 and u2 is [14/9, 46/9, 5/3], which is closest to option B.

The closest point to y in the subspace w spanned by u1 and u2 can be found using the formula:

proj_w(y) = [(y dot u1)/(u1 dot u1)]u1 + [(y dot u2)/(u2 dot u2)]u2

where dot denotes the dot product.

Substituting the given values, we get:

proj_w(y) = [(112 + 92 - 22*(-1))/(22 + 22 + (-1)(-1))] [2 2 -1] + [(11(-1) + 93 + 224)/(11 + 33 + 4*4)] [-1 3 4]

= [14/9, 14/9, -7/9] + [0, 16/3, 14/3]

= [14/9, 46/9, 5/3]

Therefore, the closest point to y in the subspace w spanned by u1 and u2 is [14/9, 46/9, 5/3], which is closest to option B.

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Answer:x=9

Step-by-step explanation:

Answer: x = 9

Step-by-step explanation:

9x + 5 = 86

9x + 5 - 5 = 86 - 5 (you subtract 5 from both sides to isolate the 9x)

9x = 81

9x/9 = 81/9 (to get the value of x, you divide both sides by 9)

x = 9

Answer:

23 is the answer u understand