The steps below show the incomplete solution to find the value of x for the equation
7x − 3x − 4 = −1 + 21:

Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20

Which of these is most likely the next step?

4x = 24
4x = 16
4x = 5
4x = 80

The value of P(0.6 ≤ z ≤ 2.12) is, 26%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

To find the value of P(0.6 ≤ z ≤ 2.12).

Now, We can simplify as;

P(0.6 ≤ z ≤ 2.12) = P( z ≤ 2.12) - P(z < 0.6)

So, From the Cumulative Standardized Normal Distribution table,

P( z ≤ 2.12) = 0.9830

P(z < 0.6) = 0.7257

Hence, We get;

P(0.6 ≤ z ≤ 2.12) = P( z ≤ 2.12) - P(z < 0.6)

P(0.6 ≤ z ≤ 2.12) = 0.9830 - 0.7257

P(0.6 ≤ z ≤ 2.12) = 0.2573

P(0.6 ≤ z ≤ 2.12) = 0.26

P(0.6 ≤ z ≤ 2.12) = 26%

Thus, The value of P(0.6 ≤ z ≤ 2.12) is, 26%

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Answer:

19.SA of a cylinder = (2 * π * r²) + (2 * π * r * h)SA = (2 * π * 5²) + (2 * π * 5 * 20)SA = (2 * π * 25) + (2 * π * 5 * 20)SA = (2 * π * 25) + (2 * π * 5 * 20)SA = (157) + (628)SA = 785The answer is A. 785 square meters.20.SA of a rectangle = 2(wl + hl + hw)w = 15l = 4h = 14SA = 2(15*4 + 14*4 + 14*15)SA = 2(60 + 56 + 210)SA = 2(326)SA = 652The answer is B. 652 square centimeters.

Step-by-step explanation: I did the math and this is what I got.

The given equation simplifies to -2n + 33 = -2n + 33, where both sides are equal, hence 'n' can be any real number. Thus the equation has infinitely many solutions.

This question pertains to solving a linear equation. The given equation is 3(n+11)-5n=-2(n-12)+9.

Let's solve this step by step:

This indicates that we have infinitely many solutions because any value of 'n' satisfies this equation.

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Answer:

Expression 1. P+1.2p

Expression 2. 2.2p

Step-by-step explanation:

These 2 equivalent expressions state that increasing a value by 120% is the same as multiplying the original value by 2.2.

Example: assume that p=50. The first expression gives p+1.2p=50+1.2(50) =110. The second expression gives 2.2p=2.2(50)=110

The two expressions 1.2p and p + 0.2p are equivalent, as they both represent the same relationship between the current stock price and the stock price last week.

What is the expression?

Expressions are defined as mathematical statements that have a minimum of two terms containing that variables or numbers.

If the stock price increased by 120% over the past week, then the current stock price is 120% of the stock price last week. This can be represented by the equation:

current price = 1.2p

Another way to represent the same relationship is to say that the current price is the stock price last week plus 120% of the stock price last week. This can be represented by the equation:

current price = p + 0.2p

To prove that these two expressions are equivalent, we can substitute a value for p into both equations and show that they give the same result. For example, if the stock price last week was $100, then:

current price = 1.2100 = $120

current price = 100 + 0.2100 = $120

Therefore, the two expressions are equivalent, as they both represent the same relationship between the current stock price and the stock price last week.

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Answer:

35 they are right

Step-by-step explanation:

The ratio of trumpet players to tuba players at the high school is 5:2. There are 2 trumpet players for every 5 tuba players.

The ratio of trumpet players to tuba players at a high school is 5:2. This means that for every 5 trumpet players, there are 2 tuba players. Therefore, option C is correct, which states that there are 2 trumpet players for every 5 tuba players.

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Answer:

x intercepts are (4,0) and (-9,0)

Step-by-step explanation:

The given function graphed f(x) = x² + 5x -36 and we have to find the x-intercepts.

Since x intercepts means points on x-axis which will  have y-coordinates as zero.

so f(x) = x² + 5x - 36 = 0

x² + 9x - 4x - 36 = 0

x(x+9) - 4(x-9) = 0

(x-4)=0 ⇒ x = 4

or ( x+9) = 0 ⇒ x = (-9)

Therefore, x intercepts are (4,0) and (-9,0)

Considering the definition of function quadratic and roots, the roots or x-intercepts of the graph of the function f(x) = x² + 5x − 36 are 4 and -9.

The function f(x) = ax²  + bx + c

with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).

The roots are those values ​​of x for which the expression is 0, so it graphically cuts the x-axis.

This can be solved by:

[tex]x1, x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

In this case you know that a=1, b= 5 and c= -36. So the roots can be determined as:

[tex]x1=\frac{-5+\sqrt{5^{2} -4x1x(-36)} }{2x1}[/tex]

[tex]x1=\frac{-5+\sqrt{25 +144} }{2}[/tex]

[tex]x1=\frac{-5+\sqrt{169} }{2}[/tex]

[tex]x1=\frac{-5+13}{2}[/tex]

[tex]x1=\frac{8}{2}[/tex]

x1= 4

and

[tex]x2=\frac{-5-\sqrt{5^{2} -4x1x(-36)} }{2x1}[/tex]

[tex]x2=\frac{-5-\sqrt{25 +144} }{2}[/tex]

[tex]x2=\frac{-5-\sqrt{169} }{2}[/tex]

[tex]x2=\frac{-5-13 }{2}[/tex]

[tex]x2=\frac{-18 }{2}[/tex]

x2= -9

Finally, the roots or x-intercepts of the graph of the function f(x) = x² + 5x − 36 are 4 and -9.

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x-30 =14-3x

subtract 1 x from each side

-30 =14-2x

subtract 14 from each side

-44 = 2x

x=-44/2 = -22

x=-22

check:-22-30 = -52

14-3(-22) = 14-66 =-52

 both equations equal

X = -22

Answer:

Intersection points are

(0.39,0) and (3.16,0)

Step-by-step explanation:

The equation of the outfield is [tex]h=-16t^2 + 65t[/tex]

The path equation is [tex]h=8t+20[/tex]

To find intersection of two equations , we make them equal and solve for t

[tex]-16t^2+65t= 8t+20[/tex]

Subtract 8t from both sides

[tex]-16t^2+57t=20[/tex]

Subtract 20 on both sides

[tex]-16t^2+57t-20=0[/tex]

Divide whole equation by -1

[tex]16t^2-57t+20=0[/tex]

Apply quadratic formula to solve for t

[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a= 16, b=-57 and c=20

[tex]t=\frac{57+-\sqrt{(-57)^2-4(16)(20)}}{2(16)}[/tex]

[tex]t=\frac{57+-\sqrt{1969}}{32}[/tex]

[tex]t=\frac{57+\sqrt{1969}}{32}=3.16[/tex]

[tex]t=\frac{57-\sqrt{1969}}{32}=0.39[/tex]

By definition, the volume of a cone is given by:

[tex] V = (\frac{1}{3}) * (\pi) * (r ^ 2) * (h)
[/tex]

Where,

r: radius of the circular base

h: height of the cone

Since we have 6 conical pots, then the total volume is:

[tex]Vt=6V[/tex]

[tex] Vt = 6 * (\frac{1}{3}) * (\pi) * (r ^ 2) * (h)
[/tex]

Substituting values we have:

[tex] Vt = 6 * (\frac{1}{3}) * (3.14) * (3 ^ 2) * (8)

Vt = 452.16 cm ^ 3
[/tex]

Rounding to the nearest cubic centimeter:

[tex] Vt = 452 cm ^ 3
[/tex]

Answer:

are needed 452 cm^3 of soil to plant the full tray

The cubic centimeters of soil are needed to plant the full tray is approximately 452cubic in

The formula for calculating the volume of a cone is expressed as:

V = 1/3πr²h

r is the radius  = 3cm

h is the height = 8cm

Substitute

V =  1/3 * 3.14 * 3^2 * 8
V = 75.36 cubic cm

Since the gardener uses a tray of 6 conical pots to plant seeds, the total volume will be expressed as:

T = 6(75.36)
T = 452cubic in

Hence the cubic centimeters of soil are needed to plant the full tray is approximately 452cubic in

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Lucy starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at post office.

Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.

From the given data:

The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.

Answer: correct choice is A.

In this exercise we have to mark the correct alternative corresponding to the location, so we have:

Letter A

The following information was then given by the statement:

Imagining the paths made by lucy as a triangle, we know that the longest path that corresponds to the hypotenuse will be from the gas station to her house, so:

We have:

[tex]180-90=90\\90/2=45\\45-15=30[/tex]

The smallest angle is at the gas station.

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