A meteorologist found that the rainfall in Campbell during the first half of the month was 3/10 of an inch. At the end of the month, he found that the total rainfall for the month was 1/2 of an inch. How much did it rain in the second half of the month?

The value of the expression ((-3)^4)^2 when simplified is 6561

Expressions are mathematical statements represented by numbers, arithmetic operations and variables

The expression is given as:

((-3)^4)^2

Start by expanding the inner bracket

((-3)^4)^2 = ((-3)*(-3)*(-3)*(-3))^2

Next, we evaluate the product (-3)*(-3)*(-3)*(-3)

This gives

((-3)^4)^2 = (81)^2

Next, expand the exponent

((-3)^4)^2 = (81) * 81

Next, we evaluate the product

This gives

((-3)^4)^2 = 6561

Hence, the value of the expression ((-3)^4)^2 when simplified is 6561

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Between 95% confidence interval and 80% confidence interval, 95% confidence interval is wider than 80% confidence interval.

Given two confidence interval 95% and 80%.

For a given sample data, each confidence interval have different width.

This is because the critical value associated with the confidence level becomes larger as the confidence level is increased which results in an increased interval.

Confidence interval is the range of estimate.

The confidence interval for a population proportion can be found by the following formula:

p±[tex]\sqrt{(pq)/n}[/tex]

The value of z will be wider if the value of p,q are greater.

Hence 95% confidence interval will be wider than 80% confidence interval.

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Step-by-step explanation:

Volume of the right circular cone=31πr2h=31×π×6×6×10=120πcm3

Answer:

Volume =  405π unit^3

which is

1272.35 unit^3 to nearest hundredth.

Step-by-step explanation:

Volume of the given cone

= 1/3 πr^2 h

= 1/3π(6)^2*10

=  120π unit^3.

The cone similar to it with radius 9 will have a volume equal to

(9/6)^3 times the given cone

= 120π * 729/216

= 405π unit^3.

Answer:

see image

Step-by-step explanation:

see image. We can use the given info and definition of isosceles (congruent sides) and reflexive property (something is congruent to itself) to prove (i) by SSS.

The using "Corresponding Parts of Congruent Triangles are Conguent" (CPCTC) to get more info to prove (ii) by SAS

The answer to the question isit has only one solution  x = 0

The equation that Kate is solving is given as

2/3(6x - 3) = 1/2(6x - 4)

Then we have to factorize the equations

Such that we would have

[tex]\frac{2(6x-3)}{3} =\frac{2(3x-2)}{2}[/tex]

The next step of the equation would have to do with opening the equation

Then we would have 4x - 2 = 3x - 2

then 4x - 3x = 0

Then x = 0

Hence the solution of the equation is that it only has one solution x = 0

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Answer:

B. The equation has one solution: x = 0.

Step-by-step explanation:

The expressions that represent number of tiles that Devon used on her mosaic:

A. 20 + 2t + 2c

D. 20 + t + t + c + c

An expression refers to a mathematical equation which shows the relationship between two or more numerical quantities or variables.

For the expressions that represent number of tiles that Devon used on her mosaic:

Mathematically, the expression is given by:

Total tiles = 20 + t + t + c + c

Total tiles = 20 + 2t + 2c.

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Complete Question:

Devon made a mosaic in art class with different-shaped tiles. She started by putting 2 rows of t triangle tiles at the top of the mosaic and 2 rows of c circle tiles at the bottom. She finished by putting 20 square tiles in between the triangle and circle tiles.

Pick all the expressions that represent how many tiles Devon used on her mosaic.

A. 20 + 2t + 2c

B. 20 + 4 ( t + c )

C. 2 ( 20 + t + c )

D. 20 + t + t + c + c

Answer:

50000

Step-by-step explanation:

Using

[tex]P(percentage) \times CP(cost \: price) = Sales \: Tax[/tex]

Putting the given values

P × 25000 = 1750

[tex]P = \frac{1750}{25000} [/tex]

[tex]P = 0.07 \times 100[/tex]

[tex]P = 7\%[/tex]

Now

For purchase price of a new car.

[tex]P \times CP=Sales \: Tax[/tex]

[tex]7 \times CP = 3500[/tex]

[tex]CP = 50000[/tex]

Hope it helps you, any confusions you may ask!

The equation that can be used to represent total tickets sales is 2170 = 5s + 2f + 10a

let

Expression for number of students tickets sold;

s = f + 15

Expression for number of faculty tickets sold;

f = 2a

Expression for number of alumni tickets sold;

f = 2a

a = f/2

2170 = 5s + 2f + 10a

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The rate at which the water from the container is being drained is 24 inches per second.

Given radius of right circular cone 4 inches .height being 5 inches, height of water is 2 inches and rate at which surface area is falling is 2 inches per second.

Looking at the image we can use similar triangle propert to derive the relationship:

r/R=h/H

where dh/dt=2.

Thus r/5=2/5

r=2  inches

Now from r/R=h/H

we have to  write with initial values of cone and differentiate:

r/5=h/5

5r=5h

differentiating with respect to t

5 dr/dt=5 dh/dt

dh/dt is given as 2

5 dr/dt=5*-2

dr/dt=-2

Volume of cone is 1/3 π[tex]r^{2} h[/tex]

We can find the rate at which the water is to be drained by using partial differentiation on the volume equation.

Thus

dv/dt=1/3 π(2rh*dr/dt)+([tex]r^{2}[/tex]*dh/dt)

Putting the values which are given and calculated we get

dv/dt=1/3π(2*2*2*2)+(4*2)

=1/3*3.14*(16+8)

=3.14*24/3.14

=24 inches per second

Hence the rate at which the water is drained from the container is 24 inches per second.

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Answer:

first 35 out of 100 then second person 34 out of 99

Step-by-step explanation:

The expected value of drawing a  marble from the jar is -$0.8.

Given that jar is filled with 50 coloured marbles out of which 8 are red , 20 are blue and 22 are green and we have to find the expected value that a player will get by drawing one marble from the jar if the prize of drawing red marble is $20 and loss of $10 if blue marble is drawn.

Probability that a red marble is drawn from jar=8/50

Probability that a blue marble is drawn from jar=20/50

Probability that a green marble is drawn from jar=22/50

Value that player can expect by drawing a red marble from jar=

=P(X=red)*20-P(X=blue)*10+P(X=green)*0

=8/50*20-20/50*10+0

=16/5-20/5

=-4/5

=-0.8

It is negative ,means that player will not get any money. In fact player will lose $0.8.

Hence the expected value that player can expect is -$0.8.

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Question is incomplete as it should include that calculate the expected value of drawing a marble.

In the case above, the option that one need to include in your answer is to Find a common denominator.

When the numerator and denominator of a fraction are known to not have common factor other than 1, then a person can say that the fraction in its simple form or say its in its lowest term.

Since there is a common numerator and the common denominator will be between 10 and 20. Since 10 is less that than 20, the common denominator will be 20 as both can divide it.

Hence, In the case above, the option that one need to include in your answer is to Find a common denominator.

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Answer:

9

Step-by-step explanation:

3 + 0 = 3

-2 + 6 = 4

2 + 18 = 20

From this:

1 + 8 = 9

Answer:

A.9

Step-by-step explanation:

✓3 + 0 = 3

✓ -2 + 6 = 4

✓ 1 + 8 = 9

✓ 2 + 18 = 20 beacuse of this the answer is 9

Answer:

Step-by-step explanation:

I assume that QP = 18 cm and m∠Q = 72°

Answer:

[tex]\fbox {P = 6.76 cm}[/tex]

Step-by-step explanation:

Finding the missing angle :

Applying the Law of Sines :

[tex]\boxed {\frac{sin P}{P} = \frac{sin R}{PQ}}[/tex]

Substituting the known values :

Answer:

True

Step-by-step explanation:

We got the formula for that:

F=ma

now if you replace the given data, it's gonna be

F=5 kg×3m/s²====> F=15kg.m/s²

Comparing with the original expression, the value that will go into the green box is 5

Given the indices expression below;

[tex]\frac{4^{-5}}{4^4}[/tex]

Since 4^-5 is equivalent to 1/4^5, hence the given expression will be equivalent to;

[tex]\frac{1}{4^5\times4^4}[/tex]

Comparing with the original expression, the value that will go into the green box is 5

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The measure of angle A in the isosceles trapezoid is:  106°.

In an isosceles trapezoid, the base angles are equal while the opposite angles are supplementary or have a sum of 180°.

The diagram given is an isosceles trapezoid. Therefor we would have:

m∠A = 180 - 74 [supplementary angles]

m∠A = 106°

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The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

In this problem we have a piecewise defined function formed by three functions: (i) Linear equation, (ii) Quadratic equation, (iii) Linear equation. The first function is y = 40, for 0 ≤ x < 15.

The second function can be found based on the knowledge of three points:

y = a · x² + b · x + c

(x₁, y₁) = (15, 40)

40 = 225 · a + 15 · b + c

(x₂, y₂) = (45, 2.5)

2.5 = 2025 · a + 45 · b + c

(x₃, y₃) = (65, 20)

20 = 4225 · a + 65 · b + c

And the quadratic equation is y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65.

And the latter linear equation is:

y = m · x + b

m = (30 - 20)/(90 - 65)

m = 0.4

And the x-intercept is:

b = y - m · x

b = 20 - 0.4 · 65

b = - 6

The linear equation is y = 0.4 · x - 6, for x ≥ 65.

The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

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Answer:

a) 10, 20, 30, ...
b) 2, 4, 6, ...
c) 10, 20, 30, ...
d) 61, 66, 71, 76, ...
e) 180, 280, 380, ...

i dont know if this is correct but hope it helps

Answer:

Step-by-step explanation:

I'm not entirely sure that this is correct, but it seems so to me from what I've  read.

The Coordinate system uses N,S,E,W to denote plus and minus. N (north) and E (east) are plus, and S (south) and W (west) are minus. North is + y and S is - y. E (east is plus x W is minus x)

(4,-7) = 4 east 7 south is what I would use as my answer.

The matricial equation of the degenerate parabola is [tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex].

A parabola is degenerated when its axis of symmetry is not parallel to any orthogonal axis (i.e. x, y). First, we have to find an "equivalent" parabola whose axis of symmetry is parallel to the y-axis and whose vertex is along that axis.

Direction of the degenerate parabola

[tex]\tan \theta = \frac{2 - 1}{2 - 1}[/tex]

tan θ = 1

θ = 45°

This means that the degenerate parabola must be rotated 45° clockwise (- 45°) around the origin with respect to the "equivalent" parabola.

Distance from the vertex to the focus

[tex]p = \sqrt{(2 - 1)^{2}+(2 - 1)^{2}}[/tex]

[tex]p = \sqrt{2}[/tex]

Vertex of the "equivalent" parabola

[tex](h', k') = (0, \sqrt{2})[/tex]

Equation of the "equivalent" parabola

[tex]y = \frac{1}{4\cdot p}\cdot x^{2} + k'[/tex]

[tex]y = \frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}[/tex]

Now we apply following rotation formula:

[tex]\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}\cos (-45^{\circ})&-\sin (-45^{\circ})\\\sin (-45^{\circ})&\cos (-45^{\circ})\end{array}\right] \cdot \left[\begin{array}{c}x\\\frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}} \end{array}\right][/tex]

[tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex]

A representation of the degenerate parabola is shown in the figure attached below.

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The statements which summarize each student's conjecture are:

Trey and Serena are both trying to find the number of stones that were in the original arch or vault. Thus, when they identify the number of stones and its main features, they would be able to determine the type of arch or vault that was built there.

The statements which summarize each student's conjecture are:

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Complete Question:

The Students' Conjectures: During an archeological dig, the students found a voussoir from a semicircular stone arch. A voussoir is a trapezoidal (wedge-shaped) stone used to build an arch or vault.

1. What are the students trying to find out? (1 point)

2. Complete the table to summarize each student's conjecture: (2 points: 1 point for each row)

Answer:

Step-by-step explanation:

a) ∠PQR=65° (alternate interior angles theorem)

∠PRQ = 60° (linear pair)

x = 55° (angles in a triangle add to 180°)

b) ∠APQ and ∠PQR are congruent alternate interior angles.

The absolute value of the number upon the given evaluation is; 22.

It follows from the task content that the number given is; -27 on the number line and subsequently, there's a movement of 5 integers to the right.

On this note, the absolute value of the result upon the evaluation is; |-27+5| = |-22| = 22.

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The statement which is true about the end behaviour of the graphed function is; As the x-values go to positive infinity, the function’s values go to positive infinity.

The graph given according to the task content is described to have its first minimum at (-2,0), and then a maximum at; (-0.5, 5) and finally a minimum at; (1.05, -41).

Additionally, since the graph has 3 zeroes as given, it follows that the graph is that of a cubic function which takes the w-form.

Consequently, it can be inferred from the statements above that; As the x-values go to positive infinity, the function’s values go to positive infinity.

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Answer:

A

Step-by-step explanation:

edge 23

Answer:

To solve this problem we first subtract 3 from both sides, giving the inequality -cw+3-3<= 15-3. We then simplify the equation to -cw<= 12. Next, we divide both sides by -c and flip the inequality. We flip the inequality because we are dividing by a negative. Now we have the inequality -cw/-c >= 12/-c. Lastly, we simplify to w >= -12/c.

A is proportional.

Lets simplify the problem,

← divide numerator/ denominator by 4

= 4/20= 1/5

Thus A form a proportion

≠ 1/5

Thus B is not a proportion

← divide numerator/ denominator by 4

=  2/5 ≠ 1/5

Thus C is not a proportion

5/1 ≠ 1/5

Thus D is not a proportion

A is proportional.

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Initially, as x increases, y decreases.

The slope of the graph is equal to 1 for all x between x=0 and x=3.

Starting at x=3, the function value y increases as x increases.

The slope of the graph is equal to 3 for x between x=3 and x=5.

For x between x=0 and x=4, the function value y decreases then increases to 0.

For x between x=4 and x=8, the function value y increases and decreases to 0.

From the graph, initially the it goes down when x increases up-to the x value 3. After that from x value 3 to 5, the graphs goes up. After that from the x value 5 it goes down to zero.

The slope of the line is the measurement of inclination of that line from the positive x-axis. It can be calculated by the following formula.

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of the graph between x=0 to x=3

[tex]Slope=\frac{-3-0}{3-0}=-1[/tex]

The slope of the graph between x=3 to x=5

[tex]Slope=\frac{3-(-3)}{5-3}=3[/tex]

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The value of x is 3. The correct option is the third option- 3

The width of the backyard is 9 yards. The correct option is the first option-  9 yards

From the question, we are to determine the value of x

13.

Perimeter of a rectangle = 2 (l + w)

Where l is the length

and w is the width

From the given information,

Perimeter = 24 cm

In the given diagram,

l = 3x cm

w = 3 cm

Thus,

24 = 2(3x + 3)

24 = 6x + 6

6x = 24 - 6

6x = 18

x = 18/6

x = 3

Hence, the value of x is 3. The correct option is the third option- 3

14.

From the given information,

The width of the yard is 3 less than 4 times the length

That is,

w = 4l - 3 --------- (1)

Also,

Perimeter = 24 yards

∴ 24 = 2(l + w) ---------- (2)

Put equation (1) into (2)

24 = 2(l + w)

24 = 2(l + 4l - 3)

24 = 2(5l - 3)

24 = 10l - 6

10l = 24 + 6

10l = 30

l = 30/10

l = 3 yards

Substitute the value of l into equation (1) to get w

w = 4l - 3

w = 4(3) - 3

w = 12 - 3

w = 9 yards

Hence, the width of the backyard is 9 yards. The correct option is the first option-  9 yards

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