Your hourly wage is $10.05 per hr when you work during the day and $12.01 per hr when you work the night shift .what is your gross pay for one week if you worked 24 hrs at night and 16 hrs during the day.

The height of bridge in the square is 15 units. This is determined by using the ratio of sides in a 30-60-90 triangle and multiplying the hypotenuse by the corresponding ratio for the shorter leg, which is 1.

Let's calculate the height of the bridge step by step using the given information

In a 30-60-90 triangle, the ratio of the sides is 1:√3:2.

Given:

Hypotenuse = 15

Step 1: Determine the length of the shorter leg (height of the bridge)

Since the ratio is 1:√3:2, the length of the shorter leg can be found by multiplying the hypotenuse by the ratio corresponding to the shorter leg, which is 1.

Length of the shorter leg = 15 * 1 = 15

Step 2: Simplify the expression for the shorter leg

Since the hypotenuse of the 30-60-90 triangle is given as 15, the length of the shorter leg is also 15.

Height of the bridge = 15

Therefore, the height of the bridge is 15 units.

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The simplification form of the provided expression is g . 6² . p⁴ option (B) g . 6² . p⁴ is correct.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The expression:

\(= \rm \dfrac{(g^3)(6^3)(p^7)}{(6)(g^2)(p^2)(p)}\)

After using the properties of integer exponent:

\(\rm =\dfrac{g^3\cdot \:6^2p^7}{g^2p^2p}\)

\(\rm =\dfrac{g\cdot \:6^2p^5}{p}\)

= g . 6² . p⁴

Thus, the simplification form of the provided expression is g . 6² . p⁴ option (B) g . 6² . p⁴ is correct.

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The rank of the system is 3, indicating that all three equations are linearly independent.

To solve the system of linear equations using row operations and determine its rank, we can set up an augmented matrix and perform row operations to transform it into row-echelon form.

The given system of equations is:

3x1 + 3x2 + 2x3 = 25

3x1 + 2x2 + 3x3 = 22

2x1 + x2 + 4x3 = 18

We can represent this system as an augmented matrix:

[3 3 2 | 25]

[3 2 3 | 22]

[2 1 4 | 18]

Our goal is to transform this matrix into row-echelon form, where each leading coefficient (the first non-zero entry in each row) is 1, and all entries below the leading coefficient are zeros.

Using row operations, we can perform the following steps:

Step 1: Subtract Row 1 from Row 2

[3 3 2 | 25]

[0 -1 1 | -3]

[2 1 4 | 18]

Step 2: Subtract (2/3) times Row 1 from Row 3

[3 3 2 | 25]

[0 -1 1 | -3]

[0 -1 8/3 | -4/3]

Step 3: Multiply Row 2 by -1

[3 3 2 | 25]

[0 1 -1 | 3]

[0 -1 8/3 | -4/3]

Step 4: Add Row 2 to Row 3

[3 3 2 | 25]

[0 1 -1 | 3]

[0 0 5/3 | -1/3]

Step 5: Multiply Row 3 by 3/5

[3 3 2 | 25]

[0 1 -1 | 3]

[0 0 1 | -1/5]

Step 6: Subtract 2 times Row 3 from Row 1

[3 3 0 | 27]

[0 1 -1 | 3]

[0 0 1 | -1/5]

Step 7: Subtract -3 times Row 3 from Row 2

[3 3 0 | 27]

[0 1 0 | 18/5]

[0 0 1 | -1/5]

Step 8: Subtract 3 times Row 2 from Row 1

[3 0 0 | 3/5]

[0 1 0 | 18/5]

[0 0 1 | -1/5]

The resulting matrix is in row-echelon form, and the system of equations is:

3x1 + 0x2 + 0x3 = 3/5

0x1 + 1x2 + 0x3 = 18/5

0x1 + 0x2 + 1x3 = -1/5

From the row-echelon form, we can see that all the variables (x1, x2, x3) are leading variables since they correspond to leading coefficients of 1. There are no free variables, which means the system has a unique solution.

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Using the inner product definition, we get:

⟨q, q⟩ = ∫ 1 −1 x²*x² dx = ∫ 1 −1 x^4 dx = [x^5/5] from -1 to 1 = 2/5

‖q‖ = √(2/5).

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

a. We have p(x) = 1 and q(x) = x². Using the inner product definition, we get:

⟨p, q⟩ = ∫ 1 −1 p(x)q(x) dx = ∫ 1 −1 1*x² dx = [x³/3] from -1 to 1 = (1/3) - (-1/3) = 2/3

Therefore, ⟨p, q⟩ = 2/3.

b. The distance between p and q is given by:

d(p, q) = ‖p - q‖ = √⟨p - q, p - q⟩

We have p(x) = 1 and q(x) = x², so p - q = 1 - x². Using the inner product definition, we get:

⟨p - q, p - q⟩ = ∫ 1 −1 (1 - x²)² dx = ∫ 1 −1 1 - 2x² + \(x^4\) dx = [x - (2/3)x³ + (1/5)\(x^5\)] from -1 to 1 = 8/15

Therefore, d(p, q) = ‖p - q‖ = √(8/15) ≈ 0.6977.

c. The norm of p is given by:

‖p‖ = √⟨p, p⟩

We have p(x) = 1. Using the inner product definition, we get:

⟨p, p⟩ = ∫ 1 −1 1*1 dx = [x] from -1 to 1 = 2

Therefore, ‖p‖ = √2.

d. The norm of q is given by: ‖q‖ = √⟨q, q⟩

We have q(x) = x². Using the inner product definition, we get:

⟨q, q⟩ = ∫ 1 −1 x²*x² dx = ∫ 1 −1 \(x^4\) dx = [\(x^5\)/5] from -1 to 1 = 2/5

Therefore, ‖q‖ = √(2/5).

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Step-by-step explanation:

for the perimeter you have to say two brackets live plus height plus with plastic

a. The limits of integration come from the fact that the triangular region has its base along the x-axis and its height along the line y = -x + 1

A = (-1, 0)

B = (1, 0)

C = (-1, 1)

D = (0, 1)

b. The integral in part (a) is 580/3.

(a) The triangle R can be split into two regions: a triangular region with vertices at (-1,0), (0,1), and (0,0), and a trapezoidal region with vertices at (-1,0), (0,0), and (1,0).

The integral can be expressed as:

∬R(5x+6y)2dA = ∫0^1∫0^(1-x)(5x+6y)2dydx + ∫-1^0∫0^(x+1)(5x+6y)2dydx

The limits of integration come from the fact that the triangular region has its base along the x-axis and its height along the line y = -x + 1, while the trapezoidal region has its longer base along the x-axis and its shorter base along the line y = x + 1.

Therefore, the limits of integration are:

A = (-1, 0)

B = (1, 0)

C = (-1, 1)

D = (0, 1)

(b) To evaluate the integral, we can use the substitution u = 5x + 6y, v = 6x - 5y. This transforms the integrand to u^2, and the limits of integration become:

0 ≤ u ≤ 5

-1/3(u-5) ≤ v ≤ 1/3(u+5)

Using this substitution, we have:

∬R(5x+6y)2dA = ∫0^5∫-1/3(u-5)^(1/3)(u+5)^(1/3)u^2dvdu

Evaluating this integral gives:

∬R(5x+6y)2dA = 580/3

Therefore, the integral is 580/3.

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Answer:

Wait did you mean how many points will it be after an entire SEASON?

Answer:

f(3)=5. Explanation: Simply substitute the value of 3 given. In other words, f(3) is the function of f(x) , however, in this case, x is 3. f(3)=3(3)−4. Distribute 3 through

Answer:

C

Step-by-step explanation:

\(\frac{3-\sqrt{3} }{3+\sqrt{3} } *\frac{3-\sqrt{3} }{3-\sqrt{3} } \\\\=\frac{(3-\sqrt{3})^{2} }{(3+\sqrt{3} )(3-\sqrt{3} )} \\\\=\frac{9-2*3\sqrt{3}+3 }{9-3}\\\\=\frac{12-6\sqrt{3} }{6} \\\\=2-\sqrt{3}\)

The value of x in sequence of number is 10.

Here, first term of sequence is x and each term there after is twice the previous term. Also Fifth term is 160.

What is geometric series?

Geometric series is an infinite series of the form:

\(a+ar+a r^{2} +ar^{3} +..........\)

where r is known as common ratio.

Now, first term is x and each term there after is twice the previous term.

So the series will be;

x , 2x , 4x , 8x, ..........

Clearly this series is geometric series with common ratio 2.

And the nth term of geometric series is \(ar^{n-1}\)

⇒ fifth term is 160

\(ar^{5-1} = 160\\ar^{4} = 160\\a 2^{4} =160\\a=\frac{160}{16} \\a=10\)

Here, first term is x.

The value of x in sequence of number is 10.

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True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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The graph of each function is given below.

When they are the same height, the height of the snowman is 15 inches.

Initial height of snowman A = 36 inches

At sunrise, Snowman A's height decrease by 3 inches per hour.

Slope = 3

Function can be represented as.

A(t) = 36 - 3t

Initial height of snowman B = 57 inches

At sunrise, Snowman B's height decrease by 6 inches per hour.

Slope = 6

Function can be represented as.

B(t) = 57 - 6t

Graph of each function will be a line.

The height of the two snowmen will be equal after,

36 - 3t = 57 - 6t

3t = 21

t = 7 hours

Height = 36 - (3 × 7) = 15 inches

Hence the height of each snowmen is 15 inches after 7 hours.

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-2x+8y-3

Hope this helps! :)

Answer:

-2x + 8y -3

Step-by-step explanation:

-2x = -2x

2y + 6y = 8y

-3  = -3

\( \longmapsto \: =25/35 \)

\( \longmapsto \: =5/7\)

\( \longmapsto \: =5:7\)

(A) The probability that none of the flights are late today is 0.32768. (B) The probability that exactly one of the flights is late today is  0.4096. (C) The probability that all of the flights are late today is 0.00032.

(A) To find the probability that none of the flights are late today, we use the binomial probability formula, which states that the probability of k successes in n trials is given by P(X = k) = nCk * p^k * q^(n-k), where n is the number of trials, p is the probability of success, q is the probability of failure (1 - p), and nCk represents the binomial coefficient. In this case, we have n = 5 (five flights) and p = 0.20 (probability of a flight being late). Since we want none of the flights to be late (k = 0), the formula becomes P(X = 0) = 5C0 * 0.20^0 * 0.80^5 = 0.32768.

(B) To find the probability that exactly one of the flights is late today, we again use the binomial probability formula. Now, k = 1, so P(X = 1) = 5C1 * 0.20^1 * 0.80^4 = 0.4096.

(C) The probability that all of the flights are late today is the probability that each individual flight is late. Since the flights operate independently, we can simply multiply the probabilities together. Therefore, the probability that all five flights are late today is 0.20^5 = 0.00032.

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The perimeter of a triangle can be calculated using the given information about the lengths of its sides and the segment formed by the angle bisector. The solution is provided in the following explanation.

Let's denote the second side of the triangle as x units. According to the given information, one side is 4 units longer than the second side, so the first side is (x + 4) units.

The ray bisecting the angle divides the opposite side into segments of length 6 units and 7 units. This means the total length of the opposite side is the sum of these two segments, which is (6 + 7) = 13 units.

To find the perimeter of the triangle, we add up the lengths of all three sides. Therefore, the perimeter is (x + x + 4 + 13) = (2x + 17) units.

Since we don't have a specific value for x, the perimeter is expressed in terms of x as (2x + 17) units.

Thus, the perimeter of the triangle is (2x + 17) units.

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Answer:

y = -23x+225

Step-by-step explanation:

Bugdet=spending

225 is the y-intercept and 23 is the slope or amount spent per day.

Answer:

142 because 125 isn't an opinion.  

Step-by-step explanation:

i took the test

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

The ratio of any corresponding coordinates will give the scale factor.

Using the x-coordinates of C' and C, we have ...

  scale factor = C'/C = 4/6 = 2/3

The dilation scale factor is 2/3.

Answer:

Step-by-step explanation:

According to the diagram we observe:

As we know the exterior angle is same as the some of the remote interior angles.

It can be shown as:

Substitute the values and solve for x:

Find the measure of m∠ABC:

The matching answer choice is D.

Answer:

36 x 2 = 72

36 divide by 2 = 18

72+18=90

90 is the answer

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

-2-y=-y

clt

-2=-y+y

-2=0

:ans is -2=0 making it with no solution

According to  Hooke's law, A force of 3 N will stretch the rubber band by 0.06 m.

Hooke's law states that force applied is directly proportional to the extension produced in a body.

Hence, for a rubber band, it is given by

F = kx where F is the force applied, k is the spring constant and x is the extension produced.

For a force of 1 N, the extension produced is 2 cm(0.02 m)

k = F/x

= 1 / 0.02

= 50 N/m

For a force of 3 N,

F = kx

3 = 50x

x = 3/50 m

= 0.06 m

Therefore, the 3 N force will stretch the rubber band by 0.06 m.

A force of 3 N will stretch the rubber band by 0.06 m.

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The solution is, the finally discounted price is 71.5.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

sale price = 90

15% discount, so, the price = 90* 85%

                                            =76.5

now, after 5 discount, price became = 76.5 - 5

                                                             = 71.5

Hence, The solution is, the finally discounted price is 71.5.

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Mother spent (4r - 8) dollars more on cherries than did the father.

An expression using numbers and related operations is called a numerical expression.

According to the question, a pound of cherries costs $4.

Mom purchased r pounds.

The price of the cherry is calculated as follows: 4r = weight x $/lb.

Father purchased 2 pounds, thus the price of the cherries is 4 (2), or $8.

We remove the smaller value from the higher value, which is 4r - 8, where r must be more than two. Given that the mother spent more money on cherries than the father, the mother's cost of cherries is a greater value.

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Answer:

Length of one of the shorter congruent side is: 6 cm

Step-by-step explanation:

In order to find the length of congruent sides we have to solve the system of equations

Given systems of equation is:

y = x + 2

2x + 3y = 36

Putting y = x+2 in second equation

\(2x + 3(x+2) = 36\\2x+3x+6 = 36\\5x+6 = 36\\5x = 36-6\\5x = 30\\\frac{5x}{5} = \frac{30}{5}\\x =6\)

As we know that x represents the shorter side, the length of short side is: 6 cm

Hence,

Length of one of the shorter congruent side is: 6 cm

ANSWER

EXPLANATION

We want to find the function that models the amount of fertilizer after w weeks.

The general form of an exponential function is written as:

but it can be re-written as:

+ is used when it an exponential growth

- is used when it is an exponential decay

Note: r stands for rate of growth/decay

From the question, we see that there is an exponential decay (decrease).

This means that the function, we need to use is:

The mistake that Sarah made was that she used her rate directly as 3% (i.e. she made b = 3) into the general function which is wrong.

She should have instead used the alternate function given above to find the function.

Therefore, the correct function is:

where w represents the number of weeks

Answer:

28

Step-by-step explanation:

▪︎ ADE and ABC are similar triangles (AAA)

▪︎ DA = DB + BA = 30 + 12 = 42

▪︎ k = DA / BA = 42 / 12 = 3.5

▪︎ DE = BC * k = 8 * 3.5 = 28