find the area of the given figure.
A)792in^2
B)464in^2
C)242in^2
D)358in^2
E)94in^2

Answer:

795

Step-by-step explanation:

First, we find the circumference of 1 ring.

c = 2πr

c = 2 × 3.14159 × 8.4 mm

c = 52.7787 mm

The circumference of 1 ring is the length of spooled gold used for 1 ring.

The spool has a total length of 42 m.

42 m × 1000 mm / 1 m = 42,000 mm

The spool has a total length of 42,000 mm.

Now we divide the length of the spool by the length of 1 ring.

42,000 mm / 52.7787 mm = 795.78

He can make 795 rings.

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer:

Ans: Rs 181.44.

Step-by-step explanation:

Major challenges for managers to ensure that they treat their employees fairly and equitably includes recognizing Biases and Inclusivity

Major challenges for managers to ensure that they treat their employees fairly and equitably includes recognizing biases and promoting inclusivity.

1:Biases: Managers must recognize and address their own biases,  the biases that may exist within the organization. Biases can be conscious or unconscious, and  lead to unfair treatment and favoritism. Managers need to be aware of these biases and actively work to mitigate their impact on decision-making processes such as promotions, assignments, and evaluations.

2:Inclusivity: Managers need to promote inclusivity by creating a work environment where all employees feel valued, respected, and included. This involves acknowledging and appreciating diversity in terms of race, gender, age, sexual orientation, ethnicity, and other dimensions of identity. Managers should ensure that opportunities for growth and advancement are accessible to all employees, and that discriminatory practices or behaviors are not tolerated.

Biases and promoting inclusivity, managers can foster a fair and equitable workplace where all employees have equal opportunities to succeed and contribute to the organization's goals.

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We get: h = 8√(p + √(p^2 - 64))

Let the base and the other leg of the right triangle be denoted by b and a, respectively. Then we have:

a^2 + b^2 = h^2 (by the Pythagorean theorem)

The area of the triangle can also be expressed as:

Area = (1/2)bh = (1/2)ab

Since the altitude is 16 cm, we have:

Area = (1/2)bh = (1/2)(16)(b + a)

Simplifying, we get:

Area = 8(b + a)

Now, the perimeter of the triangle can be expressed as:

p = a + b + h

Solving for h, we get:

h = p - a - b

Substituting for a and b using the Pythagorean theorem, we get:

h = p - √(h^2 - 16^2) - √(h^2 - 16^2)

Simplifying, we get:

h = p - 2√(h^2 - 16^2)

Squaring both sides, we get:

h^2 = p^2 - 4p√(h^2 - 16^2) + 4(h^2 - 16^2)

Rearranging and simplifying, we get:

h^2 - 4p√(h^2 - 16^2) = 4p^2 - 64

Squaring both sides again and simplifying, we get a fourth-degree polynomial in h:

h^4 - 32h^2p^2 + 256p^2 = 0

Solving this polynomial for h, we get:

h = ±√(16p^2 ± 16p√(p^2 - 64))/2

However, we must choose the positive square root because h is a length. Simplifying, we get:

h = √(16p^2 + 16p√(p^2 - 64))/2

h = 8√(p + √(p^2 - 64))

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(a) To find the amount of sugar in the tank at the beginning, we need to multiply the concentration of sugar in the incoming solution by the volume of water in the tank.

Concentration of sugar = 0.05 kg/L

Volume of water in the tank = 2700 L

Amount of sugar at the beginning = Concentration of sugar * Volume of water in the tank

= 0.05 kg/L * 2700 L

= 135 kg

Therefore, there are 135 kg of sugar in the tank at the beginning.

(b) To find the amount of sugar after t minutes, we need to consider the rate at which the sugar solution enters and drains out of the tank.

Rate of solution entering the tank = 8 L/min

Rate of solution draining out of the tank = 8 L/min

Since the rate of solution entering and draining out is the same, the amount of sugar in the tank remains constant over time. Therefore, y(t) = 135 kg for all t minutes.

(c) As t becomes large, the value of y(t) approaches the same value as the amount of sugar at the beginning, which is 135 kg. This is because the rate of solution entering and draining out of the tank is constant, so the amount of sugar in the tank does not change over time. Thus, the limit of y(t) as t approaches infinity is 135 kg.

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Ruby studied her science test for 1/2 of an hour

An equation is an expression that shows the relationship between two or more variables and numbers.

Jamal spent 1 1/2 (1.5) hours studying for his science test ruby studied for 1/3 the amount of time that Jamal studied.

Amount of time ruby studied = (1/3) * (1.5) = 1/2 of an hour

Ruby studied for 1/2 of an hour

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Answer:

so that is how it goes

Step-by-step explanation:

Answer:

7/37

Step-by-step explanation:

12+7=19 10+8=18 19+18 would be 37 so if he entered the room there is a 7 out of 37 chance the he will sit in a blue chair because there is 37 chairs in told all and 7 blue chairs that he can sit in.

The solution of the piecewise function at the given values of the independent variable g(0) is 5, g(-7) is 12 and g(2) is 7.

This is an example of a piecewise function, which is a function composed of two or more parts, each part being defined by a separate equation.

In this function, the first part is defined as g(x) = x+5 if x >= -5, and the second part is defined as g(x) = -(x+5) if x < -5.

To evaluate the function at the given values of the independent variable, we can simply substitute the values into the appropriate equation.

At x = 0,

=> g(0) = 0+5 = 5.

At x = -7,

=> g(-7) = -(-7+5) = 12.

And at x = 2,

=> g(2) = 2+5 = 7.

Therefore, the values of the function are 5, 12, and 7 respectively

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Answer: 8/15 and 1 1/3

Step-by-step explanation:

The equivalent fractions for 1 3/5 and 1 1/3 using a common denominator are 8/15 and 10/15. This is because 1 3/5 can be written as 8/15 and 1 1/3 can be written as 10/15, and the denominator (bottom number) of both fractions are the same.

The power rule for logarithms states that logb(M^p) = p * logb(M). The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.

The power rule states that logb(M^p) = p * logb(M), where M, b, and p are positive real numbers.

To understand this rule, let's consider an example. Suppose we have log2(8^2). According to the power rule, this is equivalent to 2 * log2(8).

In this case, M is 8, b is 2, and p is 2. The power rule tells us that we can bring the exponent (p) down and multiply it with the logarithm of the base (b) raised to the number (M).

So, log2(8^2) can be simplified as 2 * log2(8), which is 2 * 3 = 6.

In general, the power rule allows us to simplify logarithmic expressions by bringing the exponent down and multiplying it with the logarithm of the base.

This rule is particularly useful when dealing with complex logarithmic expressions and simplifying them to a more manageable form.

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Answer:

4 - log3 (2)

Step-by-step explanation:

2log3 (9) = log3 (9^2)

log3 (27 * 9^2 / 54)

log3 ( 3^3 * 3^4 / 9 * 6)

log3 (3^7 / 3^2 * 3 * 2)

log3 (3^7 / 3^3 * 2)

log3 ( 3^4 /2)

log3 (3^4) - log3 (2)

4 - log3 (2)

Answer:

x=10

Step-by-step explanation:

8(x-9)+6=14

Use the Distributive property

Solve

Combine like terms

Add 66 to both sides and then solve

Divide both sides by 8 to isolate x and then solve

Answer:

Step-by-step explanation:

(1)

Given vertices are A(3,4), B(2,-1) and C(4,-6).

We need to calculate the length of the sides AB,BC,AC.

We have to distance formula which can tell the distance between 2 points.

d = √(x2 - x1)^2 + (y2 - y1)^2.

(1)

AB = √(2 - 3)^2 + (-1 - 4)^2

    = √(-1)^2 + (5)^2

    = √1 + 25

    = √26.

(2)

BC = √(4 - 2)^2 + (-6 + 1)^2

    = √(2)^2 + (5)^2

    = √4 + 25

    = √29

(3)

AC = √(4 - 3)^2 + (-6 - 4)^2

    = √(1)^2 + (-10)^2

    = √1 + 100

    = √101

Therefore, the length of the sides of the triangle are √26,√29 and √101.

----------------------------------------------------------------------------------------------------------

(2)

Let the given points be A(2,-2), B(-2,1) and C(5,2).

Using the distance formula,w e find that

⇒ AB = √(-2 - 2)^2 + (1 + 2)^2

        = √16 + 9

        = √25.

⇒ BC = √(5 + 2)^2 + (2 - 1)^2

         = √49 + 1

         = √50.

⇒ AC = √(5 - 2)^2 + (2 + 2)^2

         = √9 + 16

         = √25.

Now,

⇒ AB^2 + AC^2

⇒ (5)^2 + (5)^2

⇒ 25 + 25

⇒ 50.

⇒ (BC)^2.

Therefore, AB^2 + AC^2 = BC^2.

∴ We can conclude that ΔABC is a right angled triangle

the position function is: r(t) = (3/2t^2 - 5, 4e^(-t) -  3t - 2, t^4 - 3t - 3) if acceleration  a=(3,-4e^-t,12t^2) ,velocity  v(0)=(0,1, -3) and position is r(O)=(-5,2, -3).

The acceleration of an object is given by a = \((3, -4e^(-t), 12t^2)\).The initial velocity of the object is v(0) = (0, 1, -3) and the initial position of the object is r(0) = (-5, 2, -3).We are required to determine the velocity and position functions of the object.

To determine the velocity function v(t), we need to integrate the acceleration function `a` with respect to time t.

v(t) = ∫a(t) dt v(t)

= (∫3 dt, ∫-4e^(-t) dt, ∫12t^2 dt)

v(t) = (3t + C1, 4e^(-t) + C2, 4t^3 + C3) where C1, C2, and C3 are constants of integration.

Since the initial velocity of the object is v(0) = (0, 1, -3), we can determine the constants C1 and C2.v(0) = (3(0) + C1, 4e^(0) + C2, 4(0)^3 + C3) (0, 1, -3)

= (C1, 4 + C2, C3)(C1, C2, C3)

= (0, -3, -3)

Therefore, the velocity function is:v(t) = (3t, -4e^(-t) - 3, 4t^3 - 3)

To determine the position function r(t), we need to integrate the velocity function v with respect to time t.r(t) = ∫v(t) dt r(t) = (∫3t dt, ∫(-4e^(-t) - 3) dt, ∫(4t^3 - 3) dt)

r(t) = (3/2t^2 + C4, 4e^(-t) - 3t + C5, t^4 - 3t + C6)`where C4, C5, and C6 are constants of integration .Since the initial position of the object is r(0) = (-5, 2, -3)`, we can determine the constants C4, C5, and C6.r(0) = (3/2(0)^2 + C4, 4e^(-0) - 3(0) + C5, (0)^4 - 3(0) + C6) (-5, 2, -3)

= (C4, 4 + C5, C6)(C4, C5, C6)

= (-5, -2, -3)

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Jorge has a ticket has a probability of 0.3 of winning a prize. after seven days, probability that jorge has won at least one prize is 0.9176

Let the probability of Jorge winning be 0.3 so ,

Probability of not winning be (1-0.3)⁷

(0.7)⁷

= 0.0823

Therefore, Jorge not winning is 0.0823.

If he wins at least one prize is,

1 - P(win nothing)

1 - 0.0823

= 0.9176

Therefore, the probability that the Jorge wins at least one prize is 0.9176.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

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Answer:

Hope this helps

Step-by-step explanation:

1/4x = -22 + 18

1/4x = -4

4(1/4x) = 4(-4)

x = -16

Answer:

\(( - 542) \times 45 + ( - 542) \times 55 \\ = ( - 24390) + ( - 29810) \\ = ( - 54200)\)

By using the graph of the piecewise function we can see that:

f(0) = 0.

Here we have the graph of a piecewise function, and we want to find the function when x = 0.

Remember that on a graph, an open circle means that the value does not belong to the graph, while a closed circle means taht the value belongs to the graph.

Here we can see that the closed circle at x = 0 is on the line at the middle, then we can conclude that f(0) = 0.

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(a). There is a 5.26% chance that the metal ball falls into a green slot.

(b). There is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

(c). P(00 or red)  ≈ 0.5263

(d). This event is called impossible.

(a) P(green) = 2/38 = 1/19 ≈ 0.0526.

This means that there is a 5.26% chance that the metal ball falls into a green slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 5 spins to end with the ball in a green slot. (Expected value = 100 x P(green) = 100/19 ≈ 5.26, which we round to the nearest integer.)

(b) P(green or red) = P(green) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 53 spins to end with the ball in either a green or red slot. (Expected value = 100 * P(green or red) = 2000/38 ≈ 52.63, which we round to the nearest integer.)

(c) P(00 or red) = P(00) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either 00 or a red slot on any given spin of the roulette wheel.

(d) The probability that the metal ball falls into the number 31 and a black slot simultaneously is zero, since 31 is an odd number and all odd numbers are red on the roulette wheel. This event is called impossible.

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Answer:

x y

1 3

2 6

3 9

Step-by-step explanation:

just plot the corresponding points onto your graph

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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The revenue function, R for x tickets sold which is the product of the cost per ticket and the number of tickets sold is R(x) = 7x

The cost per ticket = $7

The Revenue made from ticket sales can be calculated as :

If the Number of tickets sold is represented as x

The revenue function becomes ;

Therefore, for any given Number of tickets sold, x ; the Revenue function, R(x) = 7x

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Answer:

Step-by-step explanation:

Given function:

The vertex is (2, 3)

We know the vertex form:

Substitute coordinates to get:

Compare with given to find out:

The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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Answer:

The area of a circle is given by the formula A = πr², where A is the area and r is the radius. We are given that the area of the circle is 3.14 square yards, so we can plug this value into the formula and solve for the radius:

A = πr²

3.14 = πr²

Dividing both sides by π, we get:

r² = 3.14/π

Taking the square root of both sides, we get:

r = √(3.14/π)

Using a calculator to evaluate this expression, we get:

r ≈ 0.9997 yards

The gradient of a function is called a gradient field. The gradient field of f(x, y, z) is -\(3x(3x^2 + 2y^2 + z^2)^-3/2, -2y(3x^2 + 2y^2 + z^2)^-3/2, -z(3x^2 + 2y^2 + z^2)^-3/2\).

To find the gradient field of the function, we need to find the partial derivatives of the function with respect to x, y, and z, and then combine them into a vector function.

∂f/∂x = (-1/2)(3x^2 + 2y^2 + z^2)^-3/2 (6x)

∂f/∂y = (-1/2)(3x^2 + 2y^2 + z^2)^-3/2 (4y)

∂f/∂z = (-1/2)(3x^2 + 2y^2 + z^2)^-3/2 (2z)

Thus, the gradient field is given by:

grad(f) = ∇f = <∂f/∂x, ∂f/∂y, ∂f/∂z>

= \(-3x(3x^2 + 2y^2 + z^2)^-3/2, -2y(3x^2 + 2y^2 + z^2)^-3/2, -z(3x^2 + 2y^2 + z^2)^-3/2\)

Therefore, the gradient field of f(x, y, z) = (3x^2 + 2y^2 + z^2)^-1/2 is given by \(-3x(3x^2 + 2y^2 + z^2)^-3/2, -2y(3x^2 + 2y^2 + z^2)^-3/2, -z(3x^2 + 2y^2 + z^2)^-3/2\)

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There are 24 sticks in pattern 6. The diagram indicates that one pattern is made up of one box built from four sticks.

A geometric pattern is a pattern made out of geometric forms that are generally repeated, much like a wallpaper design.

The given figure shows that one pattern consists of one box formed from the 4 sticks.

Pattrern 1 = 1 box  

Pattern 2 = 2 box

Pattern 6 = 6 box

1 box = 4 stick

Pattern 6 = 6 box = 6 ×4 = 24 sticks

Hence,there are 24 sticks in pattern 6.

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Answer:

True

Step-by-step explanation:

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces

it should be true. Let me know if I'm incorrect.

Answer:

c) 2

Step-by-step explanation:

here you can use cross multiplication. that's where you turn the fraction into an equation. ( there's videos about it, I'm not very good at explaining )

so you can turn

\(\frac{5}{x} = \frac{15}{x + 20}\)

into

5(x + 20) = 15x

5x + 100 = 15x

subtract 5x from both sides

100 = 10x

x = 10.

the value of x/5 would be 2, since 10/5 is 2.

Since x/5 is the reciprocal of 5/x, we know that we can flip the fraction on the right hand side will be flipped.

Thus, x/5 = (x + 20)/15

Now we cross multiply, 15x = 5(x + 20)

Simplify: 15x = 5x + 100

Subtract 5x from each side: 10x = 100

Divide 10: x = 10

Now plug 10 back into the right hand side: (10 + 20)/15

So, the answer is 2.