Suppose z is a function of x and y, and tan √y^2+x^2 = z^x e^6y. Solve for dz/dx and dz/dy =

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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The measurement of the width of the rectangle can be a

polynomial quotient with a remainder

what is a polynomial ?

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. We can execute arithmetic operations on polynomial expressions, such as addition, subtraction, multiplication, and positive integer exponents, but not division by variables.

Area of rectangle, A:

A= l*w , l= length, w= width

So,

polynomial = polynomial * w

=> w= polynomial/polynomial

And we have

Dividend = Divisor × Quotient + Remainder

So, the measurement of the width of the rectangle can be a

polynomial quotient with a remainder

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The amount that Bert should deposit to earn $192 interest is $4,000 (option C).

When an account earns a simple interest, the account increases linearly. It means that the value of the account increases at a constant rate.

The rate of increase is determined by the amount deposited, the interest rate and the number of years the money was deposited for.

Amount to be deposited = simple interest / (years x interest rate)

$192 / (0.016 x 3) $192 / 0.048 = $4,000

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For any chi-square goodness-of-fit test, the number of degrees of freedom is equals to

(k - 1), where k is number of categories. So, second option is correct.

Chi-square goodness test : The chi-square goodness test is used to check whether the observed data distribution matches with the expected distribution. Since this is a non-parametric test, the data are divided into classes or groups, and the number of values that fall into those groups is compared to the expected number of values that fall into those groups. The chi-square test of goodness has

degrees of freedom equal to the number of groups minus one i.e., (k −1), where

k --> Number of classes or categories, the data is divided into.

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To find Myesha's rate of mowing in lawns per hour, we can divide the number of lawns mowed by the number of hours it took.

In this case, Myesha mowed 5 lawns in 10 hours. Therefore, her rate of mowing in lawns per hour can be calculated as:

\(\displaystyle\sf \text{Rate} = \frac{\text{Number of Lawns Mowed}}{\text{Number of Hours}}\)

Substituting the given values:

\(\displaystyle\sf \text{Rate} = \frac{5}{10}\)

Simplifying the division:

\(\displaystyle\sf \text{Rate} = 0.5\)

Therefore, Myesha's rate of mowing is 0.5 lawns per hour.

Answer:

Yep

Step-by-step explanation:

Step 1: Replace the values into the equation and simplify

\(|a-12b|\\|-5-12(\frac{1}{4} )|\\|-5-3|\\|-8|\\8\)

Answer:

110

Step-by-step explanation:

2/5=44/x

Cross multiply

2x=44(5)

2x=220

/2.  /2

x=110

Hopes this helps please mark brainliest

a. The probability of exactly 4 successes is approximately 0.2967.

b. The probability of 5 or more successes is approximately 0.5332.

c. The probability of exactly 6 successes is approximately 0.1399.

d. The expected value of the random variable is 3.96

To solve these problems, we'll use the binomial probability formula:

P(X = k) = C(n, k)× \(p^{k}\)× \((1-p)^{(n-k)}\)

where:

P(X = k) is the probability of getting exactly k successes,

n is the sample size,

p is the probability of success,

C(n, k) is the number of combinations of n items taken k at a time.

Now let's solve each part of the problem:

a. The probability of exactly 4 successes:

P(X = 4) = C(6, 4) × (0.66)⁴ × (1 - 0.66)⁽⁶⁻⁴⁾

C(6, 4) = 6! / (4! × (6 - 4)!) = 6! / (4! × 2!) = (6 × 5) / (2 × 1) = 15

P(X = 4) = 15 × (0.66)⁴ × (0.34)² ≈ 0.2967 (rounded to four decimal places)

b. The probability of 5 or more successes:

P(X ≥ 5) = P(X = 5) + P(X = 6)

P(X = 5) = C(6, 5) × (0.66)⁵ × (1 - 0.66)⁽⁶⁻⁵⁾ = 6 × (0.66)⁵ × (0.34)¹ ≈ 0.3933

P(X = 6) = C(6, 6) × (0.66)⁶ × (1 - 0.66)⁽⁶⁻⁶⁾ = 1 × (0.66)⁶× (0.34)⁰ = 0.1399

P(X ≥ 5) = P(X = 5) + P(X = 6) = 0.3933 + 0.1399 ≈ 0.5332 (rounded to four decimal places)

c. The probability of exactly 6 successes:

P(X = 6) = C(6, 6) × (0.66)⁶ × (1 - 0.66)⁽⁶⁻⁶⁾ = 1 × (0.66)⁶ × (0.34)⁰= 0.1399

d. The expected value of the random variable:

The expected value (mean) of a binomial distribution is given by:

E(X) = n × p

E(X) = 6 × 0.66 = 3.96

Therefore:

a. The probability of exactly 4 successes is approximately 0.2967.

b. The probability of 5 or more successes is approximately 0.5332.

c. The probability of exactly 6 successes is approximately 0.1399.

d. The expected value of the random variable is 3.96

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Answer:

Use the slope-intercept form  

m=\(\frac{2}{3\\}\)

Step-by-step explanation:

A square could be called a rectangle since it has four right angles.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°. Observe the rectangle given below to see its shape, sides and angles.

So,  Every square is a rectangle because it is a quadrilateral with all four angles right angles.

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The solution is

a) The total area of the rectangular grass area is 9600 feet²

b) The number of bags required is 9.6 bags

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular grass area be = A

Now , the equation will be

The length of the rectangular grass portion = 120 feet

The width of the rectangular grass portion = 80 feet

The area of the rectangular grass portion = Length x Width

Substituting the values in the equation , we get

The area of the rectangular grass portion A = 80 x 120

The area of the rectangular grass portion A = 9600 feet²

Now , each bag of the grass seed covers 1000 feet²

So , the number of bags required for the entire area = area of the rectangular grass portion A / each bag of the grass seed covers 1000 feet²

On simplifying the equation , we get

The number of bags required for the entire area = 9600 / 1000

The number of bags required for the entire area = 9.6 bags

Therefore , the number of bags required is 9.6 bags

Hence , the total area of the rectangular grass area is 9600 feet²

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Answer:

110000=p(1+0.019)^168

23.62p=110000

p=4660

credit: sqdancefan

Answer:

84330

Step-by-step explanation:

The compound interest formula gives the value of an investment.

 A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. Using your given values, we can solve for P.

 110,000 = P(1 +0.019/12)^(12·14)

 P = 110,000/(1 +0.019/12)^(12·14) ≈ 110,000/1.00158333...^168

 P ≈ 110,000/1.30446

 P ≈ 84326.04 ≈ 84,330 . . . . dollars

Answer:

-4y²

hope it helps.....

The rule for solving the given expression is multiplication and answer is  \(-4y^{2}\).

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Given

4y times -y

It is a multiplication rule to use for this problem

= \(4y(-y)\)

= \(-4y^{2}\)

The rule for solving the given expression is multiplication and answer is  \(-4y^{2}\).

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Answer:

132

Step-by-step explanation:

there are 66 hands in party so we multi 2 by 66=132

Answer:

Brauilo is wrong because he divided by (x+1) instead of (x-1)

Step-by-step explanation:

The remainder Theorem states that

if polynomial f(x) is divided by binomial x-a, the remainder will equal f(a). The factor is positive so the binomial is the same as

which is why we divide by -1, or subsitue -1 into the equation p(x).

The remainder of a polynomial division can be gotten using remainder theorem or synthetic division.

The true statement is: Brauilo did not find the value of a, because he divided by (x+1) instead of (x-1)

From the question, we have the following parameters:

\(\mathbf{p(x) = x^4 +5x^3 + ax^2 - 3x + 11}\)

\(\mathbf{Divisor =x+ 1}\)

\(\mathbf{Remainder = 17}\)

First, we set the divisor to 0.

\(\mathbf{Divisor =x+ 1 = 0}\)

So, we have:

\(\mathbf{x+ 1 = 0}\)

Solve for x

\(\mathbf{x= -1}\)

The above equation means that, the value of x that will be used to test the polynomial is -1

From the question,

Hence, Braulio is incorrect, because he used the wrong value of x

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Answer:

Step-by-step explanation:

Answer:

20.30

Step-by-step explanation:

\( = 17 \div \tan(40) \\ = 17 \div 0.8391 \\ = 20.26\)

To the nearest tenth =20.30

As per the unitary method, most responsible for the increase is more packing.

The term unitary method in math refers the process of finding the value of a single unit, and based on this value.

Here we have given that One study indicates that each individual in the United States produces about 2 kg of solid waste per day. That figure is up from about 1.2 kg in 1960.

And we need to find most responsible for the increase.

While we looking into the given question, we have identified that in 1960 the solid waste per day is 1.2 kg.

And the current solid waste per day is 2 kg.

Then the the difference between these two is calculated as,

=> 2 - 1.2

=> 0.8kg.

So, there is 800 gram of waste is increased and while looking into the given option, the resulting one is option (a).

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer:

1. x ≤ 15

2. x +3 < 12

3. x/-2 ≥ 10

4. x - 4 ≥ -6

5. x/13 ≥ 1

6. x - 8 ≤ 5

7. 3 * x > -7

8. x/2 + 5 > 11

9. -6 + x ≤ 15

Hope this helps!

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

Slope = (4-7)/(7-1)

Slope = -3/6

Slope = -1/2

Answer: This is a tricky question. Short answer yes. I’ll explain why and give examples so you can learn it

Step-by-step explanation:

Before solving the question, we should know the definition of a prime number. A prime number is a number which does not have factors other than 1 or itself. We know that 2 is the only even prime number. So, the remaining prime numbers other 2 are odd prime numbers.

Case -1:

Let us assume any two prime numbers other 2. As we assumed prime numbers other than 2, the assumed numbers are odd primes. We know that the sum of two odd numbers is an even number. So, the sum of primes other than 2 is an even number. So, the obtained even number is not a prime. In this case, we can say that the sum of primes cannot be a prime.

Example:

Let us take two prime numbers 3 and 7.

3+7=10

Sum of 3 and 7 is equal to 10. We know that 10 is an even number and it is not a prime number. So, we can say that the sum of primes cannot be a prime.

Case-2:

Let us assume two prime numbers. Let the first prime number be 2 and the other prime number be an odd prime. We know that the sum of an even number and odd number is an odd number. We know that all the prime numbers other than 2 are odd primes.

Example (a):

Let us take two prime numbers 2 and 5.

2+5=7

Sum of 2 and 5 is equal to 7. We know that 7 is an odd number and a prime number.

Example (b):

Let us take two prime numbers 2 and 13.

2+13=15

Sum of 2 and 13 is equal to 15. We know 15 is an odd number and not a prime number.

From example (a) we are having the sum of two prime numbers is a prime number.

From example (b) we are having the sum of prime numbers is not a prime number.

So, collectively we can say that the sum of two prime numbers may be a prime number or may not be a prime number.

Case-3:

Let us assume two prime numbers. Let us assume both the prime numbers as even primes. The one and only even prime number is 2. We know that the sum of 2 and 2 gives 4. We know that 4 is not a prime number.

From the above cases it is clear that the sum of two prime numbers need not be a prime number always.

In the question, we were given that the sum of two prime numbers cannot be a prime number. This statement is incorrect because the sum of two prime numbers may be a prime number which is shown in case 2.

So, option (B) is correct.

Note: We should remember that 1 is neither a prime nor a composite. So, for solving this question don’t consider that 1 is a prime number. If we consider 1 as a prime number then we may get wrong results. We know that every prime number has only 2 factors and every composite number has 3 or more factors. But 1 has only one factor. So, we can prove that 1 is neither a prime nor a composite.

Answer:

y = 2x+6

Step-by-step explanation:

y-4=2(x+1)

Distribute

y-4 =2x +2

Add 2 to each side

y-4+4 = 2x+2+4

y = 2x+6

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

Answer: 10:14, 15:21, 20:28

Step-by-step explanation: These are all multiples of 5 and 7.

5: 10, 15, 20

7: 14, 21, 28

So it is C. 10:14, 15:21, 20:28

Answer:

i got it right on my test its c

Step-by-step explanation:

The potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.

The product of the log rule says that the sum of number of logarithm functions is equal to the log function of product of all the numbers, given  that base is same.

The given logarithmic function in the problem is,

\(\log_6x+\log(6x+5)=2\)

Using the product rule of logarithmic function, the above equation can be written as,

\(\log_6(x\times(x+5))=2\\\log_6(x^2+5x))=2\)

Using the equality rule of logarithmic function, the above equation can be written as,

\(x^2+5x=6^2\\x^2+5x=36\)

Take all the terms one side of the equation as,

\(x^2+5x-36=0\)

Find the factors of above equation using the split the middle term method as,

\(x^2+9x-4x-36=0\\x(x+9)-4(x+9)=0\\(x+9)(x-4)=0\)

By equating these factor to the zero one by one, we get the potential solution as -9 and 4.

Thus, the potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.

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Answer:

-9 and 4

Step-by-step explanation:

Did it on edge :)

Answer:

-287

Step-by-step explanation:

If x + y = z, then z - y = x and z - x = y. Since 260 + x = -27, then -27 - 260 = x.

You can change the signs for a moment but you need to change them back at the end. 27 + 260 = 287, flip the signs, -27 - 260 = -287.

She  should plant 118 trees per acre to maximize her harvest area. This will yield 96 bushels per tree.

95 trees per acre x 80 bushels per tree = 7600 bushels

96 trees per acre x 77 bushels per tree = 7392 bushels

97 trees per acre x 74 bushels per tree = 7158 bushels

98 trees per acre x 71 bushels per tree = 6938 bushels

99 trees per acre x 68 bushels per tree = 6732 bushels

100 trees per acre x 65 bushels per tree = 6500 bushels

101 trees per acre x 62 bushels per tree = 6262 bushels

102 trees per acre x 59 bushels per tree = 6038 bushels

103 trees per acre x 56 bushels per tree = 5828 bushels

104 trees per acre x 53 bushels per tree = 5532 bushels

105 trees per acre x 50 bushels per tree = 5250 bushels

106 trees per acre x 47 bushels per tree = 4978 bushels

107 trees per acre x 44 bushels per tree = 4716 bushels

108 trees per acre x 41 bushels per tree = 4452 bushels

109 trees per acre x 38 bushels per tree = 4188 bushels

110 trees per acre x 35 bushels per tree = 3925 bushels

111 trees per acre x 32 bushels per tree = 3663 bushels

112 trees per acre x 29 bushels per tree = 3407 bushels

113 trees per acre x 26 bushels per tree = 3151 bushels

114 trees per acre x 23 bushels per tree = 2895 bushels

115 trees per acre x 20 bushels per tree = 2300 bushels

116 trees per acre x 17 bushels per tree = 1972 bushels

117 trees per acre x 14 bushels per tree = 1638 bushels

118 trees per acre x 11 bushels per tree = 1306 bushels

Therefore, 118 trees per acre will yield the highest harvest of 1306 bushels.

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