If you cut away a triangle with an area of 59 cm from a certain square, the area
of the remaining shape will be 85 cm². Find the length of the side of the square.

Answer:

$225

Step-by-step explanation:

3(x/4)- 1/2 ((x/10) expression can represent 70% of x.  option A is the correct answer.

4/5 in percent =80%

From the question, we have

70% of x

= 7x/10

3(x/4)- 1/2 ((x/10)

= (15x - x)/20

= 7x/10

3(x/4)- 1/2 ((x/10) expression can represent 70% of x

4/5 in percent = 4/5*100

=80%

Percentage :

Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as the fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.

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The correct value that equates to this expression is 12‐³². Letter A

.

To solve this expression, just: eliminate the parentheses and multiply the exponents among themselves;\( \boxed{ \large \sf (a {}^{n} ) {}^{m} \rightarrow a {}^{n \times m} } \\ \\ \)

\({ = \large \sf (12{}^{-4} ) {}^{8} } \)

\({ = \large \sf 12{}^{-4 \times 8} } \)

\( \pink{ \boxed{ = \large \sf 12{}^{-32} } } \\ \)

Therefore, the answer will be 12‐³²

Rodger's weekly unemployment amount is $697.54

What is the total of the quarterly wages of two consecutive quarters?

The total of the of the quarterly wages of two consecutive quarters is the sum of first quarter and second quarter wages

total of quarterly wages=$13,950.80+$13,950.80

total of quarterly wages=$27,901.60

unemployment compensation=total of quarterly wages/26

unemployment compensation=$27,901.60 /26

unemployment compensation=$1,073.14

The weekly unemployment amount is 65% of Rodger's state, unemployment compensation

weekly unemployment=65%*$1,073.14

weekly unemployment=$697.54

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Answer:

26

Step-by-step explanation:

4+6+16=26

Answer:

N^2+3

Step-by-step explanation:

Hope that helps!

When comparing two sample means, we can safely reject the null hypothesis if the calculated test statistic exceeds the critical value corresponding to the chosen significance level.

In hypothesis testing, when comparing two sample means, we typically perform a t-test or z-test depending on the characteristics of the data and assumptions. The null hypothesis assumes that there is no significant difference between the means of the two samples.

To determine whether we can reject the null hypothesis and conclude that there is a significant difference, we calculate a test statistic. The specific test statistic (t or z) depends on factors such as sample size and whether population parameters are known.

Next, we compare the calculated test statistic to the critical value. The critical value is determined based on the chosen significance level (commonly denoted as α). If the calculated test statistic exceeds the critical value, we reject the null hypothesis, indicating that there is evidence to support a significant difference between the two sample means.

The significance level determines the threshold for rejecting the null hypothesis and is typically set at 0.05 (5%) or lower, depending on the desired level of confidence.

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In the given the function,  we have to solve: f(s) = 145² + 565 +152 (5+6) (5²+45+20)" 11 F(s) = 8(5+1)² (5² +10s +34) (5² +8s + 20).

Calculation:

\(\[152(5+6)(5^2+45+20) = 152(11)(70) = 118,480\]\[145^2 = 21,025\]\[565 = 565\]\)

Therefore, \(f(s) = 210,252 + 565 + 118,480 = 329,297\).

Now, we need to find \(f(t)\) where \(t = 5\). We substitute \(s = 5\) into the function \(f(s)\):

\(\[f(t) = 8(5+1)^2(5^2 + 10(5) + 34)(5^2 + 8(5) + 20)\]\[f(t) = 8(6)^2(5^2 + 50 + 34)(5^2 + 40 + 20)\]\[f(t) = 8(36)(25 + 50 + 34)(25 + 40 + 20)\]\[f(t) = 8(36)(109)(85)\]\[f(t) = 266,160\]\)

Therefore, the value of \(f(t)\) is 266,160.

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Answer:

because there’s additional numbers to the equation

Step-by-step explanation:

it differs because of the -3 it’s -3 down

True, the three sides will form exactly one unique triangle.

A triangle is three dimensional shape, whose third length is less than the sum of the first and second length.

(b - a) < k < (b + a)

(6.3 - 5.2 ) < k (6.3  + 5.2 )

1.1 units < k < 11.5 units

The third length = 10.5 units which is greater than 1.1 units and less than 11.5 units.

Thus, the three sides will form exactly one unique triangle.

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The price elasticity of demand at any point on a demand curve with a slope equal to negative 1 is C greater than 1, but less than infinite. This is because price elasticity of demand measures the percentage change in quantity demanded in response to a percentage change in price.

The price elasticity of demand at any point on a demand curve with a slope equal to negative 1 would be C) greater than 1, but less than infinite. This is because a slope of negative 1 indicates that for every one unit increase in price, there is a one unit decrease in quantity demanded. This means that the demand curve is relatively steep, indicating that small changes in price will result in larger changes in quantity demanded. Therefore, the price elasticity of demand would be greater than 1, but not infinite, as there is still some level of responsiveness to price changes.

When the elasticity is greater than 1, it indicates elastic demand, where the quantity demanded is highly responsive to price changes.

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Answer:

1. The probability that a key opens a classroom = P(C) =  5/7

2. The probability that a key opens the teachers' lounge  P(T) =  4/7

3. The probability that a key opens a classroom and the teachers' lounge  P(C and T) =  3/7

4.  The probability that a key opens a classroom or the teachers' lounge P(C or T) =  6/7

Number of keys of the

high-school janitor has = 140

open classroom doors = 100

open   teachers' lounge = 80

open both = 60

The Probability is defined as the ratio of:

= the number of favorable outcomes /possible outcomes.

A. The Probability that a key opens a classroom:

P(c) = 100/140

      = 5/7

B. The probability that a key opens the teachers' lounge:

P(T) = 80/140

       = 4/7

C. The probability that a key opens a classroom and the teachers' lounge:

P(C and T) = 60/140

                 = 3/7

D. The probability that a key opens a classroom or the teachers' lounge:

P(C or T) = P(C) + P(T) - P(C and T)

E. Substituting the value

P(C or T) = 5/7 + 4/7 - 3/7

P(C or T) =  6/7

1. The probability that a key opens a classroom = P(C) =  5/7

2. The probability that a key opens the teachers' lounge  P(T) =  4/7

3. The probability that a key opens a classroom and the teachers' lounge  P(C and T) =  3/7

4.  The probability that a key opens a classroom or the teachers' lounge P(C or T) =  6/7

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I understand that the question you are looking for is:

A high school janitor has 140 keys on his key chain. Of these 140 keys, 100 open classroom doors, 80 open the door to the teachers' lounge, and 60 open classroom doors and the teachers' lounge. Using this information, answer each of the following questions.

Let C be the event that a randomly selected key opens a classroom and T be the event that a randomly selected key opens the teachers' lounge.

1. What is P(C), the probability that a key opens a classroom?

2. What is P(T), the probability that a key opens the teachers' lounge?

3. What is P(C and T), the probability that a key opens a classroom and the teachers' lounge?

4. What is P(C or T), the probability that a key opens a classroom or the teachers' lounge?

The normal to the parabola\(z = x^2 + y^2\) at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20).

To find the normal to the paraboloid\(z = x^2 + y^2\) at points (3, 3, 18), we first need to find the slope of the surface at that point. The gradient vector is given by

\(∇f(x,y,z) = < 2x, 2y, -1 >\)

So the gradient vector at points (3, 3, 18) is

∇f(3, 3, 18) = <6, 6, -1>

This gradient vector is orthogonal to the plane tangent to the surface at the point (3, 3, 18). So the surface normal at this point is parallel to the gradient vector and can be expressed as

x = 3 + 6t

y = 3 + 6t

z = 18 - t

To discover where this line converges the parabola once more, we ought to substitute the x, y, and z equations into the parabola's condition. 

\(z = x^2 + y^2\)

So it looks like this:

\(18 - t = (3 + 6t)^2 + (3 + 6t)^2\)

\(18 - t = 18t^2 + 36t + 18\)

\(0 = 18t^2 + 37t\)

t=0 or t=-37/18

The value t = 0 corresponds to the starting point (3, 3, 18), so we are interested in the second value t = -37/18. Substituting this value into the normal equation gives:

x = 3 + 6(-37/18) = -1/3

y = 3 + 6(-37/18) = -1/3

z=18-(-37/18)=360/18=20

therefore, the normal to the parabola \(z = x^2 + y^2\) at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20). 

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The secοnd statement is wrοng, because the PQRS form is a kite. And the first statement is true because cοnnected it Will be quadrilateral

The statement  the diagonals οf quadrilateral qrst are perpendicular is cοrrect and qrst must be either a square or a rhοmbus is wrong.

Word problems are οften described verbally as instances where a problem exists and one or more questions are pοsed, the solutions to which can be fοund by applying mathematical operations to the numerical information provided in the prοblem statement. Determining whether twο provided statements are equal with respect to a collection of rewritings is known as a word prοblem in computational mathematics.

Here the given qrst quadrilateral is Kite.

We knοw that diagonal of kite bisect each other at 90°.

Then. the qrst quadrilateral diagοnals are perpendicular.

Then secοnd statement is wrοng , because it qrst is kite.

Hence the first statement is cοrrect.

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Answer:1/2 - 1/3 = 1/6

Step-by-step explanation:

Answer: 1/6 or 0.16

Step-by-step explanation: hope this helps!

Answer:

\(f(x)\cdot g(x)=x^3-21x^2+135x-243\)

Step-by-step explanation:

We are given the two functions:

\(f(x)=x^2-12x+27\text{ and } g(x)=x-9\)

And we want to find:

\(f(x)\cdot g(x)\)

So, by substitution:

\(=(x^2-12x+27)\cdot (x-9)\)

Distribute:

\(=(x^2-12x+27)(x)+(x^2-12x+27)(-9)\)

Multiply:

\(=(x^3-12x^2+27x)+(-9x^2+108x-243)\)

Rearrange:

\(=(x^3)+(-12x^2-9x^2)+(27x+108x)+(-243)\)

Combine like terms:

\(=x^3-21x^2+135x-243\)

Hence:

\(f(x)\cdot g(x)=x^3-21x^2+135x-243\)

The number 8.0 × 10⁻⁴ in standard form is 0.0008.

To change the number 8.0 × 10⁻⁴ to standard form, we move the decimal point four places to the left because the exponent is -4. This gives us the number 0.0008, which is equivalent to 8.0 × 10⁻⁴. In standard form, the number is expressed without scientific notation, where each digit is represented by its respective place value. The original number, 8.0 × 10⁻⁴, is a small number, and writing it in standard form as 0.0008 helps visualize its relative size. Standard form is a common way to express numbers in a more familiar and readable format.

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The mean total repair cost is $100, and the variance of the total repair cost is $1500.

The total repair cost is a random variable that depends on the number of defective machines selected. This is a hypergeometric distribution problem.

In a hypergeometric distribution, the probability mass function is given by:

P(X = k) = [C(K, k) x C(N-K, n-k)] / C(N, n)

Therefore, the mean and variance of X are:

E[X] = n x (K/N) = 5 x (4/10)

= 2

Var [X] = n x (K/N)(1-K/N)[(N-n)/(N-1)]

= 5x (4/10)(1 - 4/10)[(10 - 5)/(10 - 1)]

= 0.6

Since Y = 50X, we can find the mean and variance of Y by multiplying those of X by 50 and 50^2, respectively, because if Y = aX for some constant a, then:

E[Y] = aE[X] and Var[Y] = a ² x Var[X]

Therefore, the mean and variance of the total repair cost are:

E[Y] = 50E[X]

= 50 x 2

=  $100

Var[Y] = 50 ² Var[X]

= 25000 / 6

= $1500

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The given functions f(n) = 11 and g(n) = (3/4)^(n-1) can be combined to create a geometric sequence. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term is given as 11, and the common ratio is (3/4).

The nth term of a geometric sequence is calculated using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the position of the term. By substituting the values into the formula, we can find the 9th term.

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Answer:

A line of best fit is a straight line going through a trend on a scatter plot.

Step-by-step explanation:

A well drawn line of best fit is just a line going straight through the trend of dots to approximate an exact trend from a non-exact plot, so just draw a line that stays in the middle of the dots and you should do great.

Hope this helped!

Answer:

by combining common factors i dont really know Aden =-=

Step-by-step explanation:

Answer:

3, text time get a better pic

Step-by-step explanation:

The likelihood that a shooter will hit the target at least 13 times is 27.92%.

For such a binomial distribution, the probability density function equals the amount of successes ("x").

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The required number of achievements is five (i.e., x = 13), as we are keen in the development that the objective will be hit exactly five times.

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Therefore, there is a 27.92% chance that a shooter will hit the target at most 13 times.

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Answer:

339.12 rounded to the nearest hundreth is 339

Because the hundreth place right now is 1 so anything below five keep the same

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Step-by-step explanation:

Answer: 339.10

Step-by-step explanation: The value of 2 is the hundredth and it is rounded up to 0

Answer:

(a) Proof explained below

(b) The two lines are parallel

Step-by-step explanation:

(a) In the second equation express \(x\) in terms of \(y\) to get:

\(x=2y-8\)

Then, substitute \(x\) for \(2y-8\) in the first equation to get:

\(3(2y-8)-6y=-12\)

Open parentheses using the distributive property (\(a(b-c)=ab-ac\)) which results in:

\(6y-24-6y=-12\)

Combine like terms to reach:

\(-24=-12\), which is not true. Therefore, for any values of \(x\) and \(y\), the systems of equations will have no solutions.

Since the two lines have no solutions, that means that they are parallel.

Hope this helps :)