The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 96
cm ^2 , what is the length of the diagonal?

The number which represents the difference between the numbers given -3 and -2 as in the task content is; 1.

It follows from the task content that the difference between the given numbers -3 and -2 is to be determined by means of the number line.

On this note, since, it follows that the difference between two numbers in the number line is given by the absolute value of their arithmetic difference.

It follows that the number which is required in this scenario is; |-3-(-2)| = |-1| = 1.

This follows from the fact that the absolute value big any number is that number with a positive polarity.

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Answer:

42

Step-by-step explanation:

similar triangles

24/x = (24+8)/x+14

that looks complicated so we do

8/24 = 14/x

or

24/8 = x/14

3 = x/14

x = 3*14

x = 42

we test it with the first equation

24/42 = 32/56

simplify

4/7 = 4/7

true so 42 is correct

0.03607

Absolute value is the distance of a number from zero. Since distance is always positive, the absolute value is the same number but positive.

Please note, for this problem I have rounded to 5 decimal points because the answer is irrational.

Subtracting

There are 2 different ways to approach this problem. You can either estimate the square root of 5 or plug this question straight into a calculator.

First, we can estimate [tex]\sqrt{5}[/tex] and round to 5 decimal places.

Then, take this value and subtract.

Absolute Value

Now that we have solved the subtraction problem we have to find the absolute value. As stated above, the easiest way to find absolute value is to simply make the number positive. Since the answer is already positive, this is the final answer.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textbf{Equation: }[/tex]

[tex]\large\textsf{(3x)(4x)}[/tex]

[tex]\large\textbf{Solving:}[/tex]

[tex]\large\textsf{(3x)(4x)}[/tex]

[tex]\large\textsf{= 3x} * \large\textsf{4x}[/tex]

[tex]\large\textbf{Combine the like terms:}[/tex]

[tex]\large\textsf{(3x * 4x)}[/tex]

[tex]\large\textsf{= 3x * 4x}[/tex]

[tex]\large\textsf{= 12x}^2[/tex]

[tex]\large\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{Option\ D. 12\mathsf{x}^2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

Given that graduation rate is 95.2%.

We are required to find the probability that out of 12 selected candidates atleast 11 should be graduated.

Probability is basically the chance of happening an event among all the events possible. It cannot be negative. It lies between 0 and 1.

Probability=Number of items/ Total items.

Probability that atleast 11 will be graduated out of 12 selected candidates is as under:

It will be a binomial distribution.

So,

P(X>=11)=[tex]12C_{11}(0.925)^{11} (0.075)^{1} +12C_{12}(0.925)^{12} (0.075)^{0}[/tex]

=12*0.4241*0.075+1*0.3923

=0.3816+0.3923

=0.7739

Hence the probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

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well, the regular price is really "x", which oddly enough is 100%, but we also know that $358 is really the discounted price by 20%, namely 100% - 20% = 80%, so we know that 358 is really just 80% of "x", so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 358& 80 \end{array} \implies \cfrac{x}{358}~~=~~\cfrac{100}{80} \\\\\\ \cfrac{x}{358}=\cfrac{5}{4}\implies 4x=1790\implies x=\cfrac{1790}{4}\implies x\approx 448[/tex]

Yes, the mean is 26.4 and the standard deviation is 3

We are given;

n = 40, p = 66% = 0.66, and  q = 1 – 0.66 = 0.34

If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;

Mean; µ = np

Standard deviation; σ = √npq

where;

n is the sample size.

p is the population proportion.

q = 1 – p.

Calculating np and nq gives;

np = (40)(0.66) = 26.4

nq = (40)(0.34) = 13.6

Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.

Thus, µ = np

µ = 40(0.66) = 26.4

Standard deviation;

σ = √(40 * 0.66 * 0.34)

σ = 3

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Answer:

40 apples

Step-by-step explanation:

x = (4·2)/(1/5) = 8/(1/5) = (8/1):(1/5) = (8/1)·(5/1) = 40/1 = 40 apples

It takes 10 apples to make a gram of fat. Multiply the 10 apples by 4 grams of fat to find that it takes 40 apples to make 4 grams of fat.

The most efficient measurements of the box should be 4cm long, 1cm wide and 2cm high so that its cost is $129.2

To calculate the measurements of the rectangular box we must take into account the following condition:

According to the above, we can establish that the most appropriate measurement for the bottom and top should be 1cm (width) × 4cm (length). Additionally we can establish that the height of the box would be 2cm.

To find the volume of the box we must use the following formula:

The areas of this box are:

The total price of this box is as follows:

Top and bottom:

Sides:

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The exponential model for the data is: [tex]y = 693(1.5)^x[/tex]

When the cost is of $6000, the weight is of approximately 5.3 carats.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

From the table, the rate of change is given by:

b = 4980/3210 = 3210/2140 = 2140/1430 = 1.5.

When x = 1, y = 1040, hence the initial value is found as follows:

1.5a = 1040.

a = 1040/1.5

a = 693.

So the model is:

[tex]y = 693(1.5)^x[/tex]

When the cost is of $6000, the weight is found as follows:

[tex]693(1.5)^x = 6000[/tex]

[tex](1.5)^x = \frac{6000}{693}[/tex]

[tex]1.5^x = 8.658[/tex]

[tex]\log{1.5^x} = \log{8.658}[/tex]

x log(1.5) = log(8.658)

x = log(8.658)/log(1.5)

x = 5.3

When the cost is of $6000, the weight is of approximately 5.3 carats.

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Explanation:(x)(x)=x^2 and(x)(x)(x)=x^3

Answer:

See below

Step-by-step explanation:

237/50   =    4    R 37

37/20     =     1     R 17

17 / 10     =     1     R 7

7 / 1         =     7    R 0

4   50gm's      1     20gm       1   10gm       and   7    1g wts

The required number of weights used in chemical balance to weigh 237g is 4,1,1,7 respectively.

What is mathematical expression?

A mathematical expression expression in mathematical is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g.

Now, let us find the number of weights for each weight type :

For 50g weight the maximum number of weights needed will be 4 that is :

50g x 4 = 200g

Now, for 20g weight the maximum number of weights needed will be 1 that is :

20g x 1 = 20g

Now, for 10g weight the maximum number of weights needed will be 1 that is :

10g x 1 = 10g

Now, for 1g weight the maximum number of weights needed will be 7 that is :

1g x 7 = 7g

Adding all the weights we get :

200g + 20g + 10g + 7g = 237g;

which is the required weight and the number of weights used is 4,1,1,7 respectively.

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Answer:

your question is not correct i can not find the answer

If the third term of the aritmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.

Given the third term of the aritmetic sequence is 126 and sixty fourth term is 3725.

We are required to find the first term of the arithmetic sequence.

Arithmetic sequence is a series in which all the terms have equal difference.

Nth term of an AP=a+(n-1)d

[tex]A_{3}[/tex]=a+(3-1)d

126=a+2d--------1

[tex]A_{64}[/tex]=a+(64-1)d

3725=a+63d------2

Subtract second equation from first equation.

a+2d-a-63d=126-3725

-61d=-3599

d=59

Put the value of d in 1 to get the value of a.

a+2d=126

a+2*59=126

a+118=126

a=126-118

a=8

[tex]A_{1}[/tex]=a+(1-1)d

=8+0*59

=8

Hence if the third term of the arithmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.

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The behavior of the graph with the equation y=x66x5+50x3+45x2108x108 at each of its zeros will be as follows: two of them will resemble a quadratic function, while one of them will resemble a linear function.

This is further explained below.

Generally, a diagram that illustrates the relationship between variable quantities, usually consisting of two variables, with each variable being measured along one of a pair of axes that are intersected at right angles.

In conclusion, At each of its zeroes, the graph y=x66x5+50x3+45x2108x108 will exhibit one linear behavior and two behaviors that resemble quadratic functions.

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Answer:

5

Step-by-step explanation:

where there is the decimal point,you count the numbers after the decimal point

The number of specimens should be tested is 1352.

According to the statement

we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.

so,

Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.

For an uniform distribution of bounds a and b, the standard deviation is given by:

σ = [tex]\sqrt{\frac{(b-a^{2})}{12} }[/tex]

and put the values a= 50 and b= 700 then the

standard deviation is 187.64

And here the critical value become 1.6 then

We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.

Then n is 1352.

So,  The number of specimens should be tested is 1352.

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Answer:

-1

Step-by-step explanation:

0.35 - 0.8 = -0.45

-0.1 - 0.35 = -0.45

-0.55 - 0.45 = -1

Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting.

Therefore, the correct answer is option B. the number of dogs you take for a walk each day.

Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting. Discrete data exists a count that involves integers only a limited number of values exists possible. This kind of data cannot be subdivided into distinct parts. Discrete data contains discrete variables that exist in finite, numeric, countable, and non-negative integers.

Therefore, the correct answer is option B. the number of dogs you take for a walk each day.

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Answer:

approximately 2 lb

Step-by-step explanation:

Juan: 31/7

Ari: 19/3

Juan's fraction is close to 32/8 = 4

Ari's fraction is close to 18/3 = 6

6 - 4 = 2

Answer: approximately 2 lb

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.

According to the question,

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6). Now first to find slope of the equation using below formula,

Slope of the equation (m)= (change in y axis) / (change in x axis)

= (6- (-2))/(-5 - 1)

= 8/-6

=-(4/3)

Slope of the equation (m) = -4/3. whose graph is the line through (1, -2) and (-5, 6).Formula to find Standard form of the equation is y = mx + c.

-2 = -(4/3) 1 + c

c = -2 +(4/3)

c = -2/3

The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2. y = -(4/3)x -(2/3).

⇒  3y = -4x -2.

Hence, the standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.

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Answer:

12 walls

Step-by-step explanation:

Let's take everyone paints a different wall and there are no overlaps.

Given information from the question:

1.5 hours = 1 wall

1 hour =

[tex] \frac{1}{1.5} \\ = \frac{2}{3} walls[/tex]

per person.

From the information above, we can deduce:

6 people =

[tex] \frac{2}{3} \times 6 \\ = \frac{12}{3} \\ = 4 \: walls[/tex]

Since we know 6 people can paint 4 walls in an hour,

3 hours =

[tex]3 \times 4 \\ = 12 \: walls[/tex]

The equation for the tangent plane is 12x - y + 4z - 56 = 0 and the equation for normal line is (x - 6)/12 = (32 - y) = (z - 2)/4

Finding the Equations for Tangent Plane and Normal Line:

The given function is,

f(x, y, z) = x² - y - z² = 0

∂f/ ∂x = 2x

∂f/ ∂y = -1

∂f/ ∂z = 2z

At given point (6, 32, 2),

∂f/ ∂x = 12

∂f/ ∂y = -1

∂f/ ∂z = 4

(a) The equation of tangent plane is given as follows,

(∂f/ ∂x)(x-x₁) + (∂f/ ∂y)(y-y₁) + (∂f/ ∂z)(z-z₁) = 0

12(x - 6) - 1(y - 32) + 4(z - 4) = 0

12x - 72 - y + 32 + 4z - 16 = 0

The required tangent plane is,

12x - y + 4z - 56 = 0

(b) The equation for normal line is given as,

(x-x₁) / (∂f/ ∂x) = (y-y₁) / (y-y₁) = (z-z₁) / (∂f/ ∂z)

(x - 6)/12 = (y - 32)/(-1) = (z - 2)/4

Thus, the required equation of normal line is,

(x - 6)/12 = (32 - y) = (z - 2)/4

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Answer:

45:315

Step-by-step explanation:

Add up the ratio to get the total ratio.

1+7=8

Divide the 360 by the total ratio.

360÷8=45

The number 45 tells you how many times to multiply both sets of the ratio to get a total of 360.

1×45=45

7×45=315

so,

45:315

Hope this helped. Comment below if you need more assistance! :)

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The straight angles are angles that form a straight line, and their measure = 180°

In the given figure, the Straight angles is :

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

arithmetic sequence formula: first term + (n - 1)common difference

9 + (n - 1)-2

9 + -2n + 2

= -2n + 11

Step-by-step explanation:

M(x) = 4x^3 - 3

let M(x) = Y

Y = 4x^3 - 3...swap places of x & y.

X = 4y^3 - 3

look for x in terms of y.

4y^3 = x + 3

Y^3 = x + 3 / 4...put both sides under cube root.

y = ( x + 3 / 4 )^1/3

Answer:

thanks for your support of the personal information on the direction of economics class