62. The width of a rectangle is 3 cm less than its length. The perimeter of the rectangle is 30 cm. Find the length and width of the rectangle.

Answer:

Step-by-step explanation:

Considering the given data-set, it's mean and the formula, the variance is of 870 lbs².

The variance of a data-set is given by the sum of the differences squared between each observation and the mean, divided by the number of values.

The mean is the sum of all observations divided by the number of observations, hence:

M = (145 + 175 + 180 + 205 + 120)/5 = 165.

And the variance, in lbs squared, is given by:

V = [(145-165)² + (175-165)² + (180-165)² + (205-165)² + (120-165)²]/5 = 870.

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Answer:

40

Step-by-step explanation:

Answer:

( 1, - 1 )

Step-by-step explanation:

The first step is replacing the given trigonometric functions by simpler ones and then taking the product of the denominators.

Here we have the expression:

[tex]\frac{tan(x)}{1 + sec(x)}[/tex]

Remember that:

[tex]tan(x) = \frac{sin(x)}{cos(x)}\\ \\sec(x) = \frac{1}{cos(x)}[/tex]

Replacing that would be the "step zero", we can write:

[tex]\frac{tan(x)}{1 + sec(x)} = tan(x)*\frac{1}{1 + sec(x)} = \frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} }[/tex]

The first step to simplify this, is taking the product between the denominators:

[tex]\frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} } = sin(x)*\frac{1}{cos(x) + \frac{cos(x)} {cos(x)} } = \frac{sin(x)}{cos(x) + 1}[/tex]

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Answer:

tanx(1-secx)/(1+secx)(1-secx)

Step-by-step explanation:

aP E

Answer:

Step-by-step explanation:

The domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

A carpet installer charges a flat rate of $40 and $1.50 per square foot for labor.

So the total cost for the labor depends on the amount of carpet installed, the relationship between the total cost for labor and the amount of corporate installed.

Then the domain of the relation is the range of the relation will be

Let y be the total amount and x be the number of square foot.

y = 1.5x + 40

Then the domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).

The graph is given below.

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Answer: The given triangles have an area [tex]1/2[/tex] × [tex]base[/tex] × [tex]height[/tex]

Step-by-step explanation:

The moving principle states that if you move a shape rigidly without stretching it the area does not change whereas the additivity principle states that if you combine different shapes without overlapping them then the area is the cumulative sum of each of the figures.

Since both, the principle will give out the same answers. the arrangement for the expression can be manipulated also.

For the first triangle applying the moving principle gives,

Area  [tex]=[/tex] [tex]b[/tex] × [tex](\frac{1}{2}[/tex] · [tex]h)[/tex]

For the second triangle applying the additivity principle,

Area [tex]=\frac{1}{2}[/tex] ([tex]b[/tex] · [tex]h[/tex])

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Work Shown:

[tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}\\\\\frac{1-\sin^2(\beta)}{\cos^2(\beta)}\\\\\frac{\cos^2(\beta)}{\cos^2(\beta)}\\\\1\\\\[/tex]

Therefore, [tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}=1\\\\[/tex] is an identity for all values of β for which the original expression is defined. I used the difference of squares rule for the 2nd step. Then I applied the pythagorean trig identity for the 3rd step.

Answer:

-4(-2)+2(3)-(-4)

8+6+4

16 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

Inequality:  x + 6 ≤ 24

Solution:  x ≤ 18

Step-by-step explanation:

Plus:  "+" →  to add something to something else

Less than or equal to:  "≤" → the expression on the left side of the inequality sign is smaller than the expression on the right side of the sign.

Let x be the unknown number.

A number plus 6 is less than or equal to twenty-four:

x + 6 ≤ 24

To solve the found inequality, subtract 6 from both sides:

⇒ x + 6 - 6 ≤ 24 - 6

⇒ x ≤ 18

Therefore, the solution to the inequality is x ≤ 18.  The unknown number x can be any real number equal to or less than 18.

No be n

Solve

Solution set

Using the binomial distribution, it is found that the probabilities are:

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Exercise 1:

The parameters are:

n = 15, p = 0.4, x = 4.

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228[/tex]

Exercise 2:

The parameters are:

n = 12, p = 0.2, x = 2.

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835[/tex]

Exercise 3:

The parameters are:

n = 20, p = 0.05.

The probability is:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Using the binomial formula for each value and adding them:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841[/tex]

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Answer:

Step-by-step explanation:

Part A: Since 400 is being multiplied 1.06^t, for it to be equal to 399 the value 1.06^t must be less than 1. The lowest value for t given the domain restriction is 0 which would only result in 1 which will given the initial amount of 400. t would need to be less than 0 for 1.06^t to start going below the value 1 but since there is a domain restriction since t represents time, that value cannot go below 400 to reach 399.

Answer:

5m4n3 and 15m2n2

Step-by-step explanation:

you just have to find the 2 that each are divisible by 5m2n2, which are 5m4n3 and 15m2n2.

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

The answer will be Rs. 4330.

Step-by-step explanation:

Because if you subtract 340 from 4670, you will get the answer which is 4330.

As x decreases without bound, the graph of f(x)  approaches y = 0

As x increases without bound, the graph of f(x)  increases without bound

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x)=5^(x−1)

When x -> -∞

[tex]lim_{ x- > -\infty.[/tex] f(x)= 5 ^(x-1) = 0

When x -> ∞

[tex]lim_{ x- > \infty.[/tex] f(x)= 5 ^(x-1) = ∞

Hence,

As x decreases without bound, the graph of f(x) approaches y = 0

As x increases without bound, the graph of  f(x) increases without bound

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Answer:

C

Step-by-step explanation:

 0 ≤ h ≤ 40, h ∈ R

Hope this helps :)

Two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.

Given inequality is:-

We will check all the points for the inequality:-

(−8,−1) →  x + 5y  <  2.  →  -8 +(5 x -1) < 2  →  -13 < 2 It is inequality

(−1,0)   → x + 5y  <  2   →   -1 < 2 It is inequality

(4,2)    → x + 5y  <  2   →    14 < 2  wrong

(9,6)    → x + 5y  <  2   →    39 < 2 wrong

(0,10)  →  x + 5y  <  2  →    50 < 2 wrong

Therefore the two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.

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Answer:

12 minutes

Step-by-step explanation:

added in the picture

Answer:

[tex]\huge\boxed{\sf 14\ ft}[/tex]

Step-by-step explanation:

Yard sticks = 4

12-inch rulers = 2

All are placed end to end.

We know that,

1 yard = 3 feet

4 yards = 3 × 4 feet

4 yards = 12 feet

We know that:

1 inch = 0.083 feet

24 inch = 0.083 × 24 feet

24 inch = 2 feet

= 4 yardsticks + 2 12-inch rules

= 12 ft + 2 ft

= 14 ft

[tex]\rule[225]{225}{2}[/tex]

Answer: Option 1

Step-by-step explanation:

The graphs intersect at x=0 and x=2, meaning f(2)=g(2) and f(0)=g(0).

The functions have the intersecting points at x = 2 and x = 0 and the relation is f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the first function be represented as f ( x )

Let the second function be represented as g ( x )

Now , the function f ( x ) is a parabolic function and g ( x ) is a linear function

And , the intersecting points of both f ( x ) and g ( x ) are

x = 2 and x = 0

So , both the functions f(x) and g(x) intersect at two points, one at x = 2 at the x-axis in the graph and one at y = 4 at y-axis of the graph

Therefore , f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )

Hence , the functions are solved

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The length of the actual tree will be 72 inches.

Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.

The equation whose highest degree of the variable is 1 is called a linear equation.

Here given that the length of a painting of the tree is 2/9 of the actual length of the tree.

So mathematically the length of a painting= (2/9)*the length of actual tree

Let the length of the actual tree is x

then from above it is clear that the length of a painting of the tree= (2/9)x

Given the length of the painting is 16 inches.

So the linear equation will be (2/9)x= 16

⇒ x= 16/(2/9)

⇒x= 16*9/2

⇒x=72 inches

Therefore the length of the actual tree will be 72 inches.

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Answer:

3/2+1/2+17/2=21/2

Answer: 21/2 hours or 10 1/2 hours

Step-by-step explanation:

To find out the total number of hours needed for all activities scheduled for the day, simply add the needed hours for each activity.

You just need to add them because they have the same denominator.

3/2 for homework

1/2 for home chores

17/2 for sleep

[tex]\frac{3}{2} + \frac{1}{2} + \frac{17}{2} = \frac{21}{2}[/tex] hours

Answer:

a=1.66

b=8368.12

Step-by-step explanation:

hope it helps

Answer:

177

Step-by-step explanation:

The inductive step is assuming that the statement is true for some  n = k , where  k  is one of the values we want to prove the statement for, it shows that it is also true for  n = k+1.

Suppose we have the statement 3n > 4n for all positive integers  n.

Now, the statement above is false when n = 1 , since 3 is less than 4. However, it will be true for all other positive integers.

In that case, we can still prove this statement by induction for all integers  n ≥ 2 .

Thus, the inductive step is assuming that the statement is true for some  n = k , where  k  is one of the values we want to prove the statement for, it shows that it is also true for  n = k+1.

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Both are not earning different salaries.

If a study determines the difference in average salary for subpopulations of mechanical engineers and civil engineers is NOT significant, then the subpopulations of mechanical and civil engineers are not earning different salaries.
Study determines that there is not any significant study so thats why both are not earning.


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