Find three consecutive integers such that the
sum of the first and the third is 32.

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.

Answer:

Step-by-step explanation:

Answer:

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

8+6+4

16 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

390/1000

This is the answer and hope it helps

Answer:

37.5 m

Step-by-step explanation:

Since the trapezoid area formula is ((base 1+base 2)/2)*height, we can plug in the values.

((8+7)/2)*5

(15/2)*5

7.5*5=37.5

Now we add the unit, "m" to get 37.5 m!

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

Answer:

C

Step-by-step explanation:

 0 ≤ h ≤ 40, h ∈ R

Hope this helps :)

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

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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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:

40

Step-by-step explanation:

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]

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.

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: 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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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:

[tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]

Step-by-step explanation:

Given [tex]sin(\theta)=\frac{1}{2}[/tex] , to find [tex]sec(\theta)[/tex], it will be helpful to visualize a right triangle (triangle with a 90 degree angle) associated with that particular θ.  There are a few ways to go about this:

All of the basic trigonometric functions, applied to an angle) are a ratio of two specific sides of any right triangle that holds that angle.

Remember that the Sine of an angle is defined specifically, the ratio of the opposite side (the side across from the angle in the Sine function), and the hypotenuse (the side across from the right angle).  You might remember this through SohCahToa

[tex]sin(\theta)=\frac{opp}{hyp}[/tex]

In our case, since [tex]sin(\theta)=\frac{1}{2}[/tex] , so  [tex]\frac{opp}{hyp}=\frac{1}{2}[/tex] .  While there are an infinite number of triangles that have that ratio of those sides, they are all "similar" triangles (corresponding angles congruent, and corresponding sides are proportional, yielding common ratios of sides), and for ease, we can consider simply the triangle where the value of the numerator is the length of the opposite side, and the value of the denominator is equal to the hypotenuse.  So, [tex]opp=1[/tex], and [tex]hyp=2[/tex].

While we haven't actually talked about θ yet, we can still set up the triangle that has these sides so that we can visualize what the triangle looks like. (see image)

This triangle represents the triangle for the unknown θ in the original sine function.  We're tasked with finding the secant of that particular unknown θ.

Working toward Secant

Here, it will be helpful to remember either the reciprocal identities for[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex], or the definition of the secant function [tex]sec(\theta)=\frac{hyp}{adj}[/tex].

I find that most people remember the reciprocal identities more easily than keeping track of the definitions, so, since secant is related to cosine, it will be important to remember that [tex]cos(\theta)=\frac{adj}{hyp}[/tex].  From there, take the reciprocal of the cosine-value to get the secant-value (which matches the definition of the secant function).

Either way, it comes down to knowing the lengths of the side adjacent to theta, and the hypotenuse.  We already know the length of the hypotenuse, so we just need the length of the adjacent side.

Applying the Pythagorean Theorem

Fortunately, because it is a right triangle, the Pythagorean Theorem applies: [tex]a^{2} +b^{2} =c^{2}[/tex]  (where c is the length of the hypotenuse, and a & b are the lengths of the legs)

Substituting the known values for the sides we do know...[tex](adj)^{2} +(1)^{2} =(2)^{2}\\(adj)^{2} +1 =4[/tex]

...isolating "adj" by subtraction...

[tex](adj)^2=4-1\\(adj)^2=3[/tex]

...applying the square root property...

[tex]adj=\sqrt{3}[/tex]  or  [tex]adj=-\sqrt{3}[/tex]

Identifying which Quadrant the triangle is in

Since we were given that [tex]0^o < \theta < 90^o[/tex], our triangle is an acute triangle (as drawn in the diagram), and is in quadrant I (indicating that both legs will be measured with a positive value.

Thus, we discard the negative solution and conclude that [tex]adj=\sqrt{3}[/tex].

Finding the final solution

From there, [tex]cos(\theta)=\frac{adj}{hyp}[/tex] implies [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex], and through the reciprocal relationship (or simply the definition of secant, whichever is easier for you to remember), [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]

Note:  This method did not require knowing what the angle θ was.

If you know well the values of special triangles in the unit circle, you may have identified that [tex]sin(\theta)=\frac{1}{2}[/tex]  is associated with [tex]\theta=30^o[/tex].  If so, if you also recall that the ordered pair associated with that point on the unit circle is [tex](\frac{\sqrt3}{2} ,\frac{1}{2} )[/tex], and that the [tex]cos(\theta)=x\text{-coordinate on the unit circle}[/tex], then you can quickly identify that  [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex].

This method still ends the same: recalling the reciprocal relationship between cosine and secant, giving [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex].

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.

The logical conclusion from the statement is that

B. The opposite sides of a rhombus are congruent.

From the information given, if shape is a parallelogram, then opposite angles are congruent.

In this case, since the rhombus is a parallelogram, then the opposite sides of a rhombus are congruent.

In conclusion, the correct option is B.

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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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Answer:

a=1.66

b=8368.12

Step-by-step explanation:

hope it helps

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.

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:

Answer: 1.25

Step-by-step explanation:

The explicit formula for the sequence is [tex]a_{n}=10(0.5)^{n-1}[/tex]

Substituting in n=4,

[tex]a_{4}=10(0.5)^{4-1}=\boxed{1.25}[/tex]

Answer:

12 minutes

Step-by-step explanation:

added in the picture

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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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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