5 (6 - x) - 3 = 5 + 4 (x + 3)​

Answer:

Mohamad payed 8% of sales tax.

Step-by-step explanation:

First, we need to find the additional amount he paid to find the tax percentage.

70.20 - 65.00 = $5.20

Now, we divided that answer by the original price to find the actual percentage.

5.20/65.00 = 0.08 = 8%

The sum of the interior angles in a triangle is 180 degrees.

72 + 35 + <1 = 180

107 + <1 = 180

<1 = 73 degrees

Hope this helps!

Answer:

<1 = 73

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

72+ 35+ <1 = 180

Combine like terms

107 + <1 =180

Subtract 107 from each side

<1 = 180-107

<1 = 73

Part (i)

We start with five dots to make the pattern in figure 1.

In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.

In figure 3, there are 9+4 = 13 dots

So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.

The first three terms of this arithmetic sequence are: 5, 9, 13

Your teacher wants to know what the general nth term is

We start with a = 5 and the common difference is d = 4

T(n) = nth term

T(n) = a + d(n-1)

T(n) = 5 + 4(n-1)

T(n) = 5 + 4n - 4

T(n) = 4n + 1

Let's try it out. Say we want to plug in n = 2

T(n) = 4n + 1

T(2) = 4(2) + 1

T(2) = 8 + 1

T(2) = 9

This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.

============================================================

Part (ii)

Your teacher wants to know how many dots occur when n = 50

T(n) = 4n + 1

T(50) = 4(50)+1

T(50) = 200 + 1

T(50) = 201

Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.

Answer:

the red marble was kept out so you can not draw it again

Answer:

Yes; you may not get a red marble again.

Step-by-step explanation:

there is a chance to get a red marble but it is not high

Answer:

3

Step-by-step explanation:

The value of x is 3 if the volume of the triangular prism is 54 cubic units.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that  volume of the triangular prism is 54 cubic units.

We have to find the value of x

The volume of the prism with triangular base is 54 unit³.

The base is a triangle with,

base = 4 units

height = x units

height of the prism = 3x

V= 6x²

54= 6x²

Divide both sides by 6

x² = 9

x=3

Hence, the value of x is 3 if the volume of the triangular prism is 54 cubic units.

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The missing equations are;

a + 2b + 3c = 12

3a + 2b + 5c = 22

2a + 4b + 4c = 18

Answer:

a = 2

b = 0.5

c = 3

Step-by-step explanation:

We are told that;

a represent the price per pound of apples

b represent the price per pound of bananas

c represent the price per pound of oranges

The equations system is;

a + 2b + 3c = 12 - - - (eq 1)

3a + 2b + 5c = 22 - - - (eq 2)

2a + 4b + 4c = 18 - - - (eq 3)

Divide through equation 3 by 2 to get

a + 2b + 2c = 9 - - - (eq 4)

Subtract eq 4 from eq 1 to get;

3c - 2c = 12 - 9

c = 3

Put 3 for c in eq(2) and eq 4;

3a + 2b + 5c = 22

3a + 2b + 5(3) = 22

3a + 2b + 15 = 22

3a + 2b = 7 - - - (5)

a + 2b + 2(3) = 9

a + 2b + 6 = 9

a + 2b = 3 - - - (eq 6)

Subtract eq 6 from eq 5 to get;

2a = 7 - 3

2a = 4

a = 2

Put 2 for a in eq 6;

2 + 2b = 3

2b = 3 - 2

2b = 1

b = 1/2

b = 0.5

Answer:

It's A

Step-by-step explanation:

edge 2021

Answer:

Fraction of profit from other departments = 17/28

Step-by-step explanation:

Total profit of R. White and Co = 6/7 million dollars

Profit from the spinning department = 1/4 of million dollars

Fraction of profit from other departments = Total profit of R. White and Co - Profit from the spinning department

= 6/7 million dollars - 1/4 of million dollars

= 6/7 - 1/4

Lowest common multiple (LCM) of 7 and 4 is 28

= (24-7) / 28

= 17/28

Fraction of profit from other departments = 17/28

Answer:

4w = -5-19

4w=-24

w=-6

hope that answers your question

good luck

9514 1404 393

Answer:

  can't be done. x = 6, not 36

Step-by-step explanation:

Without the diagram we must speculate that the 150 cm length is the hypotenuse. Then we have ...

  150² = (7x)² +(24x)² = (49 +576)x² = 625x² . . . . Pythagorean relation

  150²/625 = x² = 36 . . . . . divide by 625

  x = √36 . . . . . . . . . . . take the square root

  x = 6

Step-by-step explanation:

here's the answer to your question

Answer:

This is a 4th degree polynomial!

Step-by-step explanation:

Because the polynomial starts of the a number with a 4th degree and decreases down with lower numbers. Simply put, because (x^4) has the largest degree.

Hope this helps, good luck! :)

Answer:

The width of the confidence interval based on the 784 women would be narrower than the  confidence interval based on the 327 women.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

From this, we have that the margin of error, and also the width, is inversely proportional to the sample size, that is, a larger sample size leads to a smaller margin of error and a narrower interval.

How would the width of the new confidence interval compare to the width of the  confidence interval based on the 327 women in the armed forces?

New interval: 784

Old interval: 327

Sample size increased, so the new interval will be narrower, and the correct answer is:

The width of the confidence interval based on the 784 women would be narrower than the  confidence interval based on the 327 women.

Answer:

[tex]U = x[/tex]

[tex]V=10[/tex]

Step-by-step explanation:

Given

[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]

Required

Find U and V

We have:

[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]

Expand

[tex]x^2 + 6x + 9 + 14x + 42 + 49 = (U + V)^2[/tex]

Collect like terms

[tex]x^2 + 6x + 14x + 9 + 42 + 49 = (U + V)^2[/tex]

[tex]x^2 + 20x + 100 = (U + V)^2[/tex]

Expand

[tex]x^2 + 10x + 10x + 100 = (U + V)^2[/tex]

Group

[tex][x^2 + 10x] + [10x + 100] = (U + V)^2[/tex]

Factorize each group

[tex]x[x + 10] + 10[x + 10] = (U + V)^2[/tex]

Factor out x + 10

[tex][x + 10][x + 10] = (U + V)^2[/tex]

So, we have:

[tex][x + 10]^2 = (U + V)^2[/tex]

By comparison

[tex]U = x[/tex]

[tex]V=10[/tex]

Answer:

N0

Step-by-step explanation:

The sides of a triangle must be

a-b< c< a+b  where a and b are the two smaller sides and c is the larger side

3-3 <9< 3+3

0<9<6

This is not true so it cannot make a triangle

answer:

no

step-by-step explanation:

each side must be smaller than the sum of other sides

so

9+3>3-right

3+3<9-wrong

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

[tex]\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

[tex]\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta[/tex]

Simplify. The denominator uses the difference of two squares pattern:

[tex]\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta[/tex]

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

[tex]\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]

Split into two separate fractions:

[tex]\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta[/tex]

Rewrite the two fractions:

[tex]\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta[/tex]

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

[tex]\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta[/tex]

Hence verified.

Answer:

Krishna is at the 7th floor

Step-by-step explanation:

Given

[tex]Start = 12[/tex]

[tex]Up = 3[/tex]

[tex]Down = 8[/tex]

Required

The current floor

This is calculated as:

[tex]Floor = Start + Up - Down[/tex]

[tex]Floor = 12 + 3 - 8[/tex]

[tex]Floor = 7[/tex]

Answer:

7-4*(-1)

7-4*(-1)7+4

7-4*(-1)7+411

Step-by-step explanation:

hope it will help u

Answer:

A(- 1) = 11

Step-by-step explanation:

Substitute x = - 1 into A(x) , that is

A(- 1) = 7 - 4(- 1) = 7 + 4 = 11

Answer:

Step-by-step explanation:

Answer:

Here's the answers

Step-by-step explanation:

1. When two variables are in relation with a formula or a variable is related by the sum of two or more variables, then it is a partial variation. X = KY + C (where K and C are constants) is a straight line equation which is an example of partial variation.

2. The formula y=kxn y = k x n is used for direct variation. The value k is a nonzero constant greater than zero and is called the constant of variation.

Answer:

y= -6

x = 2

(2,-6)

Step-by-step explanation:

Indepedent variable = x = 2

Plug 2 in for x

f(2) = -5(2) + 4

-10 + 4 = -6

y = -6

Answer:

360

1080

Step-by-step explanation:

We can find the sum of the interior angles of any regular polygon by using this formula

(n - 2) * 180

where n = number of sides

For the square: the square has 4 sides

To find the sum of the interior angles we simply substitute 4 for n in the formula

Formula: (n - 2) * 180

Substitute 4 for n

(4 - 2 ) * 180

Subtract 4-2

2 * 180

Multiply

= 360

The sum of the interior angles of the first polygon is 360

For the second one:

We will repeat this exact process the only difference is the value of "n"

The polygon shown has 8 sides

So to find the sum of the interior angles we simply substitute 8 for n in The formula

Formula (n - 2) * 180

Substitute 8 for n

(8 - 2) * 180

Subtract 8 - 2

6 * 180

Multiply

= 1080

The interior angles of a 8 sided figure will add up to 1080

Answer:

I think it would be 100%

Step-by-step explanation: because it is certain that means its going to happen

Answer:

(8,7)

Step-by-step explanation:

Because our x-value for this ordered pair is 1, and it says to move to the right 7 units, 1+7 = 8. Therefore, our x-value for the ordered pair would be 8.

Because our y-value for this ordered pair is 6, and it says to move up 1 unit, 6+1=7. Therefore, our y-value for the ordered pair would be 7.

Once we have our x- and y-value, we can set up the ordered pair:

(8,7)

Answer:

(7, 8)

Step-by-step explanation:

In the picture below, when the point is moved up, it only changes the y part of the point, and the x part is kept the same. When the point is moved right by 7 units, the x part is changed while the y part is kept the same.

Hope this helps.

In this question, the client will buy one item, which is composed by a boot, a pair of skis and a hat. Since the items are independent, the fundamental counting principle can be used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

60 boots, 30 pairs of skis, 40 hats. So

60*30*40 = 72,000

The customer can purchase an item in 72,000 ways from the store.

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Answer: Choice D. [tex]\angle A \cong \angle E[/tex]

Explanation: Since AB is parallel to ED, this means the alternate interior angles A and E are congruent as marked below.

Angle A is congruent to angle E by alternate interior angle theorem. Therefore, option D is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle CAB is similar to triangle CED and AB is parallel to ED.

From the given figure, AB=7 miles, DC=16 ft, EC=12 ft and DE=21 ft.

Here, in figure,

∠A ≅ ∠E  (Alternate interior angles)

∠B ≅ ∠D  (Alternate interior angles)

∠ACB ≅ ∠DCE  (Vertically opposite angles are congruent)

Therefore, option D is the correct answer.

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Answer:

find the indicated functional value for the floor function: f(-3/2)

B. 0

Step-by-step explanation:

hope it helped.

° ° °

The indicated functional value for the floor function is option (C) -1 is the correct answer.

The floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted floor(x) or f(x). It gives the largest nearest integer of the specified value.

For the givens situation,

The floor function is f(-3/2).

The indicated functional value for the floor function is

⇒ [tex]f(-3/2)= f(-1.5)[/tex]

Here x = -1.5, the indicated functional value should be a greatest integer less than or equal to x.

Thus the indicated functional value of [tex]f(-1.5)[/tex] is [tex]-1[/tex].

Hence we can conclude that the indicated functional value for the floor function is option (C) -1 is the correct answer.

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Answer:

Step-by-step explanation:

On a normal distribution table with z scores of 0 as the mean and the standard deviations going to the right and to the left, 1.9 on the normal curve where 3 is the mean falls at -.275 on the normal curve where 0 is the mean. I used the normal distribution z table for negative values to get that .39165 lies to the left of -.275, which means that 1 - .39165 of the data lies to the right.

The probability that the value is greater than 1.9 is .60835, or as a percentage, 60.835%.

Answer:

Mother is presently 34

Scott is 11

Step-by-step explanation:

Let the mother's age = x

Let the son's age = y

First Equation

x + y = 45

Second equation

3*(x + 5) - 9 =  y+5                Add 9 to both sides

3(x + 5) = y + 5 + 9

3(x + 5) = y + 14                    Remove the brackets

3x + 15 = y + 14                    Subtract 14 from both sides

3x + 15 - 14 = y

3x + 1 = y

Put the first equation into the second equation

x + y = 45                             Subtract y from both sides

y = 45 - x

Put this value for y into the second equation's results.

3x + 1 = 45 - x                       Add x to both sides

3x + x + 1 = 45                    

4x + 1 = 45                            Subtract 1 from both sides

4x = 45 - 1

4x = 44                                Divide by 4

x = 44/4

x = 11

x + y = 45

11 + y = 45

y = 34

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Step-by-step explanation:

The slope of the line is - 5, the equation will be y=-5x-1.

y+5x=-1