Which expression represents the following statement? Multiply 6 by 3, and then subtract the quotient of 18 and 9.

A) 6 x (3 ÷ 18) + 9
B) 6 + 3 + (18 ÷ 9)
C) (6 x 3) − 18 ÷ 9
D) 6 x (3 + 18) + 9

Answer:

1) 0.10

2) 0.15

3) 0.100

4) No

The mode of the set of 10 observations is 2.

What is the mode?

Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency of a data set. Other measures of central tendency are mean and median.

According to the information in the question, 6 appears twice in the data set and all other values are different. Thus, 6 has the frequency of 2 which is the highest. 6 is the mode.

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The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).

We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.

Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.

We are also given that EC (a part of diagonal AC) is 8 units long.

As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).

Now, we are told that DB (a part of diagonal BD) is x - 1 units long.

To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is

(x - 1) units + (x - 1) units = 2x - 2 units.

The area of a rhombus is given by the formula:

Area = 1/2 × Product of Diagonals.

Substituting the given values, we have:

72 = 1/2 × 16 × (2x - 2).

Now, we can simplify the equation:

72 = 8x - 8.

Move the constant term to the right side:

8x = 72 + 8.

Combine the constants:

8x = 80.

Finally, solve for x by dividing both sides by 8:

x = 80 / 8 = 10.

So, the value of x is 10 units. The correct answer is B).

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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.

What is the value of x?

9

10

14

16 "--

For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.

In this question we must determine the amount of money needed to pay in taxes by the purchase of an item with a discount. Sales taxes are an example of indirect taxes, this kind of indirect tax is usually calculated on the basis of total costs, including discounts. The amount of money need for the sales tax is described below:

t = (r / 100) · (1 - d / 100) · c     (1)

Where:

If we know that d = 30, r = 5 and c = 10, then the sales tax total is:

t = (5/ 100) · (1 - 30 / 100) · 10

t = 0.35

For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.

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Angles in quadrilateral add to 360

108 +67 +10 =185

4x + 3x = 7x

185 + 7x = 360

- 185

7x. = 175

÷ 7

x = 25

Check:

4x25 = 100

100 + 67 + 108 = 275

275 + (3x25) = 350 + extra 10 is 360

Hope this helps!

Step-by-step explanation:

1 meter = 100 centimeter = 1000 millimeter

therefore, 1 cm = 10 mm

4.6 m = 4.6 × 1000 = 4600 mm

88 cm = 880 mm

and so, they cut off

880 mm + 1630 mm = 2510 mm

that means

4600 - 2510 = 2090 mm = 2.09 m

are left.

Answer:

x²y³

Step-by-step explanation:

(x²) (y³) = x²y³

Hope it helps!

Have a nice day:)

❄ Hi there,

let us find the product of the square of x and the cube of y.

[tex]\sf{The \ square \ of \ x: \ x^2}\\\sf{The \ cube \ of \ y: y^3}\\\sf{The \ product \ of \ the \ two: x^2y^3}[/tex]

The square of x means: x times x, or, as I said earlier, x².

The cube of y means: y times y times y, or, as I said earlier, [tex]\sf{y^3}[/tex].

The product means: you multiply x² times y³.

❄

The pressure, P if V is decreasing at a rate of 10in^3/sec is 120lb/in^2 per sec.option B

PV = c

where,

when P =60lb/in^2 and V=20in^3

PV = c

60 × 20 = 1200 in

Find P if V is decreasing at a rate of 10in^3/sec

PV = c

P × 10 = 1200

10P = 1200

P = 1200 / 10

P = 120lb/in^2 per sec

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Answer:

1/3.

Step-by-step explanation:

P(event a occurs) = 3/9 = 1/3

P(event b occurs) = 3/9 = 1/3

P(a) ∩ P(b) = 1/3 * 1/3 = 1/9

P(b|a) = P(a) ∩ P(b) / P(a)

          =  1/9 / 1/3

          =  1/3.

i really hate how we actually have to type something.

Answer:

1.ABC is equilateral triangle because all sides are equal

3.because they are the joined figure of a triangle

The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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Answer:

(a)

(b) range of sample means =0.6

(c)

[tex]2 \sqrt{4} + 3 \sqrt{9} \\ 2(2) + 3(3) \\ 4 + 9 = 13[/tex]

Answer:

13

Step-by-step explanation:

2×√4+3×√(9

2x2+3x3

Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Researching this problem on the internet, we have that:

Hence:

x² + 9² = 12²

x = sqrt(12² - 9²)

x = 7.9 cm.

The unknown side length of the triangle is of 7.9 cm.

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Answer:

? = 4 units

Step-by-step explanation:

'2'  is to  ' 7+2 '     as  ?   is to   '14 + ? '

2/ 9 = ? / (14 + ?)      cross mutiply

28 + 2? = 9?

28 = 7?

? = 4

Answer:

C.  They most likely used an observational study asking students to keep track of their TV habits and weight.

A.  This is an experiment because a treatment was applied to a group.

Step-by-step explanation:

According to our question:

1. The study concluded that there is a relation between watching TV and the weight gain in college freshmen.

Now, this is possible when a group of college students were asked to participate to watch TV for more than 1 hour for a specific amount of time and have a record of their weights.

So, the study is an observational study where the habits and weights of college students were observed.

Hence, option C is correct.

2. The students were divided onto two groups where one group used the computer program and the other did not to check the improvement in the reading levels.

This means that the students were given a procedure to follow during the study in order to see the results..

So, the study is an experiment where a treatment is applied to the group of students.

Hence, option A is correct.

Answer: C

For the people who want only one answer and not 2 for the question if you can only submit one answer :)

The z-score corresponding to a sample mean of m = 69 is -0.167

In this problem, we have been given :

population mean (μ) = 70, standard deviation (σ) = 12,  sample size (n) = 4, sample mean (m) = 69

We know that, the Z-score measures how many standard deviations the measure is from the mean.

Also, the formula when calculating the z-score of a sample with known population standard deviation is:

[tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

where z = standard score

μ = population mean

σ = population standard deviation

m = the sample mean

and [tex]\frac{\sigma}{\sqrt{n} }[/tex] is the Standard Error of the Mean for a Population

First we find the Standard Error of the Mean for a Population

σ /√n

= 12 / √4

= 12 / 2

= 6

So, the z-score would be,

⇒ [tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

⇒ [tex]Z=\frac{69-70}{6 }[/tex]

⇒ Z = -1/6

⇒ Z = -0.167

Therefore, the z-score corresponding to a sample mean of m = 69 is -0.167

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Answer:

255,000,000m^2

Step-by-step explanation:

Let 5:12:17:25 be 5x, 12x, 17 x, 25x respectively

So

Perimeter of quadrilateral=5x+12x+17x+25x

590m=59x

590m/59=x

10m=x

So now value

5x= 5*10 =50

12x= 12*10 =120

17x= 17*10 =170

25x= 25*10 =250

Now

Area of quadrilateral=50m*120m* 170m* 250m

=255,000,000m^2

Step-by-step explanation:

if I understand you correctly the sides are in a

5 : 12 : 17 : 25 ratio.

a ratio is basically a fraction. but instead of the denominator telling us the structure of the whole (e.g. 2/5 tells us that the whole is split into 5 equal parts), a ratio tells us this by the sum of its elements :

5 : 12 : 17 : 25

means that the whole perimeter of the quadrilateral has

5 + 12 + 17 + 25 = 59 equal parts.

since the perimeter is 590 m, we know with 59 equal parts, that one part is 590/59 = 10 m.

so, the sides are

50 m, 120 m, 170 m, 250 m

but for the area of the quadrilateral there is at least the information of one angle missing.

to have just the 4 side lengths is not enough. these sides can still have all kinds of angles between them, which creates different areas.

Steps for Factoring:

1) Find CM (common factor) for the expression: 3

   Factor out 3 =>

   [tex]3(6x^{2}+13x-5)[/tex]

2)Factor the above expression by grouping:

  The expression needs to be written as [tex]6x^{2} + ax+ bx -5[/tex]

 a and b should add up to 13 and multiply up to -30 (6 × -5)

By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)

3) Now we can rewrite [tex](6x^{2}+13x-5)[/tex] as [tex](6x^{2} -2x)+(15x-5)\\[/tex]

Factor out 2x in the first group and 5 in the second group:

[tex]2x(3x-1)+5(3x-1)\\[/tex]

As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)

(3x-1) (2x+5)

The answer is 3(3x-1) (2x+5)

Hope it helps!

Answer:

[3,0]

[0,9]

Step-by-step explanation:

9x+3y=27

9x+3(0)=27

9x=27

x=3

9(0)+3y=27

3y=27

y=9

Answer: c = 520

Step-by-step explanation:

     f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.

Given:

    f(x) = 4x³ + 7x² - x + c

Substitute:

    578 = 4(2)³ + 7(2)² - (2) + c

Distribute:

    578 = 4 * 2³ + 7 * 2² - 2 + c

Raise to the power of 3 and 2:

    578 = 4 * 8 + 7 * 4 - 2 + c

Multiply:

    578 = 32 + 28 - 2 + c

Add:

    578 = 60 - 2 + c

Subtract:

    578 = 58 + c

Subtract 58 from both sides:

    520 = c

Reflexive property:

   c = 520

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:

[tex]\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}[/tex]

[tex]\longrightarrow\sf{578= 32+28 −2+ c}[/tex]

[tex]\longrightarrow\sf{578 =58+ c}[/tex]

[tex]\longrightarrow\sf{c = 578-58}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\longrightarrow\sf{c= 520}[/tex]

Answer:

24.315°

Step-by-step explanation:

First use the pythagorean theorem to get the missing side since this is a right triangle.

a^2 + b^2 = c^2 →

b^2 = c^2 – a^2 →

b = (c^2 – a^2)^½

b = (17^2 – 7^2)^½

b = (289 – 49)^½

b = √240.

Then use the law of cosines to find the angle in between.

b^2 = a^2 + c^2 - 2ac * cos(B) →

b^2 - a^2 - c^2 = -2ac * cos(B) →

a^2 + c^2 – b^2 / 2ac = cos(B) →

cos^-1(a^2 + c ^2 – b^2 / 2ac) = C →

B = cos^-1(a^2 + c ^2 – b^2 / 2ac)

B = cos^-1(49 + 289 – √240 / 238)

B ≈ 75.685°.

A = 180 – B

A = 180 – 75.685

A = 24.315°

Answer:

-7x + 1

Associative Property can be used.

Step-by-step explanation:

Hello!

We can simply the expression by combining like terms.

Like terms are terms with the same variable and degree. They may have different coefficients.

The simplified form is 1 - 7x, or -7x + 1.

We can also represent this using the Associative property, by grouping like terms:

There is a minimum value of -81 located at (x, y) = (6, -3).

The function given to us is f(x, y) = 3y² - 3x².

The constraint given to us is 2x + y = 9.

Rearranging the constraint, we get:

2x + y = 9,

or, y = 9 - 2x.

Substituting this in the function, we get:

f(x, y) = 3y² - 3x²,

or, f(x) = 3(9 - 2x)² - 3x² = 3(81 - 36x + 4x²) - 3x² = 243 - 108x + 12x² - 3x² = 243 - 108x + 9x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = - 108 + 18x ... (i)

Equating to 0, we get:

- 108 + 18x = 0,

or, 18x = 108,

or, x = 6.

Differentiating (i), with respect to x again, we get:

f''(x) = 18, which is greater than 0, showing f(x) is minimum at x = 6.

The value of y, when x = 6 is,

y = 9 - 2x,

or, y = 9 - 2*6 = 9 - 12 = -3.

The value of f(x, y) when (x, y) = (6, -3) is,

f(x, y) = 3y² - 3x²,

or, f(x, y) = 3*(-3)² - 3*6² = 3*9 - 3*36 = 27 - 108 = -81.

Thus, there is a minimum value of -81 located at (x, y) = (6, -3).

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Answer:

4112

Step-by-step explanation:

When you plug in 3 for x you get 6.

Then you just do 4^6 which is 4096.

Then add 16 which gets you 4112.

Answer:

0.213

Step-by-step explanation:

→ Convert into binomial information

x ~ B ( 12 , 0.4 )

→ Write down probability required

p ( x = 4 )

→ Evaluate

0.2128

The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown.

Quadratic equation are equation that has a leading degree of 2 while a linear equation has a leading degree of 1.

From the given graph, the curve shown has a two solutions which is the point where the curve intersect the x-axis.

For the graph shows a system consisting of a linear equation and a quadratic equation, the solution will be the points where the line intersects the parabola.

The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown

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The distance from Sang to Jazmin is 101 yards.

From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.

The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.

From;

c^2 = a^2 + b^2

c = √a^2 + b^2

c = √(20)^2 + (99)^2

c = 101 yards.

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