find the smallest 4 digit number which is exactly divisible by 72 and 108
with explaination​

Answer:

C. -2

Step-by-step explanation:

Use A-P-E-X

How I solved it:

3/4(1/5÷3/5)(-8)

3/4(1/5×5/3)(-8)

3/4(1/3)(-8)

1/4(-8)=-2

Hope this helps!

If not, I am sorry.

Let x be a multiple of 7

Three consecutive multiples of 7 are

[tex] \\ \large\blue\longrightarrow\rm \large \:x \: + \: (x \: + \: 7) + (x \: + \: 14) \: = \: 693[/tex]

[tex] \large\blue\longrightarrow \rm \large \:3x \: + \: 21 \: = \: 693[/tex]

[tex] \large\blue\longrightarrow \rm \large \:3x \: = \: 693 \: - \: 21[/tex]

[tex] \large\blue\longrightarrow \rm \large \:3x \: = \: 672[/tex]

Dividing both sides by 3 , we have

[tex]\large\blue\longrightarrow \rm \large \: \frac{3x}{3} \: = \: \frac{672}{3} \\ [/tex]

[tex]\large\blue\longrightarrow \rm \large \: \ \: \frac{ \cancel3x}{ \cancel3} \: = \: \frac{ \cancel{672} \: \: ^{ \red{224}} }{ \cancel3} \\ [/tex]

[tex]\large\blue\longrightarrow \rm \large \:x \: = \: 224 \\[/tex]

Three consecutive multiples of 7 are

Answer:

I think A or C.

Step-by-step explanation:

Answer:

24 is the answer for the following

Step-by-step explanation:

please mark me as brainlest

A two-way conditional frequency table for this gender is shown in table A.

A frequency table can be defined as a type of table which is typically used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.

In this scenario, a two-way conditional frequency table for this gender would be constructed as follows:

Gender    Sedan    Sport     Total

Male         0.35        0.65         1

Female     0.75        0.25         1

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Answer:

7 ^ 6x + 2 = 7^15

taking log on both the sides

log 7^6x + 2 = log 7^15

6x + 2 log 7 = 15 log 7

log 7

The expansion of the polynomial is given as:

[tex](5x^3+\frac{14}{3x^4})=15625x^{18}+87500x^{11} +\frac{612500}{3}x^3+\frac{6860000}{27x^3}+\frac{4802000}{27x^{10}}+\frac{5378280}{81x^{17}}+\frac{7529536}{729x^{24}}[/tex]

An equation is an expression that shows the relationship between two or more numbers and variables.

The expansion is given as:

[tex](5x^3+\frac{14}{3x^4})=15625x^{18}+87500x^{11} +\frac{612500}{3}x^3+\frac{6860000}{27x^3}+\frac{4802000}{27x^{10}}+\frac{5378280}{81x^{17}}+\frac{7529536}{729x^{24}}[/tex]

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Answer:

A

Step-by-step explanation:

a = 3n-30       solve for 'n'

a + 30 = 3n

n = (a+30)/3

n(a) = (a+30)/3

The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The mosaic to be formed is rectangular in shape.

Area of a rectangle = length x width

The length is longer than the width by 2,

So, length = w+2

Area of a rectangle = (w+2) x w

The correct equation is B: w(w + 2) = 48

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Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{q+p}{2(p-q)}[/tex]

Step-by-step explanation:

[tex]\frac{4(p+q)}{p-q} *\frac{q+p}{8(p+q)}[/tex]

We will cancel out like terms.

[tex]\frac{4}{p-q} *\frac{q+p}{8}\\=\frac{4(q+p)}{8(p-q)} \\=\frac{q+p}{2(p-q)}[/tex]

Answer:

w = 3 or 6

Step-by-step explanation:

[tex]w {}^{2} - 9w + 18 = 0 \\ w {}^{2} - 6w - 3w + 18 = 0 \\w(w - 6) - 3(w - 6) = 0 \\ w - 3 = 0 \\ w - 6 = 0 \\ w = 3 \: or \: 6[/tex]

Answer:

Maybe the question could've been 2+2+1. I'd say read the question properly.

Step-by-step explanation:

In which case, 2+2+1= 5

Answer:

206°

Step-by-step explanation:

The bearing of y from w is the angle y makes with w moving from the north pole in clockwise direction.

So from the north pole, move in clockwise direction and stop at the line joining w and y

the angles there are 90+116= 206°

Therefore the bearing of Y from W is 206°

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

Work Shown:

x = price before the discount

30% of x = 0.30x = amount saved

x - 0.30x = 0.70x = price after discount = 1659

0.70x = 1659

x = 1659/(0.70)

x = 2370

First we'll have to convert the percent into decimal.

We'll have to divide the value by 100.

[tex]\frac{30}{100}[/tex]

[tex]\bold{=0.30}[/tex]

Now, we can find the original price.

[tex]\large\boxed{\bold{Formula:OP= \frac{price}{1-Discount}}}[/tex]

We have all the necessary values to find the original price.

Let's solve!

Substitute the values according to the formula.

[tex]OP=\frac{1659}{1-0.30}[/tex]

OP= $2370

Therefore, the original price of the television set is $2370

Answer:

34 and ⅔

Step-by-step explanation:

added in the picture

The value of the expression for the given values is 1294139

From the question, we are to rewrite the expression

(11j⁻³k²) (j³k⁴)

This can be rewritten as

11 × j⁻³ × k² × j³ × k⁴

11 × j⁻³ × j³ × k² × k⁴

11 × j⁻³⁺³ × k²⁺⁴

11 × j⁰× k⁶

= 11 × 1 × k⁶

= 11k⁶

Now we are to evaluate the expression for when j = -8 and k  = 7

The expression is

= 11 × k⁶

= 11 × 7⁶

= 1294139

Hence, the value of the expression for the given values is 1294139

Here is the complete question:

Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to

complete the statement.

(11j⁻³k²) (j³k⁴)

When j = -8 and k = 7

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Answer:

539

Step-by-step explanation:

Answer:

Carpet costs = 300£

Step-by-step explanation:

• First calculate the area of the floor:

Area of floor = length x width

                     = 5m² x 3m²

                     = 15m²

• As one m² of carpet costs £20, 15m² of carpet costs:

15 x 20

= 300£

Answer:

x+(x+1)+(x+2)=42

3x+3=42

3x=42-3

3x/3=39/3

x=13

Step-by-step explanation:

hope I helped

Answer:

Option C is correct

Correlation coefficient of the following data is 0.37

Step-by-step explanation:

Correlation coefficient formula :

r = Σ [([tex]x - x_{m}[/tex]) × ([tex]y - y_{m}[/tex])] ÷ √ [Σ [tex](x - x_{m})^{2}[/tex] × Σ [tex](y - y_{m}) ^{2}[/tex]]

x =  Data points in Data set x

y =  Data points in Data set y

[tex]x_{m}[/tex]= Mean of Data set x

[tex]y_{m}[/tex]= Mean of Data set y

Now put all the values and sumation it as of given in the formula

Mean of Data set x = (1+4+8+6+2)÷5 = 21÷5 = 4.2

Mean of Data set y = (16+20+15+22+9)÷5 = 82÷5 = 16.4

Now put the values in the equation

r = Σ [(x - 4.2) × (y - 16.4)] ÷ √ [Σ [tex](x - 4.2)^{2}[/tex] × Σ [tex](y - 16.4) ^{2}[/tex]]

Now put every single value of x and y and after we will get the required Correlation coefficient.

And that is Correlation coefficient of the following data is 0.37

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Considering the area of a rectangle, the equation that could be used to determine the width for which the costs are the same is:

125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)

The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:

A = lw

In this problem, the dimensions are given as follows:

w = x, l = x + 5.

Hence the area in square feet is:

A = x(x + 5) = x² + 5x.

Then the costs are given as follows:

The costs will be equal when:

A(x) = B(x)

125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Answer:

B

Step-by-step explanation:

Answer: By adding 2 to y and subtracting x by 3.

Step-by-step explanation: Let’s use the equation y = x since it’s simple. In order to translate an equation anywhere to the right, you have to subtract x by a unit. Since it’s 3 units, the equation is now y = x - 3. To translate an equation down, you have to add a unit to y. Since the questions asks for two units, add 2 to y. The equation should now be y + 2 = x - 3.

If (x + q) is factor of two polynomial [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex] than [tex]a = \frac{n - q}{m- p}[/tex].

x + a is factor of equations  [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex]

Polynomial equation is equation of independent variables.

Putting it in both the equations

[tex]x^2+px+q=0[/tex]                          
[tex](-a)^2+p(-a)+q=0\\a^2-ap+q=0 ........(1)[/tex]  

[tex]x^2+mx=n = 0\\(-a)^2+m(-a)+n=0\\a^2-am+n=0 .....(2)[/tex]

subtracting (2) from (1)

[tex]-am+ap+n-q=0[/tex]
[tex]a=\frac{n-q}{m-p}[/tex]

Thus, the required expression is [tex]a=\frac{n-q}{m-p}[/tex].

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Answer:

7pi/6

Step-by-step explanation:

Using the formula for arc length in radians, we get:

Answer:

x = 70 and the labeled angles are 110 and 70

Step-by-step explanation:

This is a trapezoid, the bases are parallel.

Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:

x + 40 + x = 180 add like terms

2x + 40 = 180 subtract 40 from both sides

2x = 140 divide both sides by 2

x = 70 and the labeled angles are 110 and 70

Yes, the line r is parallel to the line s and the line p is parallel to the line q.

Here the given lines are p, q, r, s.

Line p and q are parallel to each other.

and the line p is parallel to the line q.

Therefore, Yes, the line r is parallel to the line s and the line p is parallel to the line q.

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The table is a function and the relation f(x) = 5x + 14 has a greater value when x = 9

The table of values is given as:

Input (x) 2 5 9 12

Output (y) 20 15 12 8

In the above table of values, each x value have a unique y value.

This means that the table is a one-to-one relation

A one-to-one relation is a function

Hence, the table is a function.

The function is given as:

f(x) = 5x + 14

This gives

f(9) = 5 * 9 + 14

Evaluate

f(9) = 59

From the table, we have:

y = 12 when x = 9

Hence, the relation f(x) = 5x + 14 has a greater value when x = 9

We have

f(x) = 5x + 14

This gives

5x + 14 = 64

Subtract 14 from both sides

5x = 50

Divide by 5

x = 10

Hence, the value of x when f(x) = 64 is 10

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Using the normal distribution, it is found that the probability that the sample mean is above 80 is of 0.1056 = 10.56%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 75, \sigma = 24, n = 36, s = \frac{24}{\sqrt{36}} = 4[/tex].

The probability that the sample mean is above 80 is one subtracted by the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{80 - 75}{4}[/tex]

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

1 - 0.8944 = 0.1056.

0.1056 = 10.56% probability that the sample mean is greater than 80.

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