Tyler's playlist has 36 songs. Noah’s playlist has one quarter as many songs as Tyler's playlist. How many songs are on Noah’s playlist?

The number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.

In this question,

Positive integers are 0,1,2,3,4,5,6,7,8,9

Total number of integers = 10

This can be solved by permutation concepts.

Case 1: 4-digit positive integers with no repeated digits,

First digit, cannot be zero. So remaining 9 digits.

Second digit, can be any digit other than the first digit. So 9 digits.

Third digit, can be any digits other than first and second. So 8 digits.

Fourth digit, can be any digits other than first, second, third digit. So 7 digits.

Thus, Number of ways of 4-digit positive integers with no repeated digits ⇒ (9)(9)(8)(7)

⇒ 4536 ways.

Case 2:  4-digit positive integers, there may be repeated digits, but all digits are odd

Odd integers are 1,3,5,7,9

Number of digits = 5

In this case, we can repeat the digits. So all places can have 5 possibilities.

Thus number of ways of 4-digit positive integers with repeated digits, but all digits are odd = (5)(5)(5)(5)

⇒ 625 ways.

Hence we can conclude that the number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.

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The expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.

In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.

The side of the square is given to be x feet.

We are asked to write expressions for the length and width of the rectangular garden.

For the length of the rectangle:-

We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.

Thus, the length of the garden can be shown as the expression 3x + 2 feet.

For the width of the rectangle:-

We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Thus, the width of the garden can be shown as the expression x + 5 feet.

Thus, the expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

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The provided question is incomplete. The complete question is:

"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.

Enter the correct answer in the box."

The area of the rectangle is 108 square centimeters.

Given Information

The following information has been given in the question,

Length of the diagonal of the rectangle, l = 15 cm

Length of one of the sides of the rectangle, a = 9 cm

Let the other side of the rectangle be b.

Finding the Other Side of the Rectangle

According to Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,

l² = a² + b²  [∵ The diagonal makes the hypotenuse]

(15)² = (9)² + b²

b² = (15)² - (9)²

b² = 225 - 81

b² = 144

b = √144

b = 12 cm

Calculating the Area of the Rectangle

Area of the rectangle, A = a × b

A = 9 × 12

A = 108 cm²

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Answer: Option 4

Step-by-step explanation:

[tex]m\angle 20=62^{\circ}[/tex] (linear pair)

[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)

[tex]m\angle 12=110^{\circ}[/tex] (linear pair)

The equivalent value of the given expression is -21.4

Decimals are values that include decimal points. Given the expression below

-8.2 - 5−8.2

Collect like terms

-8.2 −8.2 - 5

Convert to fractions

-82/10- 82/10 -  5

-164/10 - 5

-16.4 - 5

Take the sum

-21.4

Hence the equivalent value of the given expression is -21.4

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The probability that each guest of each type m+n will receive a roll is 79.

Given that the breakfast should have consisted of three types of rolls, one each of the nut, cheese and fruit rolls, and the cook should have wrapped each of the nine rolls.

The denominator of m/n equals the total number of possible role configurations assigned to the three people. It [tex]${9 \choose 3}{6 \choose3}$[/tex] is the same as the number of ways to choose three roles out of 9 to give to the first person [tex]${9 \choose 3}$[/tex], and three rolls of 6 [tex]${6 \choose3}$[/tex]. After that, the remaining three roles have no more configurations.

The numerator is the number of ways to assign a roll of each type to each of the three people, which can be done by defining the three types of roles such as flavored x, flavored y and flavored z.

xxx, yyy, zzz

So we have to choose one x, one y and one z to give to the first person. There are 3x, 3y and 3z to choose from, resulting in 3³ combinations. Multiply that by the combinations of xs, ys and zs for the second person, which is clearly 2³ since there are two of each letter left. simplify to our fraction m / n, which is 9/70. If you add them together, you get 9 + 70 = 79.

Thus, the probability that each guest has obtained a roll of each type is m / n, where m and n are relatively prime, so m + n is 79.

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Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at  B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C  which is at D(1, 5).

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

Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at  B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C  which is at D(1, 5).

The location of point A, B, C and D is located on the graph.

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Answer:

Step-by-step explanation:

hello :

P(E and F)=0.7×0.6 =0.42

There are 2 people are stepping onto the roller coaster per minute at peak time

According to statement

Given Flow time = 10 minutes.

Given Inventory = 20.

We use the formula then

I = R × T,

Therefore R = I / T.

Substitute the values in formula then

Flow rate = 20 / 10 = 2 people per minute.

So, There are 2 people are stepping onto the roller coaster per minute at peak time

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The circle E, circle F and circle G are the circles which are congruent (similar) to the circle A has a radius of 6.

Let us discuss about the structure of each circles.

The circle D has the secant with the length 12. The secant means the straight line joining two points on the circle. So, we can't conclude that the secant will always be the diameter. Hence, it has different shape compared to circle A.

The circle E has the radius with length 6. The radius is same as the radius of the circle A. So, it is similar to the circle A.

The circle D has the secant with the length 6. Similar to the condition of circle D, it is not congruent to circle A.

The circle F has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.

The circle G has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.

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Answer:

Circles E and F are congruent to circle A

The true statement about the plane include:

It should be noted that a vertical plane simply passes through a vertical line.

In this case, Point H is not on plane R and the e line containing points F and G is on plane R.

The correct options are 1,2,4, and 5.

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Answer:

a,b,d,e

Step-by-step explanation:

The number of observation given in the following data set 14. This is also called the size of the population.

It is important to note that the above data possess the minimum value of 12 and the maximum value of 25. As indicated in the attached image, the data set is normally distributed.

The measures of central tendency are given as follows;

Q1 --> 15

Q2 --> 18.5

Q3 --> 22
IQR  = 7

Mean Absolute Deviation (MAD) = 3.5

Min = 12

Max = 25.

It is to be noted that the above indictors are called Descriptive Statistics.

The features of a sample or data set, such as a variable's mean, standard deviation, or frequency, are described or referred to as descriptive statistics.

We can better grasp a data sample's constituent parts by using inferential statistics.

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The coefficients for the polynomial with degree 3, roots: x = 2, x =

-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.

It is given that the polynomial is of degree 3 and its roots are,

x = 2

x = -1

x = 3

Thus, the factors of the polynomial would be,

(x - 2), (x + 1), and (x - 3)

The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,

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

= (x² -2x + x -2)(x - 3)

= (x² -x -2)(x - 3)

= x³ - 3x² - x² + 3x - 2x + 6

= x³ - 4x² + x + 6

= x³ + (-4)x² + x + 6

Hence, the required coefficients of the polynomial are, (-4) and 6.

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The perimeter of a rectangle is the sum of its side lengths.

A rectangle is special in that sides opposite one another have equal length. So if [tex]x[/tex] is the length of the horizontal sides, the total perimeter of the rectangle is

[tex]4\,\mathrm{cm} + 4\,\mathrm{cm} + x\,\mathrm{cm} + x\,\mathrm{cm} = (8+2x)\,\mathrm{cm}[/tex]

We're given the perimeter is actually 18 cm, so

[tex]8+2x = 18[/tex]

Solve for [tex]x[/tex].

[tex](8 + 2x) - 8 = 18 - 8[/tex]

[tex]2x = 10[/tex]

[tex]\dfrac12 \cdot 2x = \dfrac12 \cdot 10[/tex]

[tex]\boxed{x = 5}[/tex]

Answer:

16

Step-by-step explanation:

You replace m with 14. 2 + 14 = 16.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Assuming equation:}[/tex]

[tex]\mathsf{\dfrac{m}{2} + m}[/tex]

[tex]\huge\textsf{If so, let's solve for your equation:}[/tex]

[tex]\mathsf{\dfrac{m}{2} + m}[/tex]

[tex]\mathsf{= \dfrac{14}{2} + 14}[/tex]

[tex]\mathsf{= 7 + 14}[/tex]

[tex]\mathsf{= 21}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{21}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

6

Step-by-step explanation:

The arc length is (2)(pi)(27)(40/360)=6pi.

So, k=6.

Answer:

28.5 ft²

Step-by-step explanation:

shaded area = area of triangle minus area of rectangle

shaded area = (1/2)bh - LW

base of triangle = 5 ft + 4 ft = 9 ft

height of triangle = 3 ft + 6 ft = 9 ft

shaded area = (1/2)(9 ft)(9 ft) - (4 ft)(3 ft)

shaded area = 40.5 ft² - 12 ft²

shaded area = 28.5 ft²

Here, given

sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)

Let, 3 = x1 & 7= y1   , 3= x2  & 7= y2   , 7= x3  & 3= y3   ,  7=  x4  & 7= y4

[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}

[tex]\frac{1}{2}[/tex] (32)

16cm^2

Hence, the area of the polygon is 16cm2.

The formula for calculating the area of ​​a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].

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Applying exponential properties, the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

The function is represented by the following definition:

[tex]f(x) = 2\sqrt[3]{27^{2x}}[/tex]

As an exponent, the function is given by:

[tex]f(x) = 2(27)^{\frac{2x}{3}}[/tex]

27 can be simplified as follows:

27 = 3 x 3 x 3 = 3³

Hence:

[tex]f(x) = 2(3^3)^{\frac{2x}{3}}[/tex]

Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:

[tex]f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}[/tex]

Hence the simplified base for the function is given as follows:

[tex]f(x) = 2(3)^{2x}[/tex]

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The number of blue balls that are needed to balance four green, two yellow and two white balls is 16 blue balls.

Green(g)

Blue (b)

Yellow (y)

White (w)

First step is to formula an equation

3g=6b

g=2b

2y=5b

y=5/2b

4w=6b

w=3/2b

Second step is to substitute

4g+2y+2w

=4(2b)+2(5/2b)+2(3/2b)

=8b+5b+3b

=16b

Therefore 16 blue balls are needed.

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Step-by-step explanation:

12 = 2 × 2 × 3

18 = 2 × 3 × 3

56 = 2 ×2 × 2 × 7

Now

Common factor = 2

Remaining factor = 2 × 3 × 2 × 3 × 7

LCM = RF × CF

= 504

hence the lCM of 12 , 18 and 56 is 504...

[tex]...[/tex]

VARIABLE is a symbol which is used for representation in a  math.

According to the statement

we have to explain about the what is a variable.

So, VARIABLE is a symbol which is used for representation in a  math.

It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.

A variable may also be called a data item.

It is used to represent a data like country name, name, age, date of birth etc.

we know that the every thing is changeable. So, like ther things variables are also changeable.

The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.

So, VARIABLE is a symbol which is used for representation in a  math.

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The tax due for the single taxpayer whose income is as described is; $14,459.5.

It follows from the task content that the tax due for a single taxpayer whose taxable income is; $65,725 is to be determined.

Since, the taxable income falls between the range; $40,526 to $86,375, 22% of the income is the tax due and hence, the tax due can be evaluated as follows;

= (22/100) × $65,725

= 14,459.5

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Part A - Tara cuts [tex]12[/tex] pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] feet of rope.

Part B - The quotient means the amount of foot pieces so it is [tex]12[/tex] foot pieces.

How can we find the foot pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex]  rope. ?

from part A

we solve the fraction

[tex]4\frac{4}{5} =24/5[/tex] rope

And Tara needs to pieces of [tex]2/5[/tex] foot

So we need to divide

[tex]\frac{24/5}{2/5} \\=\frac{24}{5} *\frac{5}{2} \\=\frac{24}{2} \\=12[/tex]

For part B

When we using the information from part A we decide that the quotient means the amount of foot pieces Tara can cut from the [tex]4\frac{4}{5}[/tex] feet of rope.

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Answer:

Question 6) Neither (Not an inverse variation)

Question 7) Inverse variation

Question 8) Inverse variation

Step-by-step explanation:

These are the two formulas we need to know prior to solving the question.

Direct variation: c times x

Inverse variation: c times 1/x --> c/x

- Here, c is the constant

6. y = x + 7

This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.

7. 14 = xy

This equation is an inverse variation.

xy = 14

y = 14/x

14 is the constant, and the format is the same as for an inverse variation.

8. x = -8/y

This equation is an inverse variation.

yx = -8

y = -8/x

-8 is the constant, and the format is the same as for an inverse variation.

So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.

General forms

Direct

Inverse

so

#6

Not inverse and direct also as 7 is present

#7

Yes

#8

Yes

The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

A triangle with two sides and angles of equal length and degrees is an isosceles triangle.

Acute Triangle:-

A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.

Therefore, all the three angles are less than 90 degrees and two angles are equal.

If one angle is 36 degrees, the other two angles will be 72 degrees each.

If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..

Therefore, the angles will be 36°, 36° and 72°.

Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

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Answer:

[tex]\sf Equation: \quad \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

The number is 2.

Step-by-step explanation:

The reciprocal of a number is simply 1 divided by the number.

The reciprocal of a fraction is where the numerator and denominator are swapped (so the fraction is turned upside down).

Let x be the positive number.

The reciprocal of the positive number x:

[tex]\sf \implies \dfrac{1}{x}[/tex]

The reciprocal of 3 more than the number x:

[tex]\sf \implies \dfrac{1}{x+3}[/tex]

The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is 7/10:

[tex]\implies \sf \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

To solve, make the denominators of the two fractions on the left side the same by multiplying them.

Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.

Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.

[tex]\implies \sf \dfrac{1(x+3)}{x(x+3)}+\dfrac{1(x)}{(x+3)(x)}=\dfrac{7}{10}[/tex]

[tex]\implies \sf \dfrac{x+3}{x(x+3)}+\dfrac{x}{x(x+3)}=\dfrac{7}{10}[/tex]

Add the numerators and keep the denominator so that there is now one fraction:

[tex]\implies \sf \dfrac{2x+3}{x(x+3)}=\dfrac{7}{10}[/tex]

Cross multiply:

[tex]\implies \sf 10(2x+3)=7x(x+3)[/tex]

Expand:

[tex]\implies \sf 20x+30=7x^2+21x[/tex]

Rearrange so the equation is equal to zero:

[tex]\implies \sf 7x^2+x-30=0[/tex]

Split the middle term:

[tex]\implies \sf 7x^2+15x-14x-30=0[/tex]

Factor the first two terms and last two terms separately:

[tex]\implies \sf x(7x+15)-2(7x+15)=0[/tex]

Factor out the common term (7x + 15):

[tex]\implies \sf (x-2)(7x+15)=0[/tex]

Apply the zero product property:

[tex]\sf (x-2)=0 \implies x=2[/tex]

[tex]\sf (7x+15)=0 \implies x=-\dfrac{15}{7}[/tex]

As x is a positive number, x = 2.

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Answer:

Option A.

Step-by-step explanation:

Demonstration

[tex]y=\frac{7}{4} x+7[/tex]

for x = -4

[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]

for x= 0

[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]

for x= 4

[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]

Hope this helps

Answer: S=6√6 m².

Step-by-step explanation:

                                   Heron's formula

                            [tex]\displaystyle\\\boxed {S=\sqrt{p*(p-a)(p-b)(p-c)} }[/tex],

a, b, c - sides of a triangle,

[tex]\displaystyle\\p=\frac{a+b+c}{2}[/tex]

S - triangle area.

a=7 m,  b=5 m,  c=6 m.

[tex]p=\frac{7+5+6}{2} \\p=\frac{18}{2} \\p=9 (m).[/tex]

Hence,

[tex]S=\sqrt{9*(9-7)*(9-5)*(9-6)}\\S=3*\sqrt{2*4*3}\\S=3*2*\sqrt{2*3} \\S=6\sqrt{6} \ (m^2).[/tex]

Answer:

200

Step-by-step explanation:

Let's call the number x :
12.5% of x = 25

Changing 12.5% into decimal would be 0.125

Now we have the equation :

0.125x = 25

Divide both sides by 0.125 to make x the subject :

x = 25 ÷ 0.125

x = 200

To check we can substitute this value into the question :

12.5% of 200 = 25

Hope this helped and have a good day