Finish this sequence:
15,20,30,_,65,_,120
pls fill the blanks

Answer:

[tex] \frac{1}{24} [/tex]

Step-by-step explanation:

When you're dividing a fraction, you multiply the denominator

For example, taking this question

[tex] \frac{1}{4} \div 6[/tex]

The dominator is 4

You're dividing by 6

So multiply the denominator and what you're dividing by

[tex]4 \times 6 = 24[/tex]

Now that you have that, 24 will be the new denominator

[tex] \frac{1}{24} [/tex]

Let the width be [tex]w[/tex] inches and the length be [tex]w+15[/tex] inches.

So, the dimensions of the box are [tex]w-6[/tex], [tex]w+9[/tex], and [tex]3[/tex] inches.

[tex]3(w-6)(w+9)=1350 \\ \\ (w-6)(w+9)=450 \\ \\ w^2+3w-54=450 \\ \\ w^2+3w-504=0 \\ \\ (w+24)(w-21)=0 \\ \\ w=-24,21[/tex]

Rejecting the negative case, [tex]w=21[/tex].

So, the dimensions are 21 by 36 inches.

The value of angle ∠DEC  = 60 degree.

In the given the figure , m∠BAC = 64° and m∠CBA = 56°.

A triangle is a polygon with three sides and three vertices and three angles.

WE are given that AB || CD

Let BC be the transversal , then ∠CBA = ∠DCB (by alternate opposite angles)

∠DCB = 56 degree

As we know the sum of opposite interior angle sis equal to exterior angle therefore, ∠ ECB = 120 degree

∠DCE = 120-56 = 64 degree

BC || DE

∠EDC = ∠DCB = 56 degree (By alternate opposite angles)

The Sum of all the interior angles of a triangle is equal to 180 degree.

56 +64+∠DEC = 180

∠DEC  = 60 degree.

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Answer:

5 units^2

Step-by-step explanation:

The area of the shaded region is πr² - (2 × 13.5π).

Given is a shaded region inside a circle.

The area of each section is -

A{S} = 13.5π

We can write the area of the shaded region as -

πr² - (2 × 13.5π)

Therefore, the area of the shaded region is πr² - (2 × 13.5π).

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The value of the angle ∠I = 13

An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.

in this figure, it is an isosceles triangle as two sides of the triangle are equal.

given in the ΔGHI is an isosceles triangle.

So the other two angles will be 13

Hence The value of the angle ∠I =13°

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Answer:

15.94

Step-by-step explanation:

(2+h)² + h² =24²

4+4h+h²+ h² =24²

2+2h+h²= 576/2

h²+2h-286=0

solve h=15.94

Answer:

1/2

Step-by-step explanation:

On the clock from 3 to 9, the hour hand turns clockwise 1/2 of the revolution. On the clock from 4 to 7, the hour hand turns clockwise 1/4 of the revolution

Triangle congruence is proved by a sequence of reflections and translations.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17).

By using distance formula, distance =√(x₂-x₁)²+(y₂-y₁)²

AB = 6 units   BC = 11 units AC = 12.53 units

∆XYZ  X(-10, 5), Y(-12, -2), and Z(-4, 15)

XY = 7.14 units   YZ = 18.79 units XZ = 11.66 units

∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).

MN = 6 units   NO = 11 units MO = 12.53 units

∆JKL  J(17, -2), K(12, -2), and L(12, 7).

JK = 5 units   KL = 9 units JL = 10.30 units

∆PQR  P(12, 3), Q(12, -2), and R(3, -2)

PQ = 5 units   QR = 9 units PR = 10.30 units

So, we have the ∆ABC and the ∆MNO  

With all three sides equal are congruent  

We have the ∆JKL  and the ∆PQR

with all three sides equal are congruent  

Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or rotations).

1) If ∆MNO by a sequence of reflections and translation, it can be obtained ∆ABC, then ∆MNO ≅ ∆ABC  

a) Reflection (On x-axis)

The coordinate notation for the Reflection is (x,y)→(x,-y)

∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).

M(-9, -4)→ M1(-9,4)

N(-3, -4)→ N1(-3,4)

O(-3,-15)→ O1(-3,15)

B) Reflection (y-axis)

The coordinate notation for the Reflection is (x,y)→(-x,y)

In ∆M'N'O', M'(-9, 4), N'(-3, 4), and O'(-3, 15).

M'(-9, -4)→M"(9,4)

N'(-3, -4)→N"(3,4)

O'(-3,-15)→O"(3,15)

C) Translation

The coordinate notation for the Translation is (x,y)→(x+2,y+2)

∆M"N"O", M"(9,4), N"(3,4), and O"(3, 15).

M"(9, 4) → A(11,6)

N"(3,4)→B(5,6)

O"(3,15)→C(5,17)

So, we have ∆ABC,  A(11, 6), B(5, 6) and C(5, 17)

From ∆MNO to ∆M'N'O' reflection, from ∆M'N'O' to ∆M"N"O" reflection, and from ∆M"N"O" to ∆ABC its translation.

2)If ∆JKL, by a sequence of rotation and translation

We obtained ∆PQR

So, ∆JKL ≅ ∆PQR  

D) Rotation 90 degree anticlockwise

The coordinate notation for the Rotation is (x,y)→(-y, x)

In ∆JKL, J(17, -2), K(12, -2), and L(12, 7).

J(17, -2)→J'(2,17)

K(12, -2)→K'(2,12)

L(12,7)→L'(-7,12)

E) Translation:

The coordinate notation for the translation is (x, y)→ (x+10, y-14)

Then, ∆J'K'L' has vertices J'(2, 17), K'(2, 12), and L'(-7, 12).

J'(2, 17)→P(12,3)

K'(2, 12)→Q(12,-2)

L'(-7, 12)→R(3,-2)

So, ∆PQR has P(12, 3), Q(12, -2) and R(3, -2)

From ∆JKL to ∆J'K'L' its rotation and from ∆J'K'L' to ∆PQR its translation.

Therefore, ∆JKL ≅ ∆PQR  

Hence, triangle congruence is proved by a sequence of reflections and translations.

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The value of x in the equation x^x = 4^(x + 16) is 16

From the question, we have the following parameters that can be used in our computation:

x^x = 4^(x + 16)

Take the logarithm of both sides

So, we have

xlog(x) = (x + 16)log(4)

At this point, we make use of a graphing calculator

From the calculator, we have

x = 16

Hence, the solution is x = 16

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The probability that a randomly selected password has no digits is 10.24%.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that, a seven-character database password is formed from 10 digits and 26 upper-case letters.

Number of characters in passwords: 7

The possible number of ways to formed the first value of passwords is sum of 26 (upper letters) and 10 (0 to 9 numbers).

The required number of possible passwords is 36⁷

= 78364164096

Favorable out comes is 26⁷

= 8031810176

Now, probability of an event = 8031810176/78364164096

= 0.1024

= 10.24%

Therefore, the probability that a randomly selected password has no digits is 10.24%.

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The composite function c(x) = 0.8x - 3, and the cost of a $30 item would be $21.

When the output of one function is given to the input of another function they are called composite functions.

In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Let, 'x' be the original cost of the item.

A store offers a 20% discount on all items,

So, f(x) = [(100 - 20)/100]×x.

f(x) = (80/100)×x.

f(x) = 0.8x.

Again, you also have a $3 coupon.

Let, g(x) = x - 3.

Now, The composition of the functions f(x) and g(x) is f(x) + g(x) = C(x).

C(x) = 0.8x - 3.

Now, The cost of an item is $30.

Therefore, C(30) = 0.8×30 - 3.

C(30) = 24 - 3.

C(30) = 21.

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Answer:

Independent variable: The variable that is changed or manipulated in an experiment to observe its effect on the dependent variable. Example: The number of hours of studying (Independent variable) and the test score (Dependent variable)

Dependent variable: The variable that is being measured or observed in an experiment. Its value is dependent on the independent variable. Example: The temperature of water (Independent variable) and the volume of the water (Dependent variable)

Answer:

y=5x

Here y is dependent variable because it's depend on x but x is not depend on any other variable. So, it's independent variable.

Answer:

The equation of a circle can be represented in the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.

A diameter of a circle is a straight line passing through the center of the circle and has endpoints on the circle.

Given that the equation of the diameter of a circle is x+y-14=0 and 2x-y-4=0, we can find the center of the circle by solving for the intersection of these two lines.

We can find the intersection point of these lines by solving the system of equations using the substitution method:

x+y-14=0 and 2x-y-4=0

x = 14/3, y = 10/3

So the center of the circle is (14/3, 10/3)

Since we know that the point (3,4) lies on the circle, we can use the distance formula to find the radius of the circle.

r = sqrt((x-h)^2 + (y-k)^2)

r = sqrt((3-(14/3))^2 + (4-(10/3))^2) = sqrt(5)

Therefore, the equation of the circle is (x-14/3)^2 + (y-10/3)^2 = 5^2

or (x-14/3)^2 + (y-10/3)^2 = 25

So, the equation of the circle passing through point (3,4) and having equation of its diameter x+y-14=0 and 2x-y-4=0 is (x-14/3)^2 + (y-10/3)^2 = 25

The panel of the window is 3.15 ft width.

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.

Given that, Rachel's bedroom window is rectangular with an area of 81.9 square feet, and the panel is 26 feet long

We need to find the width of the window,

Let the width be w

Area of a rectangle = width × length

81.9 = w × 26

w = 81.9 / 26

w = 3.15

Hence, the panel of the window is 3.15 ft width.

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a) for initial value 4 function oscillate between 4 and -2

b) for a initial value of 2 function oscillate between 2 and 0

c) for a initial value of 1 function value is constant = 1

A function is a relationship between a set of inputs that each have one output. A function, in simple terms, is a relationship between inputs, with each input corresponding to exactly one output. Each function has a domain as well as a co-domain or range. The general notation for a function is f(x), where x is the input. A function is generally represented as y = f. (x).

In math, there are various types of functions. Among the most important types are:

f(x) = 1/2.x + 1

f(4) = 1/2*4+1=3

f(4) = 1/2*3+1=2.5

f(4) = 1/2*2.5+1=2.25

f(4) = 1/2*2.25 + 1 = 2.125

f(4) = 1/2*2.125+1 = 2.0625

f(4) = 1/2*2.0625 + 1 = 2.0123

As the iteration increases function value converges to 2

You can write a simple MATLAB program to check it

matlab code:

clc;

clear all;

close all;

syms x;

f=-x+2;

y(1)=4;

g(1)=2;

h(1)=1;

for n=1:20

   y(n+1)=subs(f,x,y(n));

   g(n+1)=subs(f,x,g(n));

   h(n+1)=subs(f,x,h(n));

end

t=[y',g',h'];

output :

t =

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

   -2     0     1

    4     2     1

a) for initial value 4 function oscillate between 4 and -2

b) for a initial value of 2 function oscillate between 2 and 0

c) for a initial value of 1 function value is constant = 1

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The surface area of the composite bin can be found using the expression  6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]

Please find attached the drawing of the net of the composite bin, created with MS Word

The surface area of a composite figure can be found finding the sum of the individual exposed surface area of the composite figure.

Please find attached the possible drawing of the diagram in the question, created with MS Word

The possible complete expression in the question, obtained from a similar, online question, is presented as follows;

6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]

The surface area of the figure consists as follows;

Two trapezoidal faces (in front and on the rear

Four rectangular faces, orthogonal to the trapezoidal faces

Please find attached the net of the composite bin created with MS Word

The area of the trapezoidal faces = (3 + 6)×4/2 = ((1/2)·(3·4) + ((1/2)·(6·4))

((1/2)·(3·4) + ((1/2)·(6·4)) = ((1/2)·(3·4) + (3·4)

((1/2)·(3·4) + ((3·4)) = 3·4 + (1/2)·(3·4)

Therefore, the area of the two trapezoidal faces = 2 × (3·4 + (1/2)·(3·4))

The area of the four rectangular faces are;

Face              [tex]{}[/tex]                  Area

Orthogonal rear face = 6 × 5

Orthogonal front face = 3 × 5

Face at the bottom of the figure = 4 × 5

The slant face at the top = 5 × 5

The area is therefore;

The surface area of the composite bin, A, is therefore;

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Answer:

Step-by-step explanation:

Slope intercept form is

[tex]y=mx+b[/tex]

Start with your equation and move y terms to one side and all other terms to the other side:

[tex]1-x-2y=-6[/tex]

[tex]1-x+6=2y[/tex]

Combine numbers:

[tex]7-x=2y[/tex]

Divide both sides by 2

[tex]\frac{7}{2} - \frac{x}{2} =y[/tex]

Write y on the left hand side and put the rest of the equation in standard slope intercept form:

[tex]y=-\frac{1}{2}x+\frac{7}{2}[/tex]

This is slope intercept form with m = -1/2 and b =7/2

Bashir earns $235.6 in 15.5 hours.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope= 501.60-349.60/33-23

=152/10

=15.2

Now let us find the y intercept

228=15.2(15)+b

228=228+b

b=0

Now let us find how much he earns in 15.5 hours.

y=15.2(15.5)

y=235.6

Hence, Bashir earns $235.6 in 15.5 hours.

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Answer:

10 4/6 = 10 2/3

Step-by-step explanation:

dude this is easy and not for college but thanks anyway

The fraction which is closest to 1/2 is, 3/8. So option B is correct

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

A fraction number 1/2

In decimal form = 0.5

Closest fraction number = ?

Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,

Lets take, A fraction 1/6

In decimal form it can written as,  0.167

Difference 1 =  0.5 - 0.167

                  =   0.333

Similarly, For numbers 3/8, 3/4, -1/2

Difference 2 =  0.5 - 0.375  = 0.125

Difference 3 =  0.5 - 0.75  = -0.25

Difference 4 =  0.5 - (-0.5)  =  1.0

It can be seen that,

Magnitude of difference in case of 3/8 is very less

Hence, the closest number is 3/8

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Answer:

The ratio for 63 inches to 4 yards is 1:16. To calculate this, divide 63 inches by 4 yards, which is equal to 48 inches per yard. Therefore, the ratio for 63 inches to 4 yards is 1:16.

Answer: 31

Step-by-step explanation:

You need to find the perimeter of something, you just add the numbers of the sides.

6 + 9 = 15

15 + 5 = 20

20 + 3 = 23

23 + 5 = 28

28 + 3 = 31

Perimeter = 31 in.

A perimeter of any shape is just the total length of all its sides. In other words, is the distance around the edge of the shape.

Perimeter = 5 in + 3 in + 5 in + 9 in + 6 in + 3 in = 31 in.

Perimeter = 31 in.

Answer:

84

Step-by-step explanation:

Number of skiers = Number of athletes * Fraction of skiers
= 240 * 7/20
= 84 skiers

Answer:

84

Step-by-step explanation:

240/20=12

12*7=84

The given  expression √(a³-7)+ | b |, when a = 2 and b = -4, the value of the expression is, 5

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

√(a³-7) + | b |

where, a = 2

b = -4

Now, by putting values of a and b in the given equation,

⇒ √(a³-7) + | b |

⇒ √(2³-7) + | -4 |

For whatever value of x, |x| will give always positive value

So, now it can be further written as,

⇒   1  + 4

⇒   5

Hence, the value is 5

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Answer:

D. x < 1

is correct answer

Answer:

40 dollars per hour