a)the perimeter of a rectangle is 56 m and it's length is 18cm find its breadth​

Answer: 72

Step-by-step explanation

Let's just look at the denominators for this problem.

8 and 18

8 can go into 24, 3 times but 18 does not multiply into 24

18 can go into 36, 2 times but 8 does not multiply into 36

Therefore 72 is the least common denominator.

8 times 9 = 72

18 times 4 = 72

72 is the least common denominator.

An expression which describe the given sequence is, an = -2 + n.

Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.

an = -2 + n is an expression which describe the given sequence

The general rule for the arithmetic sequence is given by,

 an = a + (n - 1)d  ......[1]

where, denotes the initial word.

the common difference

there are n terms;

The given order is -1, 0, 1, 2,.....

This is a frequent difference arithmetic sequence.

Since,0-(-1) = 1

1-0 =1

2-1 = 1 ....

Here, a1 = -1

When you replace [1] with the value of d = 1, you get, a1 = -1

an = -1 + (n -1)(1)

an = -2 + n

Consequently, the following expression describes the given sequence: an = -2+n.

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1405 in base 7 = 544 in base 10

What is base-7 number system ?

The heptimal system is another name for base-7 numbers. Base 7 numbers are represented by the digits 0, 1, 2, 3, 4, 5, and 6.

The digits of a Base 10 number, on the other hand, are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If there isn't a subscript at the supplied number, Base 10 is used to write that number. The decimal system is sometimes known as base-10 numbers. Currently, in daily life, we frequently use numbers in the base 10 range.

base 7 to  base 10 conversion:

Multiply each digits by the powers of 7 as follows:

Base 7 digits:   1         4        0         5

Multiply by:      7^3      7²      7^1      7^0

  ( 1*7^3) + (4*7² ) + (0* 7^1 )+ ( 5 *   7^0)

= 343 + 196 + 0 + 5

= 544

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As per the binomial distribution, the value of the normal approximation is 0.6573

The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

Here we have given that n = 95 P = 0.96 and q = 0.04

Now, here we have to check  the binomial distribution to see whether it can be approximated by the normal distribution.

While we looking into the given question we know that the value of n = 95 P = 0.96.

Then as per the binomial distribution formula, the normal distribution is calculated as,

=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴

When we simplify this one then we get the value as 0.6573

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The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius

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

Area of a circle

The formula for the area of a circle is represented as

A = πr²

Express the formula as a product

So, we have the following representation

A = π * r²

In the above formula, we can see that the square of r is multiplied by pi

Hence, the required quantity is the square of the radius of the circle

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Answer:

(3,0)

have a nice day.(I needed 20 charecters so yeah i needed to say this)

Answer:

(3,0)

Step-by-step explanation:

The first number in the ordered pair tells us how far we are from the orgina (0,0) (the middle of the graph).  We are 3 units to the right.  The second number in the ordered pair tells us how far up or down from (0,0) we are.  You do not go up for down so that number should be zero.

Answer:

42

Step-by-step explanation:

If 2/7 left that means that 5/7 are still there.

5/7x = 30  Multiple both sides by 7/5

x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]

x = 42

The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.

Probability

A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.

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Answer:

1) -10x + 5

2) 5p - 26

3) -5y + 6

The amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.

The data for the given question-

Thus, the total cost becomes-

Total cost = 2 x reclining chairs + coffee table + shipping cost

Total cost = 2 x 230 + 350 + 100

Total cost = $910

For the amount of each payment when there are 5 equal payments.

Total cost = 910/5

Total cost = $182

Thus, the amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.

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The angle A is an obtuse angle of the regular polygon.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The interior angle of a polygon is [(n-2)180°]/n.

Where n is the number of sides of the polygon.

The number of sides of the polygon is 8.

The measure of the interior of the polygon is [(8-2)180°]/8

= 135°

The obtuse angle is an angle that more than 90°.

Therefore angle is an obtuse angle.

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third side,  AB= 14.318 Units  and  tanB = 0.461

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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Using Pythagoras theorem, Third side,  AB= 14.318 Units  and tanB = 0.461

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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Answer:

first option

Step-by-step explanation:

using the property of logarithms

ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )

given

[tex]17^{(0.3x+5)}[/tex] = 12

take the ln of both sides

ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then

(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )

0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )

0.3x ≈ - 4.12293 ( divide both sides by 0.3 )

x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )

0.3% is the percentage rate of increase  in exponential function.

What exactly makes a function exponential?

A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.

                   The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

We have,

y = 50( 1.3)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is

y(x)= a(1-r)^x such that r is the growth percent.

   1 + r = 1.3

     r = 0.3 ⇒  0.3%

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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We get the following answers;

(a) The necessary histogram has been created and is supplied below.

(b) According to the data, it is indeed dangerous to drive close to home. Because 23% and 29% of accidents occur within 1 to 5 miles of home, respectively.

Step 1: in 2001, progressive insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. the data are summarized in the table.

Step 2:

Table :

Miles from home          % of accidents      Cumulative

Less than 1                               23                        23

1 to 5                                         29                        52

6 to 10                                       17                         69

11 to 15                                       8                          77

16 to 20                                     6                         83

over 20                                     17                        100

(a) the required histogram is made and attached below.

(b) Yes, the data indicates that driving near home is particularly dangerous. Because, less than , 1 to 5 miles from home 23%, 29% of accidents.

Hence we get the required answers.

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when retail cost of the computer is 37% of the wholesale price then Retail price is 1.37times wholesale price

Retailers who acquire products in bulk are subject to wholesale pricing.

Selling products at a greater price than what it costs to produce them allows businesses to turn a profit.

Retail pricing is what merchants decide to charge customers as their ultimate selling price.

Consumers are the primary focus of retail pricing.

According to the question,

The retail cost of a computer is 37% more than its wholesale cost

Let Retail cost be "x" and wholesale cost be "y"

So , x = y + 0.37y

=> x = 1.37y

Therefore , The retail price is 1.37times the wholesale price

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The equation of the parabola is y = -1/4 x² + 3/2 x - 17/4. Where the vertex of the equation is at (3, -2) and the focus is at (3, -2 2/16) that opens downwards.

The equation of the parabola with vertex at (h, k) is

y = a(x - h)² + k

The focus of the parabola is represented by (h, k + 1/4 a).

It is given that, the vertex of the parabola is (h, k) = (3, -2)

And the focus of the parabola is (h, k + 1/4 a) = (3, -2 1/16)

From the focus point, we can calculate the value of 'a'.

(h, k + 1/4 a) = (3, -2 1/16)

⇒ k + 1/4 a = -2 1/16 = -33/16

⇒ -2 + 1/4 a = -33/16

⇒ 1/4 a = -33/16 + 2

⇒ 1/4 a = -1/16

⇒ a = -1/16 × 4

∴ a = -1/4

Since a is negative the parabola is downwards.

Now, the equation of the parabola is

y = a(x - h)² + k

On substituting the values, we get

y = -1/4(x - 3)² - 2

  = -1/4(x² - 6x + 9) - 2

  = -1/4 x² + 3/2 x -9/4 - 2

  = -1/4 x² + 3/2 x - 17/4

Therefore, the equation of the parabola is y = -1/4 x² + 3/2 x - 17/4.

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Answer: The coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.

Step-by-step explanation: The coefficient of the term with a certain power of t and a certain power of q in the expansion of a binomial raised to a power can be found using the binomial formula. The formula is given by:

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(a + b)^n = sum_{k=0}^n choose(n, k) * a^(n-k) * b^k

In this case, we have a = 3t, b = -q, and n = 17. We want to find the coefficient of the term with t^3 and q^14, which means we need to find the coefficient of the term with a^(n-k) = t^3 and b^k = q^14. Plugging these values into the formula, we get:

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(3t - q)^17 = sum_{k=0}^17 choose(17, k) * 3^(17-k) * (-1)^k * t^(17-k) * q^k

To find the coefficient of the term with t^3 and q^14, we need to find the value of choose(17, k) for k = 3. The binomial coefficient choose(n, k) is equal to the number of ways to choose k items from a set of n items. It can be calculated using the formula:

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choose(n, k) = n! / (k! * (n-k)!)

where n! is the factorial of n, which is the product of all positive integers less than or equal to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

In our case, we have n = 17 and k = 3, so the coefficient we are looking for is:

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choose(17, 3) = 17! / (3! * (17-3)!) = 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (3 * 2 * 1 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 17 * 16 / 3 = 816 / 3

Therefore, the coefficient of the term with t^3 and q^14 in the expansion of (3t - q)^17 is 816 / 3.

Answer: i think 15/8 but, im not sure

Step-by-step explanation:

Answer:

no c is right answer

Step-by-step explanation:

angle b and e should be supplementary

Answer:

A, B and C

Step-by-step explanation:

Statement A

According to the Alternate Exterior Angles Theorem, when a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.

Given ∠c ≅ ∠f, and as ∠c and ∠f are alternate exterior angles, then p ║ q.

Statement B

According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

GIven ∠d ≅ ∠g, and as ∠d and ∠g are corresponding angles, then p ║ q.

Statement C

According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.

Given ∠b and ∠e are supplementary, and as ∠b and ∠e are the interior angles on the same side of the transversal [tex]\ell[/tex], then p ║ q.

Statement D

∠f and ∠g are a linear pair, therefore ∠f and ∠g are supplementary.  However, this does not given enough information to prove p ║ q.

Answer:

Amy has to pay $600 every month for rent.

Step-by-step explanation:

To take 1/4 of a number is to multiply 1/4 and said number.

So you can do 0.25*number

or number/4.

For this problem, the number is 2400 because Amy is going to pay 1/4 of 2400 for rent.

[tex]rent = 2400/4\\rent = 600[/tex]

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Answer: P/2 - L = W

Step-by-step explanation:

P = 2L + 2W. We are isolating W. Subtract 2L from both sides to isolate the term first
P - 2L = 2W. Divide by 2 on both sides to isolate W.
P/2 - L = W

The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.

Given

Sides = x+7 and 3x-4

Area of rectangle

Length ×Breadth

(x + 7) (3x - 4)

Multiplying,

x(3x - 4) + 7(3x - 4)

3x² - 4x + 21x - 28

3x² + 17x - 28

The area of a rectangle with the sides of x+7 and 3x-4 is 3x² + 17x - 28.

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The equations that represent given problem is

P + S = 384 and 2.50P + 1.25S = 696.25.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given that the cost of 1 slice pizza is $2.50.

The cost of 1 bottle can of soda is $1.25.

In total sell for a day is 384.

Assume that you sell P slice of pizza and S number of soda bottle.

Thus your total sell is P + S.

Therefore, P + S = 384.

The cost 1 slice pizza is $2.50

Then the cost P slice of pizza is $2.50P.

The unit rate of soda bottle is  $1.25.

Then the cost S bottles of soda is $1.25S.

Therefore the total sell for that day is 2.50P + 1.25S

2.50P + 1.25S = 696.25

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Answer: 75%

Step-by-step explanation:



93 is 75 percent of 124.

Explained in the picture attached...

Hope that helps...

Answer:

final answer would be $6,550

Step-by-step explanation:

To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:

Income Range: $0 - $10,000

Progressive Tax Rate: 3%

Tax Owed: $0 - $10,000 * 3% = $0 - $300

Income Range: $10,001 - $50,000

Progressive Tax Rate: 5%

Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500

Income Range: $50,001 - $100,000

Progressive Tax Rate: 5.5%

Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500

Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.

A quadratic equation of at the origin, estimate the error = 0.000859M

The approximation is valid because  is very small.

Calculation of  concentration:

Since

0.85 M             0           0

(0.85-x)M         x            x

Now the value of x should be

x = 0.0000229

So based on this, the above concentration should be determined.

In order to demonstrate that the same value of x may be achieved either way, you will now solve using the quadratic formula rather than iterations. What are the values of a, b, and c and x, where a, b, and c are the coefficients in the quadratic equation [tex]ax^{2} +bx+c=0[/tex] and x is [h3o+], when using the quadratic equation to determine [h3o+] in 0.00250 m hno2? Keep in mind that ka=4.5104.

a : 1

b : 4.5x[tex]10^{-4}[/tex]

c : 1.125x[tex]10^{-6}[/tex]

[[tex]H_{3} O^{+}[/tex]] = 0.000859M

As [tex]HNO_{2}[/tex] is a weak acid, its equilibrium in water is:

[tex]HNO_{2} (aq)+H_{2} O(I)[/tex] ⇄ [tex]H_{3} O^{+} (aq)+N_{2} O^{-} (aq)[/tex]

Equilibrium constant, ka, is defined as:

ka = 4.5x[tex]10^{-4}[/tex] = [[tex]H_{3} O^{+}[/tex]]  [NO₂⁻] / [HNO₂]                    (Equation-1)

Equilibrium concentration of each specie are:

[HNO₂] = 0.00250M - x

[H₃O⁺] = x

[NO₂⁻] = x

Replacing in (1):

4.5x[tex]10^{-4}[/tex] = [tex]\frac{x*x}{0.00250M-x}[/tex]

1.125x10⁻⁶ - 4.5x10⁻⁴x = x²

0 = x² + 4.5x10⁻⁴x - 1.125x10⁻⁶

As the quadratic equation is ax² + bx + c = 0

Coefficients are:

a: 1

b: 4.5x10⁻⁴

c: 1.125x10⁻⁶

Now, solving quadratic equation:

x = -0.0013 → False answer, there is no negative concentrations.

x = 0.000859

As [H₃O⁺] = x; [H₃O⁺] = 0.000859M

Therefore,

A quadratic equation of at the origin, estimate the error = 0.000859M

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The equivalent rate is 163.7 meters.

What is an equivalent rate?

Equivalent rates are different rates that have the same value. Similar to finding equivalent ratios, you may find an equivalent rate by multiplying or dividing the numerator and denominator by the same number.

Here, we have

Given: the height of one Tampa city center is 537 feet.

We have to convert 537 feet to meters by finding an equivalent rate.

1 feet = 0.3048 meter

So, 537 feet = 537 × 0.3048 = 163.7 meters.

Hence, the equivalent rate is 163.7 meters.

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Answer:

Hence, on a number line,-12 lies to the left of Zero.

Step-by-step explanation:

On a number line, zero lies exactly at the middle of the number line.Left to the zero, negative number lies and right to the zero, positive number lies.