Translate the following statement into a mathematical equation:Five times a number, minus three, is twelve.5(n - 3) = 125n - 3 = 125 - 3n = 125n = 12 - 3

Since girls and boys have equal probability, iin a family with four children, they have probability equal to

so, the probability of having 3 boys and 1 girls is

that is, the answer is 3/16 which is equal to 0.19.

Answer:

-4/27

Step-by-step explanation:

Answer: 2,3,4

Step-by-step explanation:

y=1/4x +2

x=0  y=2

x=4  y=3

x=8  y=4

The length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.

Given that, in triangle GHJ, ∠G=25°, ∠H=46°, and h = 37 mm.

The sine rule of a triangle is sin A/a = sin B/b = sin C/c.

From triangle GHJ

∠G+∠H+∠J = 180°

⇒ 25°+46°+∠J = 180°

⇒ ∠J = 109°

Using sine rule

sin 109°/g = sin 25°/37

⇒ 0.945/g = 0.4226/37

⇒ 34.965 = 0.4226g

⇒ g = 82.73 mm

⇒ g ≈ 83 mm

Therefore, the length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.

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For this system of equations, there will be infinitely many solutions.

Two equations are said to represent a line when they have the same slope and y-intercept. In this instance, one equation is created by adding a constant to the other equation.

Such equations will lay on each other on a graph if we plot them since they represent the same line. We can claim that these equations have an endless number of solutions because every point on that line will satisfy both of the aforementioned equations.

Here's an illustration:

Eq. 1: 2x + y = 4.

4x + 2y Equals 8 in equation 2

The second equation is created by multiplying the previous equation by two, as can be seen if you look at the two equations. The same outcome will be obtained for both if we write them in slope intercept form, as illustrated below:

Equation 1's slope intercept form is y = -2x + 4

Equation 2's slope intercept form is 2y = -4x + 8 and y = -2x + 4

The y-intercept and slope of both equations are identical. Equation 2 applies to any place that satisfies Equation 1. We can therefore draw the conclusion that there are an endless number of solutions to two linear equations with the same slope and y-intercept.

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Answer:

1

Step-by-step explanation:

The linear equation that represents how much he spent is given as y = 1.25x + 9.55

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear function is given y = mx + c

To solve this problem, we can simply use the values given to write a linear equation.

Can be written as

[tex]30.75 = 1.25x + c\\x = 17\\30.75 = 1.25(17) + c\\c = 30.75 - 21.25\\c = 9.55\\[/tex]

The equation to represent this problem is y = 1.25x + 9.55

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The biggest number you can make from the numbers 12, 1, 4 and 7 is given by:

336 = 12 x 1 x 4 x 7.

The operation that leads to the bigger number is the power operation, however, as stated in the problem, you cannot use any powers in this problem.

After the power, the operation that leads to the highest numbers is the multiplication operations.

These are no constraints relating the symbols, only that each number cannot be used more than once, hence the biggest number is obtained multiplying all values, as follows:

12 x 1 x 4 x 7 = 336.

If one of the numbers had been a fraction with a greater denominator than numerator, the fraction should be divided, as dividing by a fraction is the same as multiplying by the inverse of the fraction.

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Answer:

(- 3, - 1 )

Step-by-step explanation:

1 down means subtract 1 from the y- coordinate

2 units right means add 2 to the x- coordinate

(- 5, 0 ) → (- 5 + 2, 0 - 1 ) → (- 3, - 1 )

The Ratios 5 : 3 and 17 : 12 does not form a proportion.

What is Proportion?

A Proportion, in mathematics, can be defined as when two ratios are set equal to each other.

Now, the given ratios are: 5 : 3 and 17 : 12

We can also write the ratios as: [tex]\frac{5}{3}[/tex] and [tex]\frac{17}{12}[/tex]

To determine, if they are a proportion, we can cross multiply and get the same answers on both the sides.

When we multiple, the numerator from the first by the denominator of the second, we get

5 * 12 = 60                             …(1)

Now, multiply the denominator from the first by the numerator of the second, we get

3 * 17 = 51                             …(2)

Since, (1) and (2) are not equal. Therefore the ratios does not form a proportion.                

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1/4π is area of a circle when the radius is 6 cm.

What is the circumference of a circle?

 A = πr²

differentiate both sides with respect to 't'

dA/dt = πr² dr/dt

dA/dt = 2πr dr/dt

dA/dt = 3  ,     r = 6

3 = 2π * 6dr/dt

dr/dt = 1/4π

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Marcy is a 5-ft-5 in. She took measurements of both her own shadow. h=520 is the building's height.

Given that,

Marcy is a 5-ft-5 in. She took measurements of both her own shadow and that of the structure in order to determine its height.

We have to find what is the building's height, h.

Use the fact that 1 feet is equivalent to 12 inches to convert all measures to a single unit, inches.

We convert

MN=26×12=312 inches.

QR=3×12+3=36+3=39 inches.

PQ=5×12+5=60+5=65inches.

Since the Sun's rays that generate LN and PR are parallel, they are also parallel. the angles they make with the earth as a result are consistent:

∠N≅∠R

The Right Angle Congruence Theorem illustrates ∠M≅∠Q.

As a result, according to the Angle-Angle Similarity △LMN~△PQR

Calculate a ratio using the known lengths of the sides and the unknown length (height of the building).

PQ/QR=LM/MN

65/39=h/312

h=65×312/39

h=20280/39

h=520

Therefore, h=520 is the building's height.

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The sequence's 61st term is -972.

The sequence is -12 , -28 , -44.

The following arithmetic sequence is: -12, -28, -44, ..

Find the common difference between the succeeding and preceding terms.

         c.d = first term - second term

-28 - (-12) = -28 + 12 = -16

-44 - (-28) = -44 + 28 = -16

As a result, the distinction between the terms remains constant.

This is a mathematical sequence.

The formula for the nth term of an arithmetic sequence is:

an = a1 + (n - 1 ) d

Where,

an is the sequence's nth term.

a1 is the sequence's first term.

The common difference between terms is denoted by d.

-12, -28, -44 are the numbers in the given sequence.

By changing the values in the formula,

a1 = -12

d = -16

Substituting values,

an = -12 + (n - 1 )(-16)

an = -12 - 16n + 16

an = 4 - 16n

Substitute n = 61 to find the 61st term.

a61 = 4 - 16 x 61

a61 = 4 - 976

a61 = -972

As a result, the sequence's 61st term is -972.

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Answer:

4x + 9

Step-by-step explanation:

the product of 4 and x is 4x

then 9 more is addition, so 4x + 9

Answer:

Step-by-step explanation:

0

By the concept of permutation and combinations there are 7,484,400 ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box.

Putting things or numbers in order is known as a permutation. Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.

The number of ways to sort identifiable things into indistinguishable bins is 11 or "double-factorial," which is defined as 11 (as shown). Given that the bins are distinct, that is multiplied by 6! Following are several explanations for the 11!!11!! There are 11 potential companions for the chosen "first" object. Following that decision, there will be 10 items left, which indicates that the next arbitrary object will have 9 companions. then do it again. A more traditional strategy would be this. The objects that fit in the first container have 122 possibilities, the second bin has 102 possibilities, and so on.

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Answer:

A and D

Step-by-step explanation:

its A and D, trust

Answer: The slope is 3.

Step-by-step explanation: Hope this helps :)

The standard deviation for the number of seeds germinating in each batch is 1.3.

Given, the probability that a radish seed will germinate is 0.7.

In binomial distribution, standard deviation is given as:

σ = √np(1-p)

Where "n" is the number of observations

"p" is probability of getting success

We are given that:

Total batches of seed = 8

Probability that a radish seed will germinate is 0.7

Here success is getting radish seed germinated

Then, the standard deviation for the number of seeds germinating in each batch.

Plugging in values in formula, we get:

σ = √(8)(0.7)(1-0.7)

= √(8)(0.7)(0.3)

= √1.68

= 1.29614 ≈ 1.3

Therefore the standard deviation for the number of seeds germinating in each batch is 1.3

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The area of the Caribbean Sea is 2.7182 × 10^6 km2, The area of the South Atlantic Ocean is 4.027 × 10^7 km2, then the total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².

We are to determine the total area of the Caribbean Sea and the South Atlantic Ocean.

From the given information,

The area of the Caribbean Sea is 2.967 × 10⁶ km² and

The area of the South Atlantic Ocean is 4.149 × 10⁷ km²

To determine the total area, we will add the given areas together,

   2.7182 × 10⁶ km²

+  4.027 × 10⁷ km²

So, That is,

   2.7182 × 10⁶ km²

+  40.27 × 10⁶ km²

----------------------------

42.9882 × 10⁶ km²

So,

We can write,

= 4.29882 × 10⁷ km²

Therefore,

The total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².

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The equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.

As given in the question,

Line passes through the point ( x₁ , y₁ ) = ( 20, 19)

Slope of the line that passes through (20 , 19) is 55

Equation of a line in point-slope form that passes through the point (20,19) with slope 55

y - y₁ = m ( x- x₁)

⇒ y - 19 = 55 (x - 20)

⇒ y -19 = 55x - 1100

⇒ y= 55x - 1091

Therefore, the equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.

The complete question is:

Use point-slope form to write the equation of a line that passes through the point (20,19) with slope 55.

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The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively. The perimeter of the triangle is 42 feet.

Given that,

Kat is using reflective orange paint to outline a triangle stage prop. The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively.

We have to find if x = 4, what is the triangle's perimeter.

The perimeter of the triangle is equal to sum of the three sides of the triangle.

=3x - 4 + x² - 1 + 2x² - 15

=3x²+3x-20

Take the x value as 4

We get,

=3(4)²+3(4)-20

=3×16+3×4-20

=48+14-20

=62-20

=42

Therefore, The perimeter of the triangle is 42 feet.

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Answer:

The slope of the line represented by the table value is -8/5

√ x/4 + 4 is the inverse of the function f(x)=4x^2-16

What is inverse function?

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f

Given  f(x)=4x²-16

Let f(x) = y

So we can say y =4x²-16

We will then make x the subject:

Since y = 4x²-16

4x² = y + 16

x² = y + 16/4

x = √ y/4 + 4

since x = f⁻¹(y)  = √ y/4 + 4

Thus  f⁻¹(x)  = √ x/4 + 4

Therefore, the inverse of f(x)=4x^2-16 is √ x/4 + 4

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If a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .

The Percent Error can be calculated by the formula

Percent Error = (measured value - actual value)/(actual value)  ×100

In the question ,

it is given that

the original length of the stick is 60 inches .

the measured length of the stick is 63 inches .

So, the measured value = 63 inches ,

actual value = 60 inches .

Substituting the measured values and actual value in the percent error formula , we get

Percent Error = (63-60)/60 × 100

= 3/60 × 100

= 1/20 × 100

= 100/20

= 5 %

Therefore , if a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .

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Answer:

She will earn 18 dollars in interest.

Step-by-step explanation:

0.09*(100*2)

0.09*(200)

18