1) 77.2 - 43.778 =


2) 2.072 ÷ 5.6 =


3) 6.811 × 4.997 =


4) 27.001 - 7.5 =


5) 4.23 × 9 =


6) 19.2 + 31.82 =


7) 97.68 - 32.3 =


8) 0.468 ÷ 6.5 =


9) 0.6144 ÷ 1.6 =


10) 4.4 × 2.727 =


11) 20.97 + 85.62 =


12) 48 + 58.1 =
Add computations
Adding 3 points with computation

Answer: the midpoint

Step-by-step explanation:

It is proved that 1) AB = AC, 2) angle B = angle C fo the given triangles.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Here in Delta ADB and Delta ADC.

i) Three pair of equal parts are:

AD = AD ( common side )

BD = CD ( as d is the mid point of BC)

AB = AC (given in the question)

ii) Now,

by SSS Concurrency rule,

Delta ADB\cong \Delta ADC

iii) As both triangles are congruent to each other we can compare them and say

angle B = angle C.

To know more about Congruent triangle visit:

brainly.com/question/22062407

#SPJ4

Complete question:

In figure AB=AC and D is the mid point of BC state the 3 pairs of equal parts in

Triangle ADB and triangle ADC

is ADB= ADC? give reason

is <B = <C? why?

PLEASE ANSWERRR ASAP​

There are two ways to fence the garden in 3 areas with some equal sections.

2/5, 2/5, 1/5 and 3/5, 1/5, 1/5.

Fraction definition

A fraction depicts a segment or component of the whole. It represents the equal parts that make up the whole. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that are taken.

Given The garden is divided into 5 equal pieces, each of which is 1/5 of the total garden size.

By arranging some equal parts together, she will fence the garden into three sections. There are two ways to do this.

(1/5 +1/5) = 2/5

(1/5 +1/5) = 2/5

1/5

these are the 3 areas 2/5, 2/5, 1/5.

and

(1/5 +1/5 + 1/5) = 3/5

1/5, 1/5

these are 3 areas =  3/5, 1/5, 1/5.

Hence there are only two ways to fence the garden into three areas by grouping some equal sections.

Learn more about fractions;

brainly.com/question/10354322

#SPJ4

Therefore , the value of the given problem of trigonometry comes out to be  x = 2 √3.

Trigonometry is the branch of mathematics that studies the relationship between triangle side length The field was first developed in the Classical era, most likely in the third century BC, as a product of the fusion of geometry and astronomy research. Certain geometric equations and potential applications to calculations are covered in precise methods to mathematics. In trigonometry, there are six typical trigonometric operations. Sine, quadrature, tangent, secant, etc. are some of the names and acronyms that they go by (csc). Trigonometry is the study of triangle properties, particularly those of right triangles. However, understanding about the properties of all polygons is a necessary part of mastering geometry.

Here,

Given : Let x be the given

2 is the base

Using trigonometric ratio comes out to be :

=> Tan 30 = 2/x

=> 1/√3 = 2/x

=> x = 2 √3

Therefore , the value of the given problem of trigonometric comes out to be  x = 2 √3.

To know more about trigonometry visit:

https://brainly.com/question/29002217

#SPJ1

Square pyramid has triangles and square, pentagonal prism has two pentagons and five rectangles,  triangular prism has nine triangles and  triangular pyramid has triangles

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Net of a square pyramid consist of triangles and square.

The net of a pentagonal prism consists of two pentagons and five rectangles.

The net of a triangular prism consists of nine triangles

The net of a triangular pyramid consists of four triangles

Hence, square pyramid has triangles and square, pentagonal prism has two pentagons and five rectangles,  triangular prism has nine triangles and  triangular pyramid has triangles

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

Answer:

Step-by-step explanation:

We are given that,

The surveyor is located 340 meters from one entrance at an angle of 58°.

The surveyor is located 193 meters from one entrance at an angle of 21°.

Let the length of the tunnel = x meters

Using the Law of Cosines,

[tex]x^{2} =(340)^{2}+(193)^{2}-(2)(340)(193)cos(21+58)\\x^{2} =115600+37249-131240cos(79)\\x^{2} =115600+37249-25041.77255\\x^{2} =127807.2274\\x=\sqrt{127807.2274} \\x=357.50 meters\\[/tex]

There are a total of 9 women and 6 men on the council, for a total of 15 council members.

If we randomly choose 2 of them to co-chair a committee, the number of ways to choose 2 people of the same gender is:

So the total number of ways to choose 2 people of the same gender is 3+15 = 18.

The total number of ways to choose 2 people without considering their gender is 15 choose 2 = 105

So the probability of choosing 2 people of the same gender is 18/105 = 6/35

So, the probability that these chairpersons are the same gender is 6/35.

On solving the provided question, we can say that  fraction of her apple cider will she put in each bottle x = 1/48

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Let's refer to the quantity of apple cider she will add to each bottle as:

She divides her apple cider across six bottles since, as you know, she wants to bottle 1/8 of it.

As a result, you can compose the following sentence while keeping the facts above in mind:

6x = 1/8

x = 1/6*8

x = 1/48

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ4

A zero solution, also known as the trivial solution, refers to a solution of a system of equations in which all variables are equal to zero.

This type of solution occurs when the coefficients in the system of equations are set up in such a way that the only solution to the system is for all the variables to be equal to zero.

A zero solution is the answer to a system of equations where all the variables are equal to zero. This happens when the coefficients in the equations are set up such that the only solution is for all the variables to be equal to zero. This type of solution is also known as the trivial solution. A trivial solution can be thought of as a “placeholder” for when there is no other meaningful solution to a system of equations.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

On solving the provided question, we can say that the probability of both = 4/9*1/3 or 4/27

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

18 marbles  = 8 are blue and 6 are red .

probability  a blue marble = 8/18 = 4/9.

probability of getting a red marble i=6/18 = 1/3.

probability of both = 4/9*1/3 or 4/27

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ4

The given system of equations  intersect in quadrant II at (-6,2)

What is linear equation ?

linear equation can be defined as the equation in which highest power is one.

Given system of equations,

y = (-1/3) x -4

y = (2/3) x + 2

In the first equation ,

y = (-1/3)x- 4

the 1st line slopes up with y intercept = -4

y = (2/3) x + 2

the 2nd line slopes down with y intercept = 2  

By equating the equations , we get

(-1/3) x -4 =  (2/3) x + 2

-4-2 = (2/3) x + (1/3) x

-6 = x

x = -6

By putting x = -6 in y = (-1/3) x -4

we get ,

y= (-1/3 ) -6 - 4

y = 2-4

y = -2

Hence, The given system of equations  intersect in quadrant II at (-6,2).

To learn more about linear equation from the given link.

https://brainly.com/question/21835898

#SPJ1

Answer:

480ft.it does not matter how much east or west they are.it asks how much"they are apart"

so it should be 480.

The solution of the equation 2x + y = 10 is B. x = 5, y = 0.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x, y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, A linear equation 2x + y = 10.

To find the solution we can put the solutions given in the options.

Let, x = 2, y = 3.

So, 2x + y = 10.

4 + 3 ≠ 10.

Let,

x = 7, y = - 2.

14 - 2 ≠ 10.

let,

x = 3, y = 3.

6 + 3 ≠ 10.

Let, x = 5, y = 0.

10 + 0 = 10    (satisfied).

Q.Which of the following is a solution of the equation 2x+y =10 ?

A.x=2, y =3

B.x = 5, y =0

C.x=7, y=-2

D.x= 3, y =3

learn more about ordered pairs here :

https://brainly.com/question/13210202

#SPJ1

The probability that 75% or more of the women in the sample have been on a diet is 0.944.

The probability that 75% or more of the women in the sample have been on a diet can be calculated by using the binomial formula. The formula is P(X>=x) = 1 - P(X<x). The parameters in this case are as follows: n = 267, p = 0.7, and x = 201.5 (which is 75% of 267). Therefore, the probability that 75% or more of the women in the sample have been on a diet is 1 - P(X<201.5). Solving for this probability, P(X>=201.5) is 0.944. Therefore, the probability that 75% or more of the women in the sample have been on a diet is 0.944.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

Answer:

11. Slope = 1, y-int = (0, -3)

Step-by-step explanation:

Move the numbers so that they math the formula y=mx+b, m being the slope, and b being the y intercept. If for example its 2y, divide the entire equation by 2. Basically you separate "y" on one side, and whatever is next to the x is your slope.

Two examples below:

The principal stresses are the maximum normal stresses in the x, y, and z directions.

These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.

The principal stresses are determined using Mohr's circle and the absolute maximum shear stress is equal to one-half the difference between the two principal stresses.

The principal stresses are the maximum normal stresses in the x, y, and z directions.

These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.

Learn more about maximum here

https://brainly.com/question/29156925

#SPJ4

x = 2 is the solution to the equation 5x - 2 = 8.

What is the logarithm?

A logarithm is a power to which a number must be raised in order to get some other number. For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100.

The change of base formula for logarithms allows us to change the base of a logarithm without changing the value of the logarithm.

The formula is: logb(x) = (logc(x)) / (logc(b))

To solve 5x - 2 = 8 using the change of base formula, we will first bring the equation to one side and get 2 = 5x - 8.

Then we will add 8 to both sides of the equation to get 2 + 8 = 5x, which gives us 10 = 5x.

Finally, we will divide both sides of the equation by 5 to get x = 2.

x = 2

Therefore, x = 2 is the solution to the equation 5x - 2 = 8.

To learn more about the logarithm visit,

https://brainly.com/question/25710806

#SPJ4

In the given time interval [0,7]:

(a) the maximum speed is 1096.63 units at t = 7 and

(b) the minimum speed is 0.91 units at time t = ln2/4.

Parametric equations of the curve

x(t) = [tex]e^t + e^{-t}[/tex]

y(t) = [tex]e^{-t}[/tex]

so, dx/dt = [tex]e^t - e^{-t}[/tex]

dy/dt = [tex]-e^{-t}[/tex]

So, speed: v(t) = [tex]\sqrt{(dx/dt)^2 + (dy/dt)^2}[/tex] = [tex]\sqrt{(e^t-e^{-t})^2 + (-e^{-t})^2}[/tex]

When v(t) is maximized or minimized, evidently v² is also maximized or minimized because speed is a positive quantity.

or (speed)² = v² = [tex](e^t-e^{-t})^2 + (-e^{-t})^2[/tex] = [tex](e^{2t} + 2e^{-2t} -2)[/tex]

Now, to get the maxima or minima of a curve we have to derivate function

d/dt(v²) = 0 or d/dt[tex](e^{2t} + 2 e^{-2t} -2)[/tex]

or [tex]2e^{2t} -4 e^{-2t} = 0[/tex] or [tex]e^{2t} = 2 e^{-2t}[/tex]

taking logs on both sides

4t lne = ln2 or 4t = ln2 or t = ln2/4

so, the only critical point is t = ln2/4 ∈ [0,7]

To calculate the maxima/minima of v, we will find functional values at the critical point and boundary values of the given interval [0,7].

At t = 0 : v(0) = [tex]\sqrt{e^0 + 2e^0 - 2} = \sqrt{1+2-2}[/tex] = 1

At t = ln2/4: v(ln2/4) = [tex]\sqrt{e^{2ln2/4} + 2e^{-2ln2/4} - 2} = \sqrt{2\sqrt{2} -2 }[/tex] = 0.91

At t = 7: v(7) = [tex]\sqrt{e^{14} + 2e^{-14} - 2}[/tex] = 1096.63

Therefore, in the given time interval [0,7]: (a) the maximum speed is 1096.63 units at t = 7 and (b) the minimum speed is 0.91 units at time t = ln2/4.

#SPJ4

To learn more about the maxima/minima of a curve:

https://brainly.com/question/29006375

The expression shows the differences of cubes is (5x⁷)³-(4y)³. Therefore, option C is the correct answer.

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y³.

A) 27x¹⁵-9y³

= 3³x¹⁵-3²y³

= (3x⁵)³-3²y³

B) 3x⁹-64y³

= 3x⁹-4³y³

= 3x⁹-(4y)³

C) 125x²¹-64y³

= 5³x²¹-4³y³

= (5x⁷)³-(4y)³

D) x⁶+27y⁹

= (x²)³+(3y)³

Therefore, option C is the correct answer.

Learn more about the perfect cube here:

brainly.com/question/29056294.

#SPJ1

If the dimensions of the box were all doubled, then the surface area of the box be 640 square units.

Use the concept of prism defined as:

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat sides, and identical bases.

Without bases, the prism's faces are parallelograms or rectangles. And any n-sided polygon, whether a triangle, square, rectangle, or other, might serve as the prism's basis.

Given that,

The dimension of the rectangular prism = 2yd x 10yd x 5yd

Since we know that,

Dimension of prism = length x breadth x height

length x breadth x height =  2yd x 10yd x 5yd

Therefore,

Length = 2 yd

Breadth = 10 yd

Height = 5 yd

Now if dimension doubled the,

The dimension of the new prism = 4yd x 20yd x 10yd

Then,

Length 'l' = 4 yd

Breadth 'b'= 20 yd

Height 'h' = 10 yd

Since we know that,

The surface area of a rectangular prism is,

A=2(bl+hl+hb)

Substitute the values,

A = 2(20x4 +10x4 + 10x20)

A = 640 square units.

Hence the surface area is 640 square units.

To learn more about Prism visit:

https://brainly.com/question/2918181

#SPJ4

When two line segments are of equal length then both the line segments are congruent to each other.

As given in the question,

Therefore, the two line segments with equal lengths they both are congruent to each other.

learn more about line segments here

brainly.com/question/30072605

#SPJ4

The numbers that are potential roots of the function given above are:
Option B-D. That is -  ±1, ±2, and ±12.

It is correct to state that in mathematics, a root of an equation is a value that, when substituted into the equation, makes the equation true.

To obtain the potential roots of the expression p(x) = x⁴ + 22x² - 16x - 12:

Note that from the rational root theorem, all the possible roots of the function are in the form of a rational number.

x =  ± p/q

x = ± (Factors of the constant term)/ (Factors of leading coefficient)

Thus, according to the polynomial above,  we know that

Factors of 1 are ±1.

Thus, according to the theorem of rational root, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

Therefore, the potential roots of the function from the options listed are: are ±1, ±2, and ±12.

Learn more about Potential Root:
https://brainly.com/question/25895514
#SPJ1

Full Question:

Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² - 16x - 12?

± 5
±1

±2

±12

±17

A triangle is a three-edged polygon with three vertices. The length of QS is equal to 17 units.

How do triangles work?

A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. A triangle's total angles are always equal to 180 degrees.

Given that the line segment RQ is bisected at point T by the perpendicular bisector Line l. As a result, RT = QT is the length of the two lines.

Now, in ΔRST and ΔQST,

RT ≅ QT

ST ≅ ST {Common side}

Now, since the two triangles are the right-angled triangle, therefore, the two triangles are congruent. Thus, we can write,

RS = SQ

Given that the Line segment, RS is 3x+2. Line segment SQ is 5x-8.

RS = SQ

3x + 2 = 5x - 8

2 + 8 = 5x - 3x

10 = 2x

x = 5

QS = 5x - 8

    = 5(5) - 8

    = 25 - 8

    = 17 units

Hence, the length of QS is equal to 17 units.

Learn more about Triangle here:

brainly.com/question/2773823

#SPJ4

The time estimates for units 2, 3, 4, and 5, rounded to 2 decimal places, are 4.8 hours, 34.56 minutes, 4.14 minutes, and 0.48 minutes respectively.

A learning percentage is the percentage by which the time required to complete a task decreases as the number of units produced increases. In this case, the learning percentage is 88%.

To develop the time estimates for units 2, 3, 4, and 5, we can use the formula:

Time for unit n = Time for unit 1 (1 - learning percentage)⁽ⁿ⁻¹⁾

Where n is the unit number, and the learning percentage is expressed as a decimal.

For example, to find the time estimate for unit 2:

Time for unit 2 = Time for unit 1 (1 - 0.88)⁽²⁻¹⁾

= 40 (1 - 0.88)

= 40 × 0.12 = 4.8 hours

To find the time estimate for unit 3:

Time for unit 3 = Time for unit 1 (1 - 0.88)²

= 40 (1 - 0.88)²

= 40 × 0.12²

= 0.576 hours

= 34.56 minutes

To find the time estimate for unit 4:

Time for unit 4 = Time for unit 1 * (1 - 0.88)^(4-1)

= 40 * (1 - 0.88)^3

= 40 * 0.12^3

= 0.069 hours

= 4.14 minutes

To find the time estimate for unit 5:

Time for unit 5 = Time for unit 1 * (1 - 0.88)^(5-1)

= 40 * (1 - 0.88)^4

= 40 * 0.12^4

= 0.008 hours

= 0.48 minutes

To know more on learning percentage

https://brainly.com/question/30206486

#SPJ4

Answer:

so the square root is x so when you point the square root at the rwaterfall you waill have your

Step-by-step explanation:

the drone would need to be 1.4 miles away from your to be the opposite value. pou pou pou pou pou pou pou pou pou pou pou pou ufo p

Step-by-step explanation:

The value of the expression [tex]\frac{999999999\times 999999999}{1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1}[/tex] , which involves the division of a large number is obtained by making use of a scientific calculator is; 12345678987654321

Depending on the processor of the calculator, and the number of digits the calculator can handle, the exact value following the operations with very large numbers can be obtained. Graphing calculators can also be made to increase the number of digits of precession, up to 9999 digits.

The expression in the question can be presented as follows;

999999999 × 999999999 ÷ (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1)

The value can be computed using a calculator;

999999999 × 999999999 = 999999998000000001

(1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 81

999999999 × 999999999 ÷ (1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1) = 999999998000000001 ÷ 81 = 12345678987654321

Learn more about operations with large numbers here: https://brainly.com/question/2292046

#SPJ1

There are 33 short-answer questions on the test and 33 * 4 = 132 points are from short-answer questions.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include operations such as addition, subtraction, multiplication, and division.

We know that the test has 75 questions and it is worth 216 points total.

We know that multiple-choice questions worth 2 points each and short answer questions worth 4 points each.

To calculate the number of points from short-answer questions, we need to find out how many questions are short-answer and multiply that by 4 (points per question).

Let x be the number of short-answer questions.

We know that x + 75 - x = 75, which is the total number of questions on the test.

Also, we know that x * 4 + (75-x) * 2 = 216, which is the total number of points on the test.

Solving for x, we get:

x * 4 + 150 - 2x = 216

2x = 66

x = 33

So there are 33 short-answer questions on the test and 33 * 4 = 132 points are from short-answer questions.

To learn more about algebra visit : brainly.com/question/24875240

#SPJ4

So, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate

To find out how many days it takes for all 24 gallons of water to leak out of the pool, we need to determine the rate at which the water is leaking and use that to calculate the total time it takes for the pool to empty.

We know that the pool initially has 24 gallons of water and that it is leaking out at a rate of 2 gallons every 3 days. This means that the pool loses 2/3 of a gallon of water per day.

To find out how many days it will take for the pool to empty, we can divide the total amount of water in the pool by the rate at which it's leaking out.

24 gallons / (2/3 gallons/day) = 24*3/2 = 36 days

Therefore, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate.

To learn more about Rate of Change

visit; brainly.com/question/29518179

#SPJ4

The initial weight of the toy before removing the spare parts was found to be 440gm since the weight after 25% removal was given as 330gm

The final weight of the toy after removal of spare parts is given as 330g

Percentage weight removed in the form of spare parts from the toy= 25%

Let us consider the initial weight to be x

The equation becomes,

x – 0.25x = 330, since 25% is removed from the original weight of the toy to give us the final weight of 330gm

0.75x= 330

x = 330/0.75

x = (330*100)/75

x = 440

Therefore, initial weight of the toy was found to be 440g

Learn more about percentage here brainly.com/question/12948737

#SPJ4

The experimental probability of a cube tossed 60 times, landing on a number greater than 4 is the option;

18 over 60

A probability is the fraction or proportion of the times an event will occur when an experiment or task is repeated. It is the measure of the liklyhood an event will occur

Probability compares the number of times an event occurs to the number of times all possible event outcomes occurs.

The formula for the experimental probability is presented as follows;

[tex]Probability = \frac{The \ sum \ of \ the \ times \ the \ event \ takes \ place}{The \ sum \ of \ the \ trials}[/tex]

The number of times the outcome from tossing the coin is greater than 4 obtained by adding the frequencies when for the outcomes of 5 and 6 are;

Number of outcomes greater than 4 = 10 + 8 = 18

The sum of all trials = 12 + 13 + 11 + 6 + 10 + 8 = 80

Therefore, the experimental probability = 18/60

The correct option is; 18 over 60

Learn more about experimental probability here: https://brainly.com/question/1275164

#SPJ1

Answer: B: 18/60 (18 over 60)

Step-by-step explanation: