A board, 27 cm long is cut into three pieces such that the second piece is twice as
long as the first and the third is 2 cm longer than the second.
Find the length of the shorter piece.

As per the figure, the angle equation p + q + r = 180 is proved.

In geometry, an angle is defined as the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. When two lines are parallel, the angles opposite to each other are called corresponding angles.

In the given figure AB || CD, we are asked to prove that the sum of angles p, q, and r is equal to 180 degrees. This can be proven using the concept of corresponding angles.

Since lines AB and CD are parallel, the angles opposite to each other are equal, i.e., p = r. Therefore, the sum of angles p and r can be represented as 2p.

Furthermore, since lines AB and CD are parallel, the alternate interior angles are equal. This means that angle q is equal to angle p.

Therefore, the sum of all three angles, p, q, and r, can be represented as 2p + q.

And since we know that p = q, we can simplify this to 3p.

Finally, since the sum of angles in a triangle is always 180 degrees, we know that

=> 3p = 180 degrees.

Solving for p, we find that p = 60 degrees.

Therefore, the sum of angles p, q, and r is equal to

=> 2p + q = 2 * 60 + 60 = 180 degrees,

which proves the statement p + q + r = 180 degrees.

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Answer: 20 units

Step-by-step explanation: Set the two half diagonal values equal to each other. When you solve for x, the value is 3. Substitute it back in and the half diagonals equal 10. Multiply it by two and the dial length is 20. You can use this length for TE because it is a diagonal. Hope this helps!

Answer: Let's denote the original number of pages Mark planned to read as "P".

From the first statement, we know that P - 18 pages will take 5 more days, which means P pages will take 5 days less, or 5 - 5 = 0 days.

From the second statement, we know that P - 24 pages will take 8 more days, which means P pages will take 8 days less, or 8 - 8 = 0 days.

So, we have two equations:

P - 18 = 5 * X

P - 24 = 8 * Y

Where X and Y are the number of pages Mark reads per day.

Since X and Y are equal, we can substitute one of them for the other:

P - 18 = 5 * (P - 24) / 8

Expanding the right side and solving for P, we find that P = 288 pages.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Substitute for r.

1/5(1/4) + 9/20  ->  1/20 + 9/20 = 10/20.

Simplify the final answer.

10/20 = 1/2

Step-by-step explanation:

the function is

d(n) = sqrt(1.49×n)

so,

85 = sqrt(1.49×n)

85² = 1.49×n

n = 85²/1.49 = 7225/1.49 = 4,848.993289... ft

≈ 4,849 ft

The one-digit integers that satisfy the inequality k≥0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

The given inequality is k≥0, k greater than or equal to zero.

The negative values on the number line are -1, -2, -3...-9 while the value greater than or equal to zero are 1, 2, 3, 4,...9

Hence, the one-digit integers that satisfy the inequality k≥0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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[tex]-1+6x < 5[/tex]

Simplify:

[tex]6x-1 < 5[/tex]

Add 1 to both sides:

[tex]6x-1+1 < 5+1[/tex]

[tex]6x < 6[/tex]

Divide both sides by 6:
[tex]\dfrac{6x}{6} < \dfrac{6}{6}[/tex]

[tex]\boxed{x < 1}[/tex]

(a) The probability of having all six children be girls is (1/2)^6, or 1/64.
(b) The probability of having all six children be the same sex (either all boys or all girls) is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) The probability of having at least one boy is 1 - 1/64, or 63/64

The probability of having a child of a particular sex is 50%. Given a family with six children, we can calculate the probability of each event as follows:
(a) All the children being girls: the probability is (1/2)^6, or 1/64.
(b) All the children being the same sex (either all boys or all girls): the probability is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) At least one boy being in the family: the probability is 1 - (1/2)^6, or 63/64. This can be calculated by finding the probability of having no boys (all girls) and then subtracting it from 1.
In summary, the probability of having a particular outcome in a family with six children depends on the number of children of each sex and can be calculated using the formula (1/2)^n, where n is the number of children of a particular sex.


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Complete question:

Assume that the probability of the birth of a child of a particular sex is 50%. In a family with six children, find the probability of each event.

(a) All the children are girls.

(b) All the children are the same sex.

(c) There is at least one boy.

The probability of drawing a green ball in one draw is 8/14 = 4/7. Since the balls are replaced after each draw, each draw is independent of the others. Therefore, the probability of getting 6 green balls in a row is (4/7)^6 ≈ 0.066.

Rounding to three decimal places, the probability is approximately 0.066.

Answer:

y=1 1/2x

Step-by-step explanation:

y= mx+c

1st point : (2,3)

2nd point : (4,6)

m= 3-6/2-4

= -3/-2

= 1 1/2

y=1 1/2x

The Frequency table for grouped data using four classes are given in the table below.

The frequency table is to represent the data in the table form in which larger data are arranged according to their characteristics. In which frequency is the number which represents how many times the particular data occurs in it.

Here, there are 20 hours for each employee is given, we have to group into four classes.

Let us split the hours as,

0 - 5 ----this includes- 1,1,2,2,3,3,5(7 hours)

5 - 10---this includes - 8,10(2 hours)

10 - 15--this includes - 12,13,15,15(4 hours)

15 - 20-this includes - 17,18,18,19,19,20,20(7 hours)

(Note:This is exclusive classes i.e., upperlimit is not included)

Using this data the frequency table is constructed as shown below:

No. of hours              Frequency

     0 - 5                               7

     5 - 10                              2

    10 - 15                              4

    15 - 20                             7

Hence, the frequency table for the given data are grouped using four classes.

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If the rates are the same ones, the tank will be filled in 15 minutes.

Let's define R as the rate at which we fill the tank, we know that we can fill a volume V in 6 minutes, then:

R*6 min = V

R = V/6min

Then r is the rate at which we empty the tank, we know that a volume V is emptied in 10 minutes, then:

r*10 min = V

r = V/10min

If both valves are open, the rate at which we will fill the tank is:

R - r

Now we need to find the value of time T such that:

(R - r)*T = V

(V/6min - V/10min)*T = V

(1/6min - 1/10min)*T = 1

(5/30min - 3/30min)*T = 1

(2/30 min)*T = 1

T = (30min/2)

T = 15 minutes.

The tank will be filled in 15 minutes.

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Answer:-4/7y+4/7x

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

The equation for this problem is this:

First, we need to find a common denominator between  [tex]\frac{5}{3}[/tex] and [tex]\frac{2}{9}[/tex].

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To find the common denominator, we can multiply the denominators, 3 and 9.

Now we know that the two new fractions are going to have a denominator of 27.

Now, we can use these equations to solve for the numerator.

Now, the fractions look like this:

To add them together, we can use this equation:

Now, we need to convert [tex]1 \frac{9}{8}[/tex] into an improper fraction.

An improper fraction is a fraction that has a numerator that is greater than the denominator. For example, [tex]\frac{3}{2}[/tex] is a improper fraction.

To convert [tex]\frac{51}{27}[/tex] and [tex]\frac{17}{8}[/tex] into common denominators, we need to multiply the denominators, like we did above.

The new fractions will look like this:

To solve for the numerators, we can use these equations:

The fractions now look like this:

Now, convert them to mixed numbers.

Therefore, 5 thirds + 2 ninths < 1 9/8.

The solution for the equation is x = 65.

Equation is a physical and mathematical statement that describing physical sonoma nadigai the relationship between different physical quantity typically consist of pramod variable richard simple representing physical quantity and then it personal variable maybe point it such as  that your energy.

This can be determined by solving the equation for x one step at a time.

First, 3 = 5 can be solved by subtracting 3 from both sides,

thus yielding

x = 2.

Then,

5 = 13 can be solved by subtracting 5 from both sides,

thus yielding

x = 8.

Finally,

13 = 65 can be solved by subtracting 13 from both sides,

thus yielding

x = 65. This is the final answer to the equation.

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Answer:

its x=3



Step-by-step explanation:

first x 2/3 to both sides than solve for x

Answer:

1 harmful

Step-by-step explanation:

2 they will be not use if you not use

Step 1: Calculate the initial number of hospitals. In 2000, there were 5,727 hospitals, so the initial number of hospitals (H0) is 5,727.

Step 2: Calculate the rate of change. From 2014 to 2017, the number of hospitals decreased by 156. Therefore, the rate of change (r) is -156.

Step 3: Calculate the equation. The equation for the number of hospitals H in this country t years since 2000 is H = H0 + rt. Substituting in the values from Steps 1 and 2, this gives us H = 5,727 – 156t.

Therefore, the equation for the number of hospitals H in this country t years since 2000 is H = 5,727 – 156t.

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). More than one variable may be present in a linear equation.

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There are 31 bags of  [tex]$\frac{1}{3}[/tex] pound bags of trail mix he can make.

As per the data given:
Diego is making a trail mix for him and his friends to take with them on a hike next week.

He mixes [tex]$4\frac{2}{6}[/tex] pounds of nuts, [tex]$3\frac{3}{6}[/tex] pounds of raisins, and [tex]$2\frac{3}{6}[/tex] pounds of chocolate chips.

Here we have to determine how many [tex]$\frac{1}{3}[/tex] pound bags of trail mix can he make.

First, we have to convert all the mixed fractions to improper fractions.

[tex]$4\frac{2}{6} = \frac{26}{6}[/tex]

[tex]$3\frac{3}{6} = \frac{21}{6}[/tex]

[tex]$2\frac{3}{6} = \frac{15}{6}[/tex]

The total number of pounds he mixed with nuts, peanuts, and chocolate chips.

Add up all the improper fractions.

[tex]$=\frac{26}{6}+ \frac{21}{6} +\frac{15}{6}[/tex]

As all the denominators have the same value we can add all the fractions directly.

[tex]$=\frac{26+21+15}{6}[/tex]

[tex]$=\frac{63}{6}[/tex]

[tex]$=\frac{31}{3}[/tex]

To see how many [tex]$\frac{1}{3}[/tex] bag he can have, we have to divide the total by [tex]$\frac{1}{3}[/tex].

So we have:

[tex]$=\frac{\frac{31}{3} }{\frac{1}{3} }[/tex]

= 31

Therefore the answer is 31.

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The skid marks would be approximately 1.9 ft in length to the nearest foot.

The drag factor of the road is given as 0.97 and the braking efficiency as 90%. To calculate the skid marks, we need to use the coefficient of friction (μ) between the tires and the road surface. The formula for calculating this is: μ = (2 x Drag Factor x Efficiency) / 100.

Therefore, μ = (2 x 0.97 x 0.9) / 100 = 0.0174

Once we have the coefficient of friction, we can use the following equation to calculate the skid marks: Skid Length = Initial Speed x Reaction Time x 0.5 x μ.

Since the speed is given as 35 mi/h and the reaction time is assumed to be 0.75 seconds, the skid marks will be: Skid Length = 35 mi/h x 0.75 s x 0.5 x 0.0174 = 1.9 ft

Therefore, the skid marks would be approximately 1.9 ft in length to the nearest foot.

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In many ways we can use the number -5.

-5 degrees Celsius or -5 degrees Fahrenheit can be used to represent temperatures below freezing. For example, if the outside temperature is -5 degrees Celsius, water will freeze.

Backward Counting: In mathematics, -5 can be used to count backwards from zero. For example, if we subtract 5 from 0, we get -5. This is frequently used when counting down from a starting number, such as in a countdown timer.

Credit Balance: A negative balance or debt owed in a financial account, such as a credit card or loan, can be represented by -5 in accounting. For example, if someone has a -5 dollar credit card balance, it means they owe the credit card company $5. it means they owe the credit card company $5 and have a negative balance on their account.

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Answer:

x = 49

Step-by-step explanation:

We can find the sum of the interior angles of a polygon using the formula

[tex]S_{n}=(n-2)*180[/tex], where n is the number of sides the polygon has.

Because the figure in the picture is a trapezoid and has four sides, we can find the sum of all the interior angles in the polygon by substituting 4 for n:

[tex]S_{4}=(4-2)*180\\ S_{4}=2*180\\S_{4}=360[/tex]

Since we know that the sum of all the angles in the trapezoid is 360, we can find x by subtracting the sum of the angles already given from 360:

[tex]x+118+104+89=360\\x+311=360\\x=49[/tex]

Answer:

1 day

Step-by-step explanation:

Assuming all the electricians work at the same rate, we can use the formula:

(time x workers) = constant

So, if 2 electricians took 5 days, we have:

(5 x 2) = (time x 10)

Simplifying, we get:

10 = time x 10

Dividing both sides by 10, we get:

time = 1

Therefore, it would take 10 electricians 1 day to wire the house.

The probability of having an IQ score below the minimum Mensa IQ is 0.98, or the probability of having an IQ score above or equal to the minimum Mensa IQ is 0.02.

The features of the normal distribution can be used to determine the minimal IQ required to join Mensa if we assume that IQ scores follow a normal distribution. We can determine the IQ score that represents the 98th percentile of the IQ distribution because Mensa members make up the top 2% of all IQs.

We can determine the z-score for the 98th percentile using a typical normal distribution table, which is roughly 2.33. This indicates that the IQ score that is 2.33 standard deviations above the mean IQ is the minimal IQ required to join Mensa.

The formula: can be used if we are aware of the mean and standard deviation of the IQ distribution.

IQ equals (z-score) x standard deviation plus mean.

to determine the Mensa membership cutoff IQ. We are unable to determine the actual IQ score since the question does not include the mean or standard deviation of the IQ distribution.

The following is the probability statement for this issue:

P(IQ minimum Mensa IQ) = 0.02, or P(IQ minimum Mensa IQ) = 0.98, in other words. This indicates that the likelihood of having an IQ score below the minimum Mensa IQ is 0.98 and the likelihood of having an IQ score equal to or higher than the minimum Mensa IQ is 0.02.

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Answer:

A. y = 1/2x + 3

Step-by-step explanation:

y = mx + b

m is the slope, b is the y-intercept

since 1/2 is the slope we now have

y = 1/2x + b

y-intercept is (0,3) which means b = 3 since 3 is the y value

y = 1/2x + 3

The variables t and d are best described by the speed S = d / t.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that During a road trip, Sterling keeps track of the time he spends driving, t, and the distance he drives, d.

The expression for the relation between the distance and the time will be calculated as:-

Speed = Distance / Time

Speed = d / t

Therefore, the speed S = d / t provides the best description of variables t and d.

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sum of the two polynomials is 5x^2 - 5x + 10. The two polynomials we are adding are:

− x 2 + 2 − x 2 + 2 and 3 x 2 − 7 x + 8

A polynomial is an expression consisting of variables and coefficients, combined using only addition, subtraction, and multiplication. The highest power of the variable in a polynomial is called its degree. In this case, both polynomials have degree 2, meaning the highest power of x is x^2.

When adding polynomials, we add the corresponding coefficients for each power of the variable. In this case, we have:

− x 2 + 2 + 3 x 2 = 2x^2

And:

− x 2 + 2 + 3 x 2 − 7 x + 8 = 2x^2 + 2 + 3x^2 - 7x + 8

= 5x^2 - 5x + 10

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D. $128.94. is the total amount of money Nate will earn after taxes when he buys a CD for $1000  The formula for compound interest is:

A = P * (1 + r/n)^(nt), where A is the amount after t years, P is the principal amount, r is the interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.

We can use this formula to calculate the amount of money Nate will have after 5 years:

A = 1000 * (1 + 0.03/4)^(4 * 5) = 1000 * (1 + 0.0075)^20 = 1000 * 1.1629 = 1162.9

The interest earned is 1162.9 - 1000 = $162.9.

And the amount of interest taxed is 20% of $162.9, which is 20% * $162.9 = $32.58.

So, the total amount of interest earned after taxes is $162.9 - $32.58 = $130.32.

Therefore, the correct answer is D. $128.94.

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The solutions of the quadratic equation:

x^2 - 3x - 4 =0

are x = 4 and x = -1

Here we want to solve the quadratic equation:

x^2 - 3x - 4 =0

To do so, we just need to use the quadratic formula, remember that for:

a*x^2 + b*x + c = 0

The solutions are:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Then in this case the solutions are:

[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4*1*-4} }{2*1}\\\\x = \frac{3 \pm 5 }{2}[/tex]

Then the two solutions are.

x = (3 +5)/2 = 4

x = (3 - 5)/2 = -1

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Yes, a plane figure can be transformed in various ways, including translations, rotations, reflections, and dilations.

A translation is a type of transformation that moves all the points in a figure through the same distance and in the same direction. The horizontal and vertical translations, denoted by h and v, respectively, specify the distance and direction of the movement.

For example, if h=2 and v=3, this would mean that the figure is moved 2 units to the right and 3 units up.

In general, the coordinates of a point (x, y) in the translated figure will be (x+h, y+v) in the new figure.

Hence , a plane figure can be transformed in various ways, including translations, rotations, reflections, and dilations.

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Answer: the slope of line c is 7/9 because the slope of a line perpendicular is the opposite (reciprocal) of the slope of the original line.

Step-by-step explanation: