two marathon runners leave the starting gate, one running 10 mph and the other 8 mph. if they maintain the pace, how long will it take for them to be one-half of a mile apart?

The least positive integer we can get as the product is 2.

Here we have the following set of numbers:

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

And we want to take the product between 3 of them and find the least positive integer that we can get as the product.

So it makes sence to choose the smallest absolute value numbers (not zero) such that one is positive and two are negative (we want two negative ones so the signs cancell eachother)

Then we will get:

1*(-1)*(-2) = 2

That is the least positive integer we can get as the product.

Learn more about products at:

https://brainly.com/question/794810

#SPJ1

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.

For more questions like number of hospitals visit the link below:

https://brainly.com/question/21649997

#SPJ4

By graphing the system of equations, we can see that the solution is (4, -2)

Here we want to solve the system of equations:

y = (-3/2)*x + 4

y = (1/2)*x - 4

To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.

The graph can be seen on the image at the end.

We can see that the solution is (4, -2)

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

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

To know more about Polynomial

https://brainly.com/question/15702527

#SPJ4

Answer:

See table below.

Step-by-step explanation:

Enter each x value into the equation x^2+2x+5 to find the value of y.

For example, when x = -2:

x^2-2x+5

(-2)^-2(-2)+5  for x = -2  

4 + 4 + 5

y = 13

======

In the same manner:

x   y

-2  13

-1    8

0   5

1    4

2   5

3   8

The estimate for the number of the paintings that are over 70 years old is given as follows:

56.

The histogram shows the number of observations that appear in each range of the data-set.

12 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:

12/(3 x 2) = 2 units.

Then the estimate of those over 70 years old is given as follows:

Hence the sum is given as follows:

22 + 22 + 12 = 56.

More can be learned about histograms at https://brainly.com/question/25983327

#SPJ1

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.

Learn more about rates at:

https://brainly.com/question/843074

#SPJ1

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.

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

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 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

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

The equivalent answer for the expression mentioned in question is 2x + 5y - 3.

Firstly we will solve the mentioned equation followed by checking each answer. Now, rewriting the equation provided in question -

3x + 5y - x + 2 - 5

Solving the values with x variable and without any variable. For this, we will perform subtraction of. the two pairs.

2x + 5y - 3

Now we see that second option is same as the solved part of the first answer. The first option has 3x and - 3x, which will eventually yield 0, further leaving the equation only with y variable. Therefore, it is the correct answer.

Learn more about expression -

https://brainly.com/question/1859113

#SPJ4

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.

To know more about angle here.

https://brainly.com/question/4316040

#SPJ4

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.

To know more about Probability Statement visit:

https://brainly.com/question/28462288

#SPJ1

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]

The angle 1 and angle 2 are congruent by alternate interior angles.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

1. Angle1 and angle2 are complementary. angle2 and angle 3 are complementary.

= sum of these angles is 180 degree because they are linear angles

2. m angle1+ m angle2 = 90° m/2+m/3 = 90°

=There sum makes right angle

3. m angle1+ m angle2 = m angle2 + m angle3

= sum of both the sides is 180 degree

4. m angle2 = m angle2

= sum of both the sides is equal

5. m angle1= m angle3

= sum of both the sides is equal

6. angle1 congruent angle3

=They are alternate interior angles.

Therefore, by the triangles properties angle 1 and angle 3 are congruent.

Learn more about the triangles;

https://brainly.com/question/2773823

#SPJ1

Answer:

Step-by-step explanation:

To keep the photo in proportion to its negative, you need to maintain the same aspect ratio, which is the ratio of the width to the height of the image. The aspect ratio of the negative is 5.4 cm / 1.35 cm = 4. To maintain this aspect ratio, the aspect ratio of the enlargement must also be 4.

The aspect ratio of the photo paper is 10.2 in / 2.4 in = 4.25. So, the largest length and width that you can use to keep the photo in proportion to its negative is 2.4 in * 4 = 9.6 in and 9.6 in / 4 = 2.4 in, respectively.

Answer:

Step-by-step explanation:

Conversion

First convert the dimensions of the photo paper to centimeters:

[tex]\implies \sf 10.2\;in=10.2 \times 2.54=25.908\;cm[/tex]

[tex]\implies \sf 2.4\;in=2.4 \times 2.54=6.096\;cm[/tex]

Therefore, the dimensions of the photo paper in centimeters are:

To determine the dimensions of the photo if the image is enlarged to fit on a 25.908 × 6.096 cm piece of photo paper, first calculate the scale factor by dividing the shortest side of the photo paper by the shortest side of the negative:

[tex]\sf Scale\;factor=\dfrac{6.096}{1.35}=4.51555...[/tex]

Multiply this scale factor by the longest side of the negative to determine the proportional length of the photo:

[tex]\implies \sf 4.51555...\times 5.4=24.384\;cm[/tex]

As 24.384 cm is less than the longest side of the photo paper, this scale factor will work to keep the photo in proportion to its negative.

Therefore, the largest length and width you can use to keep the photo in proportion to its negative is:

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 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.

Learn more about speed here:

https://brainly.com/question/2004627

#SPJ4

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.

Learn more about frequency table here:

https://brainly.com/question/12576014

#SPJ1

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.

To learn more about Accounting.

https://brainly.com/question/5399294

#SPJ4

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:

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.

To learn more on Inequalities click:

https://brainly.com/question/28823603

#SPJ1

(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.


Learn more about probability here: brainly.com/question/30034780
#SPJ4

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 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.

To know more about Equation click-

https://brainly.com/question/29657992

#SPJ4

Answer:

its x=3



Step-by-step explanation:

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

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

Step-by-step explanation:

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.

Learn more about Plane figure at:

brainly.com/question/28022990

#SPJ1

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.

For more questions on fractions

https://brainly.com/question/17384634

#SPJ4

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.

To know more about an expression follow

https://brainly.com/question/17979041

#SPJ1