Ben's mom is 22 years older than ben. In 5 years she will be 3 times as old as he will be. How old are they now?

The value of x is 10.66

Complementary angles  is when the sum of two angles is equal to 90 degrees. for example, 30 degrees and 60 degrees are complementary angles.

If the sum of two angles is 90 degrees then we say that they are complementary. Thus, the complement of an angle is obtained by subtracting it from 90. for example the complement of 40° is 90° - 40° = 50°

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

Collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Therefore, the value of x is 10.66

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To create a frequency polygon calculate the midpoint,  locate the midpoints and connect them with lines.

A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.

So, we must determine the midpoint or average of the range for each category.

0 < t < 10 = 5

10 < t < 20 = 15

20 < t < 30 = 25

30 < t < 40 = 35

2. Add a point where the data of the axis Y and X form an intersection.

3. Connect the points.

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3 and 2/3 as a mixed number will be 11/3.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold  Z.

A mixed number is a combination of a whole number and a fraction. It represents a number that is greater than zero but less than the next whole number. A mixed number is written with the whole number followed by a space and then the fraction.

[tex]=3+2/3[/tex]

[tex]=(3*3+2)/3[/tex]

[tex]=(9+2)/3[/tex]

[tex]=11/3[/tex]

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The lower left-hand corner of the graph is the third quadrant.

It contains the negative values of both x and y.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.

Cartesian system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

coordinates

Coordinates are numbers which determine the position of a point or a shape in a particular space.

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Answer: A. To find the number of glass squares each student will receive, we need to divide the total number of squares by the number of students.

We can write this as:

x = number of glass squares per student

x = 1240 / 121

B. To find the number of squares each student will receive, we need to solve for x by dividing 1240 by 121.

1240 ÷ 121 = 10.246753246753247

C. Each student will get 10 whole glass squares.

D. The remainder in this context is the number of glass squares that cannot be distributed evenly among the students. In this case, the remainder is 30. It means that there will be 30 glass squares left over after each student has received 10 squares. It's like remainder in division where after dividing 1240 by 121 the quotient is 10 and the remainder is 30.

Step-by-step explanation:

The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel algorithm over a sequential algorithm.

The differences between parallel algorithm and sequential algorithm are-

Sequential algorithm

Parallel algorithm

Due to capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel algorithm over a sequential algorithm.

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Answer:

the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

Step-by-step explanation:

To find out how many minutes it will take for a bus to cover 5km at a speed of 9km/h, we need to use the formula:

time = distance / speed

In this case, the distance is 5 km, and the speed is 9 km/h. To convert the speed to km/min we can divide 9 by 60.

9 km/h = 0.15 km/min (by dividing 9 by 60)

Now we can substitute the distance and speed into the formula:

time = 5 km / 0.15 km/min = 33.33 min

So, the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

It's important to note that in this problem km/h is the speed and the distance is given in km, so you need to convert it to km/min in order to find the time. Also the time you get will be in minutes.

When working with a normal distribution, you can use the z-score to determine how many standard deviations away from the mean a certain data point is.

Given that the average price for houses in the area is $280,000 and the standard deviation is $12,000, we can use the z-score formula to find the price of a house whose z-score is 2.5:

z = (x - mu) / sigma

where x is the price of the house, mu is the mean price of houses in the area, and sigma is the standard deviation of the price of houses in the area.

In this case, we are looking for the value of x, which is the price of a house whose z-score is 2.5, so we can rearrange the formula to solve for x:

x = (z * sigma) + mu

x = (2.5 * $12,000) + $280,000

x = $350,000

So the price of a house whose z-score is 2.5 is $350,000

It's worth noting that the value of Z-Score 2.5 is considered an outlier, it is usually very rare to find houses that far from the average and standard deviation.

The answer choice which represents a number line for the intersection of the given intervals is; (-∞, 2).

The answer choice which represents a number line for the union of the given intervals is; (-∞, ∞).

It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.

Since the given intervals are; (-∞, 2) and [0,∞).

It follows that the intersection of both intervals is the interval; (-∞, 2).

Also, the interval which represents the union of both intervals is; (-∞, ∞).

Hence, the image which represents both scenarios is attached.

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Answer:

-x

Step-by-step explanation:

3x - y = -2y

add y to both sides

3x = -3y

divide both sides by -3

-x = y

Answer:

v = 1/-3

Step-by-step explanation:

cross multiply

-3v = 1

then:

divide through by the coefficient of v which is -3

-3v/-3 = 1/-3

[tex]-1=\dfrac{1}{3} v[/tex]

Flip:

[tex]\dfrac{1}{3} v=-1[/tex]

Multiply both sides by 3:

[tex]3\times(\dfrac{1}{3} v)=3\times(-1)[/tex]

[tex]\fbox{v = -3}[/tex]

The sides of the triangle having length as  5 units , 12 units and 13 units make a Right Triangle because the condition to form a right triangle is satisfied by the given sides .

The Pythagoras Theorem is used to check whether the sides form a right triangle or not , it  states that square of the lonest side (hypotnuse) of the triangle is equal to  sum of  square of other two sides ( perpendicular and Base) ,

The side lengths of  triangle = 5 units , 12 units and 13 units ,

By  Pythagoras theorem , we have  [tex]13^{2} = 12^{2} + 5^{2}[/tex]

On simplifying ;

we get ;

[tex]169 = 144 + 25[/tex] ;

[tex]169 = 169 ;[/tex]

the condition of Pythagoras theorem is satisfied ,

that means the sides form a right triangle .

Therefore , the side 5 units , 12 units and 13 units  make a right triangle .

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For two numbers to be proportional, they need to be directly increasing or decreasing in a constant ratio.

If Donny makes $9.75 per lawn, we can make a table that looks like this:

1 Lawn = $9.95

2 Lawns = $19.90

3 Lawns = $29.85...

And so on.

You can see this is proportional because it has a constant ratio between both elements.

(1 to 9.95)

So, it is proportional.

The difference in perimeters is 6.

We  have  3  possible  points  for  the  last  vertex.

These  are

[ -1 + 2 , 0 + 4 ]  - [ 2 , -4 ]  =  [  [ 1 , 4] - [2 , - 4 ] =   ( -1, 8  )

The perimeter of this parallelogram = [tex]2 [ \sqrt{(-1-2)^{2} + (8-4)^2]} + 8][/tex]

                                                            = [tex]2 [ \sqrt{9+16}+ 8 ][/tex]

                                                            = 2 [ 5  + 8 ]

                                                            = 26

Another possible  point is

[ 2 + 2, 4 - 4]  - [-1,0] =  [ 4, 0]  - [ -1,0]  = (5,0)

The perimeter of this parallelogram

= [tex]2 [ \sqrt{(5-2)^{2} +(0-4)^{2} } + \sqrt{(2+1)^{2}+ (4-0)^{2} } ][/tex]

= [tex]2 [ \sqrt{3^{2}+ 4^{2} } + \sqrt{3^{2}+ 4^{2} }][/tex]

= [tex]2(\sqrt{25} +\sqrt{25})[/tex]

= 2(5 + 5)

= 20

The third feasible point won't change either the largest perimeter of 26 or the smallest perimeter of 20; therefore, we don't need to calculate it.

Difference = 26-20

                  = 6

Hence, the difference in perimeters is 6.

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"17/8" pounds of apples were left to give to his grandmother.

Since we have given that

The quantity of apples he picked is given by 6.1/2⇒13/2 pounds.

The quantity of apples he picked for his aunt is given by 2.3/4⇒11/4 pounds.

The quantity of apples he picked for his mother is given by 1.5/8⇒13/8 pounds.

So, the total quantity left for his grandmother is given by

first we have to add the quality of apples he picked for his aunt and the number of apples he picked for his mother.

After subtracting from what he picked.

⇒13/2-(11/4+13/8)

⇒13/2-(22+13/8)

⇒13/2-(35/8)

⇒52-35/8

⇒17/8

Hence, 17/8  pounds are left for his grandmother.

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Answer:

Step-by-step explanation:

so

120 = 2x

x = 120 : 2

x = 60

120 = 2 x 60

120 = 120

Answer:

Step-by-step explanation:

a.[tex]1.9[/tex]·[tex]10^{-8}[/tex]=190000·[tex]10^{-13}[/tex]

b.so 190000÷4.2=4523

c.finally, about 4523 times

The slope of the line is given by the equation slope m = 3/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the first point be P = P ( 0 , 1 )

Let the second point be Q = Q ( 2 , 4 )

Now , the slope of the line between the two points is

Slope m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 4 - 1 ) / ( 2 - 0 )

On simplifying the equation , we get

Slope m = ( 3 / 2 )

Therefore , the value of m is 3/2

Hence , the slope of the line is 3/2

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x = liters of solution at 20%

y = liters of solution at 70%

[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{acid only}}&\stackrel{\textit{liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{Sol'n at 20\%}&x&0.2&0.2x\\ \textit{Sol'n at 70\%}&y&0.7&0.7y\\ \cline{2-4}&\\ mixture&50&0.4&20 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.2x+0.7y=20 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies x=50-y}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.2(50-y) + 0.7y=20} \\\\\\ 10-0.2y+0.7y=20\implies -0.2y+0.7y=10\implies 0.5y=10 \\\\\\ y=\cfrac{10}{0.5}\implies \boxed{y=20}[/tex]

According to probability, total number of handshakes will be 36.

Handshakes equal n * (n - 1)/2. This is the case because a handshake between two people is not counted twice and each of the n people can shake hands with n - 1 people (they wouldn't shake their own hand). Any number of people can be calculated using this formula.

The first person will need to shake eight (8) people's hands. Only seven (7) hands will need to be shook by the second person because the first handshake will not be repeated. Due to the same factors as mentioned above, only six (6) people will require a handshake from the third person. This continues until the final person has no one left to shake hands with because everyone has already done so.

The formula to calculate how many handshakes were exchanged is n = 8 + 7 + 6 +... + 1 = 36.

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The absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

population mean assumed to be 2925

sample mean = 2515

standard deviation of sample = 585.

sample size = 15

t-score is indicated because the standard deviation is taken from the sample rather than from the population.

t-score = (x - m) / s

x is the raw score

m is the raw mean of the population

s = standard deviation of sample/sqrt (sample size) = 585/sqrt(15) = 151.6217 rounded to 4 decimal places.

degrees of freedom = 15 minus 1 = 14.

t-score = (2515 - 2925)/151.6217 = -2.7123 rounded to 4 decimal places.

you need to know the confidence level.

at a 95% confidence level, the two-tailed critical t-score with 14 degrees of freedom = plus or minus 1.7613 rounded to 4 decimal places.

since the absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

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If frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week.

a. When they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

b. Based on the calculation both of them has the same amount of weight.

a. Weight

Let d represent the number of dieting days for this happen.

Since Frank gains 2 lb a day or a total of 2d lbs and John loses 3 lb a day for a total of 3d lbs

So,

John's weight = Frank's weight

Hence,

208 - 3d = 160 + 2d

Combine like terms

208 - 160 = 2d + 3d

48 = 5d

Divide both side by 5d

d = 48/5

d = 9.6 dieting days

The amount the weigh

Using John equation

Weigh = 208 - 3(9.6)

Weigh = 208 - 28.8

Weigh = 179.2 lbs

b. The amount they both weigh is the same as John weigh 179.2ilb and Frank as weigh the same.

Using Frank's equation

Weigh = 160 + 2(9.6)

Weigh = 160 + 19.2

Weigh = 179.2 lbs

Therefore when they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

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A distribution is negatively skewed if the mode is larger than the mean. The final answer is C.

In a negatively skewed distribution:

A. the median is larger than the mode.

B. the mean is larger than the mode.

C. the mode is larger than the mean.

D. the mean is larger than the median.

Negatively Skewed Distribution:

left skewed distributions occur when the long tail is on the left side of the distribution. Statisticians also refer to them as negatively skewed. This condition occurs because probabilities taper off more slowly for lower values. Therefore, you’ll find extreme values far from the peak on the low side more frequently than the high side.

The distribution is negatively skewed if the data values are clustered on the right side of the curve causing it to have a peak on the right but a flatter tail on the left side. This happens when the data set has more frequently occurring higher values than lower values.

When the median is closer to the box’s higher values and the lower whisker is longer, it’s a left skewed distribution. Notice that the longer tail extends towards the lower values, making it negatively skewed.

To find out if the data set follows a normal or skewed distribution, the three measures of central tendency (mean, median, and mode) can be compared.

The mean is greater than the median. The mean overestimates the most common values in a positively skewed distribution

The distribution is negatively skewed  if the mean is lesser than the median and the median is lesser than the mode.

The given scenario is the same as negatively skewed I if the mode is larger than the mean. The final answer is C.

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Hello there!

Answer:

33 days

Step-by-step explanation:

Every day you give 5 ml of medicine to 6 donkeys. So you spent 5 ml * 6 = 30 ml per day

1 L = 1000 ml

To find the answer you should volume of bottle divide by 30 ml per day:

1000 ml / 30  = 33.333...

It means that if will be possible to use the bottle 33 days but then it will be left

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

Consider two triangles ABC and XYZ, if ∠ A = ∠X and ∠C = ∠Z then

ΔABC ~ΔXYZ.

If, two triangles ΔABC and ΔXYZ are similar only if,

i)∠A =∠X, ∠B =∠Y and ∠C=∠Z

ii)AB/XY=BC/YZ=AC/XZ

"AAA" means "Angle, Angle, Angle" when we know all three angles of a triangle, but no sides.

If two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

An AAA triangle is a triangle where only the three angles are defined:

α + β + γ = 180°

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On solving the provided question we can say that the new Mean = 610 mean .

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). is 50.

What is mean?

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean).

The mean score is calculated by dividing the total number of tests taken by all of the scores. The mean will therefore rise if you give each test a higher mark. The standard deviation is calculated as the square root of the product of the power of two of all test results, multiplied by the number of tests, and then subtracted from the mean.

Each score you raise by 10 will result in a 10 change in the mean. But as there will be no change in the distance between each score and the mean, the standard deviations will also not change.

Mean = 600

Average deviation is 50.

Scores went up by 10

Mean = 610

Average deviation is 50.

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The probability that either the words BAD or CAB will appear as part of the row  is 16.7%

We have 4 places where we can put the cards.

Let's count the number of possible outcomes for each place.

In the first place, we can put one of 4 cards.

In the second place, we can put one of 3 cards (because one card was taken in the first place).

In the third place, we can put one of 2 cards

In the last place, we can put one of one cards.

The total number of different combinations is the product between the number of options for each place, then we have:

4×3×2×1 = 24

Now we need to count the number of combinations such that the words BAD or CAB appear. We have:

BADC

CBAD

CABD

DCAB

That is 4 out of 24.

Thus, the probability that either the words BAD or CAB will appear as part of the row will be:

P(BAD or CAB) = 4/24 = 16.7%

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The probability is 16.7%