The box plot shows the times for sprinters on a track team.

A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.

Which value does 50% of the data lie above, and what is it called?

48, the lower quartile
50.5, the median
56, the median
53, the upper quartile

Mrs. Tran's son mowed more land than she and 9/28 of the land still need to be mowed.

let us convert all the fractions into equivalent fractions to make our calculations easy.

The land mowed by Mrs Tran = 1/4 x 7/7 = 7/28

The land mowed by her son = 3/7 x 4/4 = 12/28

Hence, we can clearly see that Mrs. Tran's son mowed more land than she.

The total land mowed by both of them = 7/28 + 12/28

                                                                       = 19/28

The total land to be mowed = 1 - 19/28

                                               = (28 - 19)/28

                                               = 9/28

Hence, the land still to be mowed is 9/28.

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The complete question is -

Mrs. Tran mowed 1/4 of the lawn. Her son mowed 3/7 of it. Who mowed more? How much of the lawn still needs to be mowed?

Answer:

Parralel lines are congruent

Step-by-step explanation:

Tbh i would say that RU is congruent to TS because they are both parralel lines to eachother, and parralel lines are always congruent to eachother.

I hope this helps

:))

The value of x from the triangle CAE is x = 6

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔCAE

Now , the second triangle is ΔCBD

And , ΔCAE ≅ ΔCBD

So , Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

And ,

CE / CD = CA / CB

Substituting the values in the equation , we get

( 30.5 + 12.2 ) / 30.5 = ( 15 + x ) / 15

On simplifying the equation , we get

42.7 / 30.5 = ( 15 + x ) / 15

Multiply by 15 on both sides of the equation , we get

640.5 / 30.5 = 15 + x

15 + x = 21

Subtracting 15 on both sides of the equation , we get

x = 21 - 15

x = 6

Therefore , the value of x is 6

Hence , The value of x from the triangle CAE is x = 6

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Answer:

neither

Step-by-step explanation:

The slopes are neither equal nor negative reciprocal.

Answer:

B

Step-by-step explanation:

The lines are B. Neither.

To determine whether two lines are parallel, perpendicular, neither, or coinciding, we can look at their slope. The slope of a line is a measure of how steep the line is. It is calculated by taking the difference in the y-coordinates of two points on the line, and dividing it by the difference in the x-coordinates of those points.

In this case, the two lines have the equations y = -3x + 7 and y = 3x - 7. To find their slopes, we can plug in the coordinates of two points on each line, and then calculate the slope using the formula mentioned above.

For the first line, we can use the points (0, 7) and (1, 4) to calculate the slope:

Slope = (4 - 7) / (1 - 0) = -3

For the second line, we can use the points (0, -7) and (1, -4) to calculate the slope:

Slope = (-4 - (-7)) / (1 - 0) = 3

Since the slopes of the two lines are the opposite of each other (i.e. one is positive and the other is negative), the lines are not perpendicular or coinciding to each other. This means that they do intersect at a right angle, and are not parallel or coinciding. Therefore, the correct answer is B, neither.

Answer: b) increasing

Step-by-step explanation: It seems evident that the sequence is made up of all the odd numbers.

[tex]\begin{gathered} \bold{a_1=1}\\ \bold{a_2=3=a_1+2}\\ \bold{a_3=5=a_2+2}\\ \bold{a_4=7=a_3+2} \\ \bold{a_n=a_{n- 1}+2}\end{gathered}[/tex]

As we can see, in the nth position (any position), we take the value of the previous position and add 2 to it. This leads us to conclude that the sequence is monotonic increasing since as we add 2 to the values, these grow up.

Answer:

Step-by-step explanation: The points that have a distance of 3 units between them are:

N=(1,4) and P=(1,1)

P=(1,1) and R=(1,-2)

P=(1,1) and Q=(3,1)

[tex]\frac{1}{10}[/tex] part of movie the Lonna will watch at night.

As per the given data in question:

Watched movie in morning = [tex]\frac{1}{2}[/tex]

Movie Left to watch = [tex]\frac{2}{5}[/tex]

Subtraction of fractions: Subtracting fractions include the subtraction of two or more fractions with the same or different denominators.

Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.

Movie she watch at night = 1 - Watched movie in morning - Movie Left to watch

Movie she watch at night = 1 - [tex]\frac{1}{2}[/tex] - [tex]\frac{2}{5}[/tex]

LCM denotes the least common factor or multiple of any two or more given integers.

By taking L.C.M

Movie she watch at night = [tex]\frac{(10-5-4) }{10}[/tex]

[tex]=\frac{10-9}{10}[/tex]

Movie she watch at night = [tex]\frac{1}{10}[/tex] Part

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Answer:

3x+10y

Step-by-step explanation:

3x+2y(5) =

3x+2(5)y =

3x+2*5y = 3x+10y

The option that correctly describes the given box plot is; e. approximately half of the males in the sample of customers spent at least as much time in the store as any females in the sample of customers.

A box plot is defined as a method for graphically showing the locality, spread and skewness groups of numerical data through their quartile.

Some of the terms in box plot is as follows;

Minimum Score; This is the lowest score, that excludes the outliers (located at the end of the left whisker).

Lower Quartile; This is twenty-five percent of scores that fall below the lower quartile value (the first quartile).

Median; This is the mid-point of the data and is shown by the line that divides the box into two parts.

Now, looking at the box plot in the given attachment, we see that the middle line on a boxplot graph is the same as the median of the data, which for the males was equivalent to the highest value for females. This tells us that approximately half of the males spent more time in the store than any females.

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The graph of the linear function is attached below as it passes through the origin

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line.

where;

Assuming we let;

We can write a linear function to model the problem given as

4x + 2y = 20

Graphing this linear equation;

Kindly find the attached graph below.

b) The graph of the linear function shows a straight line passing through the origin of the graph which is at a coordinate (0, 0)

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Let the number of popcorns be x and number of drinks be y.

The cost of popcorns is 4x and the cost of drinks is 2y as per question.

The total amount can be spent is $20.

It can be represented as function:

Simplify by dividing both sides by 2:

The intercepts are:

The graph is attached. It contains the line between the x- and y-intercepts

Using integer values of one variable between the intercepts helps to determine the other variable, that limits the spending amount to $20.

Example:

The values of a function represent the actual values of the function.

X has a value of 5.

An expression, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). Functions abound in mathematics, and the sciences rely on them to build physical links.

If any vertical line drawn through the graph may only cross it once, it is a function. If there are any points on the graph where a vertical line might cross it twice or more, the graph is not a function.

In a spreadsheet program, a function is a programmed calculation, whereas an Excel formula is an equation that the user has developed.

The functions are

f(x) = 2.5x - 10.5

g(x) = 64(0.5x)

x = 3 to 5 results in:

f(3) = 2.5(3) - 10.5 = -3

f(4) = 2.5(4) - 10.5 = -0.5

f(5) = 2.5(5) - 10.5 = -2

x = 3 to 5 results in:

g(3) = 64(0.5³)= 8

g(4) = 64(0.5x4) = 4

g(5) = 64(0.5x 5)= 2

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Answer:

x = - 2 , x = 6

Step-by-step explanation:

x² - 4x = 12 ( subtract 12 from both sides )

x² - 4x - 12 = 0 ← in standard form

to factor, consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 4)

the factors are - 6 and + 2 , since

- 6 × 2 = - 12 and - 6 + 2 = - 4 , then

(x + 2)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 6 = 0 ⇒ x = 6

Answer:

Step-by-step explanation:

a) 10/18 · 9/17

5/9 · 9/17

5/17

b) 8/18 · 7/17

4/9 · 7/17

28/153

c) 10/18 · 8/17

5/9 · 8/17

40/153

Answer:

[tex]\textsf{a)} \quad \dfrac{5}{17}=29.4\%[/tex]

[tex]\textsf{b)} \quad \dfrac{28}{153}=18.3\%[/tex]

[tex]\textsf{c)} \quad \dfrac{40}{153}=26.1\%[/tex]

Step-by-step explanation:

Bag of 18 fruit drop sweets:

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

The probability of the first sweet chosen being apple flavoured is:

[tex]\implies \sf P(apple)=\dfrac{10}{18}[/tex]

Now there are 9 apple flavoured sweets and a total of 17 sweets remaining, so the probability of choosing a second apple flavoured sweet is:

[tex]\implies \sf P(apple)=\dfrac{9}{17}[/tex]

Therefore, the probability of both sweets being apple flavoured is:

[tex]\implies \sf P(apple)\;and\;P(apple)= \dfrac{10}{18} \times \dfrac{9}{17}=\dfrac{5}{17}[/tex]

The probability of the first sweet chosen being blackberry flavoured is:

[tex]\implies \sf P(blackberry )=\dfrac{8}{18}[/tex]

Now there are 7 blackberry flavoured sweets and a total of 17 sweets remaining, so the probability of choosing a second blackberry flavoured sweet is:

[tex]\implies \sf P(blackberry )=\dfrac{7}{17}[/tex]

Therefore, the probability of both sweets being blackberry flavoured is:

[tex]\implies \sf P(blackberry )\;and\;P(blackberry )= \dfrac{8}{18} \times \dfrac{7}{17}=\dfrac{28}{153}[/tex]

The probability of the first sweet chosen being apple flavoured is:

[tex]\implies \sf P(apple)=\dfrac{10}{18}[/tex]

Now there are 9 apple flavoured sweets, 8 blackberry sweets, and a total of 17 sweets remaining, so the probability of choosing a blackberry flavoured sweet is:

[tex]\implies \sf P(blackberry)=\dfrac{8}{17}[/tex]

Therefore, the probability of the first sweet being apple flavoured and the second sweet being blackberry flavoured is:

[tex]\implies \sf P(apple)\;and\;P(blackberry)= \dfrac{10}{18} \times \dfrac{8}{17}=\dfrac{40}{153}[/tex]

Answer: The mean score for this class is 17.13.

Step-by-step explanation:

Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249

Add the mean score for the girls: 249 + 8 = 257

Add up the number of students in the class: 10 + 5 = 15

Divide the total score by the number of students to find the mean: 257 / 15 = 17.13

What do you understand by mean and how many methods are there to find it ?

Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:

Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.

Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.

There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.

To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys. We have: 78+58+79+45+39 = 249

Next, let's add the mean score for the girls, which is 8.

So the total is now: 249 + 8 = 257.

Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.

Therefore, the mean score for this class is :

257/15 = 17.13.

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The mean score for this class is 17.13.

Add up all of the scores for the boys: 78 + 58 + 79 + 45 + 39 = 249

Add the mean score for the girls: 249 + 8 = 257

Add up the number of students in the class: 10 + 5 = 15

Divide the total score by the number of students to find the mean: 257 / 15 = 17.13

What do you understand by mean and how many methods are there to find it?

Mean is a statistical term that refers to the average value of a set of data. There are two main methods for finding the mean:

Arithmetic mean: This is the most common method of calculating the mean. It is simply the sum of all the values in the set of data, divided by the number of values in the set.

Geometric mean: This method is used when the data set includes both positive and negative values. It is the nth root of the product of all the values in the set, where n is the number of values in the set.

There are also other methods for finding the mean, such as the harmonic mean, the weighted mean, and the trimmed mean, but these are less commonly used.

To find the mean score for the entire class, we need to add up all of the scores and divide by the total number of students. First, let's start by adding up all of the scores for the boys.

We have: 78+58+79+45+39 = 249

Next, let's add the mean score for the girls, which is 8.

So the total is now: 249 + 8 = 257.

Now we need to divide this total by the number of students in the class to find the mean score. There are 10 boys and 5 girls in the class, for a total of 10 + 5 = 15 students.

Therefore, the mean score for this class is :

257/15 = 17.13.

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In the given graph of the function, the function is not differentiable for values of x is -1 and 2.

Therefore the answer is -1 and 2.

In the given graph we can observe that the graph is not continuous at x = -1 and also that there is a sharp corner at x = 2.

The condition for differentiability of a function is that it should be continuous. Also a function is not differentiable at a corner point as the slope is not defined at that particular point.

Therefore, the values of x at which the given graph is not differentiable is x = -1 and x = 2.

--The question is incomplete without the figure, answering to the figure attached--

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Answer:

The ratio of a to b is 3:5, which means that the value of a is 3/8 of the value of b. This means that if the difference between the angles a and b is 36°, then the size of angle a is 3/8 * 36° = 9°.

To find the size of angle C, we need to add the size of angle a to the size of angle b. Since the size of angle a is 9° and the difference between the sizes of angles a and b is 36°, the size of angle b is 36° + 9° = 45°.

The size of angle C is the sum of the sizes of angles a and b, so the size of angle C is 9° + 45° = 54°. Therefore, the size of angle C is 54°.

To find the account balance at the end of the first year, we need to calculate the amount of interest earned. The interest rate is 6%, or 0.06. The initial balance is $6,000, so the interest earned is 0.06*$6,000 = $360.

Adding the interest to the initial balance gives us the account balance at the end of the first year: $6,000 + $360 = $<<6000+360=6360>>6360.

Therefore, the account balance at the end of the first year will be $6360.

When two friends are playing a video game where the player goes on quests to earn coins with an average number of 2000 coins earned in a quest, if one plays an average of 20 quests a day and other play 5 quests a day, none of them are likely to record an average earning below 1500 coins in a day.

Therefore the answer is both Heather and Suzanne are less likely to record an average earning below 1500 coins.

Here the average number of coins earned in a quest is not dependent on the number of quests played in a day. So for both Heather and Suzanne the average earning is to be 2000, so they are less likely to earn below 1500 coins.

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The inequality describes the problem of a local ice cream shop has a parking lot with enough space for 18 cars is x + 7 ≤ 18

In mathematics, an inequality describes a relationship between two values of an algebraic expression that are not equal. “If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then, this relationship is called an inequality." For example, x>8 (x should be greater than 8).

We have, a local ice-cream shop has a parking lot with enough space.

The maximum number of cars will be parked in parking lot = 18.

At right now, the number of cars in parking lot= 7. Let assume that x be number of more cars can park in the lot. We have to express this in form of an Inequality. Total cars in parking lot = 7 + x but this number of cars cannot exceed the 18 , so x + 7 ≤ 18

Hence, required Inequality is x + 7 ≤ 18.

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Answer:

450%<cube root of 92

Step-by-step explanation:

Answer:

First one

Step-by-step explanation:

first one because of the 2 letters which occur the same number an causing a little change

Answer: look at explanation <3

Step-by-step explanation:

Steps to find the equation of a line from two points:

Find the slope using the slope formula

Use the slope and one of the points to solve for the y-intercept (b).

One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

The probability that at least one will have defect is 0.1855 if a manufacturing machine has a 5 % defect rate.

If manufacturing machine has 5% defect rate. The probability is ration of the number of favorable outcomes.  Probability is the branch of math in which we calculate he number of observation and favorable outcomes of a certain event to be occur. if the manufacturing company has 5% defect rate then there is also to find the number probability of non defect rate.   so,  

Probability of defect (p) = 0.05 

Probability of non defect (q) = 1- 0.05 = 0.95 

4 items are chosen at random .

We have to calculate the probability that at least one will have a defect.

Now ,

P ( at least one will have defect ) = 1 - P ( None will have defect )

P ( none will have defect) = 1 × 1 × 0.81450625

P (none will have defect) = 0.81450625

putting the value we get,

P ( at least one will have defect) = 1 - 0.81450625

P ( at least one will have defect) = 0.18549375

P ( at least one will have defect) = 0.1855

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The graph that represents the number line is number line with closed circle on point on negative 2 with arrow shaded right

Information from the problem include

graph represents the solution to the inequality 1.5 is greater than or equal to the product of a number and −0.75

The word problem is solved first, let the number be x

1.5 ≥ -0.75x

1.5 / -0.75 ≥ -0.75x / -0.75

dividing both sides by negative 0.75 will make the less than or equal to sign change to greater than or equal to

-2 ≤ x

the solution of the inequality is -2 ≤ x

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The percentage decrease when original is 180 and the new is 150 is 16.7%

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

In this case, the original is 180 and the new is 150. The percentage decrease will be:

= (180 - 150) / 180 × 100

= 30/180 × 100

= 1/6 × 100

= 16.7%

The percentage is 16.7%

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The measure of z on the right triangle shown at the end of the answer is given as follows:

z = square root of 80.

To obtain the measure of z, the first step is obtaining the measure of y, which is obtained using the geometric mean property, as follows:

y = square root of (16 x 4) = square root of 64 = 8.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

For the smaller right triangle, we have that:

Then the length of the hypotenuse z is obtained applying the Pythagorean Theorem as follows:

z² = 4² + 8²

z² = 16 + 64

z² = 80

z = square root of 80.

The triangle is given by the image shown at the end of the answer.

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Answer:

Read it carefully below

Step-by-step explanation:

Based on the formula you provided, the function appears to model exponential decay. In general, exponential decay occurs when the growth rate of a quantity is proportional to its current value, and the growth rate is a fixed constant less than 1.

In this case, the growth rate is given by the constant factor 7/3 (which is less than 1), and the function uses the variable t as the exponent. As t increases, the value of the function decreases exponentially.

False. Consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices.

The highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices.The definition of a minimum spanning tree states that it is a subset of edges of a graph that connect all of the vertices without forming any cycles, and with the minimum total weight. If a graph contains an edge with the highest weight, it may still be included in the MST if it is the only connection between two vertices. To illustrate this, consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices. In this case, the highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices, and thus the minimum total weight is achieved.

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Answer: x = 40 degrees

Step-by-step explanation:

Quick Maths

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

so,

180 = 60 + 80 + APQ

APQ = 180 - 60 - 80 = 40°

the triangles APQ and ABC are similar. one meaning of that is that they have the same angles.

so,

x = angle APQ = 40°