Serenity worked as a waitress. She earned $12. 50 per hour and made $175 tips on

Saturday. How many hours did Serenity work if she made a total of $262. 50?

Therefore , the solution of the given problem of slope comes out to be the slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.

Define slope.

The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in

the formula y = 3x - 7.

Here,

The slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.

:  

:  B not equal to 0

The slope is equal to zero according to the null hypothesis, however the slope is not equal to zero according to the alternative hypothesis.

The alternative hypothesis therefore asserts that the slope is not equal to zero, whereas the null hypothesis asserts that the slope is equal to zero.

Therefore , the solution of the given problem of slope comes out to be the slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.

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Answer:

yes

Step-by-step explanation:

[tex]2xA^{3}[/tex]  is a polynomial as a result.  Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.

In mathematics, a polynomial is an expression made up of variables (also known as indeterminates) and coefficients that exclusively uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).

given

[tex]2xA^{3}[/tex]  is a polynomial as a result. Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.

It is impossible to classify an expression as a polynomial if it contains a variable with exponents that are negative or fractional, divides by a variable, or is included inside a radical.

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The expression for area of the rectangles are obtained as x² + 10x + 21 and  x² - 9x + 8 respectively. The correct options for both parts are (C) and (B) respectively.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The dimension of both the rectangles are given as,

First rectangle : (x + 3) and (x + 7)

Second rectangle : (x - 1) and (x - 8)

Since, the area of a rectangle is product of its dimensions.

It can be obtained as,

Area of first rectangle is given as,

⇒ (x + 3) × (x + 7)

⇒ x² + 10x + 21

Area of second rectangle is given as,

⇒ (x - 1) × (x - 8)

⇒ x² - 9x + 8

Hence, the area of both the rectangles are obtained as  x² + 10x + 21 and  x² - 9x + 8 respectively.

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Answer: 14 pieces.

Step-by-step explanation: 1 foot = 12 inches

12 feet of rope = 144 inches of rope

144 / 20 = 7.2 = 7 sections can be cut from each package.

The greatest number of pieces from 2 packages = 14 pieces

Answer

14 pieces

Step-by-step explanation:

First you need to convert the 24 feet into inches. Do this by multiplying 24 (feet) by 12 (inches) since 1 foot has 12 inches in it and you have 12 feet. This means he has 288 inches of rope. Then divide 288 by 20 since he wants to see how many 20 inch pieces he can cut. You should get 14.4 but since it asks for the greatest number of pieces you need to round it down to 14 since he wants full 20 inch pieces.

The value of y from the equation is y = 5

The measure of RS = 38

The measure of ST = 18

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , on the number line , the measures of the sides are

The measure of RS = 7y + 3   be equation (1)

The measure of ST = 2y + 8   be equation (2)

The measure of RT = 56

Now , from the line segment ,

RT = RS + ST   be equation (3)

Substituting the values in the equation , we get

7y + 3 + 2y + 8 = 56

On simplifying the equation , we get

9y + 11 = 56

Subtracting 11 on both sides of the equation , we get

9y = 45

Divide by 9 on both sides of the equation , we get

y = 5

Substitute the value of y in equations (1) and equation (2) , we get

The measure of RS = 7 ( 5 ) + 3 = 38

The measure of ST = 2 ( 5 ) + 8 = 18

Hence , the equations are solved and the value of y = 5

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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

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:

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.

In the given the diagram of a circle, the measure of angle MON is 60°.

A circle is a two-dimensional shape created by a collection of points that are spaced uniformly or uniformly apart from a fixed point (centre) on the plane. The radius of a circle is the fixed distance between each point and the fixed point, which together make up the circle's origin or centre.

All angles add upto 360°

100 + 140 + ∠MOP =  360

∠MOP = 120°

Draw an imaginary straight line extending MO, making MOM'

∠QOM' = 180 - 140

            = 40 = ∠MOQ'  (vertically opposite)

Draw an imaginary straight line extending NO, making NON'

Draw an imaginary straight line extending PO, making POP'

P'OQ = 180 - 100

         = 80 = ∠Q'OP   (vertically opposite)

Draw an imaginary straight line extending QO, making QOQ'

P'OM = 60° = M'OP  (vertically opposite)

Now, ∠N'OQ = 180 - 60 - 2(40)

                     = 20°

Then, ∠P'ON' = 80 - 20

                     = 60

And ∠MON = 40 + 20

                    = 60°

Hence, In the given the diagram of a circle, the measure of angle MON is 60°.

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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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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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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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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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Answer:

14 Quarts

Step-by-step explanation:

1 Gallon = 4 Quarts.

3x4 = 12 + 2 = 14 Quarts.

After solving, the length of the trains in meters is 60 meters.

In the given question, it takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.

We have to find the length (in meters) of the train.

Let the length of the train is x.

The length of the bridge is 100 meters.

As we know that the formula of the speed is the ratio of distance that he traveled in the certain duration of time.

So Speed = Distance/Time

So according to the question;

(x + 100)/40 = x/15

Now solving the expression using the cross multiplication

15x + 1500 = 40x

Subtract 15x on both side, we get

25x = 1500

Divide by 25 on both side, we get

x = 60 meters

Hence, the length of the trains in meters is 60 meters.

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A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds.  4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds

What is endurance race?

A type of motorsport racing known as endurance racing is designed to test both the participants' and the equipment's endurance. Teams of several drivers attempt to travel a long distance in a single race while being allowed to change drivers at any time.

The given table is attached below.

The number of laps in the range 82 to 84 seconds = 1

The number of laps in the range 84 to 86 seconds = 4

The number of laps in the range 86 to 88 seconds = 2

The number of laps in the range 88 to 90 seconds = 4

The number of laps in the range 90 to 92 seconds = 6

The number of laps in the range 92 to 94 seconds = 5

The number of laps in the range 94 to 96 seconds = 2

The number of laps in the range 96 to 98 seconds = 0

Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;

A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds.  4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds.

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Answer:A

Step-by-step explanation:

One of the way by which we can solve equivalent questions is by multiplying both the numerator and the denominator by a same number .

The number chosen for the purpose should be same and should be a non zero number. Example, if we want to find the equivalent of 2/8 then we can simply multiply 2 and 8 which are the numerator and the denominator by a same number say 3 .

Then we will get the result as 2 x 3 /8 x 3 = 6 / 24 .

The result will be a number equivalent to the given fraction. This can be checked by reducing the result to its lowest terms.

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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%

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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When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

given

The grocery store is 31.92 wide overall, with 10 equally wide parking spaces.

If you assume that the width of these 10 parking spaces is equal to the width of the grocery store as a whole, you will have:

10x=31.92

on both sides of the equation, multiply by 10.

10x/10 = 31.92/10

x = 3.192

When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

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The 95% confidence interval for the true mean number of reproductions per hour for the bacteria is given as follows:

(3.78, 4.22)

The bounds of the confidence interval are calculated according to the equation presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]\overline{x} = 4, \sigma = 1.9, n = 283[/tex]

Hence the lower bound of the confidence interval is of:

[tex]4 - 1.96\frac{1.9}{\sqrt{283}} = 3.78[/tex]

The upper bound of the confidence interval is of:

[tex]4 + 1.96\frac{1.9}{\sqrt{283}} = 4.22[/tex]

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The requried inequality to determine the range of body temperature is given as 98.8 ≤ x ≤ 101.2.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
The normal body temperature for an adult horse is 100 degrees F, but it can vary by as much as 1.2 degrees.
Let x be the average temperature of the horse,
100 - 1.2 ≤ x ≤ 100 + 1.2

98.8 ≤ x ≤ 101.2

Thus, the requried inequality determines the range of body temperature is given as 98.8 ≤ x ≤ 101.2.

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The unit rate of constant means that for every 1 pound, the output is 1.96 dollar.

Proportionality is a relationship between two variables in which their ratio is always equal to a constant value. In mathematical terms, it can be expressed as y = kx, where y and x are the two variables, and k is the constant of proportionality.

A rate is a measure of how one quantity changes in relation to another quantity. It is usually expressed as a ratio and has units of measurement, such as miles per hour, dollars per pound, etc. A unit rate is a rate in which the second quantity is one unit of measurement.

The unit rate of the constant of proportionality is found by dividing the change in y (output) by the change in x (input).

In this case:

$9.8/5$ = $1.96$, so the unit rate of the constant of proportionality is 1.96 pounds/dollar.

It means that for every 1 pound, the output is 1.96 dollar.

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Answer:

------------------------------

The product of 7/9 and 6 is:

Answer:

[tex]\textsf{C)} \quad 4\frac{2}{3}[/tex]

Step-by-step explanation:

To find the product of two numbers, multiply them.

[tex]\implies \dfrac{7}{9} \times 6[/tex]

To multiply a fraction by a whole number, first rewrite the whole number as a fraction by dividing it by 1:

[tex]\implies \dfrac{7}{9} \times \dfrac{6}{1}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{a \times b}{c \times d}[/tex]

[tex]\implies \dfrac{7 \times 6}{9 \times 1}[/tex]

Simplify:

[tex]\implies \dfrac{42}{9}[/tex]

Reduce the fraction by dividing the numerator and denominator by the common factor of 3:

[tex]\implies \dfrac{42 \div 3}{9 \div 3}[/tex]

[tex]\implies \dfrac{14}{3}[/tex]

Divide the numerator by the denominator:

[tex]\implies 14 \div 3=4\;\rm remainder\;2[/tex]

The mixed number answer is the whole number and the remainder divided by the denominator:

[tex]\implies 4\frac{2}{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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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]

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.