This question has two parts. First, answer Part A. Thenanswer Part B

Part A

BAKERY Aisha can work up to 20 hours per week Working at a bakery, she earns $7 per hour most of the time and $ 8.50 per hour during the early morning shift. Aisha needs to earn at least $150 this week to pay for a trip with her friends. Determine the number of regular and early morning hours that Aisha could work

Part A Select the correct system and graph. Let r=regular hours and m = early morning hours

R<20
7r+8.5m>=150

R+m <=20
r+m<=150

r+m<= 20
7r+ 8.5m >= 150

7r+8.5m>20
7r+8.5m>= 150

Part B
Drag every viable solution to the bin.

Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.

Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.

Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.

Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.

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From the survey of 50 people 20 people like chocolate.

A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.

To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.

The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both

= 30 - 10= 20

This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.

Therefore, 20 people like chocolate.

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Answer:

Step-by-step explanation:

m∠O = 90° - 34° = 56°

cos M = [tex]\frac{MN}{MO}[/tex]  ⇒  MO = [tex]\frac{12}{cos34}[/tex] ≈ 14.5 cm

tan M = [tex]\frac{ON}{MN}[/tex]  ⇒  ON = 12 × tan 34° ≈ 8.1 cm  

Answer:

(3480 - 600)/2 = 1440cm

Step-by-step explanation:

The result of each trigonometric functions are:

a) sin X = 7√149 / 149

b) sin Z = 10√149 / 149

c) cos X = 10√149 / 149

d) cos Z = 7√149 / 149

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows

sin X = YZ / XZ = 7 / √149

cos X = XY / XZ = 10 / √149

sin Z = XY / XZ = 10 / √149

cos Z = YZ / XZ = 7 / √149

To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:

sin X = 7√149 / 149

cos X = 10√149 / 149

sin Z = 10√149 / 149

cos Z = 7√149 / 149

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The given question is incomplete, the complete question is:

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

Over a year, the Blue Valley Glacier typically moves about the same distance as the Silver Lake Glacier, and Blue Valley has the same variability in its annual movement compared to Silver Lake.

The median annual movement of the Blue Valley Glacier is 300.2 feet, and the interquartile range is 14 feet.

The interquartile range indicates the spread of the data within the middle 50% of the data

So we know that the annual movement of the Blue Valley Glacier falls within a range of 300.2 ± 7 feet (i.e. 293.2 to 307.2 feet)

Similarly, the median annual movement of the Silver Lake Glacier is 300.4 feet, and the interquartile range is also 14 feet

So the annual movement of the Silver Lake Glacier also falls within a range of 300.4 ± 7 feet (i.e. 293.4 to 307.4 feet)

Since the ranges for both glaciers overlap and have the same size, we can conclude that they typically move about the same distance over a year, and that the variability in the annual movement of Blue Valley is comparable to that of Silver Lake.

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When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.

The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.

Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.

The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.

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Using  the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)

We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:

-4x + y = 3 (Equation 1)

5x - 2y = -9 (Equation 2)

Solving Equation 1 for y, we get:

y = 4x + 3

Now, we substitute this expression for y into Equation 2 and solve for x:

5x - 2(4x + 3) = -9

5x - 8x - 6 = -9

-3x = -3

x = 1

We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:

-4(1) + y = 3

y = 7

Therefore, the solution to the system of equations is (x, y) = (1, 7)

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When a point is rotated, it must be rotated around a point.

See attachment for the image of the rotation about point K

We should note the following:

In order to construct triangles, you will need a protractor, a pair of compasses and a ruler. To draw the triangle, three properties must be taken into account: length, angle and shape

The given parameters are:

ΔEFG

The angle of rotation is

∅ = 180⁰

The above angle of rotation means that:

The translated triangle will be 180 degrees from ΔEFG about point K.

It also means that:

ΔEFG and ΔE'F'G' will be equidistant from point K

See attached image for ΔE'F'G'

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There are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.

There are a total of 6 outcomes for the rolling cube and 3 outcomes for picking a card. To find the total number of outcomes, we can use the multiplication rule of counting:

Total number of outcomes = number of outcomes for picking a card x number of outcomes for rolling a cube

Total number of outcomes = 3 x 6 = 18

Therefore, there are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.

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The solutions for the systems of inequalities are:

a) (0, -100), (0, -150), (0, -1000)

b)  (0, 50), (0, 55) , (0, 1,204).

When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.

The first one is:

y ≤ x - 8

y < -3x - 9

Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:

-100  ≤ 0 - 8 = -8

-100 < - 3*0 - 9 = -9

Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.

For the second system:

y > 5x + 1

y > 3

Let's do the same thing, x = 0 and y gets really large values, like y = 50

50 > 5*0 + 1 = 1  this is true.

50 > 3   this is true.

so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).

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Answer:

The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:

(10a-6) + (7a+4) + (7a+4) + (10a-6)

Simplifying the expression:

= 34a - 4

Therefore, the perimeter of the quadrilateral is 34a - 4.

Answer:

2125 ft/min

33,000 ft

y = -2125x + 33,000

Step-by-step explanation:

A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).

B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.

C. Plug in the values you got for A and B into the slope formula y = mx + b

y = -2125x + 33,000

In mathematics, a logarithm is a mathematical operation that determines how many times a given number (known as the base) must be multiplied by itself to produce another given number.

Logarithms are used to simplify complex calculations involving exponents and to convert between exponential and logarithmic expressions.

The logarithm of a number x to a given base b is represented as logb(x). For example, log10(100) = 2 because 10 multiplied by itself twice equals 100.

Logarithms have a wide range of applications in various fields, including mathematics, physics, engineering, finance, and computer science. They are particularly useful in scientific calculations involving large numbers, where working with exponents can become cumbersome. Logarithms are also used in the study of exponential growth and decay, as well as in the analysis of data sets with a wide range of values.

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In the given elementary matrix, the corresponding elementary row operation is multiplication of the second row of a given matrix with a scalar of 5. The given matrix is an elementary matrix because it can be obtained by multiplying an identity matrix by an elementary matrix. The inverse of the given matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix.

The given elementary matrix is:
[1 0 0]
[0 0 5]
[0 1 0]

The corresponding elementary row operation for this matrix is multiplication of the second row of a given matrix with a scalar of 5. This means that if we have a matrix A and we multiply the second row of A with a scalar of 5, we get a new matrix B which is represented by the above elementary matrix.

The inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]

The inverse of a given elementary matrix can be obtained by applying the inverse of the corresponding elementary row operation to an identity matrix. In this case, the inverse of the given elementary matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix. This gives us the above inverse matrix.

Therefore, the corresponding elementary row operation for the given matrix is multiplication of the second row of a given matrix with a scalar of 5 and the inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]

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Answer: The cost of painting is Rs.254.4

Step-by-step explanation:

let  l and b be the sides

        b=3m 20 cm=3.20m    

                                          = 5.30×3.20

                                           =16.96m²

We are given that, the measures of sides of blackboard are 5 m 30 cm and 3m 20 cm.

__________________________________________

[tex] \bf \implies5 m + 30 cm \\ [/tex]

[tex] \sf \implies 5 m + \dfrac{30}{100}m \\ [/tex]

[tex] \sf \implies 5 m + \dfrac{3\cancel{0}}{10\cancel{0}}m \\ [/tex]

[tex] \sf \implies 5 m + 0.3 m \\ [/tex]

[tex]\purple{ \bf \implies 5.3~ m } \\ [/tex]

[tex] \bf \implies3 m + 20 cm \\ [/tex]

[tex] \sf \implies 3 m + \dfrac{20}{100}m \\ [/tex]

[tex] \sf \implies 3 m + \dfrac{2\cancel{0}}{10\cancel{0}}m \\ [/tex]

[tex] \sf \implies 3 m + 0.2 m \\ [/tex]

[tex] \purple{\bf \implies 3. 2 ~m} \\ [/tex]

_______________________________________________

[tex] \pink{\frak{\implies Area _{(Blackboard) }= Length \times Breadth ~m^2}} \\ [/tex]

[tex] \sf \implies Area _{(Blackboard) } = 5.3 \times 3.2 ~m^2 \\ [/tex]

[tex] \sf \implies Area _{(Blackboard) } = 16.96 m^2 \\ [/tex]

[tex] \sf \implies 15 \times 16.96 \\ [/tex]

[tex] \pink{\sf \implies Rs ~254.4 } \\ [/tex]

They would each need to sell 5 bicycles to make the same amount of money and if they both sell 5 bicycles, they would each make $500.

What do you mean by finding the break-even point ?

The key concept used here is the idea of finding the break-even point between two scenarios. In this case, the break-even point is the number of bicycles that Jim and Tom each need to sell in order to make the same amount of money. This is found by setting their total earnings equal to each other and solving for the number of bicycles. Once the break-even point is found, the total earnings for that number of bicycles can be calculated by plugging it back into the original equations. This concept is commonly used in business and finance to determine the minimum level of sales needed to cover costs and make a profit.

Calculating the number of bicycle and money :

To make the same amount of money, Jim and Tom would have to each sell the same number of bicycles, let's call it "b".

So Jim would make a total of:

250 + 50b dollars

Tom would make a total of:

400 + 20b dollars

To find the value of "b" where they both make the same amount of money, we can set the two expressions equal to each other and solve for "b":

250 + 50b = 400 + 20b

30b = 150

b = 5

Therefore, they would each need to sell 5 bicycles to make the same amount of money.

To find out how much they would make, we can substitute "b=5" into either of the expressions above:

Jim:

250 + 50(5) = $500

Tom:

400 + 20(5) = $500

Therefore, if they both sell 5 bicycles, they would each make $500.

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Answer:

Use the quadratic formula to solve. Show work describe solution.

Step-by-step explanation:

The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.

For example, let's say we have the equation 2x^2 + 5x - 3 = 0.

Here, a = 2, b = 5, and c = -3.

Plugging these values into the quadratic formula, we get:

x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)

Simplifying the expression inside the square root:

x = (-5 ± sqrt(49)) / 4

x = (-5 ± 7) / 4

We get two solutions:

x = (-5 + 7) / 4 = 1/2

x = (-5 - 7) / 4 = -3

So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.

These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.

The expression represents the difference of 7 and twice the product of a and b is 7 - 2ab

Let's break down the given problem step by step. First, we need to find the product of a and b, which is done by multiplying the two variables together using the multiplication symbol (*). Then, we need to multiply this result by 2, which is done by placing the entire product inside parentheses and then multiplying it by 2 using the multiplication symbol again.

Once we have found twice the product of a and b, we need to subtract it from 7. This can be done using the subtraction symbol (-), which we place between 7 and the expression we just found.

Putting it all together, the expression we get is:

7 - 2ab

where a and b are the two variables we were given.

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Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.

Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.

We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.

Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.

Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.

Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.

Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.

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Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.

Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.

Here,

The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:

2 × (length + width) = 2 × (175 m + 96 m) = 542 m

Therefore, the cost of fencing the garden at 17.50 per meter is:

Cost of fencing = length of fence × cost per meter

= 542 m × 17.50

= 9485

Hence, the cost of fencing the garden is ₹9485.

To find the cost of plowing the garden, we need to first calculate its area, which is given by:

Area = length × width

= 175 m × 96 m

= 16800 m²

Therefore, the cost of plowing the garden at 4.50 paise per square meter is:

Cost of plowing = area of garden × cost per square meter

= 16800 m² × 0.045

= 756

Hence, the cost of plowing the garden is ₹756.

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The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:

Square both sides of the equation to eliminate the square root:

√y = (6/p)x - (2/q)

√y^2 = (6/p)x - (2/q)^2

Simplifying the right-hand side, we get:

y = (36/p^2)x - (4/q) + 4/q^2

Rearrange the equation to the form y = mx + c:

y = (36/p^2)x + (4/q^2 - 4/q)

So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).

Step-by-step explanation:

Answer:

y-intercept is (0,3) and the slope is 3

Step-by-step explanation:

Answer: the slope is 3x while 3 is the y-intercept.

Step-by-step explanation:

Answer:

X≈ 2,37 cm

x= (-11+√637)/6 cm

Step-by-step explanation:

Answer:

y = 3x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (- 1, - 6 )

m = [tex]\frac{-6-6}{-1-3}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 6 )

6 = 3(3) + c = 9 + c ( subtract 9 from both sides )

- 3 = c

y = 3x - 3 ← equation of line

The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.

[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]

[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{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]

Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.

The given problem can be solved using the concept of binomial distribution.

In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.

Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).

Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.

Number of ways = 48C4 = 194,580

Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :

[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]

Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]

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Answer:

7/12 pizzas have been eaten

Step-by-step explanation:

3 + 4= 7

7/12

7-12=5

5 pizzas left