Learning Task 1: Show the following decimals using grids. Write your
answer in your notebook.
1) 0. 9 2) 0. 1 3) 0. 24 4) 0. 21 50. 11 6) 0. 15​

Answer:

The supervisor started with ___77____ pieces of construction paper.

Step-by-step explanation:

Each student received 3 pieces of construction paper.

There are 25 students.

25 × 3 = 75

The students received 75 pieces altogether.

She had 2 pieces left.

75 + 2 = 77

She started with 77 pieces.

The supervisor started with ___77____ pieces of construction paper.

The length of x for the given shape is 3 cm.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given the shape, and area of the figure is  54 cm²,

the figure is of L shape,

which consist of two rectangles,

the dimensions of the first rectangle are 6 cm by 7 cm

and dimensions of the second rectangle are x cm by 4 cm (reducing 6 from 10)

Area of shape = sum of the area of both rectangles

Area of shape = 6*7 + x*4

54 = 42 + 4x

4x = 54 - 42

x = 12/4

x = 3 cm

Hence the value of x is 3 cm.

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The research hypothesis would be Ha : μ > 80,000.

The research hypothesis for a consumer group testing the claim that a large tire manufacturing company's top line tire will last more than 80,000 miles would be: "The large tire manufacturing company's top line tire will last more than 80,000 miles."

Ha : μ > 80,000

A research hypothesis for a consumer group testing the claim that a large tire manufacturing company's top line tire will average more than 80,000 miles would be Ha : μ > 80,000 miles. The "Ha" stands for the alternative hypothesis, which states that the population mean (μ) of the tire's mileage is greater than 80,000 miles. This hypothesis is chosen because it represents the claim made by the tire manufacturing company and it is what the consumer group is trying to test against the null hypothesis (H0) which is the opposite of the claim, in this case, H0 : μ <= 80,000 miles.

So, the research hypothesis would be Ha : μ > 80,000.

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If a ship is 90 miles South and 20 miles east of Port , then for the captain to travel directly to port , the captain should take a bearing of N 12.53° W .

the distance of ship = 90 miles south and 20 miles east of port .

let the bearing that the captain should take to directly travel to the port is = θ ;

So , the bearing angle can be calculated by using the trigonometric ratio ;

⇒ Tanθ = 20/90 ;

⇒ Tanθ = 2/9 ;

⇒ θ = arctan(2/9) = N 12.53° W   ;

Therefore , The captain should take a bearing of N 12.53° W .

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The Greatest Common Factor(GSF) of -6x12y and -3xy is 3xy.

To find the greatest common factor (GCF) between two numbers or expressions, we need to identify the highest power of each common factor that divides both numbers or expressions.

In this case, we are trying to find the GCF between -6x12y and -3xy.

The prime factorization of the first expression is -6x12y = -2 * 3 * x * 2 * 2 * 3 * y

And, the prime factorization of the second expression is -3xy = -3 * x * y. The common factors between these two expressions are 3, x, and y.

Since, we are finding the greatest common divisor, we neglect the minus sign to obtain the largest value possible.

We can see that both expressions share a factor of 3, x, and y.

Since the GCF is the highest power of each common factor that divides both expressions, in this case, the GCF of -6x12y and -3xy is 3xy.

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Sides [tex]\overline{JM}[/tex] and [tex]\overline{KL}[/tex] are not given to be parallel.

The required part of a bag of popcorn will each student receive is 2/5.

Use "part" when a part of the whole lacks significance on its own; use "a part" when a part of the whole has meaning when combined with other meaningful parts of the same total. For instance, this object is a part of my collection even if my leg is a part of my body.

We have,

4 bags of popcorn for the party and There are 10 students in the class.

Part of popcorn bag each student receive.

Part of popcorn = 4/10 = 2/5

Thus, 2/5 part of bag each  student receive.

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So each student will receive 0.4 bags of popcorn or 4/10 which is 2/5 of a bag of popcorn.

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1. The system of equations is given as follows:

2. The system of equations has no solutions.

The amounts are obtained solving a system of equations, for which the variables are given as follows:

On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships, hence:

4x + 2y = 96.

2x + y = 48.

Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership, hence, spending $72, hence:

2x + y = 72.

The system of equations has no solutions, as the linear functions have the same slope but different intercepts.

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The product of the rational expressions shown is equal to: B. 2x/(x² - 1).

In Mathematics, a rational expression simply refers to a type of expression  which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:

In this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;

Product of numerator = 2 × x

Product of numerator = 2x

For the denominator, we have the following:

Product of denominator = (x + 1) × (x - 1)

Product of denominator = x² - x + x - 1

Product of denominator = x² - 1

Therefor, the product of the rational expressions is given by 2x/(x² - 1).

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El valor de las 18 bandejas es un total de $117.000

$78,000 for 12 bandejas

18 bands:

Bandeja 1:

We must first determine the price of one bandeja in order to determine the price of 18 bandejas.

solo divide 78 ÷ 12 que te dará 6.5 después multiplicas 6.5 × 18 que te dará:117

así que la respuesta es 117 pesos

entonces...

78.000÷12= 6.500

Now we have the price for 18 bandejas.

First, split $78.000 by 12 to determine the cost of each bandeja of eggs.

The result is $6.500, which you will multiply by 18 to determine their cost. This gives us a result or answer of $117.000.

RPTA: The cost of 18 bandejas is $117,000

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The domain of the function h(x)=9x/x(x²-49) is (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).

In math the term called the domain of a function is the set of its possible inputs which is the set of input values where for which the function is defined.

Here we have know the function is h(x)=9x/x(x²-49)

And we need to find the domain of the function.

Here we know that this function is defined for values where the denominator is not equal to zero.

Which is written as,

=> x(x²-49) ≠ 0

When we elaborate the equation based on the difference between the two squares property, it can be written as,

=> x(x + 7)(x - 7)  ≠ 0

Based on this we have identified that the value of x must not be

=> x  ≠ -7, 7, 0

Then the domain of the function is written as,

=> (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).

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Answer:

[tex]\rm{ \dfrac{1250}{7776}\; or\; 0.16075\\\\}[/tex]

Step-by-step explanation:

This probability can be determined using combinatorics. The number of ways a sample of size r can be obtained from a larger set of n items is given by the formula

[tex]C(n,r) = \dfrac{n!}{( r! (n - r)! )}[/tex]

We pronounce C(n, r) as n choose r

We are rolling the die five times. So n = 5

On each roll a 2 can appear or not

We need two 2's . This is our r

The number of ways two 2's can appear is given by 5 choose 2

[tex]C(5,2)\\\\= \dfrac{5!}{( 2! (5 - 2)! )}\\\\= \dfrac{5!}{2! \times 3! }\\\\[/tex]

5! is the factorial of 5, 2! is the factorial of 2 and 3! is the factorial of 3

5! = 5 x 3 x 3 x 2 x1

3! = 3 x 2 x 1

2! = 2 x1

[tex]C(5,2) = \dfrac{5\times 4 \times 3 \times 2 \times 1}{((2 \times 1) \times (3 \times 2 \times 1)}\\\\= 10\\[/tex]

You need not go through this laborious process to find 5 choose 2 there are calculators available

So two 2's can appear 10 times.

The probability of getting a 2 on one roll is 1/6 and the probability of not getting a 2 on a single roll is 1-1/6 = 5/6

This works out to a binomial probability which can be computed by the formula

P(x) = C(n, x) pˣqⁿ⁻ˣ

Where x is the number of times the desired outcome succeeds and n the total number of trials

Here x = 2, n = 5, C(5, 2) = 10

[tex]\rm{So\:P(two\:2s\:on\:5\:throws)\: = 10 \cdot \left(\dfrac{1}{6}\right)^2\cdot \left(\dfrac{5}{6}\right)^3\\\\[/tex]

[tex]{= \dfrac{10 \cdot 1\cdot 125}{{6^5}} = \dfrac{1250}{7776} = 0.16075\\\\[/tex]

The sum of the fractions 1/3 and 2/5 is 11/15.

How can we add two fractional numbers?

For the addition of fractions with the same denominator, we just add the numerators of two fractions, keeping the denominator common. We can then simplify the fraction to the lowest form.

For the addition of fractions with different denominators, we first find the LCM of the denominators and rationalise them. Then we add the numerators and simplify the fraction.

Following the above rules, we can add 1/3 and 2/5.

Now they have different denominators.

LCM of 3 and 5 is 15.

So we rationalise them.

[tex]\frac{1*5}{3*5} +\frac{2*3}{5*3} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}[/tex]

Therefore the sum of the given fractions is 11/15.

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you roll a fair six-sided die with the hopes of rolling a 5 or a 6. these two events are because they have no sample points in common mutually exclusive events

Hence, option (b) is the correct choice.

Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot occur at the same time. The set of outcomes of a single coin toss, which can result in either heads or tails but not both, is a good example.

Events that are mutually exclusive do not occur at the same time. For example, when a coin is tossed, the outcome will be either head or tail, but we cannot obtain both. Such occurrences are also known as disjunct events since they do not occur at the same time.

Events that are mutually incompatible cannot occur at the same moment. Right and left hand turns, even and odd numbers on a dice, winning and losing a game, or running and walking are all examples.

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Answer:

Step-by-step explanation:

y= 12+c

The number of muffins that the quick bread recipe will yield is given as follows:

24 muffins.

The number of muffins that the quick bread recipe will yield is obtained applying the proportions in the context of this problem.

We have that:

Hence the number of muffins that the quick bread recipe will yield is calculated as follows:

6/(1/4) = 6 x 4 = 24 muffins.

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1. The probability of drawing a red or yellow ball from a standard set of pool balls is 4/7.

2. The probability of first getting a 3 and then getting another odd number is 1/12.

1. Tom has a standard set of pool balls, which includes 7 different colored balls: red, yellow, blue, purple, orange, green, and black. There are 2 red balls and 2 yellow balls out of 7 total balls.

To find the probability of drawing a red or yellow ball, we will add the probabilities of drawing each color separately.

Probability of drawing a red ball = 2/7

Probability of drawing a yellow ball = 2/7

Probability of drawing a red or yellow ball = (2/7) + (2/7) = 4/7

Hence, the probability of drawing a red or yellow ball is 4/7.

2. If a single die twice, the total possible outcomes are =  6x6 = 36.

To find the probability of getting a 3 on the first throw and then getting another odd number on the second throw, we have to find the number of outcomes that meet these conditions and then divide it by the total number of outcomes.

First throw: 3 (1 outcome)

Second throw: odd number (3, 5) (3 outcomes)

So there are a total of 1x3 = 3 outcomes that meet the given conditions.

Thus, Probability = 3/36 = 1/12

So, the probability of first getting a 3 and then getting another odd number is 1/12.

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Using the equation y = 50x/3 + 350, Beth will have $700 after 21 months.

We have to determine how much money Beth will have after 21 months.

The equation is:

y = 50x/3 + 350

The value of x = 21.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variables is an expression when it implies that equations in the variable share the same value.

Putting the value of x in equation y = 50x/3 + 350

y = (50×21)/3 + 350

y = 50 × 7 + 350

Simplify

y = 350 + 350

y = 700

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Answer:

50 to 7

Step-by-step explanation:

number of stars to number of red stripes

all acceptable ways to represent ratios:

50 to 7

50 : 7

50 over 7

After class, Mrs. Sandoval picked up several pieces of paper containing students' work from the floor and  Mrs Sandoval probably picked up the pieces of paper because she wanted to properly dispose of them.

The second reason for her act is she may have also wanted to make sure that students' work was not lost or damaged.

A thing is an action when it is carried out, not just thought about or said. A person might do anything from blink to invade a nation. Agere, a Latin verb that means "to do," is where action originates.

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Answer:

Step-by-step explanation:

No, The Salk vaccine study found that it did not prevent polio but rather caused it in youngsters.

Data is information that has been converted into a format that can be moved or processed effectively in computers. Data is information that has been translated into binary digital form for the computers and transmission mediums of today. Both a singular subject and a plural subject can be used when referring to data.

A collection of information, whether numerical or not, can take any shape and is referred to as data in mathematics. Calculable information, such as student test scores, employee salaries, football team member heights, etc., is known as numerical data and is always gathered in numerical form. facts compiled in the form of words, statistics, measurements, and observations. discrete information.

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If Kylie invested $2800 for interest rate of 5(1/2)% compounded annually and Ariana invested $2800 at rate of  5(3/4)% compounded continuously , then  after 12 yrs Ariana would have $259.023 more than Kylie.

We have to find the difference in amount of money in the Kylie and Ariana's accounts after 12 years, we need to calculate the value of each investment after 12 years .

For Kylie's investment:

The formula for calculating the future value of a sum invested at a interest rate compounded annually is:

Value = Principle × (1 + r)ⁿ

Where:

Amount invested (P) = 2800 ;

r = interest rate = 5(1/2)% = 11/2% = 5.5% = 0.055  ;

n (time) = 12 years

⇒ Value = $2800 ×  (1 + 0.055)¹²

= $2800 ×(1.055)¹²

= $5323.38 .

For Ariana's Investment , the rate is compounded continuously ;

the future value can be calculated by using exponential function ;

Value = 2800 × e^(rt) ;

Where: initial investment = 2800 ;

r = interest rate = 5(3/4)% = 23/4% = 5.75% = 0.0575  and

n (time) = 12 ;

⇒ Value = $2800 × e^(0.0575×12)  

= $5582.403  .

Therefore , After 12 years Ariana would have $5582.403 and Kylie would have $5323.38, Ariana would have $259.023 more than Kylie.

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If we are interested in the number of customers in the two queues that will form for the counters, we would take all the ordered pairs in the form of (x,y) as sample space.

The suitable sample space for the number of customers in the two queues formed in the post office should be the set of all possible combinations of the number of customers in each queue formed. This can be represented in the form of a set of ordered pairs, in which the first element of the ordered pair would represent the number of customers in the first queue and the second element of the same ordered pair would represent the number of customers in the second queue.

For example, if we consider a maximum of 15 customers in the first queue and a maximum of 20 customers in the second queue, the sample space would consist of all the ordered pairs in the form of (x,y),

where x will represent the possible number of customers in the first queue ranging from 0 to 15

and y will represent the possible number of customers in the second queue ranging from 0 to 20.

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The mathematical model of communication would classify this issue as channel capacity.

The greatest quantity of data that can be transferred error-free across a communication channel, such as a mobile phone network, is represented by the channel capacity. In this instance, the phone's battery power determines the channel capacity. As the battery depletes, the phone's ability to send and receive information declines, making it impossible to hear the person on the other end of the line.

Communication models are streamlined depictions of the communication process. Most models attempt to explain both verbal and nonverbal communication, and frequently regard it as a message-exchange. Their purpose is to provide a concise picture of the intricate communication process.

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Variability in a production process is a crucial indicator of the process's quality. A significant variance frequently represents a chance to improve the process by figuring out how to lower the variance.

It will be stated as, what machine 1's mean is.

[tex]x1= \frac{2.95+3.16+3.2+3.45+...+3.35+3.12}{25} =3.3284[/tex]

Thus, machine 1's average is 3.3284.

Following that, we'll provide the variance of machine 1.

[tex]s21= \frac{∑(x−¯x1)^{2} }{n−1 } \\ = \frac{(2.95−3.3284)2+(3.16−3.3284)2+...+(3.12−3.3284)^{2} }{24} =0.0489[/tex]

So machine 1 has a variance of 0.0489.

I'll provide the machine 2 mean as,

[tex]x2= \frac{3.22+3.38+3.30+...+3.33}{22} =3.27[/tex]

Therefore, machine 1's mean value is 3.2782.

Following that, the variance of machine 2 will be given as.

[tex]s22= \frac{∑(x−¯x2) ^{2} }{n−1} \\ [/tex]

[tex]\frac{(3.22−3.2782)2+(3.38−3.2782)2+(3.30−3.2782)2+...+(3.33−3.2782)^{2} }{21} \\ =0.0059[/tex]

Thus, machine 2's variance is 0.0059.

Here are the proposed hypotheses:

[tex]H0:σ21=σ22 \\ H1:σ21>σ22[/tex]

To verify the theory, the F-test will be applied. The test statistic is as follows:

[tex]TS= \frac{s21}{s22} × \frac{σ22}{σ21} \\ =0.04890.0059=8.29[/tex]

As will be used to calculate the p-value.

P(F24,21>8.29)=1−0.99999=0.00001.

The null hypothesis will be rejected because the p-value is less than the level of significance of 5%. This indicates that machine 1 offers a greater opportunity for quality improvements.

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If the triangle has sides with lengths of 49 cm, 68 cm, and 92 cm , then the triangle is not a Right Triangle .

If the Triangle is a right triangle , then the sides of the triangle should satisfy the Pythagoras Theorem which states that the sum of the square of two smaller sides is equal to square of longest side(hypotnuse) .

that means ⇒ (Hypotnuse)² = (Perpendicular)² + (Base)² ;

Substituting the longest value as 92 and other values as 49 and 68 ,

we get ;

⇒ 92² = 49² + 68² ;

⇒ 8464 = 2401 + 4624 ;

⇒ 8464 ≠ 7025 .

the sides 49 cm, 68 cm, and 92 cm do not satisfy Pythagoras theorem ,

Therefore , the side lengths do not form a Right Triangle .

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The conversion of the equation from slope-form to standard form is -2x + y = -3.

In Mathematics, the slope-intercept form of a line can be represented or modeled by using this linear equation:

y = mx + c

Where:

Generally speaking, the standard form of a linear function is given by this mathematical expression:

Ax + By = C

Where:

A, B, and C represents a numerical value (number).

Rewriting the given linear function in standard form, we have the following:

-2x + y = -3.

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The probability that the first item is not the first to be delivered is 0.6667

Let's call the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.

Therefore, the probability that one of the other two items arrives first is

1/3 + 1/3 = 2/3.

The probability that the first item is not the first to be delivered is

1 - 2/3 = 1/3

Evaluate

1 - 2/3 = 0.6667

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