The two lines graphed below are not parallel how many solutions are there to the system of equations

Clοsure: Clοsure is a Gestalt principle οf grοuping that states that the brain is predispοsed tο fill in the gaps in an image tο make a cοmplete picture.

A circle is a shape that cοnsists οf all pοints in a plane that are at an equal distance frοm a given pοint called the center. This distance is knοwn as the radius. A circle is οne οf the mοst basic shapes in geοmetry, and it is alsο the mοst symmetrical. Circles can be used tο make a variety οf οther shapes, such as triangles, squares and pοlygοns. Circles are alsο used tο represent many ideas and cοncepts, such as infinity, unity and perfectiοn.

In the illustratiοn, the gaps between the circles are filled in with a sοlid cοlοr, suggesting that the circles are all cοnnected and fοrm a cοmplete image.

b. Prοximity: Prοximity is a Gestalt principle οf grοuping that suggests that elements that are clοse tοgether are perceived as related. In the illustratiοn, the circles are arranged in a grid pattern, with each circle clοse tο several οther circles. This arrangement implies that the circles are related tο each οther.

c. Cοntinuity: Cοntinuity is a Gestalt principle οf grοuping that suggests that elements that are arranged in a curved οr linear pattern are seen as related. In the illustratiοn, the circles are arranged in a curved pattern, suggesting that they are all part οf the same image.

d. Illusοry Cοntοurs: Illusοry cοntοurs is a Gestalt principle οf grοuping that suggests that elements that are arranged in a pattern can give the impressiοn οf a three-dimensiοnal οbject. In the illustratiοn, the circles are arranged in a pattern that gives the impressiοn οf a curved οbject.

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In a case whereby a  journey to school takes a girl 53 minutes the time she arrive if she leaves home at 08:38 is 09:31.

Based on the question, we werr told that the time she will used to get to school is 53 minutes, and were told that she left home around 08:38, then we can calculate the time she will get there as

[08:38 + 00:53]

= 09:31

Then we can conclude that the time that she will she will arrive at school  can be expressed as  09:31 which could be in the morning or night since it was not stated.

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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False. Line charts are best suited for representing data that follows a sequential order, such as time series data. Nonsequential data is better represented by other types of charts, like scatter plots or bar graphs.

Line charts are graphical representations of data points connected by lines. They are commonly used to display trends over time or sequential data. For example, they are often used to show the change in stock prices over a period of time or the temperature variations throughout the day. This sequential order is the key feature of line charts.

However, for data that does not follow a sequential order, line charts may not be the best choice. Nonsequential data, such as categorical or unrelated data points, are better represented by other types of charts. Scatter plots, for instance, are useful for showing the relationship between two variables that are not necessarily ordered. Bar graphs can also be used to compare nonsequential data points in different categories.

In summary, line charts are not best suited for representing data that follows a nonsequential order. They are most effective when used to display data that has a clear sequential relationship, allowing for easy interpretation of trends and patterns.

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Answer:

32 degrees

Step-by-step explanation:

180 - 116 = 64

64/2 = 32

Answer:

32°

Step-by-step explanation:

as it is an isosceles triangle from the sides mentioned above

so the other unknown angle is also x

interior angles of triangle sum up 180

so 116 + 2x = 180

2x = 180 -116

2x = 64

x = 32°

The distance between points a and b in a triangle shape is 70.17 m

Triangle is a special shape that has the rule that the total angle in the triangle should be 180⁰

A + B + C = 180⁰

where A, B, and C are the angles in the triangle.

Moreover, the triangle has a sine rule which shows the relationship between sides and angles. It is given as :

a/sinA = b/sinB = c/sinC

From the question above, we know that :

A = 70.5⁰

C = 38.83⁰

b = 105.6 m

It is needed to determine the angle of B

A + B + C = 180⁰

70.5⁰ + B + 38.83⁰ = 180⁰

B = 70.67⁰

Then, determine the distance between points a and b (c) by using the sine rule

b/sinB = c/sinC

105.6 / sin(70.67⁰) = c / sin(38.83⁰)

105.6 / 0.94 = c / 0.63

c = 70.17 m

Hence, the distance between points a and b is 70.17 m

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Number 1

\(AB=BC\)

Prove : \(AC=2(AB)\)

\(AB=BC\)   ⇒  Given

We call this given because it is the first thing that we see in the problem and is the exact equation that we will use to solve

________

Next...

\(AC=AB+BC\)  ⇒  Congruent Angles

We call these Congruent Angles because They have the same measure

\(AC=AB+AB\)  ⇒  Substitution

We call this Substitution because we are substituting \(BC\) for \(AB\) since they equal the same

\(AC=2(AB)\)  ⇒  Segment Addition Postulate

___________________

Number 2

m∠\(1=120\)   ⇒  Given

We call this given because it is the first thing that we see in the problem and is the exact equation that we will use to solve

∠\(1=\)∠\(2\)  ⇒  Given

m∠\(1=\) m∠\(2\)  ⇒ Given

\(120 =\) m∠\(2\)  ⇒  Definition of Congruent Angles

m∠\(1=\) m∠\(2\)  ⇒ Symmetric Property

we need to randomly sample 145 individuals from the population and calculate their mean IQ.

To determine the required sample size for estimating the population mean with 98% confidence to within 4 IQ points of the true mean, we can use the formula:
n = \((Z\alpha /2 × σ / E)^{2}\)
Where: n = sample size
Zα/2 = the Z-score for the desired confidence level (98% confidence corresponds to Zα/2 = 2.33)
σ = the population standard deviation (given as 16 IQ points)
E = the desired margin of error (4 IQ points)
Plugging in these values, we get:
n = \((2.33 × 16 / 4)^{2}\)
n = 144.49
Rounding up to the nearest whole number, we get a required sample size of n = 145.

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The Venn diagram shows that the number of students who offer accounting is 30 and offer Accounting and Economics are only 5.

It should be noted that a Venn diagram is an illustration which uses circles to show the relationship between the objects.

We are given that class of 50 students, the number of students who offer accounting is twice as the number who offer Economics 10 students offer neither of the two subjects and 5 students offer both subjects

The number of students who offer Economics are;

= 10 + 5

= 15

Since accounting is twice as the number who offer Economics.

The number of students who offer accounting are;

= 25 + 5

= 30

The number of students who offer only one subject will be as follows;

= 25 + 10

= 35

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Answer:

4.359/10

Step-by-step explanation:

The error made by the Gabriel in calculating the change amount, is that he subtract the $2 instead of adding $2.

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

The expression used by the Gabriel to represent his total cost  is,

\(2.5x+2y - 2\)

As, Gabriel has to receive the change amount of $30. Thus, he has to subtract this amount from the total cost. This statement can be present as,

\(\rm Change=30-(2.5x+2y - 2)\\\rm Change=30-2.5x-2y + 2\\\rm Change=32-2.5x-2y\)

Now, the expression used by him to represent the amount of change he should receive from $30 is,

\(28 -2.5x - 2y\)

Hence, the error made by the Gabriel in calculating the change amount, is that he subtract the $2 instead of adding $2.

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Answer:

20 ÷ 10 = 2

So x = 20

Step-by-step explanation:

Hope this helps!

Answer:

x = 20

Step-by-step explanation:

1. Multiply 10 on both sides

2. The 10 on he left said will cancel out

3. x = 20

Answer:

7.4

Step-by-step explanation:

400 ÷ 54 =7.407407...

7.407407... rounded to the nearest tenth is 7.4

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The one is not a characteristic of a normal curve is its spread increases as its mean increases that is Option 2.

One of the numerical values that is frequently calculated in both descriptive and inferential statistics is statistical variance. If we know the mean, the value of each data point, and the number of samples, we can determine this value.

The spread of scores in a data set normally increases as the variance of that data set increases. The main reason for this is because variance is a number that represents the average departure of each data point from the mean.

Because the normal distribution is symmetrical on both sides of the mean and is a continuous probability distribution, the right side of the center is the opposite of the left side.

Probability is represented by the area under the normal distribution curve, and the total area under the curve equals one.

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Complete question:

Four of the following statements are correct descriptions of a Normal curve. Which one is NOT a characteristic of a Normal curve?

The velocity of seawater flowing through a horizontal tube with a variable cross-sectional area, having dimensions of 21cm and 7cm, and manometric pressures of 2.5 N/cm and 3.9 N/cm at the narrow and wide sections respectively, can be calculated using Bernoulli's equation.

According to Bernoulli's equation, the total pressure at any point in a fluid is equal to the sum of its static pressure, dynamic pressure, and potential energy per unit volume. In this case, we can assume that the height difference between the narrow and wide sections is negligible, so the potential energy term can be ignored. Thus, we can write:

where P1 and P2 are the manometric pressures at the narrow and wide sections respectively, ρ is the density of seawater (1.07 g/cm³), V1 and V2 are the velocities at the narrow and wide sections respectively.

Solving for V2, we get:

Substituting the given values, we get:

Therefore, the velocity of seawater flowing through the tube can be calculated using this equation.

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Complete Question:

In a horizontal tube of variable section, the cross sections are 21cm and 7em respectively. If seawater (1.07 g/cm*) flows through the tube and the gauge pressures in the narrowing and wide part are 2.5 N/cm and 3.9N/cm

(275 + 325) / 25

= 600/25

=24

Answer:

\(24\)

Step-by-step explanation:

\(275 + 325 \\ =60 0 \div 25 \\ = 24\)

Answer:

0.8,√2,2π

Step-by-step explanation:

Answer:

the second one, then the first, then the last one

Step-by-step explanation:

the first one is = to 1

the second one is = to 6.3

the third one is = to .8

Answer:

Step-by-step explanation:

\(we \ can \ show \\(a^{b})^{c}=a^{bc}\\,as,\\2^{-2}t^{6}\\a^{-b}=\frac{1}{a^{b}}\\2^{-2}t^{6}=\frac{1}{4}t^{6}\)

Answer:

See below.

Step-by-step explanation:

We are asked to simplify the given expression.

Let's begin by identifying an important rule. Because there's a negative exponent and a negative exponent outside of the parentheses, we multiply the exponents and the product will be a positive exponent.

We also need to remember that the exponent outside of the parentheses acts on everything inside the parentheses.

Evaluate:

\((2t^{-3} )^{-2} = 2^{-2} \times t^{6}.\)

Further Evaluate:

\(2^{-2} = \frac{1}{2^2} = \frac{1}{4}. \\t^{6} = t \times t \times t \times t \times t \times t.\)

Multiply:

\(t^{6} \times \frac{1}{4} = \frac{t^{6} }{4} \ or \ \frac{1}{4} (t^6) .\)

We can't simplify any further.

Therefore, our final answer is \(\frac{t^{6} }{4} \ or \ \frac{1}{4} (t^6).\)

Answer:

103 students tickets were sold

Step-by-step explanation:

103 times $5 = $515

212 times $8 = $1696

$515 + $1696 = $2211

Answer:

B) Likely

Step-by-step explanation:

Unlikely = < 50%

Likely = > 50%

Certain = 100%

Equally likely = 50%

In a simple regression model, the unexplained variation in the response variable is determined by summing the squares of errors. This method, known as residual sum of squares (RSS), quantifies the discrepancy between the observed values and the predicted values by the regression model.

In a simple regression model, the goal is to find a line that best fits the relationship between a single predictor variable (X) and a response variable (Y). However, due to various factors and sources of variability, the observed values of the response variable may not perfectly align with the predicted values based on the regression line.

The errors, or residuals, are the differences between the observed values and the predicted values. To quantify the unexplained variation, the errors are squared to eliminate negative values and emphasize larger deviations. These squared errors are then summed up, resulting in the residual sum of squares (RSS).

By calculating the RSS, one can assess the amount of unexplained variation or "error" in the regression model. A smaller RSS indicates that the model provides a better fit to the data, as it suggests less unexplained variation. On the other hand, a larger RSS implies a less accurate fit, with more unexplained variation in the model.

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Answer:

8 3/4 (8.75)

Step-by-step explanation:

I divided 35 by 4 on a calculator to get 8.75

I know that 8.75 is the same as 8 3/4

So, say you're dividing 35 jellybeans with 3 of your friends (you're the fourth person, because you need some jellybeans too!)

Each would get 8 jellybeans. But there are 3 left over.

Split each jellybean into 4 parts.

Each of you would get 3/4 of one of the jellybeans. (three tiny parts of the total four tiny pieces)

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The situation represents an arithmetic sequence because the successive y-values have a common difference of 30.

An arithmetic sequence is a sequence of numbers where each term is equal to the previous term plus a constant difference. In this case, the constant difference is 30.

The first night costs $240, and each subsequent night costs $210. So, the total cost of staying at the hotel for x nights is $240 + (x - 1) * 30.

We can see that the successive y-values in this sequence have a common difference of 30. For example, the second y-value is 240 + 30 = 270, and the third y-value is 270 + 30 = 300. Therefore, the situation represents an arithmetic sequence.

Here is a table of the first few terms of the sequence:

Term Value

1          240

2             270

3         300

4          330

5          360

As you can see, the successive terms of the sequence have a common difference of 30. This is why the situation represents an arithmetic sequence.

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The single integral in the form y b a fs(x) dx is:

∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx - ∫ y=2 to 5 fs(x) dx - ∫ y=1 to 21 fs(x) dx

To write the given expressions as a single integral in the form y b a fs(x) dx, let's break it down step by step.

1) y = 2 to 22: ∫ fs(x) dx

2) y = 1 to 5: ∫ fs(x) dx

3) y = 21 to 22: ∫ fs(x) dx

Now, to combine these integrals into a single expression, we need to find a common interval that encompasses all three given intervals.

The smallest common interval that covers all three intervals is from 1 to 22.

Therefore, we can rewrite the expressions as:

∫ y=2 to 22 fs(x) dx = ∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx

∫ y=5 to 2 fs(x) dx = -∫ y=2 to 5 fs(x) dx

∫ y=21 to 22 fs(x) dx = ∫ y=1 to 22 fs(x) dx - ∫ y=1 to 21 fs(x) dx

Combining these expressions, we get:

∫ y=2 to 22 fs(x) dx - ∫ y=5 to 2 fs(x) dx + ∫ y=21 to 22 fs(x) dx

= (∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx) - (-∫ y=2 to 5 fs(x) dx) + (∫ y=1 to 22 fs(x) dx - ∫ y=1 to 21 fs(x) dx)

= 2∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx - ∫ y=2 to 5 fs(x) dx - ∫ y=1 to 21 fs(x) dx

Therefore, y b a fs(x) dx, the single integral is:

∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx - ∫ y=2 to 5 fs(x) dx - ∫ y=1 to 21 fs(x) dx

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The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Answer: 7:4

Step-by-step explanation:

40 boys and girls 3:2 = 24 boys + 16 girls

4 boys are added  28 boys + 16 girls /4  = 7:4

Answer:

7:11

Step-by-step explanation:

We know the total number of students and the ratio of boys to girls.  The total for the ratio of boys and girls would be 5 (3+2).  Now we can set up proportions knowing these numbers.

b = 3

g =2

t =5

Let's find out how many actual boys there are by setting up a proportion

3/5 = b/40  

I will look at the denominators to find x.  5 times what gives me 40? (8).  So, I will multiple the top number (numerators).  Since I need to multiple the bottom number by 8 to get the number 40, I will now multiple the top number by 8 and get 24.

Now, I know how many actual boys and girls were in the original class.  There were 24 boys, 16 girls (40 - 24) and 40 total students.  

Now I will take this new information and apply it to the new situation.  Now I have 28 boys (24 + 4) and a new total 44.

The ratio of boys to girls would not be 28: 16 or 7:4

Answer:

P=40%

Explanation: 5000/50=100

20/50=2/5

2/5=0.4

0.4=40%

Answer:

yea he is wrong

Step-by-step explanation:

He is wrong because you cant not just switch the variable. If you move the variable the value will change.

(Hard) A composite number n is called a Carmichael number bn−1 ≡ 1 (mod n) for every number b such ... Base case: When n = 2 the formula a + c ≡ b + d (mod m) was already given. ... The sequence goes 1, 3, 7, 15, 31,... guess that it is equal to 2n+1 − 1. ... Prove (now using induction on n) that fm|fmn for all n ≥ 1.

Answer:

That would be n\(\geq 1\\\)

Step-by-step explanation: