1:
Sam arrives at an amusement park with $61 that he
can spend at the amusement park. The entrance fee at
the amusement park is $20. It costs $3 to play a game
and $4 for each ride. He plays 6 games and goes on x.
rides. The inequality shown below represents this
situation.
38+4x≤61
The solution of the inequality is x ≤ 5.75. Based on the
solution, which statement must be true?

A.Sam went on at most 5 rides

B.Sam went on at most 6 rides

C.Sam went on more than 6 rides

D.Sam went on fewer than 5 rides

Answer: The answer is {x,y}={17/5,-68/5}

The numbers on the mailboxes could be considered either categorical or quantitative data. The correct Option is C: Either categorical or quantitative data.

The numbers on the mailboxes can be considered either categorical or quantitative data, depending on the context in which they are being used.

If the numbers are simply labels for the mailboxes, with no inherent numerical value or order, then they can be considered categorical data. In this case, the numbers would be treated as labels for the different categories or groups, rather than as measurements with numerical significance.

On the other hand, if the numbers are being used to represent a quantity or a position in a sequence, then they can be considered quantitative data. For example, if the numbers represent the physical location of the mailbox within a building, or the order in which mail is sorted and delivered, then they can be treated as numerical measurements.

Therefore, without further context, the numbers on the mailboxes could be considered either categorical or quantitative data.

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A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

To find integer matrices A and B that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B), we can start with the following matrices:

A = [1 0 0; 0 1 0; 0 0 0]

B = [1 1 0; 0 0 0; 0 0 0]

The null space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the null space of B also consists of all vectors of the form [x; y; 0]. Therefore, Nul(A) = Nul(B).

The column space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the column space of B also consists of all vectors of the form [x; y; 0]. Therefore, Col(A) = Col(B).

We can verify that A and B are not multiples of each other by computing their determinants. The determinant of A is 0, while the determinant of B is 0 as well. However, A and B are not multiples of each other because the first column of A is [1; 0; 0], while the first column of B is [1; 0; 0] + [0; 1; 0], which is a linear combination of the columns of A.

Therefore, A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

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Find integer matrices A, B not multiples of each other such that Nul(A)=Nul(B)andCol(A)=Col(B)?

The correct options for the given polynomial are:

To analyze the end behavior of a polynomial we need to look at the degree and the sign of the leading coefficient.

Remember that the degree is the largest exponent of the polynomial.

Here we can see that the degree is 12, so it is even.

And the leading coefficient (the coefficient in the term with the largest exponent) is -10, so it is negative.

Then the first correct option is:

NEG/EVEN

That means that in both ends the polynomial tends to negative infinity, so:

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Answer:

2 units

Step-by-step explanation:

To find the difference between 10 and 12, we can use this equation:

Or:

Therefore, the difference is 2.

Answer: x = -11

Step-by-step explanation:

[tex]\frac{-x+10}{3} = 7[/tex]

⇒-x+10 = 7x3
⇒-x+10 = 21
⇒-x = 21-10
⇒-x = 11
∴ x = -11

Answer:

n = 4

Step-by-step explanation:

Remove the radical by raising each side to the index of the radical.

The simplified form of the expression x² - 8x +16 is (x - 8)²

Expressions are mathematical statements that involve operations, such as addition, subtraction, multiplication, and division. In this problem, we are given the expression x² - 8x + 16 and asked to simplify it.

The expression can be simplified by using factoring techniques. We can factor the expression as (x - 8)(x - 8), which can be further simplified as (x - 8)2. The simplified expression is (x - 8)²

Therefore, the simplified expression for x² - 8x + 16 is (x - 8)². This shows that the expression is a perfect square, which can be written as (x - 8)², where (x - 8) is the square root of the expression

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Complete Question:

Simplify the expression x² - 8x + 16

Answer:

B. 360

Step-by-step explanation:

A rule of polygons (octagon included) is that the sum of the exterior angles always equals 360 degrees.

The relative retention of compound B with respect to compound A is 0.053.

The relative retention is defined as the ratio of the difference in retention times of two compounds (α) to the retention time of the first eluting compound (tr1):

α = (tr2 - tr1) / tr1

where tr2 is the retention time of the second compound.

In this case, compound A eluted at 12.63 min and compound B eluted at 13.30 min. The compound that is not retained by the stationary phase eluted at 1.145 min.

Therefore, tr1 = 1.145 min, tr2 = 13.30 min, and:

α = (13.30 - 12.63) / 12.63

α = 0.053

Therefore the relative retention of compound B with respect to compound A is 0.053.

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Answer:

Step-by-step explanation:

Starting with the left-hand side (LHS) of the identity:

(cos x)(tan x + sin x cot x)

We can simplify using trigonometric identities. First, we can rewrite tan x as sin x/cos x and cot x as cos x/sin x:

(cos x)(sin x/cos x + sin x(cos x/sin x))

Simplifying, we get:

(sin x + cos2 x)/sin x

Next, we can multiply the numerator and denominator by the conjugate of sin x + cos2 x, which is sin x - cos2 x:

[(sin x + cos2 x)/(sin x + cos2 x)] * [(sin x - cos2 x)/(sin x - cos2 x)]

Expanding and simplifying, we get:

[(sin x)(sin x - cos2 x) + (cos2 x)(sin x - cos2 x)] / [(sin x)(sin x - cos2 x) + (cos2 x)(sin x + cos2 x)]

Simplifying further, we get:

(sin2 x - cos2 x + cos2 x sin x - cos4 x) / (sin2 x + cos2 x)

Using the identity sin2 x + cos2 x = 1 and simplifying, we get:

(sin x - cos2 x) / 1

Finally, using the identity cos2 x = 1 - sin2 x, we can simplify to:

(sin x - (1 - sin2 x)) / 1

Simplifying further, we get:

2 sin x - 1

So the left-hand side is equal to 2 sin x - 1.

Now, let's simplify the right-hand side (RHS) of the identity:

sin x + cos2 x

Using the identity cos2 x = 1 - sin2 x, we can rewrite the RHS as:

sin x + 1 - sin2 x

Simplifying further, we get:

1 - sin2 x + sin x

Finally, using the identity sin2 x + cos2 x = 1, we can rewrite as:

cos2 x + sin x

So the right-hand side is equal to cos2 x + sin x.

Since the left-hand side is equal to 2 sin x - 1 and the right-hand side is equal to cos2 x + sin x, the identity is not true in general. Therefore, the given identity does not hold true.

hope this helps

Answer:

m∠1=46°

m∠2=44°

m∠3=44°

m∠4=90°

m∠5=73°

m∠6=17°

m∠7=17°

Answer:

ED

Step-by-step explanation:

Since,

Δ ABC ≅ Δ DEF

Side AB is congruent to side DE

Or

BA is congruent to ED.

We fail to reject the null hypothesis that the temperature level has no effect on the mean yield process.

Summary of Result:

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

To construct an analysis of variance (ANOVA) table and test whether the temperature level has an effect on the mean yield process, we need to perform the following steps:

Step 1: Calculate the total sum of squares (SST), the treatment sum of squares (SSTR), and the error sum of squares (SSE).

SST = ΣΣ(yij - ȳ)^2 = 359.2

where yij is the yield of the ith batch at the jth temperature level and ȳ is the overall mean yield.

SSTR = Σ(nj(ȳj - ȳ)^2) = 118.2

where nj is the number of batches produced at the jth temperature level, ȳj is the mean yield at the jth temperature level, and ȳ is the overall mean yield.

SSE = SST - SSTR = 241.0

Step 2: Calculate the degrees of freedom (df) for SST, SSTR, and SSE.

df(Total) = N - 1 = 14

where N is the total number of observations.

df(Treatment) = k - 1 = 2

where k is the number of treatment levels.

df(Error) = df(Total) - df(Treatment) = 12

Step 3: Calculate the mean square (MS) for SSTR and SSE.

MS(Treatment) = SSTR / df(Treatment) = 59.1

MS(Error) = SSE / df(Error) = 20.1

Step 4: Calculate the F-statistic.

F = MS(Treatment) / MS(Error) = 2.94

Step 5: Determine the critical value of F for a 0.05 level of significance with df(Treatment) = 2 and df(Error) = 12.

From a table of F-distributions, the critical value of F is 3.89.

Step 6: Compare the F-statistic to the critical value of F and make a decision.

Since 2.94 < 3.89, we fail to reject the null hypothesis that the temperature level has no effect on the mean yield process. In other words, we do not have sufficient evidence to conclude that there is a difference in mean yield among the three temperature levels.

Step 7: Summarize the results in an ANOVA table.

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

Note: The p-value is calculated as P(F > 2.94) = 0.095, which is greater than the significance level of 0.05. Therefore, we do not reject the null hypothesis.

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Graphs - 9, 10, and 12 are classified as non-proportional graphs and Graph 11 will be a Proportional graph.

A proportional graph is a graph that represents a proportional relationship between two variables. In other words, as one variable increases, the other variable also increases, and the relationship between the two variables can be expressed as a constant ratio or proportion.  

In a proportional graph, the plotted points will lie on a straight line that passes through the origin (0,0).  

Here we have

4 types of graphs  

Where

Graph - 9 is a curve and doesn't pass through the origin

Graph - 10 is a straight line and doesn't pass through the origin  

Graph - 11 is a straight line and passes through the origin

Graph - 12 is  a straight line and doesn't pass through the origin    

As we know

A proportional graph should pass through the origin and it should be a straight line.

Therefore,

Graphs - 9, 10, and 12 are classified as non-proportional graphs and Graph 11 will be a Proportional graph.

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Answer:

Step-by-step explanation:

With this the probabiitiy is high. In saying that look at 3 that is your answer. So that answer would be mostly 0.100. Hope this helps

The variance is 0.745

The  standard deviation is 0.863

A probability is a number that describes how likely an event is to occur in science. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The probability of an event increasing as its likelihood increases

How to solve

X is a random variable and is the number of in the group of three who do online course.

The probability distribution is given below:

x        P(X=x)

0       0.108

1        0.355

2       0.395

3      0.142

A summation of this is 0.108 + 0.355 + 0.395 + 0.142

= 1

Since it is equals to 1, the distribution is a probability distribution.

To find the mean,

0(0.108) + (1) (0.355) + (2) (0.395) + (3)(0.0.142)

= 1.571 students

Approx

1.6 students

The variance is

3.213 - 2.468 = 0.745

The standard deviation is \sqrt0.745 = 0.863

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The length of the box is x = 13 inches. To find this, we need to solve the equation V = l*w*h = 180, where l is the length, w is the width, and h is the height.

We know that w = l - 5 and h = l + 2, so we can substitute these into the equation to get 180 = l(l - 5)(l + 2). After rearranging, we get

This can be solved using the cubic formula, which gives us l = 13. We can thus conclude that the length of the box is 13 inches.

To calculate this, we first need to set up the equation. We know that the volume of the box is 180 in³ and the width is 5 inches less than the length, and the height is 2 inches more than the length. We can then substitute this into the equation V = lwh to get 180 = l(l - 5)(l + 2).

After rearranging, we get

This can be solved using the cubic formula, which gives us l = 13. We can thus conclude that the length of the box is 13 inches.

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The correct graph is the first one.

Graph is a data structure composed of nodes connected by edges, which represent a relationship between the two notes of are used to represent networks of communication that organized and even extract concept like thought or riders the nodes in the graph are often represent by Circle and it's by line but the other safe of the symbol are also use copper power Bluetooth for a organizing and understanding data and can be used to solve complex problem.

It represents the equation y = 20 + 10x, which means that the gymnast pays a flat fee of $20 for each month plus an additional $10 for each class he attends. Therefore, the graph will show a line going from the point 0, 20 through the point 1, 30.

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The solution is, the value of 6k − j^2 + 2k ÷ l when j = 5, k = 12, and l = 3, is 13.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

6k − j^2 + 2k ÷ l

now, we have to simplify the given expression, using multiplication , division, addition & subtraction , as per the BODMAS rule.

so, we get,

6k − j^2 + 2k ÷ l

when j = 5, k = 12, and l = 3.

putting the values, we get,

30 - 25 +24 /3

=30 -25 + 8

=5+ 8

=13

Hence, The solution is, the value of 6k − j^2 + 2k ÷ l when j = 5, k = 12, and l = 3, is 13.

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The converted value of measuring mass 145 kilograms to pounds is equal to 320 pounds ( round off to near pounds )

Standard relation between kilograms and pounds are :

One kilograms is equal to 2.20462 pounds

Now substitute the required converted value 145 kilograms in the above standard relation we have ,

⇒ ( 1 × 145 ) kilograms = ( 145 ) ×  ( 2.20462 ) pounds

⇒ 145 kilograms = 319.67 pounds

⇒ 145 kilograms = 320 pounds ( round off to near pounds )

Therefore, after conversion of mass unit kilograms into pounds is given by  145 kilograms = 320 pounds ( round off to near pounds ).

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Answer:

<1,6>

Step-by-step explanation:

We are adding vectors.  Add the first components together.  Then add the second components together.

<5, -2> + <-4, 8>

< 5+-4, -2+8>

<1,6>

(a) The probability of finding oil is 0.85

(b) The firm interpret the soil test as the probability of finding oil has decreased since the prior probabilities.

c) The revised probabilities is 100%.

A oil company has purchased an option on land in Alaska.

To determine the likelihood of finding oil, the company conducted preliminary geologic studies to assign prior probabilities of finding high-quality oil (0.65), medium-quality oil (0.20), or no oil (0.15). Therefore, the probability of finding oil is 0.65 + 0.20 = 0.85.

After 200 feet of drilling on the first well, a soil test was taken to determine the likelihood of finding high-quality oil (0.20), medium-quality oil (0.80), or no oil (0.20).

The results of this test should be interpreted as follows: the probability of finding oil has decreased since the prior probabilities.

Therefore, the revised probabilities are 0.20 + 0.80 = 1.00. This means that the oil company has a 100% probability of finding either high-quality or medium-quality oil.

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The image point of (-7, 5) after the translation is (-2, 9).

What is the translation in the coordinate system?

A translation in the Cartesian plane can be described by a rule that indicates how to move each point of a figure to its image under the translation. The rule is usually given as a pair of numbers (a, b), where a is the horizontal distance to move each point (positive to the right, negative to the left), and b is the vertical distance to move each point

To find the image point of the point (-7, 5) after a translation right 5 units and up 4 units, we need to add 5 to the x-coordinate and add 4 to the y-coordinate.

The new x-coordinate will be -7 + 5 = -2, since we're moving the point to the right 5 units.

The new y-coordinate will be 5 + 4 = 9, since we're moving the point up 4 units.

Hence, the image point of (-7, 5) after the translation is (-2, 9).

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Answer: 96

Step-by-step explanation:

Answer:

You are correct! The actual distance, in miles, between Zionsville and Lafayette is 96 miles. This is calculated by multiplying 8 inches (the distance on the map) by 12 miles (the scale of the map), which results in 96 miles.

The method to convert mililitres to litres is the formula - Quantity in litres = quantity in mililitres/1000.

Remember that ml is the unit of volume which is abbreviated to mililitres. Now, going to the relation between mililitres and litres. We are aware that 1 litre is equal to 1000 mililitres. So, converting mililitres to litres, we need to use the following formula -

Quantity in litres = quantity in mililitres/1000

Using an example to verify the mentioned relation. Let us say we have 4000 mililitres of acid. So, what will be the volume of acid in litres.

Quantity of acid in litres = 4000/1000

Performing division

Quantity of acid in litres = 4 litres

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The volume of the figure is 18 cubic units

From the question, we have the following parameters that can be used in our computation:

The figure

The figure can be divided into two 3-D figures represented below

Cube: side length = 2

Cuboid: 2 by 5 by 1

The volume of the figure is then calculated as

Volume = Volume of cube + Volume of cuboid

So, we have

Volume = 2 * 2 * 2 + 2 * 5 * 1

Evaluate

Volume = 18

Hence, the volume is 18 cubic units

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Answer:

12x + 50 =210

Step-by-step explanation:

Given the data on the world problem, we know that one of our terms will be 12x because it says "each month" in the problem. If his mom is going to give him 50 dollars, and the Jordans cost 210, then we can write  a simple equation.

x = number of months it will take him

[tex]12x+50=210[/tex]

Answer: 5.8=x

Step-by-step explanation:

$210=Price

$12=Each Month

$50=From Mom

120-50=70

70/12=5.8 Months

Company can produce 130 bags of seedlings, 110 bags of general plotting and 50 bags of hardwood plants. The solution has been obtained by using linear equation.

What is a linear equation?

The degree of the linear equation is 1. It is very clear that linear equations with exponents greater than one lack variables. The equation for this graph yields a straight line.

Let S be the bags of seedlings, G be for general potting, and H be for hardwood plants.

It is given that each bag of seedling soil needs 2 units of sand, each bag of general soil needs 1 unit of sand, and each bag of hardwood soil needs 2 units of sand. We have 450 units of sand.

So, from this we get

2S + G + 2H = 450      ...(1)

Similarly, for units of loam and peat moss, we get the equations as

S + 2G + 2H = 450      ...(2)

S + G + 2H = 360         ...(3)

Now, on subtracting (3) from (2), we get

G = 110

On substituting this, we get

2S + 2H = 360    ...(4)

S + 2H = 230    ...(5)

S + 2H = 250    ...(6)

Now, we subtract (2) from (1), we get

S = 130

On substituting this in equation (5), we get

130 + 2H = 230

2H = 100

H = 50

Hence, company can produce 130 bags of seedlings, 110 bags of general plotting and 50 bags of hardwood plants.

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Step-by-step explanation:

4³ = 4 × 4 × 4

4³ = 16 × 4

4³ = 64

Answer: 4³ = 4 × 4 × 44³ = 16 × 44³ = 64

Step-by-step explanation: hope this helps0^0