When Uim surveyed 5 sixth-grade students at the community skating rink, he found that only 1 out of the 5 had
completed the science project. He knows there are about 160 sixth-grade students in his community, so he infers that
around 32 students have finished their science project. Is this good inference?
No, Jim did not make a good inference because his sample is too small and may be biased because he only asked
students that were at the rink.
No, Jim did not make a good inference because his sample is too small and 32 IS not in the same proportion to the
population as 1 to 5.
Yes, Jim made a good inference
because 32 is the same proportion to the population as 1 to 5.
Yes, Jim made a good inference because most students at the rink were sixth graders.

Answer:

see below

Step-by-step explanation:

7.    1/3 ( n+2) = 5

Multiply each side by 3

n+2 = 5*3

n+2 = 15

Subtract 2 from each side

n+2-2 = 15-2

n = 13

8.x = bills

He started with 300 and paid 1/4 of the bills and ended up with -50

300 - 1/4 x = -50

Rearranging the order on the left

-1/4x + 300 = -50

Answer:

(A) \(-\frac{1}{4}x+300=-50\)

Step-by-step explanation:

I "reversed" this problem to find the equation that works for it.

The balance was originally $300. If he's now at a balance of -50$ after paying off \(\frac{1}{4}\) of his bills, then \(\frac{1}{4}\) of his bills are $350, since \(300 - (-50) = 350\).

If  \(\frac{1}{4}\)  of his bills are $350, then his full bill is \(350\cdot4=1400\)$.

So I tested each equation, where \(x=1400\) to see if the equation worked out.

For a:

\(-\frac{1}{4}x + 300 = -50\\\\-\frac{1}{4}\cdot1400 + 300 = -50\\\\-350 + 300 = -50\)

-350 + 300 is indeed -50, so I knew this equation works.

Hope this helped!

Answer:

it isn't correct

\(x {}^{2} - 6x - 7 = 0 \\ d = 36 + 28 = 64 \\ x1 = \frac{6 - 8}{2} = - 1 \\ x2 = \frac{6 + 8}{2} = 7\)

Answer:

her solution isn't correct .

because she had done a slight mistake in her calculation.

i.e.

\(\sqrt{16}=4 \:\:not \:\:16\)

Step-by-step explanation:

solution given:

x²-6x-7=0

making it a perfect square

we must make it on the form of (a+b)²or(a-b)²

so

x²-2*3*x+3²-3²-7=0

(x-3)²-9-7=0

(x-3)²-16=0

adding 16 on both aide

(x-3)²=16

doing square root on both side

\(\sqrt{(x-3)²}=\sqrt{16}\)

x-3=±4

taking positive

x-3=4

adding 3 on both side

x=7

and.

taking negative

x-3=-4

adding 3 on both side

x=-4+3

x=-1

x=-1 or 7

Answer:

24/6=c

Step-by-step explanation:

Well to split 24 you need to divide by 6 and that will equal the answer. An equation always has a equal sign so you know that you would be solving for c

Step-by-step explanation:

Use TOA. (tan angle = opposite/adjacent)

Given angle A = 58

adjacent = 6 mi

\( \tan(a) = \frac{opposite}{adjacent} \\ \tan(58) = \frac{bc}{6} \\ bc = 6 \tan(58) \\ = 9.6mi(nearest \: tenth)\)

Answer:

0.33333333333

Step-by-step explanation:

(0.83333333333)-(0.5)=0.33333333333

Answer:

the answer is 2/6 or 1/3 if needed to be simplified

when subtraction fractions, if they have the same denominator, you only have to subtract the numerators

Step-by-step explanation:

As the number of people visiting each day is the same 404 people visited on Sunday.

We have,

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday and the number of people who visited on each day is the same.

As the number of visitors is same on each day and the total number of days is three each they the number of people visited is,

= (1212/3).

= 404.

So, On Sunday 404 visitors were there.

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complete question:

The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday. If the same number of people visited each day, how many visitors were there on Sunday

The AVERAGE function has two required arguments and one optional argument.

The AVERAGEIF function is used to calculate the average of all cells in a given range that meet certain criteria. The function has a total of 3 parameters - the first 2 are required and the last is optional: Range (required) - The range of cells to test against the condition.

In plain language, an average is a single number represented as a list of numbers, usually the sum of the numbers divided by the number of numbers in the list (arithmetic mean). For example, the numbers 2, 3, 4, 7, and 9 (for a total of 25) have an average of 5. Depending on the context, the average can be another statistic, such as the median or the mode.

Average personal income, for example, is often given as the median – a figure below 50% of personal income and above 50% of personal income – because the average would be higher if some personal income of billionaires were included. Therefore, it is recommended to avoid using the word "average" when referring to measures of central tendency.

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Answer:

AB=DE

Step-by-step explanation:

they're literally the only pair on the same sides lol

The side AB is equal to DE or AB ≅ DE option (A) AB ≅ DE is correct.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

We have two triangles shown in the picture.

As we know from the definition of the congruent triangle, the same size, and shape.

The three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle

Thus, the side AB is equal to DE or AB ≅ DE option (A) AB ≅ DE is correct.

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The answer will be 0.037, using a gradient.

To find the gradient of the given data, horizontal as well as the vertical distance between two points in parallel is necessary to find.

Therefore gradient of the slope is:

Hence the answer is 0.037.

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Answer:

D

Step-by-step explanation:

You are looking for a triangle that has the sides 14mm and 15mm forming an angle of 100 degrees

First, you can eliminate A and B because they don't have an angle that is 100 degrees!

Now all you have left is C and D

In figure C, the sides 14 and 15 do not make up the angle of 100 degrees

But 14 and 15 make a 100 degree angle in figure D!

Therefore the answer is D

Answer:

The value of the expression is -12

Step-by-step explanation:

Evaluate Algebraic Expressions

It's required to evaluate the following expression:

\(\sqrt{361}-2a^2-\mid b-17\mid\)

For a=-3 and b=4

Substituting the values:

\(\sqrt{361}-2a^2-\mid b-17\mid=\\\sqrt{361}-2(-3)^2-\mid 4-17\mid\)

The square root of 361 is 19, operating:

\(=19-2*9-\mid -13\mid\)

The absolute value of -13 is 13:

\(=19-18-13\)

\(=-12\)

The value of the expression is -12

Answer:4840

Step-by-step explanation:

Answer:

so each chair will cost 205

205 will be our cost C this is our dependent due to the entire cost being base on how many chairs that will get order

the independent variable will be how many chairs that will be ordered and there are 34 chairs being ordered

34*205= 6970

the total cost will be 6970

Option C) is correct z +3 is also an odd number

z- 3 is odd number,

odd number are given as 1, 3, 5, 7, 9,11,.. etc.

since z - 3 odd number

mean while
if we add 3 to z will also be the odd number cause subtracting 3 twice from z-3 returns the reverse value i.e.
so z + 3 also an odd number.

Thus, z +3 is also an odd number

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Answer: this is not a reasonable answer because 20 – 5 – 2 = 13

Step-by-step explanation:

   Let us see how much he will have actually have left.

       $20 - $5.10 - $1.90 = $13

➜ Our answer appears to be "this is not a reasonable answer because 20 – 5 – 2 = 13"

➜ This option rounded $5.10 to $5 and $1.90 to $2, which helps give a reasonable answer.

Answer:

D

Step-by-step explanation:

Firstly, the question is phrased very very badly as the four answers provided are coordinate points rather than how far apart the cities are in units.

To calculate the distance between two points, we have to use Pythagoras' Theorem as it's just pretty much a right-angle triangle. Please look at the (terribly drawn) image provided.

Keep in mind that these points are only roughly placed on the map.

But firstly, to use Pythagoras' Theorem (a^2 + b^2 = c^2), we must find the length of the two sides.

To find the length of the horizontal line (which from now on I'll refer to as 'a'), we must subtract the smaller x value from the larger one.

47 - 35 = 12

To find the length of the vertical line (which from now on I'll refer to as 'b'), we must subtract the smaller y value from the larger one.

122 - 78 = 44

I assume that the answer you should pick is D. (12, 44)

However, that doesn't exactly answer the question... it's worded a little weirdly.

To solve the rest of the equation, do the following:

Now that we know that the length of a = 12 and the length of b = 44, we can use Pythagoras' Theorem.

a^2 + b^2 = c^2

12^2 + 44^2 = c^2

144 + 1936 = c^2

2080 = c^2

c = \(\sqrt{2080}\)

c = 45.61

The answer is 45.61 units.

Answer:

B and D

Step-by-step explanation:

One thing is for certain. The final answer will be 1/r^12 or r^(-12)

When written as the given of (r^-4)^3, the powers are multiplied.

The first one is false. There are 4 factors of r^-4 If you get an answer that says it is true, then the question means that r^-4 is 3 equal factors of r^-12

B is true

C: not true. The exponents are multiplied, not added.

D is true

E: not true. This is the same thing as C.

The function y=x²+5x-6 has a minimum value. All real numbers are included in the function's domain. The function has a range of y ≤ 12.25, the correct option is (c).

The parabola has a minimum value and widens upwards since the x² term's coefficient is positive.

To find the minimum value, we can use the formula for the x-coordinate of the vertex:

x=-b/2a=-5/(2 × 1)=-2.5.

Plugging this value into the equation, we get

y=(-2.5)²+5(-2.5)-6=-12.25.

Therefore, the function has a minimum value of -12.25.

The function is a polynomial, which means it is defined for all real numbers.

Since the function has a minimum value of -12.25, the range of the function is all real numbers less than or equal to -12.25, i.e., {y ≤ 12.25}.

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The complete question is:

Consider the equation y=x^(2)+5x-6. Determine whether the function has a maximum or minimum value. State the maximum or minimum value. What are the domain and range of the function

a. minimum; 0; D: (all real numbers); R: {all real numbers}

b. maximum; 0; D (all real numbers); R: {y <-0}

c. minimum; -12.25; D (all real numbers); R: {y <-12.25}

d. maximum; -12.25; D {x <- 2.5}; R: {all real numbers}

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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a. i) Linear, ii) Time-invariant, iii) Non-causal, iv) BIBO stable, v) Has memory.

b. i) Non-linear, ii) Time-invariant, iii) Causal, iv) BIBO stable, v) Has memory.

c. i) Linear, ii) Time-invariant, iii) Causal, iv) BIBO stable, v) Has memory.

Let's analyze each system based on the given properties:

a. y[n] = 10 x[-n]

i) Linear or non-linear: The system is linear because it satisfies the principle of superposition. If we input a scaled sum of signals, the output will be the scaled sum of the individual outputs.

ii) Time-invariant or time-varying: The system is time-invariant because the output is a delayed and scaled version of the input, which remains consistent regardless of the time at which the input is applied.

iii) Causal or non-causal: The system is non-causal because the output depends on future values of the input (negative index values).

iv) BIBO stable or unstable: The system is BIBO (Bounded-Input Bounded-Output) stable because it does not exhibit unbounded or explosive behavior for bounded inputs.

v) Memoryless or has memory: The system has memory since the output depends on past and future values of the input (negative and positive index values).

b. y[n] = sin(2πx[n+1]) + 5x[n]

i) Linear or non-linear: The system is non-linear because it contains a non-linear operation, the sine function.

ii) Time-invariant or time-varying: The system is time-invariant because the output is a function of the delayed input, which remains consistent regardless of the time at which the input is applied.

iii) Causal or non-causal: The system is causal because the output only depends on present and past values of the input (no future values are involved).

iv) BIBO stable or unstable: The system is BIBO stable since the presence of a bounded input does not cause the output to become unbounded or exhibit explosive behavior.

v) Memoryless or has memory: The system has memory since the output depends on past values of the input (delayed by one sample).

c. y[n] = (1/2)^n * x[n]

i) Linear or non-linear: The system is linear because it satisfies the principle of superposition. If we input a scaled sum of signals, the output will be the scaled sum of the individual outputs.

ii) Time-invariant or time-varying: The system is time-invariant because the output is a delayed and scaled version of the input, which remains consistent regardless of the time at which the input is applied.

iii) Causal or non-causal: The system is causal because the output only depends on present and past values of the input (no future values are involved).

iv) BIBO stable or unstable: The system is BIBO stable because the output remains bounded for any bounded input, as the exponential decay factor (1/2)ⁿ ensures that the output does not exhibit unbounded behavior.

v) Memoryless or has memory: The system has memory since the output depends on past values of the input (delayed by n samples).

In summary:

a. i) Linear, ii) Time-invariant, iii) Non-causal, iv) BIBO stable, v) Has memory.

b. i) Non-linear, ii) Time-invariant, iii) Causal, iv) BIBO stable, v) Has memory.

c. i) Linear, ii) Time-invariant, iii) Causal, iv) BIBO stable, v) Has memory.

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Answer:

1.6 ounces of cheese

Step-by-step explanation:

To make 6 slices of pizza, 9.6 ounces of cheese is used.

Therefore,

6 slices = 9.6 ounces of cheese

To find the ounces of cheese for 1 slice,

1 slice = 9.6 ÷ 6

= 1.6 ounces of cheese

Answer:

74,009,234= 7^6+ 9^3+2^2+3^1+4^0

Step-by-step explanation:

Answer:

\(\sf y =\dfrac{-1}{3}x + 7\)

Step-by-step explanation:

Equation of line: y =mx +b

 Here, m is the slope and b is the y-intercept.

Parallel lines have same slope.

            \(\sf y =\dfrac{-1}{3}x + 4\)

     So, the slope of the required line = -1/3

Equation of the required line:  

                \(\sf y =\dfrac{-1}{3}x + b\)

Point(6,5) goes through the line. substitute x = 6 and y =5 in the above equation and then we can find the value of y-intercept 'b'

    \(\sf 5 =\dfrac{-1}{3}*6 +b\\\\ 5 = -2 + b\\\\5+2 = b\\\\\boxed{b = 7}\)

Equation of the require line:

           \(\sf \boxed{\bf y =\dfrac{-1}{3}x+7}\)

Answer:

c) 27.9

Step-by-step explanation:

Since MN is the midsegment ,

MN = (AB + CD)/2

21.1 = (AB + 14.3)/2

21.1*2 = AB + 14.2

AB = 42.2 - 14.2

AB = 27.9

Answer:

C

Step-by-step explanation:

the midsegment is equal to half the sum of the parallel bases, that is

\(\frac{1}{2}\) (AB + CD) = MN ( substitute values )

\(\frac{1}{2}\) (AB + 14.3) = 21.1 ( multiply both sides by 2 to clear the fraction )

AB + 14.3 = 42.2 ( subtract 14.3 from both sides )

AB = 27.9 cm

100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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According to Siegler, the pattern of learning math concepts involves a gradual development and refinement of strategies. Siegler's theory, known as the overlapping waves model, suggests that learners use multiple strategies simultaneously and gradually shift towards more efficient ones over time. This process allows for a better understanding and application of math concepts, ultimately leading to improved problem-solving skills.

According to Siegler, the pattern of learning math concepts involves a gradual progression from using counting strategies to more efficient and accurate strategies. Children initially rely on counting strategies to solve math problems, such as counting fingers or objects. As they progress, they begin to use more advanced strategies, such as decomposition or mental math, which allow them to solve problems more quickly and accurately. Siegler also emphasizes the importance of practice and repetition in developing math skills and the role of feedback and instruction in promoting learning. Overall, Siegler's theory suggests that children's math skills develop through a combination of innate abilities and environmental factors, including exposure to math concepts and opportunities for practice and instruction in time.

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Answer:14.7 games

Step-by-step explanation:

0.70 times 21 = 14.7

Answer:

5x

Step-by-step explanation:

First, calculate the product.
You gave 7x-3×4x+5x×2​
3x4 is 12 and 5x2 is 10.
Therefore, we now have 7x-12x+10x

Now collect like terms.
7x-12x+10x which will now be (7-12+10)x will give you 5x. 5x is your answer.