A 6th-grade class did a weekend fitness challenge.




Each student set a goal of `75` minutes of fitness.




Amanda exercised for `78` minutes.




What percent of the goal did she achieve?

Yes, it wasn't fair because some kids got more pizza.

What is simplest form of a fraction?

When the numerator (top) and denominator (bottom) of the fraction do not have any common factors, the fraction is said to be in its simplest form. For instance, 1/2 is the most basic version of 6/12.

Given that, there were 14 players.

Six players sat at one table and got 4 small pizzas to share equally.

Applying unitary method,

Thus each players got 4/6 part of a pizza.

                                    = 2/3 [ Divide denominator and numerator by 2]

The other 8 players sat at a different table and got 6 small pizzas to share equally.

Each players got 6/8 part of a pizza.

                            = 3/4 [Divide denominator and numerator by 2]

Now compare 2/3 and 3/4:

The LCM of the denominators 3 and 4 is 12.

Multiply 4 with denominator and numerator of 2/3:

(2×4)/(3×4) = 8/12

Multiply 3 with denominator and numerator of 3/4:

(3×3)/(4×3) = 9/12

Therefore, 9/12 >  8/12

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Answer:

Inequality Form:

x<−3

Interval Notation:

(−∞,−3)

Step-by-step explanation:

To sum it up

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Sorry just trying to get points

Step-by-step explanation:

a) The point estimate of the proportion of the population that would provide Yes responses is; 0.50

b) The estimate of the standard error of the proportion is; 0.0224

c) The 95% confidence interval for the population proportion is; CI = (0.4569, 0.5431)

a) The point estimate of proportion in a sample of n out of which x belongs to the favorable event is;

p^ = x/n

Thus, we are given; x = 250 and n = 500

p^ = 250/500

p^ = 0.5

b) The standard error  is defined as a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. It is given by the formula;

S = √(p^(1 - p^)/n)

Plugging in the relevant values gives;

S = √(0.5(1 - 0.5)/500)

S = 0.0224

c) A confidence interval is defined as the mean of your estimate plus and minus the variation in that estimate. The confidence interval is given by the formula;

CI = p^ ± z√(p^(1 - p^)/n)

where z is z-score at confidence level

z at 95% confidence level = 1.96

Thus;

CI = 0.5 ± 1.96√(0.5(1 - 0.5)/500)

CI = 0.5 ± 0.04312

CI = (0.4569, 0.5431)

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Answer:

  (a)  ∠HFE, ∠EFH

  (b)  FG, FE

  (c)  F

Step-by-step explanation:

You want the different names for the angles shown, and for their parts.

This question is about naming bits of geometry. Here, you're mainly naming rays and combinations that form angles. A ray is always named by naming its end point first, then another point on the ray. An angle is formed by two rays with a common end point.

An angle can be named by naming rays that form it (with the vertex in the middle of the name), by naming the vertex alone (if that is unambiguous), or by using a designator, such as ∠2.

Angle 2 is made from rays FH and FE, so can be named either of ...

If ray FG were not present, it could also be named angle F, the name of the vertex point.

The 3-letter angle name tells you the names of the sides. The end point of each ray must be named first in the ray name. It is named in the middle of the angle name.

The vertex of angle 1 is the point that is also the vertex of angle 2:

Answer:

63*

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

B would be the answer to this quadratic equation.

Answer:

B. x = 5 ± 10i

Step-by-step explanation:

ax² + bx + c = 0

quadratic formula = (-b ± [tex]\sqrt{b^{2}-4ac }[/tex])/2a

y = x² - 10x + 125

substitute the values:

(-(-10) ± [tex]\sqrt{(-10)^{2}-4(1)(125) }[/tex])/2(1)

= (10 ± [tex]\sqrt{100 - 500}[/tex])/2

= (10 ± [tex]\sqrt{-400}[/tex])/2

= (10 ± 20i)/2

= 5 ± 10i

The probability of growing seed exactly one is 0.0033.

The probability of a seed not growing is 0.46, because if it has a 54% chance of growing, then  100% - 54% to find the odds that it will not grow, which is 46%.

The probability of 7 seeds growing is equivalent to asking what the probability is of a seed growing and another seed growing and another seed growing and another seed, and so on until I say a total of 7seeds. The point is that "and" in probability means to multiply.

To calculate the likelihood of seven seeds growing,

(0.46)(0.54)⁷

Probability = 0.0033

Probability = 0.0033 x 100

                  = 0.33%

Therefore probability of growing exactly one seed is 0.0033.

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Answer:

x=5

Step-by-step explanation:

or, 3x-9-4=2

or, 3x-13=2

Now, Adding 13 on both sides we get,

or, 3x-13+13=2+13

or, 3x=15

Now, Dividing both sides by 3 we get,

or, (3x)/3=15/3

Therefore, x=5

Answer: (12,-6)

Step-by-step explanation:

(a) According to the graph :  Local minimum point is : -3 , 4

(b) Local minimum values of g is: 1, -2

"Information available from the question"

In the question:

Here is a graph of the function g

Use the graph to find the following.

If there is more than one answer, separate them with commas.

(a) All values at which g has a local minimum:___

(b) All local minimum values of g :___

Now, According to the question:

If a function has a definite value at every neighborhood of a point and the value at that point is the minimum. The value of the function at that point is the local minimum.

(a)  All values at which g has a local minimum:

According to the graph :  Local minimum point is : -3 , 4

(b)  All local minimum values of g:

Local minimum values of g is: 1, -2

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Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Domain is:

Range is:

This is a function as it passes the vertical line test.

Domain is:

Range is:

This is a function as it passes the vertical line test.

Answer:

32.a)  Domain:  (-6, 6)

32.b)  Range:  (-6, 2]

32.c)  Function:  Yes

33.a)  Domain:  (-6, 6]

33.b)  Range:  (-1, 5]

33.c)  Function:  Yes

Step-by-step explanation:

Definitions

Interval notation

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the endpoints of the continuous curve are:

As the endpoints are open circles, the x-values are excluded from the domain.  Therefore, the domain in interval notation is:

The smallest y-value is y = -6 and the greatest y-value is y = 2.  

y = -6 is excluded from the range since it is the y-value of the open circle endpoint, whereas y = 2 is included in the range.  Therefore, the range in interval notation is:

The graph is a function as is each input (x-value) is related to exactly one output (y-value).

From inspection of the graph, the endpoints of the continuous line are:

As the graph is a straight line, the x and y values of the endpoints are the x and y values of the domain and range.

As the (-6, -1) endpoint is an open circle, the values are excluded from the domain and range.

As the (6, 5) endpoint is a closed circle, the values are included in the domain and range.

Therefore, the domain and range in interval notation are:

The graph is a function as is each input (x-value) is related to exactly one output (y-value).

a) Using conditional probability, the likelihood that a driver purchases oil, given that he or she purchases gasoline is 5.62%.

b) Based on conditional probability, the chance that a driver purchases gasoline, given that he or she purchases oil is 71.43%.

Conditional probability is the likelihood or chance of an event or outcome occurring, based on a previous event or outcome that occurs.

Conditional probability considers two events occurring relatively.

The formula for conditional probability is intersection probability divided by base probability.

The percentage (proportion) of drivers who stop at a gas station to buy gasoline = 89%

The probability of buying both gasoline and oil = 5%

The percentage (probability) of purchasing oil = 7%

a) The probability that a driver purchases oil, given that he or she purchases gasoline = the probability of buying both gasoline and oil/the probability of stopping and buying gasoline.

= 5.62% (0.05/0.89).

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b) The probability that a driver purchases gasoline, given that he or she purchases oil = the probability of buying both gasoline and oil/the total probability of those who purchase oil.

= 71.43% (0.05/0.07 x 100).

Of the drivers who stop at a gas station, 89% purchase gasoline, and 5% purchase both gasoline and oil. A total of 7% purchase oil.

(a) What is the probability that a driver purchases oil, given that he or she purchases gasoline? Round your answer to the nearest hundredth.

b) What is the probability that a driver purchases gasoline, given that he or she purchases oil? Round your answer to the nearest hundredth.

The number of different pasta dishes the customers can create are 180.

According to its definition, a combination is "An arrangement of objects where the order in which the objects are selected is irrelevant." The phrase "Selection of things" denotes a situation in which the chronological order of events is irrelevant.

Given,

Number of noodle options = 3.

Number of sauce options = 3.

Number of vegetable options = 4.

Number of meat options = 5.

To find the number of possible combinations we need to take the total number of each option and multiply them together as there is no repetition allowed.

Possible combinations = 3×3×4×5

                                      = 180

Thus, the number of pasta dishes created = 180.

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By using the concept of control chart, it can be concluded that

A large number of plots are on or near the centerline.

Third option is correct.

What is control chart?

Control chart is used to show how a process changes over time.

There are three lines in a control chart.

They are the central line for the average, upper line for the Upper Control Limit (UCL) and a lower line for the Lower Control Limit (LCL)

It is known that the highest performance of a process is obtained when it is between the LCL and the UCL.

That means to get the best result, samples needs to be concentrated near the centerline.

So the third option is correct

A large number of plots are on or near the centerline.

Third option is correct.

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Complete Question

Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is not a reason that the process being monitored with the chart should be investigated?

A sudden and sustained shift in the plots toward the upper or lower control limit

There is an upward trend in the plots

A large number of plots are on or near the central line

A single plot falls outside of the control limits

The quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 are the only correct equations having only one solution.

Quadratic equations has it highest power to the degree of two and they have two solutions that makes them true. The solutions could be different or similar ( which implies there is only one solution). From the question we shall concentrate on the equations which have similar solution or rather only one solution.

For the equation 5x² + 20x + 20 = 0;

we divide through by 5 to get;

x² + 4x + 4 = 0

x² + 2x + 2x + 4 = 0 {we group the terms}

x(x - 2) +2(x + 2) = 0 {factorize}

(x + 2)(x + 2) = 0

either; x + 2 = 0 or x + 2 = 0

x = -2 or x = -2 {which are the same solutions}

For the equation x² + 6x + 9 = 0;

x² + 3x + 3x + 9 = 0 {we group the terms}

x(x + 3) + 3(x + 3) = 0 {factorize}

(x + 3)(x + 3) = 0

either; x + 2 = 0 or x + 2 = 0

x = -2 or x = -2 {which are the same solutions}

Therefore, the quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 each have only one solution which are -2 and -3 respectively.

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Answer:

8 beads per ring.

Step-by-step explanation:

50/6 = 8.333..

Since you cannot have less than half of a ring, the answer is 8.

Answer:

Step-by-step explanation:

x < 2

I think is the answer when you subtract 7 from both sides you get 3x <6 and then you divide both sides by 3 getting x < 2 (not sure if that's how you solve this one but usually it would be solved like this. if wrong then I'm sorry)

According to the geometric series 0.08 is the sum or state that the series diverges.

A geometric series is a series for which the ratio of each two consecutive terms is a constant function of the summation index . The more general case of the ratio a rational function of the summation index. produces a series called a hypergeometric series.

Given:

[tex]$$\sum_{n=2}^{\infty} \frac{3^n}{12^n}$$[/tex]

In the first term, it represents an unlimited geometric series.

b = 9/144

And the common ratio,

q = 3/12

By the ratio test ,it is convergent

Sum is

S = b/1-q

[tex]$=\frac{\frac{9}{144}}{1-\left(\frac{3}{12}\right)}$[/tex]

S = [tex]\frac{108}{1296}[/tex]

S = 0.08

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The complete question is-

Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent seris).

                                         [tex]$$\sum_{n=2}^{\infty} \frac{3^n}{12^n}$$[/tex]                                

Greatest common factor (GCF): 12a³b + 8a²b² - 20ab³. = 4ab(3a² + 2ab - 5b²) that is option 2

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the biggest, we refer to the GCF of 12, 20, and 24 as four.

There are two stages to get the GCF since 12a3b + 8a2b2 - 20ab3. contains both integers and variables (HCF). Find GCF for the variable component first, then for the numeric part.

How to locate GCF

1. Find the GCF for the 12, 8, 20 numerical portion.

2. Calculate the GCF for the variable component (a3b, a2b2, and ab3).

3. Add the values together and multiple them

Find the common factors for the numerical part: 12 ,8,20 is

factors of 12 -1,2,3 ,4,6,12

factors of 8 - 1,2,4,8,

factor of 20 - 1,2,4,5,10,20

the common factor will be 1,2,4

so GCF = 4

Next, find the common factors for the variable part: a³b , ,a²b² ,ab³.

the common factors will be ab

so GCF = ab

for the equation 12a³b + 8a²b² - 20ab³.

4ab is common , if we take 4ab common then remaining parts are

12a³b = 3a²

8a²b² = 2ab

20ab³. = 5b²

greatest common factor: 12a³b + 8a²b² - 20ab³. = 4ab(3a² + 2ab - 5b²)

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Journalizing the entries to record the transactions is as follows:

Date      Account Titles and Explanation    Debit    Credit

Nov. 21 Notes Receivable                        $48,000

            Accounts Receivable                               $48,000

(To record the receipt of a 60-day 9% note dated November 21 from McKenna Outer Wear Co. on the past account.)

Dec. 31 Interest Receivable                         $480

            Interest Revenue                                           $480

(To accrue interest revenue on the note at year-end.)

Jan. 20 Cash                                          $48,720

             Notes Receivable                                  $48,000

             Interest Receivable                                     $480

             Interest Revenue                                        $240

(To record the full settlement of the note and interest.)

Journal entries are the first recording of business transactions in the company's day book.

With the journal entries, debit and credit accounts are identified, helping to organize the general ledger.

Nov. 21 Notes Receivable $48,000 Accounts Receivable $48,000

60-day 9% note dated November 21

Dec. 31 Interest Receivable $480 Interest Revenue $480 ($48,000 x 9% x 40/360)

Jan. 20 Cash $48,720 Notes Receivable $48,000 Interest Receivable $480 Interest Revenue $240 ($48,000 x 9% x 20/360)

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Answer:hi

Step-by-step explanation:

Temperature at 6 a.m. was:

The difference is:

Temperature in Buffalo at noon was 19 °F greater:

Answer:

The inequality represented in the given picture is:

[tex]x \le 5[/tex]

Note the inclusive less than sign since the graph has a filled-in dot.

This can be represented in interval notation as:

[tex](-\infty, 5][/tex]

Note the bracket on enclosing the 5, representing inclusiveness.

Answer:

Step-by-step explanation: 0.2=1/5 0.002=1/500

1/5*1/500=1/2500 which equals 0.0004

we calculated confidence interval = 0.48±0.16

confidence interval represents the accuracy of a particular estimation.

proportion of population is the ratio of random sample to the total available sample.

Given, size of samples that means number of total iPhones, n = 25

size of random samples that means iPhone with 85 downloaded apps, p= 12,

critical value for 90% confidence interval z* = 1.65

proportion of samples, p^ = p/n = 12/25 =0.48

finally, confidence interval = p^±z*[√{p^(1-P^)/n}]

                                               0.48±1.65[√{0.48(1-0.48)/25}]

                       hence, the confidence interval = 0.48±0.16

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By studying the given situation, it can be concluded that

Heath is engaged in p- hacking.

What is p-hacking?

p-hacking is the misuse of statistical data to make a result statistically significant.

Heath analyzes his data using a bivariate correlation, as he previously planned; however, to his frustration, he quickly learns that his results are just short of being statistically significant.

Heath's main target is to make his result statistically significant.

He decides to try conducting a multiple-regression analysis instead and is pleased to see that with this method of data analysis, the results are statistically significant. Because the results were so similar, Heath doesn't bother reporting the bivariate correlation in his paper, as he thinks that clearly multiple regression was the correct test to run.

She Heath did not report the bivariate correlation in his paper, he is misusing the data to make his data statistically significant.

So Heath is engaged in p-hacking.

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Answer:

b) D => d. 9/7

Step-by-step explanation:

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (-5 - 4)/(-4 - 3)

→ m = (-9)/(-7)

→ [ m = 9/7 ]

Hence, the slope is 9/7.

The perimeter of a triangle with sides 4, 6, and 8 feet is 18 feet.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the perimeter of a triangle is the sum of it's all three sides.

In the case of an equilateral triangle, the perimeter is 3×side as all three sides have the same length.

∴ The perimeter of a triangle with sides 4, 6, and 8 feet is,

= (4 + 6 + 8) feet.

= 18 feet.

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