The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called__________

Answer:

Step-by-step explanation:

Check the attachment for solution

Answer:

46 jumps

Step-by-step explanation:

Since the grasshopper is two inches long, and can jump a distance of 40 inches, then its jump ratio is 2:40 = 1:20.

The athlete's body-length is 5 feet 9 inches. We convert this to inches which is 5 × 12 = 60 inches. We then add the remaining 9 inches to make it 60 + 9 = 69 inches. Since our jump ratio for the grasshopper equals that for the athlete, 1:20 = 69: 20 × 69= 69 : 1380. Thus the athlete's jump ratio is 69 inches to 1380 inches.

The athlete wants to cover one mile and we know that 1 mile = 63360 inches. So, we divide the distance the athlete wants to cover(1 mile = 63360 inches) by his jump-length(1380 inches) to get the number of jumps it takes to cover a mile. Number of jumps × jump-length of athlete = one mile, so Number of jumps = one mile/jump-length of athlete = 63360 inches/ 1380 inches= 45.9 jumps ≈ 46 jumps.

It would take the athlete approximately 46 jumps to cover one mile.

To solve this problem, we'll start by establishing the jumping ratio of the grasshopper and then applying that ratio to the athlete to determine how many jumps it would take for the athlete to cover one mile.

First, let's calculate the jump ratio for the grasshopper:

- Grasshopper's length: 2 inches

- Grasshopper's jump length: 40 inches

The ratio of the grasshopper's jump length to its body length is:

[tex]\[ \text{Jump ratio} = \frac{40 \text{ inches}}{2 \text{ inches}} = 20 \][/tex]

Next, let's find the athlete's height in inches:

- Athlete's height: 5 feet 9 inches

- 1 foot = 12 inches

Thus, the athlete's height in inches is:

[tex]\[ 5 \text{ feet} \times 12 \text{ inches/foot} + 9 \text{ inches} = 60 \text{ inches} + 9 \text{ inches} = 69 \text{ inches} \][/tex]

Using the grasshopper's jump ratio, we can determine the distance the athlete could jump:

[tex]\[ \text{Athlete's jump length} = 69 \text{ inches} \times 20 = 1380 \text{ inches} \][/tex]

Now, we need to determine the total number of jumps the athlete would need to cover one mile. First, convert one mile to inches:

- 1 mile = 5280 feet

- 1 foot = 12 inches

Therefore, the distance of one mile in inches is:

[tex]\[ 5280 \text{ feet} \times 12 \text{ inches/foot} = 63360 \text{ inches} \][/tex]

Finally, the number of jumps required for the athlete to cover this distance is:

[tex]\[ \text{Number of jumps} = \frac{63360 \text{ inches}}{1380 \text{ inches/jump}} \][/tex]

Calculating this value:

[tex]\[ \text{Number of jumps} \approx \frac{63360}{1380} \approx 45.92 \][/tex]

Since the number of jumps must be a whole number, we round 45.92 to the nearest whole number:

[tex]\[ \text{Number of jumps} \approx 46 \][/tex]

Therefore, it would take the athlete approximately 46 jumps to cover one mile.

Following steps and calculations, the missing coordinate r is -3. This point lies on line with slope of 2 along with other given point (4, -11).

Step-by-Step Calculation:

1. Identify the slope formula:

The slope (m) of a line passing through points (x1, y1) and (x2, y2) is calculated as:

m = (y2 - y1) / (x2 - x1)

2. Plug in known values:

We know the slope (m) is 2, points (x1, y1) are (4, -11), and points (x2, y2) are (8, r). Substitute these values:

2 = (r - (-11)) / (8 - 4)

3. Simplify the equation:

2 = (r + 11) / 4

2 × 4 = r + 11

8 = r + 11

4. Isolate r:

8 - 11 = r

r = -3

The value of missing coordinate "r" is -4

Solution:

Given that,

The points (1, r) and (4, -13) lie on a line with slope – 3

To find: missing coordinate r

The slope of a line is given by formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Where, "m" is the slope of line

Here in this sum,

m = -3

[tex](x_1, y_1) = (1, r)\\\\(x_2, y_2) = (4, -13)[/tex]

Substituting the values in formula,

[tex]-3 = \frac{-13-r}{4-1}\\\\-3=\frac{-13-r}{3}\\\\-9 = -13 - r\\\\r = -13+9\\\\r = -4[/tex]

Thus the value of missing coordinate "r" is -4

Answer:

There were 25 problems on the science quiz

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Grade Manuel got on the science quiz = 80% or 80/100

Number of correct answers = 20

2. How many problems were on the science quiz?

Let's use the Rule of Three Simple, this way:

Problems on the science quiz   Percentage

20                                                    80

x                                                       100

x * 80 = 20 * 100

80x = 2,000

x = 2,000/80

x = 25

There were 25 problems on the science quiz

Answer:

25

Step-by-step explanation:

20 x 100/80 = 25

or 20/80 = x/100

Answer:

The number of shoes Paisley own is 75.

Step-by-step explanation:

Given:

Paisley was organizing her shoe collection.

She counted 24 pairs of sandals.

This represents 32% of the total number of shoes she owns.

Now, to find the number of shoes Paisley own.

Let the number of shoes Paisley own be [tex]x.[/tex]

According to question:

32% of [tex]x[/tex] = 24.

[tex]\frac{32}{100} \times x=24[/tex]

[tex]0.32x=24[/tex]

Dividing both sides by 0.32 we get:

[tex]x=75.[/tex]

Therefore, the number of shoes Paisley own is 75.

Answer:

The total number of shoes Paisley owns = 75

Step-by-step explanation:

Given:

24 pairs of sandals represent 32% of the shoes Paisley owns.

To find the total number of shoes Paisley owns.

Solution:

Let the total number of pairs of shoes be = [tex]x[/tex]

Thus, number of sandals can be represented as:

⇒ 32% of [tex]x[/tex]

⇒ [tex]0.32\times x[/tex]

⇒ [tex]0.32x[/tex]

Number of sandals = 24

So, we can write the equation as:

⇒ [tex]0.32x=24[/tex]

Solving for [tex]x[/tex]

Dividing both sides by 0.32.

⇒  [tex]\frac{0.32x}{0.32}=\frac{24}{0.32}[/tex]

⇒ [tex]x=75[/tex]

Thus, the total number of shoes Paisley owns = 75

Step-by-step explanation:

Answer:

The number of fiction books is 500 and non fiction books is 1500.

Step-by-step explanation:

Given:

Total book library contains = 2000.

There are 3 times as many non fiction books as fiction books.

Now, to determine the number of non fiction books and fiction books.

Let the fiction books be [tex]x.[/tex]

And the non fiction books be [tex]3x.[/tex]

Total books = 2000.

Now, to get the number of non fiction books and fiction books we put an equation:

[tex]3x+x=2000.[/tex]

[tex]4x=2000.[/tex]

Dividing both sides by 4 we get:

[tex]x=500.[/tex]

Fiction books = 500.

Non fiction books = [tex]3x=3\times 500=1500.[/tex]

Therefore, the number of fiction books is 500 and non fiction books is 1500.

To solve for the number of nonfiction and fiction books in the library, set up a system of equations and solve them to find there are 500 fiction books and 1500 nonfiction books.

To determine the number of nonfiction and fiction books in the library, we can use a system of equations. Let's denote the number of fiction books as F and the number of nonfiction books as NF. According to the problem, the total number of books in the library is 2000, and there are 3 times as many nonfiction books as there are fiction books.

Our two equations will be:

F + NF = 2000 (Total number of books)

NF = 3F (3 times as many nonfiction books)

To solve these equations:

Substitute the second equation into the first one:

F + 3F = 2000

4F = 2000

Divide both sides by 4 to find F:

F = 2000 / 4

F = 500

There are 500 fiction books. Now we can find the number of nonfiction books by multiplying 500 by 3:

NF = 3 * 500 = 1500

So, the library has 500 fiction books and 1500 nonfiction books.

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Answer: C) 44 mph

Step-by-step explanation:

We know that [tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

Given : A car drives 40 miles on local roads at 20 mph.

i.e. Time taken : [tex]t_1=\dfrac{40}{20}=2\ hour[/tex]

Also, it drives 180 miles on the highway at 60 mph.

i.e. Time taken : [tex]t_2=\dfrac{180}{60}=3\ hour[/tex]

We know that the formula for Average speed is given by :-

[tex]A.V.=\dfrac{\text{Total distance}}{\text{Total Time}}[/tex]

So the average speed of the entire trip will be :-

[tex]\dfrac{40+180}{t_1+t_2}\\\\\\=\dfrac{220}{2+3}=\dfrac{220}{5}\\\\=44[/tex]

Hence, the average speed of the entire trip is 44 mph.

Therefore , the correct answer is C) 44 mph.

Answer:

Step-by-step explanation:

He used a coupon for 1/2 off the price of the bat which is $69. With the coupon applied, the cost of the bat would be 69 × 1/2 = $34.5

He also used a coupon for 1/2 off the price of the glove which is $75. With the coupon applied, the cost of the bat would be 75 × 1/2 = $37.5

Therefore, a numerical expression to find the total cost of the bat, the glove, and 3 baseballs which are 5.50 each would be

34.5 + 37.5 + 3 × 5.5 = $88.5

The total cost of the bat, the glove, and the baseballs is $88.5 and this can be determined by using the given data and arithmetic operations.

Given :

He used a coupon for 1/2 off the price of the bat which is $69 and the glove which is $75.

The following steps can be used to evaluate the total cost:

Step 1 - Find the cost of the bat after the discount.

[tex]= \dfrac{1}{2}\times 69[/tex]

= $34.5

Step 2 - Find the cost of the glove after the discount.

[tex]=\dfrac{1}{2}\times 75[/tex]

= $37.5

Step 3 - Now, evaluate the cost of the baseballs.

[tex]=3\times 5.5[/tex]

= $16.5

Step 4 - Add all the costs to determine the total cost.

= 16.5 + 37.5 + 34.5

= $88.5

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Answer:

B

Step-by-step explanation:

This question is asking to make a conversion from kilolitres to liters.

There is a total of 1000L in 1kL.

Hence to make the conversion from KL to L , we have to multiply the KL by 1000. Hence, for 505KL, its equivalent measurement in L would be 505 * 1000 = 505,000

Hence, 505kL expressed in L is 505,000

Answer:

b. a person

Step-by-step explanation:

The conducted study demonstrates the commuting patterns of people. Here, the information is collected from a person about amount of time consumes in travel to their work on a certain day of the week. Thus, here the individual is "a person" because the information is collected from a person about their time travel.

Answer:

A. Stereo Store Job is highest paying Job.

B. The Difference between the weekly salaries of these two jobs is $45.

Step-by-step explanation:

Given:

Annual Pay of job in stereo store =  34.6K

Now K here means (1000).

So we can say that;

Annual Pay of job in stereo store = [tex]\$34.6\times 1000= \$34600[/tex]

Also Given:

Weekly salary of Job at clothing store = $620

We need to find which job is the higher-paying job.

Also We need to find the difference in the weekly salaries of these two jobs

Solution:

First we will find the weekly salary of  job in stereo store.

Now we know that there are 52 weeks in a year.

So weekly salary of  job in stereo store can be calculated by Annual Pay of job in stereo store divided by total number of weeks.

framing in equation form we get;

weekly salary of  job in stereo store = [tex]\frac{34600}{52}=\$665.38[/tex]

Now we see that weekly salary of  job in stereo store is greater than Weekly salary of Job at clothing store.

Hence Stereo Store Job is highest paying Job.

Now we need to find the  difference in the weekly salaries of these two jobs.

difference in the weekly salaries can be calculated by weekly salary of  job in stereo store minus weekly salary of  job in clothing store.

framing in equation form we get;

Difference = [tex]\$665.38-\$620 =\$45.38[/tex]

Rounding to nearest dollar we get;

Difference = $45

Hence the Difference between the weekly salaries of these two jobs is $45.

A. The job in the clothing store is the higher-paying job. B. The difference in the weekly salaries of these two jobs is $45.

To determine which job is higher-paying, we need to compare the annual salaries of both jobs and convert them to weekly salaries for a fair comparison, assuming a standard work year of 52 weeks.

A. Comparing the annual salaries:

1. The job at the stereo store pays $34,600 per year. To find the weekly salary, we divide this amount by 52 weeks:

[tex]\[ \frac{34,600}{52} = 665.38 \][/tex]

So, the weekly salary for the job at the stereo store is approximately $665.38.

2. The job at the clothing store pays a weekly salary of $620.

Now, comparing the weekly salaries:

Stereo store: $665.38 per week

Clothing store: $620 per week

The job at the clothing store pays more per week than the job at the stereo store.

B. Calculating the difference in weekly salaries:

To find the difference between the weekly salaries of the two jobs, we subtract the weekly salary of the stereo store job from the weekly salary of the clothing store job:

[tex]\[ 665.38 - 620 = 45.38 \][/tex]

Rounding to the nearest dollar, the difference in the weekly salaries is approximately $45.

However, the question asks for the difference in the weekly salaries of these two jobs, not the difference in the weekly salary of the stereo store job from the clothing store job. Since the clothing store job pays more, we should actually subtract the weekly salary of the clothing store job from the weekly salary of the stereo store job to find the additional amount the clothing store job pays per week:

[tex]\[ 620 - 665.38 = -45.38 \][/tex]

Since we are looking for a positive difference, we take the absolute value:

[tex]\[ |-45.38| = 45.38 \][/tex]

Rounding to the nearest dollar, the difference in the weekly salaries of these two jobs is approximately $45. However, it seems there was a mistake in the initial answer provided for part B. Let's correct this:

The correct calculation for the difference in weekly salaries is:

[tex]\[ 665.38 - 620 = 45.38 \][/tex]

Rounding to the nearest dollar, the difference is $45.

Answer:

the answer is D

Step-by-step explanation

the ratio of the triangles is 3:1 (you find that out because 21:7 is simplified to 3:1.

when you plug in 6 as x then you get 18:6 which simplifies to 3:1 also

Answer:

correct answer is e. Side-by-side boxplots

Step-by-step explanation:

given data

IQ test

sample = 540 students

solution

here Side-by-side boxplots that is apply it to the data set with 1 quantitative and 1  categorical variable

Side-by-side boxplots is also very useful in the comparing fundamental information for 2 data set

eg median value and range of value they cover from data

and

Side-by-side boxplots also provide target summary and it analysis the data

so here correct answer is e. Side-by-side boxplots

The relation between the two dataset can be shown by placing the

dataset side-by-side, to give a meaningful display.

Correct response:

The number of student in the study = 540

The categories of the data = Oldest/In Between/Youngest

The category of the other data collected = Their score on IQ test

Required:

To choose the option that would be a meaningful display of the data

from the study.

Solution:

The number of categories of the order of birth = 3

Therefore, a meaningful display of the order of birth is possible using a boxplot.

The IQ test scores can be categorized as follows;

Therefore, the dataset for the order of birth and the dataset for the IQ

test score can be presented side-by-side, thereby providing a

meaningful display.

The correct option is therefore;

Learn more about side-by-side boxplots here:

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Answer:

Step-by-step explanation:

let the eq. of circle be a(x²+y²)+bx+cy+d=0

x²+y²+b/a x+c/a y+d/a=0

if it passes through (0,0)

0²+0²+b/a*0+c/a*0+d/a=0

so d=0

Hence x²+y²+b/a x+c/a y=0

if it passes through (1,2) and (3,-1)

1²+2²+b/a×1+c/a×2=0

5+b/a+2c/a=0   ...(1)

and 3²+(-1)²+b/a*3+c/a*(-1)=0

10+3b/a-c/a=0   ...(2)

(1)+2(2) gives

5+b/a+2 c/a+20+6 b/a -2 c/a=0

7 b/a+25=0

b/a=-25/7

from (1)

5-25/7+2 c/a=0

2 c/a+10/7=0

2 c/a=-10/7

c/a=-5/7

so eq. of circle is x²+y²-25/7 x-5/7 y=0

7(x²+y²)-25 x-5 y=0

Answer: B) All teenagers.

Step-by-step explanation:

In statistical survey , a population is a large group of individuals that share some similar characteristics according to the researchers's point of view or the demand of the study.

When the population very large , then he take a sample of population that represents the whole population.

For example : If a researcher wants know the average weight of women in the university , he will need the data of all women in university which is the population for this study.

As per given :  A national polling organization wants to estimate the percentage of all teenagers who believe social security will 'be there' for them.

Here , the population of interest : All teenagers.

Sample :  1500 teenagers

37% : sample proportion of teenagers says that they believe social security will 'be there' for them.

Hence, the correct answer is : B) All teenagers.

Answer:

Step-by-step explanation:

When two triangles are similar, it means that the ratio of their corresponding sides is equal.

Therefore

96/(6x + 28) = 24/25

Crossmultiplying,

1) 96 × 25 = 24(6x + 28)

2400 = 144x + 672

144x = 2400 - 672 = 1728

x = 1728/144

x = 12

2) angle A and angle D is equal because they are alternate angles.

(2x + 6)/(x + 6) = 10/8

Crossmultiplying

8(2x + 6) = 10(x + 6)

16x + 48 = 10x + 60

16x - 10x = 60 - 48

6x = 12

x = 12/6 = 2

3) both triangles are right angle triangles. All angles are similar in both triangles. It also means that all the sides are similar. Therefore

45/30 = 40/x

Crossmultiplying

45 × x = 30 × 40

45x = 120

x = 120/45 = 26.7

Answer:

a,d,e

Step-by-step explanation:

x=1,x-1=0

x=6

x-6=0

if 1,6 are roots then (x-1) and (x-6) are factors of f(x)

Answer:a,d,e

Step-by-step explanation:

Final answer:

To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder.

Explanation:

To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Since the volume of the cylinder is given as 6, we can use the formula V = πr^2h to find the height of the cylinder. Plugging in the values, we get 6 = πr^2h. Since the radius of the cylinder is half the length of side AB, which is 3, we can solve for h to find that h = 4/π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder. Plugging in the values, we get θ = 6π/3 = 2π.

10n * f  where f is the number of frogs in that community.

Step-by-step explanation:

The growth rate is given as 10g /day

For 10 days, the weight in grams will be 10*10 =100 grams

This means that for n days, the weight gained by a new frog will be; n*10 g

=10n grams

Lets assume the frog community has a population of f frogs, then total weight of the frog community will be;

10n * f  where f is the number of frogs in that community.

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Answer:

0.4

Step-by-step explanation:

Equation is

x-(-3.8)=2(x-1.7)

solving for x,

x+3.8=2x-3.4

x=0.4

Final answer:

The value of x is found by setting up an equation based on the distances provided and considering two separate cases for the absolute value. After solving the equation, the positive value of x is determined to be 7.2.

Explanation:

To solve for the value of x in this problem, we need to set up an equation based on the information given about the distances on a number line. The distance between x and -3.8 is twice the distance between x and 1.7. This translates to the following equation:

|x - (-3.8)| = 2|x - 1.7|

We then solve this equation step-by-step:

Therefore, the value of x to the nearest tenth is 7.2.

Answer:

  26 2/3

Step-by-step explanation:

The easiest way to find the answer is to look at the graph value for 1 hour. It is slightly more than 25, but the graph isn't detailed enough to let us read a precise value.

The next best way is to find a grid intersection that the line goes through. We observe that (1.5 hours, 40 miles) is on the plotted line, so the proportion is ...

  (40 mi)/(1.5 h) = 26 2/3 mi/h

Answer: 0.25 or 25%

Step-by-step explanation:Women have two chromosomes XX and men have two also XY.

From the question, it can be seen that colorblindness is an X-linked recessive condition.

Let the X-linked recessive gene be specified as [tex]X^{-}[/tex] and the dominant gene which is not colorblind linked as [tex]X^{+}[/tex].

The question says the woman has a father who is colourblind which means her father possesses the X-linked recessive gene [tex]X^{-}[/tex] which means he has chromosomes [tex]X^{-}Y[/tex] and therefore must have given his daughter the recessive gene

For her husband who has normal vision his chromosomes will be [tex]X^{+} Y[/tex].

So, the probability that their son will be colourblind will be;

Chromosomes [tex]X^{+}[/tex] Y

[tex]X^{+}[/tex] [tex]X^{+} X^{+}[/tex] [tex]X^{+}Y[/tex].

[tex]X^{-}[/tex] [tex]X^{-} X^{+}[/tex]. [tex]X^{-}Y[/tex].

Therefore, the probability that their son will be color blind = ¼ or 0.25 or 25%

Answer:

The answer is C because the principal goes down and interest goes up. The part of your payment goes to....

Step-by-step explanation:

Answer:

1.6%

Step-by-step explanation:

The real GDP is given by the nominal GDP divided by the GDP deflator, the real GDP for year 1 and year 2, respectively, were:

[tex]GDP_1=\frac{2250}{0.72}\\GDP_1=\$3,125\ billion\\\\GDP_2=\frac{2,508}{0.79}\\GDP_2=\$3,174.68\ billion[/tex]

The percentage change in GDP is:

[tex]P=\frac{3,174.68-3,125}{3,125}\\ P=0.016=1.6\%[/tex]

Between year 1 and year 2, real GDP rose by 1.6%.

Answer:

  y = (8/5)√10

Step-by-step explanation:

You seem to have ...

  [tex]y=kx\sqrt{z}[/tex]

We can find k from the given values ...

  [tex]\dfrac{y}{x\sqrt{z}}=k=\dfrac{6}{3\sqrt{9}}=\dfrac{6}{3\cdot 3}=\dfrac{2}{3}[/tex]

Then for the new values, ...

  [tex]y=\dfrac{2}{3}\cdot 4\sqrt{3.6}=\dfrac{8\sqrt{90}}{3\cdot 5}=\dfrac{8\sqrt{10}}{5}[/tex]

Answer:

its d

Step-by-step explanation:

if im wrong then sorry :(

Answer:

A

100% Correct ANSWER. Pls, give me brainliest. Thank You!

Answer:

Finance Charge = $1.42

New Account Balance = $90.02

Step-by-step explanation:

APR (Annual Percentage Rate) = 22%

Periodic Rate = 1.83% (APR/12)

Beginning Balance = $102.33

Payment made on 15th day = $25.00

Purchase made on 25th day = $11.27

Finance Charge = (Beginning Balance - Payment made on 15th day) x Periodic Rate

Finance Charge = ($102.33 - $25.00) x 0.0183

Finance Charge = $77.33 x 0.0183

Finance Charge = $1.42

New Account Balance = Beginning Balance - Payment made on 15th day + Purchase made on 25th day + Finance Charge

New Account Balance = $102.33 - $25.00 + $11.27 + $1.42

New Account Balance = $90.02

The finance charge is approximately $1.67, and the new account balance after accounting for the payment and purchase is $90.27.

We start with the account balance on April 1st, which is $102.33. On April 15th, a payment of $25.00 is made, and on April 25th, a purchase of $11.27 is made.

1: Calculate the Average Daily Balance

Average Daily Balance = ( (14 * 102.33) + (10 * 77.33) + (6 * 88.60) ) / 30 = $91.22

2: Calculate the Finance Charge

Given the annual interest rate of 22%, we first find the monthly rate: 22% / 12 = 1.833%.

Then we calculate the finance charge:

Finance Charge = Average Daily Balance * Monthly Rate
Finance Charge = $91.22 * 0.01833 ≈ $1.67

3: Calculate New Account Balance

New Balance = Previous Balance - Payment + Purchase + Finance Charge

New Balance = $102.33 - $25.00 + $11.27 + $1.67 = $90.27

The new account balance is $90.27.