The table shows how fast four students ran the 200-meter dash.

200-Meter Dash Results
Student Time (seconds)
Ben 40.53
Katie 34.02
Griffin 29.80
Kristin 44.56

How much faster did Griffin run the 200-meter dash than Ben? Enter your answer in the box.

Answer:

y = 2x + 1 --> linear

y = -4x + 7 --> non-linear

Not a solution for linear system.

Step-by-step explanation:

for (a), y = 2x+1, substitute the x and y values. keep in mind, that in a linear pair, (x, y). So, for the first equation you get:

7 = 2x3 + 1. This is correct, because 6 + 1 is 7. Therefore, (a) is linear.

for (b), we have to substitute our values again. You get:

7 = -4x3 + 7, which is

7 = -12+7, which is not true. So, (b) is not linear.

This means that for the linear pair (3, 7), it does not satisfy both equations, which means that it is not a solution for the linear system.

Answer: NO

Step-by-step explanation: quizzez

This refers to the total amount of money that the federal government owes to creditors, including individuals, businesses, and foreign governments. It is primarily the result of unpaid budget deficits, which occur when the government spends more money than it collects in revenue. The federal debt can increase over time due to interest charges on the outstanding debt, as well as additional deficits in future years. Rising interest rates, periods of structural unemployment, and competitive devaluations of currency can all have an impact on the economy and government finances, but they do not directly contribute to the federal debt.

The Federal Reserve can change the discount rate, which is the interest rate at which banks can borrow from the Fed, to influence the borrowing behavior of banks. If the Fed lowers the discount rate, it becomes cheaper for banks to borrow money, which can lead to increased lending activity and economic growth. Conversely, if the Fed raises the discount rate, it becomes more expensive for banks to borrow money, which can decrease lending activity and slow down economic growth.

 A marginal tax on sellers of a good will increase the costs of production, leading to a decrease in supply. This means that sellers will produce and offer less of the good at any given price, which will shift the supply curve to the left.

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Answer:

1.9k=21.3

Step-by-step explanation:

1.9k+5.7=27 then subtract 5.7 from 27 and have 1.9k=21.3

Answer:

k = 15

Step-by-step explanation:

Answer:

ur welcome

Step-by-step explanation:

A.    729.1

b.    243.04  

c.    60.76

Answer:

Step-by-step explanation:

Answer:

lowkey dont know the answer

Step-by-step explanation:

Answer:

44.5 percent is shaded.

from whole model, 44.5% is shaded of 100%

Answer:

Step-by-step explanation:

Coupon gives $3 off
$25 - $3 = $22
After first coupon, the pizza price will be $22

10% dicscount
90% of 25 = 22.5
22.50 - 3 = 19.50
After first coupon and discount, the pizza price will be $19.50

The profit P(x) = -0.5x² + 23x - 13.

We have,

Q(x) = 45x - 0.5x² and L(x) = 12x + 13

To calculate the profit the formula used

P(x) = Q(x) - L(x)

P(x) = 45x - 0.5x² - (12x+ 13)

P(x) = 45x - 0.5x² -12x - 13

P(x) = -0.5x² + 23x - 13

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If you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.

What is Null hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.

Consider the given process:

      \(x_{t} = c+\alpha x_{t-1}+\beta _{t} \\E[\beta _{t}]=0\\\)

Obtain mean,

     \(E[x _{t}]=\frac{c}{1-\alpha }\)

This works only when |α|<1. If α=1 this doesn't work, it blows up, because , \(E[x _{t}]\neq E[x _{t-1}]\) i.e. the process is not stationary.

The constant refers to the term c.

The trend is easy too:

    \(x_{t} +c+\alpha t+\alpha x_{t-1} +\beta_{t}\)

In this case,

  \(E[x _{t}]=\frac{c+\alpha t}{1-\alpha }\)

So, if you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.

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An x-intercept is a point where the graph of a function crosses the x-axis, meaning the corresponding y-value is zero. To find the x-intercepts from the given table, we look for entries in the second column (f(x)) where the value is zero.

Looking at the second column, we can see that the function f(x) has an x-intercept at x = -1 since f(-1) = 0. Therefore, the correct x-intercept from the options provided is (-1, 0).

Answer:

The inverse is 1/3x-2

Step-by-step explanation:

y = 3x+6

Exchange x and y

x = 3y+6

Solve for y

Subtract 6 from each side

x-6 = 3y+6-6

x-6 = 3y

Divide by 3

x/3 -6/3

1/3x -2 = y

The inverse is 1/3x-2

Answer:

\(f^{-1} (x)=\frac{1}{3}x-2\)

Step-by-step explanation:

Replace f(x) with y

y=3x+6

Swap x and y

x=3y+6

Solve for y

3y=x-6

y=1/3x-2

A biconditional statement is a logic statement that includes the phrase, "if and only if," sometimes abbreviated as "iff." The logical biconditional comes in several different forms:

. p iff q

. p if and only if q

. p↔q

Example of biconditional statement

A conditional statement is a logic statement that includes the phrase, "if-then." For example, "If a polygon has three sides, then it must be a triangle."

None of the answers has if then

Therefore, None of the above

The volume of the shapes are;

1. 228 in³

2. 1140 in³

3. 5.94 ft³

4. 126 yd³

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space.

The volume of a cuboid is expressed as;

V = l × b × h

1. Total volume = 14×3× 4 ) + (4× 5× 3)

= 168 + 60

= 228 in³

2. Total volume = 25×4 × 5) + (16×8×5)

= 500 + 640

= 1140 in³

3. Total volume = 0.8 × 1.2 × 1.5 ) + (3 × 1.5 × 1)

= 1.44 + 4.5

= 5.94 ft³

4. Total volume = (4 × 6 × 5 ) + ( 1× 3 × 2)

= 120 + 6

= 126 yd³

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Hi there! The answer for this question would be 9!

Explanation:

0.09 is also 9 since 1.00 is 1 whole in fraction form. This means that 0.09 is also 9/100 in fraction form.

Final Result: 9

Answer: 9

Step-by-step explanation:

On both sides of the equation, there is the 27/100. So we can essentially ignore that because the other two terms just have to be equal. The 0.09 has a 9 in the hundredths place. So that means the decimal is equivalent to 9/100

The opportunity cost of washing a car for Ted is 4 cars, and the opportunity cost of washing a car for Ishana is 3 cars.

To determine each person's opportunity cost of washing a car, we need to compare the alternative activity they would have to give up in order to wash a car.

For Ted:

Ted can wax 4 cars or wash 12 cars. So, the opportunity cost of washing a car for Ted is the number of cars he could have waxed instead. In this case, Ted would have to give up waxing 4 cars to wash a car.

For Ishana:

Ishana can wax 3 cars or wash 6 cars. So, the opportunity cost of washing a car for Ishana is the number of cars she could have waxed instead. In this case, Ishana would have to give up waxing 3 cars to wash a car.

Therefore, the opportunity cost of washing a car for Ted is 4 cars, and the opportunity cost of washing a car for Ishana is 3 cars.

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Answer:

4

Step-by-step explanation:

Answer:

your answer is 4

Step-by-step explanation:

you welcome

The measure of variability that should never be used alone to reach conclusions regarding the variance of a distribution is the range.

The range only considers the difference between the maximum and minimum values in a dataset and does not take into account the distribution or dispersion of the data between these extreme values. Therefore, relying solely on the range to assess variance would not provide a comprehensive understanding of the distribution's spread and may lead to misleading conclusions.

It is recommended to use other measures of variability, such as standard deviation or interquartile range, in conjunction with the range to gain a more accurate representation of the variance.

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A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.

No, a triangle is not always 360 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.

This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).

Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.

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Answer:

6x

Step-by-step explanation:

3x/y=x/2y

Since 2y is 2X greater than y, 6x is 2X greater than 3x.

So,

The answer is 6x.

Answer:

Step-by-step explanation:

2

There are approximately 0.976 grams of carbon (C) in the given sample of the carbohydrate (C9H11O6).

To find the number of grams of carbon (C) in the sample, we need to first determine the molar mass of the carbohydrate.

The molar mass of C is approximately 12.01 g/mol. The molar mass of H is approximately 1.01 g/mol, and the molar mass of O is approximately 16.00 g/mol.

The molar mass of the carbohydrate (C9H11O6) can be calculated as follows:

(9 * 12.01 g/mol) + (11 * 1.01 g/mol) + (6 * 16.00 g/mol) = 162.18 g/mol

Next, we can use the Avogadro's number (6.022 x 10^23) to determine the number of moles in the sample:

4.9 x 10^22 molecules / 6.022 x 10^23 molecules/mol = 0.0813 mol

Finally, we can calculate the mass of carbon in the sample by multiplying the number of moles by the molar mass of carbon:

0.0813 mol * 12.01 g/mol ≈ 0.976 g

So, there are approximately 0.976 grams of carbon in this sample.
There are approximately 0.976 grams of carbon (C) in the given sample of the carbohydrate (C9H11O6).

To find the mass of carbon in the sample, we first need to determine the molar mass of the carbohydrate. The molar mass of an element or compound is the mass of one mole of that substance. In this case, we have the formula C9H11O6, which indicates that the carbohydrate consists of 9 carbon atoms (C), 11 hydrogen atoms (H), and 6 oxygen atoms (O).

The molar mass of carbon is approximately 12.01 g/mol, hydrogen is approximately 1.01 g/mol, and oxygen is approximately 16.00 g/mol. To calculate the molar mass of the carbohydrate, we multiply the number of atoms of each element by their respective molar masses and sum them up.

Therefore, the molar mass of C9H11O6 is

(9 * 12.01 g/mol) + (11 * 1.01 g/mol) + (6 * 16.00 g/mol) = 162.18 g/mol.

Next, we can use the Avogadro's number (6.022 x 10²³) to determine the number of moles in the given sample. The given sample contains 4.9 x 10²²molecules of the carbohydrate. Dividing this by Avogadro's number gives us the number of moles:

4.9 x 10 molecules / 6.022 x 10^23 molecules/mol = 0.0813 mol.

Finally, we can calculate the mass of carbon in the sample by multiplying the number of moles by the molar mass of carbon: 0.0813 mol * 12.01 g/mol ≈ 0.976 g. Therefore, there are approximately 0.976 grams of carbon in the given sample.

In conclusion, the sample of the carbohydrate (C9H11O6) contains approximately 0.976 grams of carbon (C).

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Answer:

Step-by-step explanation:

first step

let's create the equation word problem

let's solve

let my mother's and sister's age be x and y respectively

according to the first condition,x=4y....(I)

according to the 2nd condition,x+5=2(y+5×2).....(ii)

so the system of linear equations is

x=4y

x+5=2(y+5×2)

gets from the second equation

x+5=2(y+10)

x+5=2y+20

4y+5=2y+20 (as x=4y)

2y=15

y=7.5

so the age of mother is

x=4.(7.5)

x=30

Functiοn mοdels the relatiοnship between the cοncentratiοn οf the medicatiοn in milligrams is P(t) = 25.5(0.838)ˣ and number οf hοurs since the medicatiοn was taken, t is 2 hοurs.

The cοncentratiοn οf the drug in the blοοdstream at t = 8 hοurs is 24 mg/L. Frοm t= 0 tο t= 2 hr, the cοncentratiοn is increasing and after 2 hrs the cοncentratiοn is decreasing. The level οf the drug in the blοοdstream reaches its maximum value at t=2 hrs , and  the cοncentratiοn in the blοοdstream at that time is 25.5 mg/L.

\After the drug reaches its maximum level in the blοοdstream, 8 additiοnal hοurs are required fοr the level tο drοp    tο 16 mg/L. As at t= 10 hrs, cοncentratiοn is 16 mg/L and maximum cοncentratiοn is at t=2hrs. Sο, additiοnal hοurs= 10-2=8 hrs

P(t) = 25.5( 1-16.2%)ˣ

= 25.5((100 - 16.2)/100)ˣ

= 25.5(83.8/100)ˣ

P(t) = 25.5(0.838)ˣ

Hence, functiοn mοdels the relatiοnship between the cοncentratiοn οf the medicatiοn in milligrams is P(t) = 25.5(0.838)ˣ and number οf hοurs since the medicatiοn was taken, t is 2 hοurs.

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Complete question:

9. A patient has taken 25.5 mg of a prescribed medication. The concentration of the medication in the body decreases at a rate of 16.2% per hour.

Which function models the relationship between the concentration of the medication in milligrams, p(t), and the number of hours since the medication was taken, t?

Answer:

5 miles

Step-by-step explanation:

It is a right triangle, with 3 miles down, and 4 miles to the right

the shortest distance would be and southeast line.

Using the Pythagorean theorem, you get:

3^2 + 4^2 = x^2

9 + 16 = x^2

25 = x^2

x = 5

We have to apply the rule of three to solve this.

We will use the equivalencies of the first row to complete the others.

The cups of flour needed are 3 cups/loaf.

The water needed is 12 tablespoons/loaf.

The salt needed 1 teaspoon/loaf.

With these equivalencies we can calculate the ingredients needed for any number of loaves:

2.4  [1.12, 15.28] is the  mean breaking point of the 95% confidence interval estimator.

2.5 [0.73, 0.87] is the population proportion at  98% confidence interval estimator.

2.4) The given data:

Mean breaking point of fish line = 8.2 pounds

Sample size (n) = 18

Sample standard deviation (s) = 12 pounds

Confidence level = 95%

The formula to calculate the 95% confidence interval estimator for the mean breaking point is:

$\bar{x} \pm z_{\alpha/2} \frac{s}{\sqrt{n}}$

Where:

$\bar{x}$ is the sample mean

s is the sample standard deviation

n is the sample size

$z_{\alpha/2}$ is the z-value from the standard normal distribution table.

The value of $z_{\alpha/2}$ can be calculated as:

$z_{\alpha/2}$ = $z_{0.025}$ = 1.96 (from the standard normal distribution table)

Substituting the given values in the formula, we get:

95% Confidence interval estimator for mean breaking point:

$8.2 \pm 1.96 \frac{12}{\sqrt{18}}$

$8.2 \pm 7.0775$

Hence, the 95% confidence interval estimator for the mean breaking point is [1.12, 15.28].

The company claims that the average break point of the line is more than 8 pounds. Since the interval [1.12, 15.28] contains 8 pounds, it cannot support the company's claim.

2.5) The given data:

Sample size (n) = 150

Number of successful broods (x) = 120

The sample proportion, $\hat{p}$ = 120/150 = 0.8

Confidence level = 98%

The formula to calculate the 98% confidence interval estimator for the population proportion is:

$\hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Where:

$\hat{p}$ is the sample proportion

n is the sample size

$z_{\alpha/2}$ is the z-value from the standard normal distribution table.

The value of $z_{\alpha/2}$ can be calculated as:

$z_{\alpha/2}$ = $z_{0.01}$ = 2.33 (from the standard normal distribution table)

Substituting the given values in the formula, we get:

98% Confidence interval estimator:

$0.8 \pm 2.33 \sqrt{\frac{0.8(1-0.8)}{150}}$

The 98% confidence interval estimator for the population proportion is [0.73, 0.87].

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Answer:

the 2nd one is 1,5

Step-by-step explanation:

the 3rd one is 8,5

The time it will take the population to reach 10 is 13.28 minutes.

An exponentially decaying function has a general form f(x) = (1 -r)ˣ, where r is called the decay rate. it can be found by having any two values of x for which f(x) is known.

The initial population of cells is given as 100000.

And, the half life is 1 minute.

The expression for the population at t minutes can be written as follows,

P(t) = 100000 × \(1/2^{t}\)

Substitute P(t) = 10 to obtain as,

⇒ 10 = 100000 ×  \(1/2^{t}\)

⇒ \(1/2^{t}\) = 1/10000

⇒ t log 2 = log 10000

⇒ t = 4/0.301

⇒ t = 13.28

Hence, the required time to reach the given population is 13.28 minutes.

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Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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Answer:

\(log_{2}\) 20

Step-by-step explanation:

using the rule of logarithms

loga + logb = logab

then

\(log_{2}\)4 + \(log_{2}\)5

= \(log_{2}\) (4 × 5)

= \(log_{2}\)20