bentley is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 1.75 gallons of gas. How much gas would be in the tank after driving for 4 hours? How much gas would be left after t hours?
gas left after 4 hours-
gas left after t hours-

Answer:

-75

Step-by-step explanation:

-123 + 48

-*+ = -

123-48

75

But as the bigger number i.e 123 has a negative sign before so the answer will be in negative

i.e -75

The correct option or equation that applies to the given situation is 7*6 = (4*6) + (3*6).

According to the question,

We have the following information:

Akela drew smaller arrays to find the product of a larger array.

Now, we have two figures where one has 6*3 boxes (6 horizontal boxes and 3 horizontal boxes) and in the second figure we have 6*4 boxes (6 horizontal boxes and 4 vertical boxes).

Now, to find the correct option, we will look for these two in options:

So, the option that has both of them is  7*6 = (4*6) + (3*6).

Now, we can verify whether the sides of the equation given are correct or not.

We have:

7*6 = 42

On right hand side, we have:

(4*6) + (3*6)

24+18

42

Hence, the correct option is 4th one.

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Answer: d i think

Step-by-step explanation:

The percentage of the students at the university which are foreign are 25% by conditional probability formula.

According to the question,  10% of all college students are foreign students who also smoke and it is also known that 40% of all foreign college students smoke.

We use the conditional probability formula to solve this question.

Let foreign students be denoted as F

Let students smoking be denoted as S

We know that 10% of all college students are foreign students who also smoke this means

P(F ∩ S) = 0.1

and 40% of all foreign college students smoke which means

P(S/F) = 0.4

So, the percentage of the students at this university who are foreign can be calculated as  

\(P(F) = \frac{0.1}{0.4}\) = 0.25

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Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;

Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴

Given the cash flows;

Year 0: $0

Year 1: $600

Year 2: $500

Year 3: $400

Then the Future value of uneven cash flow

= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³

= $600/1.11 + $500/1.23 + $400/1.36

=$540.54 + $405.28 + $293.00

=$1,238.82

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

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Answer:

According to the given data, if it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6.

Step-by-step explanation:

Past studies indicate that about 60 percent of the trees in a forested region are classified as softwood.

A botanist studying the region suspects that the proportion might be greater than 0.60.

The botanist obtained a random sample of trees from the region and conducted a test of H0:p=0.6 versus Ha:p>0.6.

Therefore, he p-value of the test was 0.015, indicating the past studies.

In year 1, the GDP price deflator is calculated to be 0.66 (or 66%), and in year 2, it is 0.77 (or 77%). The rate of inflation between years 1 and 2, as measured by the GDP price deflator, is approximately 16.67%. In contrast, the CPI rate of inflation is calculated to be 20%. The differences in these results can be attributed to the differences in the composition and weighting of the goods included in the GDP price deflator and the Consumer Price Index (CPI).

a) The GDP price deflator measures the average price change of all goods and services produced in an economy. To calculate the GDP price deflator in year 1, we use the formula: (Nominal GDP / Real GDP) * 100. Given the quantities and prices of broccoli and cauliflower in year 1, the nominal GDP is (100 million * $0.50) + (30 million * $0.80) = $65 million, and the real GDP is (100 million * $0.50) + (30 million * $0.50) = $55 million. Thus, the GDP price deflator in year 1 is (65/55) * 100 = 118.18%. In year 2, the nominal GDP is (80 million * $0.60) + (60 million * $0.85) = $88 million, and the real GDP is (80 million * $0.50) + (60 million * $0.50) = $70 million. Therefore, the GDP price deflator in year 2 is (88/70) * 100 = 125.71%. The rate of inflation between years 1 and 2, as measured by the GDP price deflator, is ((125.71 - 118.18) / 118.18) * 100 = 6.36%.

b) The Consumer Price Index (CPI) measures the average price change of a basket of goods and services typically consumed by households. To calculate the CPI in year 1, we assign weights to the prices of broccoli and cauliflower based on their consumption quantities. The CPI in year 1 is (100 million * $0.50) + (30 million * $0.80) = $65 million. In year 2, the CPI is (80 million * $0.60) + (60 million * $0.85) = $81 million. The CPI rate of inflation between years 1 and 2 is ((81 - 65) / 65) * 100 = 24.62%.

c) The differences in the results between parts (a) and (b) can be attributed to the differences in the composition and weighting of goods included in the GDP price deflator and the CPI. The GDP price deflator considers the prices of all goods and services produced in the economy, reflecting changes in production patterns and the overall price level. On the other hand, the CPI focuses on a fixed basket of goods and services consumed by households, reflecting changes in the cost of living. The differences in the weighting and composition of goods between the two measures result in variations in the calculated inflation rates.

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Expression for the nth term of the sequence: (n + 1) / (n + 3).The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.

To find the expression for the nth term of the sequence, we observe that each term can be expressed as (n + 1) divided by (n + 3), where n represents the position of the term in the sequence.

Let's verify this formula with the given terms:

For n = 1: (1 + 1) / (1 + 3) = 2 / 4 = 1/2 (first term of the sequence)

For n = 2: (2 + 1) / (2 + 3) = 3 / 5 (second term of the sequence)

For n = 3: (3 + 1) / (3 + 3) = 4 / 6 (third term of the sequence)

For n = 4: (4 + 1) / (4 + 3) = 5 / 7 (fourth term of the sequence)

For n = 5: (5 + 1) / (5 + 3) = 6 / 8 = 3 / 4 (fifth term of the sequence)

Therefore, the first five terms of the given sequence are: 1/2, 3/5, 4/6, 5/7, 3/4.

The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.

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Answer:

After saving for 5 weeks he would have 130. 6x5=30+100=130

expression (6x5)+100

Step-by-step explanation:

Answer:

$130

$100 + $6w

Step-by-step explanation:

By question , Tariq had $100 . In one week he can save , $6 . So in 5 weeks he will save ,

=> $6 × 5

=> $ 30 .

Therefore after 5 weeks he will have ,

=> $ 100 + $ 30

=> $ 130 .

=> $100 + $6w

The measure of the mid - segment is 53 .

Given :

the measures of the bases of a trapezoid are 35 and 71.

What is trapezoid ?

A trapezoid is a four-sided shape which has one pair of sides as parallel. It is basically a two-dimensional shape or figure similar to a square etc .

Mid segment :

A mid segment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

A trapezoid mid segment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.

Measure of mid segment = sum of two bases / 2

= 35 + 71 / 2

= 106 / 2

= 53

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The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)

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The rules of logarithms are as: 

1. Rule of product.

2. Rule of division.

3. The Power/Exponential Rule.

4. A new fundamental rule.

The alternate format for writing exponents is with logarithms. A number appears base-based logarithm is approximately equivalent to another number. A logarithm performs exponentiation's exact opposite function.

1. Rule of product: According to this rule, adding the individual logarithms of two logarithmic values results in the multiplication of those values.

\(Log_b (mn)= log_b m + log_b n\)

2. Rule of division: The difference between each logarithm is equivalent to the division of two logarithmic values.

\(Log_b \left(\frac{m}{n}\right)= log_b m - log_b n\)

3. The Power/Exponential Rule: According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.

\(Log_b (m^n) = n log_b m\)

4. A new fundamental rule:

\(Log_b m =\frac{log_a m}{log_a b}\)

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Answer: The answer is 0.201

Step-by-step explanation: do the multiplication algorithm and Multiply 0.67 * 0.3 to get 0.201 because 7 x 3 = 21 carry the 2 above the 6 and do 6 x 3 = 18 + 2 = 20 and carry the decimal over three times between the 0 and 2 so the answer is 0.201

Answer:

809

Step-by-step explanation:

787 susifx

Density = Mass / Volume, so you could use that information to solve for each value in the graph.

2. Mass = Density * Volume = 8.07 * 1.04 = 8.59 g

3. Volume = Mass / Density = 8.26 / 8.10 = 1.02 mL

4. Density = Mass / Volume = 7.91 / 0.99 = 7.99 g/mL

5. Mass = Density * Volume = 8.05 * 0.98 = 7.89 g

6. Volume = Mass / Density = 8.53 / 8.05 = 1.06 mL

Answer:

x = 0.333...(repeating or .34 if u round)

Step-by-step explanation:

add 4x and 2x= 6x

20- 12 = 8

6x + 8 = 10

  -8      -8

6x = 2

6      6

x = 0.333...(repeating or .34 if u round)

Plane X contains point C. Plane Y contains points A andB. there are three planes that pass through points A, B, and C.To find these planes, we need to draw a triangle connecting points A, B, and C.

The three planes that pass through A, B, and C are the planes that are parallel to the sides of the triangle and that contain points A, B, and C. These planes divide the space into three sections. Each plane will contain one of the points of the triangle. The three planes together form a three-dimensional space that is bounded by the three planes. This space contains all the points A, B, and C, and all the points in the triangle. Therefore, there are three planes that pass through points A, B, and C.

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Answer:

55

Step-by-step explanation:

(55+55+58+48) ÷4

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The correct option of the given statement "The present value of $5,325 to be received in one period at a rate of 6.5%" is d. 5,000.

it can be found using the formula:

PV = FV/(1 + r),

where

PV is the present value,

FV is the future value,

and r is the interest rate expressed as a decimal.

Here, FV = $5,325 and r = 0.065 (6.5% expressed as a decimal).

Substituting these values into the formula gives:

PV = $5,325/(1 + 0.065)PV

    = $5,325/1.065PV

     ≈ $5,000

Therefore, the present value of $5,325 to be received in one period if the rate is 6.5% is approximately $5,000.

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a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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Answer:

probability

Step-by-step explanation:

pls mark me as brainlist

Answer:

11 < √131 < 12

Step-by-step explanation:

121 and 144 are perfect squares.

11² = 121

12² = 144

√131 = 11.445523

√131 lies between 11 and 12, which are consecutive integers.

The missing mean should be 70.

To determine the value for the missing mean that would result in no main effect for factor B, we need to calculate the overall mean for each level of factor B.

The main effect for factor B is the difference in means between the two levels of factor B (B1 and B2). If there is no main effect for factor B, it means that the means for B1 and B2 are equal.

Let's calculate the overall mean for B1 and B2 using the given data:

Mean for B1 = (20 + 30 + 40 + 50) / 4 = 35

Mean for B2 = (10 + 20 + 40 + ?) / 4 = (70 + ?) / 4

Since we want no main effect for factor B, the mean for B2 should be equal to the mean for B1. Therefore, we can set up the equation:

(70 + ?) / 4 = 35

Solving this equation, we find:

70 + ? = 35 * 4

70 + ? = 140

? = 140 - 70

? = 70

Therefore, the missing mean should be 70 in order to have no main effect for factor B.

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Answer: John is now 18 years old

Step-by-step explanation:

Let, John's age is now x years.

5 years ago, he was (x - 5) years old

In 8 years, he will be (x + 8) years old

By the given condition,

x - 5 = 1/2 (x + 8)

⇒ 2 (x - 5) = x + 8

⇒ 2x - 10 = x + 8

⇒ 2x - x = 8 + 10

⇒ x = 18

The probability that this project will be completed within 130 days is 0.8413.

Expected duration (ED) = (Optimistic + 4 x Most Likely + Pessimistic) ÷ 6.

Optimistic = 41

Most Likely = 50

Pessimistic = 59ED = (41 + 4 × 50 + 59) ÷ 6 = 50

Duration = 50

Optimistic = 54

Most Likely = 60

Pessimistic = 66ED = (54 + 4 × 60 + 66) ÷ 6 = 60

Duration = 60

Optimistic = 58

Most Likely = 70

Pessimistic = 82ED = (58 + 4 × 70 + 82) ÷ 6 = 70

Duration = 70

Optimistic = 32

Most Likely = 41

Pessimistic = 44ED = (32 + 4 × 41 + 44) ÷ 6 = 41

Duration = 41

Total Project Duration = 50 + 60 + 70 + 41 = 221

Expected time for completing project = 221 days

The standard deviation of the critical path is obtained by using the following formula:

σ = P - O/6

Where σ represents the standard deviation of the critical path, P represents the pessimistic time, and O represents the optimistic time.

σ = 66 - 54/6 = 2.

Then, the probability that this project will be completed within 130 days:

z = (130 - 221) / 2 = -45.5P(z < -45.5) = 0 (due to negative value)

P(z < -4.5) = 0 (from normal distribution table)

Thus, the probability that this project will be completed within 130 days is 0.8413.

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The result for the given data are-

Part A: A geometric sequence is being modelled by the data because they share a common ratio = 2.

Part B: The time in which she will complete station 5 calculated by recursive formula is 64 units.

Part C: The time in which she will complete the 9th station calculated by  explicit formula 512 units.

Any term of a series can be defined by its preceding term in a recursive formula (s).

We learn two things from recursive formulas: the first phrase in the series. The pattern rule states that any term can be derived from its preceding term.

Now, according to the question;

Part A: The data are modeling a geometric sequence since they have a common ratio of 2.

Part B: Use a recursive formula to determine the time she will complete station 5.

f(n)=f(n-1)×r

Where, r is the common difference

f(n)=f(5-1)×2

f(n)=f(4)×2

f(n)=(32)×2   {since, f(4) = 32)}

f(n)= 64

Part C: Use an explicit formula to find the time she will complete the 9th station.

f(n)=f(1)×r^(n-1)

f(n)=4×2^(8-1)

f(n)=4×(2^7)

f(n)=4×128

f(n)=512

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The complete question is -

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 4), (2, 8), (3, 16), (4, 32)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence?

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Answer:

The result for the given data are-

Part A: A geometric sequence is being modelled by the data because they share a common ratio = 2.

Part B: The time in which she will complete station 5 calculated by recursive formula is 64 units.

Part C: The time in which she will complete the 9th station calculated by  explicit formula 512 units.

What is recursive formula?

Any term of a series can be defined by its preceding term in a recursive formula (s).

We learn two things from recursive formulas: the first phrase in the series. The pattern rule states that any term can be derived from its preceding term.

Now, according to the question;

Part A: The data are modeling a geometric sequence since they have a common ratio of 2.

Part B: Use a recursive formula to determine the time she will complete station 5.

f(n)=f(n-1)×r

Where, r is the common difference

f(n)=f(5-1)×2

f(n)=f(4)×2

f(n)=(32)×2   {since, f(4) = 32)}

f(n)= 64

Part C: Use an explicit formula to find the time she will complete the 9th station.

f(n)=f(1)×r^(n-1)

f(n)=4×2^(8-1)

f(n)=4×(2^7)

f(n)=4×128

f(n)=512

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The complete question is -

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 4), (2, 8), (3, 16), (4, 32)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence?

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Explore all similar answers

Step-by-step explanation:

a) For chi-squared distribution with v=3 degrees of freedom, the statistic that can be constructed using Xi's is:

X2 = Σ i=1 3 (Xi − i)2 / 3.

X2 has chi-squared distribution with 3 degrees of freedom.

b) For t-distribution with v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

T = (X1 − 1) / [(X2/2)0.5].

T has t-distribution with 2 degrees of freedom.

c) For F-distribution with v1=1 and v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

F = [(X1 − 1)/1] / [(Σi=2 to 3 Xi2) / 2].

F has F-distribution with 1 and 2 degrees of freedom.

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348-k=48

hoped that helped

k fewer than 348 is 48 can be express as an equation below;

348 - k = 48

We have to represent the word expression as an algebraic expression. Therefore,

An algebraic expression is a combination of terms by the operations such as addition, subtraction, multiplication, division etc.

Therefore, k fewer than 348 is 48 can be represented as follows:

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The standard error of the of the sampling distribution is 0.073.

The standard error of a proportion is given by the formula:

standard error = √[(p * (1 - p)) / n]

where p is the proportion and n is the sample size.

In this case:

p = 20% = 0.2

n = 30

Substituting the given values:

standard error = √[(0.2 * (1 - 0.2)) / 30]

standard error = 0.073

Therefore, the standard error of the sampling distribution of the proportion of employees who are allergic to pets is 0.073.

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