Find the vertex of the parabola.
y = 3 x squared minus 30 x + 77


a.
( -2, -5)
c.
( 5, 2)
b.
( -5, -2)
d.
( 2, 5)

Answer:

Step-by-step explanation:

ss

The estimated number of students at the M College who agree climate change is a serious issue is  1759

The percentage of total students is 59.42%

The method used can be biased.

The students surveyed are the sample while the students in the M College are the population. A population is the party of interest in an experiment. A population consists of all the members of the group. A sample is a smaller group of the population.

The limitation of using a sample to estimate for the population is that the sample might be a biased estimate of the population. If the sample is biased, the result of the experiment would be inaccurate.

Estimated number of students at M College = (sample that agree that climate change is a serious problem / total number of people surveyed) x number of students

(205 / 345) x 2960 = 1759

Percentage = (1759 / 2960) x 100 = 59.42%

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It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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Answer:

c = -4

Step-by-step explanation:

2c-4+c= -8+2c

Combine like terms

3c -4 = 2c-8

Subtract 2c from each side

3c-2c-4 = 2c-8-2c

c-4 = -8

Add 4 to each side

c-4+4 = -8+4

c = -4

Answer:

  5/10

Step-by-step explanation:

An equivalent fraction will have the numerator and denominator multiplied by the same value.

The denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...

  \(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)

Answer:

fd

Step-by-step explanation:

The amount owed in 5 years with monthly compounding, considering a $19,000 personal loan with a 15% interest rate, will be $34,558.52.

1. Convert the interest rate to a decimal: 15% = 0.15.

2. Determine the number of compounding periods: Since the loan compounds monthly, multiply the number of years by 12. In this case, 5 years * 12 months/year = 60 months.

3. Calculate the monthly interest rate: Divide the annual interest rate by 12. In this case, 0.15 / 12 = 0.0125.

4. Use the compound interest formula to calculate the future value:

  Future Value = Principal * (1 + Monthly Interest Rate)^(Number of Compounding Periods)

  Future Value = $19,000 * (1 + 0.0\(125)^{(60\))

5. Evaluate the expression inside the parentheses: (1 + 0.0\(125)^{(60\)) ≈ 1.954503.

6. Multiply the principal by the evaluated expression: $19,000 * 1.954503 = $37,133.57 (unrounded).

7. Round the final answer to the nearest cent: $34,558.52.

Therefore, in 5 years with monthly compounding, the amount owed on the $19,000 personal loan will be approximately $34,558.52.

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10 m

Explanation:

Data:

Second side : x

Third side : four times the second side : 4*x

The other side : 5 m longer than the second side : 5 + x

Perimeter of the triangle : 65 m

Formula:

Perimeter of a triangle = one side + second side + third side

Solution:

65 = 5 + x + x + 4 * x

65 = 5 + 6 * x

65 - 5 = 5 + 6 * x - 5

60 = 6 * x

60 / 6 = 6 * x / 6

10 = x

Answer:

( 4, 0 ) and ( 0,-8 )

Step-by-step explanation:

→ Rearrange into y = mx + c format

4x - 2y = 16

→ Minus 4x from both sides

-2y = -4x + 16

→ Divide everything by 2

-y = -2x + 8

→ Multiply everything by -1

y = 2x - 8

→ Substitute x = 0 to find the y-intercept and y = 0 to find the x intercept

x = 0 then y = -8 so ( 0,-8 )

y = 0 then x = 4 so ( 4, 0 )

Answer:

a = 9.2

Step-by-step explanation:

a^2+4^2= 10^2

a^2 + 16 = 100

a^2 = 84

a = 9.2

Answer:

The increasing interval is \(S=(-2,\infty)\)

Step-by-step explanation:

This absolute function has a vertex in x=-2. Now, from this point, the function has a positive slope (increasing), which means for values of x equals to -1,0,1,2,3,...,n.

Therefore the interval will

\(S=(-2,\infty)\)

I hope it helps you!

2 places to the right

2 zeros

Answer:

121

Step-by-step explanation:

f(-3)=2[1-4(-3)]-5[3(-3)-10]

or,f(-3)=2*13-5*(-19)

or,f(-3)=26+95

f(-3)=121

To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

5.3 cups

Step-by-step explanation:

1 liter = 4.2 cups

1.25 × 4.2

= 5.3 cups

Answer:

36 Bins are needed .

Step-by-step explanation:

3×2×1.5/12×8×6

= 36

Due to the higher proportion of customers driving less than 5 miles, it would be a likely event at store X.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For each store, the proportion of customers driving less than 5 miles is given by:

Hence, due to the higher proportion of customers driving less than 5 miles, it would be a likely event at store X.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

26 children

Step-by-step explanation:

346-8*40

346-320

26

The linear function which represents a slope of -3 as required in the task content is; A two column table with five rows. The first column, x, has the entries, negative 5, negative 1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8.

It follows that the task requires that a linear function whose slope, i.e rate of change is -2 is to be determined.

Since slope is the rate of change in y with respect to x;

The required linear function is; A two column table with five rows. The first column, x, has the entries, -5, -1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8 so that we have;

Slope = (24 - 32) / (-1 -(-5)) = -8 / 4 = -2.

Remarks: The complete question is such that the required slope is -2.

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Answer: the second option

Step-by-step explanation:

i took the assignment

Answer:

what in the world

Step-by-step explanation:

number 1. is c

number 2. is d

number 3. is a

number 4. is c

number 5. is b

hope this helps

Answer:

2 2/3 hours.

Step-by-step explanation:

If her washs once a week, he will wash 4 times in 4 weeks.

2/3 * 4 = 8/3

2 2/3.

Answer:

Domain of a function means the set of values of the variable for which the given function exists.

(g circle f) (x) means g{f(x)}.

g{f(x)} will exists for all the real values of x except x = 7 and that particular x for which f(x) = -3.

Hence the domain of g{f(x)} will be all real values except x = 7 and the x for which f(x) = -3

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

Unfortunately, without additional information or data, it is not possible to estimate the number of people running right now using the given equation N/Ntotal = T/Ttotal.

The equation only relates the fraction of people engaged in an activity to the fraction of time spent on that activity. It does not provide any information about the actual number of people or the total population size.

To estimate the number of people running right now, we would need additional data, such as the total population size, the fraction of people who typically engage in running as an activity, and the total time spent running by the people who do engage in the activity.

We can calculate the approximate number of persons running using the formula \(N/N_t_o_t_a_l = T/T_t_o_t_a_l\) and the estimated fraction of people running (T/Ttotal) coupled with data on the total population (Ntotal).

A fraction is a mathematical unit used to express a portion of an integer or a ratio of two integers. It consists of a horizontal line between the numerator and denominator of two numbers.

We may use the formula provided to get the approximate number of individuals running at any one time if we know the entire population (Ntotal) and the entire amount of time (Ttotal) that people are engaged in activities.

More specifically, we have to know what percentage of total time (T) people spend jogging at this time (Ttotal). To calculate the approximate total number of runners (N), we can use the equation N/Ntotal = T/Ttotal.

We may make use of information gathered through surveys, fitness devices, or even other sources that monitor exercise behaviors to determine the percentage of time individuals devote to running.

We can calculate that roughly 20,833 individuals are currently jogging (1/48 of 1 million people), for instance, if there are 1 million people in total and we assume that 1/48 of them are runners.

Thus, we can calculate the approximate number of persons running using the formula \(N/N_t_o_t_a_l = T/T_t_o_t_a_l\) and the estimated fraction of people running (T/Ttotal) coupled with data on the total population (Ntotal).

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Answer:

i would chose thw last one

Step-by-step explanation:

the last one but its youe choice

Answer:

The Awnser is B.

Step-by-step explanation: