What is the leading coefficient of the polynomial?

30x2 + 12x + 18x3 + 10

A) 10
B) 12
C) 18
D) 30

Answer:

2 seconds.

Step-by-step explanation:

Given [tex]d=4t+16t^{2}[/tex] and d = 72 ft

We need to solve [tex]72=4t+16t^{2}[/tex]

[tex]4t+16t^{2}-72=0[/tex]

[tex]4t^{2}+t-18=0[/tex]

[tex]4t^{2}+9t-8t-18=0[/tex]

[tex]t(4t+9)-2(4t+9)=0[/tex]

[tex](t-2)(4t+9)=0[/tex]

[tex]t-2=0,4t+9=0[/tex]

[tex]t=2,t=-\frac{9}{4}[/tex]

Since, time can not be negative, so the required time is t = 2 seconds.

Final answer:

To find the time it takes for the object to travel 72 feet based on the given distance formula d=4t+16t², you can solve for t by substituting the distance value of 72 feet into the formula and solving for t.

Explanation:

Distance: To find the time it takes for the object to travel 72 feet, we can set the distance formula d = 4t + 16t² equal to 72 feet and solve for t.

Step-by-step explanation:

Given: d = 4t + 16t² and d = 72 feet

Substitute d = 72 into the formula: 72 = 4t + 16t²

Rearrange the equation: 16t² + 4t - 72 = 0

Solve for t using the quadratic formula or factoring.

The solutions for t will give you the time it takes for the object to travel 72 feet.

Answer:

3

Step-by-step explanation:

A mandatory relationship means that for every A there must be a B and vice versa. The excessive is saying that you have a relationship with 3 records each, therefore the bridge relation cannot have less than 3 records otherwise the mandatory aspect will be broke.

I hope you find this information useful and interetsing! Good luck!

Each of the four responses to the question about the graph's title has a different perspective. Some are based on the data presented on the graph, such as the proportions of votes or the relative sizes of the bars representing each candidate. One comment about media bias doesn't directly pertain to the information on the graph.

Without the precise context of the graph or its title, it is a bit tricky to answer this question directly. However, based on the details presented, let's analyze each statement:

https://brainly.com/question/11624428

#SPJ2

Answer: the total area where roses will be planted is 1520 feet²

Step-by-step explanation:

The formula for determining the area of a parallelogram is expressed as

Area = base × height

From the information given,

Base = 20 + 40 = 60 feet

Height = 38 feet

Area of the rose garden = 60 × 38 = 2280 feet²

The formula for determining the area of a rectangle is expressed as

Area = length × width

From the information given,

Length = 38 feet

Width = 20 feet

Area of the rectangular walkway is

20 × 38 = 760 feet²

Therefore, the total area where roses will be planted is

2280 - 760 = 1520 feet²

Answer:

1) $1966.62

2) $1968.12

3) $1968.88

Step-by-step explanation:

1) 1500 × (1 + .034/4)³²

= 1966.618592

2) 1500 × (1 + .034/12)⁹⁶

= 1968.123402

3) 1500 × (e^(8×0.0314))

= 1968.880502

Answer:

1968.880502

Step-by-step explanation:

Answer:

  check your math

Step-by-step explanation:

The first subtraction was correct:

  36 -7 3/4 = 28 1/4

The second subtraction needs to be revisited.

  28 1/4 -6 2/4 = 27 5/4 -6 2/4 = 21 3/4

__

You can do what you did, but you need to pay attention to the signs.

  28 1/4 -6 2/4 = (28 -6) +(1/4 -2/4) = 22 - 1/4 = 21 3/4

The result of subtracting 2/4 from 1/4 is -1/4, not +1/4.

_____

The length of the first cut piece was 21 3/4 inches.

Answer:

21 ¾ inches

Step-by-step explanation:

36 - 6½ - 7¾

36 - (6½ + 7¾)

36 - (6 + 7 + ½ + ¾)

36 - (13 + [2+3]/4) lcm:4

36 - (13 + 5/4)

36 - (13 + 1 + ¼)

36 - 14 - ¼

22 - ¼

21¾ inches

Answer:

a) Mean = 1205

Standard Deviation = 2.89

b) P( 1195 < x < 1205) = 0.5

50% of the cables lie within the given specification.

Step-by-step explanation:

We are given the following information in the question:

[tex]f(x) = 0.1[/tex]

a = 1200, b = 1210

We are given a uniform distribution.

a) Mean:

[tex]\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{1200+1210}{2} = 1205[/tex]

Standard Deviation:

[tex]\sigma = \sqrt{\displaystyle\frac{(b-a)^2}{12}}\\\\= \sqrt{\displaystyle\frac{(1210-1200)^2}{12}} = \sqrt{8.33} = 2.89[/tex]

b) P( 1195 < x < 1205)

[tex]=\displaystyle\int_{1195}^{1205} f(x) dx\\\\=\displaystyle\int_{1200}^{1205} (0.1) dx\\\\=0.1[x]_{1200}^{1205} = (0.1)(1205-1200) = 0.5[/tex]

50% of the cables lie within the given specification.

Answer:

Part 1) [tex]BC=12.2\ units[/tex]

Part 2) [tex]m\angle A=55^o[/tex]

Part 3) [tex]m\angle C=35^o[/tex]

Step-by-step explanation:

Part 1) Find AC

we know that

In the right triangle ABC of the figure

Applying the Pythagorean Theorem

[tex]AC^2=AB^2+BC^2[/tex]

substitute the given values

[tex]AC^2=7^2+10^2[/tex]

[tex]AC^2=149\\AC=12.2\ units[/tex]

Part 2) Find the measure of angle A

we know that

In the right triangle ABC

[tex]tan(A)=\frac{BC}{AB}[/tex] ----> by TOA (opposite side divided by the adjacent side)

substitute the values

[tex]tan(A)=\frac{10}{7}[/tex]

using a calculator

[tex]m\angle A=tan^{-1}(\frac{10}{7})=55^o[/tex]

Part 3) Find the measure of angle C

we know that

In the right triangle ABC

[tex]m\angle A+m\angle C=90^o[/tex] ----> by complementary angles

substitute the given value

[tex]55^o+m\angle C=90^o[/tex]

[tex]m\angle C=90^o-55^o=35^o[/tex]

The probability that both of the interviewed students are from Middle Georgia State College is 2/7 or 0.2857 rounded to four decimal places.

To calculate the probability that both interviewed students are from Middle Georgia State College, one would use the formula for conditional probability, considering the process as two sequential events. The first student being from the college and then the second one, given the first is already from the college. Since there are four students from the college out of a total of seven, the probability of picking one Middle Georgia State College student first is 4/7. After the first student from the college has been picked, there are now three remaining Middle Georgia students out of the remaining six students. Thus, the probability for the second pick is 3/6, which simplifies to 1/2. The total probability is the product of these two probabilities: (4/7) * (1/2) = 2/7, or approximately 0.2857 when rounded to four decimal places.

Answer:

B

Step-by-step explanation: pORBABLITY

Using the Central Limit Theorem, it is found that:

a) 174.

b) 26.

c) Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.

d) 0.87

e) 0.0238

f) 0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.

-------------------------------------

The Central Limit Theorem establishes that for a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex] , if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]

In this problem:

Item a:

This is

[tex]np = 200(0.87) = 174[/tex]

Item b:

This is:

[tex]n(1-p) = 200(0.13) = 26[/tex]

Item c:

Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.

Item d:

The mean is:

[tex]\mu = p = 0.87[/tex]

Item e:

The standard deviation is:

[tex]s = \sqrt{\frac{0.87(0.13)}{200}} = 0.0238[/tex]

Item f:

Using z-scores, the probability is the p-value of Z when X = 0.85.

We have that:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.85 - 0.87}{0.0238}[/tex]

[tex]Z = -0.84[/tex]

[tex]Z = -0.84[/tex] has a p-value of 0.2005.

0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.

A similar problem is given at https://brainly.com/question/15581844

Answer:

20.5

Step-by-step explanation:

ur welcome :D

Answer:

Please see the attached pictures for full solution.

The average rate of change of f over intervals of x from x = 3 to  = 3.5 is - 159.

Given that the function is,

f (x) = - 5x³

Used the formula for the average rate of change of function f at interval [a, b] is,

f' (x) = [ f (b) - f (a) ] / (b - a)

Here, f (x) = - 5x³

At x = 3;

f (3) = - 5 × 3³

= - 135

At x = 3.5;

f (3.5) = - 5 × (3.5)³

= - 214.4

Hence, the average rate of change of f over intervals of x from x = 3 to  = 3.5 is,

f ' (x) = [- 214.5 - (- 135)] / (3.5 - 3)

f ' (x) = [- 79.5] / 0.5

f ' (x) = - 159

To learn more about the function visit:

https://brainly.com/question/11624077

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Final answer:

The average rate of change of the function f(x) = -5[tex]x^3[/tex] from x = 3 to x = 3.5 is -158.75.

Explanation:

The average rate of change (ARoC) can be determined using the formula:

ARoC = (f(x2) - f(x1)) / (x2 - x1)

In this case, the given function is f(x) = -5x^3. To find the ARoC from x = 3 to x = 3.5, substitute these values into the formula:

ARoC = (-5[tex](3.5)^3 - (-5(3)^3)[/tex]) / (3.5 - 3)

Simplifying the equation gives:

ARoC = (-5(42.875) - (-5(27))) / (0.5)

ARoC = (-214.375 + 135) / 0.5

ARoC = -79.375 / 0.5

ARoC = -158.75

Therefore, the average rate of change of f(x) from x = 3 to x = 3.5 is -158.75.

Answer:

30%

Step-by-step explanation:

Given:

Every morning he starts with 150 tomatoes.

On Sunday Austin sells 45 of the 150 tomatoes.

Question asked:

What percent of the tomatoes he sold ?

Solution:

As Austin sells 45 tomatoes out of 150 tomatoes, we will find percent of the tomatoes he sold by using :

Percent of the tomatoes he sold = Number of tomatoes he sold divided by total number of tomatoes he starts with.

[tex]Percentage =\frac{45}{150} \times100\\[/tex]

                  [tex]=\frac{4500}{150} \\ = 30[/tex]

Therefore, 30% of the tomatoes he sold on Sunday.

the answer is 30%

step by step problem

Answer

Answer:

The -15°C temperature of the ice in their snow cones mean that the temperature of that ice is 15° below the freezing point of water.

Step-by-step explanation:

It is explained that Celsius scale was calibrated based on water. The scientists use 0°C to represent the freezing point of water and subsequently use positive numbers to indicate temperatures above the freezing point of water and negative numbers to indicate temperatures lower than the freezing point of water.

So, a temperature of -15°C simply means that the temperature is 15° lower than the freezing point of water.

Hope this Helps!!!

Answer:

Its A

Step-by-step explanation:

Answer:

a) The marginal cost function is given by

C'(x) = 4 + 0.04x + 0.0003x² (in dollars)

b) C'(70) = $8.27

Step-by-step explanation:

C(x) = 1000 + 4x + 0.02x² + 0.0001x³

a) Marginal cost is usually defined as the cost of producing one extra unit of product. It expresses how much the total cost is changing with respect to number of units of product.

Mathematically,

MC = (dC/dx) = C'(x)

For this question,

C'(x) = 4 + 0.04x + 0.0003x²

b) C'(70) means the marginal cost at x = 70 units, that is, how much the total cost is changing after the production of 70 units; the cost of producing one extra unit of product after producing 70 units.

C'(x) = 4 + 0.04x + 0.0003x²

C'(70) = 4 + 0.04(70) + 0.0003(70²)

C'(70) = $8.27

Hope this helps!

Answer: the probability that exactly 2 buyers would prefer red is 0.0320

Step-by-step explanation:

We would assume a binomial distribution for the color preferences of new car buyers. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 40% = 40/100 = 0.4

q = 1 - p = 1 - 0.4

q = 0.6

n = 14

x = r = 2

Therefore,

P(x = 2) = 14C2 × 0.4^2 × 0.6^(14 - 2)

P(x = 2) = 91 × 0.16 × 0.0022

P(x = 2) = 0.0320

Final answer:

The trigonometric functions and their inverse functions are related to each other because they undo each other's actions. Inverse trigonometric functions give the angle whose trigonometric ratio is a given value. The domains and ranges of inverse trigonometric functions are restricted to ensure that they are well-defined.

Explanation:

The trigonometric functions and their inverse functions are related to each other because they undo the actions of the other function. Let's take the sine function as an example. The sine function takes an angle as input and gives the ratio of the opposite side to the hypotenuse as output. Its inverse function, arcsine, takes a ratio as input and gives the angle whose sine is that ratio as output.

These comparisons make sense in the light of the definition of the inverse of a function because an inverse function undoes the action of the original function. In the case of trigonometric functions, they represent a ratio between the sides of a right-angled triangle, and their inverses give the corresponding angle.

The domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions because they are restricted to a specific range to ensure that the inverse function is well-defined. For example, the domain of arcsine function is [-1, 1] because the output of sine function is always between -1 and 1. By restricting the domain, we can ensure that the inverse function is a one-to-one mapping and has a well-defined output for each input.

Answer:

a) [tex]\hat \mu = \bar X = 145[/tex]

b) [tex]145-1.64\frac{35}{\sqrt{25}}=133.52[/tex]  

[tex]145+1.64\frac{35}{\sqrt{25}}=156.48[/tex]  

So on this case the 90% confidence interval would be given by (133.52;156.48)  

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]\bar X=145[/tex] represent the sample mean  

[tex]\mu[/tex] population mean (variable of interest)  

[tex]\sigma=35[/tex] represent the population standard deviation  

n=25 represent the sample size  

a) For this case the best point of estimate for the population mean is the sample mean:

[tex]\hat \mu = \bar X = 145[/tex]

b) Calculate the confidence interval

The confidence interval for the mean is given by the following formula:  

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)  

Since the confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that [tex]z_{\alpha/2}=1.64[/tex]

Now we have everything in order to replace into formula (1):  

[tex]145-1.64\frac{35}{\sqrt{25}}=133.52[/tex]  

[tex]145+1.64\frac{35}{\sqrt{25}}=156.48[/tex]  

So on this case the 90% confidence interval would be given by (133.52;156.48)  

Answer:

y = mx + b

Hope I helped!!! :)

~Nuha

Complete Question:

The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.

Answer:

The total number of vehicles sold = 32

Step-by-step explanation:

Since the ratio of sales is 4:5:7

Let m be a common factor

The number of sedans sold = 4m

The number of trucks sold = 5m

The number of vans sold = 7m

In (1)

Since the number of vans sold was between 10 and 20. i.e 10 ≤ 7m ≤20

The only multiple of 7 between 10 and 20 is 14

Therefore, 7m = 14; m=2

in (2)

The number of sedans sold was less than 10 i.e. 0 < 4m < 10

There are two multiples of 4 between 0 and 10, they are 4 and 8

for 4m = 4; m=1

for 4m = 8; m=2

m = 2 is the only consistent value in (1) and (2)

The number of sedans sold = 4m = 4 *2 = 8

The number of trucks sold = 5m = 5 * 2 = 10

The number of vans sold = 7m = 7*2 = 14

The total number of vehicles sold = 8 + 10 + 14

The total number of vehicles sold = 32

COMPLETE QUESTION

The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.

Answer:

32 Vehicles

Step-by-step explanation:

Take a look at the image to see the explanation

Answer:

The range is 9,100

Step-by-step explanation:

Six different figures for the account balance for the six months are given.

The range of a set of numbers is defined as the difference between the highest and the lowest of the numbers.

In this question, we have;

Highest: 9200

Lowest: 100

Range = Highest - Lowest = 9200 - 100 = 9100

Answer:

There is a typo in your question it's supposed to be 200 not 9200

Step-by-step explanation:

Answer:

60 combinations for single file.

Step-by-step explanation:

Bloopin has 12 combinations where he leads the single file line of 3 only reindeer's at a time including the reindeer that leads the file. This is not a file of five but as the question asks for 3 there are 5 reindeer's that each have a turn of 12 each, to single file 3 reindeer's, it is here we get 12 for each combination.

12 x 5 = 60 combination.

Answer:

The answer to your question is 34°

Step-by-step explanation:

Data

m∠1 = 34°

m∠2 = 116°

m∠3 = ?

Process

1.- If lines l and m are parallel then angles 1 and 3 are interior alternate angles.

2.- Interior alternate angle measure the same.

3.-  m∠1 = m∠3

4.- m∠3 = 34°

5.- Another information given is not necessary to answer this question.

Answer: 34°

Step-by-step explanation:

There may be another way to do it; angle 1 is equal to 34°, angle one and the supplement of 3(we will call it angle 4) are supplementary. So if angle 1 equals 34, angle 4 = 180-34 (which equals 146). since angles 3 and 4 are supplementary, angle 3; would equal 180 - 146 (which equals 34).

Have a nice day! Good luck with the exam.

Answer: $17505 must be deposited today.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited.

From the information given,

A = 30000

r = 8% = 8/100 = 0.08

n = 1 because it was compounded once in a year.

t = year

Therefore,.

30000 = P(1 + 0.08/1)^1 × 7

30000 = P(1.08)^7

30000 = 1.7138P

P = 30000/1.7138

P = $17505

Final answer:

To have $30,000 in 7 years for a down payment on a house, approximately $19,882.68 must be deposited today into an account with annual compounding and an APR of 8%.

Explanation:

To calculate the amount that must be deposited today, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money desired, P is the principal amount (the amount to be deposited), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years. In this case, A = $30,000, r = 0.08 (8% as a decimal), n = 1 (compounded annually), and t = 7 years:

A = P(1 + r/n)^(nt) ⇒ $30,000 = P(1 + 0.08/1)^(1*7)

Now, we can solve the equation for P:

P = $30,000 / (1 + 0.08/1)^(1*7) ≈ $19,882.68

Therefore, approximately $19,882.68 must be deposited today to have $30,000 in 7 years for the down payment on a house.

Answer:

-2/3

Step-by-step explanation:

using rise over run from point B you go up 2 points and then to point A left 3 and since the line is going down the slope will be negative so -2/3

Answer:

  y = 4x -3

Step-by-step explanation:

The line perpendicular to the given line can be written as the same equation with the coefficients of x and y swapped, and one of them negated. The constant may be different, so we'll call it "c".

  4x -y +c = 0 . . . . . line perpendicular to that given

The y-intercept of the second given line can be found by setting x=0. That gives the equation -y -3 = 0. The perpendicular line with x=0 would have equation ...

  -y +c = 0

Comparing these two tells us c = -3.

So, the general form of the perpendicular line we want is ...

  4x -y - 3 = 0

We can add y to put this in slope-intercept form:

  y = 4x -3

Answer:

Eli used 1.25 pounds of butter to make mashed potato.            

Step-by-step explanation:

We are given the following in the question:

Amount of potato used by Eli = 12.5 pounds

Amount of butter used =

[tex]\dfrac{1}{10}(\text{Amount of potato used})[/tex]

Thus, pounds of butter used by Eli is:

[tex]\dfrac{1}{2}\times 12.5\\\\=1.25[/tex]

Thus, Eli used 1.25 pounds of butter to make mashed potato.

Answer:

5 dollars and 19 cents

Step-by-step explanation:

hsgd

Answer:

24000 pieces.      

Step-by-step explanation:

Given:

Side lengths of cube = [tex]\frac{1}{4} \ foot[/tex]

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

[tex]Volume\ of\ cube =a^{3}[/tex]

                          [tex]=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot[/tex]

Length = 8 foot, Breadth = [tex]6\frac{1}{4} =\frac{25}{4} \ foot[/tex], Height =[tex]7\frac{1}{2} =\frac{15}{2} \ foot[/tex]

[tex]Volume\ of\ rectangular\ prism =length\times breadth\times height[/tex]

                                                [tex]=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot[/tex]

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = [tex]\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube[/tex]

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.