the function f(t)= -5t^2+20t +60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the objects to hit the ground?

Answer:

• linear angles

• supplementary angles (all linear angles are supplementary)

Step-by-step explanation:

If the angles share a side and are measured in opposite directions from that side, the non-common edges of these angles form a straight line, so these angles are sometimes called "linear" angles.

Since their sum is 180°, they are always "supplementary" angles. (Supplementary angles need not share a vertex or a side.)

Answer:

4.4, 4.4 : 1, 22 : 5

Step-by-step explanation:

There are many ways to solve this, but I'll do it by finding the ratio between V'T' and VT.

That's easy, we're given the lengths of these two. The ratio would be 8.8/2. 8.8/2 = 4.4, or (8.8*5)/(2*5) = 22/5

Answer:

see explanation

Step-by-step explanation:

To evaluate the expression for the given values.

Substitute the given values for x into g(x)

a

g(0) = 3(0)² - 4(0) + 3 = 0 - 0 + 3 = 3

b

g(- 1) = 3(- 1)² - 4(- 1) + 3 = 3 + 4 + 3 = 10

c

g(2) = 3(2)² - 4(2) + 3 = 12 - 8 + 3 = 7

d

g(- x) = 3(- x)² - 4(- x) + 3 = 3x² + 4x + 3

e

g(1 - t)

= 3(1 - t)² - 4(1 - t) + 3

= 3(1 - 2t + t²) - 4 + 4t + 3

= 3 - 6t + 3t² - 4 + 4t + 3

= 3t² - 2t + 2

Answer:

Step-by-step explanation:

- 5 + (-3) + 3 is the correct option.

Answer:

-5 + (-3) + 3

Step-by-step explanation:

Answer:

Dividend

Step-by-step explanation:

If you take a simple division problem like A = B / C

A is the quotient (result)

B is the dividend

C is the divisor

So, a number by which another number is to be divided is called a dividend, like A in the example above.

If C doesn't divide B in an exact manner (like in the case of 7 / 2), there's a remainder for the operation.

A divisor is a number by which another number, the dividend, is divided. In scientific notation, division involves dividing the coefficients and subtracting the exponents of the divisor from the dividend. Division is fundamentally related to multiplication, as it can be represented by multiplying by a reciprocal.

Answer: the coefficient of 13m is 13.

Answer:

The coefficient of 13 m is 13.

Step-by-step explanation:

Consider the provided expression.

[tex]13m[/tex]

Numbers appear with variables are called coefficients.

Alphabets in an expression are called variables.

Numbers appear without variables are called Constant terms.

Here we need to identity the coefficient.

From the above definition we know the number appear with the variables are coefficients.

Since m is variable, thus the number 13 must be the coefficient.

Hence, the coefficient of 13 m is 13.

Answer:

  [tex]\text{D.}\quad d=\dfrac{206-8(10)}{7}[/tex]

Step-by-step explanation:

The total length of the space between rungs is the overall length less the width of 8 rungs, so is 206 -8(10). That space is divided into 7 equal parts, as shown by the equation in choice D.

_____

Choice A looks similar, but is not. In that equation, only the term 8(10) is divided by 7. You want the difference to be divided by 7, so must have a grouping symbol of some kind. Choice D uses the division bar to group the terms of the numerator. Parentheses would work, too, as in ...

  d = (206 -8(10))÷7

but without them, the equation is incorrect.

Answer:2/3

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

one way we can solve this is by making a tree  using H for heads and T for tails

since it can land H or T, we put them down like this. then we can get H or T again because its a coin, so we put that under each letter. finally we do the same thing again to get 8 possibilities. now we can count how many of them was HHH, which is one

         H              T

         /  \            /   \

       H   T         H   T

      /\     /\        /\    /\

    H T H T     H T H T

    ^      this one

or do 2 x 2 x 2 because there are 2 possibilities each three times

Answer:

$3735

Step-by-step explanation:

The formula for simple interest is I = Prt, where I is the interest earned, P is the initial investment, r is the interest rate in decimal form, and t is the time in years.  We have everything we need to find the interest, which is the amount your investment earned while it sat there for 7 years.  Once we find that interest amount, we will add it to the intial investment to find the total amount after 7 years that your money has grown to.

I = 3000(.035)(7) so

I = 735

3000 + 735 = 3735

Answer:

$3,630

Step-by-step explanation:

You invest $3,000 in an account at 3.5% per year simple interest.

We have to calculate the amount in the account at the beginning of the 7th year. This means we have to calculate the interest for completed 6 years.

Formula for simple interest

A = P(1+rt)

A = Amount after maturity

P = Principal amount ( 3,000)

r = rate of interest in decimal ( 0.035)

t = time in years ( 6 )

Now we put the values in to formula

A = 3,000(1 + 0.035 × 6)

A = 3,000 ( 1 + 0.021 )

A = 3,000 × 1.21

A = $3,630

The amount would be $3,630 at the beginning of the 7th year.

Final answer:

The standard deviation of the data set is 2.98, calculated by finding the mean, squaring the differences, averaging them, and taking the square root. One standard deviation below the mean is 2.52.

Explanation:

To find the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3, follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data point and square the result.

Calculate the average of these squared differences.

Take the square root of the average to find the standard deviation.

Using a calculator or computer:

The mean of the data set is 5.5

The squared differences would be (8.2-5.5)^2, (10.1-5.5)^2, etc.

The average of these squared differences is approximately 8.86.

The square root of 8.86 gives us the standard deviation of approximately 2.98.

Therefore, the standard deviation of the data set, rounded to the nearest hundredth, is 2.98.

To find the value that is one standard deviation below the mean, you subtract the standard deviation from the mean:

5.5 - 2.98 = 2.52.

Answer:

Step-by-step explanation:

9x⁴ – 2x² – 7 = 0

Let's say that u = x²:

9u² – 2u – 7 = 0

Factor:

(u – 1) (9u + 7) = 0

u = 1, -7/9

Since u = x²:

x² = 1, -7/9

x = ±1, ±i √(7/9)

By using the substitution method, the solutions of this equation (polynomial) is equal to C. x = ±1 and ±i√(7/9).

In order to determine the solutions of this equation (polynomial), we would let "u" be equal to x² and then substitute this value into the equation as follows:

9x⁴ - 2x² - 7 = 0

Substituting the value of "u" into the equation (polynomial), we have:

9u² - 2u - 7 = 0

Factorizing the equation (polynomial), we have:

(9u + 7)(u - 1) = 0

u = 1 and -7/9

Since, u = x²:

x² = 1 and -7/9

x = ±√(1 and -7/9)

x = ±1 and ±i√(7/9).

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For this case we have that by definition:

[tex](a + b) (c + d)[/tex] is equal to:

[tex]ac + ad + bc + bd[/tex]

Applying the distributive property.

Then, it can be seen that the given binomials were multiplied correctly.

ANswer:

There is no error; the binomials were correctly multiplied together.

I don’t know what the answer is I wish I could help

3:7

Taxes are 30c and one dollar is 100c then the net income is 70c, making the income 30:70. this can be simplified to 3:7.

Answer:

I got  65

Step-by-step explanation:

The profit will be given as:

P=$15x−$225  

(where we subtracted the cost of the mower) so that  P=$750

x will be the required number of needed lawns.

We need to solve:

$750=$15x−$225  

rearranging:

x=$750+$225 /  $15  =65  lawns

Define a variable and write an inequality to represent earning a specific profit in a lawn-mowing business.

Define variable:

Let x represent the number of lawns mowed.

Write inequality:

The inequality is 15x - 225 ≥ 750, where 15x is the amount earned, 225 is the cost of the lawnmower, and 750 is the desired profit.

Answer: 30.01 feet.

Step-by-step explanation:

You need to remember this identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

Observe the figure attached, where [tex]h_t[/tex] is the height in feet of the tree.

You need to calculate [tex]h_1[/tex] of the Triangle 1, where:

[tex]\alpha= \alpha_1=42\°\\opposite=h_1\\adjacent=20[/tex]

Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_1[/tex]:

[tex]tan(42\°)=\frac{h_1}{20}\\\\h_1=20*tan(42\°)\\h_1=18[/tex]

Now you need to calculate [tex]h_2[/tex] of the Triangle 2, where:

[tex]\alpha= \alpha_2=31\°\\opposite=h_2\\adjacent=20[/tex]

Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_2[/tex]:

[tex]tan(31\°)=\frac{h_2}{20}\\\\h_2=20*tan(31\°)\\h_2=12.01[/tex]

Then the height in feet of the tree is:

[tex]h_t=h_1+h_2\\h_t=(18+12.01)ft\\h_t=30.01ft[/tex]

The height of the tree can be determined by the trigonometric ratio of tan angle.

The height of the tree is 30 feet.

Given that,

Mariela is standing in a building and looking out a window at a tree.

The tree is 20 feet away from Mariela,

Mariela's line of sight creates a 42-degree angle of elevation, and her line of sight creates a 31 degree of depression.

We have to determine,

What is the height, in feet, of the tree?

According to the question,

Let, the height of the tree be h

The tree is 20 feet away from Mariela,

First, we have to calculate the length of BD which is x,

Then,

The length of BD is given by,

[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{BD}{AD}\\\\Tan42 = \dfrac{x}{20}\\\\x = tan42 \times 20\\\\x = 0.9 \times 20\\\\x = 18[/tex]

The measurement of x is 18 feet.

Again we have to calculate the length of y,

Then,

The length of DC is given by,

[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{DC}{AD}\\\\Tan31 = \dfrac{Y}{20}\\\\y = tan31 \times 20\\\\x =0.6 \times 20\\\\y = 12[/tex]

The measurement of y is 12 feet.

Therefore,

The height of the tree is given by,

[tex]\rm h= x +y\\\\h = 18+12\\\\h = 30 \ feet[/tex]

Hence, The height of the tree is 30 feet.

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Answer:

(3.01%, 14.77%)

Step-by-step explanation:

The confidence interval of a proportion is:

CI = p ± SE × CV,

where p is the proportion, SE is the standard error, and CV is the critical value (either a t-score or a z-score).

We already know the proportion: 8/90.  But we need to find the standard error and the critical value.

The standard error is:

SE = √(p (1-p) / n)

SE = √((8/90) * (82/90) / 90)

SE = 0.03

To find the critical value, we must first find the alpha level and the degrees of freedom.

The alpha level for a 95% confidence interval is:

α = (1 - 0.95) / 2 = 0.025

The degrees of freedom is one less than the sample size:

df = n - 1 = 90 - 1 = 89

Since df > 30, we can approximate this with a normal distribution.

If we look up the alpha level in a z score table, we find the z-score is 1.96.  That's our critical value.  CV = 1.96.

Now we can find the confidence interval:

CI = 8/90 ± 0.03 * 1.96

CI = 0.0889 ± 0.0588

CI = (0.0301, 0.1477)

So we are 95% confident that the percent of patients who had their teeth whitened is between 3.01% and 14.77%.

Answer:

The answer is below

Step-by-step explanation:

Answer:

The residual e=2 when x = 5.

Step-by-step explanation:

A scatter plot containing the point (5, 29), it means the observed value at x=5 it 29.

The given regression equation is

[tex]\hat{y}=5x+2[/tex]

Substitute x=5 in the above regression equation, to find the predicted value at x=-5.

[tex]\hat{y}=5(5)+2=25+2=27[/tex]

The formula to find the residual value e is

e = Observed value - Predicted value

[tex]e=29-27[/tex]

[tex]e=2[/tex]

Therefore the residual e=2 when x = 5.

Answer: 0 ≤ t ≤ 40

Step-by-step explanation:

0 and 40 are included in all 3 number lines.

Answer:

1,800 bricks are needed

Step-by-step explanation:

First convert the Length and width of the sidewalk into inches

Entire Sidewalk: L= 100x12 =1200in and W= 4 x 12 = 48in

Then we know Area = LxW, so we will do this for both the sidewalk and the brick.

Area of sidewalk: 1200 x 48 = 57600

Bricks ( no need to convert since the measurements are already in inches): 8 x 4 = 32

Now we will divide the area of the entire sidewalk by the area of a single brick to find out how many bricks you need to complete the whole sidewalk:

57600/32= 1,800 bricks

Answer:

The mean is equal to the median, so the data is symmetrical

Step-by-step explanation:

Here is the data.

10 5 8 10 12 6

8 10 15 6 12 18

The given data:   10   5   8   10   12   6   8   10   15   6   12   18

For finding the Mean, we will have to add all numbers together and divide it by total number. i.e sum of terms divided by number of terms  

Mean= 10+5+8+10+12+6+8+10+15+6+12+18  ÷ 12

Mean = 120 ÷ 12 = 10        

For finding the Median, first we need to rearrange the data in ascending order

5   6   6   8   8   10   10   10   12   12   15   18

We can see that the middle values are 10 and 10. So, the median will be the average of those two middle values.

Median = 10+10 ÷ 2

Median = 20 ÷ 2 = 10

From the calculation, we can see that both the median and mean are equal so, the data is symmetrical  

Answer:

The sum of the first 100 terms is 60400

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

 between each two consecutive terms n is the position of the

 number

- The sum of first n terms of an Arithmetic sequence is calculate from

 Sn = n/2[a + l], where a is the first term and l is the last term

* Now lets solve the problem

- We will use method (1)

- From the table the terms of the sequence are:

 10 , 22 , 34 , 46 , 58 , 82 , 94 , ............., where 10 is the first term

∵ an = a1 + (n - 1) d ⇒ explicit formula

∵ a1 = 10 and a2 = 22

∵ d = a2 - a1

∴ d = 22 - 10 = 12

- The 100th term means the term of n = 100

∴ a100 = 10 + (100 - 1) 12

∴ a100 = 10 + 99 × 12 = 10 + 1188 = 1198

∴ The 100th term is 1198

- Lets find the sum of the first 100 terms of the sequence

∵ Sn = n/2[a1 + an]

∵ n = 100 , a = 10 , a100 = 1198

∴ S100 = 100/2[10 + 1198] = 50[1208] = 60400

* The sum of the first 100 terms is 60400

Answer:

The test statistic supports the claim

Step-by-step explanation:

413 out of 1588 people says that they smoked.

So, we can find that that is 413/1588 ≈ 0.26 = 26%.

This proves that the test statistic is supporting the claim, since the two are similar.

Answer:

  8√2

Step-by-step explanation:

The hypotenuse of a right triangle is √2 times the leg length, so you have ...

  [tex]x\sqrt{2}=16[/tex]

Dividing by the coefficient of x gives ...

  [tex]x=\dfrac{16}{\sqrt{2}}=\dfrac{16\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=8\sqrt{2}[/tex]

Each leg has length 8√2.

Answer:

17 ft

Step-by-step explanation:

I don't think you meant to put pi over 3t ... I think you meant to put pi just over 3

Just plug in 5 assuming t is time in hours.  

Evaluate 4 *cos(pi/3 *5)+15

which is  17 ft

The height of tower after 5 hours is 17.68 feet.

The graph of the cosine function looks like this: The domain of the function y=cos(x) is all real numbers (cosine is defined for any angle measure), the range is −1≤y≤1 .

The Cosine function :  f(t) = 4 cos(π/3t) + 15

and,  f(t) = 4 cos(2kπ + π/3t) + 15

where k= 0,1,2,3....

The range of cosine function is : Maximum= +1 and minimum= -1

At t=0,

For maximum, f(t)= 4 x1 +15

   = 19 feet

For minimum, f(t) =  4 x(-1)+15

                            = 11 feet

After , 6 hours ,the tide function is: 6 n=5

                                                          n= 6/5

f(t) = 4 cos ( 2* [tex]\frac{5* \pi}{6}[/tex] + [tex]\frac{\pi}{3*5}[/tex] ) +15

    = 4 cos (26 π/15) + 15

    = 4 cos[tex]312^{0}[/tex] + 15

   = [tex]4 cos 48^{0}+ 15[/tex]

   = 4 x 0.6691 +15

  = 17.68 feet.

Thus, the height of tower after 5 hours is 17.68 feet

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Answer:

Acute

Step-by-step explanation:

7² + 9² ? 11²

49 + 81 ? 121

130 is greater than 121, so it is an acute triangle

Answer:

35

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

nCk = n!/(k!(n -k)!)

7C3 = 7!/(3!(7-3)!) = 7·6·5/(3·2·1) = 7·5 = 35

_____

It is convenient to use the largest of the factorials in the denominator to cancel as many factors as you can from the numerator, then cancel factors from the remaining numbers. Here after canceling 4! = 4·3·2·1 from the numerator, we are left with 7·6·5 divided by 3! = 3·2·1 = 6. Obviously, this will cancel the 6 in the numerator product, leaving only 7·5 = 35.

Some graphing and/or scientific calculators will have this function built in.

Answer:

[tex]\large\boxed{b.\ x=\dfrac{14}{27}\ \text{and}\ c.\ x=2}[/tex]

Step-by-step explanation:

[tex]4|5-5x|=7x+6\\4|-5(x-1)|=7x+6\\4|-5||x-1|=7x+6\\(4)(5)|x-1|=7x+6\\20|x-1|=7x+6\\\\\text{First step:}\\\text{Based on the de}\text{finition of the absolute value}\\\\|x-1|=\left\{\begin{array}{ccc}x-1&\text{for}\ x\geq1\\1-x&\text{for}\ x<1\end{array}\right\\\\\text{Let}\ x<1\to x\in(-\infty,\ 1).\ \text{Then}\ |x-1|=1-x:\\\\20(1-x)=7x+6\qquad\text{use the distributive property}\\20-20x=7x+6\qquad\text{subtract 20 from both sides}\\-20x=7x-14\qquad\text{subtract}\ 7x\ \text{from both sides}\\-27x=-14\qquad\text{divide both sides by (-27)}\\x=\dfrac{14}{27}<1\qquad \bold{:)}[/tex]

[tex]\text{Let}\ x\geq0\to x\in\left<1,\ \infty\right).\ \text{Then}\ |x-1|=x-1:\\\\20(x-1)=7x+6\qquad\text{use the distributive property}\\20x-20=7x+6\qquad\text{add 20 to both sides}\\20x=7x+26\qquad\text{subtract}\ 7x\ \text{from both sides}\\13x=26\qquad\text{divide both sides by 13}\\x=2\geq1\qquad \bold{:)}[/tex]

You can solve this by using trial and error. When doing so I came with a conclusion of 8,4, and 2.

The dimensions of a rectangular prism with a volume of 64 cubic inches can be any combination of length, width, and height whose multiplication result is 64, including possibilities of 1x1x64, 2x2x16, 4x4x4 and many more.

The volume of a rectangular prism is calculated by multiplying the length, width, and height of the prism (Volume = Length x Width x Height).

If we know that the volume of the prism is 64 cubic inches, there can be several possible dimensions for the rectangular prism. To find these, we would look for different combinations of length, width and height that when multiplied, equal 64. Here are a few examples:

Length = 1 inch, Width = 1 inch, Height = 64

Length = 2 inches, Width = 2 inches, Height = 16 inches

Length = 4 inches, Width = 4 inches, Height = 4 inches

There can be many more possible dimensions, including fractions as well.

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Answer:

[tex]y=\tan x[/tex]

Step-by-step explanation:

The trigonometric function that needs a domain restriction of [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex] to make it invertible is [tex]y=\tan x[/tex].

The function [tex]y=\tan x[/tex] will pass the horizontal line test on this interval therefore making it an invertible function on this interval.

This explains why the inverse tangent function, [tex]y=\tan^{-1} x[/tex] has range [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex].

Answer:

A) [tex]f(x)=sin x[/tex]

Step-by-step explanation:

I just did the test and this was the correct answer.