A tree is making a shadow 22 feet long. The angle of elevation from the tip of
the shadow to the top of the tree is 50°.
feet. Round your answer to the nearest
The height of the tree is about
foot.

Answer: 1/2

Step-by-step explanation:

Dividing the numerator and denominator by x, we get the limit is equal to:

[tex]\lim_{x \to -\infty} \frac{-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3}{4+\frac{7}{x}}\\\\=\frac{\lim_{x \to -\infty} \left(-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3 \right)}{\lim_{x \to -\infty} \left(4+\frac{7}{x} \right)}\\\\=\frac{2}{4}=\boxed{1/2}[/tex]

Statement 1

Twice the sum of the odd numbers would be:

[tex]2(1+3+5+\cdots+99)=2+6+10+\cdots+198[/tex], which is not equal to the sum of all the even numbers from 1 to 100.

Statement 2

The sum of all the odd numbers from 1 to 100 can be thought of as an arithmetic sequence containing 50 terms, with first term 1 and common difference 2. This means the sum of the series would be:

[tex]\frac{50}{2}[2(1)+(50-1)(2)]=2500[/tex]

which is not equal to 1002.

The statement 1 and the statement 2 are incorrect.

The sum of the arithmetic series of first term a₁ and common difference d will be s= n/2{2a₁+(n-1)d

Statement 1:

Given in statement 1, Twice the sum of the odd numbers would be:

2(1+3+5+7.......+99)=2+6+10+14+.....198

which is not equal to the sum of all the even numbers from 1 to 100.

Statement 2:

The sum of all the odd numbers from 1 to 100 can be calculated as follows where this is an arithmetic sequence of 50 terms, where the first term is 1 and the common difference is 2. This means the sum of the arithmetic series would be:

s= n/2{2a₁+(n-1)d}

putting the above formula

a₁=1

n=50

d=2

s= 50/2{2(1)+(50-1)2} = 25{2+98} =2500 ≠1002

which is not equal to 1002.

Therefore statement 1 and 2 are incorrect.

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12.5% is the percentage of numbers randomly generated by Taylor's computer that is less than 0.5.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

The percentage of numbers randomly generated by Taylor's computer are less than 0.5 is given by

P(0≤X≤0.5)

=[tex]\int_{0}^{0.5}\frac{1}{4}dx[/tex]

[tex]=\frac{1}{4}x|^{0.5}_{0}[/tex]

[tex]=\frac{1}{4}(0.5-0)[/tex]

[tex]=0.25(0.5)[/tex]

= 0.125

That is 12.5%

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Answer:

i think, bond rating agencies giving CDOs very low ratings, discouraging investors to invest

Step-by-step explanation:

Answer:

2x+3+9

because plyer scored 9 points and throw 2point shotand same number 3

Answer:

[tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as |z|).

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

[tex]\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}[/tex]

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

[tex]\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]

Hence, the complex number that has polar coordinate of (4,-45°) is [tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]

Explanation:

Equation: x + 1 = 9

Solving Steps:

x + 1 = 9                 (subtract both sides by 1)

x + 1 - 1 = 9 - 1        (simplify the following)

x = 8

Then check for solution:

x + 1 = 9

                         [insert x = 8]

8 + 1 = 9

9  =  9

As both sides are equal, the statement is true.

[tex]\large\underline{ \cal{SOLUTION:}}[/tex]

[tex] \large \bold{x + 1 = 9}[/tex]

[tex] \large \bold{x = 9 - 1}[/tex]

[tex] \large \bold{x = \red{8}}[/tex]

[tex] \: [/tex]

[tex]\large\underline{ \cal{CHECKING:}}[/tex]

[tex] \large{ \bold{ \underline{ \red{8} }+ 1 = 9}}[/tex]

[tex] \large \bold{-N} \frak{unx-}[/tex]

Answer:

4mm

Step-by-step explanation:

you have to add both sides after substituting each of the 4 sides by 1mm

which gives you the total of 4

Answer:

uhm where is x1 and y1?

Step-by-step explanation:

Y – y1 = m (x – x1)

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

Write the equation of the line in P.S. form given the information below.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

We cannot write an equation in Point-Slope Form, without knowing the Point-Slope Equation. [tex]\bf{y-y1=m(x-x1)}[/tex].

Now, all that we need to do is plug in the information given, that is

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{y-(-3)=-\dfrac{1}{5}(x-0)}[/tex]

[tex]\triangledown[/tex]

[tex]\bf y+3=-\dfrac{1}{5}(x-0)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{y+3=-\dfrac{1}{5}(x-0).\;Hope\;the\;rest\;of\;your\;day\;is\;going\;to\;be\;fun!}[/tex]

[tex]\rule{300}{1.7}[/tex]

~[tex]\boxed{\bf{aesthetic \not101}}[/tex]~

Answer:

defectionist forme solb ifv

The fraction of the total number of marbles is left in the bag after removing and giving part to her friend is 3/8

let

Remaining marbles = x - 1/2x

= (2x-x) / 2

= x/2

= 1/2x

Number of marbles given to her friend = 1/4 of 1/2x

= 1/4 × 1/2x

= 1/8x

Number of marbles left in the bag = Remaining marbles - Number of marbles given to her friend

= 1/2x - 1/8x

= (4x-x) / 8

= 3x/8

= 3/8x

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Answer: Length = 9 cm, Width = 6 cm

Step-by-step explanation:

L - 3 + L - 3 + L + L = 30

2L - 6 + 2L = 30

4L - 6 = 30

4L = 36

L = 9

Length = 9 cm

Width = 9-3 = 6 cm

Answer:

Breyer

Step-by-step explanation:

1gallon=128oz half gallon=64oz

We can make both of their unit to 224oz: 14x16=224oz 64x3.5=224oz

Haagen Dazs:3.67x16=58.72/224oz

Breyer: 4.69x3.5=16.415/224oz

Breyer’s way cheaper

The correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Given parent function is f(x)=|x|

Now we have to find which function from given choices will be narrower than the parent function.

Notice that adding or subtracting some number from the parent function only shifts the graph up, down, and left of the right side.

But that will not make the function narrower or broader.

So f(x) = |x – 2| and f(x) = |x| + 3, can't be the answer.

Multiplying by some positive real number which is more than 1, makes the function narrower.

Only f(x) = 2.9|x| from remaining choices fits that case.

Hence correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|

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Answer:

D,E

Step-by-step explanation:

Answer: [tex]\frac{\sqrt{113}}{7}[/tex]

Step-by-step explanation:

As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.

Using the identity [tex]1+\tan^{2} X=\sec^{2} X[/tex],

[tex]1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}[/tex]

Answer:

the answer will be similar, because if you divide 2, 3, 2.25 by 3 you will get the answer.

The range of the function g(x) will be (–∞, –4] ∪ [2, ∞). Option C is correct.

The domain denotes all potential x values, while the range denotes all possible y values.

When we plot the graph of the given function we will get the maximum and the minimum value till we get the function plot. The difference in the value of those coordinates is the range of the function.

The range of the function g(x) will be (–∞, –4] ∪ [2, ∞).

Hence option C is correct.

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Answer:

6000 meters

Step-by-step explanation:

Each kilometer is 1000 meters so 1000 x 6 is 6000

Answer:

3059＝6940

Step-by-step explanation:

For the two examples given, we can see a consistency:

1 becomes 8 ; 8 becomes 1

5 becomes 4 ; 4 becomes 5

3 becomes 6 ; 6 becomes 3

2 becomes 7

because they are the only two digits left without a correlated pair, we can assume that 0 and 9 have the same relationship

So,

3 -> 6

0 -> 9

5 -> 4

9 -> 0

Meaning that 3059＝6940

hope this helps!! have a lovely day :)

Answer:

The answer is OPTION (D)log(y)=0.326x+0.687

It is a linear model, e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y)

The Linear regression equation for the transformed data:

We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.

(1, 13) 1.114

(2, 19) 1.279

(3, 37) 1.568

(4, 91) 1.959

(5, 253) 2.403

X            Y           Log(y)

1              13           1.114

2             19         1.740

3             37        2.543

4             91        3.381

5            253      4.226

Sum of X = 15

Sum of Y = 8.323

Mean X = 3

Mean Y = 1.6646

Sum of squares (SSX) = 10

Sum of products (SP) = 3.258

Regression Equation = ŷ = bX + a

b = SP/SSX = 3.26/10 = 0.3258

a = MY - bMX = 1.66 - (0.33*3) = 0.6872

ŷ = 0.3258X + 0.6872

The graph is plotted below:

The linear regression equation is  log(y)=0.326x+0.687

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Step-by-step explanation:

all the details You can find in the attachment.

Answer: C, 5, 5√3

Step-by-step explanation:

The short leg of a 30-60-90 triangle equal half the hypotenuse, 10/2 = 5. The long leg equals √3 times the short leg, 5*√3 = 5√3.

The correct answer is option A which is the operating profit will be $73000.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

We will consider the following notations and will make the expression for operating profit.

P = profit

S = sales = $900000

F = Fixed cost = $197000

V = 07S = variable cost

So the expression will be given as:-

P = S - F - V

P = S - F - 0.7S

P = 9000000 - 1797000 - ( 0.7 x 9000000)

P = 703000 - 630000

P = $73000

Therefore the correct answer is option A which is the operating profit will be $73000.

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Both statements are true. Therefore (4,2) is a solution and option D is correct.

The given inequalities are [tex]y\leq 2x-2[/tex] and [tex]y\leq x^{2} -3x[/tex].

We need to select the point that is a solution to the system of inequalities (-2,-1), (1,3), (2,1) and (4,2).

Inequalities can be seen in the speed limits on roads, the minimum age for seeing certain movies, and the distance you have to walk to go to the park. Inequalities represent a limit of what is permitted or achievable rather than a precise quantity.

Any point is a solution to this system of inequality if it satisfies both inequalities.

Check the inequalities by each option.

For (-2, -1), [tex]-1\leq 2(-2)-2 \implies -1\leq -6[/tex].

This statement is false because -1 is greater than -6. Therefore (-2,-1) is not a solution and option A is incorrect.

For (1, 3), [tex]3\leq 2(1)-2 \implies 3\leq 0[/tex]

This statement is false because 3 is greater than 0. Therefore (1,3) is not a solution and option B is incorrect.

For (2,1), [tex]1\leq 2(2)-2 \implies 1\leq 2[/tex].

[tex]1\leq 2^{2} -3(2) \implies 1\leq -2[/tex]

This statement is false because 1 is greater than -2. Therefore (2,1) is not a solution and option C is incorrect.

For (4,2), [tex]2\leq 2(4)-2 \implies 2\leq 6[/tex]

[tex]2\leq 4^{2} -3(4) \implies 2\leq 4[/tex]

Both statements are true. Therefore (4,2) is a solution and option D is correct.

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The expression (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³) is equivalent to the expression 384a⁸b⁴c¹⁴.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³)

By simplifying, we have

⇒ a⁴b²c² × 6a³b × 8c⁹ × 4ab¹ × 2c³

⇒ 384a⁸b⁴c¹⁴

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How much more he has to credit to be worth what it was at at the start of 2010 is: 3,657,000.

Firsts step

Total amount debited=8,000+207,000

Total amount debited=215,000

Total amount credited=116,000+12,000

Total amount credited=128,000

Second step

Additional amount to credit:

40 Lakhs is 4,000,000

Hence:

Additional amount to credit=4,000,000- (215,000+128,000)

Additional amount to credit=4,000,000-343,000

Additional amount to credit=

Therefore how much more he has to credit to be worth what it was at at the start of 2010 is: 3,657,000.

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The graph of the function is drawn. The open circle at -1 and 4 for -2x + 3.

The complete question is attached below.

The function that is transformed into the number of pieces is known as piecewise function.

The piecewise function is given below.

[tex]f(x)=\left\{\begin{matrix}3x-5 & x\leq -1 \\\\-2x+3 & -1 < x < 4 \\\\2 & x\geq 4 \\\end{matrix}\right.[/tex]

The graph of the function is drawn.

The open circle at -1 and 4 for -2x + 3.

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Answer: [tex]87^{\circ}[/tex]

Step-by-step explanation:

Because an angle inscribed in a semicircle is a right angle, [tex]\angle B=90^{\circ}[/tex]

So, as angles in a triangle add to 180 degrees, [tex]\angle A=180^{\circ}-90^{\circ}-3^{\circ}=\boxed{87^{\circ}}[/tex]