A street light is mounted at the top of a 6-meter-tall pole. A man 2 m tall walks away from the pole with a speed of 1.4 m/s along a straight path. How fast (in m/s) is the tip of his shadow moving when he is 15 m from the pole?

The tomato plant is 49 cm tall 22 days after Allie bought it.

What are Functions?

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is termed the domain of the function and the set Y is called the codomain of the function.

The function is H(d) = 16 + 1.5d

Since, all the options talks aabout the height of the plant after 22 days

We need to put the value of d as 22 in the function for calculating the height of the function

H(22) = 16 + 1.5(22)

H(22) = 16 + 33 = 49

The tomato plant is 49 cm tall 22 days after Allie bought it.

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Step-by-step explanation:

greater than 6=0 cause no number on a dice is greater than six

an even number=1/2

less than 4=1/2

Answer:

—4—

_x+1_/4x+3

-(4x+4)

———–––

-1

#4x+3/x+1=4-1/x+1

Answer:

Step-by-step explanation:

First factor the left expression to get

Then cancel out .[tex]\frac{(x+3)(x+2)}{(x+4)(x+2)}*\frac{x+4}{2x}\\ \\\frac{(x+3)}{2x}[/tex]

The x+2 cancel's as well as the x+4's.

The solution to the matrix equations A and B are X = (-2 0 4) and X = (-5 1)

From the question, we have the following parameters that can be used in our computation:

Solving matrix A, we have the following representations

2X=(-4 0 8)

Rewrite the equation properly

So, we have

2X = (-4 0 8)

Divide through the matrix by 2

This gives

X = (-2 0 4)

Solving matrix B, we have the following representations

3 X-(1 7)=(-16 -4)

Rewrite the equation properly

So, we have

3X - (1 7) = (-16 -4)

Add (1 7) to both sides of the equation

This gives

3X = (-15 3)

Divide through the matrix by 3

This gives

X = (-5 1)

Hence, the solutions are X = (-2 0 4) and X = (-5 1)

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To find the height of the column of water in the Fountain Hills fountain, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of elevation to the top of the fountain, the distance from the surveyor to the base of the fountain, and the height of the column of water to form a right triangle.

We can then use the tangent function to find the height of the column of water as follows:

tan(29.7°) = opposite/adjacent

opposite = tan(29.7°) * adjacent

opposite = tan(29.7°) * 980 feet

opposite = 0.56 * 980 feet

opposite = 548.8 feet

Therefore, the height of the column of water in the Fountain Hills fountain is approximately 549 feet. To the nearest 10 feet, this is 550 feet.

Step-by-step explanation:

a.

correct, the population was 18.5 million in 2000.

why ?

t = years after 2000.

so, if the year is 2000, t = 0.

A(0) = 18.5e^(0.1708 × 0)

you remember, a⁰ = 1 for any a.

so,

A(0) = 18.5×e⁰ = 18.5×1 = 18.5 million.

b.

we need to find the value of t for which A(t) = 26.6.

26.6 = 18.5e^(0.1708 × t)

26.6/18.5 = e^(0.1708 × t)

ln(26.6/18.5) = 0.1708 × t

t = ln(26.6/18.5)/0.1708 = 2.126115244... years

≈ 2 years

2 years after 2000 is 2002.

it will reach 26.6 million in the year 2002.

According to the given consumer price index, President Hoover's 1931 salary is equivalent to what amount in 2005 is $962,250

Consumer price index:

In math, the concept of consumer price index (CPI) is significant in the analysis of inflation.

The general form of CPI of current years is computed as

=> (GDP of current period / GDP of base period) x 100.

Given,

In 1931, President Herbert Hoover was paid a salary of $75,000. Government statistics show a consumer price index of 15.2 for 1931 and 195 for 2005.

Here we need to find the President Hoover's 1931 salary is equivalent to what amount in 2005.

Here we have the values of

=> CPI = 15.2 in 1931,

=> salary 75000;

=> CPI = 195 in 2005,

Then the salary is calculated as,

=> 75000 x (195/15.2)

=> 75000 x 12.83

=> 962250

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The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours

From the question, we have the following parameters that can be used in our computation:

Austin

Initial temperature = 33.5 degrees Fahrenheit

Rate of increment = 2.5 degrees Fahrenheit

San Antonio

Initial temperature = 37.5 degrees Fahrenheit

Rate of increment = 1.5 degrees Fahrenheit

The above parameters mean that

Current temperature = Initial temperature + Rate of increment x Number of hours

Austin: A(t) = 33.5 + 2.5t

an Antonio: B(t) = 37.5 + 1.5t

When Austin is colder than San Antonio, we have

Substitute the known values in the above equation, so, we have the following representation

33.5 + 2.5t < 37.5 + 1.5t

Divide both sides by 1

t < 4

Hence, the interval is less than 4 hours

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Transformation involves changing the form of a function. The transformations are:

vertical translation 1 unit up .

horizontal translation 5 units left.

The functions are given as:

f(x) = 8x

g(x) = [tex]8^{x+5}[/tex] + 1

Start by translating the function 5 units left.

The rule of this translation is:

f'(x) = f(x+5)

So, we have:

f'(x) = 8(x+5)

Next, translate the function 1 unit up

The rule of this translation is:

f"(x) = f'(x) + 1

∴ f"(x) = 8(x+5) + 1

Rewrite as:

g(x) = 8(x+5) + 1

Hence, the transformations are: vertical translation 1 unit up  and horizontal translation 5 units left

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Transformation involves changing the form of a function. The transformations are:

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

The functions are given as:

f(x) = 8x

g(x) =  + 1

Start by translating the function 5 units left.

The rule of this translation is:

f'(x) = f(x+5)

So, we have:

f'(x) = 8(x+5)

Next, translate the function 1 unit up

The rule of this translation is:

f"(x) = f'(x) + 1

∴ f"(x) = 8(x+5) + 1

Rewrite as:

g(x) = 8(x+5) + 1

Hence, the transformations are: vertical translation 1 unit up  and horizontal translation 5 units left

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The linear functions for this problem are graphed on the image given at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

Hence the functions in this problem are graphed as follows:

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Phishing is when a hacker impersonating a reliable entity sends you a phony email in the hopes that you will voluntarily divulge your personal information.

Phishing is a type of social engineering in which an attacker sends a false (for example, spoofed, phony, or other deceptive) communication with the goal of tricking a person into providing the attacker with vital information[1] or to install harmful software, such as ransomware, on the victim's infrastructure.

Phishing attacks are becoming more and more sophisticated, and they frequently transparently mirror the site that is being attacked, allowing the attacker to see everything the victim does there and to get past any further security measures with them.

[] According to the FBI's Internet Crime Complaint Center, which tracks more phishing incidents than any other type of computer crime combined, phishing attacks will be by far the most common type of hacker attack through 2020. []

For the first time, the term "phishing" was employed.

Hence, Phishing is when a hacker impersonating a reliable entity sends you a phony email in the hopes that you will voluntarily divulge your personal information.

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[tex]\begin{array}{ccll} \$&hours\\ \cline{1-2} 44 & 6\\ x& 9 \end{array} \implies \cfrac{44}{x}~~=~~\cfrac{6}{9} \\\\\\ \cfrac{ 44 }{ x } ~~=~~ \cfrac{ 2 }{ 3 }\implies 132=2x\implies \cfrac{132}{2}=x\implies 66=x[/tex]

Answer:

x = 2

Step-by-step explanation:

Given equation,

→ 4x - 22 = -14

Now the value of x will be,

→ 4x - 22 = -14

→ 4x = -14 + 22

→ 4x = 8

→ x = 8/4

→ [ x = 2 ]

Hence, the value of x is 2.

A minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.

What is the standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The given data is:

{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}

Now find the mean of the given data would be

Mean = sum of all points/n

         = 491/10

         = 49.1

Standard deviation(s) = [tex]\sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

Standard deviation(s) = 29.31988

Considering one standard deviation from the mean, the lower and upper limits are given by the following

[49.1-29.31988, 49.1+29.31988}

=[19.78012, 78.41988]

We can see that only 6 {27,32,45,57,61,73} out of the 10 points, which is 60%, confine to the interval of one standard deviation from the mean.

Hence, a minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.

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domain of (f.g)(x) is {x l x ≠ 13} i.e option (c) where f(x) = x+7 and g(x) = 1/(x-13)

Domain of a function is defined as all those values of x that can be substituted in function for which function is defined.

Given: f(x) = x+7

g(x) = 1/(x-13)

First we need to find (f.g)(x) i.e multiplication of  f(x) and g(x)

(f.g)(x) = (x+7) ×1/(x-13) = [tex]\frac{x+7}{x-13}[/tex]

Domain of function is values of x over which function is defined

For (f.g)(x) it is defined at all values of x except when x-13=0 as at this point denominator will be zero and function will become infinite that is not defined.

So,  x - 13 ≠ 0

Adding 13 on both sides, we get

x ≠ 13

So domain of  (f.g)(x) is x∈R - {13} i.e {x | x≠ 13}

Hence, option (c) is correct answer.

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You forgot the question

A graph with three zeros, one of which is at x = 4, will resemble the one below.

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.

Minimum and Maximum?

The extrema of a function are known as its maximum and minimum. The highest and smallest values of a function within the predetermined set of ranges are known as maxima and minima. The largest value of the function under the full range is referred to as the absolute maxima, while the least value is referred to as the absolute minima.

If the function has three zeros with one relative maximum and one relative minimum, it could be a cubic equation.

If it has a factor of x - 4, the graph crosses the x-axis at (4,0).

Your graph might look like the one below.

It has three zeros, one of which is at x = 4, and a local maximum and minimum.

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Answer:

Below

Step-by-step explanation:

2/3 = x-15        Just add 15 to both sides to get

15 2/3  = x  

Answer:

[tex]\frac{39}{15}[/tex] a - [tex]\frac{8}{5}[/tex]

Step-by-step explanation:

Frist combine your like terms

[tex]\frac{7}{3}[/tex] a + [tex]\frac{4}{15}[/tex] a  The common denominator will be 15

[tex]\frac{35}{15}[/tex] a+ [tex]\frac{4}{15}[/tex] a= [tex]\frac{39}{15}[/tex]a

You cannot combine this with [tex]\frac{8}{5}[/tex] because these are not like terms.  

[tex]AC \cong BC \implies \angle A \cong \angle B \\ \\ \therefore m\angle A=m\angle B \implies 3x+18=7x-58 \\ \\ \implies 18=4x-58 \\ \\ 76=4x \\ \\ \boxed{x=19} \\ \\ m\angle A=3(19)+18 \implies \boxed{m\angle A=75^{\circ}} \\ \\ m\angle A=m\angle B \implies \boxed{m\angle B=75^{\circ}} \\ \\ m\angle C=180^{\circ}-m\angle A-m\angle B \implies \boxed{m\angle C=30^{\circ}}[/tex]

Answer:

(8, 0) and (0, 4)

Step-by-step explanation:

x-intercepts occur when y = 0, so just find the row in the table when y is 0, and then put the coordinates from that row into a ordered pair:

(8, 0)

y-intercepts occur when x = 0, so just find the row in the table when x is 0, and then put the coordinates from that row into a ordered pair:

(0, 4)

Value of AB = 9 units by using property of equality according to given equation.

What is  a line?

In pure mathematics, a line is associate infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas. The word line might also see a line section in existence, that has 2 points to denote its ends.

Main body:

Question 12

According to question,

AB +BC = 12

BC= 3

therefore,

AB + 3 = 12

AB = 9   -------( by using property of equality)

Hence value of AB = 9 units.

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By solving linear inequation, it can be calculated that

x < 8 is the solution of the inequality -5x+30 >-10

What is linear inequation?

At first, it is important to know about algebraic expression.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now, algebraic expressions are of different types. They are-

Monomial, Binomial and trinomial.

Algebraic expression with only one term is called monomial

Algebraic expression with two terms are called binomial

Algebraic expressions with three terms are called trinomial.

Algebraic expressions with more than three terms are called polynomial.

Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on

Algebraic expression of degree one is called linear

Algebraic expression of degree two is called quadratic

Algebraic expression of degree one is called cubic

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >,<, ≥, ≤

A one degree inequation is known as linear inequation.

Here the given inequality is-

-5x+30 >-10

Now,

-5x + 30 > -10

-5x > -10 - 30

-5x > -40

x < [tex]\frac{-40}{-5}[/tex]

x < 8

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The probability that a student passes both the tests is 0.5896.

The conditional probability deals with dependent events. In order to evaluate it, Bayes' theorem is applied which can be written as P(B|A) = P(A ∩ B)/P(A), where B|A denotes the event of occurring B when A has already happened and A ∩ B denotes the occurring of both events simultaneously.

The given problem can be solved as follows,

Suppose A be the event a student passes French 101 and B be the event that he passes French 102.

Then, as per the question the probabilities are given as,

P(A) = 0.67,

And, P(B|A) = 0.88.

Suppose, A ∩ B be the event a student passes both tests.

Apply Bayes' theorem to obtain,

P(B|A) = P(A ∩ B)/P(A)

Substitute the corresponding values in the above expression.

0.88 = P(A ∩ B)/0.67

=> P(A ∩ B) = 0.88 × 0.67

=>  P(A ∩ B) = 0.5896

Hence, the probability that a student selected at random will pass both French 101 and French 102 is 0.5896.

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The number whose product of 5 and the difference between a number and 7 is 75 is, 22.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given statement is The product of 5 and the difference

between a number and 7 is 75.

Let, The unknown number be 'n'.

∴ 5(n - 7) = 75.

Now, 5 will move from the numerator to the denominator.

n - 7 = 75/5.

n - 7 = 15.

Now, we'll move the constant to the other side such that the variable and the constants are on different sides for our further calculation.

n = 15 + 7.

n = 22.

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Answer:

Option 2

Step-by-step explanation:

[tex]\begin{bmatrix} 3+6 & 9+0 \\ 5-8 & -2+4 \end{bmatrix}=\begin{bmatrix} 9 & 9 \\ -3 & 2 \end{bmatrix}[/tex]

Answer:

  (b)

Step-by-step explanation:

You want the sum of the given matrices.

The sum of two matrices is the matrix of the sums of corresponding terms.

Here, we observe that we can choose the correct answer by finding the bottom right term. The sum of bottom right terms is  -2+4 = 2. The only answer choice with that value at bottom right is the second answer choice.

__

Additional comment

You need to know how to work the problem, but you don't actually need to work the whole problem in order to make the correct answer choice. (This is often the case with multiple choice questions, so it pays to look before you leap.)

The percentage of occupancy for the month of December is 86.5%.

What is percentage?

Percentage is a fundamental concept in mathematics that describes a portion or proportion of a whole number. It is expressed as a fraction or ratio of two numbers and is typically represented with a percent symbol (%). This concept is frequently used in business, finance, and other fields to compare and analyze data. For example, a company might use a percentage to track the success of a marketing campaign or to compare the amount of sales between two different stores. Percentage can also be used to calculate discounts, taxes, and other types of fees.

Given: Community Hospital December, 20XX

PCU Inpatient Service Days Bed Count Percentage of Occupancy

⇒ Med/Surg 1876, 70 = (1,876 x 100)/ (70 x 31)

= 187,600/ 2,170 = 86.45 = 86.5%

⇒ ICU 300, 10 (300 x 100)/ (10 x 31)

= 30,000/ 310 = 96.77 = 96.8%

⇒ CCU 240, 8 (240 x 100)/ (8 x 31)

= 24,000/ 248 = 96.77 = 96.8%

⇒ Rehabilitation 300, 12 (300 x 100)/ (12 x 31)

= 30,000/372 = 80.6%

⇒ Burn 75, 5 (75 x 100)/ (5 x 31)

= 7,500/ 155 = 48.38 = 48.4%

⇒ Psychiatry 200, 15 (200 x 100)/(15 x 31)

= 20,000/465 = 43.0%

⇒ Pediatric 870, 30 (870 x 100)/ (30 x 31)

= 87,000/ 930 = 93.5%

⇒ Total for patient care 3861, 150 (3,861 x 100)/ (150 x 31)

= 386,100/ 4,650 = 83.0%

⇒ Nursery 280, 10 (280 x 100)/ (910 x 31)

= 28,000/ 310 = 90.3%

For example, Med/Surg has 1,876 inpatient service days and 70 beds in the month of December (31 days). The percentage of occupancy is therefore the inpatient service days multiplied by 100 and divided by the product of the number of beds (70) and the number of days (31) to get 86.5%

⇒ (1,876 x 100)/ (70 x 31)

= 187,600/ 2,170 = 86.45 = 86.5%

Hence, the percentage is 86.5%.

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