EXER 1. Evaluate the following (a) 28-{15 (3+2)​

Answer: [tex]x\approx 6.2[/tex]

Step-by-step explanation:

Detailed explanation is attached below.

Answer:

We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1

Now we can substitute this value into the original equation and simplify:

y = -3 + tan(1/2 (0 + π/2))

y = -3 + 1

y = -2

The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down

The horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.

To answer the question, we need to use trigonometry. In this case, we can use the sine function, which relates the opposite side of a right triangle to its hypotenuse. In this case, the ladder is the hypotenuse, and the horizontal distance between the base of the ladder and the wall is the opposite side.

The angle formed by the ladder and the ground is the angle of interest.

Let x be the horizontal distance between the base of the ladder and the wall. Then, using the sine function, we have:

sin(64 degrees) = x/18

Multiplying both sides by 18, we get:

x = 18 sin(64 degrees) ≈ 16.2 feet

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.

It is important to note that when using trigonometry, we need to use the appropriate trigonometric function depending on the sides and angles we are given. In this case, we were given the hypotenuse and the angle opposite the horizontal distance, so we used the sine function.

For more such questions on horizontal

https://brainly.com/question/30197734

#SPJ8

The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is  [tex]f(x) = x^3 - 76x + 210.[/tex]

To write a polynomial function in factored form with the given roots, we can use the factored form equation:

f(x) = (x - r1)(x - r2)(x - r3)...

Where r1, r2, r3 represent the roots of the polynomial.

Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:

f(x) = (x - 7)(x + 10)(x - 3)

Expanding this equation will give us the polynomial function in factored form:

[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]

[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]

[tex]= (x^2 + 3x - 70)(x - 3)[/tex]

[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]

[tex]= x^3 - 76x + 210[/tex]

For similar question on polynomial function.

https://brainly.com/question/7693326  

#SPJ8

The interval representing the range of the graphed function in this problem is given as follows:

a) (0, ∞).

From the image of the problem, the output y of the function is composed by the positive values, hence the interval representing the range is given as follows:

(0, ∞).

More can be learned about domain and range at https://brainly.com/question/26098895

#SPJ1

The angle that has been formed and is shown as x is shown as 52.1°.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The tangent function is denoted as tan.

We can see that we need to find the tangent of the angle;

Tan x = 36/28

x = Tan-1(36/28)

x = 52.1°

Thus it is clear from the calculation that we have done above that the angle that is marked x is 52.1°.

Learn more about angle :https://brainly.com/question/31818999

#SPJ1

The calculated value of the conditional probability P(Not A | Not B) is 0.8125

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

The table of values

The probability P(Not A | Not B ) is calculated as

P(Not A | Not B ) = (Not A and Not B)/(Not B)

Using the above as a guide, we have the following:

(Not A and Not B) = 0.65

(Not B) = 0.80

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

P(Not A | Not B ) = 0.65/0.80

Evaluate

P(Not A | Not B) = 0.8125

Hence, the probability P(Not A | Not B) is 0.8125

Read more about probability at

https://brainly.com/question/31649379

#SPJ1

Step-by-step explanation:

One rectangle  10 x 6 = 60 cm^2

Two sqaures     2 *    4x4 =  32 cm^2      Total = 92 cm^2

The scatter plot that accurately describes the data is given as follows:

Scatter plot A.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

The input and output variables for this problem are given as follows:

Hence the points are given as follows:

(13, 23), (17, 17), (21, 17), ..., (70,30).

And all these points are marked on the scatter plot given by option A.

More can be learned about scatter plots at brainly.com/question/6592115

#SPJ1

Answer:

Question 3:    5

Question 4:    91

Step-by-step explanation:

[tex](x+5)2-y[/tex]

[tex]x = -2[/tex]

[tex]y =1[/tex]

[tex](-2 + 5)2 - 1[/tex]

[tex](3)2-1[/tex]

[tex]6-1 = 5[/tex]

[tex]3x +4y^2[/tex]

[tex]x = -3[/tex]

[tex]y=5[/tex]

[tex]3(-3)+4(5)^2[/tex]

[tex]-9 + 100[/tex]

[tex]=91[/tex]

The transformations to the parent function are given as follows:

The parent function for this problem is given as follows:

y = 1/x.

The transformed function for this problem is given as follows:

y = 3/(x + 5) - 3.

Hence the  transformations to the parent function are given as follows:

More can be learned about transformations at https://brainly.com/question/28687396

#SPJ1

The portion of scores that are between 59 and 91 is 98%.

The portion of exam scores that are less than 67 is 16%.

The portion of exam scores that are between 67 and 91 is 82%.

A normal distribution curve is a type of probability distribution that is commonly used in statistics to represent a large set of data. It is also known as a bell curve. The curve is bell-shaped, symmetrical, and smooth.

Comparing the exam score diagram in the question, to a standard normal distribution curve, we will have the following;

The portion of scores that are between 59 and 91 is;

= 100% - (59 to 43 portion)

= 100% - 2%

= 98%

The portion of exam scores that are less than 67 is;

= (67 to 59) + (59 to 43)

= 14% + 2%

= 16%

The portion of exam scores that are between 67 and 91 is ;

= (67 to 75) + (75 to 83) + (83 to 91)

= 34% + 34% + 14%

= 82%

Learn more about normal distribution here: https://brainly.com/question/4079902

#SPJ1

Answer:

Angles 1 and 8 are alternate exterior angles.

Answer: 2916 cubic feet

Step-by-step explanation:

V=(4/3)*3*(9^3)

V=(4/3)*3*729

V=2916

The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

Read more about Two way frequency table at: https://brainly.com/question/16148316

#SPJ1

The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

Read more about Two way frequency table at: https://brainly.com/question/16148316

#SPJ1

The mode of the data is 0

Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.

It provides an accurate description of the entire data.

The three major measures of central tendency are given as;

The mode is defined as the measure of central tendency representing the most occurring number in a given data set

From the information given, we have;

0, 4 , 3, 4, 0, 9, 1

Then, the mode is 0

Learn more about mode at: https://brainly.com/question/14532771

#SPJ1

The straight-line distance from your starting point at the end of driving is approximately 24.4 miles.

To find the straight-line distance from your starting point, we can use the Pythagorean states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance you drove west and turned left forms two sides of a right triangle, and the straight-line distance from the starting point will be the hypotenuse.

Given:

Distance driven west = 20 miles

Distance driven south = 14 miles

Using the Pythagorean:

Hypotenuse² = (Distance driven west)² + (Distance driven south)²

Hypotenuse² = 20² + 14²

Hypotenuse² = 400 + 196

Hypotenuse² = 596

To find the length of the hypotenuse (straight-line distance), we take the square root of both sides:

Hypotenuse = √596

Hypotenuse ≈ 24.4 miles (rounded to the nearest tenth)

For similar questions on straight-line distance

https://brainly.com/question/18222624
#SPJ8

Answer:

Use systems of equations to solve.

Let x represent the cost per pound of the espresso coffee beans and

y represent the cost per pound of the vanilla coffee beans.

6x + 5y = 77.50

20x + 13y = 234.50, both of these are given.

Rewrite these equations so you can eliminate one of the variables;

60x + 50y = 775, Multiply both sides of the equation by 10

60x + 39y = 703.5, Multiply both sides of the equation by 3

Now Subtract equation 2 from equation 1,

11y = 71.5

y = 6.5

Solve for x,

6x + 5(6.50)= 77.50

x = 7.50

Therefore, the cost per pound of the espresso coffee beans is $7.50, and

the cost per pound of the vanilla coffee beans is $6.50.

Answer: 2^(4/5)=16

Step-by-step explanation:

log a (b)=c

this converts to:

a^c=b

so...

2^(4/5)=16

The probability of getting Two Tails is 0.1 or 10%.

Let's assume that '2. Tails' appeared x times.

According to the given information, 'No Tail' appeared 3x times, and '1 Tail' appeared 2 × 3x = 6x times.

The total number of tosses is 360. We can express this information in an equation:

x + 3x + 6x = 360

Simplifying the equation:

10x = 360

x = 36

Now we know that '2. Tails' appeared 36 times, 'No Tail' appeared 3x = 3 × 36 = 108 times, and '1 Tail' appeared 6x = 6 × 36 = 216 times.

To find the probability of getting Two Tails, we divide the number of times '2. Tails' appeared by the total number of tosses:

Probability of Two Tails = Number of times '2. Tails' appeared / Total number of tosses

= 36 / 360

= 0.1

Therefore, the probability of getting Two Tails is 0.1 or 10%.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth.

For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

Received message. For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth. For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

hopes thats help thank you

Answer:

Sin θ = 3/5 cos θ = 4/5 tan θ= 3/4

Answer:

The answer is number 2

The statement which is true is he has enough of each type of juice to make 1 recipe, the correct option is B.

We are given that;

Orange juice cup= 6

Pineapple juice cup=3

Now,

PART A: To answer this question, we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Felicia has pineapple juice in fluid ounces. We can use the fact that 1 cup = 8 fluid ounces to convert Felicia’s amount of pineapple juice to cups:

32 fluid ounces = 32 / 8 cups = 4 cups

The recipe requires 3 cups of pineapple juice, so Felicia has more than enough pineapple juice. The correct answer is B.

PART B: we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Jared has each type of juice in pints. We can use the fact that 1 pint = 2 cups to convert Jared’s amounts of juice to cups:

8 pints = 8 * 2 cups = 16 cups

Jared has 16 cups of each type of juice. The recipe requires 6 cups of orange juice, 3 cups of pineapple juice, and 1 cup of cranberry juice. This adds up to 10 cups of juice for one recipe. So, Jared has enough of each type of juice to make one recipe and have some left over. However, he does not have enough of each type of juice to make two recipes, since that would require 20 cups of juice in total. T

Therefore, by unitary method the answer will be He has enough of each type of juice to make 1 recipe.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ1

Answer:

[tex]\huge\boxed{\sf 0.00008\ km}[/tex]

Step-by-step explanation:

= 8 cm

= 8 / 100,000 km

[tex]\rule[225]{225}{2}[/tex]

Answer:

0.00008

80 cm is 0.0008 so you know I just assumed

the solution to the equation log2x + log4x + log16 = 7  the logarithms using the properties of Logarithms is x ≈ 53.408.

To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.

First, we can use the property loga + logb = log(ab) to combine the logarithms:

log2x + log4x + log16 = log(2x * 4x * 16)

Next, we simplify the expression inside the logarithm:

log(2x * 4x * 16) = log(32x^3)

Now, our equation becomes:

log(32x^3) = 7

To eliminate the logarithm, we can rewrite the equation in exponential form:

32x^3 = 10^7

Simplifying further:

32x^3 = 10,000,000

Now, we can solve for x by dividing both sides of the equation by 32:

x^3 = 10,000,000 / 32

x^3 = 312,500

To find the value of x, we take the cube root of both sides:

x = ∛312,500

x ≈ 53.408

Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.

To know more about Logarithms .

https://brainly.com/question/29779861

#SPJ8

Answer:

The Answer is 80√3 or 138.56 to 2d.p

Step-by-step explanation:

sin 60=L/8

L=sin60×8

L=4√3

Area of rectangle =L×W

A=20×4√3

A=80√3=138.56 to 2d.p