Carrie is told that a tree is 17 meters high. If the angle from where she is standing to the top of the tree is 53 degrees, how far from the tree is she standing?

The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To solve the equation 3/5x - 4 - 3√7x + 8 = 0:

First, simplify the expression by combining like terms:

3/5x - 3√7x + 4 = 0 + 8

3/5x - 3√7x + 4 = 8

Next, move the constant term to the right side:

3/5x - 3√7x = 8 - 4

3/5x - 3√7x = 4

Factor out x from the left side:

x(3/5 - 3√7) = 4

Divide both sides by (3/5 - 3√7):

x = 4 / (3/5 - 3√7)

To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):

x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]

x = 12/5 + 12√7/5 / (9/25 - 63/25)

x = 12/5 + 12√7/5 / (-54/25)

x = -10√7/9

Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

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Answer: Increase in percentage by 42% and with baggage 43.2%.

Step-by-step explanation:

we know that the price is increased from $250 to $ 335

the percentage change by increasing the price is

$355 - $ 250 = $105

percentage change will be change/original = 105/250*100 = 42%

additional charges $ 50, $105+ $50 = 155

percentage change = 155/355*100 = 43.2%

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Answer:

The Correct answer is Carter

The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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Mohal will be able to paint 9 bookcases for the amount of paint.

An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.

Given that, he has 1 1 /8​ gallons of paint.

Thus, number of bookcases are:

1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9

Hence, Mohal will be able to paint 9 bookcases for the amount of paint.

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The missing step in the proof is: D. ADCA

In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).

Therefore, we have the following proportional sides:

DC/AC = AC/BC

Given that DC = BA (given statement), we can substitute BA for DC in the proportion:

BA/AC = AC/BC

Now, we can cross-multiply to get:

BA * BC = AC²

Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:

BA * BC = AC * AC

Use the definition of congruent sides to replace BA with DC:

DC * BC = AC * AC

And finally, use the substitution property of equality to replace BC with 6 units (given statement):

DC * 6 = AC * AC

From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.

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Answer:

D

Step-by-step explanation:

Answer:

D. [tex]8a^{9} -4a^{3} +1[/tex]

Step-by-step explanation:

Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :

Solve for [tex]r(2a^{3} )[/tex] :

1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]

2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]

3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

Answer:

So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].

Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]

The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.

This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.

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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).

Which statement best explains whether the student's answer is correct or incorrect?

OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).

C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).

OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).

100 people = 360° of circle

For n people, the degree for the circle is (n×360)÷100

30 people = (30×360)÷100 = 108°

15 people = 54°

12 people = 43.2° ≅ 43°

14 people = 50.4° ≅ 50°

29 people = 104.4° ≅ 104°

Area of composite shape = 12 + 9

                                         = 21 cm²    

Area of composite shapes:

13) Figure 1:

        Figure1 is a rectangle.

        l = 4 cm & w = 2 cm

Area of figure1 = l * w

                        = 4 * 2

                        = 8 cm²

Figure2:

             Figure2 is a parallelogram

              base = b = 4 cm

                 h = 4 cm

  Area of figure2 = b * h

                            = 4 * 4

                           = 16 cm²

Area of composite shape = 8 + 16

                                         = 24 cm²

14) Figure1:

      Figure 1 is a trapezium. a & b are parallel sides and h is the height

      a = 4 cm ; b = 6 cm; h = 4 -2 = 2 cm

Figure2:

  Figure2 is a rectangle. l = 6 cm ; w = 2 cm

 Area of figure2 = 6*2

                            = 12 cm²

Area of composite shape = 10 + 12

                                         = 22 cm²

15) Figure 1 & figure 2:

          Figure 1 and  figure 2 are congruent triangles

            base = b = 3 cm & h= 4 cm

= b *h

= 3 * 4

= 12 cm²

Figure3:

   Figure 3 is a square.

     side =  3 cm

 Area of figure3 = side *side

                            = 3 * 3

                           = 9 cm²

Area of composite shape = 12 + 9

                                         = 21 cm²                      

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The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.

To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.

A. 5n = 5(4) = 20

B. n + 30 = 4 + 30 = 34

C. 50 - n = 50 - 4 = 46

D. 80 ÷ n = 80 ÷ 4 = 20

The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n

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The total net amount the supermarket owes the wholesaler for the order is $231.31.

A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.

To find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.

The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:

Discounted cost = List price - (Discount rate x List price)

For the soup, the discounted cost per case is:

$18.90 - (0.39 x $18.90) = $11.51

For the baked beans, the discounted cost per case is:

$33.50 - (0.39 x $33.50) = $20.42

Now we can calculate the total net amount owed by the supermarket to the wholesaler:

Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)

Total net amount = (13 x $11.51) + (4 x $20.42)

Total net amount = $149.63 + $81.68

Total net amount = $231.31

Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.

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5. The real zero occurs located

6. The x-coordinate at which a relative minimum occurs is at

In the context of a graph of a function

A real zero, also known as a root or a solution, is a value of the independent variable (usually denoted as x) for which the value of the dependent variable (usually denoted as y) is equal to zero.

Geometrically, a real zero corresponds to the x-coordinate of a point where the graph of the function intersects the x-axis.

A relative minimum, on the other hand, is a point on the graph where the function has a local minimum value.

Geometrically, a relative minimum corresponds to a point where the graph changes from decreasing to increasing, and is located at the bottom of a valley or a trough.

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Answer:

84 paid with three 50p coins.

Answer:

mean: 20mins

Step-by-step explanation:

add them all together to get 240

then divide by how many there are

240÷12=20

so the mean is 20mins

Answer: length = 20 feet and width = 5 feet

Step-by-step explanation: Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.

Nick's monthly mortgage payment is $482.16.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:

$145,500 x 0.75 = $109,125

Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:

3.15% / 12 = 0.002625

Now we can use the following formula to calculate Nick's monthly payment:

M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]

Where:

M = Monthly payment

P = Loan amount (principal)

i = Monthly interest rate

n = Number of payments (in months)

Plugging in the values we have:

M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]

M = $482.16

Therefore, Nick's monthly mortgage payment is $482.16.

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The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to gather data from a sample or population and to draw conclusions or make predictions based on that data.

There are two main branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics is the process of summarizing and presenting data in a meaningful way, such as by calculating measures of central tendency (e.g. mean, median, mode), variability (e.g. range, variance, standard deviation), and correlation. Inferential statistics involves using probability theory to make inferences about a larger population based on a sample of data.

Statistics is used in a wide variety of fields, including business, economics, psychology, social sciences, medicine, and engineering. It is often used to test hypotheses, identify trends, and make predictions based on data. The field of statistics has evolved over time, with the development of new techniques and technologies for collecting and analyzing data.

The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying. Surveying a larger group of fifth grade students or every teacher at the school would not be as effective since it would include girls and boys who are not in the fifth grade, and teachers who may not have as much knowledge about the specific video game preferences of fifth grade boys. Surveying every boy who will pass to fifth grade next year would also not be as effective since they are not currently in the fifth grade and their preferences may change by the time they reach that grade. Therefore, surveying the 25 fifth grade boys would provide the most relevant and accurate data for Ryan's study.

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The complete question is:

Ryan wants to find the favorite video game of the fifth grade boys at his school. Which group would be BEST for Ryan to survey? 25 fifth grade boys 25 fifth grade students every teacher at his school every boy who will pass to fifth grade next year

Answer:

To solve this problem, we need to integrate the derivative f'(x) to obtain the function f(x).

∫f'(x) dx = ∫(4x - 3) dx

f(x) = 2x^2 - 3x + C

where C is the constant of integration.

To find the value of C, we need to use the fact that f(0) = 5. Substituting x = 0 into the above equation, we get:

f(0) = 2(0)^2 - 3(0) + C = C

Therefore, C = 5.

Hence, the function f(x) is:

f(x) = 2x^2 - 3x + 5

Now, we can find f(5) and f(-1) and compute their difference:

f(5) - f(-1) = (2(5)^2 - 3(5) + 5) - (2(-1)^2 - 3(-1) + 5)

f(5) - f(-1) = (50 - 15 + 5) - (2 + 3 + 5)

f(5) - f(-1) = 35 - 10

f(5) - f(-1) = 25

Therefore, f(5) - f(-1) = 25.

By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.

A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).

To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.

With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:

slope = (y change) / (change in x)

slope = (16 - (-8)) / (9 - (-3))

slope = 24 / 12

slope = 2

We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:

y = mx + b 0 + b b = 2(1) + b b = -2

Hence the linear function's slope-intercept equation is:

y = 2x - 2

As a result, the linear function denoted by the table is y = 2x - 2.

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Answer:

(3x + y)(2x + 3)

Step-by-step explanation:

6x² = 2 * 3 * x * x

2xy = 2*x * y

Common factor = 2x.

        9x = 3 * 3 * x

        3y = 3 * y

Common factor = 3

Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.

6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)

                              = (3x + y)(2x + 3)

Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).

Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.

90 students are in a club and play a sport.

140 total students play a sport.

Therefore, 140 - 90 = 50 students play a sport but are not in a club.

The total number of students who play a sport is 140 + 50 = 190.

200 total students are in a club.

Therefore, 200 - 90 = 110 students are in a club but do not play a sport.

The total number of students who do not play a sport is 325 - 190 = 135.

The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.

This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.

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When two sample means are significantly different, "the difference is too great to attribute to chance".

The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).

Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.

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All options except "How high you hit the ball" would affect the ball's height and distance.

The following factors would make a difference in the height and distance that the ball goes when an athlete hits a ball:

Therefore, all options except "How high you hit the ball" would affect the ball's height and distance.

When an athlete hits a ball, there are several factors that can affect the ball's trajectory, including the force and angle of the swing, as well as external environmental factors such as wind, temperature, and humidity.

The harder the athlete hits the ball, the more force will be imparted to the ball, and the farther it will travel.

Similarly, the angle of the swing can affect the trajectory of the ball, with a higher or lower angle resulting in different heights and distances traveled.

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Answer: What is the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic?

Let's call the number of pulled-pork sandwiches "P" and the number of barbeque chicken sandwiches "C". According to the problem, the organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches. This means that:

P/C = 2/5

To simplify this ratio, we can multiply both sides by a common factor that will make the denominators the same. In this case, the smallest common multiple of 2 and 5 is 10, so we can multiply both sides by 10:

10(P/C) = 10(2/5)

Simplifying this expression, we get:

2P = 4C

Dividing both sides by 2, we get:

P/C = 2/4

Simplifying this fraction, we get:

P/C = 1/2

Therefore, the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic is 1:2.

Step-by-step explanation:

Mohal will be able to paint 9 bookcases for the amount of paint.

An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.

Given that, he has 1 1 /8​ gallons of paint.

Thus, number of bookcases are:

1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9

Hence, Mohal will be able to paint 9 bookcases for the amount of paint.

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The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3

What is an absolute value equation?

An absolute value equation can be written as |expression| = value

To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.

We can write,

|x + 5| = 3

To solve for x, we have two cases,

Case 1: x + 5 is positive

If x + 5 is positive, then the equation becomes x + 5 = 3

Solving for x,

x = -2

This matches one of the solutions we want.

Case 2: x + 5 is negative

If x + 5 is negative, then the equation becomes -(x + 5) = 3

Solving for x,

x = -8

This also matches the other solution we want.

Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.

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Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:

300 + 40x = 9300 - 50x

Simplifying and solving for x:

90x = 9000

x = 100

Now that we know x, we can use either equation to find y:

y = 300 + 40(100) = 4300

So the equilibrium point is when x = 100 and y = 4300.

Step-by-step explanation: