4. Find the value of x. Please show your All your work!
120°
172°
X
X =
95
125
I
120°
work:

If Mary needs to have $9,000 in 9 years at 4% interest compounded quarterly, she should deposit $208.93 in a sinking fund at the end of each quarter.

Compound interest refers to the system that charges interest on both the accumulated interest and the principal at the end of each period.

The compounding period may vary from annual, quarter, and monthly to daily.

N (# of periods) = 36 quarters (9 years x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

FV (Future Value) = $9,000

Results:

Periodic (Quarterly) Deposit (PMT) = $208.93

The sum of all periodic payments = $7,521.44

Total Interest = $1,478.56

Thus, Mary needs to deposit $208.93 each quarter.

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Based on the given graph, the following describes the polynomial function.

The function has an odd degree. (Option B)

The function has one turning point. (Option C)

The function does not have a negative leading coefficient since its leading coefficient is positive. It also has x-intercepts at x=-6, x=-2, x=4, and x=6, so the statement "the function has zero x-intercepts" is incorrect.

A polynomial function is a mathematical function that consists of one or more terms, where each term is a constant, a variable, or a product of a constant and a variable raised to a non-negative integer power.

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[tex]\sin(X )=\cfrac{\stackrel{opposite}{36}}{\underset{hypotenuse}{45}}\implies \sin(X )=\cfrac{4}{5} \\\\\\ \cos(X )=\cfrac{\stackrel{adjacent}{27}}{\underset{hypotenuse}{45}}\implies \cos(X)=\cfrac{3}{5} \\\\\\ \tan(X )=\cfrac{\stackrel{opposite}{36}}{\underset{adjacent}{27}}\implies \tan(X)=\cfrac{4}{3}[/tex]

The results of the experiment might support the hypothesis, or might not.

The correct statement is that the results of the experiment might support the hypothesis, or might not. It is important to design a well-controlled experiment that tests the hypothesis in a rigorous and systematic way. The goal is not to prove the hypothesis correct, but rather to gather evidence that either supports or contradicts the hypothesis. It is also important to conduct the experiment in a suitable environment with appropriate equipment and procedures to ensure accurate and reliable results.
Your question focuses on understanding the relationship between a hypothesis, an experiment, and the possible outcomes.
An experiment is designed to test a hypothesis, which is an educated guess or prediction about a phenomenon. When conducting an experiment, the results might either support the hypothesis or contradict it, leading to further investigation and refinement of the hypothesis. A well-designed experiment should be able to provide valuable data and insights, regardless of the outcome.

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The statement that is true is:

"The results of the experiment might support the hypothesis or might not."

A scientist designs an experiment to test a hypothesis.

In such a scenario, it is important to note that the outcome of the experiment cannot be predicted with certainty.

The scientific method involves formulating a hypothesis, designing an experiment to test the hypothesis,

collecting and analyzing data and drawing conclusions.

The hypothesis is an educated guess that can be tested through experimentation.

It is important to remember that a hypothesis can never be proven to be 100% correct, only supported or refuted by the evidence obtained through experimentation.
It is not accurate to say that if the experimenter does the test correctly, the hypothesis will be proven correct.

This is because there are many variables that can affect the outcome of the experiment, and it is impossible to control all of them.

Additionally, a good experiment is not necessarily one that produces the most data.

A good experiment is one that is well-designed, carefully controlled, and yields reliable results.

The use of lab equipment is also not a requirement for conducting experiments.

While it is often necessary for certain types of experiments, many experiments can be conducted with simple materials and equipment.
Ultimately, the results of the experiment might support the hypothesis, or might not. If the results support the hypothesis, it can be considered a step towards validating the hypothesis.

The results do not support the hypothesis, it does not necessarily mean that the hypothesis is incorrect.

It could mean that the experiment was flawed, or that the hypothesis needs to be revised based on the new information obtained from the experiment.
Designing and conducting experiments is an important part of the scientific method.

Guarantee that an experiment will yield the desired results, a well-designed and carefully controlled experiment can provide valuable information that can help scientists understand the natural world.

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According to unitary method, there are 10 30¢ cards and 8 35¢ cards in the box, which adds up to a total of $5.80.

Let's start by defining our units. In this case, our units are the number of 30¢ cards and the number of 35¢ cards. We know that the box of cards is being sold for $5.80, which means the total value of all the cards in the box is $5.80. We can use this information to set up an equation:

0.30x + 0.35y = 5.80

where x is the number of 30¢ cards and y is the number of 35¢ cards.

Next, we are given the information that the number of 30¢ cards is six more than one half the number of 35¢ cards. Using the unitary method, we can set up an equation that relates the number of 30¢ cards to the number of 35¢ cards:

x = 0.5y + 6

Now we can use this equation to eliminate x from our first equation:

0.30(0.5y + 6) + 0.35y = 5.80

Simplifying this equation gives:

0.15y + 1.80 + 0.35y = 5.80

0.50y = 4.00

y = 8

So there are 8 35¢ cards in the box. We can use the unitary method again to find the number of 30¢ cards:

x = 0.5y + 6

x = 0.5(8) + 6

x = 10

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The volume of the sink basin is approximately 7430.9 cubic inches.

What is hemisphere?

A hemisphere is a three-dimensional geometric shape that is obtained by slicing a sphere into two halves along a plane passing through its center. A hemisphere is a half-sphere, meaning that it has one curved surface that is shaped like a circle and has a constant radius, and a flat circular base.

The volume of a hemisphere with radius "r" is given by the formula:

(2/3) x π x r³.

In this case, the radius of the sink basin is 15 1/4 inches, which is equivalent to 61/4 inches. Therefore, we can calculate the volume of the sink as follows:

Volume = (2/3) x (22/7) x (61/4)^3

= 2/3 x 22/7 x 3546.58

=  7430.9 cubic inches (rounded to the nearest tenth)

Therefore, the volume of the sink basin is approximately 7430.9 cubic inches.

Complete question : Nabhitha measure the volume of a sink basin by modeling it as a hemisphere. Nabhitha measures its radius to be 15 1/4. find sink's volume in cubic inches. round your answer to the nearest tenth.

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The ratio of the areas of the similar kites with the given corresponding diagonals is calculated as: 1/49.

The ratio of the areas of similar polygons are the square of their corresponding sides that are proportional to each other.

Thus, let the kites have diagonals d1 and d2, with d1/d2 = 1/7. Since the kites are similar, their corresponding sides are also proportional.

Therefore, the ratio of their areas = square of d1 / square of d2

ratio = 1² / 7²

= 1/49

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Complete Question?

The ratio of the lengths of corresponding diagonals of two similar kites is 1/7. What is the ratio of their areas?

The constant of proportionality is $8.40

The constant of proportionality is a value that relates two quantities that are proportional to each other. It is represented by the letter k and is found by dividing the dependent variable by the independent variable. In this case, the constant of proportionality is $8.40 for the given data set.

According to the given information:

To find the constant of proportionality, we can use any two data points from the table and plug them into the equation y = kx.

Let's use the first and second data points: (0.75, $6.30) and (2.5, $21.00).

We can set up the equation as:

$6.30 = k(0.75)

Solving for k, we get:

k = $6.30/0.75 = $8.40

Now, we can check our work by using another data point. Let's use the third data point: (4, $33.60).

Plugging in the values, we get:

$33.60 = k(4)

k = $33.60/4 = $8.40

Since we get the same value for k, we can be confident that our answer is correct.

Therefore, the constant of proportionality is $8.40.

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Answer:

22√5

Step-by-step explanation:

√20=√4x5 = √4 x √5 = 2√5

√45 = √9 x 5 = √9 x √5 = 3√5

√80 = √16 x 5 = √16 x √5 = 4√5

4√20 = 6 √45 - √80 = 4(2√5) + 6(3√5)- 4√5

8√5 + 18√5 - 4√5 = 22√5

So its 22√5

Answer:

[tex]22 \sqrt{5} [/tex]

Step-by-step explanation:

the explaination is avaliable in the picture i sent you

and please give me branliest

The surface area of the composite solid is 162 unit²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The composite solid has 6 faces . The area of each face is calculated as follows;

Face 1

area = 5×7 = 35 units²

face 2

area = 1/2bh + l×b

= 1/2 ×3×4 + 3×4

= 6+12 = 18units²

face 3 = face 2

area = 18units²

face 4

area = 3× 7 = 21units²

face 5

area = 4×7

= 28units²

face 6

area = 3×7 + 3×7

= 21+21 = 42units²

Therefore total surface area = 42+28+21+18+18+35

= 162 units²

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There have been numerous cases of athletes being accused of using performance-enhancing drugs, and the numbers may vary depending on the sport, country, and time period in question.

Additionally, determining how many athletes were using or not using performance-enhancing drugs would require specific information on individual cases.

Regarding the percentage of athletes falsely accused of using performance-enhancing drugs, it is difficult to determine an accurate figure without examining each case in detail. False accusations may occur due to various reasons, such as flawed testing procedures or contaminated supplements, and the percentage of false accusations may vary depending on the situation.

If you have a specific case or sport in mind, I can try to provide you with more information on that topic.

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Formula:

98% Confidence Interval = (Mean - (2*Standard Deviation/√n), Mean + (2*Standard Deviation/√n))

98% Confidence Interval = ($775 - (2*$110/√45), $775 + (2*$110/√45))

98% Confidence Interval = ($735.56, $814.44)

The time required to have number of bacteria to be 100,000 is equal to 15.96 hours.

Let us consider,

N = final number of bacteria

   = 100,000 bacteria

N₀ = initial number of bacteria

    = 2500 bacteria

t = time elapsed

T = time it takes for the population to double

   = 3 hours

Use exponential growth formula to solve this problem,

N = N₀ × 2^(t/T)

Substitute the values in the formula,

⇒ 100,000 = 2500 × 2^(t/3)

Simplify this equation by dividing both sides by 2500,

⇒ 100,000/2500 = 2^(t/3)

⇒ 40 = 2^(t/3)

To solve for t, we can take the logarithm of both sides of the equation,

⇒ log40 = (t/3) log 2

⇒ t/3 = log 40 /log 2

⇒t = 3 × ( log 40 /log 2)

Using a calculator, we can evaluate this expression to get,

t ≈ 15.96 hours

Therefore, it will take approximately 15.96 hours for the number of bacteria to reach 100,000.

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The differential of the function Z is -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ

To find the differential function of Z = e⁻⁴ˣ cos(4πt), we will use the product rule of differentiation. The product rule states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first function.

Let's apply the product rule to our function Z:

First, we differentiate the first function e⁻⁴ˣ with respect to x. The derivative of e⁻⁴ˣ is -4e⁻⁴ˣ.

Next, we differentiate the second function cos(4πt) with respect to t. The derivative of cos(4πt) is -4πsin(4πt).

Therefore, the differential function of Z is:

dZ/dt = -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ

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The area of the trapezoid is 72 square meters.

In order to find the area of a trapezoid, we need to use the formula:

Area = (b1 + b2) x h / 2

where b1 and b2 are the lengths of the parallel sides, and h is the height of the trapezoid.

In this case, we are given the lengths of the parallel sides as 6m and 12m respectively, and the height of the trapezoid is 4m.

So, we can plug these values into the formula to get:

Area = (6m + 12m) x 4m / 2

Area = 18m x 4m Area = 72m²

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Complete Question:

Find the area of the trapezoid.

Base 1 = 6 m

Height = 4 m

Base 2 = 12 m

Rounding to the nearest tenth, the circumference of the circle is 69.1 cm.

Diameter is a term used to describe the measurement of a straight line passing through the center of a circle or sphere and connecting two points on its circumference. It is the longest chord that can be drawn in a circle, passing through the center and splitting the circle into two equal halves.

In other words, the diameter is the distance across the circle or sphere, passing through its center, and it is twice the length of the radius. The diameter is a fundamental measurement in geometry and is used to determine other important properties of circles and spheres such as their circumference, area, volume, and surface area.

Diameter is commonly denoted by the symbol "d" and can be calculated using the formula:

d = 2r

where "r" is the radius of the circle or sphere. The diameter can also be found using the Pythagorean theorem, where the diameter is the hypotenuse of a right triangle with sides equal to the radius.

Understanding the concept of diameter is important in many fields, including mathematics, engineering, and science, and is useful for solving problems related to circular and spherical objects.

The formula for the circumference of a circle is C = πd, where d is the diameter.

Given that the diameter is 22 cm, we can plug this into the formula:

C = πd

C = 3.14 × 22

C = 69.08

Rounding to the nearest tenth, the circumference of the circle is 69.1 cm.

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The perimeter of the rectangle P'Q'R'S' is 64

If we let k be the dilation factor, then for any point (x, y) in PQRS and its corresponding point (x', y') in P'Q'R'S', we have:

k = distance from (0, 0) to (x', y') / distance from (0, 0) to (x, y)

To find the dilation factor, we can use the given points P and P':

k = distance from (0, 0) to (8, 2) / distance from (0, 0) to (2, 0.5)

k = √(8^2 + 2^2) / √(2^2 + 0.5^2)

k = √(68) / √(4.25)

k = 4

Given that

The perimeter of PQRS is 16.

So, we have

Perimeter of (PQRS)' = 16 * 4

Evaluate

Perimeter of (PQRS)' = 64

Hence, the perimeter of (PQRS)' is 64

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Answer:

A. the number of tornadoes decreased by 11

Step-by-step explanation:

point A rests on 13, point B rests on 2. therefore 13-2 = 11

according to the question the probabilities of event can be P(s)= 14/2525, P(C) = 6/2525, P(S and C) = 5/2525, P(S or C) = 3/505

Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.

given,

To solve the problem, we can use the formula:

P(A and B) equals P(A) plus P(B) minus P(A or B)

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A or B) is the probability of either A or B occurring (including the case where both A and B occur).

P(S): the probability that a student writes steak is 14/2525.

P(C): the probability that a student writes chicken is 6/2525.

The likelihood that a student would write steak plus chicken equals 5/2525.A or B. P(A and B) Equals P(A) +P(B), which -P(P(S or C))

P(S or C): the probability that a student writes steak or chicken can be calculated as:

P(S or C) = P(S) + P(C) - P(S and C)

= (14/2525) + (6/2525) - (5/2525)

= 15/2525

= 3/505

Therefore, the answers to the questions are:

P(S) = 14/2525

P(C) = 6/2525

P(S and C) = 5/2525

P(S or C) = 3/505

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If the decision variables for a problem have to be integers, rounding the linear programming optimal solution for that problem will always result in a feasible solution.

However, this solution may not always be optimal. It may result in either a feasible or infeasible solution depending on the problem constraints.

Rounding may also result in an optimal solution if the optimal solution happens to already have integer values for the decision variables. Therefore, rounding may result in a feasible and optimal solution or just a feasible solution but not necessarily always optimal.

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The percent of change from 12 to 6 is -50%. This indicates a decrease of 50%.

A measure of the relative difference between two values is the percent of change, also known as percentage change or percent change.

It is frequently used to convey how much a quantity has changed over time, as well as how much it has risen or fallen relative to its starting point.

To find the percent of change between two values, we use the formula:

Percent change = [(New value - Old value) / Old value] x 100%

In this case, the old value is 12 and the new value is 6.

Adding these values to the formula yields the following results:

percent change = [(6 - 12) / 12] x 100%

percent change = (-6 / 12) x 100%

percent change = -0.5 x 100%

percent change = -50%

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The rate at which the gray whale swims is 6.7 kilometers per hour.

What is the equation that relates the distance, rate, and time?

The equation that relates the distance, rate, and time is distance = rate × time

This equation can be used to calculate any one of the three variables if the other two are known.

For example, if you know the rate at which an object is moving and the time it has been moving, you can use this equation to find the distance it has traveled. Or, if you know the distance traveled and the time it took to travel that distance, you can use this equation to find the average rate of travel.

We are given that the distance traveled by the gray whale is 161 kilometers in 24 hours. Therefore, we can use the equation to find the rate at which the gray whale swims,

rate = distance / time = 161 km / 24 h ≈ 6.7 kph

Rounding to the nearest tenth, the rate at which the gray whale swims is approximately 6.7 kilometers per hour.

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Answer:

The area of Jack's rhombus is four times the area of Soshi's rhombus.

Step-by-step explanation:

First, calculate the area of Soshi's rhombus. Use the formula for the area of a rhombus:

[tex]A = bh=\\A=(12)(10)=\\A=120[/tex]

Now, we have the Soshi's rhombus is 120 [tex]in^2[/tex].

Jack's rhombus' base and height are double those of Soshi's; multiply each value by two.

[tex]12*2=24\\\\10*2=20[/tex]

Now, substitute the values in the formula for the area of a rhombus:

[tex]A = bh=\\A=(24)(20)=\\A=480[/tex]

Notice that 480 is 4 times 120.

This is because area is a two-dimensional measure (measured in units squared, like [tex]in^2[/tex]) while length is a one-dimensional measure (measured in regular units, like cm and in), The one-dimensional measures of Jack's rhombus are double those of Soshi's, and to translate this to the two-dimensional measure of area, square 2 (2 squared is 2 times 2).

2 squared is 4, so:

the area of Jack's rhombus is four times that of Soshi's.

Option b is correct.

The null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.

In the chi-square test of hypothesis, the null hypothesis states that the variables under consideration are independent. That is, there is no relationship between the two variables being studied.

The chi-square test is a statistical method used to determine if two categorical variables are associated or independent. Categorical variables are those that take on values that are categories or labels.

For example, gender (male or female) or educational level (high school, college, graduate school) are categorical variables.

The chi-square test determines the expected frequency of each category based on the null hypothesis, which assumes independence between the two variables.

The observed frequency is then compared to the expected frequency, and if the difference is significant enough, it suggests that the null hypothesis should be rejected, and the two variables are considered to be associated or dependent.

Therefore, in summary, the null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.

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Answer:

3/11

Step-by-step explanation:

-5/11-(-8/11)

-5/11+8/11

3/11 will be the answer

Answer:

5/11 from -8/11 is equal to -3/11.

Step-by-step explanation:

To subtract fractions with like denominators, you simply subtract the numerators and keep the denominator the same.

So, to find -5/11 from -8/11, we have:

-8/11 - (-5/11)

= -8/11 + 5/11 (Note: subtracting a negative is the same as adding a positive)

= (-8 + 5)/11

= -3/11

Yes, a triangle can be constructed with sides of 2/3, 4/5, and 1/2. the value of x is 17.

Since a triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

To determine if a triangle can be constructed, we need to check if the sum of the two smaller sides is greater than the largest side.

In this case, we can see that

2/3 + 1/2 > 4/5,

2/3 + 4/5 > 1/2,

1/2 + 4/5 > 2/3,

Therefore, a triangle can be formed.

The value of x can be calculated as;

45 + 68 + 3x + 16 = 180

3x = 51

x = 17

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1. 1001 (in base 2) - 111 (in base 2) = 2 (in base 2).

2. 313 (in base 4) - 123 (in base 4) = 210 (in base 4).

3. 234 (in base 5) - 12 (in base 5) = 222 (in base 5).

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To perform the subtractions in different bases, we need to convert the numbers to the same base and then subtract them.

1. 1001 (in base 2) - 111 (in base 2):

First, we need to align the two numbers by adding leading zeros to the second number:

1001

0111

0010

Therefore, 1001 (in base 2) - 111 (in base 2) = 2 (in base 2).

2. 313 (in base 4) - 123 (in base 4):

Again, we need to align the two numbers by adding leading zeros to the second number:

313

123

210

Therefore, 313 (in base 4) - 123 (in base 4) = 210 (in base 4).

3. 234 (in base 5) - 12 (in base 5):

Once again, we need to align the two numbers:

234

012

222

Therefore, 234 (in base 5) - 12 (in base 5) = 222 (in base 5).

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The given 3D model is a trapezoidal pyramid.

A pyramid is a 3D polyhedron having three or more triangle-shaped faces that meet above the base and a polygonal base. The point above the base is referred to as the apex, while the three sides are referred to as faces. The base and apex are joined to form a pyramid. To distinguish them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.

Hence, the given 3D model is a trapezoidal pyramid.

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In this instance, the three trigonometric ratios are:

Sinx = 15/17

Cosx =  8/17

Tanx = 15/8

Mathematical trigonometric functions connect the angle of a right-angled triangle to the ratios of its two side lengths.

In all areas of study that involve geometry, such as geodesy, solid mechanics, celestial mechanics, and many others, they are widely used.

Review the trigonometric ratios for sine, cosine, tangent, cotangent, secant, and cosecant.

So, the 3 trigonometric ratios in the given situation would be:

Sinx = O/H = 15/17

Cosx = A/H = 8/17

Tanx = O/A = 15/8

Therefore, in this instance, the three trigonometric ratios are:

Sinx = 15/17

Cosx =  8/17

Tanx = 15/8

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