Solve for the missing side in each triangle

Answer:

Step-by-step explanation:

To write the standard equation of a circle with its center in the fourth quadrant tangent to x=7, y=-4 and x=17, we can first find the center of the circle.

Since the center is in the fourth quadrant and tangent to x=7, y=-4 and x=17, the center must lie on the line x=12 (the midpoint between 7 and 17) and y=-4 (the point of tangency).

So the center of the circle is (12, -4).

Next, we need to find the radius of the circle. Since the circle is tangent to x=7 and x=17, the radius is the distance from the center to either x=7 or x=17.

The radius is thus 12 (the difference between 12 and 7) or 5 (the difference between 12 and 17).

So the standard equation of the circle is:

(x - 12)^2 + (y + 4)^2 = 25

The speed limit for the highway in rounded to the nearest whole is 33 mi/h.

The speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.

There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and  yards (yd).

For solving this exercise, you need to know the relation between the given units for distance and time.

The question gives - 100 km/h. The kilometer (km) is a multiple of the  standard unit of distance -  the meter (m) and the hour is a submultiple of the  standard unit of time  - the second (s)

For solving this question, it is necessary that you know the relation between km/h and mi/h. See  below.

[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]

Now you can solve the question from a math tool - Rule of three. Thus,

[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]

[tex]100 \ \text{km/h}= \text{x mi/h}[/tex]

[tex]\text{x}= 100 \times 0.6[/tex]

[tex]\text{x}=33 \ \text{mi/h}[/tex]

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Answer:

Based on the hypothesis test conducted with a significance level of 5%, we fail to reject the null hypothesis that the proportion of smokers in the city is 20%. This means that we do not have sufficient evidence to conclude that the proportion of smokers is less than 20%. The p-value of 0.828 suggests that there is a high probability that the observed proportion of smokers in the sample is due to chance and not a true difference in the proportion of smokers in the population. Therefore, we cannot conclude that the city has a lower proportion of smokers than 20%.

In this hypothesis test set up by the researcher, the p-value is 0.828, which is greater than the significance level (0.05). Therefore, we do not reject the null hypothesis, meaning there is not enough statistical evidence to validate the researcher's claim that the proportion of smokers is less than 20%

A hypothesis test in statistics uses test statistics based on sample data to accept or reject a null hypothesis. In this scenario, the null hypothesis (H0) states that the proportion of smokers (p) is 20%. The alternative hypothesis (Ha) claims that the proportion of smokers is less than 20%. The p-value is a measure of the probability that the observed data could occur under the null hypothesis. In our case, a p-value of 0.828 means that there is an 82.8% chance of observing the data if the true proportion of smokers is 20%, or higher.

Usually a threshold known as the significance level (in this case 5% or 0.05) is used to determine whether the null hypothesis should be rejected or not. If the p-value is less than or equal to the significance level, it suggests that the observed data is inconsistent with the null hypothesis, and the null is usually rejected. However, since our p-value is greater (0.828 > 0.05), we would not reject the null hypothesis, suggesting that there is not enough evidence to support the researcher's claim that the proportion of smokers is less than 20%.

Therefore, the conclusion is that the researcher's claim cannot be validated using the provided data.

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Here is the truth table for the statement (~ p V q) → q:

```

p     q     ~p    ~p V q   (~p V q) → q

---------------------------------------

T     T     F      T           T

T     F     F      F           T

F     T     T      T           T

F     F     T      F           T

```

In the table, `p` and `q` represent the truth values of the propositions `p` and `q`, respectively. The symbol `~` represents negation (i.e., "not"). The symbol `V` represents the logical connective "or" (i.e., "inclusive or"). The symbol `→` represents the conditional connective "implies" (i.e., "if...then").

To fill in the truth table, we first evaluate `~p` and `~p V q` for each combination of truth values for `p` and `q`. Then, we evaluate `(~p V q) → q` for each combination of truth values.

We can see that the statement is always true, regardless of the truth values of `p` and `q`, except for the case where `p` is true and `q` is false.

The repeated nearest neighbor algorithm is applied to the given graph to find the circuit of lowest cost starting from vertex A. The vertices are visited in the order A, D, B, C, E, F, and back to A, with a total cost of 38. Therefore, the answer is ADBCEFA.

To apply the repeated nearest neighbor algorithm, we start at vertex A and repeatedly choose the nearest unvisited vertex until we have visited all vertices and return to the starting vertex.

Start at vertex A. Vertex D is the nearest unvisited vertex from A with a distance of 4. Move to vertex D. Vertex C is the nearest unvisited vertex from D with a distance of 5. Move to vertex C. Vertex F is the nearest unvisited vertex from C with a distance of 2.

Move to vertex F. Vertex E is the nearest unvisited vertex from F with a distance of 6. Move to vertex E. Vertex B is the nearest unvisited vertex from E with a distance of 8. Move to vertex B. Return to vertex A to complete the circuit.

Therefore, the circuit starting and ending at vertex A using the repeated nearest neighbor algorithm is ADFCEBA with a total distance of 38.

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The correct choice is: B. The statement is false because the reference values for the decrease and increase are not the same. The true improvement over the past two years is 8.56%.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

Mathematically, percentage increase can be calculated by using this mathematical equation (formula):

Percentage increase = [Final value - Initial value]/Initial value × 100

Based on the information provided about the high school test scores, we have the following:

True improvement = (100% - 8%) × (100 + 18)

True improvement = (92%) × (100 + 18)

True improvement = (0.92) × (118)

True improvement = 108.56 ⇒ 8.56%.

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To calculate the percentage of questions Danielle got correct on her math test, we can divide the number of questions she got correct by the total number of questions on the test and then multiply by 100. In this case, Danielle got 23 out of 25 questions correct, so we can calculate her percentage as follows: (23/25) * 100 = 92%. Therefore, Danielle got 92% of the questions correct on her math test.

Percent = amount per 100

23/25 = amount per 25

25 x 4 = 100

23 x 4 = 92

92/100 = 92%

Answer = 92%

Hope this helps!

Answer:

2 1/3

Step-by-step explanation:

add then multiplying to the nearest one.

x = 3.6 units

First, some definitions before working the problem:

The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.

The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.

Working the problem

For the given triangle, the right angle is in the top right, so the side on the bottom left is the hypotenuse.

We know the angle in the lower right corner (angle S), so the side touching it (side ST) with unknown length is the adjacent side.  (notice that the points that form the side include the vertex of the angle -- so, it's the adjacent side).

For this triangle, the "adjacent" leg is unknown, our "goal to find" side.  Additionally, the "hypotenuse" is known.

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "adjacent" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "a" & "h" is "Cah".  So, the desired function to use for this triangle is the Cosine function.

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]cos(69^o)=\dfrac{x}{10}[/tex]

To isolate "x", multiply both sides by 10...

[tex]10*cos(69^o)=x[/tex]

Make sure your calculator is set to degree mode, and calculate:

[tex]10*(0.3583679495453...)=x[/tex]

[tex]x=3.583679495453...[/tex] units

Rounded to the nearest tenth...

x = 3.6 units

The equivalent value of the expression is y = + 3/5 and y = -3/5

Given data ,

Let the expression be represented as A

Now , the value of A is

y = ±3/5

On simplifying the equation , we get

y = +3/5

And, y = -3/5

Now , the decimal values of y are

y = ±0.6

Hence , the expression is y = ±0.6

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Is this compound interest or simple interest? I'll just do it by the simple interest method. The answer is 9 months!

Area of the base of the pyramid is 16 square centimeters

Area of one lateral face of the pyramid  is  14 square centimeters

The lateral surface area of the pyramid is  56 square centimeters

The total surface area of the pyramid is 72  square centimeters

Area of the base of the pyramid = length x length

= 4 x 4

=16 square centimeters

Area of one lateral face of the pyramid = area of a triangle

=1/2×base×height

=1/2×4×7

=14 square centimeters

The lateral surface area of the pyramid =  4 x area of one lateral face

= 4 x 14

= 56square centimeters

The total surface area of the pyramid = lateral surface area of the pyramid +  area of the base

=56+16

=72 square centimeters

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The probability that none of the four adults is very confident in the nutritional information on the restaurant menus is 0.208 or approximately 20.8%. 

Ready to approach this issue by utilizing the hypergeometric conveyance, since we are examining without substitution from a limited populace of two sorts (those who are exceptionally sure and those who are not exceptionally sure).

Let X be the number of grown-ups in a sample of 4 who are not exceptionally sure about the wholesome data on eatery menus.

At that point, X takes after a hypergeometric dissemination with parameters N = 1000, n = 4, and K = 850 (since 850 grown-ups are not exceptionally certain).

The likelihood that none of the 4 grown-ups are exceptionally certain can be communicated as:

P(X = 4) = (K select 4) / (N select 4)

where (K select 4) speaks to the number of ways to select 4 grown-ups from the population of 850 who are not exceptionally sure,

and (N select 4) speaks to the entire number of ways to select 4 grown-ups from the populace of 1000.

Utilizing the equation for binomial coefficients, ready to disentangle this expression as:

P(X = 4) = [(850*849*848*847) / (4*3*2*1)] / [(1000*999*998*997) / (4*3*2*1)]

= 0.208

Hence, the likelihood that none of the four grown-ups are exceptionally certain within the wholesome data on eatery menus is 0.208 or approximately 20.8%. 

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Answer:

D. its a two dimensional object

Answer:

A. It is a polygon

C. It is a one-dimensional object

The shape is a polygon in two dimensions since a polygon must have at least three straight sides.

Adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

row 1 of the given matrix are: 1, 2, 1, and -5, multiplying -4(row1) will gives;

-4 × 1 = -4

-4 × 2 = -8

-4 × 1 = -4

-4 × -5 = 20

-4(row 1) + row 3 will result to:

-4 + 4 = 0

-8 + (-1) = -9

-4 + 6 = 2

20 + (-8) = 12

Therefore, adding -4(row 1) to row 3 in the matrix will produce: 0, -9, 2, and 12 respectively.

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Answer:

2

Step-by-step explanation:

The value of cube root of 8, ∛8, is 2.

Answer:

2

Step-by-step explanation:

cube root 8 means:

a number x such that x * x * x = 8

the answer is 2, since 2 * 2 * 2 = 8

The correct statements are as follows:-

There is a cluster from 3 to 4.

There is a gap between 1 and 3.

There is a peak at 4.

The data is skewed left.

We have,

Scatter plots are graphs that show how two variables in a data collection relate to one another. On a two-dimensional plane or in a Cartesian system, it represents data points.

The right statements for the dot plots are as follows:-

There is a cluster from 3 to 4.

There is a gap between 1 and 3.

There is a peak at 4.

The data is skewed left.

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Answer:

Step-by-step explanation:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{-1-0}{0+3}[/tex]

m = [tex]\frac{-1}{3}[/tex]

Answer: -[tex]\frac{1}{3}[/tex]

The airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds

Let,

Weight of airplane = y

Amount of fuel = x

The general linear equation can be written as, y=mx + c, where, (m) is slope, and (c) is a constant.

It is given,

2091 = 14m + c ..... (1)

2312 = 48m + c ..... (2)

On subtracting, (1) with (2), we get

221 = 34m

m= (221/34)= 6.5

Now, on putting the value of (m) in (1), we get,

2091 = 14(6.5) + c

So,

c = 2000

Therefore, the linear equation can be written as,

y = (6.5)mx + 2000

Now to find the airplane weight at 52 gallons of fuel, we put x = 52, to find y.

That is,

y = (6.5)(52) + 2000

y = 2338

So, the airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds.

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The function limit of f(x) as x approaches 2 is 67 and the limit of f²(x) as x approaches 2 is 4489.

The function f(x) can be rewritten as:

f(x) = (5x³ + 3x² - x)/(x+2)

Using direct substitution, we see that f(2) is undefined, as the denominator of the function becomes 0.

To evaluate the limit, we can use L'Hopital's rule:

[tex]\lim_{x \to 2\[/tex] f(x) = lim x→2 (5x³ + 3x² - x)/(x+2)

= [tex]\lim_{x \to 2\[/tex] (15x² + 6x - 1)/(1)

= (15(2)² + 6(2) - 1)/(1)

= 67

To find the limit of f²(x) as x approaches 2, we can simply square the limit:

f(x) = [tex]\lim_{x \to 2\}[/tex]f²(x)

= [tex]\lim_{x \to 2[/tex] f²(x)  

= 67²

= 4489

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The equation of the line parallel is y = mx + (1 + 2m).

We have,

The equation of the line.

y = mx + c

Slope = m

And,

(-2, 1) = (x, y)

So,

1 = m x -2 + c

c = 1 + 2m

Now,

y = mx + c

y = mx + (1 + 2m)

Thus,

The equation of the line parallel is y = mx + (1 + 2m).

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Answer:

Step-by-step explanation:

To predict the number of bacteria after 10 hours using the formula P = Aekt, where P is the final population, A is the initial population, k is the growth rate, and t is the time elapsed, we need to first find the value of k.

dw

We know that after 4 hours, the population grew from 3,000 bacteria to 3,600 bacteria. So we can set up an equation:

3,600 = 3,000e^(4k)

Dividing both sides by 3,000 gives:

1.2 = e^(4k)

Taking the natural logarithm of both sides gives:

ln(1.2) = 4k

Solving for k, we get:

k = ln(1.2)/4

k ≈ 0.051

Now that we have the value of k, we can use the formula to predict the number of bacteria after 10 hours:

P = 3,000e^(0.051*10)

P ≈ 5,426

Therefore, we predict that after 10 hours, there will be approximately 5,426 bacteria present in the culture.

Answer:

x = 4√3

y = 8√3

Step-by-step explanation:

The interior angles of the given right triangle are 30°, 60° and 90°.

Therefore, the triangle is a special 30-60-90 triangle.

In a 30-60-90 triangle, the measures of its sides are in the ratio 1 : √3 : 2.  

Therefore, the formula for the ratio of the sides is b : b√3 : 2b where:

From inspection of the given triangle, the side opposite the 60° angle is 12 units in length. Therefore:

[tex]b\sqrt{3} = 12[/tex]

Solve the equation for b:

[tex]\begin{aligned}b&=\dfrac{12}{\sqrt{3}}\\\\b&=\dfrac{12 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}\\\\b&=\dfrac{12\sqrt{3}}{3}\\\\b&=4\sqrt{3}\end{aligned}[/tex]

"x" is the side opposite the 30° angle. Therefore:

[tex]\begin{aligned}x& = b\\x& = 4\sqrt{3}\end{aligned}[/tex]

"y" is the side opposite the right angle. Therefore:

[tex]\begin{aligned}y&=2b\\y&=2 \cdot 4\sqrt{3}\\y&=8 \sqrt{3}\end{aligned}[/tex]

Therefore, the values of x and y are:

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Answer: 87.964594300514 feet3 or 87.96 feet3

Step-by-step explanation:

πr^2 h

=  π×2^2×7

=  28π

=  87.964594300514 feet3

the value of 4% as a fraction is 1/25

4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.

The number of flowers needed is 226

The circumference is the perimeter of a circle or ellipse. The circumference is the outer body of a circle and it can also be called perimeter of a circle.

The circumference of a circle is expressed as!

C = 2πr , where r is the radius.

the radius of the garden is 18ft

C = 2 × 3.14 × 18

C = 113.04

This means the perimeter of the garden is 113.04

For a space of 6 inches, the flower needed is calculated as;

113.04 × 12/6 ( since 1 foot is 12 inches)

= 113.04 × 2

= 226 flowers ( nearest whole number)

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We can start by finding the rate at which the printer is printing photos. Since it takes 3 minutes to print 6 photos, we can calculate the rate as 6 photos / 3 minutes = 2 photos/minute. This means that for every minute that passes, the printer prints 2 photos.

Now that we know the rate, we can use it to find out how long it will take to print 16 photos. Since the rate is 2 photos/minute, we can set up an equation to solve for y (time) when x (photos) is 16: 2 = 16/y. Solving for y, we get y = 16/2 = 8.

Therefore, when x (photos) is 16, y (time) is 8 minutes. This means that it will take the printer 8 minutes to print 16 photos.

If y (time) is 5 minutes, we can use the rate we calculated earlier to find out how many photos the printer will print in that time. Since the rate is 2 photos/minute, we can multiply it by the time to find out how many photos will be printed: 2 photos/minute * 5 minutes = 10 photos.

Therefore, if y (time) is 5 minutes, the printer will print 10 photos.

If y (time) is 7 minutes, we can use the rate we calculated earlier to find out how many photos the printer will print in that time. Since the rate is 2 photos/minute, we can multiply it by the time to find out how many photos will be printed: 2 photos/minute * 7 minutes = 14 photos.

Therefore, if y (time) is 7 minutes, the printer will print 14 photos.

The quadratic equation is solved and discriminant is 5, so it has two real solutions

Given data ,

The given equation is a quadratic equation in the standard form ax² + bx + c = 0, where a = 1, b = -1, and c = -1

The discriminant of a quadratic equation is given by b² - 4ac. So, the discriminant of the given equation is

(-1)² - 4(1)(-1) = 1 + 4 = 5

Since the discriminant is positive (not zero or negative), the equation has two real solutions.

Hence , its discriminant is 5, so it has two real solutions

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5 seconds.

In a function expressing altitute (h) in terms of time (t), finding the vertex will provide the time and altitute when the object reaches the maximum height. Therefore, let's use the vertex formula to see exactly when this happens:

"x" vertex value: [tex]-\dfrac{-b}{2a}[/tex]

a) For using that equation, first write the given equation on its standard form.

Standard form of quadratic equations: [tex]ax^{2} +bx+c=0[/tex]

b) You can substitute h(t) by 0 on the origina equation:

[tex]-0.2t^{2} +2t=0[/tex]

c) Idenfity the coefficients.

a= -0.2, beacuse "t²" is being multiplied by -0.2.

b= 2, beacuse "t" is being multiplied by 2.

d) Substitute in the formula and calculate.

[tex]\sf X\,value_{Vertex} =-\dfrac{-b}{2a}=-\dfrac{-(2)}{2(-0.2)}=-\dfrac{-(2)}{-0.4}=5[/tex]

So the "x" value of this h(t) equation is located on x= 5, therefore, the maximum point happens at x= 5. Since this is an equation that expresses altitute in terms of time, this means that 5 seconds after the object starts its movement it reaches its maximum altitute.

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Answer:

70.7°

350 feet

Im not too sure about the last one