Find the area of the triangle below.

Answer:

7 2/5 and/or -37/5

Step-by-step explanation:

It can also be 7.04 also

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.

Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

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The probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm is 0.01715.

A normal distribution is a probability distribution that has been symmetrical around this mean, with most observations clustering around the central peak and probabilities tapering off evenly in both directions.

Now, according to the question,

The formula for normal distribution is;

z = (x - μ)/(σ/√s)

x is the sample size (= 96)

μ = standard mean (= 92)

σ = standard deviation (= 10)

s = random sample (= 28)

Substituting all the values in the equation;

z = (96 - 92)/(10/√28)

z = 2.117

Now, calculate the probability;

P(X > 96) = 1 - P(X ≤ 96)

               = 1 - P(X ≤ 2.117)

               = 1 - 0.98285

P(X > 96) =  0.01715

Therefore, the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm is 0.01715.

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The complete question is-

The reading speed of a second grade students in a large city is approximately normal with a mean of 92 words per minute and a standard deviation of 10 wpm. What is the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm?

The value of tangent of 210 degrees can be calculated using the unit circle.

The unit circle is a circle whose radius is one and whose center is at the origin of a coordinate plane, the x-axis is a line that passes through (1, 0), and the y-axis is a line that passes through (0, 1).

A point on the unit circle represents an angle that is measured in radians.

To calculate the tangent of 210 degrees, follow these steps:

Step 1: Convert the angle from degrees to radians.

1 degree = π/180 radians

Therefore,

210 degrees = 210 * π/180 radians

                     = 7π/6 radians

Step 2: Locate the point on the unit circle that corresponds to the angle 7π/6 radians.

The point (-√3/2, -1/2) corresponds to 7π/6 radians.

This can be seen from the labelled sketch below.

Step 3: Calculate the tangent of 7π/6 radians.

tan(7π/6) = y/x

                = (-1/2)/(-√3/2)

                = (1/2)√3

Therefore, the exact value of tan 210 degrees is (1/2)√3.

The labelled sketch is attached below.

https://www.cuemath.com/trigonometry/tan-210-degrees/

(Note: The angle is marked in radians on the sketch, but the process remains the same for degrees as well.)

Labelled sketch:

Explanation:

Total words used = 166 words.

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The tangent of 210º is given as follows:

tan(210º) = \(\frac{\sqrt{3}}{3}\)

The angle for this problem is given as follows:

210º.

Which is on the third quadrant, as 180º < 210º < 270º.

The equivalent angle to 210º on the first quadrant is given as follows:

210 - 180 = 30º.

The tangent of 30º is given as follows:

tan(30º) = \(\frac{\sqrt{3}}{3}\)

On the third quadrant, the tangent is positive, just as in the first quadrant, hence the tangent of 210º is given as follows:

tan(210º) = \(\frac{\sqrt{3}}{3}\)

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Answer:

Step-by-step explanation:

y=-4x+13

if

the slope-intercept form of a linear equation is

where,m is slope and b is y-intercept

let's justify the first and second statement

our given equation is

y=-4x+13

where -4 is our slope or m

therefore,

1 and 2 statements are False

let's justify the third and fourth statement

our given equation is

y=-4x+13

where,13 is our y-intercept which means the line passes y-intercept when x=0

therefore,

third and fourth statements are False

The statement which is true regarding the line y = -4x + 13 is; The line passes through the point, (0, 13)

The equation of a straight line in slope-intercept form is usually of the form; y = mx + c

where m = slope and c is the y intercept with coordinate (0, c)

The statement which is true is therefore; The line passes through the point, (0, 13)

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To find the area of the region enclosed by the curves y and y = x^2, we can set up an integral and evaluate it.

The curves y and y =\(x^2\) intersect at two points. To find the bounds for integration, we need to determine the x-values where the curves intersect. Equating the two equations, we get \(x^2\) = y. Solving for x, we find that x = ±√y.

To find the area between the curves, we integrate the difference in the y-values of the curves over the interval where they intersect. Since the curve y = \(x^2\) is above y for the region of interest, the integral becomes ∫[0, 1] (\(x^2\)- y) dy, where the bounds of integration are determined by the intersection points.

Evaluating this integral will give us the area of the region enclosed by the curves y and y = x^2. The integral represents the signed area, so if the result is negative, we take the absolute value to obtain the actual area."

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well, if he sold 10 for $25, let's see how much he sold all 12 for.

\(\begin{array}{ccll} eggs&\$\\ \cline{1-2} 10 & 25\\ 12& x \end{array} \implies \cfrac{10}{12}~~=~~\cfrac{25}{x} \\\\\\ \cfrac{5}{6} ~~=~~ \cfrac{25}{x}\implies 5x=150\implies x=\cfrac{150}{5}\implies x=30\)

so he sold all 12 for $30, whilst he bought them for $25, so he had $5 profit, now, if we take 25(origin amount) as the 100%, what's 5 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 25 & 100\\ 5& y \end{array} \implies \cfrac{25}{5}~~=~~\cfrac{100}{y} \\\\\\ 5 ~~=~~ \cfrac{100}{y}\implies 5y=100\implies y=\cfrac{100}{5}\implies y=\stackrel{ \% }{20}\)

Answer:

The median would be found in the middle of the histogram

Step-by-step explanation:

It looks like 70-79, would fall in being the median because it is in the middle and it has the most results. In this case, I think it 70-79.

Hope this helps.

Answer:

70-79

Step-by-step explanation:

I took the test :)

Answer:

12 possibilities

Step-by-step explanation:

The first choice can be any of the four colors. For each of these 4 first choices there are 3 second choices. Therefore there are 4 x 3 = 12 possibilities.

The total number of possibilities is 15 ways can she form a set consisting of some of the marbles if she must choose at least one marble.

A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.

Alyssa has four marbles to choose from, and she must choose at least one of them. Therefore, there are 5 total possibilities for the set of chosen marbles:

A single marble: Alyssa can choose any of the 4 marbles, so there are 4 possibilities.

A pair of marbles: Alyssa can choose any pair of marbles, so there are 6 possibilities (since there are \(${4 \choose 2} = 6$\) pairs of marbles).

A triple of marbles: Alyssa can choose any triple of marbles, so there are 4 possibilities (since there are \(${4 \choose 3} = 4$\) triples of marbles).

All 4 marbles: There is only 1 possibility, which is to choose all 4 marbles.

Therefore, the total number of possibilities is 4 + 6 + 4 + 1 = 15.

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Answer:

-40

Step-by-step explanation:

Let me know if you have any more questions

\(\huge\text{Hey there!}\)

\(\mathsf{8 = 2x + 88}\\\mathsf{2x + 88 = 8}\\\large\text{Subtract 88 to both sides}\\\mathsf{2x + 88 - 88 = 8 - 88}\\\large\text{Simplify it:}\\\mathsf{2x = 8 - 88}\\\mathsf{2x = -80}\\\large\text{Divide 2 to both sides:}\\\mathsf{\dfrac{2x}{2} = \dfrac{-80}{2}}\\\large\text{Simplify it:}\\\mathsf{x = \dfrac{-80}{2}}\\\\\mathsf{x = -40}\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{x = -40}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

2

Step-by-step explanation:

to answer this algebraic question use BDMAS rule

first solve bracket then division, multiplication,addition then subtraction.

6+8-12

14-12

2

Answer:

9.8

Step-by-step explanation:

convert your decimal into a fraction so 2.3= 23/10

23/10 + 8 - 1/2

then calculate your sum or difference

leaving you with

49/5

meaning your answer is

9.8

Answer:

tendrá la capacidad de hacer 6 parches

Step-by-step explanation

Answer:

x = 8

Step-by-step explanation:

These are corresponding so they are congruent.

Your equation is: 14x-4=12x+12

x=8

Step-by-step explanation:

these numbers are corresponding angle to each other

so =>14x–4=12x+12

14x–4=12x+12collect like terms

=>14x–12x=12+4

=>2x=16 divide both side by 2 you get

=>x=8

The probability of getting a black ball is 5/13, if odds of choosing one black ball fron urn are 5 to 8.

According to the given question.

The odds of choosing one black ball from an urn are 5 to 8.

As we know that "the odds for an event is the ratio of the favorable outcomes to the unfavorable outcomes".

Therefore,

The favorable outcomes of getting black ball = 5

Unfavorable outcomes of getting black ball = 8

So, total outcomes = 5 + 8 = 13

Thereofre,

The probability of getting a black ball

= favorable outcomes/ total number of outcomes

= 5/13

Hence, the probability of getting a black ball is 5/13.

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Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

The quadratic example is ax² + b x + c = 0 where x stands for an unknown value and where a, b, and c stand for known numbers is known as a quadratic equation in algebra.

Quadratic equations are second-degree polynomial equations with at least one squared term. It is also referred to as quadratic equations.

The numerical coefficients a, b, and c are known, while the unknown variable x is. For example , x2 + 2x + 1. It also goes by the name quadratic equation as in: b x +c=0    

The terms a, b, and c are also referred to as quadratic coefficients.    

'Examples of Quadratics

x² –x – 9 = 0

5x² – 2x – 6 = 0
3x² + 4x + 8 = 0

-x² +6x + 12 = 0  (an example of non-quadratic equation is x³ − x² − 5 = 0)

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Answer:

Step-by-step explanation:

Sorry I didn't mean to do that.

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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Answer:

d= 2√a/π

To calculate the diameter, rewrite the formula to isolate D

Because a negative diameter doesn’t make sense, eliminate the negative answer from the solution

Simplify further to get the solution

The formula to calculate the diameter of the circle is d = 2 √( A/π )

where d = diameter of the circle

A = area of the circle

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the radius of the circle be = r

So , the diameter of the circle = 2r

Now , the area of the circle = πr²

Substituting the value for r , we get

Area of the circle = ( 1/4 ) πd²

So , A = ( 1/4 ) πd²

Now , solving the equation for diameter of circle d , we get

Multiply by 4 on both sides of the equation , we get

πd² = 4A

Divide by π on both sides of the equation , we get

d² = 4A/π

Taking square roots on both sides of the equation , we get

d = 2 √A/π

Therefore , the value of d is 2 √A/π

Hence ,

The formula to calculate the diameter of the circle is d = 2 √( A/π )

where d = diameter of the circle

A = area of the circle

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Answer:

with what

Step-by-step explanation:

Answer:

Yes I would be truly  willing to help u so what do u need help with

Step-by-step explanation:

**One advantage of using K-maps over De Morgan's theorem for simplifying logic** is that K-maps provide a visual representation that makes it easier to identify patterns and simplify expressions. **K-maps** (also known as Karnaugh maps) are graphical tools that allow for systematic reduction of Boolean expressions. They help in minimizing the number of gates and inputs required in a circuit, leading to more efficient designs. By visually grouping and combining adjacent cells, K-maps provide a structured approach to simplification, reducing the likelihood of errors compared to manual application of De Morgan's theorem.

De Morgan's theorem, on the other hand, is a mathematical technique used to simplify Boolean expressions. It involves negating both sides of an equation and applying specific rules. While De Morgan's theorem is effective for algebraic simplification, it lacks the visual representation and systematic approach offered by K-maps. Therefore, for complex logic simplification tasks, K-maps often prove to be more advantageous due to their intuitive graphical nature.

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Answer:

8/21

Step-by-step explanation:

the ratio is 5:8:8 so the total is 21 and since green is 8,the fraction is 8 over the total which is 8/21

Answer:

(x + y)(x + 8)

Step-by-step explanation:

Answer:

(x + y) (x + 8)

Step-by-step explanation:

\(x^2+xy+8x+8y\)

\(=\left(x^2+xy\right)+\left(8x+8y\right)\)

\(\mathrm{factor\;out\;x\;from\;x^2+xy}:x(x+y)\)

\(\mathrm{factor\;out \;8\;from\;8x+8y}:8(x+y)\)

\(=x\left(x+y\right)+8\left(x+y\right)\)

\(\mathrm{Factor\:out\:common\:term\:}x+y\)

\(=\left(x+y\right)\left(x+8\right)\)

Answer = \(\left(x+y\right)\left(x+8\right)\)

~Learn with Lenvy~

Answer:

y = 1

x = 4

Step-by-step explanation:

x + 3y = 7 → ( 1 )

2x - y = 7 → ( 2 )

First, let us make x the subject in equation ( 1 ).

x = 7 - 3y  → ( 3 )

Let us find the value of y.

For that let us take equation (1) & replace x with ( 7 - 3y ).

2x - y = 7

2 ( 7 - 3y ) - y = 7

Solve the brackets.

14 - 6y - y = 7

Combine like terms.

14 - 7y = 7

Subtract 14 from both sides.

-7y = 7 - 14

-7y = -7

Divide both sides by -7.

y = 1

Let us find value of x

For that let us take equation (3) & replace y with 1.

x = 7 - 3y

x = 7 - 3 × 1

x = 7 - 3

x = 4

Answer:

7y + 15 - 2y = 5(y + 3)

Step-by-step explanation:

So two equations have infinitely many solutions, when they are exactly the same equation, in their most simplified form, for example: 2x = 3x-x which simplifies to 2x=2x. So in the options, three of the options have the same equation on the right side, so I'll distribute the 5. \(5(y+3) = 5y+15\). Now let's look at the options:

7y + 3-2y

5y+3 (this is not the same as 5y + 15)

7y + 15 (this is not the same as 5y + 15)

7y + 15 - 2y

5y + 15 = 5y + 15 (this is the same)

Answer:

Step-by-step explanation:

Exponent law:

    \(\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}\)

    \(\sf a^{-m}=\dfrac{1}{a^m}\)

       First convert radical form to exponent form and then apply exponent law.

 \(\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}\)

\(\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}\)

                      \(= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}\)

Answer:

-1 and 4/3

Step-by-step explanation:

So first we want to find the equation for the linear function g(x):

We know that it is linear, so it will follow the equation

y = mx + b

m is the slope, and b is the y-intercept

First, find the slope:

We can see that every time the x increases by 1, the output value is increased by 2

This means that the slope will be 2

Then, find the y-intercept:

The y-intercept is when the x value is equal to 0, so in this table, when the x value is 0, the output is 7

So putting these number into the equation will give us:

y = 2x + 7

Now to find the solutions:

You have to set these equations equal to each other and solve for x

The set up should look like this:

\(3x^{2} + x +3 = 2x+7\)

Put all of the values on one side:

\(3x^{2} -x-4 = 0\)

And then solve for x by factoring:

\(3x^{2} +3x-4x-4\) = 0

\((3x^{2} +3x)+(-4x-4)\) = 0

\(3x(x+1)-4(x+1)\) = 0

(x+1)(3x-4) = 0

Finally, to get the x values:

x + 1 = 0

x = -1

and

3x - 4 = 0

3x = 4

x = 4/3

So the answers are:

x = -1 and 4/3

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).

A polynomial function is a relation where a dependent variable is equal to a  polynomial expression. A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.

The highest power to a variable is the degree of the polynomial expression.

When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

The quadratic function is given to us:

f(x) = 3x² + x + 3.

We need to determine the linear equation g(x). Since it's a linear equation we use the two-point method to determine the equation.

The two-point formula is:

y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(2) = 11, g(1) = 9

g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)

or, g(x) - 9 = ((11-9)/(2-1))*(x-1)

or, g(x) - 9 = 2(x-1)

or, g(x) = 2x - 2 + 9 = 2x + 7

∴ g(x) = 2x +7, is the linear function g(x)

We are asked to find the solution to the system of equations f(x) and g(x).

To find the solution we need to check what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).

3x² + x + 3 = 2x + 7

or, 3x² - x - 4 = 0

or, 3x² + 3x - 4x - 4 = 0

or, 3x(x+1) -4(x+1) = 0

or, (3x-4)(x+1) = 0

∴ Either 3x-4=0 ⇒ x = 4/3

or, x+1=0 ⇒ x = -1.

g(-1) = 5 (from the table)

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

g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3

f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3

∴ f(-1) = g(-1) and f(4/3) = g(4/3), so

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).

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Answer:

2.2%

Step-by-step explanation:

i took the test!

Answer:

Gianna spent 21% more

Step-by-step explanation:

30-9=21