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There are 52 quarters and 15 half-dollars

Let's represent the number of half-dollars as "x" and the number of quarters as "y".

From the problem statement, we know that:

x + y = 67 (because there are a total of 67 coins)

y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)

We can use substitution to solve for x:

x + (3x + 7) = 67

4x + 7 = 67

4x = 60

x = 15

So there are 15 half-dollars. We can use this to find the number of quarters:

y = 3x + 7

y = 3(15) + 7

y = 52

So there are 52 quarters.

Therefore, there are 52 quarters and 15 half-dollars.

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The equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

A straight line can be used to symbolise a function that is linear, meaning that for each unit change in the input, the output (y) changes by a fixed amount (x). While a parabola can be used to depict a function, a quadratic function has an output (y) that changes by a non-constant amount for each unit change in the input (x). In other words, a quadratic function curves because of the squared term in its equation.

Given, the parabola has vertex at point (2, -11) and passes through the point (0, 5).

Thus, the equation of parabola in vertex form is:

y = a(x - 2)² - 11

Now, the parabola passes through the point (0, 5) we have:

5 = a(0 - 2)² - 11

5 = 4a - 11

16 = 4a

a = 4

Hence, the equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

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Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

Answer: x = -1 and x = 9

Step-by-step explanation:

Lets solve this equation step by step

1. Simplify both sides of the equation

x^2 - 8x + 16 = 25

2. Subtract 25 from both sides

x^2 - 8x + 16 - 25 = 25 - 25

3. Factor the left side of the equation

(x + 1) (x - 9) = 0

4. Set the factors equal to zero

x + 1 = 0 or x - 9 = 0

Thus your answers are x = -1 and x = 9

You can check by inputting the values into the original equation

(-1 - 4)^2 = 25 and (9 - 4)^2 = 25

Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).

To show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.

We can prove that it meets the mean condition this way:

E(Y) = E(aX + b) = aE(X) + b = aμX + b

Next, we can prove that it meets the variance condition thus:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2

Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.

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Answer:

16.77 cm²

Step-by-step explanation:

Area of rectangle = L x W

L = 4.3 cm

Width = 3.9 cm

Let' solve

4.3 x 3.9 = 16.77 cm²

So, the area of the rectangle is 16.77 cm²

Answer:

Step-by-step explanation:

2.1 so a

Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

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The third quartile range is the difference between the median height of the third grade class and the fourth grade class, so the answer is two times.

Since -4 is less than or equal to -2, we use the first part of the definition of f(x) which is f(x) = x + 4 if x ≤ -2. Therefore,

f(-4) = (-4) + 4 = 0.

So, the answer is D. 0.

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.

In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.

Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.

Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.

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None of the given numbers make the equation 8/y² + 2 true.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.

Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.

Substituting y=1 would give us:

8/1² + 2 = 8 + 2 = 10

So, 1 is not the answer.

Substituting y=2 would give us:

8/2² + 2 = 8/4 + 2 = 2 + 2 = 4

So, 2 is not the answer.

Substituting y=3 would give us:

8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888

So, 3 is not the answer.

Substituting y=4 would give us:

8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5

So, 4 is not the answer.

Therefore, none of the given numbers make the equation 8/y² + 2 true.

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The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)

To calculate (f/g)(x), we need to divide f(x) by g(x):

(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)

The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f/g)(x) is x ≥ 5/3.

To calculate (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)

The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f-g)(x) is x ≥ 5/3.

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Answer:5

Step-by-step explanation: hope this helps

In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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The discount allowed for a cash payment of GH 5,600.00 is given as follows:

GHC 280.00.

The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.

There is a 5% discount, hence the value of the discount is obtained as follows:

0.05 x 5600 = GHC 280.00.

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Answer:

1629.24m

Step-by-step explanation:

starting with the easy ones

1) Rectangle 1:

Surface area of rectangle=Length x width

SAR= 24x21

= 504m

2) Rectangle 2:

SAR= 19x21

=399

3) Rectangle 3

SAR= 21x8

=168

4) Rectangle 4:

SAR= 21x11

=231

*because the top and bottom are trapeziums the formular for it is

A=1/2(a+b)h

although those trapeziums don't have h(Height)

it needs to be broken down into two triangles and a rectangle. to find the height*

5) side/height of triangle A:

formula: C squared= a squared + b squared

in this case we already have C and A. meaning we have to rearrange the formula to:

x = c^2 - a^2

x = 8^2 - 2.5^2

x = sqrt 57.75

x = 7.61

6) Trapezium

SA= 1/2(a+b)h

SA= 1/2(19+24)7.61

=163.62

7) add all surface area together

which should equal 1629.24m

The answer is , (a)  For equation 1 Use the quadratic formula , (b) For equation 2 use of Factor out the common factor , (c) For equation 3 use of Complete the square.

A quadratic equation is a type of equation in algebra that contains a variable of degree 2, meaning that the highest power of the variable is 2.

Quadratic equations can have two real roots, one real root, or two complex roots, depending on the value of the discriminant (b² - 4ac). If discriminant is positive, equation has two real roots, if it is zero, equation has one real root (a "double root"), and if it is negative, equation has two complex roots.

Inga can use the following steps to solve the quadratic equation 2x² + 12x - 3 = 0:

Therefore, steps that Inga could use to solve quadratic equation are given:

Use the quadratic formula

Factor out the common factor

Complete the square

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1. In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times. 2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. 3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. 4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker.

Speech is the act of expressing thoughts, ideas, or emotions through spoken words. It is a form of communication that allows individuals to convey information, share opinions, ask questions, and express feelings to others.

1. Three differences between the Robinson version and the Gage version of the speech are:

In the Robinson version, Truth says "I have as much muscle as any man" while in the Gage version she says "I have ploughed and planted, and gathered into barns, and no man could head me!".

In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times.

In the Robinson version, Truth refers to herself as a "colored woman" while in the Gage version she uses the term "African American".

2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. The differences between the two versions show how editors and publishers can change the meaning and impact of a text by making small modifications to it. Additionally, hearing both versions allows us to appreciate the nuances of language and dialect, and how different speakers can bring their own interpretations and emphasis to a text.

3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. For example, the reference to "colored women" in the Robinson version would have been seen as more confrontational and controversial in certain regions. Today, the differences may help us appreciate the diversity and complexity of language, and how it reflects the cultural and historical contexts in which it is spoken.

4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker. The dialect used in each version reflects the cultural and historical context of the time, and the different audiences that the speeches were intended for. By hearing the dialect of each version, we can better appreciate the ways in which language shapes our understanding of history and identity.

As for the next set of questions:

When women's rights activists spoke out, they were advocating for both white women and African-American women, although the experiences and struggles of African-American women were often ignored or marginalized within the movement.

Truth makes several distinct arguments in her speech, including that women deserve the same rights and respect as men, that the stereotype of women as weak and dependent is unjust, and that the experiences of African-American women are often overlooked in discussions of women's rights.

Truth is saying that women deserve equal rights and respect as men, and that the societal norms that limit women's opportunities and autonomy are unjust and unfounded.

Truth is arguing that women need to fight for their own rights, rather than waiting for men to give them these rights. She also emphasizes the importance of solidarity and mutual support among women.

Truth's speech reflects intersectionality by recognizing the ways in which race and gender intersect to create unique experiences of oppression and marginalization. She argues that the struggles of African-American women cannot be separated from the struggles of all women, and that a truly equitable society must address the needs and concerns of all marginalized groups. One passage that reflects this is when she says, "I have borne thirteen children, and seen most all sold off to slavery, and when I cried out with my mother's grief, none but Jesus heard me! And ain't I a woman?" This passage highlights the intersection of race, gender, and motherhood in Truth's experience.

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Answer:

the answer is 110-23i

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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Step-by-step explanation:

a) factorize A

A = (2x-1)²+2(3-6x)(4x-7)-4x²+1

expand the terms

(2x-1)²-52x²+108x-41

factorize

(2x-1)²-(26x-41)(2x-1)

factor out the common factor 2x-1

-(2x-1)(24x-40)

A = -8(2x-1)(3x-5)

b) show that B = (3x-11)(2x-1)

6x²-25x+11

6x²-3x-22x+11

3x(2x-1)-11(2x-1)

(2x-1)(3x-11)

c) Expand and reduce A

(2x-1)²+2(3-6x)(4x-7)-4x²+1

-48x²+108x-40

d) Calculate A for x=0 and x=-1

when x=0 -48(0)²+108(0)-40

A=0

x=-1 -48(-1)²+108(-1)-40

A=-196

e) Reduce 2A-3B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-3(6x²-25x+11)

-96x²+216x-80-18x²+75x-33

-144x²+291x-113

f) Factorize 2A-B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-(6x²-25x+11)

-96x²+216x-80-6x²+25x-11

-102x²+241x-91

x=(241 + sqrt(20953))/204

x=(241 - sqrt(20953))/204

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Answer:

Step-by-step explanation:

BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn

The true statements are:

1. The radius of the circle is 3 units

2. The standard form of the equation is (x-1)^2+y^2=3

3. The center of the circle lies on X-axis

4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9

The given equation is: x^2+y^2-2x-8=0

The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle

The given equation in standard form can be written as

(x^2-2x+1)+y^2-9=0

(x-1)^2+y^2=3^2

Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.

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Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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The correct answer is: Both the mean and median are appropriate measures of center.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.

Here,

The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:

37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500

And there are seven salaries. Therefore, the mean is:

307,500 / 7 = 43,928.57

The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:

35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000

The median is the middle value, which is 40,000.

The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.

Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.

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Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.

If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.

(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)

Step-by-step explanation: