Find the area and perimeter of the parallelogram. (Hint: Don't forget your units!)
7 cm
8 cm
4 cm

Answer:

Step-by-step explanation:

Make a chart.

units                    hours

2                             5

4                             10

6                             15

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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The solutions are: x = ln(2) for 2eˣ = 4,  x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.

To solve these equations using natural logarithm, we can use the following rules:

Using these rules, we can solve the given equations as follows:

2eˣ = 4

Divide both sides by 2 to get

eˣ = 2.

Take the natural logarithm of both sides to get

ln(eˣ) = ln(2).

Using rule 1 above, we can simplify ln(eˣ) to x, and we get

x = ln(2).

e⁴ˣ = 25

4x = ln(25).

Divide both sides by 4 to get

x = ln(25)/4.

eˣ = 72

Take the natural logarithm of both sides to get

x = ln(72).

e³ˣ = 124

Take the natural logarithm of both sides to get

3x = ln(124).

Divide both sides by 3 to get

x = ln(124)/3.

For the second set of equations, we use the same rule as above

So, we have

ln(x - 3) = 2

x - 3 = e²

x = e² + 3.

x ≈ 10.389.

Therefore, the solution is x ≈ 10.389.

ln(2t) = 4

2t = e⁴

t = 0.5 * e⁴

t ≈ 27.299.

Therefore, the solution is t ≈ 27.299.

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Answer:

The coins are picked without replacement.

The probability of picking at least one Canadian quarter is 1 minus the probability of picking 6 U.S. quarters:

[tex]1 - ( \frac{41}{50} )( \frac{40}{49} )( \frac{39}{48} )( \frac{38}{47} )( \frac{37}{46} )( \frac{36}{45} ) [/tex]

[tex] = 1 - .28296 = .71704[/tex]

So the probability of picking at least one Canadian quarter is about 71.7%.

Answer:

36 ft

Step-by-step explanation:

9x4=36. if the bulletin board is 9ft on each side, (9x4) the amount of border she needs would be 36ft.

a.He will win a prize.

b.Tina needs to walk 4 more miles to meet the goal for the Bike Riding activity and win a prize.

a. How to find the distance Tony runs in one week?

To find the distance Tony runs in one week, we need to multiply the distance he runs in one day (which is 1/2 mile) by the number of days in a week (7):

Distance run in 1 week = 1/2 mile per day x 7 days = 3.5 miles

Since Tony has run a total of 3.5 miles in a week, he has met the goal for the Swimming activity, which requires running 1 mile in 2 weeks. Therefore, he will win a prize.

b. How to find the total distance walked by Tina in one week?

To find the total distance walked by Tina in one week, we need to multiply the distance she walks to the library and back (which is 1 mile each way) by the number of times she walks per week (which is 3):

Distance walked in 1 week = 2 miles per walk x 3 walks = 6 miles

Since Tina has walked a total of 6 miles in a week, she has met the goal for the Walking activity, which requires walking 6 miles in 2 weeks. Therefore, she will win a prize.

To find out how much more Tina needs to walk to meet the goal for the Bike Riding activity, we need to subtract the distance she has already walked (6 miles) from the total distance required (10 miles):

Distance left to walk = 10 miles - 6 miles = 4 miles

Therefore, Tina needs to walk 4 more miles to meet the goal for the Bike Riding activity and win a prize.

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Option (a) is the correct answer. When two figures are similar, it means they have the same shape but different sizes.

How to solve the question?

In other words, their corresponding angles are congruent, and their corresponding side lengths are proportional.

Option (b) and (d) suggest that the corresponding side lengths of A and B are related by a constant factor (either 2 or 1/2). However, this is not necessarily true for all similar figures. The constant of proportionality can be any positive real number.

Option (c) suggests that the corresponding side lengths of A and B are equal, which means that A and B are not just similar but congruent. This is not necessarily true for all similar figures, as similar figures can differ in size.

Therefore, option (a) is the only answer that must always be true for similar figures. The corresponding side lengths of similar figures are proportional, which means that if one side of figure A is twice as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 2:1. Similarly, if one side of figure A is three times as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 3:1. This proportional relationship holds true for all pairs of corresponding sides in similar figures

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Option (a) is the correct answer.  The corresponding side lengths of A and B are proportional, must always be true if Figure A is similar to Figure B.

When two figures are similar, their corresponding angles are congruent, and their corresponding side lengths are proportional. This means that if we take any two corresponding sides of the figures, the ratio of their lengths will be the same for all pairs of corresponding sides.

Option b and d cannot be true, as they both suggest a specific ratio of corresponding side lengths, which is not necessarily true for all similar figures.

Option c is not necessarily true, as two similar figures can have corresponding side lengths that are not equal but still have the same ratio.

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Answer: 5 * 5 = 20

20 divided by 1 = 20

If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.

Area of composite shape = 12 + 9

                                         = 21 cm²    

Area of composite shapes:

13) Figure 1:

        Figure1 is a rectangle.

        l = 4 cm & w = 2 cm

Area of figure1 = l * w

                        = 4 * 2

                        = 8 cm²

Figure2:

             Figure2 is a parallelogram

              base = b = 4 cm

                 h = 4 cm

  Area of figure2 = b * h

                            = 4 * 4

                           = 16 cm²

Area of composite shape = 8 + 16

                                         = 24 cm²

14) Figure1:

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

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

Figure2:

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

 Area of figure2 = 6*2

                            = 12 cm²

Area of composite shape = 10 + 12

                                         = 22 cm²

15) Figure 1 & figure 2:

          Figure 1 and  figure 2 are congruent triangles

            base = b = 3 cm & h= 4 cm

= b *h

= 3 * 4

= 12 cm²

Figure3:

   Figure 3 is a square.

     side =  3 cm

 Area of figure3 = side *side

                            = 3 * 3

                           = 9 cm²

Area of composite shape = 12 + 9

                                         = 21 cm²                      

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The probability that the mean amount of cereal x-bar in 5 randomly selected boxes is at most 9.65 is 0.0001.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

Mean μ=9.70

Sample size=n=5

standard deviation=σ = 0.03

Now in order to use the table we have to to figure out z value.

z=(x-μ)/σ

z=(9.65-9.70)/0.0134

z=-3.73

From the probability index tables, so P(z≤-3.73)=0.0001

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Answer:

To solve the equation sin 2x = 4cos 2x, we can use the trigonometric identity:

sin 2x = 2sin x cos x

cos 2x = cos^2 x - sin^2 x = 1 - 2sin^2 x

Substituting these identities into the equation, we get:

2sin x cos x = 4(1 - 2sin^2 x)

Expanding and simplifying, we get:

2sin x cos x = 4 - 8sin^2 x

Rearranging, we get:

8sin^2 x + 2sin x cos x - 4 = 0

We can factor the left-hand side of this equation:

(2sin x - 1)(4sin x + 4) = 0

Setting each factor equal to 0 and solving for sin x, we get:

2sin x - 1 = 0 or 4sin x + 4 = 0

sin x = 1/2 or sin x = -1

If sin x = 1/2, then x is a multiple of π/6, so the general solution in this case is:

x = π/6 + 2πn or x = 5π/6 + 2πn

Where n is an integer.

If sin x = -1, then x is a multiple of π plus an odd multiple of π/2, so the general solution in this case is:

x = π/2 + πn

Where n is an integer.

Therefore, the general solution for sin 2x = 4cos 2x is:

x = π/6 + 2πn or x = 5π/6 + 2πn or x = π/2 + πn

Where n is an integer.

Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

The x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be 36x^7y^2.

In the given problem, we have the binomial expansion of (x - y)^n, which includes the term 126x^5y^4.

We will use the binomial coefficient formula to find the coefficients of the desired terms.

The general term of the binomial expansion is given by:

T(k) = C(n, k) * x^(n-k) * y^k

where C(n, k) is the binomial coefficient and can be calculated as:

C(n, k) = n! / (k!(n-k)!)

From the given term, 126x^5y^4, we have:

126 = C(n, 4)

x^5 = x^(n-4)

y^4 = y^4

Now we can find the value of n:

126 = n! / (4!(n-4)!)

Let's solve for n:

126 * 4! = n! / (n-4)!

504 = n! / (n-4)!

Now, we will find the coefficients of the terms x^6y^7 and x^7y^2.

The x^6y^7 term in the expansion will be:

T(k) = C(n, 7) * x^(n-7) * y^7

Since x^5 = x^(n-4), we have n - 4 = 5, so n = 9.

Substituting the value of n:

T(k) = C(9, 7) * x^2 * y^7

Using the binomial coefficient formula:

C(9, 7) = 9! / (7!2!) = 36

So, the x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be:

T(k) = C(n, 2) * x^(n-2) * y^2

We already found that n = 9, so substituting the value of n:

T(k) = C(9, 2) * x^7 * y^2

Using the binomial coefficient formula:

C(9, 2) = 9! / (2!7!) = 36

So, the x^7y^2 term in the expansion will be 36x^7y^2.

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Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }

Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}

Answer: 18

Step-by-step explanation:

Step-by-step explanation:

you are in college, and need help with that ?

remember,

a > b

then also

a × c > b × c

c × a > c × b

and that is what we have here

a = 20, b = 30, c = 1/2

so, 30×1/2 is larger.

because 30 > 20.

a = 2/3, b = 2, c = 15

15×2 is, of course, larger.

because 2 > 2/3.

Answer:

1. 90

2. 468

Step-by-step explanation:

Answer:

Question 1). 45 in

Question 2). 234 m

Step-by-step explanation:

Area = base x height x 1/2

10 x 9 = 90

90 x 1/2 = 45

Question 2)

30 x 15.6 = 468

468 x 1/2 = 234 m

To convert the expression, Y=x^2-64/16 into the polar form, we would have: r = 2 / √(sin^2θ + cos^2θ).

The polar form of a mathematical expression is a way of representing complex numbers using their magnitude and angle.

For a complex number z = a + bi, where a and b are real numbers, its polar form is given by z = r(cosθ + i sinθ), where r is the magnitude of z and θ is the angle that z makes with the positive real axis.  

So, for the given expression, the polar form can be converted this way:

r^2 sin^2θ = r cos^2θ - 4

r^2(sin^2θ + cos^2θ) = 4

r = 2 / √(sin^2θ + cos^2θ)

Therefore, the polar form is r = 2 / √(sin^2θ + cos^2θ).

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The correct option C: the domain can contain only whole number for the function of the number of students attending  dance.

The collection of all possible inputs for a function is its domain. Graphing and algebra are the two techniques used to determine a function's domain. Use the equation to consider inputs that would result in an undefined value, including such fractions and square roots, in order to obtain the domain algebraically. Decide where the function is graphed and note the x-values of the region(s) to locate it by graphing.

For the given question:

x axis - number of students attending dance classes n.

y axis - cost of hosting a dance

Domain - is the input value taken from x axis only.

So, all value lying on x axis ate taken as the domain for the function.

Thus,  the domain can contain only whole number for the function of the number of students attending dance classes.

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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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If the group is too large to survey everyone, you may consider using a sampling technique to select a representative subset of the group for the survey.

Here are some common sampling techniques you could use:

When selecting a sampling technique, it's important to consider the size of the group, the available resources, and the research question. It's also important to ensure that the sampling technique is unbiased and representative of the group being studied.

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Answer:

12 dozen eggs is 12x12 which is 144 eggs there are 12 eggs in 1 dozen so 12+12+12+12+12+12+12+12+12+12+12+12=144 hope that helped

144

1dozen =12 eggs

12×12=144

we can rewrite cos³(x) in terms of first powers of cosine as:

cos³(x) = (1/4)(3cos(x) + cos(3x))

What is power-reducing identity?

trigonometric identities that enable us to translate higher-order trigonometric expressions into lower-order trigonometric expressions.

We can use the power-reducing identity:

[tex]cos^3(x) = (1/4)(3cos(x) + cos(3x))[/tex]

To see how this identity is derived, we start with the double-angle identity:

[tex]cos(2x) = 2cos^2(x) - 1[/tex]

Rearranging this equation, we get:

[tex]cos^2(x) = (1/2)(1 + cos(2x))\\\\cos^3(x) = (1/2)cos(x)(1 + cos(2x))\\\\cos^3(x) = (1/2)cos(x) + (1/2)cos(x)cos(2x)\\\\cos^3(x) = (1/2)cos(x) + (1/2)cos(x)[2cos^2(x) - 1]\\\\cos^3(x) = (1/2)cos(x) + (1/2)(2cos^3(x) - cos(x))\\\\cos^3(x) = (1/4)(3cos(x) + cos(3x))[/tex]

Therefore, we can rewrite cos³(x) in terms of first powers of cosine as:

cos³(x) = (1/4)(3cos(x) + cos(3x))

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The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.

Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.

The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.

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Answer:

Step-by-step explanation:

The quadratic formula is used to find the zeros of a quadratic equation. The zeros are the values of x that make y equal to zero. The quadratic formula is:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

For the equation y = 3x² - 10x + 5, we have:

a = 3 b = -10 c = 5

Substituting these values into the quadratic formula, we get:

x = (-(-10) ± sqrt((-10)² - 4(3)(5))) / 2(3)

Simplifying this expression gives us:

x = (10 ± sqrt(100 - 60)) / 6

x = (10 ± sqrt(40)) / 6

x = (10 ± 2sqrt(10)) / 6

x = (5 ± sqrt(10)) / 3

Therefore, the zeros of the quadratic equation y = 3x² - 10x + 5 are (5 + sqrt(10))/3 and (5 - sqrt(10))/3.

or b

An observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.

To determine the outliers in a dataset using the five-number summary, we need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).

IQR = Q3 - Q1

Where

Q1 = 52

Q3 = 63

So, we have

IQR = 63 - 52

IQR = 11

An observation is considered an outlier if it is:

Below Q1 - 1.5 × IQR

Above Q3 + 1.5 × IQR

Substituting the values, we get:

Below 52 - 1.5 × 11 = 35.5

Above 63 + 1.5 × 11 = 79.5

Therefore, an observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.

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