Derek made a quilt for his cousin's doll. The quilt had a 7 × 7 array of different color square patches. If each patch is 1 _ in long, what is the area of the whole quilt? *

Answer:

2/5

Step-by-step explanation:

2 can also be written in fraction form as 2/1

So, you have 2/1 times 1/5. So, you multiply numerators and you multiply denominators.

Numerators: 2 times 1 =2

Denominators: 1 times 5 =5

So, you have 2/5

Conclusion: There is sufficient evidence to say that, this represents a difference from the national average

Step 1)

Null hypothesis

H  o : μ = 8.5

Alternative hypothesis

\(H_{1}:\mu\neq 8.5\)

Step 2)

i.e. Z critical values are for two-tailed alternative hypothesis at \(a-0.05 =\pm 1.96\)

Step 3)

We have been given,

Using the Z test statistic formula

Z = 2.17

Step 4 ) Z test statistic value is 2.17 > Z critical value 1.96

Therefore, we reject H0 at a-0.05

Step 5) Conclusion: There is sufficient evidence to say that, this represents a difference from the national average

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Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

Answer:

\((x-4)^2+(y-5)^2=49\)

Step-by-step explanation:

So we want to find the equation of a circle with the center at (4,5) and which passes through the point (-3,5).

First, recall the standard form for a circle, given by the equation:

\((x-h)^2+(y-k)^2=r^2\)

Where (h,k) is the center and r is the radius.

We already know that the center is (4,5). So, substitute 4 for h and 5 for k. Therefore, our equation is now:

\((x-4)^2+(y-5)^2=r^2\)

Now, we need to find the radius.

Remember that our circle passes through the point (-3,5). In other words, when x is -3, y is 5. So, substitute -3 for x and 5 for y to solve for r. Therefore:

\((-3-4)^2+(5-5)^2=r^2\)

Subtract within the parentheses:

\((-7)^2+(0)^2=r^2\)

Square:

\(49=r^2\)

Square root:

\(r=7\)

Therefore, the radius is 7.

So, substitute 7 into our equation, we will acquire:

\((x-4)^2+(y-5)^2=(7)^2\)

Square:

\((x-4)^2+(y-5)^2=49\)

So, our equation is:

\((x-4)^2+(y-5)^2=49\)

And we're done!

The interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

In this question we have an expression that combines polynomic and exponential expression, whose variable x cannot be cleared by analytical approaches, but by numerical and graphical methods. Herein we decide to find the interval by graphical methods, using a graphing tool:

First, write the function in explicit form (f(x) = 3 · x - eˣ). Second, find the two points such that the function goes through the x-axis (horizontal axis). Third, define the set of possible x-values by interval notation such that y > 0.

Then, the points of the function that are on the x-axis are (x₁, y₁) = (0.6191, 0) and (x₂, y₂) = (1.5121, 0). Then, the interval of the function f(x) = 3 · x - eˣ such that the function shall be positive is x ∈ (0.6191, 1.5121).

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Answer:

D.-610

Step-by-step explanation:

-6 ×4 =-24

7 times 3 =21

we can say that there are 15 male teachers for every 35 female teacher

\(\stackrel{\textit{\large ratio 1}}{\cfrac{15}{35}\qquad \cfrac{male}{female}} ~\hspace{10em} \stackrel{\textit{\large ratio 2}}{\cfrac{\stackrel{3}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{7}{~~\begin{matrix} 35 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{3}{7}\qquad \cfrac{male}{female}}\)

Answer:

Total cost of cementing the path = Rs. 17,000.

Step-by-step explanation:

Let the square garden be PQRS

Let the region inside the garden (PQRS) be KLMN.

Given the following data;

Length of sides of PQRS = 90m

Width of path = 5m

Cost = Rs. 10 per m²

Area of PQRS = 90 * 90

Area of PQRS = 8100m²

To find the area of KLMN;

KL = KN = 90 - (5 + 5)

KL = KN = 90 - 10

KL = KN = 80m

Area of KLMN = KL * KN

Substituting into the equation, we have;

Area of KLMN = 80 * 80

Area of KLMN = 6400 m²

Area of path = Area of PQRS - Area of KLMN

Area of path = 8100 - 6400

Area of path = 1700 m²

Total cost of cementing the path = Area of path * Cost

Total cost of cementing the path = 1700 * 10

Total cost of cementing the path = Rs. 17,000

Step-by-step explanation:

Area of the trapezoid = height x average of bases

                 area = 4 x (8+13)/2) = 42 in^2

Area of triangle  = 1/2 base * height   = 1/2 (13-8) * 4 = 10 in^2

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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In the given problem, the function f₁(x) = x² is already in the form of f(x), so f(x) = x². f₁(x) = x² is in the form of a polynomial function, specifically a quadratic function.

The form of a function typically refers to how the function is written or represented.

The form for f₁(x) = x² is a specific type of polynomial function called a quadratic function.

A quadratic function has the general form f(x) = ax² + bx + c, where a, b, and c are constants. In the case of f₁(x) = x², the coefficient of x² is 1, and the coefficients of x and the constant term are both 0. Therefore, the function can be written in the simpler form f(x) = x².

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The logarithmic equation log(x+9)-logx=3 has a solution of x = 0.0090

From the question, we have the following parameters that can be used in our computation:

log(x+9)-logx=3

Apply the quotient rule

So, we have

log((x + 9/x) = 3

Remove the logarithmic expression

So, we ave

(x + 9)/x = 10^3

Evaluate

(x + 9)/x = 1000

So, we have

1000x = x + 9

Subtract

999x = 9

So, we have

x = 0.0090

Hence, the solution is x = 0.0090

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We have the following situation:

We need to find the degree measure of each angle, A, and C since we already know that angle B = 90 degrees.

To answer this question, we need to remember that the sum of the interior angles of a triangle is equal to 180 degrees.

Then we can write the next equation to find the value of x as follows:

Now, we need to add the like terms as follows:

Now, we can subtract 90 from both sides of the equation:

If we divide both sides by 9, we finally have for x:

Therefore, the value for x = 10.

If we substitute the value of x into the corresponding expressions for angles A and C, then we have:

We can proceed in a similar way here. Then we have:

Therefore, in summary, we can say that:

[We already knew that the measure of angle B is 90 degrees (right angle).

We can also check that the sum of all the angles is equal to 180 degrees:

.]

The simplified polynomial in standard form that represents the result of subtracting (z-7)² from 62 is -z² + 14z + 13.

Given that, ( z - 7 )² is subtracted from 62.

To subtract ( z - 7 )² from 62, we first need to first expand this ( z - 7 )².

( z - 7 )²

( z - 7 )( z - 7 )

z( z - 7 ) - 7( z - 7 )

Apply distributive property

z×z - z×7 - 7×z -7×-7

z² - 7z - 7z + 49

z² - 14z + 49

Now, we can substitute this expression into the original equation:

62 - (z² - 14z + 49)

Simplifying, we get:

13 + 14z - z²

-z² + 14z + 13

Therefore, the simplified polynomial is -z² + 14z + 13.

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Answer:

D. 60.3

Step-by-step explanation:

Finding the mean,

M = (sum of values of data)/(number of data)

now, number of data = 9,

calculating the mean,

M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9

M = 543/9

M = 60.333

M = 60.3

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Your expression is a little unclear, but I am assuming your expression as:

\(7+\frac{2x}{4}=5\)

The solution would still clear your concept in anyway.

Answer:

The value of x = -4

Step-by-step explanation:

Given the expression

\(7+\frac{2x}{4}=5\)

solving the expression

\(7+\frac{2x}{4}=5\)

as 2x/4 =  x/2, so

\(7+\frac{x}{2}=5\)

subtract 7 from both sides

\(7+\frac{x}{2}-7=5-7\)

simplify

\(\frac{x}{2}=-2\)

Multiply both sides by 2

\(\frac{2x}{2}=2\left(-2\right)\)

simplify

\(x=-4\)

Thus, the value of x = -4

Answer:

9/26

Explanation:

• The total number in the class = 26

• Number of men = 17

Thus, the number of women

Therefore, the fraction of women:

Answer:

0

rate of change = y2 - y1 / x2 - x1

= -1 - -1 / -2 - -4 = 0/2 = 0

Answer:

14

Step-by-step explanation:

it's a simple matter of percentage on top of basic subtraction.

As calculated from the data (1/6)² is the probability of getting 5 of same number on all the dice.

b.)If we will limit the number of winners then we will be able to provide them with large prizes and that also by taking moderate rate from everyone.

Actually, the likelihood of winning is closer to one-third (25/72).

Carnival game organizers want you to believe, like I did, that a game is fair so that you will participate.

The likelihood that you would win a game was just about 1/3, so you probably wouldn't squander your money.

Therefore,

The likelihood of getting five of the same number on all six dice is (1/6)².

Probabilities are mathematical representations of the likelihood that an event will occur or that a statement is true.

Probability can also be expressed using a tree diagram.

The tree diagram makes it easier to organize and see all of the potential outcomes. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end.

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Answer:

h = 9 m

Step-by-step explanation:

\(V_{cone}=340\: m^3\)

diameter (d) = 12 m

\(\implies radius\:(r)= \frac{12}{2}=6\:m\)

\( \because \: V_{cone}= \frac{1}{3} \pi {r}^{2} h \\ \\ \implies \: h = \frac{3V_{cone}}{\pi {r}^{2} } \\ \\ \implies \: h = \frac{3(340)}{3.14 {(6)}^{2} } \\ \\ \implies \: h = \frac{1020}{113.04} \\ \\ \implies \: h = 9.02335456 \\ \\ \implies \: h \approx 9 \: m\)

The value of the variable 'x' is 273/27. Then the measure of the angle ∠DGH will be 2.43°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The diagram is given below.

Then the equation is written as,

∠EFA + ∠DGF = 180°

x - 5 + 73x - 365 = 180°

74x = 550

x = 273/27

Then the measure of the angle ∠DGF is given as,

∠DGF = 73(273/27) - 365

∠DGF = 177.57°

Then the measure of the angle ∠DGH will be calculated as,

∠DGH + ∠DGF = 180°

∠DGH + 177.57° = 180°

∠DGH = 2.43°

The value of the variable 'x' is 273/27. Then the measure of the angle ∠DGH will be 2.43°.

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Answer:

Both

Explanation:

Given the function:

• A power function is a function with a whole number as its exponent.

• A monomial is a polynomial that has only one term.

The given funtion has 5 as its exponent, thus, it sis a power function. Furthermore, it is a monomial, thus it is also a polynomial.

f(x) is both a power function and a polynomial.

a) There are 2^6 = 64 subsets total.

b)  There are 2^3 = 8 subsets total

c) There are 2^5 = 32 subsets total

d) There are 32^4 = 48 subsets total

e)  There are (6 choose 4) = 15 subsets total

f)   There are 32 = 6 subsets total

g) There are is (6 choose 4) - (3 choose 4) = 15 - 0 = 15 subsets total

h) There are (3 choose 1) * (3 choose 3) = 3  subsets total

a) There are 2^6 = 64 subsets total.

b)  Since we need to include elements 2, 3, and 5 in a subset, we have 3 elements fixed, and we need to choose 1, 2, or 3 elements from the remaining 3 elements (1, 4, and 6). Therefore, there are 2^3 = 8 subsets that contain the elements 2, 3, and 5.

c) There are 2^5 = 32 subsets that contain at least one odd number. This can be seen by noticing that if a subset does not contain any odd numbers, then it must be {2,4,6}, which is not a valid subset since it does not satisfy the condition that it be a subset of S.

d) There are 32^4 = 48 subsets that contain exactly one even number. To see why, notice that there are 3 choices for which even number to include (2, 4, or 6), and then there are 2^4 = 16 choices for which of the remaining 4 odd numbers to include in the subset.

e) There are (6 choose 4) = 15 subsets of cardinality 4. This is the number of ways to choose 4 elements from a set of 6.

f) Since we need to include elements 2, 3, and 5 in a subset of cardinality 4, we have 3 elements fixed, and we need to choose 1 element from the remaining 3 even elements, and 1 element from the remaining 2 odd elements. Therefore, there are 32 = 6 subsets of cardinality 4 that contain the elements 2, 3, and 5.

g) The number of subsets of cardinality 4 that contain at least one odd number is equal to the total number of subsets of cardinality 4 minus the number of subsets of cardinality 4 that contain only even numbers. This is (6 choose 4) - (3 choose 4) = 15 - 0 = 15.

h) The number of subsets of cardinality 4 that contain exactly one even number is equal to the number of ways to choose 1 even number out of 3, and then the number of ways to choose 3 odd numbers out of 3. This is (3 choose 1) * (3 choose 3) = 3.

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In relation to the angle L of the right triangle the sides are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.

The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.

Let's identify the sides  j,  k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.

Therefore,

The hypotenuse side is the longest side of a right triangle.

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Answer:

as it a cyclic quadrilateral

its opposite sides sum be 180

z/2+z/4+30=180

2z+z/4=150

3z/4=150...z=200

angles...

b=z/2=200/2=100

d=80

e=200-59=141

c=180-141=39

Answer:

The half-life of this substance is of 569.27 days.

Step-by-step explanation:

Amount of a substance after t days:

The amount of a substance after t days is given by:

\(P(t) = P(0)e^{-kt}\)

In which P(0) is the initial amount and k is the decay rate, as a decimal.

Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.

This means that \(P(300) = 0.694P(0)\). We use this to find k.

\(P(t) = P(0)e^{-kt}\)

\(0.694 = P(0)e^{-300k}\)

\(e^{-300k} = 0.694\)

\(\ln{e^{-300k}} = \ln{0.694}\)

\(-300k = \ln{0.694}\)

\(k = -\frac{\ln{0.694}}{300}\)

\(k = 0.0012\)

So

\(P(t) = P(0)e^{-0.0012t}\)

What is the half-life (in days) of this substance?

This is t for which P(t) = 0.5P(0). So

\(0.5P(0) = P(0)e^{-0.0012t}\)

\(e^{-0.0012t} = 0.5\)

\(\ln{e^{-0.0012t}} = \ln{0.5}\)

\(-0.0012t = \ln{0.5}\)

\(t = -\frac{\ln{0.5}}{0.0012}\)

\(t = 569.27\)

The half-life of this substance is of 569.27 days.