Rose and her grandfather started doing the newspaper crossword together every Sunday. They keep track of how long it takes them each week. The function f(x) gives the number of minutes the crossword takes during week x. What does f(3)>f(5) tell you?

Given the second difference, the table is quadratic.

A linear function is a function that has a single variable raised to the power of 1. An example is x + 2. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. An example is 2x² + 10x + 25.

First differences:

21 - 11 = 10

35 - 21 = 14

53 - 35 = 18

75 - 53 = 22

Due to the fact that the first difference is not the same, the function is not a linear function.

Second difference:

14 - 10 = 4

18 - 14 = 4

22 - 18 = 4

Due to the fact that the second difference is fairly constant, the function is a quadratic function.

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AB = BC = CD = DA

Hence, ABCD is a rhombus.

A parallelogram ABCD's diagonal AC bisects

We could employ the alternative internal angle rule to demonstrate that the diagonal AC bisects C, and by demonstrating that almost all sides are equal, you can conclude ABCD is a rhombus.

i) ABCD is a parallelogram.

∠DAC = ∠BCA (Alternate interior angles)  

∠BAC = ∠DCA (Alternate interior angles)  

However, it is given that AC bisects ∠A.

∠DAC = ∠BAC                                          

From equations (1), (2), and (3), we obtain

∠DCA  = ∠BAC = ∠DAC = ∠BCA              

Thus, ∠DCA = ∠BCA

Hence, AC bisects ∠C.

ii) From Equation (4), we obtain

∠DAC = ∠DCA

DA = DC (Side opposite to equal angles are equal)

However, DA = BC and AB = CD (Opposite sides of a parallelogram  are equal)

Thus, AB = BC = CD = DA

Hence, ABCD is a rhombus.

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Given:

The expression is

\(arcsine\left(\dfrac{\sqrt{2}}{2}\right)\)

To find:

The value of given expression.

Solution:

We have,

\(arcsine\left(\dfrac{\sqrt{2}}{2}\right)\)

It can be rewritten as

\(=\sin^{-1}\left(\dfrac{\sqrt{2}}{2}\right)\)

\(=\sin^{-1}\left(\dfrac{1}{\sqrt{2}}\right)\)

\(=\sin^{-1}\left(\sin \dfrac{\pi}{4}}\right)\)

\(=\dfrac{\pi}{4}\)

Therefore, the correct option is B.

Answer:

B

Step-by-step explanation:

got it right

Answer:

63.62 inches squared

Step-by-step explanation:

The formula for the area of a circle is πr^2

r (Radius) is half of the diameter

r = 9/2

r = 4.5in

π x 4.5^2=

π x 20.25 = 63.6172512352

to 2 dp: 63.62 inches squared.

Answer:

The area of a plate with a diameter of 9 is 63.585

Step-by-step explanation:

A = πr²  use 3.14 as pi

r = \(\frac{1}{2}\) d

\(\frac{1}{2}\) × 9 = 4.5

r = 4.5

A = 3.14 × 4.5²

A = 3.14 × 20.25

A = 63.585

Hope this helps!

The ratio of junior to adult = 6/5

What is proportion?

An equality between two ratios. According to proportion, if 2 sets of given numbers area unit increasing or decreasing within the same quantitative relation, then the ratios area unit aforesaid to be directly proportional to every different.

Main body:

Given - data in the question

To find answer the question

Solution - Let no of junior, children and adults be x, y, z respectively.

Now, ratio of junior to children = 1/3

So, x = 3y

Ratio of children to adult = 5/2

So, 5y = 2z

.(2)

So, from (1) we get, y = x / 3

So, 5x / 3 = 2z

⇒5x = 6z

⇒ x/z=6/5

Hence, the ratio of junior to adult = 6/5

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Answer:

D

Step-by-step explanation:

It doesn't follow the rise over run rule

Answer:

I would say c and b

Step-by-step explanation:

I would say this because with out the number it would be that same thing and the same eqaution and  formation

we know ,

the probability=no of repeated value/total number

factorial of 3 and 2

and factorial of total number

=3ḷ×2ḷ/7ḷ

=3×2×1×2×1/7×6×5×4×3×2×1

=1/7×5×4×3

=1/420

=0.23809

or

=0.238

what is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

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The probability of choosing two green grapes is 0.10, while the probability of eating a green grape and then a red grape is 0.23.

Probability of choosing a green grape the first time:

Probability of choosing a green grape the second time:

Probability of choosing a green grape the first time:

Probability of choosing a green grape the second time:

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Answer:

\(x >12\)

\((12, \infty)\)

\(\{x\in\mathbb{R} : x>12 \}\)

Step-by-step explanation:

\(\dfrac{4}{9} x - 3 > \dfrac{7}{3}\)

\(\dfrac{4}{9} x > \dfrac{7}{3}+3\)

Multiply both sides by 9

\(4 x > 21+27\)

\(4 x > 48\)

Divide both sides by 4

\(x >12\)

Answer:

(a) \(x=\frac{19}{4}=4.75\)

(b) \(x=-\frac{1+\sqrt{193}}{6}\approx-2.4821, x=-\frac{1-\sqrt{193}}{6}\approx2.1487\)

Step-by-step explanation:

The detailed explanation is shown in the attached documents below.

2. The area of the cabin's window is 196 square inches.

3. The area of the doghouse is  32.5 square ft.

4. The farmer should purchase 2 begs of soil.

5. The artist needs 161.5 square in material to make the kite.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, while another contends that a trapezoid can have multiple pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid by that definition. However, the first definition excludes parallelograms from the definition of a trapezoid since it is one of the quadrilateral types that we have already mentioned.

2. The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.

The length of one parallel side is 10 inches. The length of the other parallel side is (10+4+4) inches = 18 inches.

The height of the trapezoid is 14 inches

The area of the trapezoid is 1/2 ×(10 + 18) × 14

= 196 square inches.

3.

The formula for the area of a trapezoid is 1/2 × (sum of parallel side) × height.

The length of one parallel side is 5 ft. The length of the other parallel side is (5+3) ft = 8 ft.

The height of the trapezoid is 5 ft.

The area of the trapezoid is 1/2 ×(5 + 8) × 5

= 32.5 square ft.

4.

The area of a parallelogram is the product of height and base.

The length of the base is (2.5 yards + 6.5 yard) = 9 yards

The height of the parallelogram is 6 yards.

The area of the parallelogram is 9 yards × 6 yards

= 54 square yards

Each beg can cover 40 square yards field.

The number of begs that the farmer need is 56/40 = 1.4  ≈2

5.

The area of the kite is half of the product of diagonals.

The length of diagonals are (8.5 in + 8.5 in) = 17 in and (6 in  + 13 in) = 19 in

The area of the kite is (17×19)/2 = 161.5 square in.

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Answer:

options C and D is the answer

Answer:

5 ÷ 5 = 1

125 5 25

Step-by-step explanation:

The number between the two it's the number of people who does both

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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The sum of squared regression is 650 (rounded to two decimal places).

The sum of squared regression is a calculation used in regression analysis to determine the proportion of the total variation in the dependent variable that can be explained by the independent variable(s).

To calculate the sum of squared regression, you need to follow these steps:

Step 1: Calculate the mean of the dependent variable.
Step 2: Calculate the predicted value of the dependent variable for each data point using the regression equation.
Step 3: Subtract the mean of the dependent variable from each predicted value and square the result.
Step 4: Sum up all the squared differences from Step 3.

Let's illustrate this with an example:

Suppose we have a regression model that predicts a student's test score (dependent variable) based on the number of hours they studied (independent variable). We have the following data:

Hours studied (X): 3, 4, 6, 7
Test score (Y): 70, 75, 85, 90

Step 1: Calculate the mean of the test scores:
\(\bar Y\) = (70 + 75 + 85 + 90) / 4 = 80

Step 2: Calculate the predicted values using the regression equation:
\(\hat Y\) = b₀ + b₁X
Assuming the regression equation is \(\hat Y\)  = 65 + 5X (where b₀ is the intercept and b₁ is the slope):

\(\hat Y_1\) = 65 + 5(3) = 80
\(\hat Y_2\) = 65 + 5(4) = 85
\(\hat Y_3\) = 65 + 5(6) = 95
\(\hat Y_4\) = 65 + 5(7) = 100

Step 3: Subtract the mean from each predicted value and square the result:
\((\hat Y_1 - \bar Y)^2\) = (80 - 80)² = 0
\((\hat Y_2 - \bar Y)^2\) = (85 - 80)² = 25
\((\hat Y_3 - \bar Y)^2\) = (95 - 80)² = 225
\((\hat Y_4 - \bar Y)^2\) = (100 - 80)² = 400

Step 4: Sum up all the squared differences:
0 + 25 + 225 + 400 = 650

Therefore, the sum of squared regression is 650 (rounded to two decimal places).

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The two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The vertex of a parabola in standard form, f(x) = a(x - h)² + k, is at the point (h, k).

We can rewrite the given equation, f(x) = x² - 2x - 8, in standard form by completing the square:

f(x) = x² - 2x - 8

= (x² - 2x + 1) - 1 - 8

= (x - 1)² - 9

So the vertex of the parabola is at the point (1, -9), where h = 1 is the x-coordinate of the vertex, and k = -9 is the y-coordinate of the vertex.

To verify that points (2, -8) and (0, -8) are symmetric about the vertex, we can calculate the axis of symmetry, which is x = h, or x = 1 in this case.

The distance between the vertex (1, -9) and the point (2, -8) is the same as the distance between the vertex and the point (0, -8), since these points have the same y-coordinate:

d((1, -9), (2, -8)) = d((1, -9), (0, -8))

Using the distance formula, we can calculate the left-hand side:

d((1, -9), (2, -8)) = √((2 - 1)² + (-8 - (-9))²)

= √(1 + 1)

= √(2)

Using the distance formula again, we can calculate the right-hand side:

d((1, -9), (0, -8)) = √((0 - 1)² + (-8 - (-9))²)

= √(1 + 1)

= √(2)

Hence, the two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).

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The first six digits of the mathematical sign PI are 3.14159.

Pi is a mathematical constant that is commonly used in geometry and trigonometry. The number is defined as the ratio of a circle's circumference to its diameter, and it is approximately 3.14159.

The value of PI has been computed to millions of decimal places, but the first six digits, which are 3.14159, are the most often used in computations.

The first six digits of the mathematical sign PI are 3.14159. These digits are frequently used to calculate the value of a circle's circumference or area. Pi is irrational, which means it can't be expressed as a fraction of two integers, and it goes on indefinitely without repeating.

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Answer: $44.10

Step-by-step explanation:

We are given our p, r, t in the problem.

p=40 (starting amount)

r=0.05 (5%)

t=2 (years)

With the given information, we can plug this into our equation.

B=p(1+r)^t

B=40(1+0.05)^2

B=44.1

There are 10,000,000,000 unique phone numbers that can be made with 10 digits using any single digit number (0-9) for each digit using combinations.

To determine how many phone numbers can be made with 10 digits, where any single digit number (0-9) can be used for any digit, follow these steps:

1. Understand that there are 10 possible digits (0-9) for each digit in the phone number.
2. Since there are 10 digits in the phone number, you need to calculate the total number of combinations by multiplying the number of possibilities for each digit.

To calculate this, simply raise the number of possible digits (10) to the power of the number of digits in the phone number (10):

10^10 = 10,000,000,000

So, there are 10,000,000,000 unique phone numbers that can be made with 10 digits using any single digit number (0-9) for each digit.

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Answer:

c

Step-by-step explanation:

The problem has no solution, because gift card will have negative price .

A system of equations is a set of multiple equations with multiple variables, where the goal is to find the values of the variables that satisfy all the equations simultaneously. It can be solved using different methods such as substitution, elimination and graphing.

This problem can be solved by setting up a system of equations and solving for the variables.

Let x be the cost of each gift card and y be the cost of each gift wrap.

According to the problem statement, we know that:

20x + 40y = $160 (where 20 gift cards and 40 gift wraps sell for $160)

10x + 30y = $110 (where 10 gift cards and 30 gift wraps sell for $110)

We can use these equations to find the value of x and y. To solve the system of equations, we can use the method of substitution.

We can solve the first equation for x:

x = ($160 - 40y) / 20

Now we can substitute this expression for x into the second equation:

10(($160 - 40y) / 20) + 30y = $110

Simplifying this equation:

8y = $50

then we can divide both sides by 8 to get:

y = $6.25

So each gift wrap costs $6.25

We can check our answer by substituting it back into the first equation to make sure it is consistent with the given information.

20x + 40($6.25) = $160

20x + $250 = $160

20x = -$90

x = -$4.5

We can see that x is negative, which is not a possible solution.

Therefore, the problem has no solution, because it is not possible to have negative prices for the gift cards.

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Answer:

its 58 degreese F

Step-by-step explanation:

start with 9*2 and that equals 18 then you subtract 18 from 76 which equals 58. that is your answer 59 degrees F

The sampling method described in the scenario is d. stratified sampling.

In stratified sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables. The researcher then randomly selects samples from each stratum in proportion to their representation in the population. This approach ensures that the sample is representative of the population's diversity.

In this case, the researcher has divided the population of teachers into two strata: male teachers and female teachers. By randomly selecting 50 male teachers and 50 female teachers, the researcher is ensuring that both genders are represented in the sample.

The researcher's intention is to have a sample that reflects the gender distribution of teachers in the population accurately. Therefore, stratified sampling is the appropriate method in this scenario.

Other sampling methods, such as systematic sampling, convenience sampling, random sampling, and cluster sampling, are not applicable because they do not specifically address the need to ensure proportional representation of genders in the sample.

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The expression for X⁻¹ is CD⁻¹B⁻¹A⁻¹.

To find the expression for the solution to C, substitute the given values into the equation X = CDBDA⁻¹:

X = CDBDA⁻¹

Now, solve for C:

C = X(DBDA⁻¹)⁻¹

To prove that det(X) = det(D)det(A - BD⁻¹C), we'll start with the expression for X and work towards the desired result:

X = CDBDA⁻¹

Let's denote M = DBDA⁻¹ for simplicity. Now, substitute M into the equation for X:

X = CM

Taking the determinant of both sides:

det(X) = det(CM)

Using the determinant property det(AB) = det(A)det(B):

det(X) = det(C)det(M)

Now, express M in terms of the given matrices:

M = DBDA⁻¹

= DB(A - BD⁻¹C)A⁻¹ (using the given expression A - BD⁻¹C)

Substituting this back into the equation for det(X):

det(X) = det(C)det(DB(A - BD⁻¹C)A⁻¹)

Applying the determinant property det(AB) = det(A)det(B):

det(X) = det(C)det(D)det(B(A - BD⁻¹C)A⁻¹)

Next, use the determinant property det(AB) = det(A)det(B) to expand the term B(A - BD⁻¹C)A⁻¹:

det(X) = det(C)det(D)det(B)det(A - BD⁻¹C)det(A⁻¹)

Since det(A⁻¹) is the inverse of det(A), it is equal to 1/det(A):

det(X) = det(C)det(D)det(B)det(A - BD⁻¹C)/det(A)

Now, rewrite the expression as:

det(X) = det(D)det(A - BD⁻¹C)det(CB)/det(A)

Using the property det(AB) = det(A)det(B) again, we have:

det(X) = det(D)det(A - BD⁻¹C)det(C)det(B)/det(A)

Since matrix B is a mxn matrix and matrix C is a nxm matrix, their determinants are equal:

det(X) = det(D)det(A - BD⁻¹C)det(B)det(B)/det(A)

det(B)det(B) is equal to the determinant of the square matrix B squared:

det(X) = det(D)det(A - BD⁻¹C)det(B²)/det(A)

Finally, we know that det(B²) is equal to the determinant of B multiplied by itself:

det(X) = det(D)det(A - BD⁻¹C)det(B)²/det(A)

Since we know that X is invertible, det(X) is nonzero, so we can divide both sides of the equation by det(X):

1 = det(D)det(A - BD⁻¹C)det(B)²/det(A)

det(D)det(A - BD⁻¹C)det(B)² = det(A)

Now, substituting the given value of 8 for det(X), we have:

det(D)det(A - BD⁻¹C)det(B)² = 8

This proves that det(X) = det(D)det(A - BD⁻¹C) = 8.

Finally, to find the expression for X⁻¹, we can use the fact that X = C

DBDA⁻¹:

X⁻¹ = (CDBDA⁻¹)⁻¹

= (ADB⁻¹C⁻¹D⁻¹B⁻¹A⁻¹C⁻¹)⁻¹

= CD⁻¹B⁻¹A⁻¹

Therefore, the expression for X⁻¹ is CD⁻¹B⁻¹A⁻¹.

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The probability that the selected volcano is cinder cone is P ( C ) = 13/37

The probability that the selected volcano is shield cone is P ( S ) = 18/37

The probability that the selected volcano is strato is P ( V ) = 6/37

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the selected volcano is cinder cone is P ( C )

Let the probability that the selected volcano is shield cone is P ( S )

Let the probability that the selected volcano is strato is P ( V )

Now , the total number of volcanoes = 13 + 6 + 18 = 37 volcanoes

And ,

The probability that the selected volcano is cinder cone is P ( C ) = 13/37

The probability that the selected volcano is shield cone is P ( S ) = 18/37

The probability that the selected volcano is strato is P ( V ) = 6/37

Hence , the probabilities are solved

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We know that:

The ideal selling price is P = $22,000

The price can vary dP = $1,200

let's define p as the variable that represents the possible prices of the car.

We will find that the absolute value equation that represents this is:

|p - $22,000| ≤ $1,200

Now let's see how we get that, using the initial information we can get:

The minimum price can be:

mP = P - dP = $22,000 - $1,200 = $20,800

The maximum price can be:

MP = P + dP = $22,000 + $1,200 = $23,200

Then the range of allowed prices is:

mP ≤ p ≤ MP

$20,800 ≤ p ≤ $23,200

To write this as an absolute value equation, we use the general formula:

Ix - average| ≤ amount that it can vary

Replacing it with our values we get:

|p - P| ≤ dP

|p - $22,000| ≤ $1,200

Concluding, the absolute value equation that we wanted to find is:

|p - $22,000| ≤ $1,200

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