3. Consider the function f(x) = x + 3x for the interval I = (-1,3) (a) Clearly state the assumptions of the mean value theorem and show that they are satisfied for f(x) in 1 (b) What does the mean value theorem say should happen in I? your answer should be a grammatical sentence. (C) Find all points -1

Based on the total amount of stamps that Noah has, we can calculate that those showing famous athletes number 625 stamps.

The percentage that shows famous athletes is:

= 100% - U.S. Presidents - animals

= 100% - 30% - 45%

= 25%

With a collection of 2,500 stamps, the number that is for famous athletes is:

= 2,500 x 25%

= 625 stamps

In conclusion, 625 stamps show famous athletes.

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Answer:

7,620

Step-by-step explanation:

When you move the decimal place 3 place to the right you get 7,620

I hope this helps!

Answer:

linear

y = 2.75x

Step-by-step explanation:

Price: $2.75/lb

Let y = cost.

Let x = number of pounds.

equation:

y = 2.75x

Linear equation

This is a direct proportion, so it is a linear equation.

For equal changes in x, you get equal changes in y.

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

The interpretation of the slope is that the FICO credit score increases.

The interpretation of the intercept is that it is the home equity when FICO credit score.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, a linear equation that models the home equity using FICO credit score is given by;

y = mx + b

y = 1798x + 0

In conclusion, we can logically deduce that the slope is 1798 and it represents the explanatory variable and an increase in FICO credit score because it is positive.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The third person owns 1/4 (or three twelfths) of the franchise.

To find the fraction of the franchise owned by the third person, we need to add the fractions owned by the first and second person and subtract it from the whole.

The first person owns 7/12 of the franchise, and the second person owns 1/6 of the franchise. To add these fractions, we need to find a common denominator. The common denominator for 12 and 6 is 12.

Converting the fractions to have a denominator of 12:

First person's ownership: (7/12) = (7 * 1/12) = 7/12

Second person's ownership: (1/6) = (1 * 2/12) = 2/12

Adding the fractions: (7/12) + (2/12) = 9/12

Now, we subtract the sum from the whole to find the third person's ownership. The whole is equal to 12/12.

Third person's ownership: (12/12) - (9/12) = 3/12

Simplifying the fraction, we get: 3/12 = 1/4

Therefore, the third person owns 1/4 (or three twelfths) of the franchise.

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Answer:

complete solution at jemrare dot com

Step-by-step explanation:

Answer:

728 kilograms

Step-by-step explanation:

First, you would find 30% of 560. To find 30% of 560, you would do 0.30 times 560, to get 168.

Then, you would add 560 and 168 together, to get 728.

The bakery used 728 kilograms this month.

30/15 = 2

Since 2 is a natural number, a whole number and an integer, so is 30/15.

The value of the integral from 0 to 7 of the function f(x) multiplied by α(x) is equal to 24.

To compute the integral \(\( \int_{0}^{7} f(x) \cdot \alpha(x) \, dx \)\), we first need to evaluate the product of the function x \(\( \int_{0}^{7} f(x) \cdot \alpha(x) \, dx \)\) and the piecewise function \(\( \alpha(x) = 3I(x-1) + 2I(x-4) + I(x-5) + 4I(x-6) \),\\\) where I  represents the unit step function.

Step 1: Evaluate the product \(\( f(x) \cdot \alpha(x) \)\) over the interval [0, 7].

For \(\( 0 \leq x < 1 \), \( \alpha(x) = 0 \)\), so the product \(\( f(x) \cdot \alpha(x) = 0 \).\)

For \(\( 1 \leq x < 4 \), \( \alpha(x) = 3 \), so \( f(x) \cdot \alpha(x) = (x^2 - 3x + 1) \cdot 3 \).\)

For \(\( 4 \leq x < 5 \), \( \alpha(x) = 2 \), so \( f(x) \cdot \alpha(x) = (x^2 - 3x + 1) \cdot 2 \).\)

For \(\( 5 \leq x < 6 \), \( \alpha(x) = 1 \), so \( f(x) \cdot \alpha(x) = (x^2 - 3x + 1) \cdot 1 \).\)

For \(\( 6 \leq x \leq 7 \), \( \alpha(x) = 4 \), so \( f(x) \cdot \alpha(x) = (x^2 - 3x + 1) \cdot 4 \).\)

Step 2: Integrate the product \(\( f(x) \cdot \alpha(x) \)\) over the interval [0, 7].

The integral \(\( \int_{0}^{7} f(x) \cdot \alpha(x) \, dx \)\) can be computed by evaluating the integral of each piece separately and adding them together:

\(\[\int_{0}^{7} f(x) \cdot \alpha(x) \, dx = \int_{1}^{4} 3(x^2 - 3x + 1) \, dx + \int_{4}^{5} 2(x^2 - 3x + 1) \, dx + \int_{5}^{6} (x^2 - 3x + 1) \, dx + \int_{6}^{7} 4(x^2 - 3x + 1) \, dx\]\)

After performing the integrations and evaluating the definite integrals, the result is 24.

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Answer:

None because 78 * 7 = 546

Step-by-step explanation:

None of the options equal to 546.

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

Answer:

c is it

Step-by-step explanation:

a p e x

An equivalent expression is an expression that is equal in value to a given expression. For example, consider the following expression: 4x + 2y

An equivalent expression is an expression that represents the same value as a given expression, regardless of the specific values of any variables that appear in the expression. Equivalent expressions can be obtained by applying the rules of algebra, such as the associative, commutative, and distributive properties.

This expression is equivalent to the following expressions:

2(2x + y)

2y + 4x

(4 + 2)x + 2y

All of these expressions are equivalent because they all represent the same value, regardless of the specific values of x and y. They can all be simplified to the same expression by applying the rules of the algebra.

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Answer:

They would vary directly because more number of workers means more pieces in given time and vice versa.

Step-by-step explanation:

Answer:

6*6=36

Step-by-step explanation:

6*6. 6 with exponent of 2=36

The expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³

The cube box has a side length of 9.

So, the volume of the box is:

V = 9³

The sphere has a radius of 4.5.

So, the volume of the sphere is:

v = 4/3π(4.5)³

Calculate the difference between both volumes:

d = 9³ - 4/3π(4.5)³

Hence, the expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³

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Answer: that is answer d

Step-by-step explanation:

2023 edge

The average speed of the car while taking photos in m/s is 1.6 m/s

Total photos taken = 2

Time taken = 0.5 seconds

Distance = 0.8m

Thus, this can be noted as -

Distance = Marks on the road between the two photos = 0.8 meters

Time = Time between the two photos = 0.5 seconds

Speed is defined as the rate at which a distance travelled or a height reached changes. It has a time component. In the given case, the speed camera is taking photos and we are required to calculate the average speed of the car

Calculating the speed -

Average Speed = Distance ÷ Time

Substituting the values -

= 0.8 /0.5

= 1.6

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The Height of tree is around 8.33 feet tall.

In science, we work out the Height of an item utilizing distance and points. Distance is the even distance between the items, and point is the point over the level of the article's top, which gives the item's level.

We can utilize the rule of comparable triangles.

The hypotenuse of this triangle would be the line associating Jenny's eyes to the highest point of the tree (we should refer to this distance as "h").

We can set up the accompanying extent between the two triangles:

h / 20 = (h + 5) / 8

To solve for "h", we can cross-multiply and simplify:

8h = 20(h + 5)

8h = 20h + 100

12h = 100

h = 8.33 feet

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hajshsbsgvsnshhsysabaoababzha usiwonsbsgsuwjanajaiownwnsdhbxksosbesmksi

basta yan yong answer

Answer:

AB = 154

Step-by-step explanation:

Triangle Rectangle ABC = 90

Sen 38°=0.616 = 154/250

Sen 52°=0.788 =197/250

AC =250

AB = 154

BC = 197

Answer:

\( {x}^{4} \)

Step-by-step explanation:

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

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression when simplified is equal to x⁴.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as shown below,

(-x²)²

= (-x × -x)²

Since the product of two negatives is always positive, therefore, we can write,

= -x² × -x²

As per the rule of exponents, the expression can be written as,

= x⁴

Hence, the value of the given expression when simplified is equal to x⁴.

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The distance between P₅ and P₆ is √(1 + (π/2 - π)² + (π - π/2)²).

a) The distance between points P₁ = (1, 1, 2) and P₂ = (0, 2, 3) can be calculated using the Euclidean distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²) Substituting the coordinates of the points into the formula: d = √((0 - 1)² + (2 - 1)² + (3 - 2)²) = √((-1)² + 1² + 1²) = √(1 + 1 + 1) = √3 Therefore, the distance between P₁ and P₂ is √3.

b) The distance between points P₃ = (2, π/3, 1) and P₄ = (4, π/2, 3) can be calculated using the same Euclidean distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²) Substituting the coordinates of the points into the formula: d = √((4 - 2)² + (π/2 - π/3)² + (3 - 1)²) = √(2² + (π/6)² + 2²) = √(4 + π²/36 + 4) = √(8 + π²/36) Therefore, the distance between P₃ and P₄ is √(8 + π²/36).

c) The distance between points P₅ = (3, π, π/2) and P₆ = (4, π/2, π) can be calculated using the Euclidean distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²) Substituting the coordinates of the points into the formula:

d = √((4 - 3)² + (π/2 - π)² + (π - π/2)²) = √(1² + (π/2 - π)² + (π - π/2)²) = √(1 + (π/2 - π)² + (π - π/2)²) = √(1 + (π/2 - π)² + (π - π/2)²)

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Answer:

1,980.25cm^2

Step-by-step explanation:

445mm=44.5cm
44.5^2=1,980.25

Given:

Rahul and Swapnil brought an equal amount of money for shopping.

Rahul spend rupees 95 and Swapnil spend rupees 350.

After that Swapnil had \(\dfrac{4}{7}\) of what Rahul had left.

To find:

How much money did Rahul have left after shopping.

Solution:

Let x be the amount brought by both Rahul and Swapnil.

Rahul spend rupees 95 and Swapnil spend rupees 350. So, the remaining amounts are:

Rahul's remaining amount = \(x-95\)

Swapnil's remaining amount = \(x-350\)

After that Swapnil had \(\dfrac{4}{7}\) of what Rahul had left.

\((x-350)=\dfrac{4}{7}\times (x-95)\)

\(7(x-350)=4(x-95)\)

\(7x-2450=4x-380\)

Isolate the variable terms.

\(7x-4x=2450-380\)

\(3x=2070\)

\(x=\dfrac{2070}{3}\)

\(x=690\)

Now, the remaining amount of Rahul is:

\(x-95=690-95\)

\(x-95=595\)

Therefore, the correct option is B.

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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Answer:

slope= \(\frac{2}{3}\) or 0.6

y-intercept= -1

y= 0.6x+ -1

Step-by-step explanation:

slope= \(\frac{rise}{run}\)

the y-intercept is where the line crosses the y axis

the equation for a line is y=mx+b where m is slope and  b is y

Answer:

Slope: 1.5

Y-intercept: (0,-1)

Equation of the line: y=1.5x-1

Step-by-step explanation:

Slope=

change of y/change of x=

3/2 (or 1.5)

Equation of the line:

y=1.5x+b

-1=1.5(0)+b

-1=b

y=1.5x-1

the area of shape below is 42

The area of the shape is 396 square cm.

A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.

For the given situation,

The diagram shows the polygon.

Let us consider the polygon as two rectangles as opposite sides are parallel and all the angles are right angle as shown below.

The rectangle ABCD has the dimensions length is 10 cm and breadth is 27 cm.

The rectangle DEFG has the dimensions length is 14 cm and breadth is  9 cm.

Thus the area of the polygon is the sum of areas of rectangle ABCD and DEFG.

The formula of area of rectangle, \(A =( length)(breadth)\)

Then total area of the shape is

⇒ \((27)(10)+(14)(9)\)

⇒ \(270+126\)

⇒ \(396\)

Hence we can conclude that the area of the shape is 396 square cm.

Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.

Since Point T is on line segment SU, then S, T, and U are collinear.

Collinear points refers to the points that lies on the same straight line.

IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.

ST + TU = SU

Given:

ST = 3x + 2

TU = 3x + 4

SU = 5x + 9

Substitute the expressions in the equation and solve for x.

ST + TU = SU

3x + 2 + 3x + 4 = 5x + 9

3x + 3x - 5x = 9 - 2 - 4

x = 3

Substitute the value of x in the expression for SU.

SU = 5x + 9

SU = 5(3) + 9

SU = 24

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