When she was practising for the 10K, Mirin timed herself.
Her times ranged from 66 minutes down to 54 minutes.

a) Write her times in tolerance notation as in (.... ± ...) minutes.

b) Now calculate her tolerance using percentages as.... mins (± ...%).

Answer:

The first few multiples of 6 and 9 are (6, 12, 18, 24, 30, . . . ) and (9, 18, 27, 36, . . . )

The point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the points at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j, we need to find the gradient vector of the function and equate it to the given direction vector.

The gradient vector of the function f(x, y) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x - 2

∂f/∂y = 2y - 6

Setting the gradient vector equal to the given direction vector i + j:

[2x - 2, 2y - 6] = [1, 1]

Equating the corresponding components, we have:

2x - 2 = 1

2y - 6 = 1

Solving these equations, we get:

2x = 3  =>  x = 3/2

2y = 7  =>  y = 7/2

Therefore, the point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

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Answer: x = -6

Step-by-step explanation:

4x−3y=−24

x intercept is the value ox when y = 0

4x−3y=−24

4x−3*0=−24

4x = -24

x = -6

Answer:

Step-by-step explanation:

7=c/3-1

add 1 to both sides

8=c/3

to get rid of the 3, multiply both sides 3

24=c

Answer: 1/2 converted into a percent is 50% and 1/2 converted into a decimal is 0.5

Step-by-step explanation:

This is true because what is half of 2? 1 right. Think of 2 being 100. Half of 100 is 50. This is why 1/2 as a percent is 50%.

Hope this helps :)

P.s. if you can give me a brainliest that would be cool.

The rate at which Alicia is riding is 10 miles per hour.

According to the information provided, Alicia rides for 4 hours and is 42 miles from her house. After riding for 7 hours, she is 72 miles away. Let us denote the rate or speed at which Alicia is riding by `r` miles per hour. Therefore, Alicia's rate is:

(72 - 42)/(7 - 4) = 10 miles per hour.

We are supposed to check whether the solution makes sense. Alicia rode for 7 - 4 = 3 hours. At 10 miles per hour, she should have traveled 3 × 10 = 30 miles. She was initially 42 miles from home, and so she should have traveled 42 + 30 = 72 miles.

As given, the distance covered by her in 7 hours is 72 miles. So the solution is correct. Therefore, the rate at which Alicia is riding is 10 miles per hour.

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Answer:

Fraction of the garden used =  \(\frac{5}{8}\)

Step-by-step explanation:

The fifth graders to plant a butterfly garden.

We are given that

Clover grows in ½ of the garden

Daisies grow in ¼ of the garden

Coneflowers grow in ⅛ of the garden

milkweed grows in ⅛ of the garden

The fifth graders notice that the butterflies land on the clover and milkweed.

We are asked to find out the fraction of the garden that the butterflies used.

Fraction of the garden used = clover + milkweed

Fraction of the garden used =  \(\frac{1}{2} + \frac{1}{8}\)

The LCM of 2 and 8 is 8

Fraction of the garden used =  \(\frac{4 +1}{8}\)

Fraction of the garden used =  \(\frac{5}{8}\)

Therefore, the butterflies used \(\frac{5}{8}\) fraction of the garden.

The required, expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

To find the value of b in the expression (3 + 4i)^2, we can simply expand the expression and identify the coefficient of the imaginary part.

(3 + 4i)² = (3 + 4i)(3 + 4i)

Using the FOIL method, we can multiply the terms:

= 3 * 3 + 3 * 4i + 4i * 3 + 4i * 4i

= 9 + 12i + 12i + 16i²

Since i² is defined as -1, we can substitute it:

= 9 + 12i + 12i - 16

= -7 + 24i

Comparing the expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

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Complete question:

(3+4i)²

if the expression above is written in the form a+ bi, where a and b are real numbers, what is the value of b?

Answer:

G

Step-by-step explanation:

Red marble probably currently: 12/32 = 3/8

Guess and check (using the multiple choice answers):

F: 12 + 13 / 32 + 13 = 25/45 = 5/6; does not equal 3/5

G: 12 + 18 / 32 + 18 = 30/50 = 3/5; does equal 3/5

H: 12 + 28 / 32 + 28 = 40/60 = 2/3; does not equal 3/5

J: 12 + 32 / 32 + 32 = 44/64 = 11/16; does not equal 3/5

K: 12 + 40 / 32 + 40 = 52/72 = 13/18; does not equal 3/5

Answer:

-6 because its lower than 0

Step-by-step explanation:

Answer:

yes, It's  a right triangle.

Step-by-step explanation:

First, lets convert the 4 feet into inches. You get 48 inches. 48 squared plus 55 squared equals 5329 which is equal to 73^2.

The given statement is true.

The limit of a function as x approaches a certain value is the value that the function approaches as x gets arbitrarily close to that value. In this case, we are given the function f(x) and asked to evaluate the limit as x approaches 1.

To determine the limit, we need to examine the behavior of the function as x approaches 1 from both sides (-1 and 1). If the function approaches the same value from both sides, the limit exists and is equal to that value.

In this case, the given function f(x) does not depend on x, and it is simply $(₂) - ₁. Regardless of the value of x, the function will always evaluate to 1. Therefore, as x approaches 1, the function approaches 1 from both sides.

Hence, the statement "lim fx $(₂) - ₁ 1 x-1- True" is true.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}}\implies \cfrac{-3}{4+3}\implies -\cfrac{3}{7}\)

Answer:

-0.75

Step-by-step explanation:

Hope that helps you have a great day!

Step-by-step explanation:

The formula to find the arc length of a circle is:

arc length = (central angle / 360 degrees) x 2πr

where r is the radius of the circle.

In this case, we are given the central angle of the arc, which is 36 degrees, and the length of the chord AB, which is 3 units. To find the radius of the circle, we need to use some trigonometry.

Since angle ABC is an inscribed angle that intercepts arc AC, it is half the measure of arc AC. So, we can find the measure of arc AC as 2 times the measure of angle ABC, which is:

m(arc AC) = 2 x m∠ABC

m(arc AC) = 2 x 36

m(arc AC) = 72 degrees

Now, let's use the law of cosines to find the radius of the circle:

c^2 = a^2 + b^2 - 2ab cos(C)

where a and b are the sides of the triangle and c is the side opposite the angle C.

In triangle ABC, we know that side AB has length 3 units and angle ABC has measure 36 degrees. We also know that angle BAC is a right angle, since it is formed by a chord and a radius of a circle. So, we can use trigonometry to find the length of side AC:

sin(36) = AC / 2r

2r = AC / sin(36)

r = AC / (2 sin(36))

Using the law of cosines, we can find AC:

c^2 = a^2 + b^2 - 2ab cos(C)

AC^2 = 3^2 + (2r)^2 - 2(3)(2r) cos(36)

AC^2 = 9 + 4r^2 - 12r cos(36)

Substituting the expression for r from above, we get:

AC^2 = 9 + 4/((2 sin(36))^2) - 12/((2 sin(36))) cos(36)

AC^2 = 9.259

Taking the square root of both sides, we get:

AC ≈ 3.04 units

Now that we know the radius of the circle and the central angle of the arc, we can use the formula for arc length to find the length of arc AC:

arc length = (central angle / 360 degrees) x 2πr

arc length = (72 / 360) x 2π(3.04)

arc length ≈ 3.03 units

Therefore, the length of arc AC is approximately 3.03 units, rounded to the nearest hundredth.

Answer:

he would only be able to bring 2 friends

Step-by-step explanation:

250- 100= 150    cost of table

150/ 40=3.75   cost of friends

He was would not be able to bring a .75 of a friend so you would have to round down.

The area swept clean by the wiper blade is 221.128 square inches.

To find the area swept clean by the wiper blade, we can calculate the area of the sector of a circle that the blade moves through.

The radius of the circle that the blade moves through is the length of the arm, which is 19 inches.

The angle that the blade moves through is 105 degrees.

To calculate the area of the sector, we need to convert the angle to radians:

105 degrees * (π/180) = 1.8326 radians (rounded to 4 decimal places)

The area of the sector is then:

(1/2) * r^2 * θ = (1/2) * (19^2) * 1.8326 = 325.628 square inches (rounded to 3 decimal places)

However, the area swept clean by the wiper blade is not the full area of the sector, as the blade itself has a width of 11 inches. Therefore, we need to subtract the area of the triangle formed by the blade and the two radii of the sector that intersect at the blade's pivot point.

The length of one of the radii is the length of the arm, which is 19 inches. The length of the other radius is 19 - 8 = 11 inches since the blade is mounted 8 inches from the pivot point.

Using the formula for the area of a triangle:

(1/2) * base * height = (1/2) * 11 * 19 = 104.5 square inches

Therefore, the area swept clean by the wiper blade is:

325.628 - 104.5 = 221.128 square inches (rounded to 3 decimal places)

So the area swept clean by the wiper blade is approximately 221.128 square inches.

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The probability of a negative result for a batch of size 10 is approximately 0.3487 or 34.87%.

To determine the probability of a negative result for a batch of size 10, we need to calculate the probability that all 10 samples in the batch are negative.

Given that the positivity rate is 10%, it means that the probability of a sample being positive is 0.10, and the probability of a sample being negative is 0.90.

To find the probability of all 10 samples being negative, we multiply the probabilities of each sample being negative together:

Probability of a negative result for a single sample = 0.90

Probability of all 10 samples being negative = (0.90)^10 ≈ 0.3487

Therefore, the probability of a negative result for a batch of size 10 is approximately 0.3487 or 34.87%.

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Answer:

12

Step-by-step explanation:

Step 1:

x + 5 = 2x - 7        Corresponding ∠'s

Step 2:

5 = x - 7        Subtract x on both sides

Step 3:

5 + 7 = x       Add 7 on both sides

Answer:

x = 12

Hope This Helps :)

Answer:

x=12

Step-by-step explanation:

The angles are corresponding angles and if corresponding angles are equal, then the lines are parallel

x+5 = 2x-7

Subtract x from each side

x+5-x = 2x-7-x

5 = x-7

Add 7 to each side

5+7 = x-7+7

12 =x

Answer:

See explanation

Step-by-step explanation:

\(y-y_{1} =m(x-x_{1} )\\y+2 =\frac{-1}{2} (x-1} )\\y+2=-\frac{1}{2} x+\frac{1}{2} \\y=-\frac{1}{2} x-1\frac{1}{2}\)

You want a slope that is the opposite reciprocal of the original

Answer:

1. To solve a one-variable equation, it may be necessary to first multiply by using the Distributive Property

2. The next step is to combine like terms as needed.

3. Then solve for the variable by applying inverse operations.

4. If solving lead to a true equation, then the equation has infinitely many solutions.

5. if solving leads to an untrue equation, then the equation has no solution.

Step-by-step explanation:

Ratio of adults to children= 7:3

Total no. Of people at the cricket match:150

To find the value of the ratios, 7x+3x=150 ; 10x=150 ; x=150/10:15

So, 7:3 is 7(15) adults to 3(15) children,

Total no. Of adults: 105

Total no. Of children: 45

So, as per the question, the no. Of children that attended the cricket match is 45

Step-by-step explanation:

3x + 4 + 2x +7

= 3x + 2x + 4 + 7

= 5x + 11

The term that describes -8/27 is ;

A rational number.

A rational number is a number formed when two interger

A mathematical quantity having both direction and magnitude is called a vector.

A vector is a mathematical quantity that has both direction and magnitude. It is often represented graphically as an arrow, where the length of the arrow corresponds to the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Vectors are used in many areas of mathematics and science, including physics, engineering, and computer science. Some common operations performed on vectors include addition, subtraction, dot product, and cross product.

Vectors can also be expressed in various coordinate systems, such as Cartesian, polar, and spherical coordinates, depending on the context and application.

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Explanation:

The tickmarks tell us that sides HG and FG are the same length. The triangle is isosceles. Directly from this, we know that the opposite angles F and H are congruent. Both are 4y-7 degrees.

Angle G is 90 degrees because of Thales' Theorem. This is because HF is the diameter of the circle. It's also the hypotenuse of the right triangle.

For any triangle, the three interior angles always add to 180 degrees.

F+G+H = 180

(4y-7) + (90) + (4y-7) = 180

8y + 76 = 180

8y = 180-76

8y = 104

y = 104/8

y = 13

(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

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