D. $8.00-9. This equation can be used to find h, the number of hours it will take Flo and Bryan to mow their lawn:hh= 13 6How many hours will it take them to mow their lawn?A. 6 hoursB. 3 hoursC. 2 hoursD. 1 hour

Answer:

Answer: 1. x = 10, y = 6 2. x = 12, y = 3 3. x = 5, y = 2.5 4. x = 1, y = 14 5. x = 0.6, y = 7 6. x = 11, y = 1

Step-by-step explanation:

Answer:

After adding the two expression, the value is (8x + 5).

Step-by-step explanation:

Given that;

Two expressions are,

⇒ 2x + 6 and 6x − 1

Now, Add both expressions as,

⇒ (2x + 6) + (6x − 1)

⇒ 2x + 6 + 6x − 1

⇒ 8x + 5

Answer:

Simplifying

2x + 6 + 6z + (-1) = 0

Reorder the terms :

6 + ( -1) + 2x 6z = 0

Combine the terms : 6 + (-1) = 5

5 + 2x + 6z = 0

Solving

5 + 2x + 6z = 0

Answer:

Acute angle between the two planes: approximately \(43^\circ\).

Step-by-step explanation:

Find the normal vector of each plane:

As the name suggests, there is a \(90^\circ\) angle between a plane and its normal vector. The following four angles will correspond to the vertices of a quadrilateral:

The sum of these four angles should be \(360^\circ\). Two of these four angles were known to be \(90^\circ\). Once the third angle (the angle between the two normal vectors) is found, subtractions would give the measure of the other angle (the smallest angle between these two planes.)

Make use of the dot product to find the angle between these two normal vectors. Let \(\theta\) denote the angle between these two vectors.

\(\displaystyle \cos \theta = \frac{\begin{bmatrix}1 \\ -2 \\ 5\end{bmatrix} \cdot \begin{bmatrix}2 \\ 1 \\ -3\end{bmatrix}}{\sqrt{1^2 + (-2)^2 + 5^2} \cdot \sqrt{2^2 + 1^2 + (-3)^2}} \approx -0.73193\).

Before continuing, notice that the smallest angle between the two planes would be \(360^\circ - 90^\circ - 90^\circ - \theta = 180^\circ - \theta\).

Consider the identity: \(\cos\left(180^\circ - \theta\right) = -\cos \theta\).

In other words, \(\cos\left(180^\circ - \theta\right)\), the cosine of the smallest angle between the two planes (which the question is asking for) will be the opposite of \(\cos \theta\), the cosine of the angle between the two normal vectors.

Therefore, the cosine of the smallest angle between the two planes will be \(-(-0.73193) = 0.73193\).

Apply the inverse cosine function to find the size of that angle:

\(\arccos(0.73193) \approx 43^\circ\).

Answer:

32kg

Step-by-step explanation:

0.08 x 400 = 32

hope this helped!

Answer:

Step-by-step explanation:

1 sunglass weighs 0.08 grams

400 sunglasses weight x

x = 400 * 08

x = 32 kg

Answer: 0.4337

Step-by-step explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean \(\mu=78\), Standard deviation  \(\sigma=36\)

Then, the probability that it is greater than 84 will be

\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)

Hence, the required probability = 0.4337

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Guided notes are intended to assist students in actively engaging with course material and enhancing their learning experience. It is recommended that you approach your teacher or instructor for any clarification or additional resources you may need to fully understand the content.

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This approach will not only help you grasp the subject matter more effectively but also promote personal growth and knowledge development.

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Answer:

its B

Step-by-step explanation:

Answer:

5x+6=10+10=8x-15

Step-by-step explanation:

The theoretical probability of spinning a 4 is 1/6.

The Probability in mathematics is a possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A spinner labeled 1 to 6.

S = {1, 2, 3, 4, 5, 6}

The theoretical probability of spinning a 4 is,

= 1/6

The image of the spinner is attached in the image below.

Therefore, 1/6 is the probability.

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Answer:

50

Step-by-step explanation:

To solve this problem, we can use the following formula:

(amount of solution 1) + (amount of solution 2) = total amount of mixture

We can also set up equations for the amount of acid in each of the solutions:

0.25(amount of solution 1) + 0.65(amount of solution 2) = 0.4(total amount of mixture)

We have two equations and two unknowns, so we can solve for the amounts of each solution. Let's set x to be the amount of the 25% acid solution and y to be the amount of the 65% acid solution. Then we have:

x + y = 80                (equation 1)

0.25x + 0.65y = 0.4(80)   (equation 2)

We can simplify equation 2 by multiplying everything by 100, to get rid of the decimals:

25x + 65y = 3200

Now we can solve this system of equations. One way to do this is to solve equation 1 for one of the variables, and substitute it into equation 2. We get:

x = 80 - y

25(80 - y) + 65y = 3200

2000 - 25y + 65y = 3200

40y = 1200

y = 30

So we need 30 liters of the 65% acid solution. To find the amount of the 25% acid solution, we can substitute y = 30 into equation 1:

x + 30 = 80

x = 50

So we need 50 liters of the 25% acid solution. Therefore, we need 50 liters of the 25% acid solution and 30 liters of the 65% acid solution to produce 80 liters of a 40% acid solution.

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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Answer:

(-3,0)

Step by step explanation:

make x the subject of the formula in equation 2

x-3y=-3

x = 3+3y

substitute x in equation 1

5(3+3y)-3y = -15

open the brackets

15+15y-3y = -15

15+12y=-15

12y = 15-15

12y = 0

divide both sides by 12

y = 0

substitute y in equation 2

x - 3(0) = -3

x - 0 = -3

x = -3+0

x = -3

therefore x = -3

y = 0

Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Answer:

y = 1/4x

Step-by-step explanation:

The slope changes from 4 to 1/4

so,

y = 1/4x + b

Then, plug in (4,1) into the equation

1 = 1/4(4) + b

1 = 1 + b

b = 0

y = 1/4x + 0

y = 1/4x

Step-by-step explanation:

Cos(30°) = 90 / hypotenuse

\( \frac{ \sqrt{3} }{2} = \frac{90}{hypotenuse} \)

Hypotenuse =

\(60 \sqrt{3} = 103.9\)

Answer: ≈ 103.92 feet

Step-by-step explanation:

       Since this is a right triangle we can use a trigonometry function to help us solve. Here, we will utilize cosine since we are given the hypotenuse and the adjacent side to the angle to work with. Let x be the length of the hypotenuse.

Given:

   cos(30°) = \(\frac{90\;\text{feet}}{x}\)

Multiply both sides of the equation by x:

   xcos(30°) = 90 feet

Divide both sides of the equation by cos(30°):

   x = 103.92304845 feet ≈ 103.92 feet

To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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Answer:

\( \sqrt{392 {x}^{7} } \)

Simplify

that's

\( \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } \)

Hope this helps you

"Triple the sum of K and 2" can be interpreted as a two-step procedure that involves adding K and 2 first, and then multiplying the result by 3.

Multiplication is a fundamental arithmetic operation that involves combining two or more numbers to find their product. It is represented by the symbol "x" or "•" or sometimes simply by placing two numbers next to each other.

"Triple the sum of K and 2" can be expressed mathematically as:

3(K + 2)

This expression represents the value we get by adding K and 2, and then multiplying the sum by 3.

To evaluate this expression, we first add K and 2 together, giving us a sum of (K + 2). Then, we multiply that sum by 3, giving us a final result of 3(K + 2).

As a result, "triple the sum of K and 2" can be interpreted as a two-step procedure that involves adding K and 2 first, and then multiplying the result by 3.

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The full question is How do you write "triple the sum of K and 2" as an expression?

Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

ANSWER:

3/5 miles

STEP-BY-STEP EXPLANATION:

Given:

Area: 15/45 square miles

Width: 5/9 mile

We calculate the length as follows:

The length of the park is 3/5 miles

Answer: 12√6

Step-by-step explanation:

Given the expression;

2√3 * 3√√8

= (2*3) * (√3*√8)

= 6 * (√24)

= 6 * √4*6

= 6 * (2√6)

= (6*2)√6

= 12√6

Therefore, the simplified form of the expression is 12√6.

Answer:

The discount is 20% off

hope this helps!

The angle on the unit circle is solved to be

56.01 degrees (to the nearest tenth)

To find the angle of the terminal side through the given point on the unit circle, we can use the inverse trigonometric functions.

given that P = ((√5)/4, (√11)/4)

θ = arctan ((√11)/4 / (√5)/4)

θ = arctan((√11)/(√5))

θ ≈ 56.01 degrees

hence to the nearest tenth of a degree, the angle of the terminal side through the point P = ((√5)/4, (√11)/4) on the unit circle is approximately 56.01 degrees.

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Step-by-step explanation:

< AEB + < BEC = 180° {BEING LINEAR PAIR }

26° + < BEC = 180°

< BEC = 180° - 26°

< BEC = 154°

ARC BC = < BEC ( relation between arc and central angle)

Arc BC = 154°

Hope it will help :)

The amount of money invested at 13% was $8111, while $6135 was invested at 12%.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount invested at 13% and y represent the amount invested at 12%, hence:

x +  y = 14246   (1)

Also:

0.13x = 0.12y + 318.23  (2)

Hence:

x = 8111, y = 6135

The amount of money invested at 13% was $8111, while $6135 was invested at 12%.

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Answer:

C) 2√3

Step-by-step explanation:

This is a right triangle with one of the smaller angles = 45°

Therefore the other non-right angle = 45°

Therefore this is a right isosceles triangle with two legs equal

Each leg = √6

hypotenuse of a right isosceles triangle = √2 x a where a is each of the legs

y = √2 x √6 = √2 x √(2 x 3) = √2 x √2 x √3 = 2√3

Answer:

Step-by-step explanation:

72/8 = 9 acres per day

Using the continuity concept, it is found that the function is continuous on the following interval:

C. (0, 1).

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

\(\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)\)

In the context of this problem, the numeric values are especially relevant, as the function not continuous at the zeros of the denominator.

The denominator of the function is given as follows:

(x² - 2)(x + 0.4).

Hence the discontinuity points are:

Hence the only interval in which the function is continuous over the entire interval is given by option C.

The function and the possible options are given by the image at the end of the answer.

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