Mike builds a pen for his dogs near his barn. The pen is a regular hexagon with a side length of 4 feet. What is the area of the pen?

we have drawn the graph of the inequality - 6 > t - ( - 13 ) which can also be written as t < - 19.

We are given an inequality:

- 6 > t - ( - 13 )

- 6 > t + 13

t + 13 < - 6

Subtract 13 from both the sides, we get that:

t + 13 - 13 < - 6 - 13

t < - 19

Now, we have to graph the inequality.

The line of the inequality will be t = - 19 which will be dotted as t is not equal to - 19.

The following graph is obtained.

Therefore, we have drawn the graph of the inequality - 6 > t - ( - 13 ) which can also be written as t < - 19.

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Answer:

Step-by-step explanation:

if angles are complementary, that means they add up to 90º

if one is 65.3, then the other is just 90 - 65.3

<S = 90º - <R

<S = 90º - 65.3º

<S = 24.7º

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

3(4a−5b+2)

Step-by-step explanation:

The answer should have originally been 3(4a-5b+2)

3(4a+5b+3)= 12a+15b+9 which is incorrect.

Given the linear equation

We can find the y-intercept by setting x=0 and solving for y, as shown below

To graph a linear equation, we need two points on it. We already have one (0,3), we can find a second one by setting x=1 and solving for y

Draw both points on the plane and cross them with a line, as shown in the image below

Where A=(0,3) and B=(1,7)

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Step-by-step explanation:

1/2(114)+(58*2)

1/228+(116)

1/228+116/1=

26676/228=117

The length of ML rounded to nearest tenth is 4.5.

From figure, KML is a right-angled triangle at M, with KM = 8 and KL = 9.2. Let ML = x be the length of the base.

Using Pythagorean theorem, we have:

KL² = KM² + ML²

Substituting the given values ML=x, KM = 8 and KL = 9.2, we have:

9.2² = 8² + x²

Simplifying the right-hand side, we get:

84.64 = 64 + x²

Subtracting 64 from both sides, we get:

20.64 = x²

Taking the square root of both sides, we get:

x ≈ 4.54

x=4.5 (rounded to nearest tenth)

Therefore, the length of ML is approximately 4.5.

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Based on the information, the hedgehogs have made the better offer

The Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:

PV = S(t) * e^(-rt)

The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:

PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt

= 736,918.63

Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:

PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt

= 753,472.49

Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.

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Answer:

Step-by-step explanation:

Quartile means fourth

break up the numbers in to 4 groups, start by finding the middle numbers and split the numbers in half.  Then split both of those two groups in half to find the quartiles.

Lower quartile is the group with the smallest numbers.

Median is the middle number (of the whole group).

Upper quartile is the group with the largest numbers.

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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Answer:

3:8

Step-by-step explanation:

If the ratio of red marbles to blue marbles is 8:3, and the question is asking for  the ratio of blue marbles to red marbles, all you have to do is switch the numbers around.

The ratio of blue marbles to red marbles is 3:8

Hope this helps!

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

98 degrees

Step-by-step explanation:

In a quadrilateral, we have 4 angles whose sum is 360 degrees which can be derived using the Exterior Angle Sum Theorem which essentially states that any convex polynomial will have a sum of 360 degrees for it's exterior angles.

Since we know that two of the angles are equal, we can just represent angle A and D as "x", and since they're congruent, and there is two of them, the sum can be represented as "2x"

So using all the known values we can set up the following equation:

\(2x+64+100=360\)

Simplify on the left side

\(2x+164=360\)

Subtract 164 from both sides

\(2x=196\)

Divide both sides by 2

\(x=98\)

Since we know that "x" represents both angle A and B, then the angle A is 98 degrees.

Answer:

x = 12

Step-by-step explanation:

g(x)= 2x-4

g(x)= 20

Therefore,

2x-4 = 20

Bringing -4 to the other side it becomes positive,so..

2x= 20+4

= 24

x =24/2

= 12

Answer:

The tax amount a customer will pay on one doll is $4.4

Step-by-step explanation:

To find 8% of 55, you multiply .08 by 55, which is 4.4

Please give brainliest!

Answer:

A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero.

Step-by-step explanation:

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:

m=8

Step-by-step explanation:

Based on the context of the given problem, the values of a = 3 and b = π/6. Hence, the correct answer is option b.

The height of the inner tube can be modeled by the function -

h = asinbx + 5, where 'a' represents the amplitude and 'b' represents the frequency.

In this problem, the height of the innertube fluctuates between 2 meters and 8 meters, which means that the amplitude is 3 (8 - 5 = 3) and the frequency can be calculated by using the formula -

Frequency = 1/T, where 'T' is the time between maximums.

Since the interval between maximums is 12 seconds, the frequency is 1/12. To find the value of b, we can use the formula-

b = 2πf, where 'f' is the frequency.

So b = 2π * 1/12 = π/6.

Therefore, we get the values of a = 3 and b = π/6.

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The complete question is -

A theme park guest takes an innertube into the wave pool. The innertube moves up and down in a way such that the height h of the innertube, in meters, above the floor of the pool can be modeled by the function h = asinbx + 5. When the wave pool is turned on, the innertube's height fluctuates between 2 meters and 8 meters, with an interval of 12 seconds between maximums. Based on the context of the problem, what are the values of a and b?

a. a = 3 , b= π/12

b. a = 3 , b= π/6

c. a = 6 , b= π/12

d. a = 6 , b= π/6

Answer:

given below

Step-by-step explanation:

the column if multiplied shall give 12 as product. two sides are given.

multiply the given ones and divide it by 12.

Answer:

\(P_{B}\) = 80

Step-by-step explanation:

given 2 similar figures with ratio of sides = a : b

then ratio of perimeters is also a : b

here ratio of sides = 24 : 15 = 8 : 5

the ratio of perimeters is also 8 : 5

then by proportion

\(\frac{ratioA}{P_{A} }\) = \(\frac{ratioB}{P_{B} }\) , that is

\(\frac{8}{128}\) = \(\frac{5}{P_{B} }\) ( cross- multiply )

8 \(P_{B}\) = 5 × 128 = 640 ( divide both sides by 8 )

\(P_{B}\) = 80

Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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The weight of one bucket of lobster is 18 pounds per bucket. Option b

To determine the weight of one bucket of lobster, we can use the given information about the rate of 450 pounds over 25 buckets.

The rate is defined as the amount of weight (in pounds) divided by the number of buckets. In this case, the rate is 450 pounds over 25 buckets.

To find the weight of one bucket of lobster, we can divide the total weight by the number of buckets:

Weight of one bucket = Total weight / Number of buckets

Weight of one bucket = 450 pounds / 25 buckets

Weight of one bucket = 18 pounds per bucket

Therefore, the weight of one bucket of lobster is 18 pounds per bucket.

The correct answer is option b) 18 pound per bucket.

It's important to note that this calculation assumes a constant weight per bucket throughout the given scenario. In reality, the weight of one bucket of lobster may vary depending on factors such as the size and type of lobsters being weighed. Additionally, it's possible that the weight per bucket may change over time or across different batches of lobsters.

Option B

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Answer:

Step-by-step explanation:

1 )

\(\frac{2}{5}( \frac{5x}{4} - \frac{10}{3})-\frac{4x}{3} \\\frac{x}{2} - \frac{4}{3} - \frac{4x}{3}\\ \frac{-5x}{6}-\frac{4}{3}\)

2 )

\(\frac{17x}{8}+\frac{3x}{4}+\frac{1}{6}-\frac{7x}{12}+\frac{17}{3}\\ \frac{51x}{24}+\frac{18x}{24}-\frac{14x}{24}+\frac{35}{6}\\\frac{55x}{24}+\frac{35}{6}\)

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Answer

Given the 2 equations

x = y + 4 → (1)

2x - 3y = - 2 → (2)

Substitute x = y + 4 into (2)

2(y + 4) - 3y = - 2 ← distribute and simplify left side

2y + 8 - 3y = - 2

- y + 8 = - 2 ( subtract 8 from both sides )

- y = - 10 ( multiply both sides by - 1 )

y = 10

Substitute y = 10 into (1) for corresponding value of x

x = 10 + 4 = 14

Solution is (14, 10 ) → D

Step-by-step explanation:

Answer:

x=3

x=3y=1

I hope this helps!

Step-by-step explanation:

x+y=4

2x-3y=3

y = 4-x

2x-3(4-x) = 3

2x-12+3x = 3

5x = 15

x = 3

y = 4-x

4-3 = 1

y = 1