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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

We have the coldest value of temperature \(T(\frac{3}{4},0) = -9/16 \). and the hottest value is \(T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}\).

Step-by-step explanation:

We need to take the derivative with respect of x and y, and equal to zero to find the local minimums.

The temperature equation is:

\(T(x,y)=x^{2}+2y^{2}-\frac{3}{2}x\)

Let's take the partials derivatives.

\(T_{x}(x,y)=2x-\frac{3}{2}=0\)

\(T_{y}(x,y)=4y=0\)

So, we can find the critical point (x,y) of T(x,y).

\(2x-\frac{3}{2}=0\)

\(x=\frac{3}{4}\)

\(4y=0\)

\(y=0\)

The critical point is (3/4,0) so the temperature at this point is: \(T(\frac{3}{4},0)=(\frac{3}{4})^{2}+2(0)^{2}-(\frac{3}{2})(\frac{3}{4})\)

\(T(\frac{3}{4},0)=-\frac{9}{16}\)    

Now, we need to evaluate the boundary condition.

\(x^{2}+y^{2}=1\)

We can solve this equation for y and evaluate this value in the temperature.

\(y=\pm \sqrt{1-x^{2}}\)

\(T(x,\sqrt{1-x^{2}})=x^{2}+2(1-x^{2})-\frac{3}{2}x\)  

\(T(x,\sqrt{1-x^{2}})=-x^{2}-\frac{3}{2}x+2\)

Now, let's find the critical point again, as we did above.

\(T_{x}(x,\sqrt{1-x^{2}})=-2x-\frac{3}{2}=0\)            

\(x=-\frac{3}{4}\)    

Evaluating T(x,y) at this point, we have:

\(T(-(3/4),\sqrt{1-(-3/4)^{2}})=-(-\frac{3}{4})^{2}-\frac{3}{2}(-\frac{3}{4})+2\)  

\(T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}\)

Now, we can see that at point (3/4,0) we have the coldest value of temperature \(T(\frac{3}{4},0) = -9/16 \). On the other hand, at the point \(-(3/4),\frac{\sqrt{7}}{4})\) we have the hottest value of temperature, it is \(T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}\).

I hope it helps you!

Answer:

full arrow going left from 46

Step-by-step explanation:

Inequalities are used to represent unequal expressions.

The inequality is: \(h \le 46\)

The height (h) is said to be no greater than 46 inches.

The text "no greater than" means less than or equal to.

In inequalities, less than or equal to is represented with <=

So, the inequality is:

\(h \le 46\)

See attachment for the graph of the inequality.

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Answer:

yes 40

Step-by-step explanation:

she got it correct

The order of operations (PEMDAS) states that we should perform multiplication and division before addition and subtraction. Using this order, we get:

244 - (33456 / 3456) * 345 + 13.55 - 2

= 244 - 97.02 * 345 + 13.55 - 2

= 244 - 33494.1 + 13.55 - 2

= -33238.55

Therefore, 244-33456/3456*345+13.55-2 = -33238.55.

Answer:

first equation

Step-by-step explanation:

Step-by-step explanation:

speed= distance

time

speed= 6.4

4×60

speed= 0.026 m/s

Answer:

33 bags

Step-by-step explanation:

she has 4.5 ft³

she needs 54 ft³

she must get an additional

54 ft³ - 4.5 ft³ = 49.5 ft³

each bag has 1.5 ft³

(49.5 ft³)/(1.5 ft³) = 33

Answer: 33 bags

Answer:

Step-by-step explanation:

We observe the pattern:

It can be put as:

or

The nth term is going to be:

The sum of the 31 terms will be:

or

Use the formula for sum of the first n squares:

The sum N equals:

And the value of N/31 is:

Answer:

The boat traveled 781.5 feet from point AA to point BB

Step-by-step explanation:

Find the height of the small triangle then find the base of the big triangle then subtract the two answers to find the distance between a and b

:)

We can see here that the 90% confidence interval will be: 420.2 to 585.8.

An interval of values known as a confidence interval is one that is likely to include the real value of a population parameter. A confidence interval of 95%, for instance, indicates that there is a 95% likelihood that the population parameter's real value falls inside the interval.

We will find the sample mean first:

Sample mean = sum of data points / number of data points

Sample mean = 8551 / 17 = 503

Then the standard error will be:

Standard error = population standard deviation / square root of number of data points

Standard error = 190 / √(17) = 41.7

Confidence interval = Sample mean ± 1.645 × standard error.

where 1.645 is the z-score for a 90% confidence interval.

Confidence interval = 503 ± 1.645 * 41.7 = 420.2 to 585.8

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The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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If the value of b is 8. Then the value of the expression (9 - b) will be 1.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expression is given below.

⇒ 9 - b

If the value of b is 8. Then the value of the expression will be

⇒ 9 - b

⇒ 9 - 8

⇒ 1

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Answer: $9

Step-by-step explanation: 85% off means when you multiply the number by 0.85 you subtract that from the original number, 60 times 0.85 is 51 and 60-51=9! Hope this helps!

In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.

Using this information, we can set up equations to solve for the variables.

From the given information, we have -

AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)

BE = x + 2

DE = BE = (x + 2) = g (since diagonals bisect each other at point E)

We also know that opposite sides of a parallelogram are parallel.

Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -

10/1 = 2y/1

10 = 2y

y = 5

Now we can use equation (1) to solve for x -

2x - 5 = 5x - 17

12 = 3x

x = 4

Finally, we can use x to solve for g -

(x + 2) = g

(4 + 2) = g

g = 6

Therefore, the values of x, y, and g are 4, 5, and 6, respectively.

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Answer: Let's call the present age of the son x and the present age of the father y.

We know that y = 3x and that six years ago, the sum of their ages was 45.

So, we can write the equation:

x + (y-6) = 45

x + (3x-6) = 45

4x = 51

x = 12.75

The present age of the son is 12.75 years.

Step-by-step explanation:

Answer:

4x+10

Step-by-step explanation:

Slope form: mx+b

Slope formula: y2-y1/x2-x1

(2, 18) (3,22)

22-18=4

3-2= 1

4/1=4

4x+10

By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.

We are given that,

No. of children who stayed at school is 27,

Also, 70% of the children went on an excursion.

Suppose, the total number of children in percentage is 100%

Out of which 70% went on an excursion

Thus, the children who stayed at school is 100% - 70% = 30%

By using the Unitary method, we can find out the number of 70% of children.

If 30% of the children are 27

Then 70% of the children are = 27 × 100

                                                        30

                                                 = 63

∴ the total no. of children in the school = 27 + 63

                                                                 = 90

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Answer:

X=2

Step-by-step explanation:

|2x -12| = -4x

2x-12 = -4x

2x - (-4x) = 12

2x +4x =6x

6x=12

x=12/6

x=2

Answer:

Step-by-step explanation:

S.I =720×6×5/100×365

=21600/36500

=0.59178

So balance will be 720+0.59178

=720.59178

The area of the rectangle is 1296 square feet.

Let's denote the width of the rectangle as "w" and its length as "4w" since the length is four times the width.

The formula for the perimeter of a rectangle is given by:

P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

Given that the perimeter of the rectangle is 180 ft, we can write the equation as:

180 = 2(4w + w)

Simplifying the equation:

180 = 2(5w)

180 = 10w

w = 18

So, the width of the rectangle is 18 ft.

Now, we can find the length of the rectangle:

Length = 4w = 4(18) = 72 ft

The area of a rectangle is given by the formula:

\(A = l \times w,\)

where A is the area,

l is the length,

and w is the width.

Substituting the values we found:

Area \(= 72 ft \times 18 ft = 1296 ft^2\)

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Answer

Explanation

Given:

Factor z out in the right hand side of the equation

Divide both sides by w - c⁵

Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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Answer:

10

Step-by-step explanation:

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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The children in Mme Potana's class, who count together as a whole class from 1 to 20, are developing their number recognition and counting skills. They are learning to identify and associate the spoken words with the corresponding written numerals.

On the other hand, the children in Ntate Mafodi's class, who count seeds individually by touching each seed as they count, are developing their one-to-one correspondence skills. They are learning to associate each seed with a specific number, recognizing that each count corresponds to one object.

This activity helps them understand the concept of cardinality, which is the understanding that the last number counted represents the total quantity of objects.

Both activities contribute to the children's overall number sense, which is the understanding and familiarity with numbers and their relationships. By engaging in these counting exercises, the children are building the foundation for more complex mathematical concepts such as addition, subtraction, and problem-solving skills.

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Answer:

the last one, y=x-6

Step-by-step explanation:

it is the only answer with an x-intercept of 6. you did not provide the line, but I'm assuming it is y=-x.

The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​;

(a) exactly​ three = 0.1314

(b) at least​ four = 0.7953

(c) less than eight = 0.93382

The binomial probability distribution is the probability of exactly x successes on n repeated trials, with p probability. The formula is;

P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)

We are given;

p = 41% = 0.41

n = 12

Thus;

1) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ exactly​ three;

P(3) = ¹²C₃ * 0.41³ * (1 - 0.41)^(12 - 3)

P(3) = 0.1314

2) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is at least​ four;

P(x ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

P(x ≥ 4) = 0.7953

3) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is less than eight using binomial probability calculator is;

P(X < 8) = 0.93382

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