The test scores you end up having in geometry class are 81 and 87. What possible scores can you earn on your next test to have a test average between 84 and 89​?

The total surface area of the pyramid is: 208.88 m²

The surface area of the pyramid is simply the sum of the areas of all the given surfaces.

Formula for the area of a triangle is:

Area = ¹/₂bh

where:

b is base

h is height

Area of four side triangles = 4(¹/₂ * 8 * 12) = 192 m²

Using Pythagoras theorem, the height of the base triangle is:

x = 4.22

Area of base = ¹/₂ * 8 * 4.22 = 16.88 m²

Total surface area = 192 + 16.88

= 208.88 m²

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Jane travels 8 miles much farther than her trainer. The solution is obtained using arithmetic operations.

What are arithmetic operations?

By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions add, subtract, divide, and multiply additionally allow for the specification of arithmetic operations.

3. Using pythagoras theorem, we get the equation as D² = 12² + 16².

⇒D² = 144 + 256

⇒D² = 400

⇒D = √400

⇒D = 20

4. Jane has traveled 28 miles in total whereas her trainer has traveled 20 miles.

So, the difference is 28-20= 8 miles

Hence, Jane travels 8 miles much farther than her trainer.

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To organize the provided data, we can create a table comparing the samples of couples with children (sample 1) and childless couples (sample 2) as follows:

Sample Sample Size Sample Mean Sample Standard Deviation

1 78 51.1 4.7

2 94 45.2 12.1

In this table, we have listed the sample number (1 and 2), the sample size (number of couples in each group), the sample mean (average Marital Satisfaction Inventory score), and the sample standard deviation (measure of variability in the scores) for each group. This organization allows us to compare the data and proceed with hypothesis testing on the difference in population means between the two groups.

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The value of h'(2) is 25

The chain rule is a fundamental rule in calculus that provides a method to differentiate composite functions.

A composite function is a function that is formed by taking the output of one function and using it as the input of another function.

For instance, if we have two functions f(x) and g(x), then the composite function h(x) can be defined as h(x) = f(g(x)), where g(x) is the input to f(x).

here we have

h(x) = √6 + 5f(x)

Derivative of h(x) with respect to x

h'(x) = d/dx (√6 + 5f(x))

h'(x) = d/dx (√6) + d/dx (5f(x))

h'(x) = 0 + 5f'(x)

h'(x) = 5f'(x)

Now substitute x = 2 and f'(2) = 5, to find h'(2)

h'(2) = 5f'(2)

h'(2) = 5(5)

h'(2) = 25

Therefore,

The value of h'(2) is 25

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Complete Question:

If h(x) = √6 + 5f(x), where f(2)= 6 and f'(2) = 5, find h'(2).

Answer:

2 mountains per month

Step-by-step explanation:

1/5 of a mountain : 1/10 of a month

multiply both sides by 10

10/5 = 2 mountains : month

Answer:

hdwuqdhuwehduewhud

Step-by-step explanation:

pay back

Answer: \(y-2=3(x-4)\\y=3x-12+2\\-3x+y=-10\\3x-y=10\)

Step-by-step explanation:

I showed the steps to find the equation. In case you need to know, I used point-slope form, which involves using the formula y-y1=m(x-x1), in which you use a point like (4,2) and the slope, which we know is 3x since it's parallel to the original line. Simplifying and bringing it to standard form such as Ax+By=C. Ax has to be positive, which is why -3x went to positive, and y and -10 switched signs.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

= -3 2/5 - 5/6

= - 17/5 - 5/6  ---- LCM of 5 & 6 is 30

= _  17 * 6   _   5 * 5  

       5 * 6        6 * 5

=  _  102 - 25

            30

=  _ 127

        30

Answer:

1/5

Step-by-step explanation:

The Tower of Hanoi is a mathematical puzzle involving three rods and a series of disks that must be moved to a different rod in a specific order.

The Tower of Hanoi is a classic mathematical puzzle that consists of three rods and a series of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: Only one disk can be moved at a time. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. No disk may be placed on top of a smaller disk. It is a mathematical problem that can be solved using recursive function.

It is a great problem to understand the recursive function, backtracking and also it's used for teaching about problem-solving and algorithms.

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The dimensions that will produce the maximum enclosed area for two adjacent rectangular safe play areas of equal size with 200 feet of fencing is 100 feet by 100 feet.

To solve this problem, use the area of a rectangle formula A = lw, where l is the length and w is the width.

Since the two play areas must be of equal size, let's call the length and width l and w, respectively.

We know that the total length of fencing is 200 feet, so l + w = 200 feet.

We can then solve for l by rearranging the equation as l = 200 - w.

We then substitute this into the area equation to get A = (200 - w)w.

To maximize the area, differentiate this equation to get A' = w - 200.

Set this to 0 and solve for w to get w = 100. Since l + w = 200, l = 100 as well.

Therefore, the maximum enclosed area is produced by dimensions of l = 100 feet and w = 100 feet.

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Answer:

300

Step-by-step explanation:

375 divided by 5=75

Each “1”=75

4x75=300

There are 300 boys.

Hope this makes sense

Answer:

300 boys

Step-by-step explanation:

Let the number of boys = x

Girls: 375

boys : girls = 4 : 5

total in the ratio is 9

girls are 5/9 of total, and are 375

boys are 4/9 of total

5/9 x = 375

x = 375 × 9/5

x = 675

Boys are 4/9 of total.

4/9 × 675 = 300

Part A: The formula for the future value of an investment with compound interest is given by:

A = P(1 + r/n)^(nt)

Where: A = the future value of the investment P = the principal investment amount r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years

For this situation, P = $1,500 r = 2.75% = 0.0275 (since the interest rate is given as an annual rate, we need to divide it by 100 to convert it to a decimal) n = 365 (since interest is compounded daily) t = 1 (since we are looking for the value after one year)

Therefore, the equation to model this situation is:

A = 1500(1 + 0.0275/365)^(365*1)

Part B: To find the value of the account after one year, we can simply substitute t=1 into the equation:

A = 1500(1 + 0.0275/365)^(365*1) = $1,543.21

Therefore, the amount of money in the account after 1 year is $1,543.21.

Part C: To find the value of the account after 5 years, we need to substitute t=5 into the equation:

A = 1500(1 + 0.0275/365)^(365*5) = $1,805.59

Therefore, the amount of money in the account after 5 years is $1,805.59.

The use of a "thumbs-up" gesture to symbolize the statement "good luck" is a common practice in many cultures. This gesture is typically used to express approval or agreement, but it can also be used to convey positive wishes, such as wishing someone good luck before an exam or a job interview.

It is believed that this gesture originated in ancient Rome, where it was used as a sign of approval in the gladiatorial arena. Today, the thumbs-up gesture has become a universal symbol of positivity and encouragement. So, if you want to wish someone good luck, a thumbs-up gesture is a great way to do it!

The use of a "thumbs-up" gesture to symbolize the statement "good luck" involves the following steps:

1. Extend your arm: To perform the thumbs-up gesture, first extend your arm in the direction of the person you want to wish good luck.
2. Make a fist: Close your fingers into a fist, with your thumb pointing upwards.
3. Show your thumb: Ensure that the thumb is clearly visible and pointing upwards. This represents the "thumbs-up" gesture.
4. Make eye contact: Look at the person you're wishing good luck to, so they know the gesture is directed at them.

By performing the thumbs-up gesture, you're using a universally recognized symbol to convey your positive sentiment and wish someone good luck in their endeavors.

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The points that he average on the last two tests will be 93 points.

A mean is the average of the set of numbers that are given.

On the first five tests that he took, he averaged 86 points. The total points will be:

= 86 × 5

= 430 points

He averaged 88 points on all seven tests. The total will be:

= (88 × 7)

= 616 points

The point average on the last two tests will be:

= (616 - 430)/2

= 186/2

= 93 points

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Answer:

f(1/4) = -5.25

Step-by-step explanation:

Plug 1/4 as x

4x^2 + 2x - 6

= 4*1/4^2 + 2x1/4 - 6

= 4*1/16 + 1/2 - 6

= 1/4 + 1/2 - 6

= 3/4 - 6

= -5 1/4 = -5.25

Answer:

f(1/4)=-5.25

Step-by-step explanation:

9514 1404 393

Answer:

  x² +3x -3 +3x/(5x² +6x +2)

Step-by-step explanation:

As with any long division, you formulate a partial quotient, then subtract the product of that and the divisor from the dividend. The result is a new dividend. You're done when the degree of the dividend is less than the degree of the divisor.

The partial quotient term is simply the ratio of the highest-degree terms in the dividend and the divisor. (That is what makes it easier than numerical long division.)

_____

Web page formatting cut off part of the "Hints" in the first attachment. The second attachment shows the full "Hints."

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[1][2]) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.

Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. Proportionality constants are written within the image: sin θ, cos θ, tan θ, where θ is the common measure of five acute angles.

The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.[3]

The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extending these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) is often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane (from which some isolated points are removed).

Contents

Right-angled triangle definitions Edit

A right triangle always includes a 90° (π/2 radians) angle, here labeled C. Angles A and B may vary. Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.

Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.

In this section, the same upper-case letter denotes a vertex of a triangle and the measure of the corresponding angle; the same lower case letter denotes an edge of the triangle and its length.

Given an acute angle A = θ of a right-angled triangle, the hypotenuse h is the side that connects the two acute angles. The side b adjacent to θ is the side of the triangle that connects θ to the right angle. The third side a is said to be opposite to θ.

If the angle θ is given, then all sides of the right-angled triangle are well-defined up to a scaling factor. This means that the ratio of any two side lengths depends only on θ. Thus these six ratios define six functions of θ, which are the trigonometric functions. More precisely, the six trigonometric functions are:[4][5]

sine

{\

Answer: 6

Step-by-step explanation:

Answer: y=6

Step-by-step explanation:

Answer:

x < 2

Step-by-step explanation:

There is an open circle at 2 so that means it is not equal to

The line goes to the left so x is less than 2

x < 2

Answer:

c.) x < 2

Step-by-step explanation:

open circle means > or <

the line is going to the left, meaning < or ≤

from this, we know the inequality is x < 2

The two triangles are congruent, as the Pythagorean Theorem ensures that the hypotenuse of the two triangles will be equal.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

If two triangles have congruent side lengths, the hypotenuse for the two triangles will also be the same, hence the Pythagorean Theorem ensures the congruence of the two triangles.

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Answer: D

Step-by-step explanation:

The exact answer is 2.571281591, which is between:

D) 2 and 3

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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The given program implements a method, canBeSortedGeoSeq, that checks if a given integer list can be sorted into a geometric sequence. The program sorts the list in ascending order and calculates the ratio between consecutive terms. It then iterates through the sorted list, comparing the ratio of each pair of consecutive terms with the initial ratio. If any ratio differs, the method returns false, indicating that the list cannot be sorted into a geometric sequence. Otherwise, it returns true.

A.

The complete program after filling the blanks is:

1 public static boolean canBeSortedGeoSeq(int[] list) {

2 Arrays.sort(list);

3 int ratio = list[1] / list[0];

4 int n = list.length;

5 for (int i = 1; i < n - 1; i++) {

6 if ((list[i + 1] / list[i]) != ratio)

7 return false;

8 }

9 return true;

10 }

B.

If the list passed to the method is {2, 4, 3, 6}, the output from the original code will be false. This is because the ratio between consecutive terms is not constant (2/4 = 0.5, 4/3 ≈ 1.33, 3/6 = 0.5).

To make the code work with double-typed ratio, we can revise the code by changing the data type of the ratio variable to double and modifying the comparison in the if statement accordingly:

public static boolean canBeSortedGeoSeq(int[] list) {

   Arrays.sort(list);

   double ratio = (double) list[1] / list[0];

   int n = list.length;

   for (int i = 1; i < n - 1; i++) {

       if (((double) list[i + 1] / list[i]) != ratio)

           return false;

   }

   return true;

}

After the revision, if the list passed is {2, 4, 3, 6}, the output will be false because the ratio is not constant (2/4 = 0.5, 4/3 ≈ 1.33, 3/6 = 0.5).

The new problem with the revised code is that it may encounter precision errors when performing division operations on floating-point numbers. Due to the limited precision of floating-point arithmetic, small differences in calculations can occur, leading to unexpected results.

In the case of checking geometric sequences, this can cause the program to mistakenly identify a non-geometric sequence as a geometric sequence or vice versa.

To address this issue, it is recommended to use a tolerance or epsilon value when comparing floating-point numbers to account for the precision limitations.

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The hash of the given message is 135.

In computing, a message digest is a fixed-sized string of bytes that represents the original data's cryptographic hash. This hash is used to authenticate a message, guaranteeing the integrity of the data in the message.

Here, it is given the message m = 23  

The formula to calculate hash is him) - (m*7;2 MOD 7793.

So, let's calculate the hash : him) - (m*7;2 MOD 7793(him) - (23*7;2 MOD 7793

⇒ (8*23) - (49 MOD 7793)

⇒ 184 - 49= 135.

So, the hash of the given message is 135.

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Answer:

Dolly Parton

Step-by-step explanation:

hopes this helps please mark brainliest

For the two supplementary angles given, the value of x is 30. Two angles are called supplementary when their measures add up to 180 degrees.

If two angles are supplementary, their sum must equal 180 degrees. Supplementary angles are double of complementary angles.  So if m∠1=124° and

m∠2=(2x - 4)°, we can set up the equation:

124 + (2x - 4) = 180

Solving for x, we can isolate x by subtracting 124 from both sides:

2x - 4 = 56

Adding 4 to both sides:

2x = 60

Finally, dividing both sides by 2:

x = 30

So the value of x is 30

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The range of the function is the set of all real numbers greater than or equal to -4.

The function assumes values of y = -4 or greater, which represent the range of the graphed function.

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To make parallelogram WXYZ a square, the following conditions must be met:

1. All four sides of the parallelogram must have equal length.

2. The angles between adjacent sides must be 90 degrees.

Since a square is a special type of parallelogram with all sides equal and all angles equal to 90 degrees, we can determine the value of m that would make WXYZ a square by ensuring that these conditions are met. To find the value of m, we need more information about the dimensions or properties of the parallelogram WXYZ. Please provide additional details or measurements related to the parallelogram. The diagonals of a square are equal in length and bisect each other at 90-degree angles. The perimeter of a square is the sum of all four sides, and the area of a square is calculated by squaring the length of one side.In order for parallelogram WXYZ to be a square, it must have congruent sides and right angles at each vertex.

Since opposite sides of a parallelogram are congruent, we can equate the lengths of adjacent sides to find the value of m that would make it a square.

Let's assume that WX and XY are adjacent sides of the parallelogram.

If WX = XY, then the parallelogram would have congruent sides.

Let's say WX = m and XY = m.

To form a square, the angles at each vertex must be right angles. This means that WX and XY must be perpendicular to each other.

In a square, opposite sides are parallel, so the slopes of WX and XY must be negative reciprocals of each other.

The slope of WX can be represented as (change in y) / (change in x). Since it is perpendicular to XY, its slope will be the negative reciprocal of the slope of XY.

Let's assume the slope of XY is denoted as a. Then the slope of WX would be -1/a.

We can now equate the slopes of WX and XY:

-1/a = (change in y) / (change in x)

Simplifying this equation, we get:

a = -1

Therefore, the slope of XY is -1.

Now, we can equate the lengths of WX and XY:

m = m

Since WX = XY and both sides have length m, we can say that m = m.

So, any value of m would make parallelogram WXYZ a square as long as the sides WX and XY are congruent and perpendicular to each other, with a slope of -1.

hence, the value of m = -1.

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The combinations of partial quotients that can be used to find the quotient of 84÷4 are given as follows:

What is the partial quotient method?

when a division is done applying the partial quotient method, consecutive subtractions are done with n groups of the divisor. Each partial quotient is the number of groups of each term and the final quotient is the sum of the partial quotients.

The final quotient of 84÷4 as follows:

84÷4 =21

hence the sum of quotients is 21.

The possible combinations are only two.

The other combinations are incorrect.