Chuck put new wallpaper in his bathroom. The pattern of the wallpaper
used 3 triangles to make a straight angle. The measures of the angles
are (9x - 72). (73x + ) and 11) What is the measure of the
obtuse angle? 7.3.5
ext
Tota

The smallest number of bananas that can grow in a bunch is 126.

To calculate the least amount of bananas that can grow in a bunch, we must identify which are the smallest possibilities, in this case they are 14 fingers per hand and 9 hands per bunch.

According to the above, the least amount of bananas per bunch would be:

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The number of questions that were answered per minute 20 questions

the question reads: Jamie answered 16 questions in 4/5 minutes. How many questions were answered per minute?

You should number that a minute is made up of 60 seconds

This implies that 4/5 of a minute is given as 4/5 * 60

This is equal to 48 seconds

So every 48 seconds, Jamie answers 16 questions

This implies that (16*60)/48 = 20

Therefore in one minute Jamie would answer 20 questions

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Answer:

I can tell it's the answer number 5

Answer:

  86.75

Step-by-step explanation:

Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.

The grade for the course, with fourth test score x, will be ...

  0.20(63.5 +76 +87) +0.40x = 80

  0.40x +45.3 = 80

Solving for x, we get ...

  0.40x = 34.7 . . . . subtract 45.3

  x = 86.75 . . . . . . . divide by 0.4

The minimum score you need on the fourth test is 86.75.

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Answer:

Step-by-step explanation:

a) the number of graduates planning to continue studying :

= (37 1/2% + 12 1/2% + 16 2/3%) × 200

\(=\frac{\left( 37\frac{1}{2} +12\frac{1}{2} +16\frac{2}{3} \right) }{100} \times200\)

= (37.5 + 12.5 + 16.666666666667)×2

= 133.333333333334

…………………………………

b) the measurement of the angle representing those who plan to work :

= (360× 33 1/2)÷100

= (360× 33.333333333333)÷100

=119.999999999999

Answer:

(g ◦ f)(x) = g(f(x)) = cos(f(x)) = cos(7x2).

The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.

In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.

The next choice shows the triangle's side length:

The point is,

The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.

Using Pythagoras' Theorem.

Use the formula:

a² + b² = c²

For 4, 8, 11

4, 8, 11

4² + 8² = 16 + 64 = 80

11² = 121

80 is not equal to 121 it cann ot form a right triangle

For 6, 8, 13

6² + 8² = 36 + 64 = 100

13² = 169

100 is equal to 169 - 69 can form a right triangle

For √3, √5, 8

(√3)² + (√5)² = 3 + 5 = 8

8² = 64

8 is equal to 64 cannot form a right triangle

For √3, √13, 4

(√3)² + (√13)² = 3 + 13 = 16

4² = 16

16 is equal to 16 can form a right triangle

In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.

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Answer:

The linear equation giving the demand x in terms of the rent p can be written as x = 40 - 0.042p, where x is the number of occupied units and p is the monthly rent.

All the ordered pairs that represent points on the graph of this equation include the following:

A. (-4, 4).

C. (-2, 1)

E. (2, -5)

F. (0, -2)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the solutions are include following;

Ordered pair = (-4, 4).

Ordered pair = (-2, 1).

Ordered pair = (2, -5).

Ordered pair = (0, -2).

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Complete Question:

Which ordered pairs represent points on the graph of this equation? Select all that apply.

2y= –3x–4

(-4, 4)

(7, 6)

(-2, 1)

(0, 7)

(2, -5)

(0, -2)

Using the parentheses to rewrite the expression 32.6 ÷ 10-5 x 8-9.16 gives 43.

Parentheses can be used in expressions to group terms and change the order of operations. The order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved.

Using the expression 32.6 ÷ 10-5 x 8-9.16

32.6 ÷ 10-5 x 8-9.16 = 32.6 ÷ (10-5) x 8-9.16

                                 = (32.6 ÷ 5) x 8-9.16

                                 = (6.52 x 8)-9.16

                                 = 52.16-9.16  

                                 = 43

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Answer

approximately 0.0067

Step-by-step explanation:

If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

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

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

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Answer:

51.3

Step-by-step explanation:

Tan(y) like all Tan Trig functions, is defined as the side opposite divided by the side adjacent.

The side adjacent is part of the reference angle.

The side opposite is not connected to the reference angle at all.

Side Opposite = 10

Side Adjacent = 8

Tan(y) = 10/8

Tan(y) = 1.25

y = Tan-1(1.25)

y = 51.34

y = 51.3

Answer:

9

Step-by-step explanation:

|-5| = 5

|4| = 4

5+4

There is a 2/17 difference between 16/17 and 14/17 as 17 is the shared denominator of both fractions.

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.

Given,

To get the difference between 16/17 and 14/17, discover their common denominator first.

17 is the shared denominator of both fractions.

To solve, multiply the result by the numerator of the fractions, then divide the sum by the common denominator:

16 - 14/17 (16 - 14) = 2/17 is the solution.

Therefore, there is a 2/17 difference between 16/17 and 14/17.

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The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

Answer:

398.6

Step-by-step explanation:

Any calculator will work.

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

The formula of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis as g(x) = 8x⁴ + 5x³- 2x²-6x + 5 .

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Reflection across the y-axis is defined as reflecting a point across they = x,  the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).

So reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

We have to determine the equation of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis.

Since reflected across the y-axis: f(x) → f(-x), So substitute the value x = -x

⇒ f(-x) = 8(-x)⁴-5(-x)³-2(-x)²+6(-x)+5

⇒ f(-x) = 8x⁴ + 5x³- 2x²-6x + 5 = g(x)

Hence, the equation of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis as g(x) = 8x⁴ + 5x³- 2x²-6x + 5 .

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Answer:

Simplify the expression.

3(y-1+2y)

3y - 3 + 6y

9y - 3

Based on the description provided, the section of the chart that represents the point where a bill is first debated in subcommittees is: C and D

In the given chart, the parallel lines represent the progression of a bill through various stages in the legislative process. The boxes on the top line represent one set of actions or steps, while the boxes on the bottom line represent another set of actions or steps.

Moving from left to right on the chart, the boxes A and B are paired, representing a particular stage in the process. Similarly, the boxes C and D are paired, indicating another stage in the process.

In the context of the question, the stage where a bill is first debated in subcommittees is represented by the boxes C and D.

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598,500 round to the nearest ten thousand is 600000.

We round nos. to make our calculation or remembering easier to get an estimated result.

According to the given question

We have to round 598500 to the nearest ten thousand.

To round 598500 to nearest ten thousand first we'll look at the digit at thousand's place in this case it 8 so in this case we'll add 1 to the digit and put 0's after it.

∴ 8500 becomes 9000

Now the number 599000 we'll look at the digit at ten thousand's place which is 9 we'll add 1 to it which will make it 0 and 1 will carry and we'll put 0's after it.

∴ 599000 will become 600000 rounded to ten thousand's place.

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x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

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To draw the 6th term, represent it visually within the context of the pattern or sequence from which it is derived.

To draw the 6th term, we need to understand the context or pattern from which the term is derived.

Drawing the term usually involves representing the elements or characteristics of the pattern in a visual form.

Without specific information about the pattern, we can provide a general approach to drawing the 6th term.

Identify the Pattern:

Determine the sequence or pattern from which the 6th term is derived.

It could be a numerical sequence, a geometric pattern, or any other pattern.

For example, if the pattern is a number sequence of multiples of 3, the first few terms would be 3, 6, 9, 12, 15, and so on.

Visualize the Pattern: Based on the identified pattern, visualize how the elements change or progress from term to term.

This could involve drawing a diagram, a graph, or any visual representation that captures the pattern.

Consider using a coordinate grid, a number line, or any other suitable visual aid.

Locate the 6th Term:

Use the information from the pattern and the visualization to determine the specific position or value of the 6th term.

In our example of multiples of 3, the 6th term would be 18.

Draw the 6th Term: Finally, represent the 6th term in your chosen visual form.

This could mean marking the position on a number line, plotting a point on a graph, or incorporating the value into a diagram.

Note that the specific method of drawing the 6th term will depend on the nature of the pattern and the context in which it is given.

Providing more details about the pattern would allow for a more accurate and specific visual representation of the 6th term.

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Answer:

a) The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).

b) The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).

c) A sample size of 12 is needed.

d) A sample size of 125 is needed.

Step-by-step explanation:

(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85.

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96\frac{0.78}{\sqrt{15}} = 0.39\)

The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.39 = 4.46

The upper end of the interval is the sample mean added to M. So it is 4.85 + 0.39 = 5.24

The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).

(b) Compute a 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.98}{2} = 0.01\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.01 = 0.99\), so Z = 2.327.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 2.327\frac{0.78}{\sqrt{11}} = 0.55\)

The lower end of the interval is the sample mean subtracted by M. So it is 4.56 - 0.55 = 4.01

The upper end of the interval is the sample mean added to M. So it is 4.56 + 0.55 = 5.11

The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.46?

95% CI means that \(z = 1.96\)

A sample of n is needed, and n is found when M = 0.46. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.46 = 1.96\frac{0.78}{\sqrt{n}}\)

\(0.46\sqrt{n} = 1.96*0.78\)

\((\sqrt{n})^2 = (\frac{1.96*0.78}{0.46})^2\)

\(n = 11.05\)

Rounding up

A sample size of 12 is needed.

(d) What sample size is necessary to estimate true average porosity to within 0.18 with 99% confidence?

99% CI means that \(z = 2.575\)

A sample of n is needed, and n is found when M = 0.18. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.18 = 2.575\frac{0.78}{\sqrt{n}}\)

\(0.18\sqrt{n} = 2.575*0.78\)

\((\sqrt{n})^2 = (\frac{2.575*0.78}{0.18})^2\)

\(n = 124.5\)

Rounding up

A sample size of 125 is needed.

Answer:

B, D, E

Step-by-step explanation:

Just took test :D

A polygon refers to a flat or two-dimensional shape which is closed and has straight sides. A polygon doesn't curved sides.

From the options given, the true statements about polygons include:

• The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.

• If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon.

• The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.

Therefore, the correct options are B, D and E.

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After solving (c+3)², the procedure is an illustration of the distributive property of equations, and c = -3.

Perhaps the most basic form has just been assumed to represent the fraction with the least process. How or when to decide mostly on fundamental form. Look for components that are present in both the denominator and the numerator. Sometimes it is possible to determine if a fractional integer is a power of two.

A algebraic theorem is a statement with two equal sides and an equal sign in the center. The degrees earned by each variable are stated in descending order, similar to an equation's general form. A linear equation has the formula x + b = 0. A three distinct linear function has the general form x + b y + c = 0. (or something similar). Mathematics can be categorized as identities or conditioned equations.

given:

\(( c+ 3 ) ^ 2\)

= by using formulas of \(( a+ b ) ^2\)

by distributive property

\(c^2 + 3^2 + 6c\)

\(= c^2 + 9 + 6c\)

\(c^2 + 3c + 3c + 9 = 0\)

= (c + 3 )(c+ 3)

c = -3

After solving (c+3)², the procedure is an illustration of the distributive property of equations, and c = -3.

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