Tabitha’s account balance is $3,800. Of this, $750 is for rent. Tabitha wants to keep a balance greater than $500. Write an inequality describing how much she can withdraw and still meet these conditions

The curvature of the curve is 55/9 in accordance with the provided declaration.

Curve, An abstract phrase used to express the trajectory of a steadily moving particle in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The IS curve displays variants of interest rates plus production levels where anticipated expenditure and income are equal. The many interest and income configurations along whom the merchandise is in homeostasis are represented by the IS Curve.

[tex]\mathbf{r}(t)=\left\langle 6 t, t^2, \frac{1}{9}\left(t^3\right)\right\rangle[/tex]

So,

[tex]x(t)=6 t, y(t)=t^2, z(t)=\frac{1}{9}\left(t^3\right)[/tex]

Then,

[tex]\begin{aligned}& x^{\prime}(t)=\frac{d}{d t}(6 t) \\& =6 \cdot \frac{d}{d t}(t)\end{aligned}[/tex]

= 6(1)

= 6

[tex]\begin{aligned}& y^{\prime}(t)=\frac{d}{d t}\left(t^2\right) \\& =2 t^{2-1}\end{aligned}[/tex]

= 2t

And,

[tex]\begin{aligned}& z^{\prime}(t)=\frac{d}{d t}\left(\frac{1}{9}\left(t^3\right)\right) \\& =\frac{1}{9}\left(3 t^{3-1}\right) \\& =\frac{1}{9}\left(3 t^2\right) \\& =\frac{1}{3}\left(t^2\right)\end{aligned}[/tex]

Now calculating length of the given curve from 0 to 1,

[tex]\begin{aligned}& L=\int_0^1 \sqrt{(6)^2+(2 t)^2+\left(\frac{1}{3}\left(t^2\right)\right)^2} d t \\& =\int_0^1 \sqrt{(6)^2+2 \cdot 6 \cdot \frac{1}{3}\left(t^2\right)+\left(\frac{1}{3}\left(t^2\right)\right)^2} d t \\& =\int_0^1 \sqrt{\left(6+\frac{1}{3}\left(t^2\right)\right)^2} d t\end{aligned}[/tex]

[tex]\begin{aligned}& =\int_0^1\left(6+\frac{1}{3}\left(t^2\right)\right) d t \\& =\int_0^1 6 d t+\int_0^1 \frac{1}{3}\left(t^2\right) d t \\& =6 \int_0^1 d t+\frac{1}{3} \int_0^1 t^2 d t \\& =6[t]_0^1+\frac{1}{3}\left[\frac{t^{2+1}}{2+1}\right]_0^1 \\& =6[1-0]+\frac{1}{3}\left[\frac{t^3}{3}\right]_0^1\end{aligned}[/tex]

[tex]\begin{aligned}& =6(1)+\frac{1}{3}\left[\frac{1^3}{3}-\frac{0^3}{3}\right] \\& =6+\frac{1}{3}\left[\frac{1}{3}-0\right] \\& =6+\frac{1}{9} \\& =\frac{54+1}{9}\end{aligned}[/tex]

= 55/9

Therefore, required arc length is 55/9

NOTE:

For a vector valued function,

[tex]\mathbf{r}(t)=\langle x(t), y(t), z(t)\rangle[/tex] arc length fro a to b

[tex]L=\int_a^b \sqrt{\left(x^{\prime}(t)\right)^2+\left(y^{\prime}(t)\right)^2+\left(z^{\prime}(t)\right)^2} d t[/tex]

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The value of m ∠ H-F-K, given the value of the corresponding and supplementary angles, is 84 degrees

The angles given of 6 ( x + 2 ) degrees and 8 ( x - 2 ) degrees are complementary and add up to 180 degrees.

The value of these angles is:

6 ( x + 2 ) = 8 ( x - 2 )

6x + 12 = 8x - 16

8x  - 6x = 16 + 12

x = 28 / 2

x = 14

The angle is:

= 8 ( 14 - 2 )

= 8 x 12

= 96 degrees

The value of m ∠ H-F-K will be supplementary to m ∠ H-F-K so the value of m ∠ H-F-K is:

=  (360 - 96 - 96 ) / 2

= 84 degrees

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The required equation in which case the left side is the power of 10 times n and the right side is the result of multiplying 0.1515 by 10 will be' (10)n = 10(0.1515).

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

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that the equation as;

(10)n=10(0.11515 -n=0.1515

(10)n = 10(0.1515).

n = 0.1515

Therefore, the resulting equation from the subtraction as;

(10n - n) = 10(0.1515) - 0.1515

9n = 9 (0.1515).

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The exact value of cos I in simplest radical form is 5 /√29

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The exact value of cos I in simplest radical form can be found by using trigonometric ratios.

cos I = adjacent / hypotenuse

The opposite is where the angle I is facing. That is opposite = 2

The hypotenuse is where the right angle is facing. That is hypotenuse = √29

The adjacent is the side left after picking opposite and hypotenuse. That is adjacent = 5

cos I = 5 /√29

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Assuming that the company’s claims are true, there is a probability of 0.9824 that the first person to have a college degree is the third person selected at random.

The company claims that 74% of its employees hold college degrees.

Taking the total number of employees as 1,

The probability of employees who do hold a college degree P(3) is 0.74

Therefore, the probability of employees who do not have a college degree is (1-0.74) = 0.26

The probability that the first 2 employees do not have a college degree P(1&2) is 0.26^2

The equation thus turns out to be;

Probability that the 3rd person is the first to hold a college degree = P(1&2)*P(3)= (0.26^2)*0.74= 0.9824

Therefore, the probability that the first person to hold a college degree in the company is the third person chosen at random is 0.9824.

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Our solution set will be {x | x R, x ≤ 7 5/6}.

What is the solution set?

The solution set for an equation is the collection of all possible solutions to that equation. If an equation has no solutions, the solution set is denoted by the ∅ symbol. ∅ refers to the null set (or empty set).

In our problem it is given:

x - 6 [tex]\frac{1}{3}[/tex] [tex]\leq[/tex]  1[tex]\frac{1}{2}[/tex]

To each side, add 6 1/3.

x [tex]\leq[/tex]  1 [tex]\frac{1}{2}[/tex] + 6 [tex]\frac{1}{3}[/tex]

Change the 1/2 and the 1/3 to a common denominator to add them together.

x [tex]\leq[/tex] 1 [tex]\frac{3}{6}[/tex] +6 [tex]\frac{2}{6}[/tex]

x [tex]\leq[/tex] 7 [tex]\frac{5}{6}[/tex]

Therefore our final solution set will be {x | x ∈ R, x ≤ 7 [tex]\frac{5}{6}[/tex]}.

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According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.

In the case of a unit rate expressed as a fraction, the denominator is 1 unit. Divide the denominator by the denominator to represent a rate as a unit rate.

According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.

Conversion Unit, This unit of conversion, also known as a rate, is utilized to help us map out greater numbers on a smaller piece of paper. Miles to Inches conversion factor is

Data provided 3/10 in equals 7/8 miles.

This suggests that we would depict the real 7/8 miles of distance on the map by 3/10 inches. Inevitably, this would result in a reduction in size or length.        

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Answer:

[tex]\textrm{P(2 heads in a row) } =\boxed{\dfrac{3}{8}}[/tex]

Step-by-step explanation:

Let H represent the event that the coin turns up heads and T the event that coin turns up tails

So we can get H on the first toss, then 2 T's on the next two tosses, a T on the first toss and 2 H on the next two tosses, two T on the first two tosses and a H on the third toss etc.

The sample space for 3 tosses of a coin consists of 2³ elements since there are two possible outcomes for each of 3 events

The sample space is enumerated below

1 H H H

2 T H H

3 H T H

4 T T H

5 H H T

6 H T T

7 T H T

8 T T T

There are 3 possibilities where 2 H appear in a row

These are the ones in bold in the table above

Since only 3 outcomes out of a total of 8 possible outcomes can result in 2 heads in a row,

[tex]\textrm{P(2 heads in a row) } =\dfrac{3}{8}[/tex]

The equation and the accompanying justification that describes a line that is parallel to EF is: C. Y = -1/3x + 5 1/3 the slopes are equal.

If two lines are said to be parallel to each other, their equations that is expressed as y = mx + b, will have the same slope value of m. Y = mx + b is the slope-intercept form of any equation that represents a line.

Given that the equation y = -1/3x + 4 represents the line EF, its slope is -1/3. This means the slope of any line that is parallel to y = -1/3x + 4 will be the same as -1/3.

Therefore, the correct justification is: C. Y = -1/3x + 5 1/3 the slopes are equal.

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Manny walked more likely on the circular nature trail.

As a circular path always starts and ends at the same location, we may infer this from the fact that the reference point at the beginning and finish was the same.

Other situations, like going up a slope from the bottom, exclude using the same reference point.

The beginning point and finishing point on a sidewalk or a straight track cannot have the same reference point, in a similar manner.

Therefore we can say that

Hence, Manny walked more likely on the circular nature trail.

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If everyone picks zero, they all win. Only Nash equilibrium is when everyone guesses zero or an extremely low number.

There is no purely dominant tactic in this game. There is a special pure strategy Nash equilibrium, though. Through the iterative elimination of weakly dominated techniques, this equilibrium can be discovered.

Since it cannot potentially be 2/3rds of the average of any guess, guessing any number that lies above 66.67 is dominated for every player. These might be taken away.

Any estimate above 44.45 is weakly dominated for every player once these techniques are removed for each player since no player would guess above 66.67 and 2/3 of 66.67 is roughly 44.45. This procedure will keep going until all numbers higher than 0 are gone.

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Answer: The appropriate hypotheses for this significance test are:

Null hypothesis (H0): The true mean travel time for all students who attend this school is equal to 20 minutes.

Alternative hypothesis (Ha): The true mean travel time for all students who attend this school is greater than 20 minutes.

The null hypothesis states that there is no difference between the claim (20 minutes) and the sample mean (22.4 minutes). The alternative hypothesis states that there is a difference and the sample mean is greater than the claim. The student will use the sample data and a chosen significance level (such as α = 0.05) to decide whether to reject or fail to reject the null hypothesis.

Step-by-step explanation:

No, dividing by 1/2 is not the same as dividing by 2. Dividing by 1/2 means to take a number, and then divide it by 1/2. For example, 8 divided by 1/2 would be 16.

Dividing by 1/2 means to take a number, and then divide it by 1/2. For example, 8 divided by 1/2 would be 16.

Dividing by 2 means to take a number, and then divide it by 2. For example, 8 divided by 2 would be 4.

Dividing by 1/2 involves taking a number and dividing it by one half of itself. For example, if you were to divide the number 8 by 1/2, the result would be sixteen. On the other hand, dividing by 2 means taking a number and dividing it by two. If you were to divide the number 8 by 2, the result would be four. Both operations involve division, but the results are not the same. Dividing by 1/2 involves taking a number, doubling it, and then dividing the result by two, while dividing by 2 involves taking a number and simply dividing it by two. The difference in results can be seen when comparing 8 divided by 1/2, which is 16, and 8 divided by 2, which is 4. Consequently, these two operations are not the same.

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The exponential equation described that passes through (-1, 1.5), (0, 3), (1, 6) is:

y = 3*(2)^x

A general exponential function can be written as:

y = A*(b)^x

Where A is the initial value and b is the base.

First, we know that the function goes through (0, 3), then we can replace these values to get:

3 = A*(b)^0

3 = A

So we have:

y = 3*(b)^x

We also know that the graph passes through the point (-1, 1.5)

Replacing these values we get:

1.5 = 3*(b)^-1

1.5 = 3/b

b = 3/1.5 = 2

Then the exponential equation described is:

y = 3*(2)^x

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The value of y in the rectangle is 11.

A rectangle is a quadrilateral with opposite sides equal to each other. The opposite side are also parallel to each other.

The diagonal of a rectangle divides it into two congruent right triangles. The diagonals also bisect each other. The diagonals are congruent.

Therefore, the length BE is equals to length BC.

Hence,

BE = BC

BE = 4y - 26

BC = 3y - 15

Therefore, let's find y in the rectangle.

BE = BC

4y - 26 = 3y - 15

4y - 3y = -15 + 26

y = 11

Therefore,

y = 11

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Answer:

hola buenos skskskskseolelelldd

Step-by-step explanation:

[tex]area = \frac{\pi ({12}^{2}) }{4} - \frac{1}{2} \times {12}^{2} [/tex]

The answer to the word problem is 14 2/3.

A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Expressing the word problem into an expression;

2 3/4 x 5 1/3

= 11/4 x 16/3

= 44/3

= 14 2/3

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Answer:

-11 1/2.

Step-by-step explanation:

To solve the equation 25 + x/9 + x = 13 + x/47 - x, we'll start by combining like terms on both sides:

25 + x/9 + x = 13 + x/47 - x

(25 + x) + (x/9 - x/47) = 13

(25 + x) + x * (9/47) = 13

Next, we'll isolate x by subtracting 25 from both sides:

x + x * (9/47) = -12

Finally, we'll isolate x by dividing both sides by 1 + (9/47):

x = -12 / (1 + (9/47)) = -12 / (1 + (9/47)) = -12 / (48/47) = -12 * 47/48

So the solution to the equation is x = -12 * 47/48 = -11 1/2.

Answer: 53

Step-by-step explanation:

If 9 ≤ 3/4 + x,

x ≥ 8 1/4 (Transpose the 3/4)

So, the least possible value of 8x - 13 will be when x is the least or, x is 8 1/4

or 33/4

8 x 33/4 - 13 = 66 - 13 = 53

Answer:

I hope my answer is correct!

The least possible value of 8x-13 when 9 <= 3/4 +x is -13. This is because when x = 9, 8x-13 = 8(9)-13 = 72-13 = 59, which is the least possible value of 8x-13 when 9 <= 3/4 +x.

Answer:

76683932992840842842774839498289294929x91983918938019308926753234793357888890878676932 is a very large number and its exact value is not possible to calculate by hand or with common calculators. However, it can be calculated using a computer with advanced mathematical software.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The height of the Eiffel Tower was halved repeatedly to make a model around 30 cm. We know that 30 cm = 0.3 meters.

We can set up an equation:

324m / 2^n = 0.3m

We can solve for n by logarithm base 2:

n = log(324/0.3) / log(2)

n = log(1080) / log(2)

n ≈ 10.6

The height of the Eiffel Tower was divided by 2^10.6, which is not a whole number.

It means that the height of Eiffel Tower was divided by a number that is between 10 and 11 times by 2.

Answer: $6085.15

Step-by-step explanation:

Substituting into the exponential decay formula yields [tex]9250(1-0.051)^8 \approx \$6085.15[/tex].

x + 3y = 70 represents the number of 1-point and 3-point questions in an assignment worth 70 points.

What is algebraic equation ?

An algebraic equation is a mathematical statement that shows that two expressions are equal. It typically consists of a combination of numbers, variables and mathematical operations such as addition, subtraction, multiplication, and division.

The equation that represents the situation where the teacher is creating an assignment worth 70 points and it will consist of questions worth 1 point and questions worth 3 points, where x represents the number of 1-point questions and y represents the number of 3-point questions is:

x + 3y = 70

This equation states that the total number of points, which is the sum of the number of 1-point questions (x) multiplied by 1 and the number of 3-point questions (y) multiplied by 3 is equal to 70.

x + 3y = 70 represents the number of 1-point and 3-point questions in an assignment worth 70 points.

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Answer:

no

Step-by-step explanation:

.63 is different from .603

Answer:

He needs to sell 157 sandwiches to earn $125

Step-by-step explanation:

●$10.50×6 hrs= $63

●$125 - $63= $62 {So he needs to sell $62 worth of sandwiches}

●$0.40 × 157= $62

pov:《$62 + $63 = $125》

Answer:

155 sandwiches

Step-by-step explanation:

First we see what the base rate is for his six-hour shift. We do this by multiplying 10.50 by 6 which is 63. Then we do 125-63 which is 62. As he gets 42 cents per sandwich so we do 62÷0.40, which equals 155 so he needs to sell 155 sandwiches.

Answer:

I hope this is right :)..

Answer:

Jennifer

Step-by-step explanation:

The domain of a function is the set of x-values that result in defined and real values for that function.

In this case the requirement was to plot a graph so that the domain is between -4 and 5 inclusive

We can represent this mathematically as -4 ≤ x ≤ 5

If you look at both graphs, Ashton's graph on the left has a minimum
x-value of -4 and a maximum x-value of 5. So his graph is correct

Carlie's graph on the right does have a minimum x-value of -4 but its maximum x-value is between 2 and 3. So this graph is incorrect

Therefore Jennifer's statement is correct

Answer: Jennifer

Using multiplication we know that the correct option in the given situation is (C) 1L for $1.80 which saves $0.30 when compared to (D).

Multiplying numbers is essentially the same as adding groups of numbers.

Multiplying is the process of repeatedly adding a number. (Before we can use the number to multiply, all of the digits must be the same.)

Learning the time's tables makes sense when seen in this light.

A 5 multiplied by 4 results in 20 (5 + 5 + 5 + 5).

We multiplied the number five by four times.

Due to this, multiplication is occasionally referred to as "times."

So, now compare all options with option (D) as follows:

2L for $3.90

(A) 250 mL for $0.50  with (D) 2L for $3.90

0.50*8

$4 for 2L > 2L for $3.90

(B) 500 mL for $1.10  with (D) 2L for $3.90

1.10*4

$4.4 for 2L > 2L for $3.90

(C) 1L for $1.80 with (D) 2L for $3.90

1.80*2

$3.6 for 2L < 2L for $3.90

(Correct option)

Therefore, using multiplication we know that the correct option in the given situation is (C) 1L for $1.80 which saves $0.30 when compared to (D).

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Complete question:
Milk is sold in four sizes. Which is the better buy? 1 point

A. 250 mL for $0.50

B. 500 mL for $1.10

C. 1L for $1.80

D. 2L for $3.90