. The following list of monthly expenses for a first-year student at a post-secondary
institution are presented. The student has a monthly income of $1,450. Is the student
following the recommended rule of allocating 50% of monthly income to needs, 30% to
wants and 20% to savings or debt?
Income: $1,450

The equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.

The given function is f(x) = 6x2 - x3.

We need to find the equation of the tangent line to the given curve at the point (1, 5).

To find the equation of the tangent line, we need to find the slope of the tangent line. The slope of the tangent line is given by the derivative of the curve at the given point.

The derivative of the given curve is f' (x) = 3x2 + 12x.

Substituting the value of x as 1, we get the slope of the tangent line at (1, 5) as f' (1) = 3(1)2 + 12(1) = 15.

Therefore, the equation of the tangent line at (1, 5) is given by y – 5 = 15(x – 1).

This can be simplified to y = 15x – 10.

Hence, the equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.

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The price difference, which can then be used to determine the extra he can charge for the front row tickets.

To calculate the price difference between the front row and second row tickets, Jim should first identify the mean price of the second row tickets, P2. He can then compare the mean price of the second row tickets to the mean price of the front row tickets, P1. He can then calculate the price difference between the two rows by subtracting the mean price of the second row tickets from the mean price of the first row tickets, (P1-P2). This will give him the price difference, which can then be used to determine the extra he can charge for the front row tickets.

For example, if the mean price of the second row tickets, P2, is $15 and the mean price of the first row tickets, P1, is $20, then the price difference would be $5, meaning he can charge an extra $5 for the front row tickets.

Formula: Price Difference = P1 - P2

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a. To determine if the sample differs from the claim, we can use a hypothesis test. The null hypothesis is that the mean life of the AA batteries in toys is 5 hours, and the alternative hypothesis is that the mean life is different from 5 hours.

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Using a t-test with a significance level of 0.05, we can calculate the t-statistic and the p-value.

The t-statistic is calculated as (mean - hypothesized mean) / (standard deviation / sqrt(sample size))

t = (3.58 - 5) / (1.85 / sqrt(16)) = -2.06

The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true.

p-value = P(t < -2.06) = 0.048

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that the sample mean of 3.58 hours differs significantly from the claim of 5 hours.

b. The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true. If we change the significance level to 0.001, the p-value would be less than 0.001, which would still be less than the new significance level. Therefore the conclusion would still be the same, the sample mean of 3.58 hours differs significantly from the claim of 5 hours.

However, it's worth mentioning that a lower significance level (0.001) would require a stronger evidence against the null hypothesis, therefore it would be more stringent in accepting the alternative hypothesis.

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If there is only one answer, it is the coordinates. y = 1/2x - 1, y = 4x + 6 equals (0,6) (-3/2, 0), and so forth.

Given,

y = 1/2x - 1

y= 4x + 6

You may also rapidly graph them on paper as follows.

To get two points for each line, find the x and y intercepts for each line.

y = 1/2x - 1

(0, -1) (2, 0)

For the next line

y= 4x + 6

(0, 6) (-3/2, 0)

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To solve for x in this problem, we need to use the Law of Cosines.

We can set up the equation as follows:

a² = b² + c² - 2bc cos(x)

We can substitute the values for a, b, and c, which are 22, 10, and 10 respectively. This gives us the equation:

22² = 10² + 10² - 2(10)(10) cos(x)

Simplifying the equation gives us:

484 = 200 - 200cos(x)

Therefore,

200cos(x) = 284

We can divide both sides by 200 to get cos(x) = 1.42.

We can take the inverse cosine of both sides to get x = 54.15°.

Rounding to the nearest tenth, x = 54.

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The diagram of the required shaded region of the Venn representing the set of elements (A ∩ B)' ∪ C, created with MS Word, is attached.

A Venn diagram consists of circles or curved enclosures, representing sets, located in a universal set which is a rectangle.

The sdets shown in the Venn diagram = Set A, Set B, and Set C

The required region to be shaded in the Venn diagram = (A ∩ B)' ∪ C'

A ∩ B (A intersection B) is the set of elements common to both Set A and Set B

(A ∩ B)' (A intersection B) complement is the set of all elements which are not in the set of elements common to both Set A and Set B

(A ∩ B)' ∪ C (A intersection B)  comliment union C; The set of elements not in the intersection of Set A and Set B, but contains the elements in Set C

(A ∩ B)' ∪ C' (A intersection B)  comliment union C complement; The set of elements not in the intersection of Set A and Set B, but includes elements in the universal set, excluding all elements in the Set C.

The required shaded region is; A ∩ (B ∪ C)', B ∩ (A ∪ C)' and (A ∪ B ∪ C)'

Please find attached the diagram of the Venn diagram, created with MS Word, with the shaded region representing (A ∩ B)' ∪ C'

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The water volume in the kiddie pool is 6561π [tex]in^{3}[/tex], the correct answer is B. 6561π  [tex]in^{3}[/tex].

The volume can be found by using cylinder volume formula V = π[tex].r^{2}.h[/tex]

So, the kiddie pool has 6561π [tex]in^{3}[/tex] of water.

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The mean of the sampling distribution is related to the mean of the population, the standard deviation of the sampling distribution is related to the standard deviation of the population and the shape of the sampling distribution is affected by the sample size.

a. The mean of the sampling distribution is related to the mean of the population. The mean of the sampling distribution is an estimate of the population mean and is usually denoted by x⁻. The mean of the sampling distribution is expected to be close to the population mean, as the sample size increases. However, if the sample size is small, there will be more variation in the sample means and the sample mean will not be an accurate estimate of the population mean.

b. The standard deviation of the sampling distribution is related to the standard deviation of the population. The standard deviation of the sampling distribution is an estimate of the population standard deviation and is usually denoted by s. The standard deviation of the sampling distribution is expected to be smaller than the population standard deviation, as the sample size increases. The standard deviation of the sampling distribution is also affected by the sample size, it decreases as sample size increases.

c. The shape of the sampling distribution is affected by the sample size. As the sample size increases, the shape of the sampling distribution becomes more normal and less skewed, regardless of the shape of the population. The larger the sample size, the less spread in the sample means and more likely that the sample mean will be close to the population mean.

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Answer:

2:35

Step-by-step explanation:

you are gust adding so 25 +10 = 35

It has a diameter of 1.25 inches and yield stress of 63,000 psi. Find the variable component stress.

alternative the fee of weight for pressure in the formula for stress, σ = F/A, wherein F is the force and A is the vicinity of go-phase.

In easy phrases we can define pressure because the pressure of resistance per unit area, provided by means of a frame against deformation. strain is the ratio of force over area (S =R/A, in which S is the strain, R is the inner resisting force and A is the move-sectional location).

while the forces acting on the frame are trying to squash it's far compression. The method underneath is used to calculate the pressure: strain =force/ cross-sectional location. σ= F/A.

If we are about to layout a beam or a member. We need strain fee to evaluate with extraordinary pass-sectional shapes and distinct material homes to reach at a feasible section.”

Therefore, It has a diameter of 1.25 inches and yield stress of 63,000 psi.

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The probability of exactly 4 of the 7 hens contracting the disease is ⁷C₄(0.15)⁴(0.85)³.. The ideal response is (A).

How can the binomial distribution be used to calculate probability?

The binomial theorem, which can be expressed as (a + b)n = nC0anb0 + nC1an1b1 + nC2an2b2 +....+ nCna0bn, is the foundation of the binomial distribution.Events must be independent of one another and have probabilities that add up to 1 in order for the probability to be used.

Due to that,There is a 15% chance that the chicken will be affected it is spelled as as,

15% P(infected)

= 15/100

= 0.15

Consequently, the likelihood of avoiding diseased chicken is,

P(not contaminated) = 1 - 0.15= 0.85

Seven chickens in all will be used for the test.

Now, the binomial distribution may be used to determine the likelihood of having exactly 4 sick chickens.

nCxpxqnx is a general expression for the binomial distribution.

n = 7 and x = 4 for the case where p = P(infected) and q = P(not infected) are given

Consequently, the likelihood is given as,

P = 7C4(0.15)4(0.85)3 (Exact 4 are infected).

Therefore, the likelihood that the virus infects precisely 4 out of the 7 chickens sampled is ⁷C₄(0.15)⁴(0.85)³.

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The probability result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners.

The podcast host is polling the next 100 listeners who send her fan emails in order to find out how they like the show. The results of the poll show that 80 out of 90 listeners polled said they liked it. This result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners. This means that the results of the poll may not be reflective of the opinion of all of the podcast host's listeners. Furthermore, the results may be influenced by the volunteer bias, as the respondents may have volunteered to take part in the poll because they already liked the show and wanted to show their support. Additionally, the results may be affected by non-response bias, as those who chose not to take part in the poll may have different opinions than those who did.

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The right response is E. n = 100 at whatever degree of confidence.

We are aware that the sample size's square root and the margin of error are inversely proportional. The margin of error therefore decreases as n increases, but we also know that margin of error is proportional to the critical value, which increases as confidence level increases. However, for t and z, and for a relevant confidence level, the critical value lies between 1-3, so the sample size has the greatest impact.Because of this, choice E is the right one.

Therefore, The right response is E. n = 100 at whatever degree of confidence.

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Katie  after 1 hour of driving, he had 6.75 gallons of gas. Also, after 6 hours of driving, she had 1.5 gallons left.

We can write these values as coordinate points, on the form:

As a result, the sentence: "After an hour of driving, Katie had $6.75 worth of gas." can be seen as the following:

(1,6.75)

And: "After 6 hours of driving, there was only 1.5 gallons left" will have the point:

(6,1.5)$

Part B

With this in mind, we can find the slope of a linear function that passes through those two points. Then,

[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1.5-6.75}{6-1}=\frac{-5.25}{5}=-1.05$[/tex]

Thus, the slope is -1.05.

Part C

Now, we will write a linear equation that relates[tex]$\mathrm{g}$[/tex] and[tex]$\mathrm{h}$[/tex]. As we already have the slope, we can use it to find the y-intercept as:

[tex]$$y=m x+b$$[/tex]

[tex]$g=m h+b$[/tex]Writing it with the variable[tex]s $\mathrm{g}$[/tex]and [tex]$\mathrm{h}$[/tex].

[tex]$$1.5=(-1.05)(6)+b$$[/tex]

[tex]1.5+6.3=b \\[/tex]

7.8=b

This means that an equation for g in terms of h is given by:

[tex]$$g=-1.05 h+7.8$$[/tex]

Part D

For this portion, we will apply the linear equation we discovered for calculating how much gas she will still have after a three-hour drive. Thus, h will have a value of 3, and we replace on the function to get the following result:

[tex]g=-1.05(3)+7.8 \\[/tex]

=-3.15+7.8

=4.65

This means that Katie will have 4.65 gallons left after driving for 3 hours.

The complete question is,

Katie noticed that after 1 hour of driving, she had 6.75 gallons of gas. After 6 hours of driving, there was only 1.5 gallons left. (Hint: Leave your answers as decimals). A.) Represent the information as two coordinate pairs in the form of (h, g), where h is the number of hours driven and g is the gallon of gas left. B.) Calculate the slope between the two coordinates. C.) Assuming the relationship between h and g is linear, create an equation for g in terms of h. D.) How much gas would she have left after dving for 3 hours?

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Answer:

10 $1 bills

7 $5 bills

Step-by-step explanation:

Let s = number of $1 bills.

Let f = number of $5 bills.

1s + 5f = 45

s = f + 3

f + 3 + 5f = 45

6f = 42

f = 7

s = f + 3 = 7 + 3 = 10

10 $1 bills

7 $5 bills

The length of the x is 12 units .

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c² = a²+ b², where c is the hypotenuse and a,b are the other two sides.

Since the given triangle is a right anlgled triangle so we will use Pythagorean theorem:

using Pythagorean theorem :

H² = P² + B²

where H is hypotenuse , P is perpendicular and B is base of the triangle

H = 13

P = 12

B = x

=> 13² = 12² + x²

=> 169 = 144 + x²

=> x² = 169- 144

=> x² =25

=> x = 5

so the value of x = 5 units

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Complete question:

given the triangle below, find the length of side x.

The smallest positive real number c that satisfies the above inequality is [tex]$c = \frac{2}{\sqrt{xy}}[/tex]

We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized. We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. The smallest positive value that c can take is[tex]$\frac{2}{\sqrt{xy}}$[/tex].

We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized.

We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$c \ge \frac{2}{\sqrt{xy}|x - y|}$[/tex]. The smallest positive value that c can take is [tex]$\frac{2}{\sqrt{xy}}$[/tex].

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A. Binomial distribution. B. Poisson distribution. C. Normal distribution. D. Multinomial distribution. is the types of distribution as given in the conditon below.

A binomial distribution should be utilized since the answer—whether or not an employed person commutes more than 10 minutes to work—is a yes or no question.

B. The answer is the percentage of days a week on which a working person travels more than 10 minutes to go to work. The Poisson distribution should be utilized since the number of days is a count variable and the mean number of days does not always equal the variance.

C. The answer is the number of minutes a student studies each week. Since the number of study minutes is a continuous variable with an equal mean and variance, the normal distribution should be applied.

D. The answer is the subject's blood type (A,B,AB, or O). Given that there are four alternative outcomes for blood type, multinomial distribution should be employed.

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The ratio for number of chairs with wheels and number of chairs without wheels is 7:2.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

The ratio value is given as 7/9.

There are 7/9 chairs that are with wheels.

This means that the total number of chairs is 9.

Out of the 9 chairs 7 chairs have wheels.

The number of chairs that have no wheels is -

Total number of chairs - Number of chairs with wheels

= 9 - 7

= 2

So, the number of chairs with no wheels is 2

The ratio for number of chairs with wheels to no wheels is -

7:2

Therefore, the ratio value is obtained as 7:2.

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The distance covered on the triangular path to home along point A to B to C is 23.42 miles.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Given that the trip to home goes from point A to point B and then to point C.

The path traced thus, represents the hypotenuse of the two triangles. Triangle BHA and triangle BCH.

The Pythagorean theorem is given as follows:

a^2 + b^2 = c^2

For triangle BHA substitute the value of a = 4 and b =6.

4^2 + 6^2 = c^2

16 + 36 = c^2

c = 7.21

For triangle BHC, substitute the value of a = 7 and b =6.

7^2 + 6^2 = c^2

49 + 36 = c^2

c = 9.21

Now, from point B to point H the additional distance is 7 miles, hence the total distance traveled is:

D = 7.21 + 9.21 + 7

D = 23.42

Hence, the distance covered on the triangular path to home along point A to B to C is 23.42 miles.

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Answer:

y=3/2x+86

Step-by-step explanation:

y=Mx+b

M is the slope and b is the y intercept. The slope of a line is rise/run, in this case 3/2 and the y intercept is where the line goes through the y axis which for this problem, is 86. So y=3/2x+86

The capacity of the container is equal to 7.6 × 10⁻³ kiloliters.

This is a unit conversion question, in which we need to determine how many kiloliters are equivalent to the capacity of a container.

According to capacity tables, a cubic decimeter or 1000 cubic centimeters equals a liter. Then, we can determine the number of kiloliters by using the following cross multiplication:

x = 7.6 dm³ × (1 L / 1 dm³) × (1 kL / 1000 L)

x = 7.6 × 10⁻³ kL

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By finding the greatest common factor between the given numbers, we conclude that the maximum number of groups will be 6.

To find it, we just need to find the greatest common factor between the numbers of boys and girls, to find it, we will decompose these numbers as a product of prime factors.

We will get:

18 = 2*3*3

12 = 2*2*3

The greatest common factor is 2*3 = 6

That is the maximum number of groups alowed, such tthat each group will have:

18/6 = 3 girls.

12/6 = 2 boys.

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To evaluate f(-x) when f(x) = x/(x^2 + 1), we need to substitute -x for x in the function.

So f(-x) = (-x)/((-x)^2 + 1)

Simplifying the denominator we get:

f(-x) = (-x)/(x^2 + 1)

The function f(-x) is equivalent to the function f(x) with the x-value negated. The value of the function f(-x) is the same as the value of the function f(x) but with the x-value negated.

It's important to note that we can also express this as f(-x) = -f(x)

So the value of f(-x) is x/(x^2 + 1) with the x-value negated.

The equation for x in terms of c is x = 29/8c (D).

From the case we have the equation of:

[tex]\frac{2}{3}(cx + \frac{1}{2})-\frac{1}{4}=\frac{5}{2}[/tex]

We will use distribution to isolate x on the left side and all terms of c from others on the right side.

2cx + 2 - 1 = 5

 3       6     4     2

We will use the lowest common multiple to eliminate the numerator:

2cx + 2 - 1 = 5

 3       6     4     2

--------------------------- x 12 --> lowest common multiple

8cx + 4 - 3  =  30

8cx + 1 = 30

8cx = 29

x = 29/8c

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The appropriate interval width for a random sample of 110 observations.

a) w=1

b) w=2

c) w=2

and d) w=4

The interval width is a value that is used to divide the usage distribution into usage rate intervals.

we shall determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following.

let's start.

we are aware the formula to calculate class width.

[tex]w=\frac{L.O-S.O}{N.C}[/tex],

where,

w for width, L.O is stand for largest observation and S.O for smallest observation and N.C is number of classes.

We solve it by options.

so first come on option (a)

given interval is 20 to 85.

[tex]w=\frac{85-20}{110} \\w=\frac{65}{110} \\w=0.59[/tex]

since we need to round upward the class width, w=1

for option (b)

[tex]w=\frac{190-30}{110} \\\\w=\frac{160}{110} =1.45[/tex]

since we need to round upward the class width, w=2

for option (c)

[tex]w=\frac{230-40}{110} \\\\w=\frac{190}{110}=1.73[/tex]

since we need to round upward the class width, w=2

for option (d)

[tex]w=\frac{360}{110} =3.27[/tex]

since we need to round upward the class width, w=4,

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Solid will this lesson focus on the regular square pyramid

Regular square pyramid.

The justification is stated below:

Four triangular faces, five vertices, and eight edges make up the typical square pyramid's square base. The main formulae for a square pyramid are volume and surface area.

By definition, a regular square pyramid is one that has a base that is square, meaning that each of its sides is the same length.

Because it has an apex, a height, lateral faces that are congruent isosceles triangles, and slant height, you can tell that it is a pyramid (the altitude of the lateral faces).

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Answer:

y²

Step-by-step explanation:

4y² - 3y² = (4 - 3) × y² = 1y² = y²

Answer:

Step-by-step explanation:

I'm sorry, I am missing more information to calculate the speed of the car at t = 10 seconds, t = 20 and t = 30. The speed of the car depends on the mathematical function that describes the position of the car in time. Without the knowledge of that function, I'm not able to determine the car's speed at different points in time.

Answer:23.2

Step-by-step explanation:

10/2=5

10/5=2

116/5=23.2

Answer:

580 ft.

Step-by-step explanation:

The height of the cellphone tower can be found using the following proportion:

(shadow of cellphone tower) / (shadow of 10 foot post) = (height of cellphone tower) / (10 feet)

Solving for the height of the cellphone tower:

(116 feet) / (2 feet) = (height of cellphone tower) / (10 feet)

Which brings us to:

116 ÷ 2 = x ÷ 10

58 = x ÷ 10

580 = x

The cell phone tower is 580 ft.