HELP math quiz please

What is the result when the number 65 is increased by 53%?

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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Answer:

(0, 0)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Everything is right except the second one. It is acute as all the angles are under 90 degrees.

A)obtuse

B)acute

C)right

D) right

Yes, this confidence interval provide evidence of an association between development of cancer and taking finasteride.

The likelihood that a parameter will fall between two values around the mean is shown by a confidence interval. Confidence intervals quantify how confident or uncertain a sampling technique is. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

Here,

Yes, this confidence interval shows a connection between using finasteride and a higher risk of developing cancer.

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Answer:

Is there anything else to the question like a equation?

Step-by-step explanation:

Answer:

337 = 3

Step-by-step explanation:

Multiply by LCM

337 = 3

and the sides are not equal so I guess there is no answer but

337 = 3

Answer:

The answer is C ( y= 2/3x - 1 )

Step-by-step explanation:

Equation Formula : y - y1 = m ( x - x1)

y - 1 = 2/3 ( x - 3 )

y - 1 = 2/3x - 2

y = 2/3x - 2 + 1

y = 2/3x - 1

The fraction of the class that overestimated Mrs. Forster's age, given the stem and leaf plot, is 1 / 5

To find the proportion of the class that overestimated Mrs. Forster's age, count the number of ages that are over the age of 48:

49, 50, 51, 52

From the stem and leaf plot, we see that the number of students in the class were 20 students.

The fraction which overestimated Mrs. Forster's age would therefore be :

= Number of students with age predictions over 48 / Number of total students

= 4 / 20

= 1 / 5

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Answer:

\(12+3\sqrt{5}\)

Step-by-step explanation:

\((\frac{33}{4-\sqrt{5}})(\frac{4+\sqrt{5}}{4+\sqrt{5}})=\frac{132+33\sqrt{5}}{16-5}=\frac{11(12+3\sqrt{5})}{11}=12+3\sqrt{5}\)

Answer:

A C D

Step-by-step explanation:

The reason for this is because rational numbers are fractions and decimals.

B is an irrational like pi and other repeating decimals

Answer

A. B. C.

Step-by-step explanation:

it is a number that can be written as a fraction or goes on forever

Answer: B

Step-by-step explanation:

Two different mathematical models that can be derived from the Fibonacci's rabbits problem are the recursive model and the matrix model.

The recursive model assumes that the rabbits reproduce at a constant rate and that each pair of rabbits needs a month to mature before they can reproduce. The model can be represented by the recursive formula Fn = Fn-1 + Fn-2, where Fn represents the number of rabbits at month n and Fn-1 and Fn-2 represent the number of rabbits at months n-1 and n-2, respectively. This model is based on the assumption that rabbits can breed indefinitely without any constraints, and it only considers the number of rabbits at each month.

The matrix model, on the other hand, assumes that the rabbits reproduce at a constant rate, but it takes into account the constraint of limited resources, such as food and space. This model is represented by a matrix equation of the form [Fn Fn-1] = [Fn-1 Fn-2][1 1; 1 0], where [Fn Fn-1] represents a vector of the number of rabbits at months n and n-1, and [Fn-1 Fn-2] represents the matrix of the number of rabbits at months n-1 and n-2, respectively. This model is based on the assumption that the growth of the rabbit population is limited by the available resources, and it considers the number of rabbits and the resources at each month.

Both models were derived from the same verbal problem of Fibonacci's rabbits, but they made different assumptions about the growth and constraints of the rabbit population. The recursive model assumes that rabbits can breed indefinitely without any constraints, while the matrix model takes into account the constraints of limited resources. These different assumptions resulted in two different mathematical formulations that provide different insights into the growth and constraints of the rabbit population.

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Answer:500 ft.-65 ft.=435 ft.

Step-by-step explanation:435 ft. is your answer because the change of elevation goes down which means you subtract so I subtracted 500-65=435 feet

Hello!

\(3x^{2} - 6x + 1 = 0\\\\x= \dfrac{-b \±\sqrt{b^{2}-4ac } }{2a} \\\\\\x = \dfrac{-(-6) \±\sqrt{(-6)^{2}-4*3*1 } }{2*3} \\\\\\x =\dfrac{6 \±\sqrt{24 } }{6}\\\\\boxed{x =\dfrac{3 \±\sqrt{6 } }{3}}\)

Answer:

3rd option

Step-by-step explanation:

the denominator cannot be zero as this would make the expression undefined.

equating the denominator to zero and solving gives the values that x cannot be.

x² - 7x - 18 = 0 ← in standard form

(x - 9)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 2 = 0 ⇒ x = - 2

then

x = - 2, x = 9 ← are the excluded values

Answer:

\(\boxed 3 \: h(x) = 14 {x}^{3} - 7 {x}^{2} + 12\)

The 99% confidence interval for the average number of hours a student spends studying for a statistics exam is (2.059, 5.941) hours.

To find a 99% confidence interval for the average number of hours a student spends studying for a statistics exam, we can use the formula:

CI = x ± z*(o/sqrt(n))

where CI is the confidence interval, x is the sample mean, z is the z-score for the desired confidence level (in this case, 99%), o is the population standard deviation, and n is the sample size.

Plugging in the given values, we get: CI = 4 ± 2.576*(6.25/sqrt(50)) CI = 4 ± 1.941 CI = (2.059, 5.941)

Therefore, the 99% confidence interval for the average number of hours a student spends studying for a statistics exam is (2.059, 5.941) hours.

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Answer:

15%

Step-by-step explanation:

The solution to this expression (√5 - 3√2)(√5 + 3√2) is equal to -13.

In Mathematics and Geometry, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:

a² - b² = (a + b)(a - b).

Where:

a and b represent numerical values (numbers or numerals).

Based on the information provided, we have the following mathematical expression:

(√5 - 3√2)(√5 + 3√2);

By comparison, we have the following:

(√5 - 3√2)(√5 + 3√2) = (a + b)(a - b)

a² - b² = (√5)² - (3√2)²

a² - b² = 5 - 18

a² - b² = -13.

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Keith should budget an average of approximately 72 minutes per customer if he wants to be 99% certain that he does not go over budget.

We need to calculate the probability that a technician will take more than 35 minutes to complete an oil change and inspection. We can do this using the standard normal distribution, because the sample size is large (n=4500) and the distribution of the oil change times is approximately normal due to the Central Limit Theorem. Specifically, we can use the formula for a z-score:

z = (x - mu) / sigma

where x is the budgeted time (35 minutes), mu is the mean time for an oil change and inspection (32 minutes), and sigma is the standard deviation of the oil change times (18 minutes).

Plugging in the numbers, we get:

z = (35 - 32) / 18 = 0.167

We can then use a standard normal distribution table or calculator to find the probability that a z-score is greater than 0.167, which is approximately 0.4325. Therefore, the probability that a technician will take more than 35 minutes to complete an oil change and inspection is 0.4325, or 43.25%.

So, based on this calculation, budgeting 35 minutes per customer may not be enough to complete the work for all 40 customers within the promotion period.

To answer the second question, we need to find the amount of time per customer that will ensure that Keith is 99% certain that he does not go over budget. In other words, we want to find the value of x such that the probability that a technician will take more than x minutes to complete an oil change and inspection is 0.01 (or 1%).

We can use the same formula as before to find the corresponding z-score:

z = (x - mu) / sigma

But this time, we want to solve for x, so we rearrange the formula as follows:

x = mu + z × sigma

where z is the z-score corresponding to the 99th percentile of the standard normal distribution, which is approximately 2.33.

Plugging in the numbers, we get:

x = 32 + 2.33 × 18 = 71.94

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Answer:

(2,7)

Step-by-step explanation:

y=6x-5

y=x+5

Since they are both equal to y, set them equal to each other

6x-5 = x+5

Subtract x from each side

6x-x-5 = x+5-x

5x-5 = 5

Add 5 to each side

5x-5 +5 = 5+5

5x=10

Divide by 5

5x/5 = 10/5

x=2

y = x+5

y = 2+5

y =7

Answer:

Choice C: (2,7)

Step-by-step explanation:

Using substitution method let y = x + 5

We have x + 5 = 6x - 5

Get let’s get rid of the 6x, so -5x + 5 = -5

Get rid of the 5 by subtracting by 5, so -5x = -10

Divide -5 on both sides and you get x = 2

Input 2 for x in y = x + 5, we get y = 2 + 5, which equals 7.

So (2,7)

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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Lines KL and MN  are related is by the lines being perpendicular. Therefore, the correct option is C.

Perpendicular lines are lines that are formed when two lines meet each other at the right angle or 90 degrees. This property of lines is said to be perpendicularity.

If a line passes through two points, then the slope of the line is

\(\text{m}=\dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

From the given graph it is clear that coordinates of points on line KL are K(-8,2) and L(6,2).

The slope of line KL is

\(\text{m}_1=\dfrac{2-2}{6-(-8)} =0\)

The slope of line KL is 0, it means it is a horizontal line.

From the given graph it is clear that coordinates of points on line MN are M(-4,8) and N(-4,-6).

The slope of line MN is

\(\text{m}_2=\dfrac{-6-8}{-4-(-4)} =\dfrac{1}{0}\)

The slope of line MN is 1/0 or undefined, it means it is a vertical line.

We know that vertical and horizontal lines are perpendicular to each other. Therefore, the lines KL and MN are perpendicular to each other.

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Answer:

x<2

Step-by-step explanation:

5<-5(3x-7)

divide by 5

1<-3x+7

3x<7-1

3x<6

x<2

To prove that triangle ADE and triangle ABC are similar, the most appropriate method would be the AA (Angle-Angle) Postulate.

The AA Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, we can examine the angles in triangle ADE and triangle ABC to determine if they are congruent.

By visually analyzing the figure, we can observe that angle A in triangle ADE is congruent to angle A in triangle ABC since they are corresponding angles. Additionally, angle D in triangle ADE is congruent to angle C in triangle ABC, as they are vertical angles.

Having identified the congruent angles, we can apply the AA Postulate to conclude that triangle ADE and triangle ABC are similar. This means their corresponding sides will have proportional lengths, allowing us to establish a proportional relationship between the two triangles.

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Answer: rs 400 and 500

Step-by-step explanation:

It is important for scientists to use all of their results because selective reporting can lead to biased or incomplete conclusions. Including all results helps ensure objectivity and transparency in scientific findings.

When the evidence neither supports nor contradicts the hypothesis, it is crucial for scientists to acknowledge and report this outcome. It indicates the need for further investigation and can contribute to the accumulation of knowledge. Scientists should explore alternative explanations, refine their hypotheses, or modify their experimental approaches to gain a deeper understanding of the phenomenon.

Scientists repeating each other's experiments serves as a vital aspect of the scientific process called replication. Replication helps validate or challenge previous findings, ensures the reliability of results, and identifies any potential errors or biases. It enhances the overall credibility and robustness of scientific knowledge by promoting consensus and reducing the likelihood of false or misleading conclusions.

Regarding whether there is any scientific knowledge that it would be better not to have, it is a complex question. Generally, scientific knowledge empowers humanity by expanding our understanding of the world and driving progress. However, ethical considerations may arise in certain areas, such as knowledge that could be weaponized or have harmful consequences if misused. Responsible dissemination and application of scientific knowledge, along with ethical frameworks, help ensure the benefits outweigh the potential risks.

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