= K. ola 2. Veronica has been working on a pressurized model of a rocket filled with nitrous oxide. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 pounds/sq in, the nitrous chamber inside the rocket will explode. The formula for atmospheric pressure, p, h miles above sea level is p(h) = 14.7e-1/10 pounds/sq in. Assume that the rocket is launched at an angle, x, about level ground yat sea level with an initial speed of 1400 feet/sec. Also, assume that the height in feet of the rocket at time t seconds is given by y(t) = -16t2 + t[1400 sin(x)]. sortanta a. At what altitude will the rocket explode? b. If the angle of launch is x = 12 degrees, determine the minimum atmospheric pressure exerted on the rocket during its flight. Will the rocket explode in midair? c. Find the largest launch angle x so that the rocket will not explode.

We can use the concept of similar triangles. Since the building and the statue are casting shadows simultaneously, the angle of elevation of the sun is the same for both. Therefore, the triangles formed by the building, its shadow, and the ground and the statue, its shadow, and the ground are similar triangles.

Let's use the given information:
- Building height = 51 feet
- Building shadow length = 48 feet
- Statue shadow length = 16 feet
- Statue height = x (this is what we need to find)

Now, set up a proportion using the ratios of the corresponding sides of the similar triangles:

(Building height / Building shadow length) = (Statue height / Statue shadow length)

(51 / 48) = (x / 16)

To find the statue height (x), cross-multiply and solve for x:

51 * 16 = 48 * x

816 = 48x

Now, divide by 48 to find the value of x:

x = 816 / 48
x = 17

So, the statue is 17 feet tall.

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15% of 850 is 127.5 and therefore the laptop would be reduced by 127.50

The sale price of the laptop is 722.50

Answer:

OK 825/1000 That is the answer.

Option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B

According to the information given in the question,

A true proportion of 0.325 represents that the two simulations will be conducted for sampling proportions from a population

Simulation A -

Sample size - 100

Trials - 1500

Simulation B -

Sample size - 50

Trials - 2000

Now due to the relation of simulation A and simulation B, they are closely equal-

The total sample size of simulation A= 1500 x 100

= 150000

The total sample size of simulation B = 2000 x 50

= 100000

From the above calculations of simulations A and B, we can see that while comparing the,

Sample Size = Simulation A > Simulation B

Variability = Simulation B < Simulation B

Therefore, option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B is correct.

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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

There are 2^8 = 256 possible truth tables for f(x, y, z). After eliminating the ones that do not satisfy the given condition, we are left with 16 different boolean functions that meet the requirement.

There are 16 different boolean functions f(x, y, z) that satisfy the condition f(x, y, z) = f(x, y, z) for all values of x, y, and z. One way to arrive at this answer is to list out all the possible truth tables for f(x, y, z) and then eliminate the ones that do not satisfy the given condition.

A truth table is a table that lists all possible input combinations for the boolean variables and their corresponding output values.

There are a total of 2^3 = 8 possible input combinations for three boolean variables, and each combination can either result in a true or false output.

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Two unit vectors that are normal to the plane determined by the points A(0, -2, 1), B(1, -1, -2), and C(-1, 1, 0) are:

v₁ = (-2, -1, 1) / √6

v₂ = (-1, 3, 1) / √11

To find unit vectors that are normal to a plane determined by three points, we can use the cross product of two vectors that lie in the plane.

Start with the given points A, B, and C: A(0, -2, 1), B(1, -1, -2), and C(-1, 1, 0).

Calculate two vectors that lie in the plane. We can take the vectors AB and AC:

Vector AB = B - A = (1, -1, -2) - (0, -2, 1) = (1, 1, -3)

Vector AC = C - A = (-1, 1, 0) - (0, -2, 1) = (-1, 3, -1)

Take the cross product of vectors AB and AC to find a vector normal to the plane:

n = AB × AC

n = (1, 1, -3) × (-1, 3, -1)

= (-4, -2, -4)

Normalize the vector n to obtain unit vectors that are normal to the plane:

v₁ = n / ||n||

||n|| = √((-4)^2 + (-2)^2 + (-4)^2) = √36 = 6

v₁ = (-4/6, -2/6, -4/6) = (-2/3, -1/3, -2/3) = (-2, -1, -2) / √6

Similarly, we can find another unit vector perpendicular to the plane:

v₂ = (-1, 3, -1) / ||(-1, 3, -1)||

||(-1, 3, -1)|| = √((-1)^2 + 3^2 + (-1)^2) = √11

v₂ = (-1/√11, 3/√11, -1/√11) = (-1, 3, -1) / √11

Two unit vectors that are normal to the plane determined by the points A(0, -2, 1), B(1, -1, -2), and C(-1, 1, 0) are v₁ = (-2, -1, -2) / √6 and v₂ = (-1, 3, -1) / √11.

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer 8

8+8²=72

8+64=72

72=72

please click thanks and mark brainliest if you like :)

We will solve a follows:

***Explanation of the procedure using change of base for a logarithm***

So:

Answer:

k = -3/4

Step-by-step explanation:

The lines will be parallel if their slopes are equal.  To find the slope of each line, write its equation in slope-intercept form (y = mx + b).  In other words, solve each equation for y and look at the coefficient of x.

2x + 3y = 4k

3y = -2x + 4k

y = (-2/3)x + 4k/3

The slope of the first line is -2/3.

x - 2ky = 7

-2ky = -x + 7

y = [1/(2k)]x - 7/(2k)

The slope of the second line is 1/(2k).

If the slopes are equal, then

1/(2k) = -2/3

Multiply by 2k.

1 = (-2/3)(2k) = (-4/3)k

1 = (-4/3)k

k = -3/4

Answer:

Option D ,i.e., 8/3 \pi is closest to the total volume in cubic inches of the ice cream.

Step-by-step explanation:

Total Volume of the ice cream = Volume of Cone + Volume of Hemisphere

Radius = 1 inches and Height = 6 inches

=> \pi r^{2} h/3 + \pi r^{3} 2/3

=> \pi (1^{2} 6/3 + 1^{3} 2/3)

=> \pi (2+2/3)

=> 8/3 \pi cubic inches.

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Answer:

6 4 6

Step-by-step explanation:

Answer: The answer is 12%

Step-by-step explanation:

Answer:

A.)  THE COST INCREASE IS 12%.

Step-by-step explanation:

The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%

The annual percentage rate (APR) for your cousin's lending arrangement,  to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:

Calculate the interest charged for a $20 loan over one month:

Interest = $40 (repaid amount) - $20 (loaned amount) = $20

Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:

Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%

Multiply the monthly interest rate by 12 to obtain the annual interest rate:

APR = Monthly Interest Rate ×12 = 100% ×12 = 120%

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Answer:

x=3

Step-by-step explanation:

x-3=0

so move the three to the other side of the equal sign to get

x=3

when you move a number to the other side you have to change the sign so your answer is x=3

PLEASE RATE!! I hope this helps!!

Derivation tree is a graphical representation for the derivation of the given production rules of the context free grammar (CFG). The given grammar is unambiguous. The Chomsky Normal Form is as follows: S → NU | NV  ,   V → VN | MU   ,  U → IE | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0   ,   M → 11   ,    N → 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0

a. Derivation tree is a graphical representation for the derivation of the given production rules of the context free grammar (CFG). It is a way to show how the derivation can be done to obtain some string from a given set of production rules. It is also called as the Parse tree.

b. A grammar is unambiguous if each string in the language generated by the grammar has exactly one parse tree. The given grammar follows this rule as for each string generated by the grammar, only one parse tree exists. Thus, the grammar is unambiguous.

c. For this grammar, the Chomsky Normal Form is as follows:

S → NU | NV

V → VN | MU

U → IE | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0

M → 11

N → 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0

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The equation of a polynomial function, R, with rational coefficients will be;

P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The zeroes of the polynomial function are;

⇒ 4 + √5 and 3i

Now,

Since, The zeroes of the polynomial function are;

⇒ 4 + √5 and 3i

So, The factor of the polynomial function are;

(x - (4 + √5)) and (x - 3i)

Hence, We can formulate the polynomial function as;

P (x) = (x - (4 + √5)) (x - 3i)

       = (x - 4 - √5) (x - 3i)

       = x² - 3ix - 4x + 12i - √5x + 3√5i

       = x² - (3i + √5 + 4)x + (12 + 3√5) i

Thus, The equation of a polynomial function, R, with rational coefficients will be;

P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i

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The Law of Detachment states:

If a ⇒ b is true and a is true, then b is true

if two figures are congruent, their areas are equal.

a = two figures are congruent

b = their areas are equal

We are given b

The area of ABCD equals the area of PQRS.

We cannot use the law of detachment in this case because we need to be given a for the law of detachment to apply.

ABCD could be a rectangle with area 10

PQRS could be a rhombus with area 10

They are not congruent

Answer:

18-22 0.169

23-27 0,324

28-32 0,265

33-37 0,243

Answer:

67%

Step-by-step explanation:

Let the percentage of the first solution = x

7 gallons + 4 gallons = 11 gallons

Our system of equation is

Seven gallons of a sugar solution was mixed with 4 gallons of a 80 percent sugar solution to make an 72 percent sugar solution.

7 gallons × x % + 4 gallons × 80% = 72% × 11 gallons

= 7x + 3.2 = 7.92

Collect like terms

7x = 7.92 - 3.2

7x = 4.72

x = 4.72/7

x = 0.6742857143

Converting to percentage

0.6742857143 × 100

= 67.42857143%

Approximately, the percent concentration of the first solution is 67%

It is important to ensure that the assumptions of the paired t-test are met, such as the normality of the differences and the independence of the pairs. If the assumptions are violated, alternative non-parametric tests like the Wilcoxon signed-rank test can be considered.

To analyze the results and determine if there is a difference in total points earned between students taught by method X and those taught by method Y, a suitable test statistic to use in this scenario would be the paired t-test.

The paired t-test is appropriate when we have paired or matched observations, such as in this case where the students were paired based on intelligence. Each pair consists of one student taught by method X and one student taught by method Y, making it a within-subject design. This test allows us to compare the means of the two related groups, taking into account the paired nature of the observations.

By using the paired t-test, we can examine whether there is a significant difference in the total points earned within each pair. The test will assess if the mean difference between the two methods is significantly different from zero, indicating a significant disparity in the total points earned.

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Therefore , the solution of the given problem of percentage  comes out to be approximately 95% of the forecasts will be accurate to within 16 points.

A statistic or statistic that is stated as a percent of 100 is referred to as "a%" in statistics. The abbreviations "pct," "pct," as well as "pc" are also uncommon. However, it is commonly denoted by the letter "%". There are no metrics; the proportion to the total sum is flat. Because the numerator of percentages almost always matches 100, they are actually numbers. Both the word fraction or the percent sign (%) must come before a number to indicate that it indicates a percentage.

Here,

A. By the empirical formula, 68% of predictions will be for one standard deviation of the mean error if the prediction errors have a normal distribution.

Since the standard deviation of the errors is measured by the root mean square error (r.m.s. error), we can estimate that approximately 68% of the forecasts will be accurate to within 8 points.

Likewise, according to the empirical norm, roughly 95% of predictions will be within two standard deviations of the mean error.

Consequently, approximately 95% of the forecasts will be accurate to within:

=> 2 * 8 = 16 points.

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Answer:

25+20+(10w+15w)

Step-by-step explanation:

in the parenthisis is what they get each week

so each week its starts with 45 plus what ever they get each week and what ever they get times w for each week so if they do it for 5 weeks its

25+20+[(10x5)+(15x5)]    

45+(50+75)= 170

The scale of measurement of a variable determines the type of statistical analysis and graphical representation that can be used. It affects decisions about statistics and graphics because the scale of measurement determines the meaningful operations and relationships that can be established between the variables.

There are four levels of measurement: nominal, ordinal, interval, and ratio.

1. Nominal measurement: This type of measurement is used for categorical variables, such as gender, occupation, or color. Nominal measurement does not have a meaningful ordering or quantitative difference between values. For this reason, statistical analysis of nominal data is limited to descriptive statistics, such as frequency tables, and bar graphs or pie charts can be used to represent the data.

2. Ordinal measurement: Ordinal measurement is used for variables that have a meaningful ordering, but no quantitative difference between values, such as levels of education or income. Statistical analysis of ordinal data is limited to non-parametric tests, such as chi-square tests or contingency tables, and bar graphs or histograms can be used to represent the data.

3. Interval measurement: This type of measurement is used for variables that have a meaningful ordering and a quantitative difference between values, such as temperature or date. Interval measurement does not have a true zero point, meaning that the difference between values is meaningful, but ratios are not meaningful. For this reason, statistical analysis of interval data can include parametric tests, such as t-tests or ANOVA, and line graphs or scatterplots can be used to represent the data.

4. Ratio measurement: Ratio measurement is used for variables that have a meaningful ordering, a quantitative difference between values, and a true zero point, such as height, weight, or income. Ratio measurement allows for meaningful ratios, meaning that the difference and ratios between values are meaningful. Statistical analysis of ratio data can include both parametric and non-parametric tests, and line graphs, scatterplots, and histograms can be used to represent the data.

In conclusion, the scale of measurement affects decisions about statistics and graphics because it determines the meaningful operations and relationships that can be established between variables and the type of statistical analysis and graphical representation that can be used.

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2^3x =10         //log

log(2^3x) = log(10)

3x*log(2) = log(10)

3x = log(10) / log(2)

3x = log₂ 10

Answer: log₂ 10 = 3x

Answer:

none/0

Step-by-step explanation:

they ate all the cake.

now harry is gonna get sick

Answer:

79/79 or 1

Step-by-step explanation:

47+14+10+8=79

If Harry, Jack, Dave, and Mary all ate 79 slices in total, then there would be no more cake left since there are only 79 slices. The fraction answer would be 79/79 or 1, because they 79/79 is equivalent to 1.

Answer:

The answer is 10 quarters and 15 nickels

Step-by-step explanation:

Lets say x equals the number of quarters and y quals the number of nickels. Since there is a total of 25 coins that means that x+y=25. But, the quarter costs 0.25, and the nickel costs 0.05. That means that we have to multiply the number of each coin with their cost. Which leads us to: (x*0.25)+(y*0.05)=3.25. By solving these two equations you'll see that x=10 and y=15.

For the utility function U(x, y) = \((x^4)/(y^4)\), we can derive the indifference curve equations by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  \((x^4)/(y^4) = 1\)

 \(x^4 = y^4\)

  Taking the fourth root of both sides, we get:

  x = y

2. When U = 2:

  \((x^4)/(y^4) = 2\)

  \(x^4 = 2y^4\)

  \(x = (2^(1/4)) * y\)

3. When U = 3:

  \((x^4)/(y^4) = 3\)

  \(x^4 = 3y^4\)

  \(x = (3^(1/4)) * y\)

The indifference curves for this utility function are shaped like a rectangular hyperbola, where the ratio of x to y remains constant along each curve.

(b) For the utility function U(x, y) = y - 2x, the indifference curves can be derived by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  y - 2x = 1

  y = 2x + 1

2. When U = 2:

  y - 2x = 2

  y = 2x + 2

3. When U = 3:

  y - 2x = 3

  y = 2x + 3

The indifference curves for this utility function are straight lines with a slope of 2. They have a positive slope, indicating a positive marginal rate of substitution between x and y.

(c) Both utility functions satisfy completeness, transitivity, and monotonicity.

1. Completeness: The preferences are complete if, for any two bundles of goods, the consumer can compare and rank them. Both utility functions provide a ranking of bundles based on their utility values, indicating completeness.

2. Transitivity: Transitivity implies that if bundle A is preferred to bundle B, and bundle B is preferred to bundle C, then bundle A must be preferred to bundle C. Both utility functions satisfy this assumption.

3. Monotonicity: Monotonicity assumes that more is better. If a bundle has higher quantities of both goods compared to another bundle, it should be preferred. Both utility functions satisfy this assumption as well.

The violations of these assumptions would affect the shape and properties of the indifference curves. For example, if completeness is violated, there may be some bundles that cannot be compared or ranked, resulting in incomplete indifference curves.

If transitivity is violated, there may be cycles of preferences, leading to inconsistent indifference curves. If monotonicity is violated, the indifference curves may not have a consistent upward slope. However, in the case of the given utility functions, all assumptions are satisfied, allowing for well-defined indifference curves.

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Answer:

12

Step-by-step explanation:

its an equal at equallrateral triangle

Answer:

x = 12

Step-by-step explanation:

Since the 3 angles in Δ ABC are congruent, then the triangle is equilateral.

The sides of an equilateral triangle are also congruent, thus

x = 12

The best answer would be 213.

Assuming that the sign denotes summation, we are adding from k=4 to k=9.

To get, we change k=4 to k=9.

We simplify obtaining,

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Summarizing mainly entails entering the values k=4, 5, 6, 7, 8, and 9 into the formula section 5K+3 and adding them all together.

So, the result is:

(5(4)+3)+(5(5) + 3) + (5(6) + 3) + (5(7) +3) + (5(8) + 3) + (5(9) + 3) 23+28+33 +38+43 + 48

= 213

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