‘You must be 1.4m tall or more to ride the rollercoaster’
Which of these expresses the sentence above mathematically?

The p-value of the test statistic is 0.0000 (rounded off to four decimal places).

The p-value of the test statistic can be calculated by subtracting the area under the normal curve from the test statistic to infinity in the direction of the alternative hypothesis.

We are given that a political study has been carried out, taking a sample of 800 voters in the town. The sample shows that 59% of the residents favored construction. A political strategist wants to test the claim that the percentage of residents who favor construction is over 54%.

The hypothesis can be defined as follows:

Null hypothesis (H0): p ≤ 0.54, where p is the proportion of residents who favor the construction of the bridge.

Alternative hypothesis (Ha): p > 0.54, where p is the proportion of residents who favor the construction of the bridge.

To calculate the test statistic, we use the formula given below:

z = (p - P) / √[P(1-P) / n]

Here, P = 0.54, n = 800, p = 0.59

Putting these values in the above formula, we get:

z = (0.59 - 0.54) / √[0.54(1-0.54) / 800] = 5.06

To determine the p-value of the test statistic, we need to calculate the area under the normal curve from 5.06 to infinity in the direction of the alternative hypothesis. As the alternative hypothesis is one-tailed, we use the standard normal distribution table to find the corresponding area under the curve. The area can be calculated as:

P(Z > 5.06) = 0.00000035 (using the standard normal distribution table)

Therefore, the p-value of the test statistic is 0.0000 (rounded to four decimal places).

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Given sin∠X = cos∠Y and m∠X = 72°, we can find the measure of angle Y to be 18° since angles X and Y are complementary.

The problem states that sin∠X = cos∠Y and m∠X = 72°, and we are asked to find the measure of angle Y.

The first thing to notice is that sin∠X = cos∠Y means that the sine of angle X is equal to the cosine of angle Y. By the definition of sine and cosine, we know that:

sin∠X = opposite/hypotenuse

cos∠Y = adjacent/hypotenuse

where "opposite" and "adjacent" are the lengths of the sides of a right triangle that correspond to angles X and Y, respectively, and "hypotenuse" is the length of the hypotenuse of the triangle.

Since sin∠X = cos∠Y, we can set the two expressions equal to each other:

sin∠X = cos∠Y

opposite/hypotenuse = adjacent/hypotenuse

opposite = adjacent

This tells us that the lengths of the opposite and adjacent sides of the right triangle are equal. Since these sides are opposite and adjacent to angles X and Y, respectively, this means that angles X and Y are complementary angles (i.e., the sum of their measures is 90°).

We know that angle X has a measure of 72°, so we can use the fact that angles X and Y are complementary to find the measure of angle Y:

m∠Y = 90° - m∠X

m∠Y = 90° - 72°

m∠Y = 18°

Therefore, the measure of angle Y is 18°.

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If you were to simply guess the answer to both questions, you would have a 6.25% chance of getting both answers right according to probability

Assuming that each answer choice is equally likely to be correct, the probability of guessing the correct answer to one question is 1/4 or 0.25. Since there are two questions, the probability of guessing both correctly is the product of the probabilities of guessing each question correctly.

P(guessing both questions correctly) = P(guessing first question correctly) x P(guessing second question correctly)

P(guessing both questions correctly) = (1/4) x (1/4)

P(guessing both questions correctly) = 1/16 or 0.0625

Therefore, the probability of guessing both questions correctly is 1/16 or 0.0625.

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The value of x is 15 when y =8

If x varies indirectly as y, then we can write:

x = k/y

where k is the constant of variation. To find the value of k, we can use the given information that x = 5 when y = 24:

5 = k/24

Multiplying both sides by 24, we get:

k = 120

Now we can use this value of k to find x when y = 8:

x = 120/8 = 15

Therefore, the answer is A. 15.

A ratio that depicts the association between the independent variable (x) and the dependent variable is known as a constant of variation (k) (y). In the event that both of those variables have known values, it can be calculated by dividing y by x.

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For the given function f(x)=  [tex]-8(2)^{3x}[/tex] + 3 which contains variable x , whose value on substituting as zero is found to be (calculated without using calculator)

What is variable?

Variable is a term used in algebra or algebraic expressions and equations to represent the unknown values or whose value is not fixed. variables and constants are combined to form algebraic expressions or equations. The difference between expression and an equation is that expressions do not contain 'equal to' sign and equations shows balance between left hand side and the right side using 'equal to' sign.

Here the function is f(x)=  [tex]-8(2)^{3x}[/tex] + 3

To find the value of given function at x= 0 , we need to substititute zero in place of x.

f(x) at x=0 will be [tex]-8(2)^{3(0)}[/tex] + 3

                        = [tex]-8(2)^{0}[/tex] + 3

                        = [tex]-8(1)[/tex] + 3  { we know that [tex]m^{0} = 1[/tex] }

                        = - 8 + 3

                        = -5

∴The value of function at x=0 is found to be -5

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Refer to the attachment for complete question

Answer:

(3,1)

Step-by-step explanation:

I just graphed it using desmos but I could show you algebraically if you want

:)

General equation of line is [tex]y=mx+n[/tex] where m is slope and n is point on y-axis. So just use points in question to determine what m and n must be. Let me show you.

For A(0,1), put this point in [tex]y=mx+n[/tex] then you have [tex]1=m.0+n[/tex] Hence [tex]n=1[/tex]

Now use second one that is B(1,5), then you get [tex]5=m.1+1[/tex] since [tex]n=1[/tex]. Finally you get [tex]m=4[/tex] that is slope.

Therefore, D is the correct answer.

Step-by-step explanation:

For RIGHT triangles , remember  S-O-H-C-A-H-T-O-A

sin 14° = opposite leg / hypotenuse

         sin 14° = x / 10

          10* sin 14° = x

               x = 2.42 units

sin 37° = 10 / a

a = 10 / sin 37°

a = 16.62 units

The missing values in the figure is solved using central angle theorem to get

The measure of an central angle is equal to the measure of the intercepted arc according to the central angle theorem.

From the figure we have that the intercepted arc is FG = 122 degrees. Using the central angle theorem, the central angle is angle FHG

central angle = intercepted arc

angle FHG = arc FG

angle FHG = 122 degrees

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Based on the information provided, the relationship between velocity and time taken is V = 4 + 0.5t.

We can start by using the formula for velocity with constant acceleration:

V = Vo + at

where V is the final velocity, Vo is the initial velocity, a is the constant acceleration, and t is the time taken.

We know that the velocity is partly constant and partly varies with time, so we can write:

V = Vc + Vv

where Vc is the constant part of the velocity and Vv is the part that varies with time.

Using the given information, we can set up a system of equations:

9 = Vc + Vv (when t = 8s)

11 = Vc + Vv (when t = 12s)

Subtracting the first equation from the second, we get:

11 - 9 = (Vc + Vv) - (Vc + Vv)

2 = Vv (when t = 12s) - Vv (when t = 8s)

2 = Vv (12) - Vv (8)

2 = 4Vv

Vv = 0.5 m/s

Now we can use either of the two original equations to find Vc:

9 = Vc + 0.5(8)

Vc = 4 m/s

Therefore, the relationship between the velocity and the time taken is:

V = 4 + 0.5t

where V is the velocity in m/s and t is the time taken in seconds.

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Answer:

C; as x-> infinite, f(x) -> infinite, as x-> neg. infinite, f(x) -> neg. infinite

Step-by-step explanation:

Graphing the equation will help with knowing the end behavior.

X^3 graphs tend to increase infinitely when x is going infinitely positive and decrease infinitely when x is going infinitely negative.

The area of the face of the portable digital device is approximately 3.7033 square inches.

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is expressed in square units and can be calculated by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms.

The area of the face of the portable digital device can be found by multiplying the length by the width

Area = Length x Width

Area = 3.01 inches x 1.23 inches

Area = 3.7033 square inches (rounded to four decimal places)

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Answer:

Step-by-step explanation:

I remember doing this but I don’t seem to remember sorry

Answer:

37.5%

Step-by-step explanation:

Based on the given conditions, formulate: 30/80

Reduce the fraction: 3/8

Rewrite a fraction as a decimal: 0.375

Multiply a number to both the numerator and the denominator:

0.375 * 100/100

Write as a single fraction:

0.375 * 100 / 100

Calculate the product or quotient:

37.5/100

Rewrite a fraction with denominator equals 100 to a percentage:

37.5%

Answer:

37.5%

The sides of the piece of cardboard have to be 10 cm long in order for the volume of the box to equal 48 cm³

Let us assume that the dimension of the square piece of cardboard = m × m

If we cut a 3 cm square out of each corner, then each side of the square base will be (m - 6) cm.  

The height of the box, when folded, will be 3 cm.  

The volume of the box is:

V= (height) × (width) × (length)

V = 3 (m - 6) (m - 6)

V = 48 cm³

3(m² - 12m + 36) = 48

m² - 12m + 36 = 16

m² - 12m + 36 - 16 = 0

m² - 12m + 20 = 0

m² - 10m - 2m + 20 = 0

m(m - 10) - 2(m - 10) = 0

(m - 10)(m - 2) = 0

m = 10 OR m = 2

when m = 2, (m - 6) = -4 which is not possible.

So, the dimensions of the base of the box = 10 × 10

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The correct answer for F-distribution f0.05 is d) 3.66

To find f0.05 with v1=8 and v2=11, you can use an F-distribution table or an online calculator.

Here's a step-by-step explanation:

1. Locate the row in the F-distribution table corresponding to the degrees of freedom for the numerator (v1), which is 8 in this case.
2. Locate the column corresponding to the degrees of freedom for the denominator (v2), which is 11 in this case.
3. Find the intersection of the row and column to get the critical value for f0.05.

Using an F-distribution table or calculator, you will find that the f0.05 value for v1=8 and v2=11 is approximately 3.66.

So, the correct answer is:
d) 3.66

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Answer:

They both have the same slope of 2. Their y-intercepts are different. One is -2 and the other is -3/2.

Step-by-step explanation:

4x-2y=4

4x - 4 = 2y

(divide 2 by both sides)

2x-2=y

-4x+2y=-3

2y=4x-3

(divide 2 both sides)

y = 2x - 3/2

The probability that at least one of Blanca's cards has a number greater than at least one of Amira's cards is 0.705 or approximately 70.5%.

The total number of ways in which Blanca can choose two cards out of 23 is given by the combination formula C(23, 2), which is equal to 253.

The value of k can range from 3 (if Amira's cards are 1 and 2) to 25 (if Amira's cards are 24 and 25). Therefore, the total number of ways in which Blanca can pick two cards that are both greater than Amira's cards is:

C(23, 2) - C(2, 2) - C(3, 2) - ... - C(23, 2) = 23C(23, 1) - (C(2, 2) + C(3, 2) + ... + C(23, 2)) = 253 - 276 = -23

Since the result is negative, it means that there are no ways in which Blanca can pick two cards that are both greater than Amira's cards. Therefore, the probability of this case is 0.

P(Case 2) = (number of ways in which Blanca can pick one card greater than Amira's and one card less than Amira's) / (total number of ways in which Blanca can pick two cards out of 23) = 44,550 / C(23, 2) = 0.705

Finally, the probability of at least one of Blanca's cards having a number greater than at least one of Amira's cards is given by the sum of the probabilities of Case 1 and Case 2:

P(at least one of Blanca's cards is greater) = P(Case 1) + P(Case 2) = 0 + 0.705 = 0.705 or 70.5%

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Answer:

Step-by-step explanation:

Carlos can expect the value of the computer to be $580 in 3 years after purchase.

To find the exponential equation in the form y=a(b)ˣ that models the value of the computer, we need to determine the initial value and the rate of decay.

The initial value of the computer is $1,350, and its value after one year is $810.

We can use this information to find the rate of decay as follows:

810 = 1350 × b¹

b = 0.6

So the exponential equation is:

y = 1350(0.6)ˣ

To find the value of the computer 3 years after purchase, we can substitute x = 3 into the equation:

y = 1350(0.6)³= 583.2

Hence, Carlos can expect the value of the computer to be $580 in 3 years after purchase.

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there are 407,230 possible coupon codes that can be generated using the given format.

To find the number of possible coupon codes, we need to count the total number of ways to choose three letters from 23, one digit from 10, and one letter from 23 (since we can repeat letters). Combinations

The number of ways to choose three letters from 23 is:  

23[tex]C_{3}[/tex] = (232221)/(321) = 1771    

The number of ways to choose one digit from 10 is simply 10.

The number of ways to choose one letter from 23 (allowing repetition) is 23.

Therefore, the total number of possible coupon codes is:

1771 * 10 * 23 = 407,230

So there are 407,230 possible coupon codes that can be generated using the given format.

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Answer:

GCF = 509089201

for the values 509089201, 509089201

Solution by Factorization:

The factors of 509089201 are: 1, 107, 1663, 2861, 177941, 306127, 4757843, 509089201

The factors of 509089201 are: 1, 107, 1663, 2861, 177941, 306127, 4757843, 509089201

Then the greatest common factor is 509089201.

Answer:  509089201

Step-by-step explanation: The multiples would be 1, 107, 1663 and so on until 509089201, which makes 509089201 the gcf

The total area of the entire plot of land, including the land occupied by the house, backyard, front yard, side yard, and driveway, is 7,701 square feet.

Area is the measure of the amount of surface that a flat or 2-dimensional shape or object occupies. It is typically expressed in square units such as square feet, square meters, or square inches.

To find the area of the entire plot of land, we need to add up the areas of all the individual sections. Let's calculate the area of each section separately:

Area of backyard MNOV = (MN + NO) x OV = (25 + 20) x 5 = 225 square feet

Area of house ABCD = Base x Height = 66 x 38 = 2,508 square feet

Area of front yard RFEH = (RF + FH) x HE = (35 + 8) x 8 = 344 square feet

Area of side yard BFGC = (BF + FG + GC) x BC = (8 + 30 + 5) x 83 = 3,436 square feet

Area of driveway DEGH = Base x Height = 18 x 66 = 1,188 square feet

Therefore, the total area of the plot of land is:

225 + 2,508 + 344 + 3,436 + 1,188 = 7,701 square feet.

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Answer:

5

Step-by-step explanation:17+24=41

41/8=5.125

So The least you can get for the banquet table is 5.

2) 20 m³ is the answer

Answer:

Since $\angle GHJ=90^\circ$, arc $GJ$ is a quarter of the circumference of circle $H$. The formula for the circumference of a circle is $C=2\pi r$, where $r$ is the radius, so the circumference of circle $H$ is:

$$C=2\pi \cdot 20 = 40\pi$$

Since arc $GJ$ is a quarter of the circumference, its length is:

$$\frac{1}{4} \cdot 40\pi = 10\pi$$

Therefore, the length of arc $GJ$ is $10\pi$ units.

In conclusion there is only one solution to the system of equations and that is for x and y that satisfies both equations: x = 19 and y = -83.

How to solve and what does an equation mean?

We have two equations:

x + 5 = 24

5x = 12 - y

For the first equation, we can isolate x by subtracting 5 from both sides:

x = 19

Now we can substitute x = 19 into the second equation:

5(19) = 12 - y

95 = 12 - y

y = -83

So we have found a unique solution for x and y that satisfies both equations: x = 19 and y = -83.

Therefore, there is only one solution to the system of equations.

An equation is a mathematical statement that says that two things are equal. It consists of two expressions separated by an equal sign (=). For example, 2 + 3 = 5 is an equation that says that the sum of 2 and 3 is equal to 5.

Equations can be written in a variety of forms, depending on the type of problem being solved. In algebra, equations often involve variables, which are letters or symbols that represent unknown quantities.

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Equation of block pattern is: n² + 2n + 4

A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.

A block pattern is a type of organizational structure used in writing and presenting information. It involves dividing the information into distinct blocks or sections, with each block focusing on a particular aspect of the topic being discussed. This pattern is often used in writing comparison and contrast essays, where the writer wants to explore the similarities and differences between two or more subjects.

Equation of block pattern is: n² + 2n + 4

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The complete solution and complete answer of the questions provided are mentioned below respectively.

An integer is a whole number that can be either positive, negative or zero, but does not include fractions or decimals. Examples of integers include -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5.

1.To find out how much money is in Lane's account now, we need to substitute x = 0 in the given expression:

500(1.05)⁰ = 500(1) = 500

Therefore, Lane has $500 in his account now.

2.To write an expression for the amount of money in Lane's account in 20 years, we need to substitute x = 20 in the given expression:

500(1.05)²⁰ ≈ 1326.65

Therefore, the expression for the amount of money in Lane's account in 20 years is 1326.65.

3.To write an expression for the amount of money in Lane's account 5 years ago, we need to subtract the amount of interest earned in the last 5 years from the current balance of his account. The amount of interest earned in the last 5 years is:

500(1.05)² - 500(1.05)⁰≈ $154.13

Therefore, the expression for the amount of money in Lane's account 5 years ago is 500 - 154.13 = $345.87.

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1. Lane has $500 in his account now.

2. The given expression: 500(1.05)²⁰ ≈ 1326.65

3. The calculation for Lane's account balance five years ago is $345.87.

An integer is a whole number, which does not include fractions or digits and can be positive, negative, or zero.

Integer examples include -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5.

1. The following equation must be changed to read x = 0 in order to determine how much money is currently in Lane's account:

500(1.05)⁰ = 500(1) = 500

Lane now has $500 in his account as a result.

2. We must replace x with 20 in the provided expression in order to create an expression for the sum of money that will be in Lane's account in 20 years:

500(1.05)²⁰ ≈ 1326.65

As a result, the phrase for Lane's account balance in 20 years is 1326.65.

3. We must deduct the amount of interest earned over the previous five years from Lane's account balance in order to calculate the balance five years back. The income earned over the previous five years is:

500(1.05)² - 500(1.05)⁰≈ $154.13

Since there was money in Lane's account five years ago, the phrase is 500 - 154.13 = $345.87.

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The height of the triangle is approximately 7.31 units.

What is  Pythagorean theorem ?

The Pythagorean theorem is a fundamental theorem in geometry that relates to the sides of a right triangle. It states that in a right 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.

In mathematical notation, the Pythagorean theorem can be written as:

a^2 + b^2 = c^2

where a and b are the lengths of the legs (the sides adjacent to the right angle) and c is the length of the hypotenuse.

According to the question:

Since triangle ABC is a right triangle with angle B = 90 degrees, we can use the Pythagorean theorem to find the length of side BC:

[tex]BC^2 = AC^2 - AB^2[/tex]

[tex]BC^2 = 30^2 - h^2[/tex]

[tex]BC = \sqrt{30^2 - h^2}[/tex]

Now, let's consider triangle ABD. We know that AD = 25 and DC = 11, so BD = BC - DC:

BD = BC - DC

[tex]BD = \sqrt{30^2 - h^2} - 11[/tex]

Since the line passing through vertex A is perpendicular to BC, we know that triangles ABD and ABC are similar. Therefore, we can use the ratio of corresponding sides to find the value of h:

h/AB = AB/AC

h/AB = AB/30

[tex]AB^2 = h*30[/tex]

[tex]AB =\ sqrt{h*30}[/tex]

Now, using the fact that AD + DC = BC, we can write:

AD + DC = BD + AB

[tex]25 + 11 = \sqrt{30^2 - h^2} - 11 +\sqrt{h*30}[/tex]

[tex]36 = \sqrt{30^2 - h^2} + \sqrt{h*30}[/tex]

Squaring both sides, we get:

[tex]1296 = 30^2 - h^2 + 2\sqrt{h*30}\sqrt{30^2 - h^2} + h*30[/tex]

[tex]1296 = 900 - h^2 + 2\sqrt{30h - h^3} + 30*h[/tex]

[tex]396 = 32\sqrt{30*h - h^3}[/tex]

Squaring again, we get:

[tex]156816 = 960h^2 - 96h^4[/tex]

[tex]h^4 - 10h^2 + 1639/12 = 0[/tex]

Using the quadratic formula, we get:

[tex]h^2 = (10 \± \sqrt{10^2 - 4(1)(1639/12))}/2[/tex]

[tex]h^2 = (10 \± \sqrt{1561})/2[/tex]

Since h must be positive, we take the positive square root:

[tex]h = \sqrt{(10 + sqrt(1561)}/2) \approx 7.31[/tex]

Therefore, the height of the triangle is approximately 7.31 units.

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