You are given a number. Do you know the number that is 1/5 as big

First five terms of the sequence are 4, 5, 9, 14, and 23.

For the given sequence an = an-1 + an-2, with a1 = 4 and a2 = 5:

1. Its first term is a1 = 4.
2. Its second term is a2 = 5.
3. To find the third term, use the formula: a3 = a2 + a1 = 5 + 4 = 9.
4. For the fourth term, apply the formula again: a4 = a3 + a2 = 9 + 5 = 14.
5. Finally, for the fifth term: a5 = a4 + a3 = 14 + 9 = 23.

So, the first five terms of the sequence are 4, 5, 9, 14, and 23.

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a) Time taken to reach maximum height is 0.5 sec.

b) Highest point is 484 feet

c) Time to hit the water is 6 sec.

A statement proving the equality of two mathematical expressions is known as an equation.

a) h(t) = - 16t² +16t + 480

Differentiation with respect to t, we get,

h(t)' = - 32t + 16

Again differentiation with respect to t, we get,

h(t)" = -32 is less than 0

Then maximum value of height,

h(t)' = 0

- 32t + 16= 0

t = 1/2 = 0.5

Therefor, Time taken to reach maximum height is 0.5 sec.

b) for highest point; Put value of t in equation

h(0.5) = -16(0.5)²+16(0.5)+480 = 484

Highest point is equal to 484 feet

c) 0 =  -16t² + 16t + 480

0 =  -16 ( t² - t - 30 )

( t - 6 ) ( t + 5) = 0

t = 6, t = -5        (negative value is neglect)

Time to hit the water is 6 sec.

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When two objects are massive and close to each other, the gravitational force between them is strong.

Gravity is a fundamental force of nature that exists between any two objects in the universe. The strength of the gravitational force depends on two factors: the masses of the two objects and the distance between them.

The larger the masses of the two objects, the greater the gravitational force between them. Likewise, the closer the objects are to each other, the stronger the gravitational force.

This relationship is described by Newton's Law of Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

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Ball A reaches a greater height than Ball B.

To determine which ball reaches a greater height, we need to compare the maximum height each ball reaches.

For Ball A, we can use the formula for the vertex of a parabola, which is given by [tex]x = - \frac{b}{2a} [/tex], where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0). In this case, a = -4.9 and b = 14.7, so the vertex of Ball A's path is at [tex]x = \frac{ - 14.7}{2 \times 4.9} = 1.5 [/tex] seconds.

To find the maximum height of Ball A, we can plug this value into the original equation:

[tex]f(1.5) = -4.9 \times {1.5}^{2} + 14.7(1.5) + 0.975 = 9.9 \: \: meters.[/tex]

For Ball B, we can look at the table and see that it reaches a maximum height of 8 meters.

Therefore, Ball A reaches a greater height than Ball B by 1.9 meters (9.9 - 8 = 1.9)

We can answer this question without graphing either function by using the properties of quadratic functions. The maximum height of a quadratic function occurs at the vertex, which can be found using the formula x = -b/2a. We can then plug this value into the function to find the maximum height. By comparing the maximum heights of the two balls, we can determine which ball reaches a greater height.

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Answer: 7/48

Step-by-step explanation:

The word of is interchangeable with multiplication.

1/6 times 7/8 = 7/48

Answer: x^2-22x+121

I believe this is correct.

Take note that Bus 18 is the most reliable in terms of trip times among the line plots shown above. With our understanding of the interquartile range, we can solve this. (IQR)

We must compare the metrics of data variability in order to identify the bus that consistently produces the best accurate results. Range and interquartile range are the metrics of variability that we can utilise in this situation (IQR).

The IQR is the difference between the third quartile (Q3) and the first quartile, whereas the range is the difference between the highest and lowest values in the data set (Q1). Because it is less impacted by extreme values than the range, the IQR provides a more accurate indicator of variability.

Using the given data, we can calculate the range and IQR for each bus:

Bus 47:

Range = 28 - 4 = 24

Q1 = 10, Q3 = 22

IQR = 22 - 10 = 12

Bus 18:

Range = 22 - 6 = 16

Q1 = 9, Q3 = 25

IQR = 25 - 9 = 16

According to these findings, Bus 18 has a narrower range and a higher IQR than Bus 47. The IQR, a more accurate indicator of variability in this situation, reveals that Bus 18's trip times are less variable than those of Bus 47's. Hence, we can say that when it comes to trip times, Bus 18 is the most reliable.

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The minimum value of the function g(x) = (x-3)² occurs at the vertex of the parabola, which is located at x = 3. At this point, the value of the function is g(3) = (3-3)² = 0.

To see why this is the case, we can use the fact that the vertex of a parabola in the form f(x) = a(x-h)² + k is located at (h,k). In the case of g(x) = (x-3)², we have a = 1, h = 3, and k = 0, so the vertex is located at (3,0).

Since the parabola opens upwards (the coefficient a is positive), the value of the function is minimized at the vertex.

Therefore, the minimum value of g(x) is 0, which occurs at x = 3.

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Answer:

55

Step-by-step explanation:

Answer:

(8÷2+9)×9−10²

hope this helped!

The probability that more than a fifth (i.e. 6 or more) of the 10 buyers would prefer green is 0.3981.

To conduct a study of the color preferences of new car buyers, a researcher wishes to conduct a research. Suppose that 30% of the population prefers green. If ten buyers are selected at random, what is the probability that more than a fifth of the buyers will prefer green?

The random variable X represents the number of buyers who prefer green. When n = 10 and p = 0.3, this is a binomial probability experiment. P(X > 2) is the probability that more than a fifth of the buyers would prefer green.P(X > 2) = 1 - P(X ≤ 2)P(X > 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]P(X > 2) = 1 - [C(10,0) (0.3)^0 (0.7)^10 + C(10,1) (0.3)^1 (0.7)^9 + C(10,2) (0.3)^2 (0.7)^8]P(X > 2) = 1 - [1(0.7)^10 + 10(0.3)(0.7)^9 + 45(0.3)^2 (0.7)^8]P(X > 2) = 0.2743

Therefore, the probability that more than a fifth of the buyers would prefer green is 0.2743, rounded to four decimal places.

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Answer:

  ∠Z = 52°

  b = 59°

Step-by-step explanation:

You want to know the measures of an angle and a variable in the given quadrilaterals with angles marked.

Segment WY divides the figure into two congruent triangles, so you know angles X and Z have the same measure. The sum of angles in a quadrilateral is 360°, so ...

  ∠W +∠X +∠Y +∠Z = 360°

  134° +∠Z +122° +∠Z = 360° . . . . . . use ∠Z for ∠X

  2·∠Z = 104° . . . . . . simplify, subtract 256°

  ∠Z = 52°

Opposite angles of a rhombus are congruent, so ...

  2b = b +59°

  b = 59° . . . . . . . . . subtract b

Answer: $2240.59

Step-by-step explanation:

To calculate the compound interest paid when an amount is borrowed at 5% p.a for 26 years and compounded monthly, you can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the amount of money you will have after t years

P = the principal amount (the amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years) for which the money is borrowed

In this case, we have:

P = the amount borrowed (not given in the question)

r = 5% p.a, or 0.05 as a decimal

n = 12 (since the interest is compounded monthly)

t = 26 years

We need to find the amount of compound interest paid, so we need to find the difference between the amount of money you will have after 26 years (A), and the amount you borrowed (P).

Let's assume the amount borrowed (P) is $1000. Then, we can substitute these values into the formula:

A = 1000(1 + 0.05/12)^(12*26)

A = 1000(1.004167)^312

A = 1000(3.240590)

A = $3240.59

So, after 26 years, the amount of money you will have is $3240.59. The compound interest paid is the difference between the amount borrowed and the final amount:

Compound interest paid = $3240.59 - $1000

Compound interest paid = $2240.59

Therefore, the compound interest paid if the amount is borrowed at 5% p.a for 26 years and compounded monthly is $2240.59.

A = $36,594.00

A = P + I

where

P (principal) = $10,000.00

I (interest) = $26,594.00

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,000.00(1 + 0.05/12)(12)(26)

A = 10,000.00(1 + 0.0041666666666667)(312)

A = $36,594.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 5% per year compounded 12 times per year over 26 years is $36,594.00.

The volume of a cone is given by the formula:

V = (1/3) * pi * r^2 * h

where r is the radius of the base and h is the height of the cone.

Substituting the given values, we get:

V = (1/3) * pi * 9^2 * 23

V = (1/3) * pi * 729 * 23

V = 6,859 pi

Therefore, the volume of the cone is 6,859 pi cubic units.

The quadratic polynomial with the given zeros is:

y = x² - 7/3

If we have a quadratic equation whose zeros are a and b, then we can write it as:

y = (x - a)*(x - b)

in this case the zeros are √7/3 and -√7/3

Then the quadratic equation is:

y = (x - √7/3)*(x +  √7/3)

y = x² - 7/3

That is the quadratic polynomial.

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The friends error was in the terms factored out in the second step

It looks like your friend attempted to factor the polynomial using the distributive property of multiplication, but made an error in the second step.

first step 3x^3+x^2+3x+1

second step 3x^2(x+1)+3(x+1)

third step 3(x^2+1)(x+1)

the error is in the terms factored out in the second step: 3x^2 and 3

The correct factorization of the polynomial is:

3x^3 + x^2 + 3x + 1

= x^2(3x + 1) + 1(3x + 1)

= (3x^2 + 1)(x + 1)

The term factored out is: x^2 and 1

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Answer:  b and c

Step-by-step explanation:

just trust the sources

Answer:

Step-by-step explanation:

[tex]3.25x - 1.5y = 1.25 \quad (a)[/tex]  

     [tex]13x - 6y = 10\quad\quad(b)[/tex]

Make [tex]y[/tex] the subject in [tex](b):[/tex]

   [tex]13x - 6y = 10[/tex]

             [tex]6y=13x-10[/tex]

               [tex]y=\frac{13}{6} x-\frac{5}{3} \quad(c)[/tex]

Substitute [tex](c)[/tex] into [tex](a):[/tex]

     [tex]3.25x - 1.5(\frac{13}{6} x-\frac{5}{3}) = 1.25 \quad \text{(I will change decimals to fractions)}[/tex]

            [tex]\frac{13x}{4} -\frac{3}{2} (\frac{13x}{6} -\frac{5}{3} )=\frac{5}{4} \quad\quad \text{(I will remove brackets)}[/tex]

                 [tex]\frac{13x}{4} - \frac{13x}{4} +\frac{5}{2} =\frac{5}{4}[/tex]

                                     [tex]\frac{5}{2} =\frac{5}{4}[/tex]

This is ambiguous meaning the system does not have a solution.

(I confirmed this on Wolfram Alpha)

9 is the centre of enlargement in triangle .

What is a triangle, exactly?

A triangle, a three-sided polygon, is made up of three vertices. When the triangle's three sides are joined end to end at a single point, the angles are created. Three angles in a triangle add up to 180 degrees in total. A triangle is a closed, two-dimensional geometry with three sides, three angles, and three vertices. Triangles are also a type of polygon.

First draw lines from point O through A, B and C, as shown in the diagram

Measure the length O A and multiply it by 1.5 to get the distance from O of the image point A'.

      O A' = 1.5 × O A

       OA' = 1.5 * √(4 - 0)² + (4 - 0)²

              = 1.5*4√2

       OA' = 6

Mark the point A' on the diagram

The images B' and C' can then be marked in a similar way and the enlarged triangle A' B' C' can then be drawn.

OB' = 1.5OB

OB' = 1.5 √(4 - (-2))² + ( 4 -0 )²

OB' = 1.5*2√13

 OB' = 3√13

 OC' = √1.5 * √(4 - (-2))² + 4 - 4

 OC' = 1.5*6

   OC' = 9

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The equation "Y^2/9 - x^2/4=1" will produce the given graph. Therefore option B would be the correct answer.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

An equation combines two expressions connected by an equal sign (“=”). These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. We generally assume the right-hand side of an equation is zero. This will not reduce the generality since we can balance this by subtracting the right-hand side expression from both sides’ expressions.

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The average rate of increase is $69 per year (to the nearest dollar).

What is average rate of increase?

The  function is defined as the average rate at which one measurement is changing(here increasing) with respect to another change. So an average rate of change function is a system that calculates the amount of change in one data divided by the corresponding amount of change in another.

The fees in 1997( x₁ say) was $3042( y₁ say)

fees in 2000(x₂ say) was $3250 ( y₂ say)

The formula is for change in average rate is  [tex]\frac{ y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

average rate of increase= (3250-3042)/(2000-1997)

                                        = 208/3

                                         =69.33

so average rate of increase to the nearest dollar  is $69 per year.

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Answer/Step-by-step explanation:

Since you know that the answer is x = 36, Then you can substitute it in the equation.

3/4(36) - 11 = 16          → Multiply 3/4 by 36

27 - 11 = 16                  → Subtract 11 from 27

16 = 16                        → They are equal

Hence as you can see, x = 36.

RevyBreeze

Answer:

h(x) = (x^2 - 64)

Step-by-step explanation:

If the solutions to h of x = 0 are x = -8 and 8, then h(x) must be a quadratic function with roots at x = -8 and x = 8.

One way to write the quadratic function that satisfies these conditions is:

h(x) = (x+8)(x-8)

where a is some non-zero constant that determines the shape of the parabola.

Expanding the above equation, we get:

h(x) = (x^2 - 64)

Therefore, one possible quadratic function that could represent h is:

h(x) = (x^2 - 64)

where a is any non-zero constant.

We can see here that the problem that can be solved using synthetic division is: A. [tex]\frac{2y^{2} + 4y - 6}{y-1}[/tex]

Synthetic division is a simplified method of polynomial division, used to divide a polynomial by a linear factor of the form (x - a). This method can be used to quickly evaluate a polynomial for a particular value of x, or to find the roots of a polynomial equation.

In order to solve with synthetic division, we have:

Step 1: Make the denominator to equal zero. The numerator is written in descending order.

Step 2: Bring the first number or the leading coefficient straight down.

Step 3: Put the result in the next column by multiplying the number in the division box with the number you brought down.

Step 4: Write the result at the bottom of the row by adding the two numbers together

Step 5: Until you reach the end of the problem, repeat steps 3 and 4.

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A chi-squared statistic provides strong evidence in favor of the alternative hypothesis if its value is A.  a large positive number.

Chi-squared statistics or chi-squared test is a statistical method used to find out if there is a significant difference between the expected and observed frequencies in one or more categories of a contingency table. This test is used to determine whether the null hypothesis can be rejected or not. Chi-squared statistics are a non-parametric test that helps to determine whether the data is close to what is expected or not. This test is used when the data is ordinal or nominal.

Chisquare test is often used for: Testing if the observed frequencies of a nominal variable are significantly different from the expected frequencies Assessing if two or more distributions are the same. The chi-squared statistic provides evidence for or against the null hypothesis. A large positive value of the chi-squared statistic indicates that the null hypothesis can be rejected.

Therefore, option A. a large positive number, is the correct answer.

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The solutions to the equation are approximately x = 0.89 and x = -0.89.

Squares as well as square root both ideas are diametrically opposed to one another. Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value. Both are hence vice-versa approaches. For instance, 2 is squared to provide 4, and 2 is the square root of 4, giving 2.

When n is a number, its square is denoted by n raised to the power 2, or n2, and its square root is denoted by the symbol "n," where "n" is referred to as a radical. The term "radicand" refers to the value under the root symbol.

The given equation is 5x² + 2 = 6.

5x² = 4

x² = 4/5

x = ±√(4/5)

x ≈ ±0.89

Hence, the solutions to the equation are approximately x = 0.89 and x = -0.89.

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Red-green color blindness is controlled by an x-linked gene in humans. The allele that causes color blindness is rare and recessive to the allele for normal vision. A man and woman both with normal vision had color-blind fathers. If this man and woman have a child, Therefore, the probability of a child being color-blind is 25%.

Red-green color blindness is an X-linked recessive disorder. This means that the gene for the disorder is found on the X chromosome. Because males have only one X chromosome (inherited from their mother), they will develop color blindness if they inherit the allele from their mother. On the other hand, females need to inherit two copies of the allele, one from each parent, to develop the disorder.A man with normal vision will have the genotype XY, and the woman will have the genotype XX.

Each child of the couple will receive one X chromosome from the mother and one Y chromosome from the father. The probability of the child inheriting the allele for color blindness from its father is 0 because he has no alleles for color blindness.

The probability of the child inheriting the allele for color blindness from its mother is 1/2 because the mother's X chromosome has a 1/2 probability of carrying the allele. Because the mother is a carrier, the probability of the child receiving the allele is 1/2.

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The number of ways car 2 or more tires can be selected out of 8 tires is 247 ways

To select 2 or more tires out of 8 tires, we can use the concept of combinations.

The total number of ways to select r items out of n items is given by the formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of items, and r is the number of items to be selected.

For selecting 2 or more tires out of 8 tires, we can find the total number of ways to select 2 tires, 3 tires, 4 tires, 5 tires, 6 tires, 7 tires, and 8 tires, and then add them together.

Adding all the above results, we get:

28 + 56 + 70 + 56 + 28 + 8 + 1 = 247

Therefore, there are 247 ways to select 2 or more tires out of 8 tires.

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The radius of the sphere when the volume and the radius are increasing at the same numerical rate is √(1/2π) cm.

The numerical rate of increase in the volume of a sphere with respect to the increase in the radius is given by numerical rate,

dn/dt=4πr² * dr/dt.

Here, dn/dt is the rate of increase of volume with time, dr/dt is the rate of increase of radius with time, and r is the radius of the sphere.

The rate of increase of radius is given as dr/dt=18 cm/s. We need to find the radius of the sphere when the volume and the radius are increasing at the same numerical rate.

Let dn/dt=18 cm³/s, which means the volume and radius are increasing at the same numerical rate. Then

18=4πr² * 18So, r²=1/2π => r = √(1/2π) cm

Therefore, In a sphere whose volume and radius increase at the same numerical rate, the radius is √(1/2π) cm.

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The interquartile range (IQR) of the given data set is 16.

To find the interquartile range (IQR), we first need to calculate the first and third quartiles of the data set:

Arrange the data set in order from smallest to largest:

22, 26, 28, 30, 32, 35, 35, 42, 45, 49, 50

Find the median (middle value) of the lower half of the data set (the first quartile, Q1):

22, 26, 28, 30, 32, 35

The median of this set is 29, which is halfway between 28 and 30.

Find the median (middle value) of the upper half of the data set (the third quartile, Q3):

35, 42, 45, 49, 50

The median of this set is 45.

Calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1

   = 45 - 29

   = 16

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