X: 1 2 3 4 5 6
Y: 782 936 966 1159 1268 1491
Use regression to find an exponential equation that best fits the data above. The equation has form y=ab^x where
a=____
b=_____

The equation that represents number of hours "h" which Ezekiel spend doing "math-homework" during the next 5 days is (d) h = 5t/4.

If Ezekiel spends 1/4 of his time on math homework, then he spends 3/4 of his time on other subjects. This means that out of every 4 hours he spends on homework, he spends 1 hour on math and 3 hours on other subjects.

So, in "t" hours, he will spend "t/4" hours on math homework.

To find the number of hours he will spend on math homework during the next 5 days, we multiply the time he spends on math homework in one day by the number of days.

⇒ Number of hours spent on math homework in 1 day = t/4,

⇒ Number of hours spent on math homework in 5 days = 5 × (t/4) = 5t/4,

The required equation is h = 5t/4,

Therefore, the correct option is (d).

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Answer: 6 feet and 2 yards are the same distance because each yard is 3 feet

Step-by-step explanation:

This statement is false because , the value of the 7 in the hundredth place is greater than the value of the 7 in the thousandth place.

Each digit in a number has a particular place value dependent on its position in the decimal number system. The digits in the number 824.377 have the following place values:

The 7 in the hundredth position has a value of 7/100, or 0.07. This is because the digit 7 is in the hundredth position, which is in the second position to the right of the decimal point.

The value of the 7 in the thousandth place is 7/1000, or 0.007. This is due to the fact that the digit 7 is in the third place to the right of the decimal point

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To complete the job in 12 days, they need 100 workers.

We know that 30 workes can complete 1 job in 40 days, then if each worker works at a rate R, then we can write:

30*R*40 days = 1 job

R = (1/1200) job/day

Then if they need to complete the job in 12 days, the number N of workers needed is:

N*(1/1200)*12 = 1

N = (1200/12) = 100

100 workers are needed.

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The expression What is 2.00x + 1.50y = cannot be added/evaluated because 2.00x and 1.50y are not like terms

From the question, we have the following parameters that can be used in our computation:

What is 2.00x + 1.50y =

The above statement is an addition expression that adds the values of 2.00x and 1.50y

However, the terms of the expression are not like terms

i.e. 2.00x and 1.50y are not like terms

This means that the expression cannot be added/evaluated

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Answer:

V = π(5^2)(11) = 275π cubic miles

= 863.9 cubic miles

The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1

Total numbers on wheel = total possible outcomes

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Grey colored portion = {3}

White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}

X = Event that wheel stops on a white slice

P(X) = number of white slices ÷ total number of slices

P(X) = 9 / 10 = 0.9

P(not X) = 1 - P(X)

P(not X) = 1 - 0.9 = 0.1

Hence the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1

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Answer:

Step-by-step explanation:

On a given day, a greengrocer sold 81 oranges and 43 melons. Write the ratio of oranges to melons in the form 1: n. Give any decimals in your answer to 2 d.p.

orange = 81

melons = 43

ratio 81 : 43

divide both side by 81

1 : 0.53

Answer: b

Step-by-step explanation:Remember that the Cartesian coordinates are given by the formulas

xy=rcosθ=rsinθ

We are told that r=8 and θ=11π6, so we can plug in to find that

x=rcosθ=(8)(cos11π6)=(8)(3‾√2)=4√3

Similarly, we find that

y=rsinθ=(8)(sin11π6)=(8)(−12)=−4

So the final answer is (4√3,−4).

The value of the integration is -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2

We have,

∫√(2 + cos²x)/(sec x - cosec x)

We can start by simplifying the integrand by using trigonometric identities.

sec x = 1/cos x and cosec x = 1/sin x.

So,

√(2 + cos²x)/(sec x - cosec x)

= √(2 + cos²x) / [(1/cos x) - (1/sin x)]

= √(2 + cos²x) / [(sin x - cos x) / (sin x cos x)]

= √[(2 + cos²x) sin x cos x] / (sin x - cos x)

= √[2 sin x cos x + cos⁴ x] / (sin x - cos x)

= √[sin² x + cos² x + 2 sin x cos x + cos⁴ x] / (sin x - cos x)

= √[(sin x + cos² x)²] / (sin x - cos x)

= (sin x + cos² x) / |sin x - cos x|

The absolute value sign is needed because the denominator, sin x - cos x, can be negative for certain values of x.

Now we can integrate this expression:

∫√(2 + cos²x)/(sec x - cosec x) dx

= ∫(sin x + cos² x) / |sin x - cos x| dx

We can split this integral into two cases: when sin x - cos x > 0, and when sin x - cos x < 0.

Case 1:

sin x - cos x > 0 (when x is between -π/4 and π/4, or between 3π/4 and 5π/4)

In this case, we can drop the absolute value sign:

∫(sin x + cos² x) / (sin x - cos x) dx

= ∫(sin x / (sin x - cos x)) dx + ∫(cos² x / (sin x - cos x)) dx

= -ln|sin x - cos x| - ∫(1 + sin 2x) / (2sin x - 2cos x) dx

To integrate the second term, we can use the substitution u = sin x - cos x, so that du/dx = cos x + sin x and dx = du/(cos x + sin x):

∫(1 + sin 2x) / (2sin x - 2cos x) dx

= ∫(1 + 2u / √2) / (2u / √2) du

= -√2 ln|2sin x - 2cos x| - √2 ln|u| + √2 [tex]tan^{-1}[/tex] (u / √2) + C

= -√2 ln|2(sin x - cos x)| - √2 ln|sin x - cos x| + √2 [tex]tan^{-1}[/tex] [(sin x - cos x) / √2] + C

= -√2 ln|sin x - cos x| - √2 ln 2 + √2 [tex]tan^{-1}[/tex] [(sin x - cos x) / √2] + C

= -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2

Note that we have used the logarithmic identity ln(ab) = ln a + ln b and the substitution u = sin x - cos x.

Thus,

The value of the integration is -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2

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The value for the missing length ST of the similar to triangle ∆STU is equal to 234

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Given that the triangle ∆STU is similar to the triangle ∆SGF, then SF correspond to SU, and SG correspond to ST. So;

SF/SU = SG/ST

75/270 = 65/ST

ST = (65 × 270)/75

ST = 13 × 18

ST = 234

Therefore, the value for the missing length ST of the similar to triangle ∆STU is equal to 234

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The formula for the volume of a rectangular prism is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of Caleigh's jewelry box is 14 cubic inches, and the area of the base is 7 square inches. Since the base of the box is a rectangle, we can use the formula for the area of a rectangle to find the length and width of the base:

A = l x w

7 = l x w

We don't know the exact values of l and w, but we do know that their product is 7.

Now we can use the formula for the volume of a rectangular prism to find the height:

14 = l x w x h

We know that l x w = 7, so we can substitute 7 for l x w:

14 = 7 x h

Dividing both sides by 7 gives:

h = 2

Therefore, the height of Caleigh's jewelry box is 2 inches.

The missing side using the Pythagorean theorem is 10.2.

We have,

We see that,

Hypotenuse = 13

Base = x (say)

Height = 8

Now,

Applying the Pythagorean theorem,

Hypotenuse² = Base² + Height²

Substituting,

13² = x² + 8²

13² = 169

8² = 64

So,

169 = x² + 64

x² = 169 - 64

x² = 105

x = √105

x = 10.24

x = 10.2

Thus,

The missing side is 10.2.

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(-35z⁴x + 32z⁴x⁶) divided by  -4z³x⁵ gives {(35z - 32zx⁵)/ (4x⁴)} by applying simple rule of division of polynomials.

Let the given polynomial be written as,

f(z,x) = -35z⁴x + 32z⁴x⁶

g(z,x) = -4z³x⁵

Here the functions of the given polynomial are composed of two variables, namely x and z, so the functions are denotes likewise.

We can divide the polynomial f(x) by g(x) by the division method as,

[tex]\frac{f(z,x)}{g(z,x)}[/tex] = (-35z⁴x + 32z⁴x⁶) / ( -4z³x⁵)

= { (-35z⁴x)/ ( -4z³x⁵) } + {(32z⁴x⁶)/ ( -4z³x⁵)}

= [tex]\frac{35z}{4x^4}[/tex] + [tex]\frac{-8zx}{1}[/tex]

= [tex]\frac{35z - 32zx^5}{4x^4}[/tex]

or, =  {(35z - 32zx⁵)/ (4x⁴)}

Thus the required value of (-35z⁴x + 32z⁴x⁶) divided by  -4z³x⁵ is {(35z - 32zx⁵)/ (4x⁴)}

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For a unique solution is: [tex]\frac{10}{a}\neq \frac{5}{b}[/tex]

For an infinitely many solution is: [tex]\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}[/tex]

An equation of the form ax+by+c=0 is called a linear equation where a, b, c∈R

We have the linear equation is:

10x + 5y = 20

Now, we have to find the unique solution and infinitely many solution:

Firstly, For a unique solution, we need an equation ax+by+c=0 such that

[tex]\frac{10}{a}\neq \frac{5}{b}[/tex]

Now, For an infinitely many solutions, we need an equation ax+by+c=0 such that:

[tex]\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}[/tex]

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For, complete question, to see the attachment.

The price that maximizes revenue from ticket sales is  $ 11, 445.

We have,

Ticket price = $47

Let x the decreasing number of the ticket price.

So, The revenue is

R =  ticket price x numbers of spectator

R(x) =  ( 47 - x )  ( 640 + 20x)

= 30,800 + 940x - 640x -20x²

= -20x² + 300x + 30,800

Now, Taking derivatives on both sides

R'(x) = -40x + 300

and, R'(x) = 0

-40x = -300

x = 7.5

So, the price per ticket is

= 47- 7.5

= $ 39.5

and, R(max) = -20(39.5)² + 300(39.5) + 30,800

R(max) = -31205 + 42650

R(max) = $ 11, 445

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Answer:

$39.50

Step-by-step explanation:

The probability that a randomly selected ticket will be a number that is not a multiple of 9 is 0.9.

To find the probability that a randomly selected ticket will not be a multiple of 9, we need to find the total number of tickets that are not multiples of 9 and divide it by the total number of tickets in the bowl.

There are 7 multiples of 9 between 1 and 70, namely 9, 18, 27, 36, 45, 54, and 63. Therefore, there are 70 - 7 = 63 tickets that are not multiples of 9.

So, the probability that a randomly selected ticket will not be a multiple of 9 is:

P(not multiple of 9) = 63/70

This can also be written as a decimal or percentage:

P(not multiple of 9) ≈ 0.9 or P(not multiple of 9) ≈ 90%

Therefore, there is a high probability that a randomly selected ticket will not be a multiple of 9.

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Answer:

When rolling two number cubes, the possible outcomes of the sum of the numbers on the top faces are from 2 (1+1) to 12 (6+6). Since we want to know how many times we can expect the sum to be 7, we need to count the number of ways to get a sum of 7.

The pairs of numbers that add up to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, there are 6 ways to get a sum of 7.

Each time we roll the two number cubes, the probability of getting a sum of 7 is 6/36 or 1/6, since there are 6 possible outcomes that result in a sum of 7 out of a total of 36 possible outcomes.

Therefore, if we repeat this process 300 times, we can expect to get a sum of 7 approximately (1/6) x 300 = 50 times.

So we can expect the two cubes to add to exactly 7 about 50 times when rolled 300 times.

Step-by-step explanation:

The triangle triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Triangle ∆BCD is not similar to the triangle ∆BTS, BT does not correspond to BC, and BS does not correspond to BD. Also, the angle m∠SBT does not correspond to m∠DBC.

Therefore, the triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

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The hypothesis test is left-tailed, and we are testing the population standard deviation.

If a hypothesis test has an equal hypothesis versus a not equal hypothesis, then it is a two-tailed test.

If it has an equal hypothesis versus a less than hypothesis, then it is a left-tailed test.

Finally, if it has an equal hypothesis versus a greater than hypothesis, then it is a right-tailed test.

This is an equal hypothesis versus a 'less than', so this is left-tailed.

Recall that is the population mean, a is the population standard deviation, and p is a population proportion.

Since the hypotheses refer to σ we are testing the population standard deviation.

Hence, the hypothesis test is left-tailed, and we are testing the population standard deviation.

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There is a statistically significant difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables by hypothesis

State the null hypothesis and the alternative hypothesis.

The null hypothesis (H₀) is that there is no difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables.

The alternative hypothesis (Ha) is that there is a difference in life expectancy between the two groups.

H₀: μ₁ = μ₂

Ha: μ₁ ≠ μ₂

Determine the appropriate test statistic and significance level.

Since we are comparing the means of two independent samples, we can use a two-sample t-test.

We will use a significance level of α = 0.05.

We can use a calculator or statistical software to calculate the test statistic.

t = -2.379

df = 8.98

p-value = 0.042

where t is the test statistic

The p-value is 0.042, which is less than the significance level of 0.05.

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The value of dy/dt is 4/3.

We have,

x² + 3xy - y² = 9

Now differentiating above equation w r t to 't' we get

d/dt x² + d/dt (3xy) - d/dt (-y²) = 0

d/dx (x²) . dx/dt + 3 dx/dt.  dy/dt - 2y dy dt = 0

2x (-1) + 3(-1) dy/dt - 2y dy/dt = 0

dy/dt(-3 -2y)= -4

dy/dt = -4/(-3)

dy/dt = 4/3

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If AOC and BOD are diameters of a circle, centre O, we can prove that triangle ABD and triangle DCA are congruent by RHS.

First, we can observe that angle AOB and angle COD are both right angles since they are angles subtended by diameters of the circle.

Since AO and BO are equal radii of the circle, they have the same length. Similarly, CO and DO are equal radii of the circle and have the same length. Thus, we have:

AO = BO = CO = DO

Now, consider triangle ABD and triangle DCA. We have:

AB = DC (both are diameters of the circle, hence have the same length)

AD = AD (common side)

∠ADB = ∠CDA = 90° (both are right angles)

Therefore, by the RHS (Right Angle-Hypotenuse-Side) congruence criterion, we can conclude that triangle ABD and triangle DCA are congruent.

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The requried larger number x is 80 and the smaller number y is 27.

Let's use the given variables:

x be the larger number

y be the smaller number

According to question

The sum of two numbers is 107 is represented by x + y = 107

The difference between the two numbers is 53 is represented by x - y = 53.

Solving the system of equations:

(x + y) + (z - y) = 107 + 53

2x = 160

x = 80

Now, z = 80, substitute this value into one of the original equations to solve for y.

x + y = 107

80 + y = 107

y = 27

Therefore, the requried larger number x is 80 and the smaller number y is 27.

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The length of the side of his garden can be16.6 ft

From the question, we have the following parameters that can be used in our computation:

He has enough compost to cover an area of 276 square feet.

This means that

Area = 276 276 square feet.

The area of a square is calculated as

Area = Length^2

Substitute the known values in the above equation, so, we have the following representation

Length^2 = 276

Take the square root of both sides

Length = 16.6

Hence, the length is 16.6 ft

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The concentration of copper(II) sulfate in one brand of soluble plant fertilizer is 0.0700% by weight. A 24.0 g sample of this fertilizer is dissolved in 2.00 L of solution. Number of moles of copper ions available in the solution is 8.77×10⁻⁵mole.

In chemistry, a mole, usually spelt mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, and other predetermined particles. The mole designates 6.02214076 1023 units, which is a very large number. In this the Worldwide System of Units (SI), the mole is defined as this number as of May 20, 2019, per the decisions of the General Conference upon Measurements and Weights. Amount of copper sulfate available in  24.0  grams of the sample =

0.07/100× 24.0 =0.014g

number of moles of copper sulfate=0.014/159.6=8.77×10⁻⁵

Number of moles of copper ions available in the solution=8.77×10⁻⁵mole

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Answer:

all triangle angle measures should add up to 180.  So given that,

40+60+80=180

Therefore it can be done

The amount invested at 15% is $2,840 and at 6% is $2,741. The interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 6% by $261.54.

Let's assume that the amount invested at 15% is x, and the amount invested at 6% is y. We know that

x + y = 5,581 (equation 1) (since the total amount invested is $5,581)

We also know that the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 6% by $261.54. This can be expressed as

0.15x - 0.06y = 261.54 (equation 2)

(since the interest earned is equal to the amount invested multiplied by the interest rate)

Now, we can use these two equations to solve for x and y.

First, we will isolate y in equation 1

y = 5,581 - x

Next, we will substitute this expression for y into equation 2

0.15x - 0.06(5581 - x) = 261.54

Simplifying this equation gives

0.15x - 334.86 + 0.06x = 261.54

0.21x = 596.40

x = 2,840

Now that we know x, we can use equation 1 to find y

2,840 + y = 5,581

y = 2,741

Therefore, $2,840 is invested at 15%, and $2,741 is invested at 6%.

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