USING TOOLS The table shows the numbers y (in thousands) of people in a city who regularly use sharable
electric scooters x weeks after the scooters are introduced.
Time, x Number of users, y
1, 1.5
4, 2.2
6, 2.4
10, 3.9
12, 5.5
15, 6.8
20, 12.3
24, 16.4
25, 17.6

1. Write function that models the data

2. Use the model to predict the number of users after 32 weeks

The number of bottles that would be left is 1

The given parameters are

Number of Bottles = 7

Number of Friends = 3

Assume that the bottles are to be shared among the friends only

The number of bottles that would be left is

Bottles left = Number of Bottles % Number of Friends

This gives

Bottles left = 7%3

Evaluate the modulo operation

Bottles left = 1

Hence, the number of bottles that would be left is 1

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You require the score of 78 to do equally well in exam 2.

To compare both the scores, we need to compute the z scores of both exams and then compare the values. The formula for z-score is:

Z = (X - μ)/σ

Where X = score obtained

           μ = mean score

          σ = standard deviation

For Exam 1:

Z = (91 - 79)/8

  = 12/8

Z = 3/2

To perform similarly well on the second exam, let x equal z 3/2.

For Exam 2:

Z = (x - 60)/12

3/2 = (x - 60)/12

By cross multiplying we get

2(x - 60) = 12 * 3

x - 60 = 36 /2

x - 60 = 18

x = 18 + 60

x = 78

Therefore, Consequently, you must achieve a score of 78 to perform equally well in Exam 2.

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Answer:

602,630

Step-by-step explanation:

Let the equation of the line perpendicular to line 3x+2y=16 is:-

2x - 3y = C. ………………(1)

Line (1) passes through the point (9,-2), therefore

2×9 - 3×(-2)= C

or, C = 24.

Thus, the required equation is:-

2x - 3y = 24.

or, 3y = 2y - 24.

or, y = (2/3).x + (-8). Answer.

Answer:

x = 5.94

Step-by-step explanation:

Answer:

128 feet

Step-by-step explanation:

8*16 is 128 feet

Answer:

  (d)  9x² -12y² -11x

Step-by-step explanation:

The sum of polynomials (8x² -9y² -4x) and (x² -3y² -7x) is found by combining like terms.

When simplifying the sum of polynomials, the distributive property comes into play. It lets you add and remove parentheses, recognizing that factors outside parentheses multiply each term inside parentheses.

  (8x² -9y² -4x) + (x² -3y² -7x)

  = 8x² -9y² -4x + x² -3y² -7x . . . . . eliminate parentheses

  = (8 +1)x² +(-9 -3)y² +(-4 -7)x

  = 9x² -12y² -11x

Answer:

1 TABLET

Step-by-step explanation:

1 tablet should be given. The aim is to ensure that the amount of medicine you give matches what was prescribed. In order to do that, we must change either the amount we ordered or the amount that is available so that they are both measured in the same unit.

To decide the number of tablets that ought to be given, we have to be change over the accessible sum from grams to milligrams.

Given:

Ordered: 100 mg

Available: 0.1 g

1 g = 1000 mg

Converting the available sum to milligrams:

0.1 g * 1000 mg/g = 100 mg

Since the available amount is equal to the ordered sum, you'd have to be give 1 tablet.

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The translation of the phrase The sum of -15y and 16y is −4 is

-15y + 16y = -4 and the value of y is -4.

An algebraic equation is written in the form of variables and constants and we combine these variables and constants with arithmetic operations.

In the given question there is a statement The sum of -15y and 16y is −4 and we have to express it in form of numerical and solve for y or find the value of y.

∴ The sum of -15y and 16y is −4 can be expressed numerically as,

-15y + 16y = -4.

y = -4.

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The answer for the given question is 59/90

A fraction is said to be in lowest terms when the greatest common factor (GCF) of the numerator and denominator is 1. Now that this is in mind, let's continue to solve.

Given, 5/9+1/10 and we have to convert or reduce it into the lowest terms.

So, let's proceed to solve this question

First add 5/9 and 1/10 i.e.,

= 5/9+1/10

Taken LCM of 9 and 10 which comes out to be 90.

Then, adding, we get

= 50+9/90

= 59/90

59/90 is already in its lowest form because the numerator and denominator have no common factor other than 1. So it's already at its most basic level.

Therefore, 59/90 is the required answer.

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When the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

The equation is given as

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

The question implies that we change the subject and make x the subject

However, in the equation;

The subject of the equation is x

This means that when the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

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Answer: B.

Step-by-step explanation:

the goal of the question is to make <AZB ≈ (around) <AYB. Answer b is the only one that makes sense because in the first answer triangle AYB is obtuse and much wider than triangle AZB. While in answer c, triangle AYB is acute and way too small to be around triangle AZB. In answer b, the angles are around the same even though one triangle is slightly larger than the other.

The amplitude of the function is 1/3

The function is given as:

y = negative one-third sine x

Rewrite properly as

y = -1/3sin(x)

A sine function is represented as:

y = Asin(x)

And the amplitude is

Amplitude = |A|

In y = -1/3sin(x), we have

A = -1/3

So, we have

Amplitude = |-1/3|

Evaluate

Amplitude = 1/3

Hence, the amplitude of the function is 1/3

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We get the speed of the object as 5365 miles / day after rounding off.

We are given that an object is moving at a speed of 360 kilometers per hour.

We know that:

1 km = 0.621 miles.

So, 360 km will be:

360 km = 223.56 miles.

Also, we know that:

we have 24 hours in 1 day.

1 day = 24 hours.

1 hour = 1 / 24 day.

Re-writing the speed of the object, we get that:

223.56 miles in 1 / 24 day

That is:

5365.44 miles / day.

Rounding off:

= 5365 miles / day.

Therefore, we get the speed of the object as 5365 miles / day after rounding off.

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The factor (r + 3) is common. Then the greatest common factor will be (r + 3).

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expression is given below.

⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)

In both terms, the factor (r + 3) is common. Then the greatest common factor will be (r + 3). Then the expression will be

⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)

⇒ [(5r - 6) - (2r - 1)](r + 3)

⇒ (3r - 5)(r + 3)

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They still loose 100 dollars

Answer:

The store lost $100....

There are two ways to say 1900 in word form.

1900 = nineteen hundred

1900 = one thousand, nine hundred

Both are equally valid.

Answer: one thousand nine hundred

Step-by-step explanation:

a) The total distance covered is 56 feet

b) The total displacement is 14 feet

c) The average speed  in the first, second, and third parts of the car’s motion are; 5 feet/sec,  0 feet/sec and  4.2 feet/sec

d) The average speed of the car is 3.5 feet/sec

e) The average velocity of the car is 0.875 feet/sec

We must understand that the distance is the difference between two points but the displacement is the distance between two points in a definite direction. This implies that the distance is a scalar quantity while the distance is a vector quantity. Being a vector quantity means that when we are computing the displacement that we must take into account the direction of the motion and this also applies to the calculation of the velocity of the car.

Let us now carry pout the calculations;

a) Total distance = 35 feet +  21 feet = 56 feet

b) Total displacement =  35 feet -   21 feet = 14 feet

c) Average speed of the first, second, and third parts of the car’s motion;

i)  35 feet / 7 seconds = 5 feet/sec

ii) 0 feet/sec ( it sat still)

iii) 21 feet/5 seconds = 4.2 feet/sec

d) The cars average speed = 56 feet/16 seconds = 3.5 feet/sec

e) Average velocity = 14 feet/ 16 seconds = 0.875 feet/sec

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Answer: Tablet costs $225

Laptop costs $135

Step-by-step explanation:

Laptop is = x

Tablet = T

x + 3t = 810

x + t = 360

x = 360 - t

360 - t + 3t =810

2t = 450

t = 225

x + 225 = 360

x = 135

Answer: l=32/3 meters

w=16/3 meters

Step-by-step explanation:

P=perimeter, l=length, w=width

P=2l+2w

32=2(2w)+2w

32=4w+2w

6w=32

w=32/6

w=16/3 meters

32=2l+2(16/3)

32=2l+32/3

(32=2l+32/3)*3

96=6l+32

6l=64

l=64/6

l=32/3 meters

Answer: 14 1/7

Step-by-step explanation:

Answer:

84 minutes

Step-by-step explanation:

360 per hour = 6 per min

140 per hour = 2 1/3 per min

Both together do 8 1/3 per min.

In 3 minutes, both machines together do 25 packages.

700/25 = 28.

In 3*28 minutes, which is 84 minutes, both machines together seal 700 packages.

Thanks!

Answer:

Step-by-step explanation:

7(4x-5) - 4(6x+5) = -91

28x - 35 - 24x -20 = -91

28x - 24x = -91 + 35 + 20

4x = -36

x = -36 : 4

x = -9

---------------

Answer:

equation : 3x + 5y + 2 = 0

Step-by-step explanation:

y - y1 = m (x - x1)

y - (-1) = -3/5 ( x - 1 )

5(y + 1) = -3(x - 1)

5y + 5 = -3x + 3

3x + 5y + 2 = 0

Let [tex]S[/tex] be the sum. Introduce a factor of [tex]\Gamma\left(\frac12\right)=\sqrt\pi[/tex] to rewrite the summand as a beta function integral. Then in the sum, interchange it with the integral, and [tex]S[/tex] reduces to a simple integral.

[tex]\displaystyle S = \sum_{n=0}^\infty \left(-\frac12\right)^n \frac{\Gamma\left(\frac{n+1}2\right)}{\Gamma\left(\frac n2+1\right)}[/tex]

[tex]\displaystyle . ~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \, \mathrm{B}\left(\frac n2+\frac12, \frac12\right) \\\\ ~~~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \int_0^1 \frac{t^{n/2}}{\sqrt t \sqrt{1-t}} \, dt \\\\ ~~~~ = \frac1{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t \sqrt{1-t}} \sum_{n=0}^\infty \left(-\frac{\sqrt t}2\right)^n \\\\ ~~~~ = \frac2{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t\sqrt{1-t}\left(\sqrt t+2\right)}[/tex]

Substitute [tex]u=\sqrt t+2[/tex] and [tex]du=\frac{dt}{2\sqrt t}[/tex].

[tex]\displaystyle S = \frac4{\sqrt\pi} \int_2^3 \frac{du}{u\sqrt{-(u-1)(u-3)}}[/tex]

Now substitute [tex]u=1+\frac2{1+t^2}[/tex] and [tex]du=-\frac{4t}{(1+t^2)^2}\,dt[/tex] - this comes from an Euler substitution of the form [tex]\sqrt{a(x-\alpha)(x-\beta)}=(x-\alpha)t[/tex]. [tex]S[/tex] reduces drastically to a trivial arctangent integral.

[tex]\displaystyle S = \frac8{\sqrt\pi} \int_0^1 \frac{dt}{t^2+3} \\\\ ~~~~ = \frac8{\sqrt\pi} \cdot \frac\pi{6\sqrt3} = \boxed{\frac43\sqrt{\frac\pi3}}[/tex]

The age of accountant is more variable than salary.

Standard deviation is the square of difference between the sets of data and mean.

Comparison for variation of data can be determined by coefficient of variation (C.V).

We know C.V = [tex]\frac{\sigma}{|\overline{x|}}[/tex] × 100.

First we are determining C.V for ages.

Where [tex]\sigma[/tex] = standard deviation and [tex]|\overline{x}|[/tex] = arithmetic mean or average.

∴ C.V for ages, where  [tex]\sigma[/tex] = 4 and [tex]|\overline{x}|[/tex] = 25 years is

C.V = [tex]\frac{4}{25}[/tex] × 100.

C.V = 16.

[tex]C.V_a_g_e[/tex] = 16%.

Now C.V for salary,

where [tex]\sigma[/tex] = 4500 and [tex]|\overline{x}|[/tex] = 30500.

C.V = [tex]\frac{4500}{30500}[/tex] × 100.

C.V = [tex]\frac{4500}{305}[/tex].

[tex]C.V_s_a_l_a_r_y =[/tex] 14.75 %.

So, the coefficient of variation of age is more than that of salary.

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Explanation:

"bisect" means to "divide in half"

So segment WY is split into two smaller equal pieces.

Segments WX and XY are the same length

WX = XY

6k+8 = 11k-12

6k-11k = -12-8

-5k = -20

k = -20/(-5)

k = 4

Answer:

Step-by-step explanation:

If a GP has a positive common ratio and negative first term, it means all its terms are negative since formed by a product of positive and negative numbers.

We can only see one sequence with all negative terms and common ratio of 5, this is REID's.

Answer:

I believe it's 15.21x

Step-by-step explanation:

10.79 - 26 * x

10.79 - 26x =

15.21x