Mrs. Martin brought 100 cookies to her class. She gave each student the same number of cookies, and had 5 cookies left over. there are more than 10 students and less than 50 students in Mrs. Martin's class. How many students are in her class? ​

Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence

[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]

Differentiating [tex]f(x)[/tex] gives

[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]

Then

[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]

[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]

[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]

which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.

Answer:

either it's 7 and 3 but not sure

Step-by-step explanation:

7x3 =21

now for the negative -10 it would basically be -7+-3=-10

Answer:

24

Step-by-step explanation:

the question translates to asking how many times does 7/8 fit in 21, so 21 divided by 7/8.

when we divide by a fraction, we can multiply by it's inverse, so 21 divided by 7/8, is 21 multiplied by 8/7. so:

21×8/7 = (21×8)/7 = (21/7)×8 = 3×8 = 24

Answer: Two pounds of beef costs $7.38.

Step-by-step explanation:

Multiply the cost for one pound by the amount of pounds you need.

$3.69×2=$7.38

I hope this helps!!

The opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

The stock of Company A gained 6% today to $87.45.

Let x be the opening price of the stock in the beginning of the day.

(x + 0.06x) = 87.45  

Because gained 6% today to $87.45

1.06x = 87.45

x = $82.5

Thus, the opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.

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The control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.

According to the information, the researcher wants to seek whether singing to plants causes them to grow taller.

The explanatory variable is singing. Therefore, the researcher can control some of the variables to determine the explanatory variable on the growth of the plant.

Hence, the control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.

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Answer:

(144)^1/2

(12^2)^1/2

12 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

12

Step-by-step explanation:

Rewrite 144 as 12²

(12²)^1/2

Apply the power rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].

12^2(1/2)

Cancel the common factor of 2.

Cancel the common factor.

Rewrite the expression

12^1

Evaluate the exponent.

12

Answer:

(-4,-3)

Step-by-step explanation:

The point where those 2 equations intersect is (-4,-3)

Answer:

The answer is 64

Step-by-step explanation:

If you find this answer helpful pls mark it the brainliest answer

it's easy 64 the key is in the pic.

Answer:

(π2,15)(π2,15) is a local maximal

(3π2,9)(3π2,9) is a local minimal

Step-by-step explanation:

The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.

We have a scatter plot shown in the table:

1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:

Standard deviation = SD

6SD(x) = 40

SD(x) = 40/6 = 6.67

6SD(y) = 20

SD(y) = 20/6 = 3.37

2) Slope of the line:

= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5

3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.

Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

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Answer:

2a² + 2b²

Step-by-step explanation:

(a - b)² + (a + b)² ← expand both factors using FOIL

= a² - 2ab + b² + a² + 2ab + b² ← collect like terms

= 2a² + 2b²

Step-by-step explanation:

Expand both classic quadratics and combine like terms to find the sum:

(a−b)2+(a+b)2

Answer:

D

Step-by-step explanation:

Original area = x * x  =  x^2

New area =   x ( x +3.5) = x^2 + 3.5x    <====the underlined is the increase in area

Step-by-step explanation:

if 900 is increased by 20% then

120/100×900=1080

Decreasing it by 20% then

80/100×1080=864

Answer:

the answer to this problem is 703.7 in^2

Answer:

A = 13 degrees

B = 65.3 degrees

C = 180 - (13 + 65.3) = 101.7 degrees

Side a = 35 km

Side b = 141.4 km

Side c = 152.4 km

Answer:

14x + 8

Explanation:

⇒ 4(5x+5) - 3(2x + 4)

distribute inside parenthesis

⇒ 4(5x) + 4(5) - 3(2x) - 3(4)

multiply the variables

⇒ 20x + 20 - 6x - 12

collect like terms

⇒ 20x - 6x + 20 - 12

subtract like term

⇒ 14x + 8

4 x 5x = 20x

4 x 5. = 20

-3 x 2x = - 6x

-3 x 4 = - 12

Line them up, collect like terms & simplify

20x + 20 - 6x - 12

20x - 6x = 14x

20 - 12 = 8

Thus, answer is 14x + 8

Hope this helps!

A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,

x - y =1300

x = 1300 + y

Also,  at the end of the year the total interest from the two investments was $1270. Therefore, we can write,

0.13x + 0.07y = 1270

Substitute the value of x from the above,

0.13(1300 + y) + 0.07y = 1270

169 + 0.13y + 0.07y = 1270

0.20y = 1101

y = 5505

substitute the value of y in the first equation,

x - y = 1300

x = 6805

Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.

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This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The correct option is B.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Since the graph of the equation is a line, therefore, it can be concluded that the relationship is linear as a result y varies directly with x.

Therefore we can write the relationship as,

y ∝ x

y = k x

The line goes through the point (-2,3), thus, substitute the points in the equation formed above,

3 = k × (-2)

k = -3/2

Now, substitute the value of k in the equation,

y = -(3/2)x

Hence, the correct option is B.

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The next three terms will be -1/16, 1/32, and -1/64. Then the correct option is B.

Let a be term and r be the common ratio. Then the geometric sequences will be

[tex]\rm a_n = a_{n -1} \cdot r[/tex]

The sequence is given below.

-1, 1/2, -1/4, 1/8,....

The common ratio will be -1/2.

Then the next three terms will be

a₅ = a₄ x (-1/2)

a₅ = (1/8) x (-1/2)

a₅ = -1/16

a₆ = a₅ x (-1/2)

a₆ = (-1/16) x (-1/2)

a₆ = 1/32

a₇ = a₆ x (-1/2)

a₇ = (1/32) x (-1/2)

a₇ = -1/64

Then the next three terms will be -1/16, 1/32, and -1/64.

Then the correct option is B.

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Answer:

C

Step-by-step explanation:

Answer:

yessss

Step-by-step explanation:

yessssssss

The condition that distinguishes organism from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction, and the power of adaptation to the environment through changes originating internally.

Step-by-step explanation:

The number of tickets sold by Dan the first day is x.

Tickets sold on the 2nd day: x+3

on the 3rd day: x+6

on the 4th day: x+9

on the 5th: x+12

Since the total of tickets sold by Dan is 40:

x+(x+3)+(x+6)+(x+9)+(x+12)=40

5x+30=40

5x=10

x=2

number of tickets sold on the third day: 8

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

y=[tex]\frac{1}{2}[/tex]x+0.5

Hope it helps!

Answer:

115

Step-by-step explanation:

You solve this by factoring.

12140 = x^2-10x+65

0 = x^2-10x-12075

0=(x+105)(x-115)

The only positive solution is x=115

The maximum number of data points that may not actually be on the line is 16. so, the correct option is D.

We know that a line of best fit is basically a straight line drawn for a given data that may or may not pass through data points.

It is given that the line is drawn for 16 data points.

Hence, the line may or may not pass through all these 16 points.

Therefore, the maximum number of data points that may not actually be on the line is 16.

so, the correct option is D.

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The graph is attached with the answer.

When two algebraic expressions are equated using an inequality operator , The statement formed is called In equality.

The given Inequality is 2x + y ≤ 2

in slope intercept form can be written as

y ≤  -2x +2 , here slope is -2 and intercept is 2

As an equation it will be

y = -2x +2

x         y

0 ,       2

1 ,       0

2         -2

The graph is plotted

The area is shaded and the test for the origin is applied , and it lies in the shaded region.

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C is the right answer.

hope it helps...

Answer:

C.

Step-by-step explanation:

Calculating this in Desmos, the closest equation to the points on the graph will have to be c

Answer:

A. -6

D. 3

Step-by-step explanation: