Noah is learning portugese, and he uses flash cards to study vocabulary. For every 5 new flash cards he practices, he reviews 10 old flash cards. Today , he practiced 45 flash cards in all. How many new flash cards did he practice?

Based on the information, the hedgehogs have made the better offer

The Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:

PV = S(t) * e^(-rt)

The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:

PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt

= 736,918.63

Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:

PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt

= 753,472.49

Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

The next sequence will be -22 because they are subtracting 7

Answer:

Rational

Step-by-step explanation:

It isnt whole because its a decimal,

It isnt an Integer because its a decimal

It isnt natural because its a decimal

Meaning it can only be rational

omg, I just said the answer was B.

The price of the item now is $8 after an 80% reduction. To find the price of the item after the 80% reduction, you can follow these steps:

1. Calculate the amount of the reduction: 80% of $40.

2. Subtract the reduction amount from the original price to get the final price.

Step 1: Calculate the amount of the reduction:

80% of $40 = 0.80 * $40 = $32

Step 2: Subtract the reduction amount from the original price:

Original Price - Reduction Amount = $40 - $32 = $8

So, the price of the item now is $8 after an 80% reduction.

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In this case, the given sample mean of 25.3 is only slightly higher than the population mean of 25, and is well within one standard deviation from the population mean. Therefore, the probability of a sample mean being less than 25.3 is 0.9582.

In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values in that dataset. It is also commonly referred to as the average.

Here,

To find the required probability, we need to calculate the z-score first:

z = (x - μ) / (σ / √n)

z = (25.3 - 25) / (1.3 / √68)

z = 1.73

Looking at the standard normal table, the probability of a z-score being less than 1.73 is 0.9582.

To determine whether the given sample mean would be considered unusual, we need to compare it to the population mean and standard deviation. A sample mean is considered unusual if it falls outside the range of values that are expected to occur with a high probability based on the population mean and standard deviation.

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Answer:

hello your question is incomplete attached below is the complete question

answer :

H0 : u = 21.62    ( Null hypothesis )

H1 : u = 21.62   ( alternative hypothesis )

Step-by-step explanation:

Formulating hypothesis that can be used to determine whether the population mean rate at 5 CCF of residential water discharged by U.S public utilities differs from $21.62

H0 : u = 21.62    ( Null hypothesis )

H1 : u = 21.62   ( alternative hypothesis )

Answer:

Basic facts:

1foot =12 inch

Step-by-step explanation:

Vidal's treehouse was 6 feet which are 72 inches

Mateo's treehouse was 48 inches

72-48=24

24/12=2      

2 feet and 0 inches

the answer is 63

Step-by-step explanation

18 x 3.5=63

Answer: 63 pages

Explanation: 18 times 3 equals 54 and then for half an hour that's 9 minutes added to 54 which is 63 pages.

We want to know the measure of the angle BCD. In this case, we see that it is an inscribed angle, and then its measure is half of the arc it intercepts (in this case BD).

With this in mind,

And then, the angle BCD has 65°.

The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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Answer:

C. 5 inches

Step-by-step explanation:

I’m area you have to multiply L • W

But since we don’t know the width we can divide the length by the area.

40/8 = 5

So the answer would be 5.

Another way to solve this problem is with using guess and check.

I hope it helps! Have a great day!

Anygays~

Answer:

C. 5 inches

Step-by-step explanation:

Use the numbers we have in the word problem, so you´d divide 40 by 8 since you´re trying to find the width. 40 is the area and 8 is the length so divide it tofind the width.

40/8 = 5

ANSWER: 5 inches

I hope it helps! Have a great day!

The solid volume created by rotating the region enclosed by the aforementioned curves about the y-axis is 8π/3.

According to the question, we have to find  the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y2 = 2x, x = 2y;about the y-axis.

In the first quadrant, the region enclosed by the curves y2 = 2x and x = 2y forms a triangle with vertices (0, 0), (1, 1), and (2, 4).

The formula for the volume of the solid generated by rotating this triangle about the y-axis is given by :

V = ∫0aπ(2x)2dx

where a is the length of the longest side of the triangle, in this case 2.

Substituting the values yields:

V = ∫02π(2x)2dx

= 2π∫02x2dx

= 2π[x2/3]02

= 8π/3

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Answer: 14 squared divided by 17 over 14 squared divided by 2 is a local maximum

The problem says we have a square flower bed to start out with.

Let's have the sides of the squares be "x". The area of this original flower bed is \(x^{2}\).

Then, one side of the square is enlarged by 2ft, and another side 3ft. Our new flower bed dimensions are now (x+2) and (x+3). Multiply (x+2) and (x+3) to find the area, which gets you \(5x^{2} +6x+6\).

We also know that the new area of the flower bed is twice the size of the original flower bed. Multiply the original area by 2, you get \(2x^{2}\).

With the new area and the doubled original area, we can now make an equation: \(5x^{2} +6x+6=2x^{2}\)

Solve for x,  you get 6.

Hope this explanation helped, maybe a bit too many details but there's your answer, 6!

The side length of the original bed is 6 units

The formula for finding the area of the square is expressed as:

A = x^2

If one side of a square flower bed was enlarged by 2 ft and the other side was enlarged by 3 ft, the area of the bed becomes;

A = (x+2)(x+3)

A = x^2 + 5x + 6

If the area of a new flower bed became twice the area of an old one, then;

5x^2 + 6x + 6 = 2x^2

On factorizing, the value of x is 6 which shows that the side length of the original bed is 6 units

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Answer:

Step-by-step explanation:

Let x be the price of tables

Let y be the price of chairs

5x + 7y = 1210

x = 3y

5(3y) + 7y = 1210

         22y = 1210

             y = $55

 x = 3(55) = $165

8(165) + 4(55) = $1540

Answer:

a.8

Step-by-step explanation:

y=-16

-16=-2x

16=2x

x=16/2=8

For every 1 orange in the fruit bowl there are three bananas.

According to the question,

We have the following information:

In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.

Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:

4 oranges = 12 bananas

Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.

So, we have the following expression:

1 orange = 12/4 bananas

1 orange = 3 bananas

Hence, for every 1 orange in the fruit bowl there are three bananas.

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The correct answer is option (b) The vertical distance between the point at -7 feet and sea level (0 feet)

What is elevation?

The elevation is the height of an object or point above a given reference point, usually sea level. It is often used to describe the height or altitude of a geographic location, such as a mountain peak or a city, and is commonly measured in feet or meters.

In the context of elevation, | -7 | feet would mean the vertical distance between the point at -7 feet and sea level (0 feet).

The vertical distance between two points is calculated by taking the absolute value of the difference between their elevations. So, in this case, the absolute value of -7 is 7, which means the point is 7 feet below sea level.

The correct answer is option (b) The vertical distance between the point at -7 feet and sea level (0 feet).

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(a) The slope of the curve at point P(3, -10) is 1.

(b) The equation of the tangent line to the curve at point P(3, -10) is y = x - 13.

(a) The slope of the curve at point P(3, -10) is clculated as follows;

The slope of a secant line passing through points P(3, -10) and Q(x, f(x));

slope = (f(x) - f(3)) / (x - 3)

slope = (x² - 5x - 4 - (-10)) / (x - 3)

= (x² - 5x + 6) / (x - 3)

The limiting value of the slope as x approaches 3;

lim(x->3) [(x - 3)(x - 2)] / (x - 3)

lim(x->3) (x - 2)

= 3 - 2

= 1

(b) The equation of the tangent line to the curve at point P(3, -10) is calculated as;

y - y₁ = m(x - x₁)

y - (-10) = 1(x - 3)

y + 10 = x - 3

y = x - 13

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Answer:

(a)  1

(b)  y = x - 13

Step-by-step explanation:

To approximate the slope of the tangent line and, consequently, the curve at a point (x, f(x)), we can calculate the slope of the secant line that connects (x, f(x)) to another point on the curve that is very close to it.

If P is (x, f(x)), then a point a small distance from P is (x + h, f(x + h)).

As h gets smaller, the distance between the two points gets smaller. The closer the points, the closer the line joining them will be to the tangent line.

The derivative of function f(x) is the limit of the slope of the secant line from (x, f(x)) to (x + h, f(x + h)) as h approaches 0:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\end{minipage}}\)

This method of differentiation is known as differentiating from first principles.

Given:  f(x) = x² - 5x - 4

Therefore:  f(x + h) = (x + h)² - 5(x + h) - 4

Substitute f(x) and f(x - h) into the formula:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=\displaystyle \lim_{h \to 0} \left[\dfrac{(x+h)^2-5(x+h)-4-(x^2-5x-4)}{(x+h)-x}\right]\\\\&=\lim_{h \to 0} \left[\dfrac{x^2+2hx+h^2-5x-5h-4-x^2+5x+4}{h}\right]\\\\&=\lim_{h \to 0} \left[\dfrac{2hx+h^2-5h}{h}\right]\\\\&=\lim_{h \to 0} \left[2x+h-5\right]\\\\&=2x-5\end{aligned}\)

As h gets close to zero, 2x + h - 5 gets close to 2x - 5.

To find the limiting value of the slope of the secant line through point P, substitute the x-value of point P into 2x + 5:

\(x=3 \implies 2(3)-5=1\)

Therefore, the limiting value of the slope of the secant line through point P is 1.

To find the equation of the tangent line to the curve at P(3, -10), substitute the found slope, m = 1 and coordinates of point P into point-slope form of a linear equation:

\(\begin{aligned}y-y_1&=m(x-x_1)\\\\\implies y-(-10)&=1(x-3)\\y+10&=x-3\\y&=x-13\end{aligned}\)

Therefore, the equation of the tangent line at P is y = x - 13.

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

An equation for a transformed cosine wave with the following properties can be written in the form:

y = A× cos(B(x - C)) + D

Where:

A = amplitude (positive value)

C = phase shift (horizontal shift of the wave)

D = vertical shift (shift of the wave up or down)

Here we have

Amplitude = 3

Period = π

Horizontal shift = None

Vertical shift  = 4 units  up  

As we know Period P = 2π/B

From the data => 2π/B = π

=> B = 2  

Hence,

Equation for a transformed cosine wave, y = 3 × cos(2(x - 0)) + 4

=> y = 3 × cos(2(x )) + 4

=> y = 3cos2x + 4  

Therefore,

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

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Answer:

the answer is 6 trust. poopoo

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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