A) y-intercept = 2; slope= 2/3
B) y-intercept = 3; slope= -2/3
C) y-intercept = 2; slope= -2/3
D) y-intercept = 2; slope= -3/2

Answer: 8x-16

Step-by-step explanation:

Answer:   8x-16

Step-by-step explanation:

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

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

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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Answer:

SI=P ×R × T

Step-by-step explanation:

P=$500

R=6%

T=3 years

SI=500×3×6 ÷100

  =$90

Answer:

option (D) is correct answer

Answer:

A)  On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Given system of linear equations:

\(\begin{cases}y=-3x+5\\y=x+2\end{cases}\)

Compare the given equations to the slope-intercept form to determine the slope and y-intercept of each line.

Line 1

Line 2

The solution to a graphed system of equations is the point of intersection of the two graphs.

Therefore, the statement that best explains the steps to solve the pair of equations graphically is:

The sum of the infinite geometric series is: ²/₅

The formula for the sum of an infinite geometric series is;

\(S_{\infty} = \frac{a}{1 - r}\)

where;

a is first term

r is common ratio

The first term is; a = ⁴/₁₅

Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃

r = ²⁰/₂₇  ÷  ⁴/₉ = ⁵/₃

Thus;

\(S_{\infty}\) = ⁴/₁₅ ÷ (⁵/₃ - 1)

\(S_{\infty}\) = ⁴/₁₅ ÷ ²/₃

= ²/₅

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Answer:

How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9)  = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5

The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%

The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

x' = 51

μ = 47

σ = 4

Thus;

z = (51 - 47)/4

z = 1

From empirical formula at 1 standard deviation above the means, the probability is 68%.

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The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

The magnitude of vector v is 2 and the angle it makes with the positive x-axis is given as θ = 3.

The component form of vector v can be found by using the following formula:

V = ||V|| (cosθi + sinθj)

Therefore, the component form of vector v is given by:

V = 2 (cos3i + sin3j)

We can calculate the components by substituting the values for ||v|| and θ in the above formula.

Therefore, the x component of vector v is given by:

Vx = 2 cos3

Vx = 1.86

The y component of vector v is given by:

Vy = 2 sin3

Vy = 3.42

Therefore, the component form of vector v is given by:

V = 1.86 i + 3.42 j

This can be represented graphically as shown in the figure.

The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

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\(-21x^{2}-588\)

let me know if anything is unclear, I'm happy to help!

Answer:

669

Step-by-step explanation:

Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.

Answer:

i actually dont know im sorry

Answer:

182.08

Step-by-step explanation:

Answer:

$528

Step-by-step explanation:

400 × 0.04 × 8

= $128

128 + 400

= $528

Answer:

46305

Step-by-step explanation:

A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.

The step in which Johnetta made her error include the following: A. step 1.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (-5/8) ÷ (-3/4)

Fraction = -5/8 × (-4/3)

Fraction = -20/24

For Johnetta, we have:

Fraction = 7/9 ÷ 3/8

Fraction = 7/9 × 8/3

Fraction = 56/27

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Based on the information given the new balance is $289.72.

First step is to calculate the finance charge

\(\text{Finance charge}=205.16\times(0.144\div12 \ \text{months})\)

\(\text{Finance charge}=205.16\times0.012\)

\(\text{Finance charge}=2.46\)

Second step is to calculate the New balance

\(\text{New balance}=205.16+2.46+82.10\)

\(\text{New balance}=\bold{\$289.72}\)

In conclusion, the new balance is $289.72.

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Answer:18×6=108

D SHOULD BE RIGHT

d is = to 108.

tell me if right

Answer:

its blurry so can't really see the numbers

Answer:

B, C, and E

Step-by-step explanation:

usa test prep, sorry if this isn't useful anymore

The period of the function is y = 3 cot ( 4 ⁢ x − 3 ⁢ π ) is π/2.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

The given function is y = 3 cot ( 4 ⁢ x − 3 ⁢ π ).

The period of a function f(x) = A sin (Bx +C) is p = 2π/|B|.

Compare the given function with f(x) = A sin (Bx +C)

A = 3

B = 4

C =  − 3 ⁢ π

The period of the given function is  2π/4

Divide denominator and numerator by 2:

= π/2

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Answer:

\(\dfrac{4096\pi}{5}\approx 2573.593\; \sf (3\;d.p.)\)

Step-by-step explanation:

The shell method is a calculus technique used to find the volume of a solid revolution by decomposing the solid into cylindrical shells. The volume of each cylindrical shell is the product of the surface area of the cylinder and the thickness of the cylindrical wall. The total volume of the solid is found by integrating the volumes of all the shells over a certain interval.

The volume of the solid formed by revolving a region, R, around a vertical axis, bounded by x = a and x = b, is given by:

\(\displaystyle 2\pi \int^b_ar(x)h(x)\;\text{d}x\)

where:

\(\hrulefill\)

We want to find the volume of the solid formed by rotating the region bounded by y = 0, y = √x, x = 0 and x = 16 about the y-axis.

As the axis of rotation is the y-axis, r(x) = x.

Therefore, in this case:

\(r(x)=x\)

\(h(x)=\sqrt{x}\)

\(a=0\)

\(b=16\)

Set up the integral:

\(\displaystyle 2\pi \int^{16}_0x\sqrt{x}\;\text{d}x\)

Rewrite the square root of x as x to the power of 1/2:

\(\displaystyle 2\pi \int^{16}_0x \cdot x^{\frac{1}{2}}\;\text{d}x\)

\(\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}\)

\(\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x\)

Integrate using the power rule (increase the power by 1, then divide by the new power):

\(\begin{aligned}\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x&=2\pi \left[\dfrac{2}{5}x^{\frac{5}{2}}\right]^{16}_0\\\\&=2\pi \left[\dfrac{2}{5}(16)^{\frac{5}{2}}-\dfrac{2}{5}(0)^{\frac{5}{2}}\right]\\\\&=2 \pi \cdot \dfrac{2}{5}(16)^{\frac{5}{2}}\\\\&=\dfrac{4\pi}{5}\cdot 1024\\\\&=\dfrac{4096\pi}{5}\\\\&\approx 2573.593\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the volume of the solid is exactly 4096π/5 or approximately 2573.593 (3 d.p.).

\(\hrulefill\)

\(\boxed{\begin{minipage}{4 cm}\underline{Power Rule of Integration}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}(+\;\text{C})$\\\end{minipage}}\)

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:

Perpendicular

Step-by-step explanation:

It js seems right. i did one very similar and the awnser was Perpendicular

Answer:

300 yd²

Step-by-step explanation:

In such 2d-situation,

Observing the figure we say there are 3 rectangles and 2 unique triangle.

Area of rectangle = length x breadth

Ar. of 1st tilted(front) rec. = 12 x 5 = 60 yd²

Ar. of 2nd tilted(back) rec.= 12 x 8= 96 yd²

Ar. of the base rec. = 9 x 12 = 108 yd²

Area of each triangle = ½ x 4 x 9 = 18 yd²

Total surface area = 60 + 96 + 108 + 18 + 18 = 300 yd²

Answer:

0.028 hectograms

Step-by-step explanation:

1 gram = 0.01 hectograms

Here I couldn't do this on Brainly but I made seperate pdf and did

The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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There are 0.5 centimeters in 5 milimeters

Here, we want to calculate the number of centimeters in 5 milimeters

For convenience sake, we write centimeters as cm and millimeters as mm

10 mm = 1 cm

5 mm = x cm

Mathematically;

x * 10 = 5 * 1

10x = 5

x = 5/10

x = 0.5 cm