You just obtained a credit card. You immediately purchase a digital camera for $160. Your credit limit is $4000. Let’s assume that you make no payments and purchase nothing more and there are no other fees. The monthly interest rate is 1.42%.

What is the growth factor of your credit card balance?
a.
0.0142
c.
14.2
b.
1.0142
d.
1.42

The vector translation of kite A to kite B and kite B to kite C indicates;

a. The coordinates of the vertices of the kite B are; (4, 10), (3, 4), (3, 3), and (5, 2)

Please find attached the drawing of the kite B created with MS Excel

b. The location of the coordinates of the vertices of the kite C are; (-2, 1), (-3, 1), (-3, 0), (-1, -1)

Please find attached the diagram of the location of the kite C created with MS Excel

c. The vector is [tex]\binom{-2}{4}[/tex]

d. The vector is; [tex]\binom{2}{-4}[/tex]

A translation transformation is a transformation in which involves the displacement of the figure to a new location.

a. The vector translation [tex]\binom{4 }{7}[/tex] indicates that the kite is translated 4 units to the right and 7 units upwards

The coordinates of the vertices of the kite A are; (0, -3), (-1, -3), (-1, -4), and (1, -5)

The coordinates of the vertices of the kite B are therefore;

b. The coordinates of the vertices of the kite C obtained from the translation of the kite B by the vector [tex]\binom{-6 }{-3}[/tex] are;

(-2, 1), (-3, 1), (-3, 0), (-1, -1)

c. The vector translation that maps kite A onto kite C is therefore;

Translation to the right of kite A with respect to kite C = -2 - 0 = -2

Translation upwards from kite A to kite C = 1 - (-3) = 4

The translation that maps kite A onto kite C is; [tex]\binom{-2 }{4}[/tex]

d) The vector translation that maps kite C onto kite A can be found as follows;

Translation to the right of kite C with respect to kite A = 0 - (-2) = 2

Translation upwards from kite C to kite A = -3 - 1 = -4

The vector translation that maps kite C onto kite A is; [tex]\binom{2}{-4}[/tex]

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The interest rate needed for an investment of $5700 to double in 7 years if interest is compounded continuously is approximately 9.9%.

We have,

The formula for continuous compounding is:

A = Pe^(rt)

where A is the final amount, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

We want to find the interest rate needed for an investment of $5700 to double in 7 years, so:

2P = Pe^(rt)

Divide both sides by P:

2 = e^(rt)

Take the natural logarithm of both sides:

ln 2 = rt ln e

Since ln e = 1, we have:

ln 2 = rt

Solve for r:

r = ln 2 / t

r = ln 2 / 7

r ≈ 0.099

Thus,

The interest rate needed for an investment of $5700 to double in 7 years if interest is compounded continuously is approximately 9.9%.

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Answer:

480

Step-by-step explanation:

320 divided by 2 (50%) is 160, so add that to the original 320 to get 480.

Answer:

A & D

Step-by-step explanation:

the numerator is greater than the denominator

Answer:

Step-by-step explanation:

Step 1:- 10x - 15y - 6x + 4y

Step 2:- 4x - 11y

Answer:

x=(11/4)y or

y=(4/11)x

Step-by-step explanation:

The solution to the equation [tex]COS^ {X}[/tex]-SINX=1/4 is: X ≈ 1.911 radians

What is Radian?

A radian is a unit of measurement for angles, used in mathematics and physics. It is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. One radian is equivalent to approximately 57.3 degrees.

Rearrange the equation to get [tex]COS^ {X}[/tex] = SINX + 1/4.

Square both sides of the equation to eliminate the square root:

[tex]COS^ {2X}[/tex]= [tex]SIN^ {2X}[/tex] + 1/2*SIN(X) + 1/16

Use the identity [tex]COS^ {2X}[/tex]+ [tex]SIN^ {2X}[/tex]= 1 to substitute for [tex]COS^ {2X}[/tex]

1 - SIN^2(X) = SIN^2(X) + 1/2*SIN(X) + 1/16

Simplify the equation and rearrange terms:

SIN^2(X) + SIN(X) - 15/16 = 0

Solve for SIN(X) using the quadratic formula:

SIN(X) = (-1 ± sqrt(1 + 120/16))/4

Simplify the expression under the square root and evaluate both solutions:

SIN(X) = (-1 ± sqrt(129))/4

Since the range of SIN(X) is [-1, 1], only the positive solution is valid:

SIN(X) = (-1 + sqrt(129))/4

Use the identity[tex]COS^ {2X}[/tex] + [tex]SIN^ {2X}[/tex] = 1 to find the corresponding value of COS(X):

COS(X) = sqrt(1 - [tex]SIN^ {2X}[/tex])

= sqrt(1 - (-1 + sqrt(129))^2/16)

Therefore, the solution to the equation C[tex]COS^ {X}[/tex]-SINX=1/4 is:

X ≈ 1.911 radians (or approximately 109.49 degrees)

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Answer:

The mode is 77.43

Step-by-step explanation:

The mode is asking which number do you see the most.

Helping in the name of Jesus.

The value that should be the area of the circle, B whole be = About 900 in². That is option C.

The formula that can be used to calculate the area of a circle = πr²

But area of circle B can be estimated using the dimensions provided for circle A.

That is;

circle A Diameter = 20 in

Circle A area = 300 in²

Circle B diameter = 60 in

Circle B diameter = X

If , 20 in = 300

60 in = X

Make X the subject of formula;

X = 60×300/20

= 18000/20

= 900 in²

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The coefficients of the expressions K - 1/3d are 1 and -1/3

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

K - 1/3d

The coefficients of expressions is the number beside the variable in the expression

Using the above as a guide, we have the following:

Coefficient of k = 1

Coefficient of d = -1/3

Hence, the coefficients are 1 and -1/3

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Answer:

Step-by-step explanation:

Answer:

After writing the values of x and y in terms of z , and substituting them in the third equation we get:

x=-1/5

y=11/5

z=-2

Step-by-step explanation:

You have to compare each side.

If they have the same ending, they are like terms.

1. E

2. A

3. D

4. B

5. C

Answer:

According to the Central Limit Theorem, the sampling distribution of sample means would have a mean of 5.4 years.

Step-by-step explanation:

For a normally distributed random variable X, with mean and standard deviation, the sampling distribution of sample means with size n can be approximated to a normal distribution with mean and standard deviation.

As long as n is at least 30, the Central Limit Theorem can also be applied to skewed variables.

We have the following problem:

Answer:

Step-by-step explanation:

The mean of the sampling distribution of sample means can be calculated using the formula:

μM = μ

where μ is the population mean and M is the sample mean.

Thus, μM = μ = 5.4 years.

Therefore, the mean of the sampling distribution of sample means would also be 5.4 years.

Answer:

A'B'C'D' will be smaller than ABCD.

Step-by-step explanation:

A is at (5, 10) so A' will be at (0.8*5, 0.8*10) = (4, 8).

By applying the same rule B' will be the point (8,8).

C' will be (8, 4) and D' (4, 4).

So the lengths of the new square will be 4 units so its smaller than ABCD.

(The sides of ABCD are 5 units long)

Answer:

6 , 5, 12,39

Step-by-step explanation:

Answer:

in the first worksheet in number (3) we are asked to factorize certain equations (mainly quadratics)

so in number one we have the quadratic equation as 4x²-12x+9. so this is an expression not equation and so therefore it is represented as the formula ax²+bx²+c

[tex]therefore \: a = 4 \\ \: \: \: \: b = - 12 \\ \: \: \: c = 9 \\ [/tex]

therefore 4 multiplied by 9 equals 36.

then we find a number that is a factor of 36 but can add to get -12. that number is -6 therefore substitute in the eqn

[tex]4 x^{2} - 6x - 6x + 9[/tex]

then factorize to get an answer of

[tex](2x - 3)(2x - 3)[/tex]

The rate of rise of the temperature is determined as 2 ⁰C/hr.

The rate at which the temperature rises this morning is the measure of increase in the temperature per unit hour.

Mathematically, the formula for the rate of rise of the temperature is calculated as follows;

Rate = ΔT/Δt

where;

The rise in temperature is given as 2⁰C

The change in time is given as 1 hour

The rate of rise of the temperature = 2⁰ C / 1 hr = 2 ⁰C/hr

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Answer:

Step-by-step explanation:

Without more information about the translation, it is not possible to determine the coordinates of A' and B'.

The translation could have shifted line AB in any direction and by any distance, so there are many possible sets of coordinates for A' and B'.

The integral [tex]\int\limits^a_{-a} \int\limits^{\sqrt{a^2 - y^2}}_{-\sqrt{a^2 - y^2}} \int\limits^{\sqrt{a^2 -x^2 - y^2}}_{-\sqrt{a^2 - x^2 - y^2}} (x^2z + y^2z + z^3) dz dx dy[/tex] when evaluated is 0

Given that

[tex]\int\limits^a_{-a} \int\limits^{\sqrt{a^2 - y^2}}_{-\sqrt{a^2 - y^2}} \int\limits^{\sqrt{a^2 -x^2 - y^2}}_{-\sqrt{a^2 - x^2 - y^2}} (x^2z + y^2z + z^3) dz dx dy[/tex]

To change to spherical coordinates, we need to express x, y, and z in terms of spherical coordinates: r, θ, and Φ .

In particular, we have

[tex]x &= r \sin\phi \cos\theta, \\y &= r \sin\phi \sin\theta, \\z &= r \cos\phi[/tex]

The Jacobian for the transformation is r² sin(Φ), and the limits of integration become

[tex]-a &\leq x \leq a \quad \Rightarrow \quad 0 \leq r \leq a, \\-\sqrt{a^2 - y^2} &\leq y \leq \sqrt{a^2 - y^2} \quad \Rightarrow \quad 0 \leq \phi \leq \frac{\pi}{2}, \\-\sqrt{a^2 - x^2 - y^2} &\leq z \leq \sqrt{a^2 - x^2 - y^2} \quad \Rightarrow \quad 0 \leq \theta \leq 2\pi.[/tex]

Substituting into the integral, we have

[tex]&\int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} (r^2\sin^2\phi\cos\theta\cdot r\cos\phi + r^2\sin^2\phi\sin\theta\cdot r\cos\phi + r^3\cos^3\phi) r^2 \sin\phi,d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} (r^3\sin^2\phi\cos\theta\cos\phi + r^3\sin^2\phi\sin\theta\cos\phi + r^3\cos^3\phi) \sin\phi, d\theta d\phi dr[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} r^3\sin\phi\cos\phi (\sin^2\phi\cos\theta + \sin^2\phi\sin\theta + \cos^2\phi) , d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} r^3\sin\phi\cos\phi (\sin^2\phi + \cos^2\phi) , d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} r^3\sin\phi\cos\phi, d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} 0, d\theta d\phi dr \&\quad = 0[/tex]

Therefore, the value of the integral is 0.

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The pattern formed will always be true due to the constant shape realized or gotten from all the patterns formed and that constant shape in it all is a triangle.

A triangle is a closed two-dimensional figure with three straight sides and three angles. Triangles can be classified according to the length of the sides and the size of the angles.

The triangle is an important geometric shape in mathematics and is used in fields such as architecture, engineering and physics.

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Answer:

log5[x^2z^9w√(x^4-81)]

Using the properties of logarithms, we can rewrite the given expression as a sum and/or difference of logarithms as follows:

log5[x^2z^9w√(x^4-81)] = 2log5(x) + 9log5(z) + log5(w) + 0.5log5(x^4-81)

Note that the square root (√) can be expressed as a exponent of 0.5, and we can use the properties of logarithms to split the logarithm of a product into a sum of logarithms of individual factors.

Step-by-step explanation:

By answering the presented question, we may conclude that In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is often referred to as a rectangle with two nearby sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Also, the diagonals of the square are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

To determine the answer, multiply the areas of the shaded squares by the overall area of the figure.

Assuming that both squares are the same size, we may combine the fractions using a common denominator:

2/12 + 2/15 = 5/60 + 4/60 = 9/60 = 3/20

As a result, the entire shaded area is 3/20 of the total area of the diagram.

We can't discover the exact area of the graphic because it's not presented. As a result, we can only represent the answer in fractions or decimals.

In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

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Answer:

Shira uses 20% of her paycheck for bills.

Step-by-step explanation:

100% - 35% - 30% - 15% = 20%

The graph of the inequalities is attached

Graphing a nonlinear inequality involves following a similar process as graphing a linear inequality, but with some additional considerations:

Simplify the inequality as much as possible to get it into a standard form.

Identify the shape of the inequality. Is it a parabola, a circle, a hyperbola, or some other shape?

Determine the direction of the inequality. Is it "greater than" or "less than" the given value?

Plot the curve that represents the boundary of the inequality, using the shape and standard form of the inequality.

Determine whether the inequality is "strict" (i.e., greater than or less than) or "non-strict" (i.e., greater than or equal to, or less than or equal to). the situation in the problem is strict

Shade the area of the graph that satisfies the inequality, based on the direction of the inequality and whether it is strict or non-strict.

The graph is attached

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Answer:

v1=15mph, v2=35mph

Step-by-step explanation:

We have the values:

s=400mi (distance travelled)

t=8h (time)

v1=x, v2=x+20 (first and second speed)

We need to work out v1 and v2.

The formula for time is equal to distance over speed. t=s/v

Because the two ships are colliding, the formula will be t=s/v1+v2

Plug in given values:

8h=400mi/x+x+20

8h=400mi/2x+20

Cross multiply:

400=8(2x+20)

400=16x+160

-16x=-240 (Divide by -16)

x=15, which means that v1=15mph

To work out v2, all we must do is add 20 to 15mph and we get v2=35mph.

Hope this helps!

The first four terms of the Taylor series for f(x) = 1/(x - 5) at a = 1 are:

[tex]-1/4 - 1/16(x - 1) + 1/64(x - 1)^2 - 3/512(x - 1)^3[/tex]

What is series?

In mathematics, a series is a sum of the terms of an infinite sequence of numbers. It is often represented by the symbol Σ (sigma) and written as an expression that adds up the terms of the sequence.

To find the Taylor series for the function f(x) = 1/(x - 5) at a = 1, we need to compute its derivatives at x = 1 and evaluate them at a = 1. We can use the formula for the Taylor series, which is given by:

[tex]f(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...[/tex]

We start by finding the derivatives of f(x):

[tex]f(x) = 1/(x - 5)\\\\f'(x) = -1/(x - 5)^2\\\\f''(x) = 2/(x - 5)^3\\\\f'''(x) = -6/(x - 5)^4[/tex]

Now, we can evaluate these derivatives at a = 1:

[tex]f(1) = 1/(1 - 5) = -1/4\\\\f'(1) = -1/(1 - 5)^2 = -1/16\\\\f''(1) = 2/(1 - 5)^3 = 1/32\\\\f'''(1) = -6/(1 - 5)^4 = -3/128[/tex]

Substituting these values into the formula for the Taylor series, we get:

[tex]f(x) = -1/4 - 1/16(x - 1) + 1/64(x - 1)^2 - 3/512(x - 1)^3 + ...[/tex]

Therefore, the first four terms of the Taylor series for f(x) = 1/(x - 5) at a = 1 are:

[tex]-1/4 - 1/16(x - 1) + 1/64(x - 1)^2 - 3/512(x - 1)^3[/tex]

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The equivalent expressions are:

5(2 + x + y) + 10

10 + 5x + 5y - 3x + 3x

10 + 2x + 3y + 2x + 2y + 5

2(5 + x) + 5y

We have,

10 + 2x + 5y + 3x can be simplified by combining like terms:

= 10 + 2x + 3x + 5y

= 10 + 5x + 5y

Any expression that simplifies to 10 + 5x + 5y is equivalent to 10+2x+5y+3x.

For example:

5(2 + x + y) + 10

10 + 5x + 5y - 3x + 3x

10 + 2x + 3y + 2x + 2y + 5

2(5 + x) + 5y

All of these expressions have different forms, but they simplify to the same value as 10 + 2x + 5y + 3x when the terms are combined.

Thus,

The equivalent expressions are:

5(2 + x + y) + 10

10 + 5x + 5y - 3x + 3x

10 + 2x + 3y + 2x + 2y + 5

2(5 + x) + 5y

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The evaluation of the sinusoidal function for the blood pressure of the individual indicates that the period, maximum and minimum blood pressure and the times are;

(a) 1/60 minutes

(b) Maximum (systolic) blood pressure = 110 mmHg

Minimum (diastolic) blood pressure = 50 mmHg

(c) The times are; n/60 + 1/240

A sinusoidal function is a periodic function based on the sine or cosine of an angle.

The specified function can be presented as follows;

p(t) = 80 + 30·sin(120·pi·t)

(a) The function is a sinusoidal function of the form; y = A·sin(B·(x - C)) + D

Where;

A = The amplitude

B = 2·π/Period

C = The phase shift

D = The vertical shift

Comparing, we get;

C = 0, D = 80, x = t

Therefore;

y = A·sin(B·(t)) + 80

B = 120·π

The period = 2·π/(120·π) = 1/60

(b) The maximum and minimum values are obtained when sin(120·pi·t) = ±1 as follows;

Maximum value = pmax = 80 + 1 × 30 = 110

Minimum value = pmin = 80 - 1 × 30 = 50

The systolic or maximum blood pressure = 110 mmHg

The diastolic or minimum blood pressure = 50 mmHg

(c) When the blood pressure is maximum, we get;

p(t) = 80 + 30·sin(120·pi·t) = 110

80 + 30·sin(120·pi·t) = 110

sin(120·pi·t) = (110 - 80)/30 = 1

120·pi·t = arcsine(1) = pi/2 + 2·n·pi

120·t = 1/2 + 2·n

t = (1/2 + 2·n)/120 = 1/240 + n/60, where n is an integer value

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Answer: D exactly 1 line

Step-by-step explanation: