A savings account starts with $312.50. After 9 years of continuous compounding at an interest rate, r, the account has $1250.

What is the interest rate percentage?

Round the answer to the nearest hundredth.

Answer:

[tex]m = \dfrac{4}{\sqrt{3}} \text{ or, in rational form: } m = \dfrac{4\sqrt{3}}{3}[/tex]

[tex]n = \dfrac{2}{\sqrt{3}} \text{ or, in rational form: } n = \dfrac{2\sqrt{3}}{3}[/tex]

Not sure which form your teacher wants the answers, would suggest putting in both

Step-by-step explanation:

The missing angle of the triangle = 180 - (60 + 90) = 30°

We will use the law of sines to find m and n

The law of sines states that the ratio of each side to the sine of the opposite angle is the same for all sides and angles

Therefore since m is the side opposite 90° and 2 is the side opposite 60°,

[tex]\dfrac{m}{\sin 90} = \dfrac{2}{\sin 60}}\\\\[/tex]

sin 90 = 1

sin 60 = √3/2

So
[tex]\dfrac{m}{1} = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2 \cdot 2}{\sqrt{3}} \\\\m = \dfrac{4}{\sqrt{3}}\\\\[/tex]

We can rationalize the denominator by multiplying numerator and denominator by √3 to get
[tex]m = \dfrac{4\sqrt{3}}{3}[/tex]
(I am not sure what your teacher wants, you can put both expressions, they are the same)

To find n
Using the law of sines we get
[tex]\dfrac{n}{\sin 30} = \dfrac{m}{\sin 90}\\\\\dfrac{n}{\sin 30} = m\\\\\dfrac{n}{\sin 30} = \dfrac{4}{\sqrt{3}}\\\\[/tex]

sin 30 = 1/2 giving

[tex]\dfrac{n}{1/2} = \dfrac{4}{\sqrt{3}}\\\\n = \dfrac{1/2 \cdot 4}{\sqrt{3}} \\\\n = \dfrac{2}{\sqrt{3}}[/tex]

In rationalized form
[tex]n = \dfrac{2\sqrt{3}}{3}}[/tex]

Answer:

A

Step-by-step explanation:

ita a bc i know its I did this before

The value of function g (5) is,

⇒ g (5) = 30/13

We have to given that;

Function is,

g (x) = {(x² + 5) / (x + 8)   if x ≠ - 8

      = { x - 1   ; if x = - 8

Hence, The value of function g (5) is,

⇒ g (5) = (x² + 5) / (x + 8)

⇒ g (5) = (5² + 5) / (5 + 8)

⇒ g (5) = (30) / (13)

Thus, The value of function g (5) is,

⇒ g (5) = 30/13

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Answer:

A trainee requires 3 days of training before they can assemble 9 heaters.

Step-by-step explanation:

We are given the formula for the number of water heaters h that a trainee can assemble per 8-hour shift as:

h = 2.1 0.9t + 4

where t is the number of days of training the trainee has received. We need to find out how many training days are required before a trainee can assemble 9 heaters. So we set h to 9 and solve for t:

9 = 2.1 0.9t + 4

Subtracting 4 from both sides, we get:

5 = 2.1 0.9t

Dividing both sides by 2.1 0.9, we get:

t = (5 / (2.1 0.9))

Using a calculator, we get:

t ≈ 2.49

Rounding up to the nearest day, we get:

t = 3

Therefore, a trainee requires 3 days of training before they can assemble 9 heaters.

Answer:

Step-by-step explanation:

Law of sines states that the lengths of the sides of a triangle are proportional to the sines of the corresponding angles.

sinM/17 = sinx/10

sin M = .94551

.94551/17 = sin x /10

cross mulitply and then divide.

.954551 · 10/17 = sin x

9.4555/17 = .5562

sin inverse is 33.793 ° or rounded to 33.8°

The inequality that represents the range of prices of winter coats the shopper can buy as 175 ≤ p ≤ 430

To write the inequality, we can use the variable p to represent the price of the coat. The inequality we can write is:

p ≥ 175

This inequality means that the price p of the coat must be greater than or equal to $175.

Now, we also know that the shopper has a budget of $430 to spend on a winter coat. This means that the price p of the coat must be less than or equal to $430. We can represent this inequality as:

p ≤ 430

This inequality means that the price p of the coat must be less than or equal to $430.

To find the range of prices that the shopper can buy, we need to find the values of p that satisfy both of these inequalities. We can do this by finding the intersection of the two inequality regions on a number line, or by solving the system of inequalities:

p ≥ 175

p ≤ 430

To solve this system, we simply need to find the values of p that satisfy both inequalities simultaneously. We can do this by taking the intersection of the two inequality regions:

175 ≤ p ≤ 430

This means that the price p of the winter coat must be greater than or equal to $175 and less than or equal to $430. Therefore, the shopper can buy any winter coat with a price in this range.

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Answer:

a) y = 5.2727x + 32.5276

b) y = 5.2727(6) + 32.5276

= 64.1638 inches

c) y = 5.2727(7.153) + 32.5276

= 70.2432 inches

a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.

(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.

To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.

Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:

19 = 0.693 / k

k = 0.693 / 19

So the formula relating y to t is:

y = 45.1 * e^(-0.693/19 * t)

(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):

y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg

So, there will be approximately 30.1 mg of the substance present after 9 minutes.

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After considering all the given data and running a series of calculation we reach the conclusion that the probability of receiving both orders as the same colors is 0.2184, under the condition that a company has the information that 32% of their customers order their product in Black and 26% in White and 22% in Grey.

Then the evaluated probability of both orders being the same color can be found by applying summation of the probability of both orders being black, both orders being white, and both orders being grey.

Now, the probability of both orders being black is 0.32 × 0.32
= 0.1024.

Similarly the probability of both orders being white is 0.26 × 0.26
= 0.0676.

Lastly, the probability of both orders being grey is 0.22 × 0.22
= 0.0484.

Hence, the evaluated probability of both orders being the same color is 0.1024 + 0.0676 + 0.0484 = 0.2184 (rounded to four decimal places).
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Answer:

x=28

Step-by-step explanation:

solve for x by simplifying both sides of the equation, then isolating the variable.

have a good day :)

Answer

x=3 1/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

chickennnnnnnnn

Answer:

B. AB = CD = sqrt(13); DA = BC = sqrt(17)

This is because in a parallelogram, opposite sides are equal in length. In this statement, AB is equal to CD and DA is equal to BC, so opposite sides are equal. The values of AB, CD, DA, and BC are given as the square root of 13 and the square root of 17, which matches the condition of the statement.

In statement A, all sides are equal in length, which means the shape is a rhombus, not necessarily a parallelogram.

Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.

To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:

Time spent on videos = 10% of 40 hours = 4 hours

Time spent on homework = 15% of 40 hours = 6 hours

Time spent on games = 20% of 40 hours = 8 hours

Time spent on social media = 25% of 40 hours = 10 hours

Time spent on shopping online = 20% of 40 hours = 8 hours

Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.

The difference between these two amounts is:

6 hours - 8 hours = -2 hours

This means that Heracio spent 2 hours more on shopping online than on doing homework.

Step-by-step explanation:

Answer:

Set your calculator to degree mode.

2) tan(43°) = x/8.2

x = 8.2tan(43°) = 7.6

3) sin(29°) = 3.5/x

x sin(29°) = 3.5

x = 3.5/sin(29°) = 7.2

The percentage of the powdered lemon mix in Dianelys's mix indicates that Dianelys's mix is more lemony.

A percentage is an expression of a ratio of two quantities as a fraction of 100.

The number of cups of water Zachary mixes with 5 cups of powdered lemon mix = 11 cups of water
Number of cups of water Dianelys mixes with 4 cups of powdered lemon mix = 7 cups of water

Zachary's percentage of powdered lemon mix = (5/(11 + 5)) × 100 = 31.25%

Dianelys's percentage of powdered lemon mix = (4/(7 + 4)) × 100 = 36.[tex]\overline{36}[/tex]%

The percentage of powdered lemon mix for Dianelys which is more than the percentage in Zachary's powdered lemon mix indicates that Danialys mix is more lemony.

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The value of,

Given function f(x) = cx for 1 ≤ x ≤ 2

a) To find the value of constant x, we have to use the following p.d.f condition as shown below,

[tex]\int\limits^a_b {x} \, dx =1[/tex]

here, a is -∞ and b is ∞.

From the above condition to find the value of c,

[tex]\int\limits^2_1{cx^2} \, dx[/tex] = 1

c * [[tex]\frac{x^3}{3}[/tex]]²₁ = 1

c * [8/3 - 1/3] = 1

c * 7/3 = 1

c = 3/7.

b) To find the value of P(x>3/2) we have to substitute the value of 3/2 in the given expression of f(x) = 3/7 * x²

f(3/2) = 3/7 * (3/2)²

         = 3/7 * 9/4

         = 27/28.

From the above solution, we solved both problems.

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1. normally distributed if the sample size is 30 or larger.

2. Not always normally distributed.

3. Skewed to the right is still normally distributed

4. normally distributed.

1. normally distributed if the sample size is 30 or larger.

2. If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is not always normally distributed. It depends on the sample size and the shape of the population distribution.

3. The sampling distribution of the sample mean for a sample of 10 elements taken from a population with a bell-shaped distribution that is skewed to the right is still normally distributed, by the central limit theorem, as long as the sample size is sufficiently large (typically at least 30) or the population distribution is approximately normal. Therefore, the answer is normally distributed.

4. The sampling distribution of the sample mean for a sample of 36 elements taken from a population with a bell-shaped distribution is normally distributed regardless of the population's skewness. Therefore, the answer is "normally distributed".

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Answer: 4.8 Inches

Step-by-step explanation:

6 is 60% of 10

Therefore  (60%*8 = 4.8)

*since they are similar, and therefore proportional

Answer:  The value of the test statistic to 2 d.p is z= 1.65

Step-by-step explanation:

P cap= 0.72

n= 170

P= 0.66

q= 1- p

q= 1- 0.66

q= 0.34

Z=( p cap - p)/√(p*q)/n

Z= (0.72- 0.66)/√(0.66*0.34)/170

Z= 0.06/0.036332

Z= 1.65

The solution is:  the following probabilities for a normal distribution is:

a. 0.5434

b. 0.5746

c. 0.2957

d. 0.0902

Here, we have,

Explanation:

To find each probability we need to use the normal distribution table that is accumulated to the left, so each probability is equal to

P(-1.80 < z < 0.20) = P( z < 0.20) - P( z < -1.80)

P(-1.80 < z < 0.20) = 0.5793 - 0.0359

P(-1.80 < z < 0.20) = 0.5434

P(-0.40 < z < 1.40) = P( z < 1.40) - P( z < -0.40)

P(-0.40 < z < 1.40) = 0.9192 - 0.3446

P(-0.40 < z < 1.40) = 0.5746

P(0.25 < z < 1.25) = P(z < 1.25) - P(z < 0.25)

P(0.25 < z < 1.25) = 0.8944 - 0.5987

P(0.25 < z < 1.25) = 0.2957

P(-0.90 < z < -0.60) = P(z < -0.60) - P(z < -0.90)

P(-0.90 < z < -0.60) = 0.2743 - 0.1841

P(-0.90 < z < -0.60) = 0.0902

Therefore, the answers are,  the following probabilities for a normal distribution is:

a. 0.5434

b. 0.5746

c. 0.2957

d. 0.0902

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Answer:

A = 5

B = 4

C = 8

D = 3

Step-by-step explanation:

This is more of a visual calculation so I can't really explain much about it other than that you match up the side in the prism with the side in the net

Answer: 108

Step-by-step explanation:

If you turn the shape, where the pointy side of the ramp is facing you and you flipped it open and laid out the sides,  that's the "net" image on right

A =  5   the long side of that triangle is also the short side of that rectangle

B = 3    it's the short side of the triangle

C = 8    long part of the rectangle

D =  4  long side of triangle

To find surface area.  Find the area of each of the shapes and add it all up

Top Rectangle:

A=Lw=C*A = 5*8 = 40

Middle Rectangle:

A=Lw = B*C =  3*8 = 24

Bottom Rectangle:

A=LW = 4*C = 4*8=32

Triangles are same

A=1/2 bh = 1/2 D*B = 1/2 * 4* 3 =6

But there are 2 of them so A=12

Now add all the shapes together

A(total)=40+24+32+12=108

The evaluation of the trigonometric identities to find the sine of the sum of angles A and B, using the values for cos(A) and sin(B) indicates;

15. sin(A + B) = -52/85

16. A + B is in Quadrant III

Trigonometric identities are equations involving trigonometric ratios that are true for the values of the input variables.

15. cos(A) = -15/17, sin(B) = 4/5

The trigonometric identity for the sine of the  addition of two angles, the addition formula indicates that we get;

sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)

cos(B) = √(1 - (4/5)²) = √(1 - 16/25) = 3/5

sin(A) = √(1 - (-15/17)²) = 8/17

Therefore; sin(A + B) = (8/17) × (3/5) + (-15/17) × (4/5) = -52/85

16. π/2 < A < π, and 0 < B < π/2

Therefore; π/2 + 0 < A + B < π + π/2

The solution from the previous question indicates that we get;

sin(A + B) = -52/85

The sine of an angle is negative in the third and fourth quadrant

The fourth quadrant is; π + π/2 < θ < 2·π

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The area of the sector is 2π/1

The formula for calculating the area of a sector is expressed as;

A = θ/360 πr²

Given that the parameters are;

From the information given, we have that;

The angle = 45 degrees

radius, r = 4

Substitute the values, we have;

Area = 45/360 × π × 4²

Divide the values

Area = 3/ 24 × π × 16

Multiply the values, we have;

Area = 48π/24

Divide the values, we have;

Area = 2π/1

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Given the above model, we can state that it's predictions were accurate.

The model uses the variable x which represents no. of years from 1970 to 2010

2010 -1970 = 40
P + (x/2) = 44

P + 40/2 = 44

P + 20 = 44
P = 44 - 20
p = 24

The model, it predicted 24% of the population would be smoking in this city in the year 2010. Whereas the data from the graph tell us that

28 %  of the adults actually smoked in the city in 2010. Hence the model is accurate .

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Full Question:

The mathematical model

p+ x/2 =44

Describes the percentage, p, of adults who smoked cigarettes x years after 1970

Does the mathematical model underestimate or overestimate the percentage of adults who smoked cigarettes in 2010? By how much?

The value of the matrix 4G + 2F is [tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]

Matrices are an essential tool in mathematics and can be used to solve a variety of problems. In this case, we are given two matrices G and F, and we are asked to find the value of 4G + 2F.

To understand how to calculate the value of 4G + 2F, we first need to understand what it means to multiply a matrix by a scalar. When we multiply a matrix by a scalar, we simply multiply every element in the matrix by that scalar.

Now that we understand scalar multiplication, we can use it to find the value of 4G + 2F. We simply need to multiply each matrix by its respective scalar and then add the results element-wise.

[tex]4G = 4\begin{bmatrix}8 &-5 &8 &-2 &10 \\-6& -7&1 & 9& 2\\4&6 &3 &7 &5 \\-4 & -3& 0& -10& -9\end{bmatrix}= \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix}[/tex]

Now we have to find the value of 2[F]. that can be calculated as follows

[tex]2F = 2\begin{bmatrix}1 &8 &-2 &-5 &9 \\-9& 10&6 &-3&0\\4&5 &-4 &3 &7 \\2 &-10&-6 & -1& -8\end{bmatrix}= \begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]

Now we can add the two matrices element-wise to get the final result:

[tex]4G + 2F = \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix} +\begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]

[tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]

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The median of this data set is equal to 9.

The mean of this data set is equal to 13.7.

The number of mode that this data set have is zero modes.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

Total, F(x) = 26+ 0 -1 + 33 + 2 + 31 + 10 + 21 + 7 + 8

Total, F(x) = 137

Mean = 137/10

Mean = 13.7.

Median = (8 + 10)/2

Median = 18/2

Median = 9.

In conclusion, the mode of the data set is non-existent or zero modes because all of the number have the same frequency.

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The probability that the water will run out on a given day is  0.0038.

To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:

where;

x = of 380 million gallons,

µ is the mean daily demand of water = 300 million gallons,

σ is the standard deviation = 30 million gallons.

Substituting the given values:

z = (380 - 300) / 30

z = 2.67

Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.

Therefore, the probability that the water will run out on a given day is  0.0038.

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Answer:

y=14

Concept Used:

Slope of a line:  [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where (x1,y1) and (x2,y2) are passing points

Step-by-step explanation:

On substitution:

[tex]4 = \frac{y-(-10)}{2-(-4)}[/tex]

Solving for y:

y = 14

The end behavior of this radical function is "as x approaches positive infinity, f(x) approaches positive infinity".

As we know that the function f(x) = 4√(x − 6) is a radical function with an even index (4), which means that the function is defined for all non-negative values of x.

As x approaches positive infinity, the value of x − 6 also approaches positive infinity, and the square root function grows without bound.

Since the function is multiplied by a positive constant (4), the entire function f(x) also grows without bound as x approaches positive infinity.

Therefore, the end behavior of the function is that as x approaches positive infinity, f(x) approaches positive infinity.

Hence, option A correctly describes the end behavior of the function.

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